WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf ·...

47
WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s: RISING DISPERSION OR FALLING MINIMUM WAGE?* DAVID S. LEE The magnitude of growth in ‘‘underlying’’ wage inequality in the United States during the 1980s is obscured by a concurren t decline in the federal minimum wage, which itself could cause an increase in observed wage inequality. This study uses regional variation in the relative level of the federal minimum wage to separately identify the impact of the minimum wage from nationwide growth in ‘‘latent’’ wage dispersion during the 1980s. The analysis suggests that the minimum wage can account for much of the rise in dispersion in the lower tail of the wage distribution, particularly for women. I. INTRODUCTION A striking feature of the United States labor market experi- ence during the past twenty years has been the dramatic rise in earnings and wage inequality that occurred during the 1980s. 1 Past research has documented the various dimensions of this trend: the sharp rise in wage differences between more- and less-educated workers, the growing wage disparity between more- and less-experienced workers, and the rise in wage inequality within groups narrowly de ned by age, education, and gender—so- called ‘‘within-group’’ inequality. 2 Researchers have proposed a number of explanations for these relative wage movements, most of which can be characterized as either a demand explanation (technological change, import competition), a supply story (immi- * I am indebted to David Card, Lawrence Katz, and Orley Ashenfelter for invaluable comments on earlier drafts. I also thank Michael Boozer, Gena Estes, Michael Greenstone, Bo Honore ´, and Thomas Lemieux for many helpful discus- sions, and Daron Acemoglu, Joshua Angrist, Kenneth Chay, Alan Krueger, Christina Lee, Andrew Oswald, Jo ¨rn-Steffen Pischke, Cecilia Rouse, two anony- mous referees, and participants of the Princeton Industrial Relations Section Labor Seminar and Labor Lunch, and of the MIT Labor Seminar for their comments and suggestions. I gratefully acknowledge the National Science Founda- tion Graduate Fellowship for nancial support, and the National Bureau of Economic Research—West, where much of this research was conducted. 1. Levy and Murnane [1992] and Katz and Autor [1999] provide a survey of research on earnings and wage inequality. Gottschalk [1997] also provides a summary of the general trends and dimensions of wage inequality in the United States. 2. See Katz and Murphy [1992]; Juhn, Murphy, and Pierce [1993]; and Murphy and Welch [1992]. r 1999 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. The Quarterly Journal of Economics, August 1999 977

Transcript of WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf ·...

Page 1: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

WAGE INEQUALITY IN THE UNITED STATESDURING THE 1980s RISING DISPERSION OR FALLING

MINIMUM WAGE

DAVID S LEE

The magnitude of growth in lsquolsquounderlyingrsquorsquo wage inequality in the United Statesduring the 1980s is obscured by a concurrent decline in the federal minimum wagewhich itself could cause an increase in observed wage inequality This study usesregional variation in the relative level of the federal minimum wage to separatelyidentify the impact of the minimum wage from nationwide growth in lsquolsquolatentrsquorsquo wagedispersion during the 1980s The analysis suggests that the minimum wage canaccount for much of the rise in dispersion in the lower tail of the wage distributionparticularly for women

I INTRODUCTION

A striking feature of the United States labor market experi-ence during the past twenty years has been the dramatic rise inearnings and wage inequality that occurred during the 1980s1

Past research has documented the various dimensions of thistrend the sharp rise in wage differences between more- andless-educated workers the growing wage disparity between more-and less-experienced workers and the rise in wage inequalitywithin groups narrowly dened by age education and gendermdashso-called lsquolsquowithin-grouprsquorsquo inequality2 Researchers have proposed anumber of explanations for these relative wage movements mostof which can be characterized as either a demand explanation(technological change import competition) a supply story (immi-

I am indebted to David Card Lawrence Katz and Orley Ashenfelter forinvaluable comments on earlier drafts I also thank Michael Boozer Gena EstesMichael Greenstone Bo Honore and Thomas Lemieux for many helpful discus-sions and Daron Acemoglu Joshua Angrist Kenneth Chay Alan KruegerChristina Lee Andrew Oswald Jorn-Steffen Pischke Cecilia Rouse two anony-mous referees and participants of the Princeton Industrial Relations SectionLabor Seminar and Labor Lunch and of the MIT Labor Seminar for theircomments and suggestions I gratefully acknowledge the National Science Founda-tion Graduate Fellowship for nancial support and the National Bureau ofEconomic ResearchmdashWest where much of this research was conducted

1 Levy and Murnane [1992] and Katz and Autor [1999] provide a survey ofresearch on earnings and wage inequality Gottschalk [1997] also provides asummary of the general trends and dimensions of wage inequality in the UnitedStates

2 See Katz and Murphy [1992] Juhn Murphy and Pierce [1993] andMurphy and Welch [1992]

r 1999 by the President and Fellows of Harvard College and the Massachusetts Institute ofTechnologyThe Quarterly Journal of Economics August 1999

977

gration of less-skilled workers) or an institutional factor (deunion-ization the minimum wage)3

An equally striking development that accompanied dramaticincreases in wage inequality in the United States during the1980s was the longest sustained decline in the real value of thefederal minimum wage in the previous four decades as it reachedits lowest point since the 1950s4 As shown below decreases in theminimum wage tend to increase measured wage inequalityregardless of its effect on employment earnings or incomeDiNardo Fortin and Lemieux [1996] demonstrate that theminimum wage is an important empirical feature of the observeddistribution of wages during the 1980s At the least their ndingssuggest that the declining real value of the minimum wagesignicantly obscures the impact of factors such as relative supplyand demand shifts or other institutional changes on the wagedistribution throughout the decade In this paper I attempt toanswer the question after accounting for the impact of theminimum wage did lsquolsquounderlyingrsquorsquo wage inequality in the UnitedStates rise during the 1980s In particular what was the netimpact of all factors other than the minimum wage on the wagedistribution

It is difficult to answer these questions from an analysis ofaggregate time series data because the steady increase in thedispersion of observed wages is closely paralleled by a steadydecrease in the relative level of the minimum wage during the1980s making it virtually impossible to separate the effect of theminimum wage from a time trend

Instead this study utilizes the differential impact of thefederal minimum wage across regions within the United States todirectly estimate the contribution of the falling relative value ofthe minimum wage to increasing wage inequality in the lower halfof the wage distribution since 1979 The interaction of statevariation in overall wage levels and a uniform federal minimumwage generates cross-state variation in lsquolsquoeffectiversquorsquo minimum wagelevels The assumption that this variation is not systematicallyrelated to the shape of the lsquolsquounderlyingrsquorsquo wage distributionmdashthedistribution of wage rates that would prevail in the absence of anyminimum wagemdashpermits the data to separately identify the

3 For a series of articles surveying the leading explanations for rising wageinequality see Johnson [1997] Topel [1997] and Fortin and Lemieux [1997]

4 In 1996 dollars using the CPI-U Nominal rates are from Bureau of theCensus [1996]

QUARTERLY JOURNAL OF ECONOMICS978

impact of the minimum wage from nationwide growth in lsquolsquolatentrsquorsquowage dispersion during the 1980s

When regional wage distribution data constructed from theCurrent Population Survey are used the resulting estimates ofthe impact of the minimum wage imply that after accounting forthe minimum wage average growth in wage dispersion in thelower tail of statesrsquo wage distributions during the 1980s is quitemodest In fact the estimates for men women as well as thecombined sample imply that almost all of the growth in the wagegap between the tenth and ftieth percentiles is attributable tothe erosion of the real value of the federal minimum during thedecade

I provide some evidence suggesting that the identifyingassumption may be inappropriate for the male sample of workersOn the other hand the same kind of evidence lends support to thevalidity of the main identication strategy when analyzing womenand when considering the unconditional distribution of wagesFor example estimates from using variation in legislated changesin minimum wages (which arise from an interaction between the1990ndash1991 federal increases and preexisting variability in state-specic minimum wage laws) are quite similar to those generatedby cross-state variability in the relative minimum

The results also imply that accounting for the minimum wageonly moderately affects the magnitude of changes in wage differen-tials by gender race educational attainment and experience andleaves the broad trends unaffected On the other hand thispaperrsquos results imply that the minimum wage may account for asmuch as 80 percent of the growth in so-called lsquolsquowithin-grouprsquorsquo wageinequality during the 1980s When examining men and womenseparately overall growth in wage inequality during the 1980sremains substantial due to the appreciable growth in dispersionin the upper tail of the wage distribution where the minimumwage is unlikely to have an impact Curiously after accounting forthe minimum wage the unconditional distribution (without re-gard to gender) of wages appears to be surprisingly stablethroughout the 1980s

The paper is organized as follows Section II provides a briefsummary of the trends in wage inequality that serve to motivatethe present study Section III discusses how state variation ineffective minimum wage levels can be used to separately identifythe effect of a declining minimum wage from an underlying rise inwage dispersion Section IV describes the empirical implementa-

WAGE INEQUALITY AND THE MINIMUM WAGE 979

tion and presents the results of the estimation Section V exam-ines the effect of the increases in the federal minimum wage onwage inequality from 1989 to 1991 Section VI uses the estimatesof this study to adjust measures of between- and within-groupwage inequality for the minimum wage effect Finally Section VIIconcludes with a discussion of the implications of the ndings inthis paper for future research

II CHANGES IN THE WAGE DISTRIBUTION IN THE 1980S

A Data

The analysis in this paper utilizes microdata from the Na-tional Bureau of Economic Research Extracts of the CurrentPopulation Survey (CPS) Outgoing Rotation Group EarningsFiles These data consist of point-in-time measures of the hourlyrate of pay which make it appropriate for a study of the impact ofa wage oor on the wage distribution For workers not paid on anhourly basis usual weekly earnings and usual weekly hours canbe used to construct an average hourly wage These datarsquos largesample sizes (three times the size of a single month of data fromthe CPS) and annual frequency make them suitable for a detailedregional analysis throughout the decade of the 1980s Details ofthe preprocessing of the data are reported in the Data Appendix

The three parts of Figure I depict the (hours-weighted) kerneldensity estimate of the distribution of log-wages from these datafor the years 1979 and 1989 for men women and all workers(men and women combined)5 In each panel the two vertical linesdenote the federal minimum wage levels in each year The guresuggests that in 1979 the minimum wage had to some extent asupporting effect on wages after its relative levelrsquos erosion duringthe decade by 1989 the minimum wage appears to have muchless of an inuence on the shape of the distribution The impres-sion that the minimum wage was an important feature of thelower part of the wage distribution is particularly striking for thefemale wage distribution Figure IC suggests the possibility thatthe decline in the relative value of the minimum wage over thedecade was primarily responsible for changes in the unconditionalwage distribution since much of the change appears to occur inthe lower tail

5 The sample includes individuals aged sixteen and over The horizontal axismeasures the log-wage relative to the overall (men and women) median in eachyear All kernel density estimates use the rule-of-thumb bandwidth h 5 079Rn 2 15where R is the interquartile range [Silverman 1986]

QUARTERLY JOURNAL OF ECONOMICS980

This paper follows the wage inequality literaturersquos usualpractice of conducting formal analyses for men and womenseparately But since changes in the lower tail appear to be arelatively more important component of the total change whenexamining the unconditional distribution of wages (without re-gard to gender) some attention will also be given to the ndingsfor the entire sample Examining the entire samplemdashthe distribu-tion of hourly pay for hours worked in the economymdashallows someabstraction from issues that arise when men and women arethought to compete in the same labor market when changes inthe male and female distributions are to some extent interdepen-dent6 Thus this paperrsquos estimates of changes in the uncondi-tional distribution of wagesmdashafter parsing out the minimumwage effectmdashcould be interpreted as the net impact of between-gender wage changes [OrsquoNeill and Polachek 1993 Fortin andLemieux 1996 Blau and Kahn 1997] and other lsquolsquowithin-genderrsquorsquoforces such as skill-biased technological change [Davis and Halti-wanger 1991 Bound and Johnson 1992 Autor Katz and Krueger1997 Doms Dunne and Troske 1997] international trade [Borjasand Ramey 1995 Feenstra and Hanson 1996] and more generallyrising lsquolsquoskill premiumsrsquorsquo stemming from an increase in the demandfor skilled labor [Katz and Murphy 1992 Berman Bound andGriliches 1994]

The available time series data on the United States wagedistribution also point to a close connection between the minimumwage and changes in inequality Figure II plots changes inpercentiles of the wage distribution relative to the median for thefth tenth twenty-fth seventy-fth and ninetieth wage percen-tiles between 1973 and 19937 These measures of wage dispersionas well as the log difference between the federal minimum wageand the median wage (also shown in the gure) are normalized tobe zero in 1979 which appears to be a turning point for several ofthe series

Figure II shows that after rising modestly during the latterhalf of the 1970s the minimum wage (relative to the medianwage) fell almost 40 log points in the period between 1979 and1989 The sharp rebound in 1990 and 1991 reects the legislatedrise in the federal minimum wage from $335 to $380 in April of

6 This issue is addressed in Fortin and Lemieux [1996] and Topel [1997]7 Includes both men and women all those aged 16 and over The data for

1973ndash1978 are taken from the May CPS dual job supplements These data containa point-in-time wage measure comparable to that from the Outgoing RotationGroup Files for 1979ndash1993

WAGE INEQUALITY AND THE MINIMUM WAGE 981

FIGURE IaWage Distribution Density Estimates Men 1979ndash1989

FIGURE IbWage Distribution Density Estimates Women 1979ndash1989

1990 and then to $425 in April of 1991 The gure illustrates thatwith the exception of the last few years of the 1980s and the periodafter 1991 movements in wage dispersion in the lower half of thewage distribution moved in close tandem with changes in theminimum wage The fth and tenth percentiles rise in the latterpart of the 1970s experience a sharp decline during much of the1980s and then rebound modestly in the early 1990s8

Finally Figure II shows that while changes in the seventy-fth wage percentile have been small there has been a steady risein the ninetieth percentile throughout the 1973ndash1993 period Thatthe minimum wage is unlikely to have played any part in thisparticular trend underscores the limited inferences that can bemade from an examination of the aggregate time series data Forexample there is nearly as much evidence here to suggest that the

8 It should be noted that trends in measures of dispersion in average hourlyearnings as computed from the Census and the March CPS differ somewhat fromthat calculated from the May CPS during the 1970s For example the 90ndash10differential for women falls by about 11 percent in the May CPS but rises 3 percentin the March CPS See Katz and Autor [1998] for a summary of differences acrossthe data sets over the past few decades

FIGURE IcWage Distribution Density Estimates Men and Women 1979ndash1989

WAGE INEQUALITY AND THE MINIMUM WAGE 983

minimum wage contributed to growth in the ninetieth percentileas there is to suggest that it caused a decline in the tenthpercentile The effective decline in the minimum wage and thegrowth in inequality in the lower half of the wage distribution areboth monotonic throughout the 1980s As a result no analysis ofthe aggregate time series data will be able to adequately distin-guish a minimum wage effect from a rising trend in lsquolsquolatentrsquorsquo wageinequalitymdashwhich I dene here to be a rise in wage inequalitythat would have occurred in the absence of a minimum wagepolicy

B Regional Variation in the lsquolsquoEffectiversquorsquo Minimum Wage

The time-series pattern of wage dispersion in the lower tail isnot uniform across regions in the United States Figure III plotsthe average 10ndash50 log (wage) differential during 1979ndash1991 fortwo groups of states the three highest-wage states (New Jersey

FIGURE IISelected Percentiles of the Wage Distribution Minimum Wage

Relative to the Median 1973ndash1993All series are normalized to be 0 in 1979

QUARTERLY JOURNAL OF ECONOMICS984

Michigan and Maryland) and the three lowest-wage states (SouthDakota Mississippi and Arkansas)9 The low-wage states whichinitially begin with a more compressed lower tail than thehigh-wage states experience an average increase in dispersion ofabout twenty log points throughout the 1980s and a subsequentcompression of about ve log points during 1989ndash1991 By con-trast the 10ndash50 differential for the highest-wage states appearsrelatively stable during the entire 1979ndash1991 period

This additional dimension of wage inequality and its relationto the relative level of the minimum wage across regions offer anopportunity to distinguish the minimum wage effect from anational trend in latent wage dispersion In particular theinteraction between a uniform federal minimum wage and wide

9 These six states were selected from the state-level panel data set describedin the Data Appendix Average median wages for the entire period were computedThe three highest and three lowest overall averages were chosen excluding allstates for which there was at least one year where the state minimum exceeded thefederal minimum wage rate The differentials are for the entire sample agedsixteen or over

FIGURE III10ndash50 75ndash50 Log(Wage) Differentials High- versus Low-Wage States 1979ndash1991

WAGE INEQUALITY AND THE MINIMUM WAGE 985

variation in wage levels across states yields variability in lsquolsquoeffec-tiversquorsquo minimum wage levels The federal minimum wage highlyimpacts low-wage states while minimally affecting high-wagestates

This is demonstrated in Figure IV which plots (hours-weighted) kernel density estimates of log-wages in 1979 for threegroups of states high- medium- and low-wage states10 Thehorizontal scale measures the log-wage relative to each grouprsquosrespective median wage The vertical lines represent the federalminimum wage also relative to each grouprsquos respective medianFigure IV gives the impression that low-wage states are indeedmore highly impacted by the minimum wage than higher-wagestates It is this variation that is exploited in the present study

Stratifying the wage distribution by a dimension other thangeography would likely produce a similar result And cross-sectional variation in effective minimum wages across educa-tional groups for example could be used to estimate a minimumwage effect However in this study variation across states has afew important advantages over variation across other groups suchas education age industry or occupation

First on a conceptual level variation in the relative mini-mum across states more closely mimics the variation that wouldbe most ideal (but that is also unattainable) for estimating theimpact of the minimum wage on the wage distribution Theseideal data would consist of a sample of independent realizations ofthe wage distribution of the United States labor market at onepoint in time and exhibit variability in the minimum wage acrossrealizations Each statersquos labor market can be more readilyconsidered a microcosm of the United States labor market thancan any particular group of workers dened by education age orindustrial or occupational sector

Second as described in detail in Section V by the late-1980sthere arose moderate variation in state-legislated minimum wagelevels This variability in state-specic minimum wages com-bined with the 1990ndash1991 legislated increases in the federalminimum generates an alternative source of variation fromwhich the impact of the minimum wage can be identied

A potential problem with utilizing the substantial regional

10 I rank each state by the mean log-wage I choose the bottom seven(Arkansas Mississippi Vermont Maine South Carolina South Dakota andNorth Carolina) middle seven (Idaho Oklahoma Kentucky Kansas VirginiaMissouri and Indiana) and highest seven (Oregon Wyoming California IllinoisMaryland Michigan and Washington) for the three groups The sample sizes forthe low- medium- and high-wage states are 12263 16190 31932 respectively

QUARTERLY JOURNAL OF ECONOMICS986

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 2: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

gration of less-skilled workers) or an institutional factor (deunion-ization the minimum wage)3

An equally striking development that accompanied dramaticincreases in wage inequality in the United States during the1980s was the longest sustained decline in the real value of thefederal minimum wage in the previous four decades as it reachedits lowest point since the 1950s4 As shown below decreases in theminimum wage tend to increase measured wage inequalityregardless of its effect on employment earnings or incomeDiNardo Fortin and Lemieux [1996] demonstrate that theminimum wage is an important empirical feature of the observeddistribution of wages during the 1980s At the least their ndingssuggest that the declining real value of the minimum wagesignicantly obscures the impact of factors such as relative supplyand demand shifts or other institutional changes on the wagedistribution throughout the decade In this paper I attempt toanswer the question after accounting for the impact of theminimum wage did lsquolsquounderlyingrsquorsquo wage inequality in the UnitedStates rise during the 1980s In particular what was the netimpact of all factors other than the minimum wage on the wagedistribution

It is difficult to answer these questions from an analysis ofaggregate time series data because the steady increase in thedispersion of observed wages is closely paralleled by a steadydecrease in the relative level of the minimum wage during the1980s making it virtually impossible to separate the effect of theminimum wage from a time trend

