AppliedEconometrics Labor Econometrics - UMasspeople.umass.edu/econ753/lectures/labor.pdfLabor...

Applied Econometrics

Labor Econometrics

Michael Ash

Econ 753

Labor Econometrics – p.1/45

Outline of Presentation

Three-day plan

1. Wage models

2. Labor demand: the employment effect of the minimum wage

3. Labor supply: the employment effect

Today—Wage models

1. Why study wage determination?• Outcome of a labor-market process• Distribution of product and surplus• Rents (both for themselves and as an indicator of market

power)

2. Building an econometric model: Theory and functional form

3. Discrimination

4. Aggregate variables and micro units


Data sources and definitions

1. Census, CPS, NLSY, PSID (US)

2. Luxembourg Income Study (OECD), GSOEP (Germany)

Wage and “wage”

• Annual earnings, weekly earnings, hourly wage, salaries

• Think about the data in rows (observations, records) and columns(variables, fields).

• Read and produce tables of regression output.


Wage-setting models

• Competitive market models◦ Market-clearing wage◦ Human Capital (HK): hedonic wage model◦ Compensating differentials

• Monopsonistic or exploitation models

• Institutional models and discrimination models◦ Segmented labor markets◦ Inter-industry wage differentials


On econometric models of wages

• Does X or Z raise wages?◦ Simultaneity/endogeneity/selection (Does X really raise your

wages, or do people with X tend to have high wage?)• Signalling critique of Human Capital• General equilibrium remark on Human Capital

◦ Aggregate explanatory variables


Functional form

• About subscripts and parameters: yi, yit , yi jt , β• Interpreting the semi-log specification

• The Return to Education

• Experience (or tenure)

• Indicator, or dummy, variables

• Indicator interactions

• Differences in the function over time/space/group (e.g.,“skill-biased technical change”)


Return to Education (HK phrasing)

Human Capital Regressions are based on a hedonic model of wagedetermination: the wage is a function of the valuable characteristics ofthe worker. What’s the return to attending one [more] year of schooling?

Career Earnings by Years of School

Years attended

t 0 1 2

0 Y0 0 0

1 Y0 Y1 0

2 Y0 Y1 Y2

3 Y0 Y1 Y2... Y0 Y1 Y2

T Y0 Y1 Y2


Return to Education

Note that more years of schooling require foregoing years of earnings.In a very simple model, the return to schooling will equalize the netpresent value (NPV) of the alternatives (0,1,2, or 3 years of schooling).

NPV(S = 0) =Y0

(1+ r)0 +Y0

(1+ r)1 +Y0

(1+ r)2 + · · · =1+ r

r·Y0

NPV(S = 1) =0

(1+ r)0 +Y1

(1+ r)1 +Y1

(1+ r)2 + · · · =1r·Y1

“Equilibrium”: NPV(S = 0) = 1r ·Y1 = 1+r

r ·Y0 = NPV(S = 1)implies

Y1 = (1+ r1) ·Y0


Returns to Education

The additional income from one year of school relative to zero years ofschool represents a return of r1. The same argument implies that

Y2 = (1+ r2) ·Y1

and so on. Substituting recursively, we find

Ys = (1+ rs)Ys−1 = (1+ rs) · · ·(1+ r1)Y0

For the moment assume that rs = rs−1 = · · · = r1 = r , a single percentreturn to an additional year of education (a testable proposition),

Ys = (1+ r)s·Y0


Measuring and Estimation

Recall that by a Taylor series approximation, 1+δ = eδ and so(1+ r)s = (er)s = ers (This might also be familiar fromcompound-interest formulas.)

Ys = ersY0

and taking log of both sides,

lnYs = lnY0 + rs

which can be interpreted as a semi-log wage equation that we canestimate:

lnYs = α+βS

Ysand S are measured (earnings and schooling) and α and β areestimated parameters. β is the return to schooling (expressed inpercent per year ) and α is the intercept (implied log earnings at zeroyears of education).


Critique of Causality

In observational studies in the U.S. and elsewhere, β is rarely estimatedbelow 0.05 (a 5 percent return to schooling) and in L.D.C.’s issometimes estimated as high as 0.20 (a 20 percent return to schooling).Is lnYs = α+βS a causal relationship, i.e., if β is positive, doesschooling cause higher earnings? Why or why not?

