Getting Back to Work:

Rehiring wages after short vs. long jobless spells

Gregory N. Johnson

August 1, 2016

1 Introduction

In his 2012 speech, “Recent Developments in the Labor Market,” then chairmanof the Federal Reserve, Ben Bernanke spoke at length about the increase in long-term unemployment. During the Great Recession, long-term unemploymentreached levels not seen since World War II. During the period of 2009 throughthe time of the speech, those with unemployment spells longer than 6 monthsmade over 40% of the unemployed. Much is said about the private and socialcosts of long-term unemployment from lost tax revenue, withdrawals of savings,and even negative health outcomes on the unemployed. He also mentions thepotential for future declines in earning, even after new work is found. On thislatter note, it may be surprising to learn that there exists little empirical researchon the causal effects of long-term unemployment on earnings after rehiring hasoccurred.1

This paper adds to that literature by empirically measuring the causal effectof long-term nonemployment on rehiring wages using U.S. data covering theGreat Recession. While there have been cross-sectional studies of the effects ofunemployment spells on post-spell wages (e.g. Addison and Portugal 1989 ),finding true causal effects is often difficult if one believes that the duration ofunemployment is endogenous. While I estimate a number of models under thesame assumption of exogeneity, I also estimate a subset of models that allow forendogenous selection into long-term nonemployment. The techniques requiredfor such models necessitate the existence of a valid instrument. Recent litera-ture suggests that the potential duration of unemployment insurance benefitsmeets the necessary criteria to satisfy the requirements for a valid instrument.Namely, that potential UI benefits induce changes in the duration of nonem-ployment and does not seem to affect wage outcomes directly, but rather onlythrough induced changes in the duration of nonemployment. While the dura-tion of UI benefits historically does not contain enough variability to work wellas an instrument, the Great Recession is an exception. Due to ever-changing

1Bernkanke 2012 cites one study. It, and a few recent papers are discussed in the literaturereview section.

1

lengths in potential UI benefits, both across time and location, there is an atyp-ical amount of variation during the Great Recession. This provides a uniqueopportunity to more robustly explore the empirical analysis of the causal effectsof the duration of nonemployment on rehiring wages.

This paper first outlines a theoretical framework for wage determination.Under various assumptions, this wage determination model can be estimated ina number of ways. In some, it is assumed that the wage determination modelis identical for both the long and short-term nonemployed, with the length ofnonemployment only causing an intercept shift in the wage determination model.Other subsets allow for the possibility that those who have experienced long-term nonemployment face a fundamentally different model of wage determina-tion. This notion is supported by the findings in another chapter of this disser-tation. The theoretical framework decomposes the wage determination processinto a combination of of factors, including the worker’s reservation wage, thefirm’s estimated productivity of the worker, and the relative bargaining powerduring the wage negotiation process. Estimation of this decomposition is notalways possible under all sets of assumptions. Estimation is done when feasible,potentially adding insight as to the nature of how long-term nonemploymentaffects the wage determination process.

A brief preview of the main findings follows. Models that assume an exoge-nous treatment status typically result in estimates showing that being out ofwork for six months or more results in lower wages. This wage penalty associatedwith long-term nonemployment vary somewhat by model, but are consistentlynegative, and around the 10% mark. I do not find evidence that this penaltyis the result of a loss of bargaining power. Evidence suggests workers lowertheir reservation wages as the duration of nonemployment decreases. Not all ofthese models are re-estimated under the assumption of endogenous treatmentstatus. For those where estimation is possible, there is not enough evidenceto suggest that long-term nonemployment causes lower rehiring wages. Variousmodels result in both positive and negative wage effects that are small in magni-tude, and not statistically significant. It is therefore possible that the observedwage differentials between the long and short-term nonemployed could be dueto unobserved differences between the groups of individuals that comprise eachgroup. This suggests that, at least in terms of rehiring wages, long-term nonem-ployment does not necessarily harm individuals. Rather, policy makers shouldconcern themselves more with the characteristics of those who find themselvesout of work for significant periods of time.

This paper proceeds as follows. Section 2 reviews the relevant literature.Section 3 presents a model of wage determination. Section 4 discusses theissue of endogenous treatment status in detail. Section 5 outlines the data use.Section 6, and it’s numerous subsections, present the estimation of a variety ofmodels under varying sets of assumptions. Section 7 concludes.

2

2 Literature Review

Past literature suggests that there are multiple mechanisms that may explainchanges in wages after long periods of nonemployment, sometimes with con-flicting effects. Some of the seminal papers on job search (e.g. Stigler (1962) )suggest that longer job searches may provide for better job matches and resultin higher post-unemployment wages. It should be noted that Stigler’s modelassumes a constant reservation wage. Others, such as Lazear (1976) , and Kikerand Roberts (1984) , propose the notion that workers may suffer depreciationof their human capital during periods of unemployment. If human capital de-preciates over the course of unemployment, then the rehiring wage may alsosuffer. This would suggest that the longer the unemployment (or nonemploy-ment) spell, the lower the rehiring wage. Heckman and Borjas (1980) speakof stigma effects that may also harm those who are unemployed for long peri-ods of time. Further evidence of a negative stigma attached to the long-termunemployed is found in Kroft et al. (2012) . They provide experimental datashowing lower call back rates for job interviews for those with longer spells ofnonemployment. Thus, there exists the possibility of a negative feedback loopwhere a long nonemployment spell increases the stigma against them, thus in-creasing the length of joblessness, thus further stigmatizing the job-searcher.This, coupled with an increasing sense of desperation, may result in decreasingreservation wages over time, eventually resulting in a lower rehiring wage. Thecurrent consensus on the overall effects of nonemployment duration are thatrehiring wages will be lower.

Estimating the effect of the duration of nonemployment on wages is com-plicated by the potential endogeneity of the length of nonemployment. Whilepapers like Addison and Portugal (1989) do attempt to control for the selec-tion into or out of unemployment using a Heckman-style selection model, mostliterature on this causal effect does not adequately deal with the potential for en-dogeneity. Recently, a few papers have attempted to estimate the causal effect ofthe duration of nonemployment using instrumental variable approaches.2 First,Autor et al. (2015) relates the presence of Social Security Disability Insurance tothe duration of nonemployment. Furthermore, they exploit the random assign-ment of individuals to judges with different mean judgment times to functionas an instrument for the duration of nonemployment. They find that extendedperiods of nonemployment significantly negatively affect earnings in both theshort and long-run (in the neighborhood of 8-13% less per year). Even morerecently, Schmieder et al. (2015) , estimated the effect of near 1% decrease inwages for every month spent unemployed.

The presence of UI benefits complicates estimating the effect of nonemploy-ment on wages as it may increase the value of not working, thus raising thereservation wage. If a worker only accepts a position higher than the reserva-tion wage, then UI benefits may increase both the duration of unemploymentand the rehiring wage (Mortensen 1976). On the other hand, increased dura-

2As far as I know, none existed when I started this paper. Two were published since then.

3

tions of UI benefits may also decrease search efforts, increase the duration ofnonemployment, and thus reduce rehiring wages (if one assumes longer spellslead to lower reservation wages.) While a few papers have shown a negativepoint estimate of UI benefits on wages ( Lalive (2007) , Card et al. (2007) ,Centeno and Novo (2009) ), none have been statistically significant. It is im-portant to sort out the effects of UI benefits on labor market outcomes beforeproceeding to estimate the effects of nonemployment spell lengths on wages.On one hand, if UI benefits directly affect rehiring wages and the duration ofunemployment estimates of the effects of the length of nonemployment on wagescould be confounding the effects of UI benefits. On the other hand, if UI ben-efits affect the duration of nonemployment, but have no direct effect on wages,other than through an increase in nonemployment spell lengths, the durationof UI benefits may be useful as a potential instrumental variable. This issue isdiscussed later in more detail.

3 Wage Determination

Assume that non-working individuals value some benefits of unemployment thatwould have to be given up if an individual accepted a job. These benefits couldinclude monetary sums such as unemployment insurance or income from oddand irregular jobs as well as a valuation of non-monetary benefits, such as leisuretime and home production. The total valuation of the benefits that must begiven up if a job is taken by an individual is denoted as ri and is assumed tobe measured in the same units as the accepted wage rate, wi. While the valueof ri may differ across individuals, it must be that wi ≥ ri for any individualwho has accepted a job. Thus, ri represents an individual’s reservation wage.While ri represents the lower bound for an acceptable wage, from the worker’sperspective, there is no upper bound.

A firm values the production of a worker at pi. Assume the firm is onlywilling to make a job offer if wi ≤ pi. That is, the firm is willing to pay up to,but no more than, the value that the individual brings to the firm’s production.While this valuation of worker productivity functions as an upper bound, thefirm is always willing to pay a lower wage.