Instead this study utilizes the differential impact of thefederal minimum wage across regions within the United States todirectly estimate the contribution of the falling relative value ofthe minimum wage to increasing wage inequality in the lower halfof the wage distribution since 1979 The interaction of statevariation in overall wage levels and a uniform federal minimumwage generates cross-state variation in lsquolsquoeffectiversquorsquo minimum wagelevels The assumption that this variation is not systematicallyrelated to the shape of the lsquolsquounderlyingrsquorsquo wage distributionmdashthedistribution of wage rates that would prevail in the absence of anyminimum wagemdashpermits the data to separately identify the

3 For a series of articles surveying the leading explanations for rising wageinequality see Johnson [1997] Topel [1997] and Fortin and Lemieux [1997]

4 In 1996 dollars using the CPI-U Nominal rates are from Bureau of theCensus [1996]

QUARTERLY JOURNAL OF ECONOMICS978

impact of the minimum wage from nationwide growth in lsquolsquolatentrsquorsquowage dispersion during the 1980s

When regional wage distribution data constructed from theCurrent Population Survey are used the resulting estimates ofthe impact of the minimum wage imply that after accounting forthe minimum wage average growth in wage dispersion in thelower tail of statesrsquo wage distributions during the 1980s is quitemodest In fact the estimates for men women as well as thecombined sample imply that almost all of the growth in the wagegap between the tenth and ftieth percentiles is attributable tothe erosion of the real value of the federal minimum during thedecade

I provide some evidence suggesting that the identifyingassumption may be inappropriate for the male sample of workersOn the other hand the same kind of evidence lends support to thevalidity of the main identication strategy when analyzing womenand when considering the unconditional distribution of wagesFor example estimates from using variation in legislated changesin minimum wages (which arise from an interaction between the1990ndash1991 federal increases and preexisting variability in state-specic minimum wage laws) are quite similar to those generatedby cross-state variability in the relative minimum

The results also imply that accounting for the minimum wageonly moderately affects the magnitude of changes in wage differen-tials by gender race educational attainment and experience andleaves the broad trends unaffected On the other hand thispaperrsquos results imply that the minimum wage may account for asmuch as 80 percent of the growth in so-called lsquolsquowithin-grouprsquorsquo wageinequality during the 1980s When examining men and womenseparately overall growth in wage inequality during the 1980sremains substantial due to the appreciable growth in dispersionin the upper tail of the wage distribution where the minimumwage is unlikely to have an impact Curiously after accounting forthe minimum wage the unconditional distribution (without re-gard to gender) of wages appears to be surprisingly stablethroughout the 1980s

The paper is organized as follows Section II provides a briefsummary of the trends in wage inequality that serve to motivatethe present study Section III discusses how state variation ineffective minimum wage levels can be used to separately identifythe effect of a declining minimum wage from an underlying rise inwage dispersion Section IV describes the empirical implementa-

WAGE INEQUALITY AND THE MINIMUM WAGE 979

tion and presents the results of the estimation Section V exam-ines the effect of the increases in the federal minimum wage onwage inequality from 1989 to 1991 Section VI uses the estimatesof this study to adjust measures of between- and within-groupwage inequality for the minimum wage effect Finally Section VIIconcludes with a discussion of the implications of the ndings inthis paper for future research

II CHANGES IN THE WAGE DISTRIBUTION IN THE 1980S

A Data

The analysis in this paper utilizes microdata from the Na-tional Bureau of Economic Research Extracts of the CurrentPopulation Survey (CPS) Outgoing Rotation Group EarningsFiles These data consist of point-in-time measures of the hourlyrate of pay which make it appropriate for a study of the impact ofa wage oor on the wage distribution For workers not paid on anhourly basis usual weekly earnings and usual weekly hours canbe used to construct an average hourly wage These datarsquos largesample sizes (three times the size of a single month of data fromthe CPS) and annual frequency make them suitable for a detailedregional analysis throughout the decade of the 1980s Details ofthe preprocessing of the data are reported in the Data Appendix

The three parts of Figure I depict the (hours-weighted) kerneldensity estimate of the distribution of log-wages from these datafor the years 1979 and 1989 for men women and all workers(men and women combined)5 In each panel the two vertical linesdenote the federal minimum wage levels in each year The guresuggests that in 1979 the minimum wage had to some extent asupporting effect on wages after its relative levelrsquos erosion duringthe decade by 1989 the minimum wage appears to have muchless of an inuence on the shape of the distribution The impres-sion that the minimum wage was an important feature of thelower part of the wage distribution is particularly striking for thefemale wage distribution Figure IC suggests the possibility thatthe decline in the relative value of the minimum wage over thedecade was primarily responsible for changes in the unconditionalwage distribution since much of the change appears to occur inthe lower tail

5 The sample includes individuals aged sixteen and over The horizontal axismeasures the log-wage relative to the overall (men and women) median in eachyear All kernel density estimates use the rule-of-thumb bandwidth h 5 079Rn 2 15where R is the interquartile range [Silverman 1986]

QUARTERLY JOURNAL OF ECONOMICS980

This paper follows the wage inequality literaturersquos usualpractice of conducting formal analyses for men and womenseparately But since changes in the lower tail appear to be arelatively more important component of the total change whenexamining the unconditional distribution of wages (without re-gard to gender) some attention will also be given to the ndingsfor the entire sample Examining the entire samplemdashthe distribu-tion of hourly pay for hours worked in the economymdashallows someabstraction from issues that arise when men and women arethought to compete in the same labor market when changes inthe male and female distributions are to some extent interdepen-dent6 Thus this paperrsquos estimates of changes in the uncondi-tional distribution of wagesmdashafter parsing out the minimumwage effectmdashcould be interpreted as the net impact of between-gender wage changes [OrsquoNeill and Polachek 1993 Fortin andLemieux 1996 Blau and Kahn 1997] and other lsquolsquowithin-genderrsquorsquoforces such as skill-biased technological change [Davis and Halti-wanger 1991 Bound and Johnson 1992 Autor Katz and Krueger1997 Doms Dunne and Troske 1997] international trade [Borjasand Ramey 1995 Feenstra and Hanson 1996] and more generallyrising lsquolsquoskill premiumsrsquorsquo stemming from an increase in the demandfor skilled labor [Katz and Murphy 1992 Berman Bound andGriliches 1994]

The available time series data on the United States wagedistribution also point to a close connection between the minimumwage and changes in inequality Figure II plots changes inpercentiles of the wage distribution relative to the median for thefth tenth twenty-fth seventy-fth and ninetieth wage percen-tiles between 1973 and 19937 These measures of wage dispersionas well as the log difference between the federal minimum wageand the median wage (also shown in the gure) are normalized tobe zero in 1979 which appears to be a turning point for several ofthe series

Figure II shows that after rising modestly during the latterhalf of the 1970s the minimum wage (relative to the medianwage) fell almost 40 log points in the period between 1979 and1989 The sharp rebound in 1990 and 1991 reects the legislatedrise in the federal minimum wage from $335 to $380 in April of

6 This issue is addressed in Fortin and Lemieux [1996] and Topel [1997]7 Includes both men and women all those aged 16 and over The data for

1973ndash1978 are taken from the May CPS dual job supplements These data containa point-in-time wage measure comparable to that from the Outgoing RotationGroup Files for 1979ndash1993

WAGE INEQUALITY AND THE MINIMUM WAGE 981

FIGURE IaWage Distribution Density Estimates Men 1979ndash1989

FIGURE IbWage Distribution Density Estimates Women 1979ndash1989

1990 and then to $425 in April of 1991 The gure illustrates thatwith the exception of the last few years of the 1980s and the periodafter 1991 movements in wage dispersion in the lower half of thewage distribution moved in close tandem with changes in theminimum wage The fth and tenth percentiles rise in the latterpart of the 1970s experience a sharp decline during much of the1980s and then rebound modestly in the early 1990s8

Finally Figure II shows that while changes in the seventy-fth wage percentile have been small there has been a steady risein the ninetieth percentile throughout the 1973ndash1993 period Thatthe minimum wage is unlikely to have played any part in thisparticular trend underscores the limited inferences that can bemade from an examination of the aggregate time series data Forexample there is nearly as much evidence here to suggest that the

8 It should be noted that trends in measures of dispersion in average hourlyearnings as computed from the Census and the March CPS differ somewhat fromthat calculated from the May CPS during the 1970s For example the 90ndash10differential for women falls by about 11 percent in the May CPS but rises 3 percentin the March CPS See Katz and Autor [1998] for a summary of differences acrossthe data sets over the past few decades

FIGURE IcWage Distribution Density Estimates Men and Women 1979ndash1989

WAGE INEQUALITY AND THE MINIMUM WAGE 983

minimum wage contributed to growth in the ninetieth percentileas there is to suggest that it caused a decline in the tenthpercentile The effective decline in the minimum wage and thegrowth in inequality in the lower half of the wage distribution areboth monotonic throughout the 1980s As a result no analysis ofthe aggregate time series data will be able to adequately distin-guish a minimum wage effect from a rising trend in lsquolsquolatentrsquorsquo wageinequalitymdashwhich I dene here to be a rise in wage inequalitythat would have occurred in the absence of a minimum wagepolicy

B Regional Variation in the lsquolsquoEffectiversquorsquo Minimum Wage

The time-series pattern of wage dispersion in the lower tail isnot uniform across regions in the United States Figure III plotsthe average 10ndash50 log (wage) differential during 1979ndash1991 fortwo groups of states the three highest-wage states (New Jersey

FIGURE IISelected Percentiles of the Wage Distribution Minimum Wage

Relative to the Median 1973ndash1993All series are normalized to be 0 in 1979

QUARTERLY JOURNAL OF ECONOMICS984

Michigan and Maryland) and the three lowest-wage states (SouthDakota Mississippi and Arkansas)9 The low-wage states whichinitially begin with a more compressed lower tail than thehigh-wage states experience an average increase in dispersion ofabout twenty log points throughout the 1980s and a subsequentcompression of about ve log points during 1989ndash1991 By con-trast the 10ndash50 differential for the highest-wage states appearsrelatively stable during the entire 1979ndash1991 period

This additional dimension of wage inequality and its relationto the relative level of the minimum wage across regions offer anopportunity to distinguish the minimum wage effect from anational trend in latent wage dispersion In particular theinteraction between a uniform federal minimum wage and wide

9 These six states were selected from the state-level panel data set describedin the Data Appendix Average median wages for the entire period were computedThe three highest and three lowest overall averages were chosen excluding allstates for which there was at least one year where the state minimum exceeded thefederal minimum wage rate The differentials are for the entire sample agedsixteen or over

FIGURE III10ndash50 75ndash50 Log(Wage) Differentials High- versus Low-Wage States 1979ndash1991

WAGE INEQUALITY AND THE MINIMUM WAGE 985

variation in wage levels across states yields variability in lsquolsquoeffec-tiversquorsquo minimum wage levels The federal minimum wage highlyimpacts low-wage states while minimally affecting high-wagestates

This is demonstrated in Figure IV which plots (hours-weighted) kernel density estimates of log-wages in 1979 for threegroups of states high- medium- and low-wage states10 Thehorizontal scale measures the log-wage relative to each grouprsquosrespective median wage The vertical lines represent the federalminimum wage also relative to each grouprsquos respective medianFigure IV gives the impression that low-wage states are indeedmore highly impacted by the minimum wage than higher-wagestates It is this variation that is exploited in the present study

Stratifying the wage distribution by a dimension other thangeography would likely produce a similar result And cross-sectional variation in effective minimum wages across educa-tional groups for example could be used to estimate a minimumwage effect However in this study variation across states has afew important advantages over variation across other groups suchas education age industry or occupation

First on a conceptual level variation in the relative mini-mum across states more closely mimics the variation that wouldbe most ideal (but that is also unattainable) for estimating theimpact of the minimum wage on the wage distribution Theseideal data would consist of a sample of independent realizations ofthe wage distribution of the United States labor market at onepoint in time and exhibit variability in the minimum wage acrossrealizations Each statersquos labor market can be more readilyconsidered a microcosm of the United States labor market thancan any particular group of workers dened by education age orindustrial or occupational sector

Second as described in detail in Section V by the late-1980sthere arose moderate variation in state-legislated minimum wagelevels This variability in state-specic minimum wages com-bined with the 1990ndash1991 legislated increases in the federalminimum generates an alternative source of variation fromwhich the impact of the minimum wage can be identied

A potential problem with utilizing the substantial regional

10 I rank each state by the mean log-wage I choose the bottom seven(Arkansas Mississippi Vermont Maine South Carolina South Dakota andNorth Carolina) middle seven (Idaho Oklahoma Kentucky Kansas VirginiaMissouri and Indiana) and highest seven (Oregon Wyoming California IllinoisMaryland Michigan and Washington) for the three groups The sample sizes forthe low- medium- and high-wage states are 12263 16190 31932 respectively

QUARTERLY JOURNAL OF ECONOMICS986

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 3: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

impact of the minimum wage from nationwide growth in lsquolsquolatentrsquorsquowage dispersion during the 1980s

When regional wage distribution data constructed from theCurrent Population Survey are used the resulting estimates ofthe impact of the minimum wage imply that after accounting forthe minimum wage average growth in wage dispersion in thelower tail of statesrsquo wage distributions during the 1980s is quitemodest In fact the estimates for men women as well as thecombined sample imply that almost all of the growth in the wagegap between the tenth and ftieth percentiles is attributable tothe erosion of the real value of the federal minimum during thedecade

I provide some evidence suggesting that the identifyingassumption may be inappropriate for the male sample of workersOn the other hand the same kind of evidence lends support to thevalidity of the main identication strategy when analyzing womenand when considering the unconditional distribution of wagesFor example estimates from using variation in legislated changesin minimum wages (which arise from an interaction between the1990ndash1991 federal increases and preexisting variability in state-specic minimum wage laws) are quite similar to those generatedby cross-state variability in the relative minimum

The results also imply that accounting for the minimum wageonly moderately affects the magnitude of changes in wage differen-tials by gender race educational attainment and experience andleaves the broad trends unaffected On the other hand thispaperrsquos results imply that the minimum wage may account for asmuch as 80 percent of the growth in so-called lsquolsquowithin-grouprsquorsquo wageinequality during the 1980s When examining men and womenseparately overall growth in wage inequality during the 1980sremains substantial due to the appreciable growth in dispersionin the upper tail of the wage distribution where the minimumwage is unlikely to have an impact Curiously after accounting forthe minimum wage the unconditional distribution (without re-gard to gender) of wages appears to be surprisingly stablethroughout the 1980s

The paper is organized as follows Section II provides a briefsummary of the trends in wage inequality that serve to motivatethe present study Section III discusses how state variation ineffective minimum wage levels can be used to separately identifythe effect of a declining minimum wage from an underlying rise inwage dispersion Section IV describes the empirical implementa-

WAGE INEQUALITY AND THE MINIMUM WAGE 979

tion and presents the results of the estimation Section V exam-ines the effect of the increases in the federal minimum wage onwage inequality from 1989 to 1991 Section VI uses the estimatesof this study to adjust measures of between- and within-groupwage inequality for the minimum wage effect Finally Section VIIconcludes with a discussion of the implications of the ndings inthis paper for future research

II CHANGES IN THE WAGE DISTRIBUTION IN THE 1980S

A Data

The analysis in this paper utilizes microdata from the Na-tional Bureau of Economic Research Extracts of the CurrentPopulation Survey (CPS) Outgoing Rotation Group EarningsFiles These data consist of point-in-time measures of the hourlyrate of pay which make it appropriate for a study of the impact ofa wage oor on the wage distribution For workers not paid on anhourly basis usual weekly earnings and usual weekly hours canbe used to construct an average hourly wage These datarsquos largesample sizes (three times the size of a single month of data fromthe CPS) and annual frequency make them suitable for a detailedregional analysis throughout the decade of the 1980s Details ofthe preprocessing of the data are reported in the Data Appendix

The three parts of Figure I depict the (hours-weighted) kerneldensity estimate of the distribution of log-wages from these datafor the years 1979 and 1989 for men women and all workers(men and women combined)5 In each panel the two vertical linesdenote the federal minimum wage levels in each year The guresuggests that in 1979 the minimum wage had to some extent asupporting effect on wages after its relative levelrsquos erosion duringthe decade by 1989 the minimum wage appears to have muchless of an inuence on the shape of the distribution The impres-sion that the minimum wage was an important feature of thelower part of the wage distribution is particularly striking for thefemale wage distribution Figure IC suggests the possibility thatthe decline in the relative value of the minimum wage over thedecade was primarily responsible for changes in the unconditionalwage distribution since much of the change appears to occur inthe lower tail

5 The sample includes individuals aged sixteen and over The horizontal axismeasures the log-wage relative to the overall (men and women) median in eachyear All kernel density estimates use the rule-of-thumb bandwidth h 5 079Rn 2 15where R is the interquartile range [Silverman 1986]

QUARTERLY JOURNAL OF ECONOMICS980

This paper follows the wage inequality literaturersquos usualpractice of conducting formal analyses for men and womenseparately But since changes in the lower tail appear to be arelatively more important component of the total change whenexamining the unconditional distribution of wages (without re-gard to gender) some attention will also be given to the ndingsfor the entire sample Examining the entire samplemdashthe distribu-tion of hourly pay for hours worked in the economymdashallows someabstraction from issues that arise when men and women arethought to compete in the same labor market when changes inthe male and female distributions are to some extent interdepen-dent6 Thus this paperrsquos estimates of changes in the uncondi-tional distribution of wagesmdashafter parsing out the minimumwage effectmdashcould be interpreted as the net impact of between-gender wage changes [OrsquoNeill and Polachek 1993 Fortin andLemieux 1996 Blau and Kahn 1997] and other lsquolsquowithin-genderrsquorsquoforces such as skill-biased technological change [Davis and Halti-wanger 1991 Bound and Johnson 1992 Autor Katz and Krueger1997 Doms Dunne and Troske 1997] international trade [Borjasand Ramey 1995 Feenstra and Hanson 1996] and more generallyrising lsquolsquoskill premiumsrsquorsquo stemming from an increase in the demandfor skilled labor [Katz and Murphy 1992 Berman Bound andGriliches 1994]

The available time series data on the United States wagedistribution also point to a close connection between the minimumwage and changes in inequality Figure II plots changes inpercentiles of the wage distribution relative to the median for thefth tenth twenty-fth seventy-fth and ninetieth wage percen-tiles between 1973 and 19937 These measures of wage dispersionas well as the log difference between the federal minimum wageand the median wage (also shown in the gure) are normalized tobe zero in 1979 which appears to be a turning point for several ofthe series

Figure II shows that after rising modestly during the latterhalf of the 1970s the minimum wage (relative to the medianwage) fell almost 40 log points in the period between 1979 and1989 The sharp rebound in 1990 and 1991 reects the legislatedrise in the federal minimum wage from $335 to $380 in April of

6 This issue is addressed in Fortin and Lemieux [1996] and Topel [1997]7 Includes both men and women all those aged 16 and over The data for

1973ndash1978 are taken from the May CPS dual job supplements These data containa point-in-time wage measure comparable to that from the Outgoing RotationGroup Files for 1979ndash1993

WAGE INEQUALITY AND THE MINIMUM WAGE 981

FIGURE IaWage Distribution Density Estimates Men 1979ndash1989

FIGURE IbWage Distribution Density Estimates Women 1979ndash1989

1990 and then to $425 in April of 1991 The gure illustrates thatwith the exception of the last few years of the 1980s and the periodafter 1991 movements in wage dispersion in the lower half of thewage distribution moved in close tandem with changes in theminimum wage The fth and tenth percentiles rise in the latterpart of the 1970s experience a sharp decline during much of the1980s and then rebound modestly in the early 1990s8

Finally Figure II shows that while changes in the seventy-fth wage percentile have been small there has been a steady risein the ninetieth percentile throughout the 1973ndash1993 period Thatthe minimum wage is unlikely to have played any part in thisparticular trend underscores the limited inferences that can bemade from an examination of the aggregate time series data Forexample there is nearly as much evidence here to suggest that the

8 It should be noted that trends in measures of dispersion in average hourlyearnings as computed from the Census and the March CPS differ somewhat fromthat calculated from the May CPS during the 1970s For example the 90ndash10differential for women falls by about 11 percent in the May CPS but rises 3 percentin the March CPS See Katz and Autor [1998] for a summary of differences acrossthe data sets over the past few decades