• Omitted variables that cause β to be an overestimate (“left” and“right” critiques)◦ Socioeconomic status causes both schooling and earnings◦ Ability causes both schooling and earnings

• Signalling

• General equilibrium and social returns

• Attitudinal modification

We will return to this question in more detail later.


Experience

Next we introduce experience and allow it to have a non-linear effect onearnings. Why?

• Human capital explanations: rational to accumulate HK whenyoung; rapid accumulation of HK in early years on the job (OJT);long time to amortize the cost of training; forgetting and HKdeterioration.

• Neo-institutional explanations: solve P/A problem with “bond”;matching and wage gains

• Institutional explanations: customs and norms; seniority inunionized and union-avoiding workplaces; limited evidence onproductivity (bus driver safety study)


Tenure and experience

• Would be helpful to resolve some of the competing hypotheses.

• Empirical problem. few datasets include measures of tenure; thenthey do, the quality is often poor (for three reasons: recollectionbias, definition of job and employer, sampling durations). PotentialExperience (Mincerian Experience for Jacob Mincer):

Potential Experience = Age− (Years of Schooling+6)

Reasonable proxy unless the aim is to make subtle points abouttenure versus experience. Note that regressions with PotentialExperience and Schooling must omit age to prevent perfectcollinearity.


Quadratic specification

lnYi = α+Siβs +ExiβEx +Ex2i βEx2 + εi

∂ lnYi

∂Exi= βEx +2ExiβEx2

This term depends on the level of experience. Typical values areβEx = 0.03 and βEx2 = −0.0004. The negative quadratic term meansthat the relationship is concave. The positive linear term and the size ofthe two terms means that the return begins positive (about 3 percentper year for a new worker at 0 years of experience) and then falls. Youcan compute the return at any given level of experience by substituting.You can compute the peak of the age-earnings profile by setting thederivative to zero:

∂ lnYi

∂Exi= βEx +2ExiβEx2 ≡ 0


Experience, continued

which implies that

Expeaki = −

βEx

2βEx2

For example, with βEx = 0.03 and βEx2 = −0.0004, the peak of the

profile would be at about 0.032(−0.0004) = 38 years of experience.


Dummy variables

Allows different intercepts for different categories.Simplest example: Each observation i is in category (Di = 1) or not(Di = 0), e.g., non-white, female, or union member. categorical nominalvariables with a simple level effect.

lnYi = α+Diδ+XiβX + εi

6

-

...................................................................

...................................................................

....................................................................

...................................................................

....................................................................

...................................................................

...................

...................................................................

...................................................................

....................................................................

...................................................................

....................................................................

...................................................................

...................

y

xα

Slope βx

Slope βx

δ

The estimated coefficient δ is the return (premium or penalty) to beingin category D, measured in log points (read as percent).Tip: give D a useful name, e.g., “Female” is a more useful name for anindicator than is “Sex”; “Nonwhite is a more useful name for an indicatorthan is “Race”.


Interpreting dummy variables

To interpret the coefficients on dummy variables:Consider a very simple wage equation:

lnYi = α+Diδ+ εi

Yi is hourly wage for person i, αis the intercept, a baseline wage, Diisan indicator variable for membership in category D, e.g., Di = 1 forcollege degree or more and Di = 0 for less than college degree.How can we interpret δ, the coefficient on Di?

ˆlnYi = α̂+Diδ̂

eˆlnYi = eα̂+Diδ̂

Yi = eα· eDiδ̂



For a person without a college degree, D j = 0 and expected earningsare:

Yj = eα̂· e0·δ̂ = eα̂

·1 = eα̂

So the baseline wage (without a college degree is eα̂.For a person with a college degree, Di = 1, and expected earnings are:

Yi = eα̂· e1·δ̂ = eα̂eδ̂

What’s the percent return?



ρ ≡Yi −Yj

Yj=

eα· eδ

− eα

eα = eδ−1

Remark: this formula for percent change always works. If you want toknow the percent return when you are given δ, you can calculate

ρ = eδ−1.

But there is a shortcut when δ is small. Consider a first-order Taylorapproximation of the percent return ρas a function of the coefficient δ.

As we just saw, ρ(δ) = eδ−1.