In a well-functioning competitive labor market it should be the case thatfirms bid on workers until the wage offered equals the marginal productivity ofhiring that worker. This is not necessarily the case if frictions exist in the labormarket, such as search costs and asymmetric information (both of which mayapply to both the firm and worker). Furthermore, the worker and firm maydiffer in their relative levels of bargaining power. For a job match to occur thewage must be high enough for a worker to accept it, but still low enough forthe firm to find the match worthwhile. For any observed wage rate, wi, it mustbe that ri ≤ wi ≤ pi, but where precisely the observed wage falls in that rangeremains uncertain.

During wage negotiations, the goal of the worker is to maximize (wi−ri) andfor the firm it is to maximize (pi−wi). I make the assumption that the realized

4

wage is the value of wi that solves the maximization problem of the weightedproduct of the net return for both the firm and worker from a job match:

wi = argmax(wi − ri)θi(pi − wi)(1−θi)

where 0 ≤ θi ≤ 1 represents the relative bargaining power of the worker and(1− θi) the relative bargaining power of the firm.

Rearranging the first order conditions of the maximization problem allowsus to write the realized wage as follows:

wi = ri + θi(pi − ri) (1)

Note, this can be rewritten as:

wi = pi − (1− θi)(pi − ri) (2)

This is analogous to the wage determination result in Pissarides [Ch. 1,2000], albeit with a simpler derivation and differing notation.

In this setup, there are three main determining factors of the wage: theworker’s reservation wage, the firm’s estimated expected level of production,and the relative bargaining powers of the firm and worker. Each of these de-terminants may vary by individual characteristics, both observed and unob-served. Concerning the observed characteristics, in theory, each of these ele-ments (ri, pi, θi) may be functions of different vectors of covariates, say Xr, Xp,and Xθ. In practice, these sets of covariates are likely to overlap heavily. Forsimplicity, define X as the union of Xr, Xp, and Xθ, and state that each elementis a function of X. Note X does not contain a constant term.

The research question is how does long-term nonemployment affect thismodel. Define Ds as a binary indicator of short-term nonemployment, andDl as a binary indicator of long-term nonemployment. Note that these statesare mutually exclusive.

I assume ri and pi are linear functions of the treatment status and observedcovariates such that for any given individual we have:

ri =αsrDsi + αlrD

li + βsrD

siXi + βlrD

liXi + eri (3)

pi =αspDsi + αlpD

li + βspD

siXi + βlpD

liXi + epi (4)

where the β’s are 1×k vectors of coefficients corresponding to the k elementsof the k × 1 vector of observable characteristics, X. The superscript on the β’sdifferentiates long-term from short-term nonemployment, allowing the effects ofvarious characteristics to potentially differ by treatment status. The effects ofany stochastic shocks and unobserved characteristics are captured by eri andepi, both of which are assumed to be iid random normal variables.

As θi represents the relative bargaining power, it is constrained to be between0 and 1. I assume there exists some function Θ(·) where:

θi = Θ(αsθDsi + αlθD

li + βsθD

siXi + βlθD

liXi) such that 0 ≤ θi ≤ 1 (5)

5

4 Data

4.1 Survey of Income and Program Participation

The Survey of Income and Program Participation (SIPP) data set collectedby the U.S. census is a true longitudinal survey, that with few exceptions, at-tempts to track all individual sample members over four years.3 The surveybegins by tracking members of households at specific addresses. Each memberis interviewed every four months about each month in the survey resulting inperson-month data. When members of the household move to new addresses,attempts are made to continue following the individual. If a new member joins ahousehold during the survey period, they are also interviewed for as long as theyremain in the sample household. If an original household member moved into anew non-survey household, members of that household are also interviewed aslong as the original survey participants remains living in that household. If alloriginal survey members move out of a household, the new occupants are notfollowed, but an attempt is made to follow the original members at their newaddress.

This paper uses the SIPP survey spanning 2008-2012. This period coversthe Great Recession, which saw a large increase in unemployment and long-term unemployment. The original full data set includes approximately 42,000households consisting of roughly 100,000 individuals. The vast majority of theseindividuals did not experience a non-employment spell during the sample pe-riod. Not all individuals who experienced a period of non-employment returnedto work during the sample period. These individuals are not included in myanalysis as the sample period ends before their rehiring is observed (if it occursat all).

The length of non-employment is calculated as the number of months be-tween reported employment. Individuals who start the sample in a state ofnon-employment are dropped from the data set as the length of their non-employment cannot be determined. The shortest observed spell is 2 months,while the longest is 52. The median length of a nonemployment spell is 5months. The mean is 6.9 months. I define a “long” spell as one that is greaterthan or equal to 6 months, and “short” as less than six months. While this dis-tinction is somewhat arbitrary, it nearly perfectly splits the difference betweenthe median and mean. It is also a length that conforms to the BLS defini-tion of long-term unemployment. Admittedly, this conflates the unemploymentmeasure of BLS with the non-employment measure used here.

Data on wages was collected from the first observation after a period ofnon-employment.4 For hourly employees, the wage rate is reported in the data.For salaried employees, the wage rate is computed using self-reported data onearned income and hours worked.

3Exceptions include people who are institutionalized, live in a military barracks, or moveabroad.

4I also investigated the second wage observation to avoid complications regarding mid-month job starts without any noteworthy differences.

6

The SIPP dataset includes a plethora of individual level data useful for esti-mating a wage determination model. This includes age, gender, race, ethnicity,marital status, education level, job occupational codes, firm industry codes, thelength of time an individual has worked in similar jobs, as well as potentiallyuseful information on other sources of income, be they non-labor, spousal, etc.After numerous specification tests, a parsimonious specification similar to thecanonical Mincer equation was chosen. It includes age, age-squared, maritalstatus, an MSA dummy 5, race 6, union status, education level, and censusregion dummies.

To reduce the effects of schooling and retirement, I restrict the dataset toonly include those between the ages of 15 and 55. Regressions for males andfemales are done separately as is common in the literature. This paper onlypresents the analysis of the male sub-sample.

Table 1 shows the descriptive statistics for the overall data set, by treatmentstatus, and the mean difference between treatment groups. The 10% (and sta-tistically significant) difference in the average wage between treatment groupsmotives this paper. It should be noted that the duration of the nonemploymentspell is measured in months while the duration of potential UI benefits is mea-sured in weeks. Thus, the difference between potential duration of UI benefitsof 4.4 weeks corresponds closely to an additional month of benefits, on average,for the long-term nonemployed. It should be noted that both treatment groupshave potential UI benefit lengths that are much longer (17 and 18 months) thanthe six month distinction separating the short-term and long-term nonemployed.

5This denotes whether a person lives in a Metropolitan Statistical Area, a proxy for urbanvs. rural.

6A binary indicator for non-Hispanic white

7

Tab

le1:

Des

crip

tive

Sta

tist

ics

AL

LM

EN

:N

=45

30

D=

0N

=2764

D=

1N

=1766

Var

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ean

Std

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ev.

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Std

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iff.

Std

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rr.

log

wag

e2.

6411

630.

5034

99

2.6

80929

0.5

24709

2.5

78926

0.4

61696

0.1

020034***

0.0

15265

Non

Em

ple

ngt

h(m

o’s)

6.90

0662

6.40

733.3

8097

1.1

60304

12.4

094

7.3

12491

-9.0

2843***

0.1

41796

Pot

.D

ur.

ofU

I(w

k’s

)75

.954

0821

.391

78

74.2

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21.3

7262

78.6

8686

21.

14011

-4.4

78831***

0.6

4834

age

37.8

2141

9.07

6507

37.5

6693

8.9

17984

38.2

1971

9.3

07792

-0.6

527736***

0.2

76366

mar

ried

0.51

8322

0.49

9719

0.5

35094

0.4

98857

0.4

92073

0.5

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0.0

430216***

0.0

15212

met

ro0.

7856

510.

4104

15

0.7

82562

0.4

12578

0.7

90487

0.4

07076

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079255

0.0

12504

non

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6278

150.

4834

41

0.6

28437

0.4

8331

0.6

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0.0

015967

0.0

14729

un

ion

0.08

9404

0.28

5358

0.0

96599

0.2

95465

0.0

78143

0.2

68472

0.0

184564**

0.0

0869

Ed

uca

tion

Lev

el:

1.H

Sor

less

0.44

2384

0.49

6724

0.4

37771

0.4

96202

0.4

49604

0.4

97595

-0.0

118323

0.0

15133

2.S

ome

Col

lege

0.36

0927

0.48

0323

0.3

56729

0.4

79121

0.3

67497

0.4

8226

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107678

0.0

14633

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0.14

3267

0.35

0384

0.1

41462

0.3

4856

0.1

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0.0

10675

4.G

rad

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rof.

Deg

ree

0.05

3422

0.22

4898

0.0

64038

0.2

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0.0

36806

0.1

88339

0.0

272313***

0.0

0684

Cen

sus

Div

isio

n:

1.N

ewE

ngl

and

0.05

0993

0.22

0009

0.0

52098

0.2

22266

0.0

49264

0.2

1648

0.0

028345

0.0

06703

2.M

idA

tlan

tic

0.10

9934

0.31

2842

0.1

06729

0.3

08825

0.1

14949

0.3

19051

-0.0

082197

0.0

09531

3.E

ast

Nor

thC

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al0.