FIGURE IcWage Distribution Density Estimates Men and Women 1979ndash1989

WAGE INEQUALITY AND THE MINIMUM WAGE 983

minimum wage contributed to growth in the ninetieth percentileas there is to suggest that it caused a decline in the tenthpercentile The effective decline in the minimum wage and thegrowth in inequality in the lower half of the wage distribution areboth monotonic throughout the 1980s As a result no analysis ofthe aggregate time series data will be able to adequately distin-guish a minimum wage effect from a rising trend in lsquolsquolatentrsquorsquo wageinequalitymdashwhich I dene here to be a rise in wage inequalitythat would have occurred in the absence of a minimum wagepolicy

B Regional Variation in the lsquolsquoEffectiversquorsquo Minimum Wage

The time-series pattern of wage dispersion in the lower tail isnot uniform across regions in the United States Figure III plotsthe average 10ndash50 log (wage) differential during 1979ndash1991 fortwo groups of states the three highest-wage states (New Jersey

FIGURE IISelected Percentiles of the Wage Distribution Minimum Wage

Relative to the Median 1973ndash1993All series are normalized to be 0 in 1979

QUARTERLY JOURNAL OF ECONOMICS984

Michigan and Maryland) and the three lowest-wage states (SouthDakota Mississippi and Arkansas)9 The low-wage states whichinitially begin with a more compressed lower tail than thehigh-wage states experience an average increase in dispersion ofabout twenty log points throughout the 1980s and a subsequentcompression of about ve log points during 1989ndash1991 By con-trast the 10ndash50 differential for the highest-wage states appearsrelatively stable during the entire 1979ndash1991 period

This additional dimension of wage inequality and its relationto the relative level of the minimum wage across regions offer anopportunity to distinguish the minimum wage effect from anational trend in latent wage dispersion In particular theinteraction between a uniform federal minimum wage and wide

9 These six states were selected from the state-level panel data set describedin the Data Appendix Average median wages for the entire period were computedThe three highest and three lowest overall averages were chosen excluding allstates for which there was at least one year where the state minimum exceeded thefederal minimum wage rate The differentials are for the entire sample agedsixteen or over

FIGURE III10ndash50 75ndash50 Log(Wage) Differentials High- versus Low-Wage States 1979ndash1991

WAGE INEQUALITY AND THE MINIMUM WAGE 985

variation in wage levels across states yields variability in lsquolsquoeffec-tiversquorsquo minimum wage levels The federal minimum wage highlyimpacts low-wage states while minimally affecting high-wagestates

This is demonstrated in Figure IV which plots (hours-weighted) kernel density estimates of log-wages in 1979 for threegroups of states high- medium- and low-wage states10 Thehorizontal scale measures the log-wage relative to each grouprsquosrespective median wage The vertical lines represent the federalminimum wage also relative to each grouprsquos respective medianFigure IV gives the impression that low-wage states are indeedmore highly impacted by the minimum wage than higher-wagestates It is this variation that is exploited in the present study

Stratifying the wage distribution by a dimension other thangeography would likely produce a similar result And cross-sectional variation in effective minimum wages across educa-tional groups for example could be used to estimate a minimumwage effect However in this study variation across states has afew important advantages over variation across other groups suchas education age industry or occupation

First on a conceptual level variation in the relative mini-mum across states more closely mimics the variation that wouldbe most ideal (but that is also unattainable) for estimating theimpact of the minimum wage on the wage distribution Theseideal data would consist of a sample of independent realizations ofthe wage distribution of the United States labor market at onepoint in time and exhibit variability in the minimum wage acrossrealizations Each statersquos labor market can be more readilyconsidered a microcosm of the United States labor market thancan any particular group of workers dened by education age orindustrial or occupational sector

Second as described in detail in Section V by the late-1980sthere arose moderate variation in state-legislated minimum wagelevels This variability in state-specic minimum wages com-bined with the 1990ndash1991 legislated increases in the federalminimum generates an alternative source of variation fromwhich the impact of the minimum wage can be identied

A potential problem with utilizing the substantial regional

10 I rank each state by the mean log-wage I choose the bottom seven(Arkansas Mississippi Vermont Maine South Carolina South Dakota andNorth Carolina) middle seven (Idaho Oklahoma Kentucky Kansas VirginiaMissouri and Indiana) and highest seven (Oregon Wyoming California IllinoisMaryland Michigan and Washington) for the three groups The sample sizes forthe low- medium- and high-wage states are 12263 16190 31932 respectively

QUARTERLY JOURNAL OF ECONOMICS986

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 4: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

tion and presents the results of the estimation Section V exam-ines the effect of the increases in the federal minimum wage onwage inequality from 1989 to 1991 Section VI uses the estimatesof this study to adjust measures of between- and within-groupwage inequality for the minimum wage effect Finally Section VIIconcludes with a discussion of the implications of the ndings inthis paper for future research

II CHANGES IN THE WAGE DISTRIBUTION IN THE 1980S

A Data

The analysis in this paper utilizes microdata from the Na-tional Bureau of Economic Research Extracts of the CurrentPopulation Survey (CPS) Outgoing Rotation Group EarningsFiles These data consist of point-in-time measures of the hourlyrate of pay which make it appropriate for a study of the impact ofa wage oor on the wage distribution For workers not paid on anhourly basis usual weekly earnings and usual weekly hours canbe used to construct an average hourly wage These datarsquos largesample sizes (three times the size of a single month of data fromthe CPS) and annual frequency make them suitable for a detailedregional analysis throughout the decade of the 1980s Details ofthe preprocessing of the data are reported in the Data Appendix

The three parts of Figure I depict the (hours-weighted) kerneldensity estimate of the distribution of log-wages from these datafor the years 1979 and 1989 for men women and all workers(men and women combined)5 In each panel the two vertical linesdenote the federal minimum wage levels in each year The guresuggests that in 1979 the minimum wage had to some extent asupporting effect on wages after its relative levelrsquos erosion duringthe decade by 1989 the minimum wage appears to have muchless of an inuence on the shape of the distribution The impres-sion that the minimum wage was an important feature of thelower part of the wage distribution is particularly striking for thefemale wage distribution Figure IC suggests the possibility thatthe decline in the relative value of the minimum wage over thedecade was primarily responsible for changes in the unconditionalwage distribution since much of the change appears to occur inthe lower tail

5 The sample includes individuals aged sixteen and over The horizontal axismeasures the log-wage relative to the overall (men and women) median in eachyear All kernel density estimates use the rule-of-thumb bandwidth h 5 079Rn 2 15where R is the interquartile range [Silverman 1986]

QUARTERLY JOURNAL OF ECONOMICS980

This paper follows the wage inequality literaturersquos usualpractice of conducting formal analyses for men and womenseparately But since changes in the lower tail appear to be arelatively more important component of the total change whenexamining the unconditional distribution of wages (without re-gard to gender) some attention will also be given to the ndingsfor the entire sample Examining the entire samplemdashthe distribu-tion of hourly pay for hours worked in the economymdashallows someabstraction from issues that arise when men and women arethought to compete in the same labor market when changes inthe male and female distributions are to some extent interdepen-dent6 Thus this paperrsquos estimates of changes in the uncondi-tional distribution of wagesmdashafter parsing out the minimumwage effectmdashcould be interpreted as the net impact of between-gender wage changes [OrsquoNeill and Polachek 1993 Fortin andLemieux 1996 Blau and Kahn 1997] and other lsquolsquowithin-genderrsquorsquoforces such as skill-biased technological change [Davis and Halti-wanger 1991 Bound and Johnson 1992 Autor Katz and Krueger1997 Doms Dunne and Troske 1997] international trade [Borjasand Ramey 1995 Feenstra and Hanson 1996] and more generallyrising lsquolsquoskill premiumsrsquorsquo stemming from an increase in the demandfor skilled labor [Katz and Murphy 1992 Berman Bound andGriliches 1994]

The available time series data on the United States wagedistribution also point to a close connection between the minimumwage and changes in inequality Figure II plots changes inpercentiles of the wage distribution relative to the median for thefth tenth twenty-fth seventy-fth and ninetieth wage percen-tiles between 1973 and 19937 These measures of wage dispersionas well as the log difference between the federal minimum wageand the median wage (also shown in the gure) are normalized tobe zero in 1979 which appears to be a turning point for several ofthe series

Figure II shows that after rising modestly during the latterhalf of the 1970s the minimum wage (relative to the medianwage) fell almost 40 log points in the period between 1979 and1989 The sharp rebound in 1990 and 1991 reects the legislatedrise in the federal minimum wage from $335 to $380 in April of

6 This issue is addressed in Fortin and Lemieux [1996] and Topel [1997]7 Includes both men and women all those aged 16 and over The data for

1973ndash1978 are taken from the May CPS dual job supplements These data containa point-in-time wage measure comparable to that from the Outgoing RotationGroup Files for 1979ndash1993

WAGE INEQUALITY AND THE MINIMUM WAGE 981

FIGURE IaWage Distribution Density Estimates Men 1979ndash1989

FIGURE IbWage Distribution Density Estimates Women 1979ndash1989

1990 and then to $425 in April of 1991 The gure illustrates thatwith the exception of the last few years of the 1980s and the periodafter 1991 movements in wage dispersion in the lower half of thewage distribution moved in close tandem with changes in theminimum wage The fth and tenth percentiles rise in the latterpart of the 1970s experience a sharp decline during much of the1980s and then rebound modestly in the early 1990s8

Finally Figure II shows that while changes in the seventy-fth wage percentile have been small there has been a steady risein the ninetieth percentile throughout the 1973ndash1993 period Thatthe minimum wage is unlikely to have played any part in thisparticular trend underscores the limited inferences that can bemade from an examination of the aggregate time series data Forexample there is nearly as much evidence here to suggest that the

8 It should be noted that trends in measures of dispersion in average hourlyearnings as computed from the Census and the March CPS differ somewhat fromthat calculated from the May CPS during the 1970s For example the 90ndash10differential for women falls by about 11 percent in the May CPS but rises 3 percentin the March CPS See Katz and Autor [1998] for a summary of differences acrossthe data sets over the past few decades

FIGURE IcWage Distribution Density Estimates Men and Women 1979ndash1989

WAGE INEQUALITY AND THE MINIMUM WAGE 983

minimum wage contributed to growth in the ninetieth percentileas there is to suggest that it caused a decline in the tenthpercentile The effective decline in the minimum wage and thegrowth in inequality in the lower half of the wage distribution areboth monotonic throughout the 1980s As a result no analysis ofthe aggregate time series data will be able to adequately distin-guish a minimum wage effect from a rising trend in lsquolsquolatentrsquorsquo wageinequalitymdashwhich I dene here to be a rise in wage inequalitythat would have occurred in the absence of a minimum wagepolicy

B Regional Variation in the lsquolsquoEffectiversquorsquo Minimum Wage

The time-series pattern of wage dispersion in the lower tail isnot uniform across regions in the United States Figure III plotsthe average 10ndash50 log (wage) differential during 1979ndash1991 fortwo groups of states the three highest-wage states (New Jersey

FIGURE IISelected Percentiles of the Wage Distribution Minimum Wage

Relative to the Median 1973ndash1993All series are normalized to be 0 in 1979

QUARTERLY JOURNAL OF ECONOMICS984

Michigan and Maryland) and the three lowest-wage states (SouthDakota Mississippi and Arkansas)9 The low-wage states whichinitially begin with a more compressed lower tail than thehigh-wage states experience an average increase in dispersion ofabout twenty log points throughout the 1980s and a subsequentcompression of about ve log points during 1989ndash1991 By con-trast the 10ndash50 differential for the highest-wage states appearsrelatively stable during the entire 1979ndash1991 period

This additional dimension of wage inequality and its relationto the relative level of the minimum wage across regions offer anopportunity to distinguish the minimum wage effect from anational trend in latent wage dispersion In particular theinteraction between a uniform federal minimum wage and wide

9 These six states were selected from the state-level panel data set describedin the Data Appendix Average median wages for the entire period were computedThe three highest and three lowest overall averages were chosen excluding allstates for which there was at least one year where the state minimum exceeded thefederal minimum wage rate The differentials are for the entire sample agedsixteen or over

FIGURE III10ndash50 75ndash50 Log(Wage) Differentials High- versus Low-Wage States 1979ndash1991

WAGE INEQUALITY AND THE MINIMUM WAGE 985

variation in wage levels across states yields variability in lsquolsquoeffec-tiversquorsquo minimum wage levels The federal minimum wage highlyimpacts low-wage states while minimally affecting high-wagestates

This is demonstrated in Figure IV which plots (hours-weighted) kernel density estimates of log-wages in 1979 for threegroups of states high- medium- and low-wage states10 Thehorizontal scale measures the log-wage relative to each grouprsquosrespective median wage The vertical lines represent the federalminimum wage also relative to each grouprsquos respective medianFigure IV gives the impression that low-wage states are indeedmore highly impacted by the minimum wage than higher-wagestates It is this variation that is exploited in the present study

Stratifying the wage distribution by a dimension other thangeography would likely produce a similar result And cross-sectional variation in effective minimum wages across educa-tional groups for example could be used to estimate a minimumwage effect However in this study variation across states has afew important advantages over variation across other groups suchas education age industry or occupation

First on a conceptual level variation in the relative mini-mum across states more closely mimics the variation that wouldbe most ideal (but that is also unattainable) for estimating theimpact of the minimum wage on the wage distribution Theseideal data would consist of a sample of independent realizations ofthe wage distribution of the United States labor market at onepoint in time and exhibit variability in the minimum wage acrossrealizations Each statersquos labor market can be more readilyconsidered a microcosm of the United States labor market thancan any particular group of workers dened by education age orindustrial or occupational sector

Second as described in detail in Section V by the late-1980sthere arose moderate variation in state-legislated minimum wagelevels This variability in state-specic minimum wages com-bined with the 1990ndash1991 legislated increases in the federalminimum generates an alternative source of variation fromwhich the impact of the minimum wage can be identied

A potential problem with utilizing the substantial regional

10 I rank each state by the mean log-wage I choose the bottom seven(Arkansas Mississippi Vermont Maine South Carolina South Dakota andNorth Carolina) middle seven (Idaho Oklahoma Kentucky Kansas VirginiaMissouri and Indiana) and highest seven (Oregon Wyoming California IllinoisMaryland Michigan and Washington) for the three groups The sample sizes forthe low- medium- and high-wage states are 12263 16190 31932 respectively

QUARTERLY JOURNAL OF ECONOMICS986

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 5: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

This paper follows the wage inequality literaturersquos usualpractice of conducting formal analyses for men and womenseparately But since changes in the lower tail appear to be arelatively more important component of the total change whenexamining the unconditional distribution of wages (without re-gard to gender) some attention will also be given to the ndingsfor the entire sample Examining the entire samplemdashthe distribu-tion of hourly pay for hours worked in the economymdashallows someabstraction from issues that arise when men and women arethought to compete in the same labor market when changes inthe male and female distributions are to some extent interdepen-dent6 Thus this paperrsquos estimates of changes in the uncondi-tional distribution of wagesmdashafter parsing out the minimumwage effectmdashcould be interpreted as the net impact of between-gender wage changes [OrsquoNeill and Polachek 1993 Fortin andLemieux 1996 Blau and Kahn 1997] and other lsquolsquowithin-genderrsquorsquoforces such as skill-biased technological change [Davis and Halti-wanger 1991 Bound and Johnson 1992 Autor Katz and Krueger1997 Doms Dunne and Troske 1997] international trade [Borjasand Ramey 1995 Feenstra and Hanson 1996] and more generallyrising lsquolsquoskill premiumsrsquorsquo stemming from an increase in the demandfor skilled labor [Katz and Murphy 1992 Berman Bound andGriliches 1994]

The available time series data on the United States wagedistribution also point to a close connection between the minimumwage and changes in inequality Figure II plots changes inpercentiles of the wage distribution relative to the median for thefth tenth twenty-fth seventy-fth and ninetieth wage percen-tiles between 1973 and 19937 These measures of wage dispersionas well as the log difference between the federal minimum wageand the median wage (also shown in the gure) are normalized tobe zero in 1979 which appears to be a turning point for several ofthe series

Figure II shows that after rising modestly during the latterhalf of the 1970s the minimum wage (relative to the medianwage) fell almost 40 log points in the period between 1979 and1989 The sharp rebound in 1990 and 1991 reects the legislatedrise in the federal minimum wage from $335 to $380 in April of

6 This issue is addressed in Fortin and Lemieux [1996] and Topel [1997]7 Includes both men and women all those aged 16 and over The data for

1973ndash1978 are taken from the May CPS dual job supplements These data containa point-in-time wage measure comparable to that from the Outgoing RotationGroup Files for 1979ndash1993

WAGE INEQUALITY AND THE MINIMUM WAGE 981

FIGURE IaWage Distribution Density Estimates Men 1979ndash1989

FIGURE IbWage Distribution Density Estimates Women 1979ndash1989

1990 and then to $425 in April of 1991 The gure illustrates thatwith the exception of the last few years of the 1980s and the periodafter 1991 movements in wage dispersion in the lower half of thewage distribution moved in close tandem with changes in theminimum wage The fth and tenth percentiles rise in the latterpart of the 1970s experience a sharp decline during much of the1980s and then rebound modestly in the early 1990s8

Finally Figure II shows that while changes in the seventy-fth wage percentile have been small there has been a steady risein the ninetieth percentile throughout the 1973ndash1993 period Thatthe minimum wage is unlikely to have played any part in thisparticular trend underscores the limited inferences that can bemade from an examination of the aggregate time series data Forexample there is nearly as much evidence here to suggest that the

8 It should be noted that trends in measures of dispersion in average hourlyearnings as computed from the Census and the March CPS differ somewhat fromthat calculated from the May CPS during the 1970s For example the 90ndash10differential for women falls by about 11 percent in the May CPS but rises 3 percentin the March CPS See Katz and Autor [1998] for a summary of differences acrossthe data sets over the past few decades

FIGURE IcWage Distribution Density Estimates Men and Women 1979ndash1989

WAGE INEQUALITY AND THE MINIMUM WAGE 983

minimum wage contributed to growth in the ninetieth percentileas there is to suggest that it caused a decline in the tenthpercentile The effective decline in the minimum wage and thegrowth in inequality in the lower half of the wage distribution areboth monotonic throughout the 1980s As a result no analysis ofthe aggregate time series data will be able to adequately distin-guish a minimum wage effect from a rising trend in lsquolsquolatentrsquorsquo wageinequalitymdashwhich I dene here to be a rise in wage inequalitythat would have occurred in the absence of a minimum wagepolicy

B Regional Variation in the lsquolsquoEffectiversquorsquo Minimum Wage

The time-series pattern of wage dispersion in the lower tail isnot uniform across regions in the United States Figure III plotsthe average 10ndash50 log (wage) differential during 1979ndash1991 fortwo groups of states the three highest-wage states (New Jersey

FIGURE IISelected Percentiles of the Wage Distribution Minimum Wage

Relative to the Median 1973ndash1993All series are normalized to be 0 in 1979

QUARTERLY JOURNAL OF ECONOMICS984

Michigan and Maryland) and the three lowest-wage states (SouthDakota Mississippi and Arkansas)9 The low-wage states whichinitially begin with a more compressed lower tail than thehigh-wage states experience an average increase in dispersion ofabout twenty log points throughout the 1980s and a subsequentcompression of about ve log points during 1989ndash1991 By con-trast the 10ndash50 differential for the highest-wage states appearsrelatively stable during the entire 1979ndash1991 period

This additional dimension of wage inequality and its relationto the relative level of the minimum wage across regions offer anopportunity to distinguish the minimum wage effect from anational trend in latent wage dispersion In particular theinteraction between a uniform federal minimum wage and wide

9 These six states were selected from the state-level panel data set describedin the Data Appendix Average median wages for the entire period were computedThe three highest and three lowest overall averages were chosen excluding allstates for which there was at least one year where the state minimum exceeded thefederal minimum wage rate The differentials are for the entire sample agedsixteen or over

FIGURE III10ndash50 75ndash50 Log(Wage) Differentials High- versus Low-Wage States 1979ndash1991

WAGE INEQUALITY AND THE MINIMUM WAGE 985

variation in wage levels across states yields variability in lsquolsquoeffec-tiversquorsquo minimum wage levels The federal minimum wage highlyimpacts low-wage states while minimally affecting high-wagestates