ρ(δ) ∼= ρ(0)+ρ′(0) · (δ−0) near δ = 0

ρ′(δ) = eδ

ρ(0) = e0−1 = 1−1 = 0

ρ′(0) = e0 = 1

ρ(δ) ∼= 0+1 ·δ = δ

δ really tells how many “log points” are gained or lost from a unitchange in X , but log points are pretty close to percent when changesare small. If δ is small (say between −0.20and +0.20) the percentreturn is almost exactly δ.Aside, a second-order Taylor approximation starts to show moreslippage between ρand δ:


The Returns to Computer Use

John DiNardo and Jorn-Steffen Pischke. “The Returns to ComputerUse Revisited: Have Pencils Changed the Wage Structure Too?”Quarterly Journal of Economics, 112, pages 291-303, 1997. (Also agood example of a critical replication)

• Enormous increase in inequality in the United States◦ Between categories◦ Within categories (“residual inequality”)

• Skill-biased technical change◦ Alternatives: trade, trade/SBTC, institutions◦ What are the technical changes in question?◦ Alan Krueger offers computers


The Returns to Computer Use


The Returns to Computers—and Pencils!


Multiple dummy variables

Multiple nominal categories, e.g., race, industry, occupation. Create a1/0 dummy variable for each category. Must omit one of the classes orthe dummies will be collinear with the intercept. (Can alternatively omitthe intercept.) The omitted class is associated with the intercept, and alldifferences (the coefficients on the dummies) are read relative to theomitted class.

lnYi = α+D2iδ2 +D3iδ3 +XiβX + εi


Other uses for dummy variables

Can also create dummies for a small (relative to N number of orderedcategories—a less parametric approach, e.g., a return for every year ofschooling, δ1, δ2. . . δ16 instead of restricting all years to have a singlereturn, βs.Dummies are equivalent to a within-group approach. The response(slope) within every group is constrained to be the same, but the groupscan be at different levels.Many dummy variables (fixed effects), e.g., for every state, for everycity, for every person.

Needs more than one observation per fixed effect. Cannot nest fixed

effects, e.g., neighborhoods and cities.


Dummy interactions

• Dummy-dummy interactionsInteractions among categorical variables.Differences in function over time, place, or group.For example, do black women suffer as much discrimination asdo black men? Are union premiums larger for women or for men?Were union premiums larger in 1970 or in 1980?

lnYi = α+FemiβFem +NonwhiteiβNW +Femi×NonwhiteiβFem-NW +XiβX +εi

(Show regression output.) For this example, βFem < 0, βNW < 0,but βFem-NW > 0enough to “offset” one of the two forms ofdiscrimination, i.e. black women do not receive the cumulativeeffect of sex and race discrimination.


Dummy-dummy interactions

Advantages of pooling: (1) restrict other coefficients to equality; (2)easy to test hypotheses.Interact dummy variables for each category of first characteristic withdummy variables for each category of second characteristic.Include dummies (level, or main, effect) and all dummy interactions. Toinclude interactions but not the main effect, you must have a goodreason or model.Multiple interactions are possible.Preview treatment-control before-after model (identifyquasi-experimental effects):

yit = α+PostitδPost +Treatment grpitδTreatment grp +Postit ×Treatmentit ×δEffect +εit

δEffectis the effect of treatment on the outcome because it expresses the

difference between the treatment and control groups after treatment has

been received. Note the use of interacted dummy variables.Labor Econometrics – p.26/45

Dummy interactions

• Dummy-continuous interactions (different slopes for differentfolks)

6

-.................................

....................................................................

...................................................................

....................................................................

...................................................................

....................................................................

....................................................

..........................................

..........................................

..........................................

..........................................

..........................................

..........................................

..........................................

..........................................

..........................................

..........................................

..................

y

xα

δ

Slope βx,D=1

Slope βx,D=0


Aggregate explanatory variables (Moulton)

Contextual explanations of individual outcomes (neighborhood, city,industry). May want to explain an individual outcome with an aggregatecharacteristic, e.g., a worker’s wage may depend on the capital-laborratio of the industry. For worker i in industry s:

lnYis = α+Zisγ+(K/L)sβ+ εis +ηs

with

εis ∼ N (0,σ2ε)

ηs ∼ N (0,σ2η)

cov(εis,ηs) = 0

cov(εis,ε js) = 0

cov(ηs,ηt) = 0


Moulton

1. β̂OLS is unbiased; but

2. s.e.(β̂OLS) is underestimated.