1642

380.

3705

33

0.1

49783

0.3

56923

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0.3

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3708***

0.0

11276

4.W

est

Nor

thC

entr

al0.

0699

780.

2551

38

0.0

74168

0.2

62091

0.0

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0.2

43786

0.0

107477

0.0

07772

5.S

outh

Atl

anti

c0.

1768

210.

3815

59

0.1

75832

0.3

80746

0.1

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0.3

82932

-0.0

025371

0.0

11625

6.E

ast

Sou

thC

entr

al0.

0580

570.

2338

78

0.0

59696

0.2

36966

0.0

55493

0.2

29004

0.0

042035

0.0

07125

7.W

est

Sou

thC

entr

al0.

1247

240.

3304

42

0.1

32779

0.3

39397

0.1

12118

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15601

0.0

206608**

0.0

10063

8.M

ounta

in0.

0894

040.

2853

58

0.0

9877

0.2

98407

0.0

74745

0.2

63054

0.0

240247***

0.0

08687

9.P

acifi

c0.

1558

50.

3627

53

0.1

50145

0.3

57278

0.1

64779

0.3

71086

-0.0

146344

0.0

1105

8

4.2 A Valid Instrument

Many of the models presented in this paper explore the possibility that long-term nonemployment may be endogenous. In such cases, estimation is greatlyaided by, if not requires, the use of a variable to instrument for long-term nonem-ployment.

The salient requirements of a good instrument are that it must provide asource of exogenous variation in the treatment status without having any directeffect on the outcome variable. In this context, it must be something that canexogenously induce a change in an individual’s nonemployment duration whilehaving no direct effect on wages (other than through the induced change innonemployment duration.) Schmieder et al. (2015) provide ample evidencethat the potential length of unemployment benefits works well as an instrumentfor the duration of nonemployment.

A concern may arise under the observation that a determinant of the ob-served wage is the reservation wage. Not only that, but that a rehiring wageonly exists if a firm’s wage offer exceeds an individual’s reservation wage. Thedefinition of the reservation wage mentioned prior explicitly states that it isbased on the valuation on nonemployment benefits including (but not limitedto) UI benefits. Therefore, if an exogenous change in the length of potential un-employment benefits were to affect the reservation wage it would both directlyaffect the observed wage and whether or not a job match were to even occurin the first place, thus violating the restriction that the instrument only affectthe wage indirectly through induced changes in the duration of nonemployment.While the techniques of Schmieder et al. (2015) cannot directly measure howpotential duration of UI benefits affect the reservation wage, they are able toconvincingly show that the upper bound on the effect is essentially zero (anda negative effect is intuitively unlikely). Furthermore, they show that evidencethat changes in the potential duration of UI benefits does increase the likelihoodof longer durations of nonemployment.

The argument is not that UI benefits play no role in determining the reser-vation wage. Rather, it is that a change in the potential length of those benefitsdoes not. As an example, suppose that UI benefits allow a job searcher to collecta certain dollar amount a month. This dollar amount will affect the searcher’sreservation wage. If the length of eligibility of those benefits were in increase,this may induce a longer job search, but as the dollar amount itself is unchanged,there is no change in the valuation of the reservation wage, other than throughtime-dependency and the induced increased duration of nonemployment.

In a more practical sense, a good instrument must also have enough varia-tion. Under most US-based data sets this would preclude changes in the poten-tial duration of UI benefits from having much practical use as an instrument.Historically, UI benefit length doesn’t change with the sort of frequency neces-sary to allow for the type of exogenously induced variation one needs to identifycausal effects in labor markets. The Great Recession is an exception to this his-torical observation. During the sample period there was a tremendous amountof variation the duration of UI benefits both cross-sectionally (across states)

9

and longitudinally (across time) due to the interaction of state and federal laws,changes in laws (both on the state and federal level), and various labor marketdependent policy triggers for both state and federal laws. As such, the pe-riod of the Great Recession provides us with a historically rare chance to makeuse of potential duration of UI benefits as an instrument for the duration ofnonemployment.

4.3 UI Benefits During the Great Recession

Each state administers separate unemployment insurance (UI) programs withinguidelines established by federal law. The typical maximum length of standardUI benefits in most states is 26 weeks, with some exceptions.7 In 1970 federal lawprovided for payment of extended benefits (EB) during periods of high and risingunemployment in a state.8 This program can add 13 or 20 weeks of additionalbenefits depending on the unemployment rate in each state (and various statelevel policies). In addition to this permanent law, the federal government passedadditional temporary legislation in 2008 in response to the recession. Known asEmergency Unemployment Compensation 2008 (EUC), this program was meantto temporarily provide further weeks of benefits, broken into tiers, dependingon state-level conditions. Initially, it provided up to 13 additional weeks ofpotential benefits, but this was extended to 20 weeks in November of 2008 forstates that met certain labor market criteria. In the years that followed thislaw was expanded upon, extended, and tweaked, resulting in an ever changingsystem of multi-tiered benefits. By the end of 2009, all states were eligible forfirst tier benefits of potentially an additional 20 weeks and second tier benefitsof potentially an additional 13 to 14 weeks (the 2nd tier had previously requiredstates to reach a specific unemployment level before the tier was triggered.) Athird tier was added, adding another 13 weeks to states with a three monthaverage total unemployment rate of at least 6 percent and a fourth tier of anadditional 6 weeks (for a total of 53 from EUC) triggering at an unemploymentrate of 8.5 percent. The EUC program eventually expired at the end of 2013,after the sample period in my data set ends.

What follows is a quick summation of the above. The base level variesby state and also by local unemployment conditions. During the recession,unemployment conditions worsened enough to have the 1970 Extended Benefitslaw kick into effect in some states. Due to the variation in the timing of state-level conditions, EB triggers varied both across states and time. Later, a thirdsource of benefits, the EUC, was passed by the federal government. This lastlaw was extended, revised, and modified numerous times before it’s expirationin 2013. Various versions of the laws had different tiers, with different levels ofextended benefits, and different criteria for when each tier was triggered.

7Montana: 28, Arkansas: 25, Michigan, Missouri, and S. Carolina: 20. Four states, Kansas,Florida, Georgia, and North Carolina may offer less than 26 weeks, the exact number beingdependent upon the state’s unemployment rate. Furthermore, many states have additionalbenefits that extend beyond 26 weeks, depending on state unemployment conditions.

8The Federal-State Extended Unemployment Compensation Act of 1970.

10

To further complicate the matter, the duration of EUC and EB benefitextensions are calculated as a percentage of state-evel benefit durations. Thus,states that enacted laws changing the duration of regular benefits during thesample period resulted in changes to the duration of additional benefits providedvia EB and EUC benefits. During the years 2011 and 2012, Arkansas, Florida,Georgia, Michigan, Missouri, N. Carolina, and S. Carolina all passed legislationreducing the duration of their regular benefits (some to a set number, othersto levels dependent upon unemployment rates), which further decreased thenumber of weeks available through federal programs. Thus, some states saw adecrease in the duration of UI benefits while others saw increases.

The end result is a complicated patchwork of interacting (and ever-changing)set of State and Federal laws, inconsistent across time and states, with variouslevels of dependencies on state level unemployment rates.9 As far as I know, nogovernmental agency (federal or state) provides a definitive record of the maxi-mum potential duration of unemployment benefits from all combined programsacross time. The Office of Unemployment Insurance releases weekly bulletinsregarding the state level trigger status of the various tiers of the EUC and EBprograms.10 With these notices, along with research on state and federal laws,I compiled a data set of the maximum level of potential unemployment benefitsin each state over the sample period. To match the monthly frequency of theSIPP data, I used the first trigger notice bulletin of each month to constructmy data set.

In summation, the maximum duration of benefits in each state is jointlydetermined by three main factors, the state laws, the EB system, and the EUCsystem, all of which may change depending upon economic conditions in thestate, or because the state and/or federal government modified the programduring the relevant time frame. The combination of these multitude of factors isthe source of the required exogenous variation, across both time and geography.

5 Estimation

Equation 1 suggests there are three determinants of the observed wage, anindividual’s self-determined reservation wage (represented by equations 2.3 -2.5), the firm’s determination of the expected level of productivity, and therelative bargaining power of the two. Plugging equations 2.3 - 2.5 into equation1 yields:

9See Whittaker and Isaacs (2013) and Whittaker and Isaacs (2014) for details and a historyof legislative changes to EUC.