This is demonstrated in Figure IV which plots (hours-weighted) kernel density estimates of log-wages in 1979 for threegroups of states high- medium- and low-wage states10 Thehorizontal scale measures the log-wage relative to each grouprsquosrespective median wage The vertical lines represent the federalminimum wage also relative to each grouprsquos respective medianFigure IV gives the impression that low-wage states are indeedmore highly impacted by the minimum wage than higher-wagestates It is this variation that is exploited in the present study

Stratifying the wage distribution by a dimension other thangeography would likely produce a similar result And cross-sectional variation in effective minimum wages across educa-tional groups for example could be used to estimate a minimumwage effect However in this study variation across states has afew important advantages over variation across other groups suchas education age industry or occupation

First on a conceptual level variation in the relative mini-mum across states more closely mimics the variation that wouldbe most ideal (but that is also unattainable) for estimating theimpact of the minimum wage on the wage distribution Theseideal data would consist of a sample of independent realizations ofthe wage distribution of the United States labor market at onepoint in time and exhibit variability in the minimum wage acrossrealizations Each statersquos labor market can be more readilyconsidered a microcosm of the United States labor market thancan any particular group of workers dened by education age orindustrial or occupational sector

Second as described in detail in Section V by the late-1980sthere arose moderate variation in state-legislated minimum wagelevels This variability in state-specic minimum wages com-bined with the 1990ndash1991 legislated increases in the federalminimum generates an alternative source of variation fromwhich the impact of the minimum wage can be identied

A potential problem with utilizing the substantial regional

10 I rank each state by the mean log-wage I choose the bottom seven(Arkansas Mississippi Vermont Maine South Carolina South Dakota andNorth Carolina) middle seven (Idaho Oklahoma Kentucky Kansas VirginiaMissouri and Indiana) and highest seven (Oregon Wyoming California IllinoisMaryland Michigan and Washington) for the three groups The sample sizes forthe low- medium- and high-wage states are 12263 16190 31932 respectively

QUARTERLY JOURNAL OF ECONOMICS986

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 6: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

FIGURE IaWage Distribution Density Estimates Men 1979ndash1989

FIGURE IbWage Distribution Density Estimates Women 1979ndash1989

1990 and then to $425 in April of 1991 The gure illustrates thatwith the exception of the last few years of the 1980s and the periodafter 1991 movements in wage dispersion in the lower half of thewage distribution moved in close tandem with changes in theminimum wage The fth and tenth percentiles rise in the latterpart of the 1970s experience a sharp decline during much of the1980s and then rebound modestly in the early 1990s8

Finally Figure II shows that while changes in the seventy-fth wage percentile have been small there has been a steady risein the ninetieth percentile throughout the 1973ndash1993 period Thatthe minimum wage is unlikely to have played any part in thisparticular trend underscores the limited inferences that can bemade from an examination of the aggregate time series data Forexample there is nearly as much evidence here to suggest that the

8 It should be noted that trends in measures of dispersion in average hourlyearnings as computed from the Census and the March CPS differ somewhat fromthat calculated from the May CPS during the 1970s For example the 90ndash10differential for women falls by about 11 percent in the May CPS but rises 3 percentin the March CPS See Katz and Autor [1998] for a summary of differences acrossthe data sets over the past few decades

FIGURE IcWage Distribution Density Estimates Men and Women 1979ndash1989

WAGE INEQUALITY AND THE MINIMUM WAGE 983

minimum wage contributed to growth in the ninetieth percentileas there is to suggest that it caused a decline in the tenthpercentile The effective decline in the minimum wage and thegrowth in inequality in the lower half of the wage distribution areboth monotonic throughout the 1980s As a result no analysis ofthe aggregate time series data will be able to adequately distin-guish a minimum wage effect from a rising trend in lsquolsquolatentrsquorsquo wageinequalitymdashwhich I dene here to be a rise in wage inequalitythat would have occurred in the absence of a minimum wagepolicy

B Regional Variation in the lsquolsquoEffectiversquorsquo Minimum Wage

The time-series pattern of wage dispersion in the lower tail isnot uniform across regions in the United States Figure III plotsthe average 10ndash50 log (wage) differential during 1979ndash1991 fortwo groups of states the three highest-wage states (New Jersey

FIGURE IISelected Percentiles of the Wage Distribution Minimum Wage

Relative to the Median 1973ndash1993All series are normalized to be 0 in 1979

QUARTERLY JOURNAL OF ECONOMICS984

Michigan and Maryland) and the three lowest-wage states (SouthDakota Mississippi and Arkansas)9 The low-wage states whichinitially begin with a more compressed lower tail than thehigh-wage states experience an average increase in dispersion ofabout twenty log points throughout the 1980s and a subsequentcompression of about ve log points during 1989ndash1991 By con-trast the 10ndash50 differential for the highest-wage states appearsrelatively stable during the entire 1979ndash1991 period

This additional dimension of wage inequality and its relationto the relative level of the minimum wage across regions offer anopportunity to distinguish the minimum wage effect from anational trend in latent wage dispersion In particular theinteraction between a uniform federal minimum wage and wide

9 These six states were selected from the state-level panel data set describedin the Data Appendix Average median wages for the entire period were computedThe three highest and three lowest overall averages were chosen excluding allstates for which there was at least one year where the state minimum exceeded thefederal minimum wage rate The differentials are for the entire sample agedsixteen or over

FIGURE III10ndash50 75ndash50 Log(Wage) Differentials High- versus Low-Wage States 1979ndash1991

WAGE INEQUALITY AND THE MINIMUM WAGE 985

variation in wage levels across states yields variability in lsquolsquoeffec-tiversquorsquo minimum wage levels The federal minimum wage highlyimpacts low-wage states while minimally affecting high-wagestates

This is demonstrated in Figure IV which plots (hours-weighted) kernel density estimates of log-wages in 1979 for threegroups of states high- medium- and low-wage states10 Thehorizontal scale measures the log-wage relative to each grouprsquosrespective median wage The vertical lines represent the federalminimum wage also relative to each grouprsquos respective medianFigure IV gives the impression that low-wage states are indeedmore highly impacted by the minimum wage than higher-wagestates It is this variation that is exploited in the present study

Stratifying the wage distribution by a dimension other thangeography would likely produce a similar result And cross-sectional variation in effective minimum wages across educa-tional groups for example could be used to estimate a minimumwage effect However in this study variation across states has afew important advantages over variation across other groups suchas education age industry or occupation

First on a conceptual level variation in the relative mini-mum across states more closely mimics the variation that wouldbe most ideal (but that is also unattainable) for estimating theimpact of the minimum wage on the wage distribution Theseideal data would consist of a sample of independent realizations ofthe wage distribution of the United States labor market at onepoint in time and exhibit variability in the minimum wage acrossrealizations Each statersquos labor market can be more readilyconsidered a microcosm of the United States labor market thancan any particular group of workers dened by education age orindustrial or occupational sector

Second as described in detail in Section V by the late-1980sthere arose moderate variation in state-legislated minimum wagelevels This variability in state-specic minimum wages com-bined with the 1990ndash1991 legislated increases in the federalminimum generates an alternative source of variation fromwhich the impact of the minimum wage can be identied

A potential problem with utilizing the substantial regional

10 I rank each state by the mean log-wage I choose the bottom seven(Arkansas Mississippi Vermont Maine South Carolina South Dakota andNorth Carolina) middle seven (Idaho Oklahoma Kentucky Kansas VirginiaMissouri and Indiana) and highest seven (Oregon Wyoming California IllinoisMaryland Michigan and Washington) for the three groups The sample sizes forthe low- medium- and high-wage states are 12263 16190 31932 respectively

QUARTERLY JOURNAL OF ECONOMICS986

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 7: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

1990 and then to $425 in April of 1991 The gure illustrates thatwith the exception of the last few years of the 1980s and the periodafter 1991 movements in wage dispersion in the lower half of thewage distribution moved in close tandem with changes in theminimum wage The fth and tenth percentiles rise in the latterpart of the 1970s experience a sharp decline during much of the1980s and then rebound modestly in the early 1990s8

Finally Figure II shows that while changes in the seventy-fth wage percentile have been small there has been a steady risein the ninetieth percentile throughout the 1973ndash1993 period Thatthe minimum wage is unlikely to have played any part in thisparticular trend underscores the limited inferences that can bemade from an examination of the aggregate time series data Forexample there is nearly as much evidence here to suggest that the

8 It should be noted that trends in measures of dispersion in average hourlyearnings as computed from the Census and the March CPS differ somewhat fromthat calculated from the May CPS during the 1970s For example the 90ndash10differential for women falls by about 11 percent in the May CPS but rises 3 percentin the March CPS See Katz and Autor [1998] for a summary of differences acrossthe data sets over the past few decades

FIGURE IcWage Distribution Density Estimates Men and Women 1979ndash1989

WAGE INEQUALITY AND THE MINIMUM WAGE 983

minimum wage contributed to growth in the ninetieth percentileas there is to suggest that it caused a decline in the tenthpercentile The effective decline in the minimum wage and thegrowth in inequality in the lower half of the wage distribution areboth monotonic throughout the 1980s As a result no analysis ofthe aggregate time series data will be able to adequately distin-guish a minimum wage effect from a rising trend in lsquolsquolatentrsquorsquo wageinequalitymdashwhich I dene here to be a rise in wage inequalitythat would have occurred in the absence of a minimum wagepolicy

B Regional Variation in the lsquolsquoEffectiversquorsquo Minimum Wage

The time-series pattern of wage dispersion in the lower tail isnot uniform across regions in the United States Figure III plotsthe average 10ndash50 log (wage) differential during 1979ndash1991 fortwo groups of states the three highest-wage states (New Jersey

FIGURE IISelected Percentiles of the Wage Distribution Minimum Wage

Relative to the Median 1973ndash1993All series are normalized to be 0 in 1979

QUARTERLY JOURNAL OF ECONOMICS984

Michigan and Maryland) and the three lowest-wage states (SouthDakota Mississippi and Arkansas)9 The low-wage states whichinitially begin with a more compressed lower tail than thehigh-wage states experience an average increase in dispersion ofabout twenty log points throughout the 1980s and a subsequentcompression of about ve log points during 1989ndash1991 By con-trast the 10ndash50 differential for the highest-wage states appearsrelatively stable during the entire 1979ndash1991 period

This additional dimension of wage inequality and its relationto the relative level of the minimum wage across regions offer anopportunity to distinguish the minimum wage effect from anational trend in latent wage dispersion In particular theinteraction between a uniform federal minimum wage and wide

9 These six states were selected from the state-level panel data set describedin the Data Appendix Average median wages for the entire period were computedThe three highest and three lowest overall averages were chosen excluding allstates for which there was at least one year where the state minimum exceeded thefederal minimum wage rate The differentials are for the entire sample agedsixteen or over

FIGURE III10ndash50 75ndash50 Log(Wage) Differentials High- versus Low-Wage States 1979ndash1991

WAGE INEQUALITY AND THE MINIMUM WAGE 985

variation in wage levels across states yields variability in lsquolsquoeffec-tiversquorsquo minimum wage levels The federal minimum wage highlyimpacts low-wage states while minimally affecting high-wagestates

This is demonstrated in Figure IV which plots (hours-weighted) kernel density estimates of log-wages in 1979 for threegroups of states high- medium- and low-wage states10 Thehorizontal scale measures the log-wage relative to each grouprsquosrespective median wage The vertical lines represent the federalminimum wage also relative to each grouprsquos respective medianFigure IV gives the impression that low-wage states are indeedmore highly impacted by the minimum wage than higher-wagestates It is this variation that is exploited in the present study

Stratifying the wage distribution by a dimension other thangeography would likely produce a similar result And cross-sectional variation in effective minimum wages across educa-tional groups for example could be used to estimate a minimumwage effect However in this study variation across states has afew important advantages over variation across other groups suchas education age industry or occupation

First on a conceptual level variation in the relative mini-mum across states more closely mimics the variation that wouldbe most ideal (but that is also unattainable) for estimating theimpact of the minimum wage on the wage distribution Theseideal data would consist of a sample of independent realizations ofthe wage distribution of the United States labor market at onepoint in time and exhibit variability in the minimum wage acrossrealizations Each statersquos labor market can be more readilyconsidered a microcosm of the United States labor market thancan any particular group of workers dened by education age orindustrial or occupational sector

Second as described in detail in Section V by the late-1980sthere arose moderate variation in state-legislated minimum wagelevels This variability in state-specic minimum wages com-bined with the 1990ndash1991 legislated increases in the federalminimum generates an alternative source of variation fromwhich the impact of the minimum wage can be identied

A potential problem with utilizing the substantial regional

10 I rank each state by the mean log-wage I choose the bottom seven(Arkansas Mississippi Vermont Maine South Carolina South Dakota andNorth Carolina) middle seven (Idaho Oklahoma Kentucky Kansas VirginiaMissouri and Indiana) and highest seven (Oregon Wyoming California IllinoisMaryland Michigan and Washington) for the three groups The sample sizes forthe low- medium- and high-wage states are 12263 16190 31932 respectively

QUARTERLY JOURNAL OF ECONOMICS986

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 8: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

minimum wage contributed to growth in the ninetieth percentileas there is to suggest that it caused a decline in the tenthpercentile The effective decline in the minimum wage and thegrowth in inequality in the lower half of the wage distribution areboth monotonic throughout the 1980s As a result no analysis ofthe aggregate time series data will be able to adequately distin-guish a minimum wage effect from a rising trend in lsquolsquolatentrsquorsquo wageinequalitymdashwhich I dene here to be a rise in wage inequalitythat would have occurred in the absence of a minimum wagepolicy

B Regional Variation in the lsquolsquoEffectiversquorsquo Minimum Wage

The time-series pattern of wage dispersion in the lower tail isnot uniform across regions in the United States Figure III plotsthe average 10ndash50 log (wage) differential during 1979ndash1991 fortwo groups of states the three highest-wage states (New Jersey

FIGURE IISelected Percentiles of the Wage Distribution Minimum Wage

Relative to the Median 1973ndash1993All series are normalized to be 0 in 1979

QUARTERLY JOURNAL OF ECONOMICS984

Michigan and Maryland) and the three lowest-wage states (SouthDakota Mississippi and Arkansas)9 The low-wage states whichinitially begin with a more compressed lower tail than thehigh-wage states experience an average increase in dispersion ofabout twenty log points throughout the 1980s and a subsequentcompression of about ve log points during 1989ndash1991 By con-trast the 10ndash50 differential for the highest-wage states appearsrelatively stable during the entire 1979ndash1991 period

This additional dimension of wage inequality and its relationto the relative level of the minimum wage across regions offer anopportunity to distinguish the minimum wage effect from anational trend in latent wage dispersion In particular theinteraction between a uniform federal minimum wage and wide

9 These six states were selected from the state-level panel data set describedin the Data Appendix Average median wages for the entire period were computedThe three highest and three lowest overall averages were chosen excluding allstates for which there was at least one year where the state minimum exceeded thefederal minimum wage rate The differentials are for the entire sample agedsixteen or over

FIGURE III10ndash50 75ndash50 Log(Wage) Differentials High- versus Low-Wage States 1979ndash1991

WAGE INEQUALITY AND THE MINIMUM WAGE 985

variation in wage levels across states yields variability in lsquolsquoeffec-tiversquorsquo minimum wage levels The federal minimum wage highlyimpacts low-wage states while minimally affecting high-wagestates

This is demonstrated in Figure IV which plots (hours-weighted) kernel density estimates of log-wages in 1979 for threegroups of states high- medium- and low-wage states10 Thehorizontal scale measures the log-wage relative to each grouprsquosrespective median wage The vertical lines represent the federalminimum wage also relative to each grouprsquos respective medianFigure IV gives the impression that low-wage states are indeedmore highly impacted by the minimum wage than higher-wagestates It is this variation that is exploited in the present study

Stratifying the wage distribution by a dimension other thangeography would likely produce a similar result And cross-sectional variation in effective minimum wages across educa-tional groups for example could be used to estimate a minimumwage effect However in this study variation across states has afew important advantages over variation across other groups suchas education age industry or occupation

First on a conceptual level variation in the relative mini-mum across states more closely mimics the variation that wouldbe most ideal (but that is also unattainable) for estimating theimpact of the minimum wage on the wage distribution Theseideal data would consist of a sample of independent realizations ofthe wage distribution of the United States labor market at onepoint in time and exhibit variability in the minimum wage acrossrealizations Each statersquos labor market can be more readilyconsidered a microcosm of the United States labor market thancan any particular group of workers dened by education age orindustrial or occupational sector

Second as described in detail in Section V by the late-1980sthere arose moderate variation in state-legislated minimum wagelevels This variability in state-specic minimum wages com-bined with the 1990ndash1991 legislated increases in the federalminimum generates an alternative source of variation fromwhich the impact of the minimum wage can be identied

A potential problem with utilizing the substantial regional

10 I rank each state by the mean log-wage I choose the bottom seven(Arkansas Mississippi Vermont Maine South Carolina South Dakota andNorth Carolina) middle seven (Idaho Oklahoma Kentucky Kansas VirginiaMissouri and Indiana) and highest seven (Oregon Wyoming California IllinoisMaryland Michigan and Washington) for the three groups The sample sizes forthe low- medium- and high-wage states are 12263 16190 31932 respectively

QUARTERLY JOURNAL OF ECONOMICS986

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 9: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

Michigan and Maryland) and the three lowest-wage states (SouthDakota Mississippi and Arkansas)9 The low-wage states whichinitially begin with a more compressed lower tail than thehigh-wage states experience an average increase in dispersion ofabout twenty log points throughout the 1980s and a subsequentcompression of about ve log points during 1989ndash1991 By con-trast the 10ndash50 differential for the highest-wage states appearsrelatively stable during the entire 1979ndash1991 period

This additional dimension of wage inequality and its relationto the relative level of the minimum wage across regions offer anopportunity to distinguish the minimum wage effect from anational trend in latent wage dispersion In particular theinteraction between a uniform federal minimum wage and wide

9 These six states were selected from the state-level panel data set describedin the Data Appendix Average median wages for the entire period were computedThe three highest and three lowest overall averages were chosen excluding allstates for which there was at least one year where the state minimum exceeded thefederal minimum wage rate The differentials are for the entire sample agedsixteen or over

FIGURE III10ndash50 75ndash50 Log(Wage) Differentials High- versus Low-Wage States 1979ndash1991

WAGE INEQUALITY AND THE MINIMUM WAGE 985

variation in wage levels across states yields variability in lsquolsquoeffec-tiversquorsquo minimum wage levels The federal minimum wage highlyimpacts low-wage states while minimally affecting high-wagestates

This is demonstrated in Figure IV which plots (hours-weighted) kernel density estimates of log-wages in 1979 for threegroups of states high- medium- and low-wage states10 Thehorizontal scale measures the log-wage relative to each grouprsquosrespective median wage The vertical lines represent the federalminimum wage also relative to each grouprsquos respective medianFigure IV gives the impression that low-wage states are indeedmore highly impacted by the minimum wage than higher-wagestates It is this variation that is exploited in the present study

Stratifying the wage distribution by a dimension other thangeography would likely produce a similar result And cross-sectional variation in effective minimum wages across educa-tional groups for example could be used to estimate a minimumwage effect However in this study variation across states has afew important advantages over variation across other groups suchas education age industry or occupation

First on a conceptual level variation in the relative mini-mum across states more closely mimics the variation that wouldbe most ideal (but that is also unattainable) for estimating theimpact of the minimum wage on the wage distribution Theseideal data would consist of a sample of independent realizations ofthe wage distribution of the United States labor market at onepoint in time and exhibit variability in the minimum wage acrossrealizations Each statersquos labor market can be more readilyconsidered a microcosm of the United States labor market thancan any particular group of workers dened by education age orindustrial or occupational sector

Second as described in detail in Section V by the late-1980sthere arose moderate variation in state-legislated minimum wagelevels This variability in state-specic minimum wages com-bined with the 1990ndash1991 legislated increases in the federalminimum generates an alternative source of variation fromwhich the impact of the minimum wage can be identied