Standard OLS estimation will generate an unbiased estimate of β (howcapital-labor ratio affects wage), but the standard error of β isunderestimated.Intuition: because (K/L)sis aggregate, all workers in industry s havethe same K/L and the same industry-specific error ηs. There areeffectively S not I ×S observations. Ignoring this understates theestimated standard error of β. (Good exercise.)


Moulton variables


Moulton results


Aggregate explanatory variables (Moulton)

Alternative solutions

1. Estimate with standard errors adjusted for “clustering”

2. Estimate with dummy variables for the aggregates

yis = zisγ+δs + εis+

Then estimate the relationship between the s premium andcharacteristics of aggregate s:

δs = xsβ+us


Labor-Market Discrimination

• What are the right questions?

• What’s wrong with “reverse regression”?

• Oaxaca decomposition◦ Decomposition of inter-group average-wage gap into

average characteristics and price per characteristic.• Compute means for the explanatory variables for the two

groups• Run separate regressions for the two groups

ln(Y w)− ln(Y b) = Xwβw−Xbβb

= Xwβw−Xwβb +Xwβb

−Xbβb

= Xw(βw−βb)+(Xw

−Xb)βb

= discrimination in returns+difference in characteristics


Notes on Oaxaca decomposition

• Note and interpret the alternative decomposition.

ln(Y w)− ln(Y b) = Xwβw−Xbβb

= Xwβw +Xbβw−Xbβw

−Xbβb

= Xb(βw−βb)+(Xw

−Xb)βw

(1)

• Recall that X includes the constant “1”: [1i Si Xi X2i ]


Labor Demand

• Minimum-wage.

• Immigration

• Factor demand models


Time-Series Minimum Wage Studies

10 percent increase in the minimum wage causes a 1–3percent reduction in teenage employment.

Critiques

• Kaitz index, MWt = ∑i fit(mt/witcit

(coverage and relative wage)

• Sensitive to specification

• Publication bias (t-ratios do not grow with the square root ofsample size).

• E–MW Relationship weakened between 1950’s-1970’s and1980’s-1990’s

• Sex oddity


Minimum Wage Natural Experiment

“Employer Responses to the Minimum Wage: Evidence from theFast-Food Industry”The Employment Effects of the New Jersey Minimum Wage

• Date of New Jersey minimum-wage increase: 1 April 1992.

• New Jersey minimum wage before 1 April 1992: $4.25 per hour

• New Jersey minimum wage after 1 April 1992: $5.05 per hour

• Federal minimum wage before and after 1 April 1992: $4.25 perhour

• Pennsylvania minimum wage before and after 1 April 1992: $4.25per hour


Research Design

• Where will the minimum wage have “bite”?

• Confounding factors◦ National or regional trends◦ Policy endogeneity

• Control or comparison groups


The fast food industry

Approximately one-half of employees are 20 years of age or older.

66 percent of employees are female

77 percent of employees are white

65 percent of employees have at least a high-school diploma

Turnover is very high (one-half of employees have less than one year ofjob tenure)

Work is gender segregated; female employees and employees with

higher seniority are more likely to work in the front of the store.


Survey Method

• Telephone survey of almost 500 Burger King, KFC, Wendy’s, andRoy Rogers restaurants in eastern Pennsylvania and New Jersey.

• First wave of survey February-March 1992 (87 percent responserate)

• Second wave of survey November-December 1992 (100 percentof first-wave respondents)

• Full-time equivalent (FTE) employment ≡ full-time employees +one-half of part-time employees


Analysis

• Establish that the NJ minimum wage had bite in New Jersey andnot in Pennsylvania (the treatment group received treatment andthe comparison group did not).

• Measure the average change in employment in NJ restaurants

• Appropriate counterfactual: average change in employment inPA restaurants


Bite

*Labor Econometrics – p.42/45

Results


Other Outcomes


Labor Supply

• Participation and hours

• Structural models: income and substitution effects

• Natural experiment models

• Criticisms: labor demand

• Structural models

• Reduced form/difference–in–difference


AppliedEconometrics Labor Econometrics - UMasspeople.umass.edu/econ753/lectures/labor.pdfLabor...

Documents

Transcript of AppliedEconometrics Labor Econometrics - UMasspeople.umass.edu/econ753/lectures/labor.pdfLabor...