10Weekly trigger notice reports for EB and EUC can be found at http://www.oui.doleta.

gov/unemploy/claims_arch.asp

11

wi =(αsrDsi + αlrD

li + βsrD

siXi + βlrD

liXi + eri)

+ [Θ(αsθDsi + αlθD

li + βsθD

siXi + βlθD

liXi)]

× [(αspDsi + αlpD

li + βspD

siXi + βlpD

liXi + epi)

− (αsrDsi + αlrD

li + βsrD

siXi + βlrD

liXi + eri)]

Unfortunately, allowing the relative bargaining power, θi to vary dependingon values of Xi (or some subset of covariates therein), makes estimation diffi-cult. First, the function Θ(·), shown in equation 2.5 is not specified. By theconstruction of the model, it must result in a value of θi must lie between 0and 1. While it is possible to pick a function that meets this criteria (such as aprobit, logit, or something more exotic), we have little to guide us in terms ofwhich to use. Furthermore, even for some arbitrarily chosen function form, esti-mation is problematic. While parameters may be technically identified throughthe nonlinearity of the bargaining power function, in practice, this identificationis likely too weak to be of practical use.

Instead, I proceed with estimation when additional restrictions are added tothe model. In what follows, I estimate the model under a variety of assumptions.

5.1 Invariant Bargaining Power

As mentioned above, one of the more problematic aspects of the wage determi-nation model stems from the function that determines the relative bargainingpower of job seekers and firms. This section greatly simplifies this aspect ofthe model by assuming that bargaining power does not differ by individuals ortreatment status. That is, θi = θ ∀ i. Under this assumption, we can rewriteequation 1 as:

wi = ri + θ(pi − ri) (6)

where ri and pi are defined as in equations 2.3 and 2.4. Note, this can berewritten as:

wi = (1− θ)ri + θpi (7)

5.1.1 Pooled Estimation

In this subsection, I make one further assumption. I assume that the effects ofthe covariates contained in X are independent of treatment status for both thereservation wage function and the expected productivity function. That is, inequations 2.3 and 2.4, I now assume βr = βsr = βlr and βp = βsp = βlp. Nowequation 7 can be rewritten as:

wi = (1− θ)(αsrDsi + αlrD

li + βrXi + eri) + θ(αspD

si + αlpD

li + βpXi + epi) (8)

12

This, in turn, can be expressed as a linear combination of our treatmentstatus and observed characteristics as:

wi = δsDSi + δlDl

i + βXi + ei (9)

where:

δs =(1− θ)αsr + θαsp

δl =(1− θ)αlr + θαlp

β =(1− θ)βr + θβp

ei =(1− θ)eri + θepi

Note that if we assume eri and epi are independent and each normally dis-tributed with a mean of zero, then the linear combination of the two, ei is alsonormally distributed, mean zero.11 As such, equation 9 can be estimated viaOLS if one assumes the treatment status is exogenous. Under the assumption ofendogenous treatment status (that is, if we think treatment status is correlatedwith the error term), estimation can be carried out using two-stage least squares(2SLS), with the potential duration of UI benefits used as an instrumental vari-able in the first stage.

The major drawback of this model is that the underlying parameters ofinterest are not identifiable. Instead, only estimates of their combinations are.Nonetheless, this does allow us, under the given assumptions, to estimate theoverall effect the treatment status and observable characteristics have on therealized rehiring wage, even if we cannot identify the exact mechanism (e.g.,via changes in the reservation wage, expected productivity, or combinationsthereof.)

Estimation results are shown in Table 2.12 The OLS results show a sta-tistically significant 8.2% wage penalty for long-term nonemployment. On theother hand, the point estimate for the 2SLS estimator is smaller (-2.7%) andstatistically insignificant. While the instrument passes the weak identificationtest 13, the 95% Confidence Interval ranges from -31% to 26% and the estima-tion fails to provide much insight. In both estimations, all other covariates arehighly statistically significant, with coefficients having the expected signs andreasonable magnitudes.

5.1.2 Regime Switching Models: Estimation by Treatment Status

One can relax some of the assumptions in the previous subsection in a numberof ways. If we allow for βsr 6= βlr and/or βsp 6= βlp, then the wage determinationmodel will differ by treatment status:

11Admittedly, in this context, independence is a questionable assumption.12Note: The constant is δs and the coefficient for Dl is actually (δl − δs).13Cragg-Donald Wald F statistic is 38.316

13

Table 2: Pooled OLS and 2SLSOLS 2SLSCoeff S.E. Coeff S.E.

Dl -0.08268 0.01353 -0.02713 0.147081age 0.027069 0.007386 0.027883 0.00769age2 -0.00026 9.42E-05 -0.00027 9.96E-05married 0.113786 0.013811 0.116083 0.015078nonhiswhite 0.103833 0.014495 0.103964 0.014496metro 0.069216 0.016994 0.068571 0.017075union 0.366738 0.023378 0.370242 0.025132education:2 0.105059 0.014874 0.105058 0.014873 0.338422 0.020345 0.338402 0.020344 0.549109 0.030373 0.556067 0.035477Census Div.2 -0.1075 0.036445 -0.10825 0.0364893 -0.18304 0.034101 -0.18574 0.0348244 -0.20703 0.038636 -0.20524 0.0389145 -0.12807 0.034193 -0.12792 0.0341876 -0.23952 0.040289 -0.23831 0.0404057 -0.18659 0.035719 -0.18431 0.0362148 -0.12156 0.037259 -0.11808 0.0383649 -0.06824 0.035003 -0.06946 0.035144

cons 1.847258 0.142691 1.811838 0.170502

wli =δl + βlXi + eli if Dsi = 1 (10)

wsi =δs + βsXi + esi if Dli = 1 (11)

where the details of βj , δj , and eji , for j = l, s depends on the assumptionsmade. For example, we can assume both βsr 6= βlr and βsp 6= βlp, and even allowfor θ to differ by treatment status. This would yield:

δs =(1− θs)αsr + θsαsp

δl =(1− θl)αlr + θlαlp

βs =(1− θs)βsr + θsβsp

βl =(1− θl)βlr + θlβlp

esi =(1− θs)esri + θsespi

eli =(1− θl)elri + θlelpi

14

Table 3: OLS - SeparateDs = 1 Dl = 1

lw Coef. Std. Err. Coef. Std. Err.age 0.030117 0.009871 0.021377 0.011001age2 -0.00028 0.000126 -0.0002 0.00014married 0.126269 0.01832 0.090462 0.020844nonhiswhite 0.099228 0.019486 0.106747 0.021419metro 0.073505 0.022541 0.063569 0.025635union 0.363176 0.030006 0.375089 0.037388

education2 0.107709 0.019862 0.098562 0.022253 0.370264 0.027189 0.279741 0.0303914 0.596988 0.037303 0.421774 0.053869

census div.2 -0.07553 0.048367 -0.15663 0.0548653 -0.15461 0.045451 -0.23648 0.0510774 -0.15813 0.050489 -0.29569 0.0596435 -0.07073 0.045184 -0.2249 0.0517896 -0.17939 0.052773 -0.34883 0.0619257 -0.14785 0.046844 -0.25481 0.0547938 -0.10539 0.048388 -0.14167 0.0583679 -0.03862 0.046747 -0.12202 0.052327

cons 1.723221 0.190199 1.987126 0.212399

With different assumptions, the definitions may differ. From an estimationstandpoint, they are all indistinguishable. As in the previous subsection, we can-not separately identify the key underlying parameters. Nor can we say whichare changing across treatment status and which aren’t (other than by assump-tion). This remains a fundamental drawback of the assumption of a constantbargaining power.

If one assumes that the duration of nonemployment is exogenous, the modelcan be estimated via separate OLS regressions for each treatment status. TheOLS regression results are shown in table 3. Once we estimate the model for eachtreatment status, we can predict outcomes for all individuals in each treatmentstatus. By comparing the means we can estimate the average treatment effect.The predicted mean wage for each group, and the difference between them areshown in table 4. Again, wages are around 8% higher for those who did notexperience a long nonemployment spell.

If the treatment status is endogenous, OLS will result in biased estimates.In this case, we need to correct for the selection into treatment status. This canbe accomplished through the use of an endogenous switching regression model.

15

Table 4: OLS ATEVariable Obs Mean Std. Err.Log Wage (Short-term) 4530 2.672917 0.003748Log Wage (Long-term) 4530 2.588722 0.003253diff 4530 0.084196 0.001079

Here, the agent has two regression equations and a criterion function, Di, thatdetermines which treatment status the agent faces:

Dli =1 if γZi + ui > 0

Dsi =1 if γZi + ui ≤ 0

Treatment 1: wli =δl + βlXi + eli if Dli = 1 (12)

Treatment 0: wsi =δs + βsXi + esi if Dsi = 1 (13)

As before, wji , j = l, s is the log wage; Xi and is a vector of weakly exogenousexplanatory variables thought to influence individual wage; Zi is a vector ofcharacteristics that influences the decision regarding the treatment status; andβl, βs, and γ are vectors of parameters. Assume that ui, e

li, and esi have a

trivariate normal distribution with mean vector zero and covariance matrix:

Ω =

σ2u σsu σlu

σsu σ2s .