A potential problem with utilizing the substantial regional

10 I rank each state by the mean log-wage I choose the bottom seven(Arkansas Mississippi Vermont Maine South Carolina South Dakota andNorth Carolina) middle seven (Idaho Oklahoma Kentucky Kansas VirginiaMissouri and Indiana) and highest seven (Oregon Wyoming California IllinoisMaryland Michigan and Washington) for the three groups The sample sizes forthe low- medium- and high-wage states are 12263 16190 31932 respectively

QUARTERLY JOURNAL OF ECONOMICS986

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 10: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

variation in wage levels across states yields variability in lsquolsquoeffec-tiversquorsquo minimum wage levels The federal minimum wage highlyimpacts low-wage states while minimally affecting high-wagestates

This is demonstrated in Figure IV which plots (hours-weighted) kernel density estimates of log-wages in 1979 for threegroups of states high- medium- and low-wage states10 Thehorizontal scale measures the log-wage relative to each grouprsquosrespective median wage The vertical lines represent the federalminimum wage also relative to each grouprsquos respective medianFigure IV gives the impression that low-wage states are indeedmore highly impacted by the minimum wage than higher-wagestates It is this variation that is exploited in the present study

Stratifying the wage distribution by a dimension other thangeography would likely produce a similar result And cross-sectional variation in effective minimum wages across educa-tional groups for example could be used to estimate a minimumwage effect However in this study variation across states has afew important advantages over variation across other groups suchas education age industry or occupation

First on a conceptual level variation in the relative mini-mum across states more closely mimics the variation that wouldbe most ideal (but that is also unattainable) for estimating theimpact of the minimum wage on the wage distribution Theseideal data would consist of a sample of independent realizations ofthe wage distribution of the United States labor market at onepoint in time and exhibit variability in the minimum wage acrossrealizations Each statersquos labor market can be more readilyconsidered a microcosm of the United States labor market thancan any particular group of workers dened by education age orindustrial or occupational sector

Second as described in detail in Section V by the late-1980sthere arose moderate variation in state-legislated minimum wagelevels This variability in state-specic minimum wages com-bined with the 1990ndash1991 legislated increases in the federalminimum generates an alternative source of variation fromwhich the impact of the minimum wage can be identied

A potential problem with utilizing the substantial regional

10 I rank each state by the mean log-wage I choose the bottom seven(Arkansas Mississippi Vermont Maine South Carolina South Dakota andNorth Carolina) middle seven (Idaho Oklahoma Kentucky Kansas VirginiaMissouri and Indiana) and highest seven (Oregon Wyoming California IllinoisMaryland Michigan and Washington) for the three groups The sample sizes forthe low- medium- and high-wage states are 12263 16190 31932 respectively

QUARTERLY JOURNAL OF ECONOMICS986

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 11: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

variation in wage levels is that if high-wage states tend to possessgreater latent wage dispersion the use of the cross-sectionalvariation illustrated in Figure IV would lead to an exaggeratedestimate of the impact of the minimum wage A test of whetheroverall latent wage dispersion is empirically related to wage levelslies in being able to detect such a correlation where the minimumwage is not likely to be a factor such as at the upper tail of thewage distribution Figure III provides evidence to suggest thatsuch a systematic relation is not apparent in these data Theaverage 75ndash50 differentials for the very highest- and lowest-wagestates appear to be comparable throughout the 1979ndash1991 period

Of course the assumption that this property also holds for thelower tails of statesrsquo latent wage distributions is strictly speakinguntestable However a signicant systematic relation betweenlatent wage dispersion in the upper tail and overall wage levels(and hence the lsquolsquoeffectiversquorsquo minimum wage) across regions wouldseem to considerably weaken our condence in its validity Hencean examination of the relation between the relative minimum

FIGURE IVWage Distribution Density Estimates

Low- Medium- and High-Wage States 1979

WAGE INEQUALITY AND THE MINIMUM WAGE 987

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 12: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

wage and measures of dispersion of the upper tail will provide auseful specication check for the formal empirical analyses pre-sented below

III IDENTIFICATION OF CHANGES IN LATENT WAGE INEQUALITY

A Theoretical Relation between Wage Dispersion and theMinimum Wage

Below I formally model the relation between the variabilityin the relative lsquolsquobitersquorsquo of the minimum wage and the observed wagedistribution across regions in a way that allows separate identi-cation of the average growth in latent wage inequality Theapproach in this study is to use the various log(wage) percentiledifferentials to measure wage dispersion and the log-differentialbetween the logs of the minimum wage and some measure of thecentrality (or location) of the distribution to measure the lsquolsquoeffectiveminimum wagersquorsquo11 Below I characterize the theoretical relationbetween these two quantities under three distinct scenarios Idenote the latent and observed pth log-wage percentile of state jby w j

p and w jp respectively and the log of the nominal minimum

wage by minwage Although I utilize other measures of centralityin the formal empirical analysis I begin by considering wj

50 themedian wage Also for the sake of exposition I assume that theshapes of the latent wage distribution in all states are strictlyidentical up to location w j

p 2 wj50 5 w k

p 2 wk50 jk12

Case 1 lsquolsquoCensoringrsquorsquo no spillovers no disemployment In thisextreme case the only effect of the minimum wage is to raise thewages of those initially making less than the minimum to exactlythe level of the wage oor Across states we expect to see therelation

(1) w j10 2 wj

50 5 wj10 2 wj

50 if (minwage 2 wj50) (w j

10 2 w j50)

5 (minwage 2 w j50) otherwise

11 In the remainder of the paper I often refer to the effective minimum wageas the lsquolsquorelative minimum wagersquorsquo or simply lsquolsquothe minimum wagersquorsquo when dealingwith a cross section of states

12 That the latent distributions are strictly identical across states iscertainly false in practice but abstracting from stochastic elements which will bemore formally introduced in Section IV aids in describing the intuition behind theidentication

QUARTERLY JOURNAL OF ECONOMICS988

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 13: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

This relation across states is depicted in Figure V as line A0A113

For states that possess lsquolsquoeffective minimumsrsquorsquo that are smallerthan the latent 10ndash50 differential there is no relation between thedifferential and the relative minimum (the at portion of the line)For states where the relative minimum is above the latent 10ndash50differential the observed 10ndash50 differential is exactly equal to thedifferential between the minimum wage and the median (theportion coincident with the 45 degree line)

Case 2 lsquolsquoSpilloversrsquorsquo no disemployment More generally theminimum wage may have an effect on the pth percentile even if(minwage 2 wj

50) (wjp 2 wj

50) so that we have

(2) w j10 2 wj

50 5 g(minwage 2 wj50)

13 I am assuming that the minimum wage is never higher than the latentmedian wage for any state

FIGURE VMinimum Wage Decline and Growth in Latent Wage Dispersion

WAGE INEQUALITY AND THE MINIMUM WAGE 989

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 14: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

where g will generally be an increasing function as long as thelsquolsquospilloverrsquorsquo effect monotonically diminishes the higher the wagepercentile An example of such a function is depicted as line A0A2

in Figure V Note that across states a marginal rise in theeffective minimum even among states with minimums lower thanthe 10ndash50 differential causes an increase in the tenth wagepercentile relative to the median

Case 3 lsquolsquoTruncationrsquorsquo no spillovers full disemployment Inthis case the minimum wage has no impact on workers withlatent wages already above the minimum and causes job loss forall workers with latent wages below the minimum (ie truncationof the wage distribution) we will not observe the latterrsquos wagesThe loss of the sample in the lower tail mechanically leads tochanges in the observed percentiles of the wage distribution Forexample if for state j minwage 5 wj

10 then this model impliesthat we will not observe wages for workers who would haveearned wj

10 (or less) in the absence of the minimum As a resultthe observed (posttruncation) wj

10 cannot equal wj10 instead it

will equal the 10 1 (010 3 90) 5 19th percentile of the latentwage distribution As shown in Lee [1998] under some regularityconditions for the shape of the latent wage distribution thistruncation model implies that wj

10 2 wj50 will be an increasing

function of (minwage 2 wj50) simulations of the shape of this

relation using actual wage data show that it is generally increas-ing and exhibits curvature similar to that depicted by line A0A2 inFigure V

In each of these three cases (and in hybrids) there is anonlinear relation that is expected between the relative minimumwage measure and the observed 10ndash50 differential As the relativeminimum declines indenitely the relation asymptotes to ahorizontal line corresponding to the latent 10ndash50 differential thatis common across all states I forgo an attempt to empiricallydistinguish between disemployment (Case 3) and spillover effects(Case 2) of the minimum wage on the observed wage distributionInstead I simply note that in the arguably more realistic case ofsome disemployment and some spillover effects (a hybrid of Cases2 and 3) any positive empirical relation between wj

10 2 wj50 and

(minwage 2 wj50) will be an overestimate of true spillover effects

some of it will be a statistical lsquolsquoillusionrsquorsquo that is a natural

QUARTERLY JOURNAL OF ECONOMICS990

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 15: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

consequence of both employment loss and the fact that we onlyobserve wages for those who are working14

Consider rst a signicant decline in the relative value of thefederal minimum wage We expect a leftward shift in the locusrepresenting the 50 states from line A0A1 to B0B1 in Figure V forexample In addition if all of the states experienced an expansionin the latent 10ndash50 wage differential this would be additionallyreected in a downward shift from line B0B1 to line C0C1 Whenthese two events happen simultaneously we will only observedata corresponding to lines A0A1 and C0C1 In this example therise in observed wage dispersion of the median state (which isdenoted by the black square of each locus) is fully due to a rise inlatent wage inequality rather than to the falling relative level ofthe minimum wage Figure V also illustrates a contrastingexample where the statesrsquo relative minimums and the 10ndash50differentials are represented by lines A0A2 (in the initial period)and D0D1 (the latter period) In this case there is a much smallerincrease in latent wage inequality with most of the average rise indispersion attributable to the decline in the federal minimum

B Wage Dispersion and the Minimum Wage across States

Figure VIa is the empirical analog of Figure V constructedfrom a sample of states in 1979 and 198915 The horizontal axismeasures the federal minimum wage relative to the state medianwage and the vertical axis measures the 10ndash50 log-wage differen-tial The two solid lines represent the tted values of OrdinaryLeast Squares (OLS) regressions (weighted by the sample size ofthe state-year) one for each year of (w 10 2 w50) on(minwage 2 w50) and its squared value

The gure reveals a strong positive association between therelative positions of the tenth percentile and the minimum wageparticularly in 1979 when the tenth percentile is either at or

14 As discussed in Lee [1998] the full truncation model produces a smallnegative relation between upper tail measures of dispersion and the relativeminimum since the truncation effect diminishes higher up in the distribution Inthe more realistic case of some disemployment and some spillovers the relation iseven weaker

15 Data come from the state-level panel data set described in the AppendixSo that all the variation in the effective minimum wage comes from variation in thestatesrsquo medians I exclude states with legislated minimum wage rates higher thanthe federal minimum Alaska for 1979 and Alaska California ConnecticutHawaii Maine Minnesota Massachusetts New Hampshire Pennsylvania RhodeIsland Vermont Washington and Wisconsin for 1989 Robustness to differingsamples is mentioned in Section IV

WAGE INEQUALITY AND THE MINIMUM WAGE 991

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 16: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

slightly above the minimum wage for a majority of the states Theregression lines especially that for 1989 exhibit some nonlinear-ity as the relation between the effective minimum wage and the10ndash50 differential appears to atten to the left The estimatedcoefficients on the quadratic terms for both years are eachstatistically signicant from zero at the 005 level

Overall there appears to be little evidence of a downwardshift in the wage dispersion-minimum wage relation over time Infact an OLS regression using the data from both years andincluding a year dummy variable yields a coefficient of 0062(with a standard error of 0017) on the 1989 dummy implying thatthere is a slight upward shift in the relationmdasha decrease in latentwage dispersion as measured by the 10ndash50 wage differential Mostof the data points in 1989 are signicantly above the 45 degreeline This implies that there was a real potential for the statesrsquo

FIGURE VIa10ndash50 Log (Wage) Differential Relative Minimum Wage across States

1979 1989

QUARTERLY JOURNAL OF ECONOMICS992

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 17: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

tenth percentiles to fall farther than they did However the 10ndash50differentials fell by an amount that was no moremdashand if any-thing lessmdashthan what would be expected as a response to auniform decline in the relative level of the minimum wage

An important caveat to this empirical approach is that in thepresence of a nonlinear relation between the relative minimumand wage percentile differentials the identication of a down-ward shift in the relation becomes difficult when the minimumwage is lsquolsquotoo bindingrsquorsquo across all states For example suppose thatin 1979 all of the statesrsquo 10ndash50 lay exactly on the 45-degree line inFigure VIa Even in the absence of any change in the relativeminimum we could expect an increase in latent wage dispersionto produce no change in the empirical relation the states wouldcontinue to lie on the 45-degree line and no downward shift couldbe detected Nor could we detect a modest upward shift in the

FIGURE VIb20ndash50 75ndash50 Log(Wage) Differentials Relative Minimum Wage

across States 1979 1989

WAGE INEQUALITY AND THE MINIMUM WAGE 993

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 18: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

relation if the latent tenth percentile were initially far enoughbelow the relative minimum for all states16

The advantage of using percentile differentials as the depen-dent variable is that we can examine other wage percentileshigher up in the wage distribution where this problem does notexist17 For example Figure VIb plots the analogous empiricalrelation to Figure VIa for the 20ndash50 log-wage differential Againthe gure reveals that after accounting for the declining federalminimum there appears to be a slight decrease in wage disper-sion18 Examining samples of workers with generally higherwages (older workers men) (as is done in Section IV) similarlyalleviates the potential identication problem described above

Before presenting the formal empirical analysis it is impor-tant to clarify the nature of what appears to be a lsquolsquomechanicalrsquorsquorelation between the dependent and independent variables sincethe state median wage is used in the measure of dispersion aswell as to construct the relative minimum wage variable Itappears that the empirical relation between these two quantitiesmay exaggerate the impact of the minimum wage There are twodistinct components to this possibility

The rst arises when sampling error is an important part ofthe total variability in state median wages For example even ifno relation exists between the two variables the fact that thesample median and the sample tenth percentile are not perfectlycorrelated implies there will be a spurious positive relationbetween the 10ndash50 differential and the relative minimum How-ever the state-by-state sample sizes from the CPS OutgoingRotation Group Files are reasonably large (on average about 3000per state-year) and hence on average the sampling error for thetypical statersquos median is about 001 implying that less than 1percent of the variation in the relative minimum is due tosampling error19 Furthermore this problem can be somewhat

16 Identication is also weakened when there is little lsquolsquooverlaprsquorsquo of the rangesof the effective minimum for the two years If there is no overlap at allidentication relies heavily on functional form assumptions about the underlyingshape of the minimum wagersquos impact on wage dispersion In the formal empiricalanalysis however sufficient overlap is generated by using data from all intermedi-ate years between 1979 and 1989

17 An examination of Appendix 2 provides a sense of how close the relativeminimums are to the various wage percentiles across states

18 The coefficient on the 1989 year dummy in a (weighted by observation perstate-year) pooled regression of the 20ndash50 differential on the relative minimumand its square is 00226 with a standard error of (00123)

19 A similar calculation yields that sampling variability is about 10 percentof the within-state variance

QUARTERLY JOURNAL OF ECONOMICS994

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 19: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

alleviated by using an alternative measure of centrality to createthe relative minimum wage variable which I utilize in Section IV

Second apart from the sampling issue even the absence ofthe minimum wage there may be relatively greater variability inthe median than in percentiles of the lower or upper tails Forexample if there is relatively little variability in the tenth latentwage percentiles across states then on average a state with alarge median wage will have both a lower relative minimum aswell as a larger gap between the tenth percentile and the medianindependently of any minimum wage effect It should be notedthat this possibility is one specic example of a violation of theidentifying assumption that on average wage levels are uncorre-lated with latent wage dispersion On the other hand if we couldbe assured that locational amenities for example generatedcompensating state wage differentials that were constant acrossall of each statersquos percentiles wage distribution and that thedifference in the median was an adequate measure of the statewage differential then no relation would exist between any of thelatent percentile differentials and the relative minimum wageeven though the median would be used to construct both measures

More generally some scenarios (including the hypothesisdescribed abovemdashgreater variability across states in the middle ofthe distribution than in the tails) that posit a systematic relationbetween latent wage dispersion and the location of the distribu-tion as measured by the median will have the observableimplication of a signicant relation between upper tail measuresof dispersion and the median Figure VIb which plots the 75ndash50differential against the relative minimum for this subsampleillustrates that such a correlation is weak in these data20 Thisnding is at odds with the notion that high-wage states inherentlypossess uniformly greater latent wage dispersion

In order to be consistent with the pattern of data shown inFigure VI alternative stories positing a correlation betweenlatent wage dispersion and the median wage must be able toexplain (1) why only the upper tail measure of dispersion appearsuncorrelated with median and (2) why the empirical relation forthe lower tail is much stronger in 1979 than in 1989 diminishingover the course of the 1980s

20 The coefficient on the relative minimum variable in a pooled regression ofthe 75ndash50 differential on a year dummy and the minimum is 0046 with a standarderror of 0028

WAGE INEQUALITY AND THE MINIMUM WAGE 995

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 20: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

IV ESTIMATION OF CHANGES IN LATENT WAGE INEQUALITY1979ndash1988

A Estimating Equation

In the presence of stochastic variation in latent wage disper-sion across states the main identifying assumption used in thisstudy can be motivated as follows Suppose that each state j attime t has a latent log-wage distribution that can be characterizedby the cumulative distribution function

(3) Ft((w 2 microjt) s jt)

where microjt and s jt are centrality and scale parameters respectivelyFt(middot) the lsquolsquoshapersquorsquo of the latent wage distribution in year t isconstant across regions The latent log-wage percentile p of state jat time t is thus

(4) w jtp 5 microjt 1 s jtFt

2 1( p)

where the asterisk emphasizes that this is the latent wagepercentile Normalize the average s t 5 E[ s jt t] to be constant overtime s t 5 1 Then the quantity of interest is the change in thedispersion (particularly in the lower tail) of Ft(middot) over time

The main identifying assumption in this analysis is thatconditional on t s jt is independent of microjt conditional on the yearthe centrality measure of the state wage distribution is notsystematically correlated with latent wage dispersion acrossstates If the observed median wage w jt

50 is an adequate measure ofmicrojt (ie Ft

2 1 (50) 5 0) then for any given year and percentile p ofthe latent wage distribution

(5) cov [(w jtp 2 w jt

50) (minwaget 2 w jt50) t]

5 cov [ s jt middot Ft2 1( p) minwaget 2 microjt t] 5 0

where minwaget is the log of the federal minimum wage in year tUnder the above assumptions a positive association between therelative minimum and the observed 10ndash50 differential reects theimpact of the minimum on the lower tail of the wage distributionand a signicant association between the observed 75ndash50 differen-tial and the relative minimum for example constitutes evidencethat the identifying assumptions are violated21

21 If Ft2 1(50) THORN 0 cov [(w jt

p 2 wjt50) (minwage 2 w jt

50)] 5 2 Ft2 1(50) [Ft

2 1( p) 2Ft

2 1(50)] var [ s jt] Thus in this model a positive correlation between the upper taildifferential (like the 90ndash50 difference) and the median-deated minimum wage for

QUARTERLY JOURNAL OF ECONOMICS996

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 21: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

When the federal minimum wage is absent in years 0 and 1we can estimate the average change in the latent 10ndash50 differen-tial [F1

2 1(10) 2 F02 1(10)] by the sample analog of E[w j1

10 2 w j150] 2

E[wj010 2 w j0

50] But when the federal minimum is lsquolsquobindingrsquorsquo[F1

2 1(10) 2 F02 1(10)] is estimated as a downward lsquolsquoshiftrsquorsquo in line

A0A1 to C0C1 in Figure V for example if we knew a priori that theminimum wage had a straightforward lsquolsquocensoringrsquorsquo effect (Case 1)we could estimate [F1

2 1(10) 2 F02 1(10)] by the sample analog of

E[wj110 2 w j1

50 w j110 2 wj1

50 mwj1] 2 E[wj010 2 wj0

50 wj010 2 wj0

50 mwj0]where mwjt 5 (minwaget 2 w jt

50)Since the exact form of the minimum wage effect is unknown

(it is perhaps a hybrid of Case 2 and 3) I t the state-year data tothe parameterization