σlu . σ2l

where σ2

u is a variance of the error term in the selection equation, and σ2s and

σ2l are variances of the error terms in the wage equations. σsu is a covariance

matrix of ui and esi , and σlu is a covariance matrix of ui and eli. The covariancebetween eli and esi is not defined as wsi and wli are never observed simultaneously.

Given the assumptions of the disturbance terms, it can be shown that thelog-likelihood function for the system of equations 13 and 12 is:

lnL =∑i

(Di[lnΦ(ηsi)+ lnφ(esi/σs)/σs]

+ (1−Di)[ln1− Φ(ηli)+ lnφ(eli/σl)/σl])(14)

where Φ is the cumulative normal distribution, φ is a normal density func-tion, and:

ηji =γZi + ρjuji/σj√

1− ρ2jj = s, l

where ρj = σ2ju/σuσj is the correlation coefficient between eji and ui. See

Lokshin and Sajaia (2004) for more details. 14 The model is estimated via

14This paper describes movestay, their STATA command that was used to estimate thismodel.

16

Table 5: MoveStay Reg Results, Z = All X’s plus IVD=0 D=1 SelectionCoef. Std. Err. Coef. Std. Err. Coef. Std. Err.

age 0.040052 0.012451 0.021227 0.01168 -0.06026 0.01994age2 -0.00046 0.000159 -0.0002 0.000149 0.000785 0.000255married 0.1604 0.023189 0.090131 0.022605 -0.13139 0.037395nonhiswhite 0.091896 0.024506 0.106616 0.021607 -0.04791 0.039262metro 0.052324 0.028573 0.063579 0.025506 -0.00255 0.046008union 0.416121 0.038722 0.374541 0.040065 -0.20695 0.065591educ. 2 0.098904 0.025091 0.098466 0.022291 -0.03609 0.040302educ. 3 0.307435 0.034496 0.279155 0.034162 -0.22845 0.05622educ. 4 0.651118 0.049109 0.419839 0.07505 -0.71528 0.087689Census. Div. 2 -0.09076 0.061211 -0.15654 0.054637 0.033524 0.098926Census. Div. 3 -0.18968 0.057398 -0.23611 0.051796 0.144331 0.092545Census. Div. 4 -0.11015 0.064453 -0.29581 0.059425 -0.01458 0.10525Census. Div. 5 -0.06773 0.057308 -0.22495 0.051548 -0.00963 0.092786Census. Div. 6 -0.14141 0.067327 -0.34892 0.061655 -0.02885 0.109335Census. Div. 7 -0.09561 0.059697 -0.25498 0.054708 -0.04168 0.096945Census. Div. 8 -0.03128 0.061994 -0.14198 0.058668 -0.10799 0.10137Census. Div. 9 -0.06574 0.058943 -0.12195 0.052096 0.016779 0.094943UI Benifits 0.00239 0.000612cons 1.214006 0.2401 1.98668 0.211661 0.806417 0.386822

maximum likelihood.I present the results from two estimations. Table 7 shows the results when

the instrumental variable, total potential duration of UI benefits, is the sole vari-able included in the vector Z used in the selection eqution. Table 8 comparesthe predicted mean wages from each regime. We see a 35% decrease in wages re-sulting from long-term nonemployment. While the inclusion of an instrumentalvariable in the selection model is highly helpful, it should be noted that covari-ates in the wage equation may also be used, identified through nonlinearities inthe model. A second estimation is done using all the wage covariates along withthe instrument in the selection equation. That is, the model is re-estimated butwith the Z vector used in the selection equation including not just the instru-mental variable, but also all the variables from the X vector. These estimationresults are shown in Table 5. This dramatically changes the results. A compar-ison of predicted mean wages is shown in Table 6. In this version of the model,it is now the long-term nonemployed who are estimated to have a large wageadvantage of 31%.

5.2 Individual Bargaining Power

While the previous section is informative regarding the effect of long-termnonemployment on the realized wage, it does not provide much insight regard-

17

Table 6: MoveStay ATE, Z = All X’s plus IVVariable Obs Mean Std. Err.Log Wage (Short-term) 4530 2.268115 0.003725Log Wage (Long-term) 4530 2.585045 0.003247diff 4530 -0.31693 0.001355

Table 7: MoveStay Reg Results, Z = IV onlyD=0 D=1 SelectionCoef. Std. Err. Coef. Std. Err. Coef. Std. Err.

age 0.017921 0.009326 0.011662 0.009677age2 -0.00015 0.000119 -0.0001 0.000123married 0.116907 0.017281 0.070453 0.018282nonhiswhite 0.086103 0.01826 0.075976 0.019311metro 0.05854 0.02117 0.053899 0.02238union 0.351337 0.029201 0.291339 0.035815educ. 2 0.094265 0.018745 0.063256 0.019604educ. 3 0.259731 0.029763 0.165942 0.028536educ. 4 0.448066 0.042071 0.272179 0.052073Census Div. 2 -0.08343 0.045546 -0.17211 0.047827Census Div. 3 -0.14361 0.04295 -0.20656 0.044601Census Div. 4 -0.1365 0.047799 -0.27719 0.05229Census Div. 5 -0.07724 0.042578 -0.23821 0.045097Census Div. 6 -0.17284 0.04971 -0.29575 0.053918Census Div. 7 -0.13818 0.044164 -0.26467 0.047686Census Div. 8 -0.09627 0.045594 -0.15881 0.050535Census Div. 9 -0.0578 0.043944 -0.14015 0.045778UI Benefits 0.002277 0.000525cons 1.681535 0.178697 1.640008 0.186186 -0.45279 0.044189

Table 8: MoveStay ATE, Z = IV onlyVariable Obs Mean Std. Err.Log Wage (D = 0) 4530 2.31189 0.003039Log Wage (D = 1) 4530 1.936751 0.002359diff 4530 0.375139 0.001119

18

ing the mechanism by which nonemployment affects wages. This stems fromthe fact that if we assume bargaining power is a constant, equation 1, given theassumptions of equations 2.3 and 2.4 reduces to a linear function of the vectorof covariates, X.

Unfortunately, as previously discussed, allowing the relative bargaining power,θi to vary depending on values of Xi (or some subset of covariates therein), re-sults in a model that cannot be estimated. On the other hand, there are somecharacteristics of a wage determination model with individually determined bar-gaining power that may be useful. Recall the formulations of equations 1 and2:

wi =ri + θi(pi − ri)wi =pi − (1− θi)(pi − ri)

where ri, pi, and θi are as defined in equations 2.3, 2.4, and 2.5 respectively.In each case, the first term on the right hand side represents a linear function ofX and the second represents an interaction of functions, also of X, that resultin a strictly positive number. In essence, we have a standard linear functionplus (minus) some strictly positive term that represents the difference betweenthe theoretical lower (upper) bound of the rehiring wage and the realized wage.Thematically, this is quite similar to a stochastic frontier model, often used inthe estimation of efficiency. That model is as follows:

ln yi = ln f(Xi, β)− Sui + vi

This model usually takes one of two forms. In modeling production ineffi-ciency, y is the firm’s output, X represents a vector of the firm’s inputs, S = 1,and ui represents the inefficiency of the firm’s production process. When S = −1and y represents the costs of the firm, the model can also be used to measure thecost inefficiency of the firm. The production inefficiency version is analogous toequation 2, and the cost version to equation 1.

Using stochastic frontier analysis to estimate models of wage determinationis not a novel idea. Past papers include Ogloblin and Brock (2005), Ogloblinand Brock (2006), Bishop et al. (2007), and Kumbhakar and Parmeter (2009),among others.

One key difference between the wage determination model presented in thispaper and the standard stochastic frontier model is that in equations 1 and 2the strictly positive difference from the lower (upper) bound is a combination ofdeterministic functions of X. In the stochastic frontier literature, this strictlypositive term is typically modeled as a random draw from a one-sided dis-tribution. Commonly chosen distributions include the half-normal, truncatednormal, and exponential distributions. Under the assumption that ui and viare independent, it is relatively straight forward to find the joint-distribution ofεi = (vi + Sui), construct a likelihood function, and estimate the parameters,βj (j = l, s, depending upon if one is estimating equation 1 or 2, and the shape

19

parameters for vi and ui via maximum likelihood.15 Heterogeneity can be in-troduced by making the shape parameters of the chosen distribution for ui afunction of some set of observable covariates thought to influence the inefficiencyterm. As ui in the stochastic frontier framework corresponds to either θi(pi−ri)or (1 − θi)(pi − ri) (depending on the setup), both of which are combinationsof functions of X, it makes sense to allow the shape parameters of the chosendistribution of ui be modeled as functions of X.

A quick aside regarding the parametric assumption of ui: The half-normaldistribution is essentially the absolute value of a mean-zero normal distributionwith the variance term to be estimated. It is this variance that we can allowto be parameterized as a function of covariates. In the exponential model,the mean and variance are both functions of the same underlying estimatedshape parameter. As such, parameterizing the shape parameter on some set ofcovariates allows those variables to affect both the mean and variance of thedistribution of ui. This gives the exponential model more flexibility than thehalf-normal model. The truncated normal distribution is a normal distributionwith mean µ and variance σ2, truncated at zero. The half-normal distributionis essentially a special case of this with both the mean and truncation pointbeing equal to zero. The truncated normal allows for more flexibility than thehalf-normal, but is notoriously volatile as it can be hard to identify the separateeffects of the mean, and the variance on the distribution of the compound errorterm, εi = (vi + Sui). Because of this, allowing each to vary according to someset of covariates is especially problematic during estimation.16

While we cannot estimate directly θi(pi − ri) or it’s individual aspects, allfunctions of X, we estimate a model that assumes a distribution for the term inits entirety and have the shape parameters of that distribution be estimated interms of X. While the underlying parameters of the wage determination modelmay remain unknown this does have advantages over the models of the previoussections. For one, we can now separate the realized wage into two pieces, alower (or upper) bound, and the amount of surplus captured above or belowthat bound.

As the model is estimated according to the joint probability function ofui and vi, ui is never directly observed. Estimates of an individual’s level ofinefficiency are instead found via E[ui|εi]17, the details of which depend onthe chosen distribution for ui. In this regard, it is not purely deterministic.Rather the values of Xi and their associated parameters instead influence theexpected value of a draw from a random distribution. While this method doeshave drawbacks, it nonetheless provides insight into how various characteristicsaffect how much of the potential wage surplus is captured by the firm vs. theindividual.

While it is possible to see how individual characteristics affect the size of thecaptured surplus, condensing the complexity of the surplus negotiation into a

15See Kumbhakar and Lovell (2000) for details.16I follow Stata’s lead and allow only the mean of the distribution to depend on the covari-

ates.17In this sense, a better term would be a prediction for ui, rather than an estimate of.

20

simple efficiency term obfuscates the exact mechanism. One cannot identify andseparate differing scenarios with the same outcome, such as a smaller percentageof a large potential surplus vs. a large percentage of a smaller potential surplus.

One potential source of identification would be to estimate the cost andproduction versions of the model separately (i.e., the stochastic frontier anal-ysis versions of equations 1 and 2). This would allow us to estimate both theupper and lower bounds of the potential realized wage, wp and wr, as well asthe captured surplus. Unfortunately, inherent to data involving wages, this isproblematic. Estimation of stochastic frontier models requires the postulationof the joint distribution f(ui, vi). As a combination of a mean-zero normaldistribution (vi) and a one-sided disturbance term (ui), the joint distributionis, by it’s construction, a skewed distribution. As such, one way to check if astochastic frontier model is appropriate is estimate a model via OLS and checkfor skewness in the residuals. A “cost” stochastic frontier model for equation1 would be appropriate if an OLS estimation of ri (as defined in equation 2.3)resulted in right-skewed residuals. Similarly, a “production” stochastic frontiermodel would be appropriate if an OLS estimation of pi (as defined in equation2.4) resulted in left-skewed residuals. Until this point, both ri and pi have beendescribed as being functions of the same set of covariates, X. As such, OLSregressions of the two functions use the same regressors and regressands. Theirresiduals will be identical (and clearly not skewed in different directions). Inthis case, the residuals are right-skewed. The only way OLS estimations of riand pi will result in residuals of opposite skewness is to have each be func-tions of non-identical sets of covariates. Unfortunately, all reasonable choicesfor covariates (including variables not included in estimations presented in thispaper) always resulted in right-skewed residuals. This may represent a flaw inthe underlying model or limitations of the variable choices in the data set. Or,it may be an artifact of the underlying characteristics of wage data, such as thezero lower bound (wages cannot be negative), or the effects of policies like theminimum wage. Wage data itself is inherently right-skewed, and it should notcome as a surprise that OLS residuals therefore often are too. This means thatonly an estimation of equation 1 is possible. As such, the only parameters of theunderlying model that can be estimated are the coefficients from the reservationwage equation. Doubly unfortunate, out of all possible parameters, these areprobably the least interesting to identify given the research question.

As with the linear regressions of the previous section, models are estimatedboth in the case that the parameters corresponding to our X covariates areidentical across treatment status, and again allowing them to differ by treatmentstatus.

5.2.1 Pooled Stochastic Frontier Analysis

This section estimates the stochastic frontier model version of equation 1 underthe assumption that the parameters corresponding to each variable in X do notdiffer by treatment status. It is akin to the pooled linear model presented earlierin this chapter.

21

Table 9 reports the results under the assumption that treatment status is ex-ogenous, with three sets of parametric assumptions regarding the distribution ofu, that it is half-normal, exponential, and truncated normal. In this estimation,short-term nonemployment is the baseline case, and the coefficient on the treat-ment represents the intercept shift resulting from long-term nonemployment.While coefficients on the estimation of the reservation wage are comparableacross models, the interpretation of coefficients on the shape parameter u arenot, as interpretation differs by parametric assumption, although the signs ofthe coefficients are. 18

Of particular note are the following common features. Treatment status isinsignificant across all parameterizations in the estimation of the reservationwage. Moreover, point estimates are small. There does not seem to be muchaffect of long-term nonemployment on individual’s reservation wages. Regard-less of the precise interpretation of coefficients in the equations for the capturedsurplus, there is a common result that long-term nonemployment yields nega-tive and significant results across all sets of parametric assumptions. For thehalf-normal and exponential models this represents the influence of long-termnonemployment on the variance of u, whereas in the case of the truncated normalmodel, it is the conditional mean. All share a common qualitative interpretationthat long-term nonemployment would reduce the expected value of an individ-ual’s captured surplus. This suggests that long-term nonemployment does notlower the reservation wage (or not by much) of the individual, but rather, thewage penalty is the result of capturing less surplus during the wage negotiationprocess. Granted, this process does not allow us to identify whether the smallersurplus is due to lower negotation power or because the potential surplus itselfwas smaller due to a decline in the expected productivity of the individual.

18In the half-normal, X affects the variance, in the truncated normal, the mean, in theexponential model, both.

22

Tab

le9:

Poole

dS

FA

:E

xogen

ou

sT

reatm

ent

Half

-Norm

Exp

Tr.

Norm

Res

.W

age

Su

rplu

sR

es.

Wage

Su

rplu

sR

es.

Wage

Su

rplu

sC

oeff

.S

.E.

Coeff

.S

.E.

Coeff

.S

.E.

Coeff

.S

.E.

Coeff

.S

.E.

Coeff

.S

.E.