(6) E[w jt10 2 w jt

50 mwjt t] 5mwjt 2 a t

1 2 eB(mwjt 2 a t)1 a t

where B 0 is a lsquolsquocurvaturersquorsquo parameter This function asymptotesto E[w jt

10 2 wjt50 mwjtt] 5 mwjt as mwjt gets large More impor-

tantly it also asymptotes to E[w jt10 2 wjt

50 mwjtt] 5 a t as mwjt

vanishes which means that in this parameterization the esti-mated a t is an estimate of the average latent 10ndash50 differential inyear t or Ft

2 1(10) Note that the above parameterization capturesthe basic features of the various functions depicted in Figure V22

In particular as B 2 ` the function becomes the lsquolsquocensoringrsquorsquocase (Case 1)

An examination of Figure VI suggests that a reasonablesimple alternative to the parameterization in equation (6) is theestimation of the equation

(7) wjt10 2 w jt

50 5 a t 1 b middot mwjt 1 g middot mw jt2 1 ujt

where the approximation error ujt is assumed to be orthogonal tomwjt and its square This is simply the regression of the 10ndash50log-wage differential on the relative minimum (and its square)and year dummies using the panel of states throughout the1980s Again changes in the a trsquos represent changes in nationwidelatent wage inequality (as measured by the 10ndash50 log-wagedifferential)

example necessarily implies a negative correlation between the latent lower taildifferential (such as the 10ndash50) and the relative minimum This equation showsthat the most appropriate deator of the minimum is the best measure ofcentrality (a percentile q such that Ft

2 1 (q) 5 0)22 I am grateful to an anonymous referee for suggesting this parameteriza-

tion

WAGE INEQUALITY AND THE MINIMUM WAGE 997

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 22: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

B Results 1979ndash1988

Panel A of Table I reports the least squares estimates ofequations (7) and (6) using the panel data set of 50 states acrossten years from 1979ndash1988 for the entire sample of earners (bothmen and women) as described in the Appendix In the estimationmw is dened as log(max[state minimum wage federal minimumwage]) 2 w50 Column (1) shows that the dependent variable(w10 2 w50) declines signicantly throughout the decade Includ-ing a linear term in mw column (2) shows that the estimatedslope 0509 is highly signicant implying that a 1 percent fall inthe minimum wage leads to a 05 percent fall in the tenthpercentile relative to the median The empirical t of the regres-sion increases substantially the R2 rising from 0245 to 0755

Most importantly the coefficients on the year dummies allrise toward zero Whereas the average 10ndash50 differential is2 0107 in 1985 (relative to 1979) the average change afteraccounting for a linear term in mw is virtually zero for that sameyear In fact there is an increase of 47 log points in the relativeposition of the tenth percentilemdasha decrease in latent wage disper-sionmdashbetween 1979 and 1988 after the inclusion of mw

Column (3) includes a quadratic term and demonstrates thatthe nonlinear aspect of the empirical relation is important23 Inthis specication none of the year coefficients are negative andthe coefficient on 1988 is statistically different from zero atpositive 0043 Column (4) demonstrates that the trend towardcompression in the 10ndash50 differential is even more pronouncedwhen equation (6) is estimated by Nonlinear Least Squaresalthough the standard errors of the year coefficients riseappreciably

To alleviate at least to some extent the potential spuriouscorrelation induced by sampling error (since the sample median isused to construct both the 10ndash50 differential and mw) I examinean alternative estimate of centrality w t which is the trimmedmean (where the bottom 30 percent and top 30 percent of thesample for each state-year are eliminated) as a deator for theminimum wage Column (5) which uses mwjt 5 (minwage 2 wjt

t )shows that the coefficients are quite similar to those in column (3)Although the coefficients in column (3) and column (5) are nearlyidentical for this sample and specication for the remainder ofthe paper I utilize mwjt because sampling error in the median maybe more serious in other specications (such as a within-state

23 Cubic and quartic terms have negligible effects on the results

QUARTERLY JOURNAL OF ECONOMICS998

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 23: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

estimator where the population variability in the locational shiftof the distribution is diminished)24

One should note that in this sample period several of thestates legislated their own minimum wage rates to be higher thanthe federal rate The analysis thus far also implicitly assumesthat the nominal state-legislated minimum wage is not systemati-cally related to latent wage dispersion across states To examinehow legislative endogeneity may be affecting the results I re-peated the estimation for the subsample of states for which thestate minimum wage did not exceed the federal rate at any timeduring the 1979ndash1988 period Although not reported here theresults are quite similar suggesting that even if state-legislatedminimum wages were endogenously determined for these ex-cluded states the effect is not large enough to noticeably inuencethe basic results of Panel A of Table I25

Panel B of Table I reports results from using the specicationof column (5) in Panel A for various subsamples based on genderand age For each subsample the table reports (1) the ten-yearannualized trend of the 10ndash50 differential (based on a regressionof the year coefficients on a linear trend) (2) the estimatedannualized trend when mw and its square are included (3) thecoefficients on the linear and quadratic terms of mw (4) thederivative implied by the coefficients evaluated at the overallmean of mw for the 1979ndash1988 period and (5) the R2

As might be expected the table shows that among workerswith generally higher wages (men and older workers) the relativeminimum has a more modest impact on the 10ndash50 differentialThe implied derivative is as high as 0597 for all women earnersaged 16 and over to as low as 0182 for men aged 25ndash64 Overallthe table shows that for almost every sample most of the trend inthe 10ndash50 differential disappears when mw is included Forwomen the trend in latent wage dispersion cannot be statisticallydistinguished from zero and for the entire sample the estimatedtrend in latent wage dispersion is small but in the oppositedirection of the observed trend An important exception is thending for men aged 25ndash64 where much of the growth in

24 The root mean squared error of a regression on mw on mw is 0011 (the R2

is 0996)25 This table is reported in Lee [1998] which also includes an analysis where

the procedure of DiNardo Fortin and Lemieux [1996] is used to adjust fordifferences in observable covariates across state-year observations After adjustingfor state differences in demographic industrial and occupational composition inthis way the year coefficients analogous to those in Table I Panel A appear to bevirtually unaltered See Lee [1998] for more details and discussion

WAGE INEQUALITY AND THE MINIMUM WAGE 999

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 24: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

inequality remains after the inclusion of mw For the rest of theanalysis so that results can be readily compared with previousresearch utilizing the CPS Outgoing Rotation Group data [Di-Nardo Fortin and Lemieux 1996] I focus on workers aged 18ndash64

In principle the panel nature of the state-level data setprovides an alternative to cross-sectional identifying variationWithin-state variability in mw can also be exploited to identify the

TABLE I PANEL AOLSNLLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1979ndash1988

Variable (1) (2) (3) (4)a (5)

Year dummies1980 2 0001 0004 0006 0027 0004

(0007) (0004) (0003) (0026) (0004)1981 2 0010 2 0002 0001 0004 0002

(0007) (0005) (0004) (0027) (0005)1982 2 0040 0001 0010 0035 0012

(0007) (0007) (0004) (0024) (0005)1983 2 0065 2 0002 0010 0035 0009

(0007) (0007) (0005) (0024) (0005)1984 2 0090 2 0006 0005 0020 0007

(0007) (0009) (0007) (0023) (0007)1985 2 0107 2 0001 0007 0022 0008

(0007) (0010) (0008) (0023) (0008)1986 2 0111 0014 0018 0038 0019

(0009) (0012) (0009) (0023) (0010)1987 2 0115 0025 0025 0045 0025

(0008) (0013) (0011) (0023) (0011)1988 2 0105 0047 0043 0071 0043

(0009) (0016) (0012) (0023) (0013)(Min-median) mdash 0509 1418 2 9395 mdash

(0051) (0152) (0547)(Min-median)2 mdash mdash 0589 mdash mdash

(0114)(Min-trim mean) mdash mdash mdash mdash 1494

(0155)(Min-trim mean)2 mdash mdash mdash mdash 0634

(0116)Trend in year coefb 2 0014 0002 0003 0006 0003

(0001) (0002) (0001) (0003) (0001)R2 0245 0755 0806 mdash 0791

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Regressions are the 10ndash50 differential on the relative minimum wage In columns (2) and(3) relative minimum is max [fed min state min] 2 median in column (5) it is max [fed min state min] 2(trimmed mean) where the top 30 and bottom 30 percent of the sample are taking the mean Weighted byobservations per state-year Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state Excluded year is 1979

a Estimated by Nonlinear Least Squares Parameterization described in textb From a regression of the estimated year coefficients on a linear trend

QUARTERLY JOURNAL OF ECONOMICS1000

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 25: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

impact of the minimum wage on the wage distribution Inparticular suppose that instead of a t in equation (7) we have

(8) a jt 5 a j 1 a t

The validity of this lsquolsquoxed effectsrsquorsquo approach relies on the assump-tion that within-state wage levels are uncorrelated with latentwage dispersion after taking out year effects Hence a consistentsensitivity of latent wage inequality to regional economic boomsor downturns is likely to contaminate the true impact of mw on(w j

p 2 w j50) A disadvantage of using this variation is that most of

the variability in mw (after taking out time effects) is generated bycross-state as opposed to within-state variability The root mean

TABLE I PANEL BOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE BY GENDER AND AGE

GROUPS 1979ndash1988

Trend in10ndash50 dif

OLS Estimates

Trend inyr coef

(Minimum-trim mean)

(Minimum-trim mean)2

Derivativeat average R2

All16 1 2 0014 0003 1494 0634 0515 0791

(0001) (0001) (0155) (0116) (0038)18ndash64 2 0014 0002 1396 0588 0469 0741

(0001) (0001) (0149) (0112) (0042)25ndash64 2 0008 0003 0999 0391 0309 0564

(0001) (0001) (0196) (0124) (0036)Men

16 1 2 0013 0000 1250 0450 0407 0583(0001) (0002) (0219) (0134) (0049)

18ndash64 2 0013 2 0002 1036 0353 0364 0488(0001) (0002) (0279) (0165) (0058)

25ndash64 2 0011 2 0005 0197 0007 0182 0221(0001) (0003) (0348) (0188) (0086)

Women16 1 2 0027 2 0001 1331 0639 0597 0893

(0001) (0002) (0091) (0103) (0044)18ndash64 2 0025 2 0001 1294 0623 0561 0868

(0001) (0002) (0088) (0103) (0048)25ndash64 2 0020 2 0001 1119 0528 0424 0793

(0001) (0002) (0087) (0088) (0045)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Specication in column (5) in Panel A of Table I is used Relative minimum wage ismax [fed min state min] 2 (trimmed mean) where the top 30 and bottom 30 percent of the sample istrimmed before taking the mean Weighted by observations per state-year Derivative is computed at theaverage value of the relative minimum wage variable for each regression Trend is the average annual changein the year coefficients Standard errors (in parentheses) are heteroskedasticity-consistent and consistentwith unrestricted autocorrelation within-state

WAGE INEQUALITY AND THE MINIMUM WAGE 1001

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 26: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

squared error from a regression of mw on year dummies for thefull sample is 0125 adding state dummies to this regressionlowers it to 0031 implying that only (00310125)2 5 0062 of theresidual variance (after taking out time effects) in mw is due tolsquolsquowithin-statersquorsquo variability26 Thus we might expect identicationin a state xed effects specication to be considerably weaker thanin a pooled cross-section specication In addition the reducedidentifying variation resulting from eliminating the lsquolsquopermanentrsquorsquostate effects may magnify biases due to misspecication in thesame way biases stemming from measurement error in theindependent variable are magnied when true variation in theindependent variable is reduced

Perhaps the best available indication of which specication ismore appropriate is given by the correlation between mw andmeasures of wage dispersion in the upper tail A specication thatyields a signicant relation between mw and dispersion in the uppertail where we are reasonably condent that the minimum has noeffect might be viewed with more suspicion when considering theempirical relation between mw and dispersion in the lower tail

Table II reports the coefficient on mw in OLS regressions ofthe 60ndash 70ndash 80ndash and 90ndash50 wage differentials on mw and a set of

26 A relatively small fraction of the variation in mw is due to variability inthe nominal state-specic minimum wage The addition of these nominal rates tothe pooled cross-section and xed effects specications yield root mean squarederrors of 0121 and 0032

TABLE IIOLS ESTIMATES UPPER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differential

Pooled cross section With state dummies

All Men Women All Men Women

60ndash50 2 0019 0049 2 0033 0008 0029 2 0011(0011) (0017) (0010) (0036) (0024) (0027)

70ndash50 0022 0124 2 0035 0069 0119 0013(0018) (0029) (0019) (0041) (0039) (0033)

80ndash50 0087 0207 2 0016 0113 0256 0085(0029) (0040) (0029) (0053) (0045) (0040)

90ndash50 0162 0299 0017 0280 0438 0131(0043) (0048) (0036) (0061) (0065) (0059)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Entries are the estimatedcoefficients on the relative minimum wage variable in regressions of each upper tail differential on max [fedmin state min] minus the (top 30 and bottom 30 percent) trimmed mean year (and state) dummiesStandard errors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocor-relation within-state

QUARTERLY JOURNAL OF ECONOMICS1002

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 27: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

year dummies with and without state dummies for the threesamples Focusing on the 60ndash 70ndash and 80ndash50 differentials twopatterns emerge First it appears that the slope coefficients areconsiderably smaller for women or for the combined sample thanfor men alone For women the pooled cross-section estimates forthe upper percentiles range between 2 0035 and 2 0016 with stan-dard errors of about 001 or 002 For the combined sample the pooledcross-section coefficients for the 60ndash and 70ndash50 differentials cannot bestatistically rejected from zero but the 80ndash50 estimates arestatistically different from zero for both specications The compa-rable estimates for men are much larger in absolute magnitudefor example the 70ndash50 pooled cross-section estimate is 0124 andas high as 0256 for the 80ndash50 xed effects estimate

Second the absolute values of the coefficients tend to belarger in the state xed effects specication The 70ndash50 coefficientfor the entire sample rises from 0022 to 0069 and the 80ndash50coefficient rises from 2 0016 to 0085 for women and from 0207to 0256 for men

Although I include results for the 90ndash50 differential forcompleteness the coefficient for men and the entire sample shouldbe interpreted with caution because of the increasing importanceof the weekly earnings topcode in the latter part of the 1980s Thisis because a nontrivial and nominal topcode will naturally cause apositive association between the relative minimum and the 90ndash50differential since high-wage states will have their ninetiethpercentiles articially lowered to a greater extent than low-wagestates27

If the empirical relations between mw and the upper taildifferentials are considered a valid specication check Table IIseems to suggest that when examining the empirical results forthe lower tails we can be most condent in the results for womenin the pooled cross section more cautious about the results for theentire sample and considerably more suspicious for the resultsfor men In the same way the state xed effects might be viewedwith more caution relative to the pooled cross-sectional results

27 In order to assess the magnitude of this problem I use the 1989 data(when the topcode changed to an irrelevantly higher level) and articially topcodethe weekly earnings level to where the pre-1989 level is (adjusted by the CPI) foreach year I compare regression coefficients of the 90ndash50 differential in the actualdata for 1989 with that from utilizing the simulated data in a similar regression(that additionally includes year dummies) For the entire sample the coefficientsare 0038 and 0101 for the actual and simulated data respectively suggestingthat about 006 of the coefficient in the pooled cross section for the entire samplemay be attributable to the topcode For men the coefficients are 0190 and 02623and for women they are 2 0003 and 2 0002

WAGE INEQUALITY AND THE MINIMUM WAGE 1003

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 28: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

Table III reports for the three samples and two specications(1) the annualized trend in the average 10ndash 20ndash 30ndash and 40ndash50differentials (2) the trend when mw and its square is includedand (3) the estimated derivative evaluated at the overall mean ofmw throughout 1979ndash1988 For women in the pooled cross section theminimum wage appears to explain roughly 75 percent to virtually allof the growth in lower tail percentile differentials28 For the pooledcross-section specication using the entire sample all of the expansionin the lower tail differentials can be accounted for by mw

28 The result for the 10ndash50 differential for women should be interpreted withthe caveat that the average difference between the minimum and the tenthpercentile is about two log points 1979 (see Data Appendix) meaning thatidentication of the growth in the latent 10ndash50 is more tenuous as mentioned insubsection IIIB

TABLE IIIOLS ESTIMATES LOWER TAIL DIFFERENTIALS ON MINIMUM WAGE 1979ndash1988

Differ-ential

All Men Women

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Trend(dif)

Trend(coef)

Deriva-tive

Pooled cross section

10ndash50 2 0014 0002 0469 2 0013 2 0002 0364 2 0025 2 0001 0561(0001) (0001) (0042) (0001) (0002) (0058) (0001) (0002) (0048)

20ndash50 2 0006 0003 0262 2 0011 2 0005 0184 2 0013 2 0002 0268(0001) (0001) (0036) (0001) (0002) (0059) (0001) (0001) (0031)

30ndash50 2 0004 0000 0134 2 0005 2 0004 0058 2 0008 2 0002 0134(0001) (0001) (0025) (0001) (0001) (0037) (0000) (0001) (0019)

40ndash50 2 0002 0000 0057 2 0003 2 0003 0004 2 0003 2 0001 0056(0001) (0001) (0013) (0000) (0001) (0017) (0000) (0001) (0012)

With state dummies

10ndash50 2 0015 2 0006 0248 2 0014 2 0012 0080 2 0026 2 0012 0324(0001) (0002) (0071) (0001) (0003) (0087) (0001) (0003) (0084)

20ndash50 2 0007 2 0003 0107 2 0011 2 0011 0028 2 0014 2 0006 0190(0001) (0002) (0066) (0001) (0002) (0067) (0001) (0003) (0066)

30ndash50 2 0005 2 0002 0082 2 0006 2 0007 2 0037 2 0008 2 0005 0064(0001) (0001) (0033) (0001) (0001) (0038) (0000) (0002) (0040)

40ndash50 2 0002 0000 0044 2 0003 2 0004 2 0029 2 0003 2 0001 0049(0001) (0001) (0032) (0000) (0001) (0035) (0000) (0001) (0037)

N 5 500 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Weighted by observations per state-year Specication of column (5)of Panel A Table I is used The columns for each sample show 1) the trend in the percentile differential 2) thetrend in the year coefficients when (a quadratic of) the relative minimum (max [fed min state min] 2 trimmed(top 30 and bottom 30 percent) mean) is included and 3) the estimated slope evaluated at the overall mean ofthe relative minimum for 1979ndash1988 Lower panel includes state dummy variables Standard errors (inparentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1004

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 29: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

In light of Table II the results for the state xed effectsspecication as well as for men might be interpreted with con-siderable caution but I include them in Table III for completeness Forthe entire sample and for women the xed effects estimates implythat the minimum wage can account for about half of the rise ininequality For men the results are mixed for example the pooledcross-section estimate implies that about 55 percent of the fall in the20ndash50 differential is due to the declining minimum while thecorresponding xed effects estimate suggests 0 percent

V WAGE COMPRESSION AND THE MINIMUM WAGE 1989ndash1991

After a decade of constancy the nominal federal minimumwage rate rose effective in April 1990 from $335 to $380 andagain in April of 1991 from $380 to $425 Prior to this timeseveral of the states (see Appendix 3) had already legislated theirown minimum wage rates that were higher than the forthcomingrise in the federal rate As a result the newly imposed federalminimum generated variability in changes in the effective mini-mum wage level across states

The source of this variability stands in sharp contrast to thatwhich generated variation in the effective minimum wage in theprevious analysis It affords an opportunity to estimate the impactof the minimum wage on the wage distribution under an alterna-tive set of identifying assumptions Instead of relying on theassumption that the measures of centrality of statesrsquo wagedistributions (used to lsquolsquodeatersquorsquo the federal minimum rate) areuncorrelated with latent wage dispersion the analysis belowadopts the identifying assumption that the binding (relative)minimum rate (the maximum of the federal and the state-specicrate) is uncorrelated with changes in latent wage inequalityacross states