D-0

.00288

0.0

12789

-0.2

4876

0.0

57531

-0.0

1182

0.0

16972

-0.4

2914

0.1

22555

0.0

2193

0.0

13966

-0.1

9755

0.0

36487

age

-0.0

0219

0.0

0704

0.1

15113

0.0

31562

0.0

03381

0.0

09194

0.1

6506

0.0

65313

-0.0

057

0.0

08152

0.0

76218

0.0

20268

age2

3.7

1E

-05

9.0

9E

-05

-0.0

012

0.0

00401

-4.0

1E

-06

0.0

00118

-0.0

0177

0.0

00828

5.4

1E

-05

0.0

00107

-0.0

0076

0.0

00257

marr

ied

0.0

44037

0.0

13276

0.1

98034

0.0

57807

0.0

64754

0.0

17504

0.2

9916

0.1

22402

-0.0

0131

0.0

14977

0.2

16271

0.0

36998

non

his

wh

ite

0.0

36686

0.0

13859

0.1

82633

0.0

61855

0.0

73935

0.0

18347

0.1

57065

0.1

28196

0.0

00847

0.0

15214

0.2

00229

0.0

39423

met

ro0.0

19827

0.0

15814

0.1

86206

0.0

74434

0.0

11468

0.0

21672

0.4

25899

0.1

7859

0.0

1406

0.0

16994

0.1

148

0.0

47611

un

ion

0.2

46016

0.0

28519

0.3

85562

0.1

01995

0.4

73378

0.0

41556

-0.6

2051

0.3

82499

0.1

079

0.0

41251

0.4

11761

0.0

67423

edu

c.le

vel

20.0

28969

0.0

13903

0.2

80626

0.0

63689

0.0

48112

0.0

18995

0.4

4801

0.1

46908

-0.0

0556

0.0

1525

0.2

37934

0.0

4253

30.0

16795

0.0

22458

0.9

98298

0.0

83187

0.0

40407

0.0

2908

1.6

22929

0.1

74572

-0.0

8425

0.0

33733

0.7

21058

0.0

60814

40.0

26188

0.0

40034

1.3

22832

0.1

18949

0.1

33537

0.0

49275

1.9

32234

0.2

21747

-0.2

7997

0.1

11237

1.1

68243

0.1

29566

cen

sus

div

.2

-0.1

0627

0.0

36729

0.0

42804

0.1

53198

-0.1

4199

0.0

47289

0.1

99208

0.3

2504

-0.1

1676

0.0

45364

0.0

02883

0.0

96263

3-0

.09748

0.0

33468

-0.2

9581

0.1

44313

-0.1

5537

0.0

44104

-0.2

7691

0.3

16026

-0.0

5574

0.0

39075

-0.2

5755

0.0

89351

4-0

.13073

0.0

37937

-0.2

4284

0.1

64707

-0.1

63

0.0

49554

-0.3

2085

0.3

59727

-0.1

0816

0.0

4459

-0.2

0343

0.1

02077

5-0

.13246

0.0

34273

0.0

53175

0.1

44128

-0.1

5267

0.0

44503

0.1

14363

0.3

08963

-0.1

201

0.0

41032

-0.0

271

0.0

89597

6-0

.1677

0.0

38677

-0.1

9104

0.1

70508

-0.2

195

0.0

51288

-0.1

4841

0.3

66425

-0.1

2839

0.0

44051

-0.2

2057

0.1

06814

7-0

.11775

0.0

35019

-0.1

6768

0.1

52405

-0.1

3905

0.0

46095

-0.3

1331

0.3

35556

-0.0

7695

0.0

40745

-0.2

2226

0.0

95137

8-0

.0885

0.0

36788

0.0

10068

0.1

57472

-0.1

291

0.0

48311

0.0

85125

0.3

37005

-0.0

4618

0.0

42827

-0.1

4911

0.0

97606

9-0

.08382

0.0

3486

0.1

16809

0.1

47868

-0.1

0987

0.0

45422

0.2

62037

0.3

16815

-0.0

5015

0.0

41306

-0.0

4753

0.0

91428

con

s2.1

091

0.1

32889

-3.9

0457

0.6

11324

2.1

82133

0.1

76259

-6.8

8507

1.2

99715

2.1

86614

0.1

50451

-1.7

912

0.3

98551

23

5.2.2 Stochastic Frontier Analysis by Treatment Status

We can allow for the possibility that coefficients vary by treatment status. Thismay be the case, if, as stated previously, characteristics change over time. Forproductivity related measures, this may true in the case of human capital de-preciation. Furthermore, it is possible that the attributes which may contributeto an individual’s bargaining power change in importance over time. For ex-ample, the value of past experience during the negotiation process may lose it’seffectiveness if too much time has been spent without a job. To capture suchpossibilities, I re-estimate all of the models of the previous assumption sepa-rately by treatment status. Specifically, I estimate the following version of thewage determination equation via stochastic frontier analysis:

wli =αlr + βlrXi + gl(Xi) + vli if Dl = 1

wsi =αsr + βsrXi + gs(Xi) + vsi if Ds = 1

where gj , (j = l, s), represents the captured surplus (as a function of Xi), akinto ui in the stochastic frontier framework and the second term on the right handside of equation 1. The average treatment effect on the reservation wage can befound with E[(αlr + βlrXi)− (αsr + βsrXi)]. The average treatment effect on thecaptured wage is E[g1(Xi)− g0(Xi)], where gj(Xi) = E[uji |εi] for j = l, s.

Under the assumption that treatment status is exogenous, I estimate themodel separately for each treatment group. Results for estimation under thethree distributional assumptions for ui are given in Tables 10, 11, and 12 Coef-ficient estimations for αjr + βjrXi, (j = l, s), are labeled as “Reservation Wage.”The columns labeled “Captured Surplus” represent the estimation of the coef-ficients related to the determination of the natural log of the shape parametercorresponding to the assumed distribution of ui.

Using the above estimates, I calculated the mean reservation wage bothtreatment statuses. The captured surplus is estimated by the average of E[uji |εi]for each individual, where E[uji |εi] is calculated per the assumed distribution

of uji . I summed these together to find the average total log-wage under bothtreatment statuses. These results, as well as the differences are presented inTable 13. The results are not robust to the parameterization of the distribu-tion of uji in the stochastic frontier model. The Exponential and TruncatedNormal models both show a higher average reservation wage for those experi-encing long-term nonemployment, and a smaller amount of captured surplus.The half-normal model predicts the opposite, with a lower reservation wage,but a higher captured surplus. As mentioned previously, the truncated normaland exponential models are both inherently more flexible than the half-normal,allowing for flexibility in both the mean and variance. As such, the directionalconsistency across the two suggests these signs are more likely to be correct.Where the truncated normal and exponential model differ significantly is in theestimated magnitudes of the treatment effects. The exponential model predictsbigger differences between the treatment and non-treatment groups in both

24

Tab

le10

:S

FA

by

Tre

atm

ent

Sta

tus:ui∼

Half

-Norm

al

Lon

g-te

rmN

onem

plo

ym

ent

Sh

ort

-ter

mN

on

emp

loym

ent

Res

.W

age

Su

rplu

sR

es.

Wage

Su

rplu

sC

oef

.S

td.

Err

.C

oef

.S

td.

Err

.C

oef

.S

td.

Err

.C

oef

.S

td.

Err

.ag

e-0

.002

1455

0.0

1035

30.1

05305

0.0

4951

-0.0

04737

0.0

09822

0.1

29822

0.0

42236

age2

0.00

0037

50.0

0013

2-0

.00109

0.0

00626

0.0

000731

0.0

00128

-0.0

0137

0.0

00538

mar

ried

0.02

0436

90.0

1957

0.2

35848

0.0

92578

0.0

676702

0.0

18539

0.1

40268

0.0

7676

non

his

wh

ite

0.02

4303

90.

0207

490.2

38696

0.0

964

0.0

481782

0.0

19137

0.1

31411

0.0

82998

met

ro0.

0249

685

0.0

2353

0.1

32771

0.1

19243

0.0

14938

0.0

21843

0.2

33445

0.0

98753

un

ion

0.16

5001

20.

0418

090.5

95506

0.1

60518

0.3

30298

0.0

40202

0.1

76471

0.1

42961

edu

c.le

vel

20.

0153

354

0.02

0523

0.3

63083

0.1

00271

0.0

43053

0.0

19449

0.2

17642

0.0

85183

30.

0144

134

0.03

2519

0.9

50378

0.1

3155

0.0

101779

0.0

318

1.0

46087

0.1

10176

40.

0299

534

0.06

6107

1.2

11021

0.2

27174

0.0

301044

0.0

51996

1.3

75597

0.1

44136

cen

sus

div

.2

-0.1

7206

350.0

5509

50.1

13533

0.2

42457

-0.0

61245

0.0

50328

-0.0

0038

0.2

02717

3-0

.131

7618

0.0

4940

3-0

.34482

0.2

27919

-0.0

83251

0.0

46569

-0.2

472

0.1

91686

4-0

.179

1973

0.0

5732

5-0

.39777

0.2

72026

-0.0

99368

0.0

51883

-0.1

6461

0.2

13105

5-0

.214

9537

0.0

5099

50.0

51499

0.2

29419

-0.0

71156

0.0

47147

0.0

3714

0.1

89752

6-0

.186

3933

0.0

5664

4-0

.65923

0.2

90342

-0.1

51475

0.0

53991

0.0

17197

0.2

19948

7-0

.191

4592

0.0

5280

3-0

.147

0.2

42608

-0.0

65292

0.0

47923

-0.1

9732

0.2

01325

8-0

.131

7727

0.0

5671

70.1

56719

0.2

56395

-0.0

60481

0.0

49742

-0.0

6863

0.2

04992

9-0

.146

9337

0.0

5237

20.2

0075

0.2

32308

-0.0

4872

0.0

48127

0.0

67647

0.1

9701

con

s2.

1705

620.1

9677

3-3

.94854

0.9

56467

2.1

09362

0.1

84191

-4.2

0917

0.8

19013

25

Tab

le11

:S

FA

by

Tre

atm

ent

Sta

tus:ui∼

Exp

on

enti

al

Lon

g-te

rmN

onem

plo

yed

Sh

ort

-ter

mN

on

emp

loye

dR

es.

Wag

eS

urp

lus

Res

.W

age

Su

rplu

sC

oef

.S

td.

Err

.C

oef

.S

td.

Err

.C

oef

.S

td.

Err

.C

oef

.S

td.

Err

.ag

e0.

0098

160.

0124

110.0

97473

0.0

84451

-0.0

0474

0.0

09822

0.1

29822

0.0

42236

age2

-0.0

001

0.00

0158

-0.0

0093

0.0

01066

7.3

1E

-05

0.0

00128

-0.0

0137

0.0

00538

mar

ried

0.03

2263

0.02

3645

0.3

28475

0.1

61303

0.0

6767

0.0

18539

0.1

40268

0.0

7676

non

his

wh

ite

0.04

5212

0.02

5675

0.3

11856

0.1

70127

0.0

48178

0.0

19137

0.1

31411

0.0

82998

met

ro0.

0320

010.

0286

570.1

92078

0.2

12019

0.0

14938

0.0

21843

0.2

33445

0.0

98753

un

ion

0.24

1595

0.05

6974

0.7

04362

0.2

84243

0.3

30298

0.0

40202

0.1

76471

0.1

42961

edu

c.le

vel

20.