Card and Krueger [1995] use this latter approach to examinethe impact of the minimum wage on the wage distribution We cancompare the estimates using the approach of Card and Kruegerwith those utilizing the procedure of Section IV for the same timeperiod (1989ndash1991)29 We can further compare these estimateswith those using the data for the 1979ndash1988 period Findingconsistency among these various estimates would seem to lendsome support to the ndings of the previous section

29 Card and Krueger [1995] utilize a different minimum wage measure thefraction of workers in each state in 1989 who earn more than the 1989 rate and lessthan the 1991 rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1005

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 30: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

Table IV gives a sense of the magnitude of the averagechanges in both the minimum wage and the 10ndash50 differential fortwo groups of states the states that in 1989 had minimum wagesgreater than the federal minimum and all other states30 Formen women and the entire sample the group with state mini-mums equal to or less than the federal rate in 1989 experience anaverage increase in mw of about 8 or 9 percent by 1990 and anadditional 7 percent in 1991 By contrast the group of states

30 The states with higher minimums were California Connecticut HawaiiMaine Minnesota Massachusetts New Hampshire Pennsylvania Rhode IslandVermont Washington and Wisconsin Alaska was excluded because its stateminimum is xed relative to the federal rate

TABLE IVMEANS OF 10ndash50 DIFFERENTIAL AND MINIMUM WAGE BY STATE MINIMUM WAGE

STATUS 1989ndash1991

Minimum wage 10ndash50 differential

State fed State 5 fed State fed State 5 fed

All1989 (Level) 2 0959 2 0978 2 0662 2 0683

(0031) (0030) (0040) (0013)1990ndash1989 (Change) 2 0009 0085 2 0015 0019

(0007) (0004) (0015) (0006)1991ndash1989 (Change) 0016 0167 2 0015 0032

(0026) (0004) (0016) (0010)Men

1989 (Level) 2 1088 2 1118 2 0724 2 0723(0030) (0032) (0064) (0018)

1990ndash1989 (Change) 0001 0089 0008 0012(0008) (0004) (0014) (0009)

1991ndash1989 (Change) 0035 0176 0006 0016(0021) (0004) (0019) (0009)

Women1989 (Level) 2 0802 2 0813 2 0557 2 0583

(0033) (0028) (0028) (0009)1990ndash1989 (Change) 2 0024 0081 2 0018 0006

(0006) (0005) (0014) (0010)1991ndash1989 (Change) 2 0013 0154 2 0021 0033

(0029) (0005) (0020) (0010)N 12 38 12 38

Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See Data Appendix fordetails Workers aged 18ndash64 The relative minimum here is the max [fed min state min] minus the (top 30and bottom 30 percent) trimmed mean lsquolsquoState fedrsquorsquo means that the state had a minimum wage that washigher than the federal minimum in 1989 lsquolsquoState 5 fedrsquorsquo means that the state had a minimum wage that wasequal to or less than (or had no state minimum wage provision) the federal minimum in 1989 Standard errors(in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelation within-state

QUARTERLY JOURNAL OF ECONOMICS1006

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 31: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

beginning with higher state-specic minimums experience a verysmall change in mw

Table IV illustrates that the two groupsrsquo trends in the 10ndash50log-wage differential also diverge for women as well as for theentire sample For these samples the group of states thatexperienced the 16 percent average growth in mw witnessed anaverage compression in their 10ndash50 differentials of about 3percent whereas the remaining states experienced a 1 or 2percent expansion in the 10ndash50 gap The divergent pattern is notfound in the results for men for whom the difference between theinitial minimum and the tenth percentile in 1989 was greatest atabout 38 log points

Utilizing legislation-induced changes in the minimum wageis formally implemented by estimating the state xed effectsspecication that was used in the lower panel of Table III (usingequations (7) and (8)) Within-state variation in mw during1989ndash1991 is much smaller than the total cross-sectional variabil-ity as was the case for the 1979ndash1988 data For the combinedsample in the 1989ndash1991 period a regression of mw on timedummies yields a root mean squared error of 0137 Adding statedummies to this regression reduces it to 0040 implying that(0040201372) 5 0085 of the residual variability (after taking outtime effects) in mw is within-state and that identication will berelatively weaker than in the pooled cross-section specicationHowever virtually all of this within-state variation in mw isgenerated by changes in the legislated minimum rate as opposedto transitory within-state changes in the centrality measures ofthe statesrsquo wage distributions Adding the nominal legislated rateto the above regression brings the root mean squared error from0040 to 0013 implying that ((0040)2 2 00132)(00402) 5 0894of the lsquolsquowithin-statersquorsquo variance in mw is indeed driven by legisla-tion-induced changes for the 1989ndash1991 period as noted inSection IV the comparable gure for the 1979ndash1988 data is closeto zero

Table V presents results for the 1989ndash1991 period using the10ndash50 differential as the dependent variable For both women andthe combined sample the coefficients on both the linear andquadratic terms in the xed effects specication are quite similarto the corresponding estimates in the pooled cross section Theimplied derivatives (and standard errors) evaluated at the 1989ndash1991 mean of mw are 0262 (0096) and 0349 (0072) in the statexed effects specication for the combined sample and womenrespectively The corresponding derivatives are 0320 (0073) and

WAGE INEQUALITY AND THE MINIMUM WAGE 1007

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 32: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

0308 (0060) for the pooled cross-section specication Further-more evaluated at the 1979ndash1988 mean of mw the pooledcross-section (and xed effects) estimates of the derivative are0482 (0415) and 0578 (0597) for the combined sample andwomen respectively These are quite comparable to the estimatedderivatives from the pooled cross-section estimates reported inTable III (0469 and 0561) which used the 1979ndash1988 data

By contrast the two specicationsrsquo coefficients on mw and its

TABLE VOLS ESTIMATES 10ndash50 DIFFERENTIAL ON MINIMUM WAGE 1989ndash1991

Pooled cross section With state dummies

AllYear dummies

1990 0010 2 0007 0013 2 0002(0007) (0007) (0008) (0010)

1991 0020 2 0023 0023 2 0013(0010) (0013) (0011) (0015)

(Min-trim mean) mdash 1598 mdash 1401(0527) (0341)

(Min-trim mean)2 mdash 0702 mdash 0625(0283) (0191)

MenYear dummies

1990 0011 2 0003 0015 0014(0007) (0011) (0010) (0014)

1991 0013 2 0024 0017 0012(0008) (0013) (0009) (0020)

(Min-trim mean) mdash 1545 mdash 0713(0767) (0434)

(Min-trim mean)2 mdash 0614 mdash 0326(0366) (0195)

WomenYear dummies

1990 0000 2 0016 0002 2 0017(0009) (0009) (0009) (0009)

1991 0019 2 0019 0020 2 0023(0011) (0010) (0012) (0011)

(Min-trim mean) mdash 1532 mdash 1472(0299) (0297)

(Min-trim mean)2 mdash 0811 mdash 0744(0205) (0188)

N 5 150 Data are constructed from the CPS Merged Outgoing Rotation Earnings Files See DataAppendix for details Workers aged 18ndash64 Relative minimum variable is the max [fed min state min] minusthe (top 30 and bottom 30 percent) trimmed mean wage Weighted by observations per state-year Standarderrors (in parentheses) are heteroskedasticity-consistent and consistent with unrestricted autocorrelationwithin-state

QUARTERLY JOURNAL OF ECONOMICS1008

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 33: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

square are in less agreement for the sample of men The impliedderivatives (and standard errors) are 0033 (00120) and 0270(0068) for the xed effects and pooled cross-section specicationsrespectively This nding provides some reason to lessen ourcondence in the results for men Examination of the empiricalrelation between the upper tail percentile differentials and mwprovides some further reason to place more condence in theresults for the combined sample and women relative to theresults for men For example a regression of the 80ndash50 differen-tial on mw leads to a coefficient (standard error) of 0094 (0035)2 0003 (0027) and 0040 (0026) for men women and the com-bined sample respectively A similar qualitative pattern exists forthe various other measures of dispersion in the upper tail31

Finally note that a comparison of the year coefficients inregressions with and without mw reveals that for women andthe combined sample the modest compression in the observed10ndash50 differential of about two log points across states belies whatappears to be an expansion of the latent 10ndash50 gap of about one totwo log points during the 1989ndash1991 period

VI IMPLICATIONS FOR BETWEEN- AND WITHIN-GROUP WAGE

INEQUALITY

The analysis to this point has focused on the extent to whichthe minimum wage has contributed to growth in broad measuresof wage inequalitymdashthe various percentile differentials Sincemuch of the empirical literature has focused on changes inbetween-group wage differentials (based on gender educationage) it is instructive to consider the potential impact of theminimum wage on these wage differentials as implied by thendings in the previous sections Equally informative is theimplied effect of the minimum wage on changes in so-calledlsquolsquowithin-grouprsquorsquo inequality which constitutes a large portion of thetotal growth in wage dispersion in recent decades [Juhn Murphyand Pierce 1993]

A simple way to produce these calculations is given by

31 Using the 90ndash50 differential yields 0124 0033 and 0048 for menwomen and the combined sample respectively these are the largest (in absolutevalue) among regressions using the various upper tail percentile differentials (ie60ndash50 70ndash50 80ndash50 and 90ndash50) The largest (in absolute value) for analogousxed effects estimates using the upper tail was 2 0108 (with a standard error of0095) for the 90ndash50 differential for the combined sample all other estimates(using any of the samples or upper tail measures) were smaller in absolute valueand could not be statistically rejected from zero

WAGE INEQUALITY AND THE MINIMUM WAGE 1009

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 34: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

DiNardo Fortin and Lemieux [1996] who simulate a counterfac-tual wage density for 1988 adjusting the minimum wage to its1979 level in real terms I follow this general approach butinstead of making specic assumptions about how the minimumwage affects the lower tail of the distribution I simply employ theestimates of the previous section on the empirical relation be-tween the minimum and the lower tail percentile differentialsacross states

I do so in the following way First I determine for eachobservation in the microdata (that was used to create the state-level panel data set) its percentile in the overall wage distribu-tion on a state-by-state basis Then according to this relativeposition I add or subtract an amount to the log-wage of the workeraccording to estimates of b and g (from equation (7)) and thesimulated change in mw So for example in order to simulatewhat individuals at the pth percentile of their statersquos wagedistribution in 1989 would earn in the face of a minimum wage atits 1979 relative level I add the amount

(9) D j89p 5 b ˆ p middot (mwj79 2 mwj89) 1 g ˆ p middot (mw j79

2 2 mw j892 )

to the workerrsquos actual log-wage in 1989 where p denotes thewithin-state percentile j the state b ˆ p and gˆ p the estimatedcoefficients from the regression described by column (5) of Table IPanel A mwj89 the actual mw for state j in 1989 and mwj79 5mwj89 2 log(335) 1 log(290) 1 050 denotes the hypothetical(1979) relative level of the federal minimum wage for state j32

Although the separate estimates b ˆ p and gˆ p for men womenand the combined sample can be applied to each respectivesample the accumulation of evidence to this point suggests thatwe might place the most condence in the estimates from thepooled cross-section specication for women and for the combinedsample And in particular it suggests that the results for men beviewed with considerable suspicion Thus in the simulationexercise I adjust the wages of the entire sample of earners usingthe pooled cross-sectional estimates of b ˆ p and g ˆ p from the entiresample but report the various between- and within-group wagedispersion measures by men and women separately33 It is impor-

32 The nominal minimum rate was $290 in 1979 $335 in 1989 and thechange in the national median log(wage) for all workers was 050

33 I use estimates from regressing each of the 49 lower tail differentials(1ndash50 to 49ndash50) on a quadratic in mw using data from the entire time period1979ndash1991 weighting by the number of observations in each state-year cell

QUARTERLY JOURNAL OF ECONOMICS1010

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 35: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

tant to note that the validity of the resultant lsquolsquocounterfactualrsquorsquowage differentials rests upon the assumption that the minimumwage affects worker types (irrespective of their education genderage etc) equally conditional on the workerrsquos wage level

Panel A of Table VI reports various comparisons betweenactual wage differentials (by race education and experience) andcorresponding differentials from the adjusted microdata for maleearners aged 18ndash64 The mean wages in each group are expressedas relative to the combined-sample median wage The rst twocolumns present the differentials computed from the actual datathe third reports the counterfactual of applying the 1979 relativelevel of the minimum wage to the 1989 distribution and the lasttwo columns show the counterfactual differentials resulting fromsimulating the impact of the 1989 relative minimum on the 1979and 1989 distributions34

An examination of the rst and third columns of the tablereveals that the main beneciary of this hypothetical minimumwage increase are less-experienced high school dropouts as theiraverage log-wage rises about eight log points due to the adjust-ment of the 1989 data The lower part of the table which reportsunadjusted and adjusted changes in the differentials shows thatchanges in race experience and educational differentials are onlymoderately attenuated by an adjustment for the minimum wageIt shows that about 14 percent of the increase in the college-highschool wage differential for those with 1ndash10 years of experience isdue to the falling minimum wage throughout this period Onenotes that this is comparable to the 13 percent calculationprovided by DiNardo Fortin and Lemieux [1996] The alternativeadjusted changes in the fourth and fth columns give very similarresults

Panel A of Table VI also reports the estimated slope coefficienton years of completed schooling in a wage equation that addition-ally includes a quartic in potential experience The adjustment inthe third column implies that about (0004)(0088 2 0061) 50148 of the change in the return to schooling is attributable to theminimum wage

The adjustment has a much greater impact on the standarddeviation of the residuals from the wage regression a measure oflsquolsquowithin-grouprsquorsquo wage inequality RMSE is the root mean squarederror of a wage regression that includes a complete interaction of

34 The simulation for 1989 makes an adjustment only for workers in stateswith minimum wages higher than the federal rate

WAGE INEQUALITY AND THE MINIMUM WAGE 1011

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 36: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

TABLE VI PANEL AWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE MEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All men 0188 0127 0151 0166 0125Standard deviation 0459 0534 0501 0494 0538Differentials

10ndash50 2 0657 2 0781 2 0654 2 0739 2 078125ndash50 2 0324 2 0395 2 0375 2 0341 2 039875ndash50 0288 0351 0351 0288 035190ndash50 0561 0670 0670 0561 0670

White 0207 0149 0171 0186 0146Black 2 0015 2 0095 2 0055 2 0051 2 00951ndash10 yrs exp 0052 2 0072 2 0035 0021 2 0075

HSDO 2 0226 2 0450 2 0374 2 0292 2 0459HS 2 0010 2 0219 2 0174 2 0043 2 0223COL 0269 0291 0305 0254 0290

21ndash30 yrs exp 0329 0299 0313 0315 0298HSDO 0067 2 0141 2 0105 0041 2 0146HS 0303 0191 0205 0291 0191COL 0642 0673 0678 0637 0673

Return to education 0061 0088 0084 0064 0089RMSE 0393 0432 0405 0422 0434Residuals

90ndash10 0995 1092 1021 1060 109950ndash10 0517 0572 0508 0578 057990ndash50 0478 0520 0513 0482 0520

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0022 2 0004 mdash 2 0004(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0095 0071 mdash 0080COL-HS (1ndash10 yrs) mdash 0232 0200 mdash 0216COL-HSDO (1ndash10 yrs) mdash 0246 0184 mdash 0203COL-HS (21ndash30 yrs) mdash 0144 0135 mdash 0136

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to Education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (4) andsingle year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of the residualsin that regression

QUARTERLY JOURNAL OF ECONOMICS1012

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 37: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

TABLE VI PANEL BWAGE DIFFERENTIALS ACTUAL AND ADJUSTED FOR MINIMUM WAGE WOMEN

1979ndash1989

Year

Actual Adjusted

1979 1989(1979 min)

1989(1989 min)

1979(1989 min)

1989

All women 2 0177 2 0136 2 0093 2 0235 2 0140Standard deviation 0377 0478 0430 0433 0481Differentials

10ndash50 2 0389 2 0575 2 0447 2 0543 2 058825ndash50 2 0246 2 0323 2 0274 2 0313 2 032975ndash50 0305 0363 0346 0329 036390ndash50 0560 0669 0652 0589 0669

White 2 0170 2 0125 2 0083 2 0227 2 0129Black 2 0227 2 0222 2 0165 2 0296 2 02231ndash10 yrs exp 2 0197 2 0199 2 0147 2 0256 2 0202

HSDO 2 0443 2 0636 2 0519 2 0556 2 0647HS 2 0294 2 0404 2 0332 2 0367 2 0409COL 0053 0150 0165 0028 0148

21ndash30 yrs exp 2 0132 2 0070 2 0035 2 0183 2 0073HSDO 2 0330 2 0451 2 0375 2 0415 2 0460HS 2 0170 2 0186 2 0142 2 0222 2 0189COL 0201 0295 0306 0183 0294

Return to education 0066 0097 0088 0076 0098RMSE 0333 0399 0359 0383 0401Residuals

90ndash10 0836 1008 0895 0976 101250ndash10 0359 0485 0395 0464 048990ndash50 0478 0522 0500 0512 0523

Change from 1979 actualChange from 1979(at 1989 minimum)

Blackndashwhite mdash 2 0041 2 0025 mdash 2 0026(21ndash30 yrs)ndash(1ndash10 yrs) mdash 0063 0048 mdash 0056COL-HS (1ndash10 yrs) mdash 0207 0150 mdash 0162COL-HSDO (1ndash10 yrs) mdash 0290 0188 mdash 0211COL-HS (21ndash30 yrs) mdash 0110 0077 mdash 0079

Computed from the CPS Merged outgoing Rotation Earnings Files microdata Data from 1989 are from489ndash390 Ages 18ndash64 For variable construction see Data Appendix All average wage levels are expressed asrelative to the overall median wage The rst two columns use the actual data for 1979 and 1989 The thirdcolumn is 1989 data adjusted to the 1979 relative minimum and fourth and fth columns are the 1979 and1989 differentials adjusted to the 1989 relative minimum (for all states) The adjustment procedure isdescribed in the text Return to education is the coefficient on education in a regression of log (wage) oneducation a quartic in potential experience (age-educ-6) and a black dummy RMSE is the root mean squarederror from an hours-weighted regression of log (wage) on a set of fully interacted educational categories (four)and single year experience dummies 90ndash10 50ndash10 and 90ndash50 are various percentile differentials of theresiduals in that regression

WAGE INEQUALITY AND THE MINIMUM WAGE 1013

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 38: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

the four educational groups ( 12 12 13ndash15 16 1 ) and dummiesfor each single year of experience Rather than rising from 0393to 0432 (99 percent rise) from 1979 to 1989 it rises to 0405 (31percent) accounting for the minimum wage The following threelines lsquolsquo90ndash10rsquorsquo lsquolsquo50ndash10rsquorsquo and lsquolsquo90ndash50rsquorsquo report the correspondingpercentile differentials of these residuals It reveals that theadjustment makes a difference mostly in the lower tail of thedistribution of residuals

Panel B of Table VI reports the results for women Acomparison of the rst and fourth columns suggest that less-experienced high school dropout females would have been paidon average about 11 percent less in 1979 if it had not been for thesupporting effect of the minimum wage Although the minimumwage appears to be a proportionately greater component ofchanges in differentials by education relative to men two-thirdsof the observed changes remain after the adjustment Theadjusted college-high school wage differential continues to risesignicantly by about fteen log points for the least experiencedand the college-dropout differential rises about 19 percent

A comparison of the unadjusted and adjusted measures ofthe residual dispersion suggests that between two-thirds andthree-quarters of the approximately 20 percent rise in within-group inequality could be attributable to the declining minimumwage during the 1980s This estimate and that for men aresubstantially higher than the lower bound estimates given byDiNardo Fortin and Lemieux [1996] who nd that the mini-mum wage accounts for 242 and 340 percent of the rise inresidual dispersion for men and women respectively35

I note that while the estimates here suggest that much ofthe growth in inequality in the lower tail can be attributed to theminimum wage substantial growth in dispersion in the uppertail remains during the 1980s As shown in Panels A and B ofTable VI the 90ndash50 log-wage differential expands by about ten oreleven log points for both men and women For men theminimum wage appears to account for about 70 (or more) percentof the growth of the 50ndash10 differential but about 75 percent ofthe widening 50ndash25 gap still remains implying that an analysis

35 DiNardo Fortin and Lemieux [1996] adopt three assumptions toproduce their lower bound estimates (1) no disemployment effect (2) nospillovers and (3) the shape of the density below the minimum remains the same(even if the fraction below changes) They note that these assumptions work tounderstate the impact of the minimum The estimates in their study as well asthe present analysis depart somewhat from the analysis of Bernard and Jensen[1998] who nd virtually no role for the minimum wage in explaining differencesin residual wage inequality using cross state differences from Census data

QUARTERLY JOURNAL OF ECONOMICS1014

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 39: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

which ignores the minimum wage would not lead to a seriousoverstatement of increasing inequality if the focus is on the upper75 percent of the distribution It should also be noted howeverthat the same cannot be said for women As the upper part ofPanel B reveals the minimum appears to have had such animportant impact that about 50 to 60 percent of the thirteen logpoint rise in the 75ndash25 differential is explained by the minimum

Curiously accounting for the minimum wage has a consider-ably more striking impact on the impression of overall inequalityfor the unconditional distribution of wages (men and womencombined) As a graphical summary of the core specicationprovided in Table I Figure VII plots the actual average change(1979 to 1989) for each (from the 5ndash50 to the 95ndash50) percentiledifferential these are essentially the lsquolsquo1989rsquorsquo coefficients in column(1) of Table I for each differential36 I also plot the 1989 year

36 Here I append the data from 1989ndash1991 to the data (1979ndash1988) used forTable I

FIGURE VIISummary of Changes in Actual and Estimated Latent Log (Wage)

Differentials 1979ndash1989 by Percentile All Workers 18ndash64

WAGE INEQUALITY AND THE MINIMUM WAGE 1015

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 40: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

coefficients from the core specication (column (5) Table I) whichincludes mw for each percentile up to the median It shows thatafter accounting for the minimum wage the modest increase indispersion in the upper tail of the overall wage distributionappears to be offset by an equally modest compression in the lowertail so as to keep measures of the latent 90ndash10 or 75ndash25differential relatively constant over time This nding is roughlyconsistent with Teulings [1998] who in a recent alternativeanalysis of the impact of the minimum wage uses a exibleparameterization of the wage distribution across time and regionswithin the United States and concludes that the minimum wagecan fully explain the growth in inequality of the unconditionaldistribution of wages during the 1980s

VII SUMMARY AND CONCLUSIONS

Two principal ndings emerge from the above empiricalanalysis First estimates that exploit cross-state variation in thelsquolsquoeffectiversquorsquo minimum wage imply that a great majority of theobserved growth in inequality in the lower tail of the distributionis attributable to the erosion of the real value of the federalminimum wage rate during the 1980s The estimates imply thatthe falling relative level of the minimum wage can explain from 70to 100 percent of the growth in inequality in the lower tail of thefemale wage distribution and for men about 70 percent and 25percent of the growth in the 50ndash10 and 50ndash25 differentialsrespectively For both men and women analyzed separately muchgrowth in inequality remains (mostly in the upper tail of thedistribution) during this period Curiously however after account-ing for the minimum wage the unconditional distribution (menand women combined) exhibits a compression in the lower tail(50ndash10 differential) that is of the same magnitude as the modestexpansion in the upper tail (90ndash50 differential) of the distribution

Second the magnitudes of this studyrsquos estimates imply thatignoring the declining real value of the minimum wage leads toonly a moderate exaggeration of the growth in between-groupwage inequality the broad trends in educational and experiencedifferentials are unaffected But ignoring the minimum wageleads to a substantial overstatement of the growth in residuallsquolsquowithin-grouprsquorsquo wage inequality during the 1980s the minimumwage may explain between 60 to 80 percent of the rise in thiscomponent of wage inequality

The credibility of the estimates provided here depend on the

QUARTERLY JOURNAL OF ECONOMICS1016

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 41: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

validity of the assumption that latent wage inequality is uncorre-lated with measures of the centrality of statesrsquo log-wage distribu-tions (and hence with the relative minimums) I nd evidence thatsupports this notion for women and to a lesser extent for theentire sample of workers Also I nd evidence that casts doubt onthis notion for the sample of male workers

For example for the sample of women there are negligiblecorrelations between measures of wage dispersion in the uppertail and the relative minimum This is at odds with the notion thatan inherent relation between the overall scale and location of thestatesrsquo distributions is causing an upward bias of the estimate ofthe minimum wagersquos impact across states An analogous analysisprovides a weaker case for the validity of the cross-sectionalresults for the combined sample The weakest case is for theanalysis of the male sample where the correlations between therelative minimum and the several measures of upper tail wagedispersion are all large and statistically signicant

Second I provide estimates generated by a qualitativelydifferent source of variability in changes in the effective mini-mummdashthat which is driven by an interaction between preexistingvariability in state-legislated wage oors and the imposition of ahigher binding federal minimum in the early 1990s For womenas well as the combined sample the resulting estimates are quitesimilar to those resulting from the earlier cross-sectional analysisBy contrast the divergence of the two estimates when analyzingmen in isolation provides reason to suspect the main results forthe male sample

The ndings in this paper point have a few implications forfuture research on wage and earnings inequality First supposethat we take the ndings here at face valuemdashthat a minimumwage that kept pace with ination would have resulted in arelatively unchanging unconditional distribution of wages forhours worked in the economy during the 1980s Given the sugges-tion of the previous literature that the minimum wage played asmall role in the substantial rise in household income inequalityexplaining this rise would seem necessarily to involve a change inthe nature of the mapping between hourly wages and householdincome37

This intermediate link includes how the distributions ofwages and hours worked map into weekly earnings and in turn

37 See Brownrsquos [1999] recent survey of the literature on the minimum wagefor a discussion of these issues

WAGE INEQUALITY AND THE MINIMUM WAGE 1017

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 42: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

how weekly earnings and the distribution of weeks worked in theyear map into annual earnings It also includes issues of howindividual earners come together to form households And ofcourse the magnitude of disemployment effects due to the mini-mum wagemdashespecially at a time such as the early 1980s whenthe minimum wage was relatively highmdashis an integral part of thisintermediate link Since this study has focused exclusively on theobserved wage distribution without accounting for these issuesits ndings taken alone cannot be used to adequately assess theimpact of the minimum wage on the distribution of economicwelfare more generally

APPENDIX 1 DATA APPENDIX

State Wage Data

All computations (except for the pre-1979 data shown inFigure II) were derived from the National Bureau of EconomicResearch Extract of the Current Population Survey MergedOutgoing Rotation Group Earnings Files Unless otherwise notedthe sample includes all individuals aged sixteen or over Thesample excludes the self-employed unemployed and those not inthe labor force In order to create a wage measure consistent overthe entire time period I construct the wage from lsquolsquouneditedrsquorsquovariables of the hourly rate of pay usual weekly earnings andusual weekly hours worked since the imputation procedure forthose with missing earnings variables seems to have changedsignicantly between 1988 and 1989 In order to have a nonmiss-ing wage an individual must report either (1) the hourly rate ofpay or (2) usual weekly earnings and usual weekly hours workedIn cases where an individual had both values the higher of thetwo was used Note that since I use lsquolsquouneditedrsquorsquo wage variables allindividuals with lsquolsquoimputedrsquorsquo wages are excluded from the analysisNote also that no exclusions of observations were made due toimplausible or lsquolsquoextremersquorsquo wage values A comparable sampleselection and variable construction procedure was used for theMay CPS data for Figure II Resulting sizes per year (for workersaged 18ndash64 for example) for the Outgoing Rotation Groupsranged from about 130000 in 1979 to 140000 in 1989

Using these microdata a panel of the 50 statesrsquo wage percen-tiles was calculated for the 1979ndash1991 period Three main panelswere constructed that for men only women only and that for thecombined sample In addition separate panels were constructed

QUARTERLY JOURNAL OF ECONOMICS1018

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 43: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

for the various age-groups used in the paper 16 and over 18ndash64and 25ndash64 Wage percentiles were calculated using the sampleweight multiplied by usual hours worked In order to make thewage data correspond to the timing of minimum wage legislationdata for lsquolsquo1989rsquorsquo correspond to data from 489 to 390 Similarlylsquolsquo1990rsquorsquo and lsquolsquo1991rsquorsquo contains wage data from 490ndash391 and 491ndash392 respectively Other state-year observations use data fromJanuary to December

New state-specic minimum wage laws often came into effectmidyear and hence the following exceptions were made Wiscon-sin in 1989 actually represents data from 789 to 390 Vermont1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 789ndash390 Massachusetts 1986 785ndash686 1987 786ndash687 1988 787ndash688 Rhode Island 1986 785ndash686 1987 786ndash687 1988 787ndash688 1989 889ndash390 Connecticut 1987 1086ndash987 1988 1087ndash988 California 1988 787ndash688 Oregon 1989 189ndash889

Appendix 2 gives a summary of the (sample-size-weighted)means of selected wage percentile differentials and the log(max-[state minimum wage rate federal rate]) 2 median wage for statepanel data The average sample size for the state-year cell is about2800 with a median of about 2000

Minimum Wage Legislation by State

Information on state-specic minimum wage legislation wascompiled from the January issues of the Monthly Labor Review[Bureau of Labor Statistics] which contain an annual summary ofthe previous yearrsquos proposed and enacted state labor legislationDetails on exemption rules and coverage criteria varied acrossstates but it was possible to isolate a lsquolsquobasic adult ratersquorsquo for eachstate The District of Columbia was excluded from the sample ofstates because frequent changes in sector-specic rates andcoverage rules made it difficult to isolate a consistently broadadult rate For states that did not enact any minimum wagelegislation throughout the 1979ndash1993 period a summary of theminimum wage laws across states was available from the DailyLabor Report [Bureau of National Affairs 1990] which was alsoused to corroborate the information for the rest of the states

The statesrsquo minimum wage legislation can be broadly catego-rized into four groups (1) those with no minimum wage provision(2) those with legislated minimum rates below (3) equal and (4)higher than the basic federal rate Appendix 3 provides a graphi-cal summary of the evolution of minimum wage laws in the 50states during the 1979ndash1993 period

WAGE INEQUALITY AND THE MINIMUM WAGE 1019

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 44: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

AP

PE

ND

IX2

RE

LA

TIV

EM

INIM

UM

WA

GE

LO

WE

RP

ER

CE

NT

ILE

DIF

FE

RE

NT

IAL

S

ME

AN

SF

RO

MS

TA

TE-L

EV

EL

DA

TA

1979

ndash199

1

All

Men

Wom

en

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

Min

ndash50

Min

ndashTM

10ndash5

020

ndash50

1979

20

651

20

653

20

578

20

418

20

836

20

832

20

637

20

415

20

405

20

410

20

384

20

295

1980

20

662

20

659

20

584

20

422

20

847

20

841

20

654

20

430

20

423

20

426

20

398

20

296

1981

20

667

20

668

20

592

20

427

20

854

20

847

20

680

20

450

20

441

20

443

20

415

20

314

1982

20

729

20

729

20

625

20

440

20

915

20

904

20

713

20

475

20

512

20

517

20

465

20

337

1983

20

767

20

767

20

644

20

447

20

942

20

934

20

722

20

484

20

565

20

568

20

500

20

354

1984

20

813

20

812

20

664

20

460

20

982

20

975

20

723

20

478

20

612

20

615

20

528

20

370

1985

20

855

20

854

20

675

20

466

21

020

21

010

20

737

20

487

20

660

20

661

20

556

20

385

1986

20

894

20

890

20

681

20

469

21

050

21

045

20

731

20

491

20

703

20

705

20

569

20

395

1987

20

919

20

919

20

688

20

464

21

070

21

066

20

719

20

488

20

740

20

742

20

579

20

401

1988

20

943

20

942

20

667

20

453

21

092

21

087

20

717

20

480

20

771

20

770

20

578

20

399

1989

20

976

20

973

20

678

20

468

21

120

21

111

20

724

20

489

20

810

20

810

20

577

20

400

1990

20

916

20

913

20

668

20

466

21

049

21

044

20

713

20

484

20

753

20

756

20

577

20

399

1991

20

845

20

846

20

658

20

459

20

974

20

971

20

711

20

479

20

693

20

699

20

558

20

393

N5

50fo

rea

chye

ar

Wor

kers

aged

18ndash6

4M

inndash5

0is

max

[fed

eral

min

imu

m

stat

em

inim

um

]m

inu

sth

em

edia

nw

age

ofth

est

ate

Min

ndashTM

ism

ax[f

eder

alm

inim

um

st

ate

min

imu

m]m

inu

sth

e(t

op30

and

bott

om30

perc

ent)

trim

med

mea

nw

age

ofth

est

ate

QUARTERLY JOURNAL OF ECONOMICS1020

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 45: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

APPENDIX 3 MINIMUM WAGE LEGISLATION STATUS BY STATE 1979ndash1993

1979 1980 1981 1982 1993 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993

Alabama s s s s s s s s s s s s s s s

AlaskaArizona s s s s s s s s s s s s s s s

Arkansas d

California d d d d d d d d d d d

ColoradoConnecticut d d d d d d d d d d

Delaware d d d d d d d

Florida s s s s s s s s s s s s s s s

GeorgiaHawaii d d d d d d d d d d

Idaho d d d d

Illinois d d d d d d d d d

Indiana d

Iowa s s s s s s s s s s d d d

KansasKentucky d d d d d d d d

Louisiana s s s s s s s s s s s s s s s

Maine d d d d d d d

Maryland d d d d d d d d d d d d d d d

Massachu-setts d d d d d d d

Michigan d d d d d d d d d d d d

Minnesota d d d d d d d d

Mississippi s s s s s s s s s s s s s s s

Missouri s s s s s s s s s s s d d d d

Montana s s s s s s s d d d d d d d d

Nebraska s s s s s s s s d d d d d d d

Nevada d d d d d d d

New Hamp-shire d d d d d d d d d d d

New Jersey d d d d d d d d d d d d d

New Mexico s s d d d d d d d d d d

New York d d d d d d d d d d d d d d d

North Carolina d d d d d d d d d

North Dakota s s s s s s s s s s d d d d d

Ohio d d d d d

Oklahoma d d d d d d d d d d d d

Oregon d d d

Pennsylvania d d d d d d d d d d d d d d

Rhode IslandSouth Carolina s s s s s s s s s s s s s s s

South Dakota d d d d d d

Tennessee s s s s s s s s s s s s s s s

Texas d d d d

Utah d d d d

Vermont d d d d d d d d d

Virginia d d d

Washington d d d

West Virginia d d d d d d d

Wisconsin d d d d d d

Wyoming

Compiled from the Monthly Labor Review January issues1979ndash1994 s mdashno state provision mdashstateminimum lower than federal d mdashstate minimum equal to federal mdashstate minimum higher than federal Inyears when the law changes midyear the lsquolsquohigher rsquorsquo status is given

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 46: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

PRINCETON UNIVERSITY

REFERENCES

Autor David H Lawrence F Katz and Alan B Krueger lsquolsquoComputing InequalityHave Computers Changed the Labor Marketrsquorsquo Industrial Relations SectionWorking Paper 377 March 1997

Berman Eli John Bound and Zvi Griliches lsquolsquoChanges in the Demand for SkilledLabor with U S Manufacturing Industries Evidence from the Annual Surveyof Manufacturingrsquorsquo Quarterly Journal of Economics CIX (1994) 367ndash397

Bernard Andrew B and J Bradford Jensen lsquolsquoUnderstanding Increasing andDecreasing Wage Inequalityrsquorsquo NBER Working Paper No 6571 May 1998

Blau Francine D and Lawrence M Kahn lsquolsquoSwimming Upstream Trends in theGender Wage Differential in the 1980srsquorsquo Journal of Labor Economics XV(1997) 1ndash42

Borjas George J and Valerie A Ramey lsquolsquoForeign Competition Market Power andWage Inequalityrsquorsquo Quarterly Journal of Economics CX (1995) 1075ndash1110

Bound John and George Johnson lsquolsquoChanges in the Structure of Wages in the1980s An Evaluation of Alternative Explanationsrsquorsquo American EconomicReview LXXXII (1992) 371ndash392

Brown Charles lsquolsquoMinimum Wages Employment and the Distribution of IncomersquorsquoHandbook of Labor Economics (1999) forthcoming

Bureau of Labor Statistics Monthly Labor Review January issues 1979ndash1994Bureau of National Affairs Daily Labor Report (March 30 1990)Bureau of the Census Statistical Abstract of the United States (1996)Card David and Alan B Krueger Myth and Measurement The New Economics of

the Minimum Wage (Princeton NJ Princeton University Press 1995)Davis Steven J and John Haltiwanger lsquolsquoWage Dispersion between and within

U S Manufacturing Plantsrsquorsquo Brookings Papers on Economic Activity Micro-economics (1991) 115ndash200

DiNardo John Nicole Fortin and Thomas Lemieux lsquolsquoLabor Market Institutionsand the Distribution of Wages 1973ndash1992 A Semi-Parametric ApproachrsquorsquoEconometrica LXIV (1996) 1001ndash1044

Doms Mark Timothy Dunne and Ken Troske lsquolsquoWorkers Wages and TechnologyrsquorsquoQuarterly Journal of Economics CXII (1997) 253ndash289

Feenstra Robert C and Gordon H Hanson lsquolsquoGlobalization Outsourcing andWage Inequalityrsquorsquo American Economic Review LXXXVI (1996) 240ndash245

Fortin Nicole and Thomas Lemieux lsquolsquoThe Battle of the Sexes in the LaborMarket A Distributional Test of a Jobs Fund Modelrsquorsquo University of Montrealmimeo March 1996

Fortin Nicole and Thomas Lemieux lsquolsquoInstitutional Changes and Rising WageInequality Is There a Linkagersquorsquo Journal of Economic Perspectives XI (Spring1997) 75ndash96

Gottschalk Peter lsquolsquoInequality Income Growth and Mobility The Basic FactsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 21ndash40

Johnson George lsquolsquoChanges in Earnings Inequality The Role of Demand ShiftsrsquorsquoJournal of Economic Perspectives XI (Spring 1997) 41ndash54

Juhn Chinhui Kevin M Murphy and Brooks Pierce lsquolsquoWage Inequality and theRise in Returns to Skillrsquorsquo Journal of Political Economy CI (1993) 410ndash442

Katz Lawrence F and David H Autor lsquolsquoChanges in the Wage Structure andEarnings Inequalityrsquorsquo Handbook of Labor Economics (1999) forthcoming

Katz Lawrence F and Kevin M Murphy lsquolsquoChanges in Relative Wages 1963ndash1987 Supply and Demand Factorsrsquorsquo Quarterly Journal of Economics CVII(1992) 35ndash78

Lee David S lsquolsquoWage Inequality in the U S during the 1980s Rising Dispersion orFalling Minimum Wagersquorsquo Industrial Relations Section Working Paper No399 March 1998

Levy Frank and Richard J Murnane lsquolsquoU S Earnings Levels and EarningsInequality A Review of Recent Trends and Proposed Explanationsrsquorsquo Journal ofEconomic Literature XXX (1992) 1333ndash1381

Murphy Kevin M and Finis Welch lsquolsquoThe Structure of Wagesrsquorsquo Quarterly Journalof Economics CVII (1992) 285ndash326

QUARTERLY JOURNAL OF ECONOMICS1022

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023

Page 47: WAGE INEQUALITY IN THE UNITED STATES DURING THE 1980s ...piketty.pse.ens.fr/files/Lee1999.pdf · WAGEINEQUALITYINTHEUNITEDSTATES DURINGTHE1980s:RISINGDISPERSIONORFALLING MINIMUMWAGE?*

OrsquoNeill June and Solomon Polachek lsquolsquoWhy the Gender Gap in Wages Narrowed inthe 1980srsquorsquo Journal of Labor Economics XI (1993) 205ndash228

Silverman B Density Estimation for Statistics and Data Analysis (New York NYChapman and Hall 1986)

Teulings Coen N lsquolsquoThe Contribution of Minimum Wages to Increasing WageInequality A Semi-Parametric Approachrsquorsquo Department of Economics Univer-sity of Amsterdam January 1998

Topel Robert H lsquolsquoFactor Proportions and Relative Wages The Supply-SideDeterminants of Wage Inequalityrsquorsquo Journal of Economic Perspectives XI(Spring 1997) 55ndash74

WAGE INEQUALITY AND THE MINIMUM WAGE 1023