0281

510.

0251

720.4

9048

0.1

78943

0.0

43053

0.0

19449

0.2

17642

0.0

85183

30.

0447

850.0

3744

1.2

63787

0.2

23373

0.0

10178

0.0

318

1.0

46087

0.1

10176

40.

1157

560.0

7899

31.5

28834

0.3

70244

0.0

30104

0.0

51996

1.3

75597

0.1

44136

cen

sus

div

.2

-0.1

8605

0.06

4781

0.1

43514

0.4

02178

-0.0

6124

0.0

50328

-0.0

0038

0.2

02717

3-0

.158

310.

0593

61-0

.47039

0.3

85652

-0.0

8325

0.0

46569

-0.2

472

0.1

91686

4-0

.183

840.

0685

68-0

.66474

0.4

73342

-0.0

9937

0.0

51883

-0.1

6461

0.2

13105

5-0

.217

80.

0608

520.0

08379

0.3

85114

-0.0

7116

0.0

47147

0.0

3714

0.1

89752

6-0

.187

790.

0710

48-1

.19208

0.6

02997

-0.1

5148

0.0

53991

0.0

17197

0.2

19948

7-0

.213

390.

0637

02-0

.20013

0.4

1256

-0.0

6529

0.0

47923

-0.1

9732

0.2

01325

8-0

.152

030.

0686

770.1

78801

0.4

30616

-0.0

6048

0.0

49742

-0.0

6863

0.2

04992

9-0

.152

390.

0621

290.2

43836

0.3

8716

-0.0

4872

0.0

48127

0.0

67647

0.1

9701

con

s2.

0708

850.

2377

17-5

.35197

1.6

30954

2.1

09362

0.1

84191

-4.2

0917

0.8

19013

26

Tab

le12

:S

FA

by

Tre

atm

ent

Sta

tus:ui∼

Tru

nca

ted

Norm

al

Lon

g-te

rmN

onem

plo

ym

ent

Sh

ort

-ter

mN

on

emp

loym

ent

Res

.W

age

Su

rplu

sR

es.

Wage

Su

rplu

sC

oef

.S

td.

Err

.C

oef

.S

td.

Err

.C

oef

.S

td.

Err

.C

oef

.S

td.

Err

.ag

e-0

.008

8733

0.0

1212

50.0

70772

0.0

31729

-0.0

017573

0.0

12185

0.0

77262

0.0

2749

age2

0.00

0109

90.0

0015

6-0

.00075

0.0

00399

-0.0

000161

0.0

00165

-0.0

0073

0.0

00355

mar

ried

-0.0

1266

270.0

2248

10.2

09648

0.0

58924

0.0

140084

0.0

20846

0.1

99224

0.0

483

non

his

wh

ite

-0.0

2015

370.

0237

630.2

59436

0.0

6372

0.0

168148

0.0

20912

0.1

57287

0.0

5119

met

ro0.

0104

276

0.0

2566

40.1

18204

0.0

76525

0.0

16561

0.0

2346

0.1

10089

0.0

61522

un

ion

0.04

6706

80.

0630

660.5

26538

0.1

04954

0.1

853925

0.0

537

0.2

85889

0.0

89553

edu

c.le

vel

2-0

.003

9011

0.0

2328

30.2

3424

0.0

66965

-0.0

093806

0.0

21054

0.2

41966

0.0

5531

3-0

.068

9231

0.0

4869

50.6

34842

0.0

9361

-0.1

113588

0.0

50827

0.7

7921

0.0

83928

4-0

.298

0262

0.2

1598

31.0

88397

0.2

51308

-0.3

039359

0.1

42161

1.2

33007

0.1

63892

cen

sus

div

.2

-0.1

6219

480.0

7103

6-0

.00435

0.1

47561

-0.0

861408

0.0

60515

0.0

06268

0.1

26068

3-0

.059

1018

0.0

6035

5-0

.36743

0.1

37542

-0.0

519482

0.0

52522

-0.1

9321

0.1

16667

4-0

.116

7906

0.0

6842

4-0

.36669

0.1

65029

-0.0

891262

0.0

59671

-0.1

3707

0.1

30578

5-0

.161

2478

0.0

6309

6-0

.12112

0.1

37777

-0.0

729686

0.0

55245

-0.0

0758

0.1

17232

6-0

.130

5359

0.0

6734

1-0

.4972

0.1

90943

-0.1

134174

0.0

59477

-0.1

1756

0.1

34004

7-0

.125

0563

0.0

6391

8-0

.26118

0.1

48363

-0.0

345098

0.0

54052

-0.2

2228

0.1

23594

8-0

.063

6365

0.0

6821

9-0

.14797

0.1

54923

-0.0

342526

0.0

56992

-0.1

3607

0.1

26432

9-0

.113

5794

0.0

6712

9-0

.0256

0.1

43301

-0.0

043704

0.0

54433

-0.0

6868

0.1

18603

con

s2.

2869

640.2

2915

3-1

.7119

0.6

31028

2.0

98982

0.2

17735

-1.8

8464

0.5

33868

27

Table 13: SFA Treatment Means and DifferencesHalf-Normal Long-term Short-term DifferenceRes. Wage 2.055146 2.09615 -0.041Capt. Surp. 0.581744 0.548996 0.032748Total LW 2.63689 2.645146 -0.00826

Exponential Long-term Short-term DifferenceRes. Wage 2.230686 2.09615 0.134536Capt. Surp. 0.398026 0.548996 -0.15097Total LW 2.628712 2.645146 -0.01643

Trunc. Normal Long-term Short-term DifferenceRes. Wage 1.972752 1.968164 0.004589Capt. Surp. 0.665485 0.674849 -0.00936Total LW 2.638237 2.643013 -0.00478

reservation wage and captured surplus, albeit, two effects that nearly cancel outin the overall effect on wages. The truncated normal model predicts smallertreatment effects on both the reservation wage and the captured surplus, andan even smaller overall effect on wages. All three models predict the long-termnonemployed to receive a lower total wage, with a wage penalty ranging from-0.4% to -1.6%.

5.2.3 Endogeneity in Stochastic Frontier Analysis

As with the previous estimations under the assumption of invariant bargainingpower, it is possible that treatment status is endogenous. Once again, this maymanifest itself in two ways. If we regard treatment status as an intercept-shiftingvariable that does not affect the returns to other characteristics, we can proceedto re-estimate the pooled stochastic frontier model attempting to compensatefor any bias caused by the endogeneity of our binary treatment status variable.While such estimation is routine in the case of simple linear models (e.g., 2SLSand it’s equivalents), it is not applicable in non-linear models. While versionsof 2SLS are well-known for many common non-linear models such as the probitmodel, there does not currently exist a true consensus for the equivalent inthe stochastic frontier setting. In what follows, I discuss the current state ofresearch in this area.

Tran and Tsionas (2015) and Amsler et al. (2015) present a possible methodfor when one of the regressors in the production function (the reservation wagefunction, in the context of this paper) is correlated with the two-sided stochasticnoise component, and also, possibly with the one-sided error term (the capturedsurplus in the context of this paper.) Their method is analogous to the GMMequivalent to 2SLS (aka IV-GMM) in the standard linear setting. Recall thatunder the normal assumptions of OLS the GMM equivalent is to estimate themodel based on the moment condition E(Xiei) = 0, where ei is the idiosyncratic

28

error term in a standard linear regression of the form yi = Xiβ + ei, and Xi

are assumed to be exogenous. If this assumption is invalid and Xi are corre-lated with the error term, such that E(Xiei) 6= 0, then estimation by GMM (orits OLS equivalent) will result in biased estimates for β. If there exists someinstrumental variable (Zi) that is correlated with Xi, but has no direct effecton Yi (other than through Xi), that is uncorrelated with the error term, unbi-ased results can proceed via GMM using the moment condition E(Ziei) = 0.This methodology becomes more complicated in the stochastic frontier analy-sis setting due to the nature of the compound error term that combines thestandard two-sided stochastic noise term with a one-sided inefficiency term, theexact nature of which depends on the assumed distribution of the one-sidederror term. Nonetheless, it is relatively straight forward to construct analogousmoment conditions in the stochastic frontier setting. The standard estimationtechnique of stochastic frontier models involves the construction of a likelihoodfunction for the compound error term. The first order conditions of that like-lihood function can be used as moment conditions for an equivalent estimationvia GMM. Augmenting these moment conditions in a way analogous to thestandard linear case is relatively straight forward. Unfortunately, estimation ofthe resulting GMM model is computationally difficult, being sensitive to initialvalues, misspecification, among other things.

Amsler et al. (2015) and Karakaplan and Kutlu (2015) discuss a way toimplement a methodology similar to the LIML approach in the simple linearmodel to a stochastic frontier analysis setting. This methodology allows forendogenous regressors to appear in both the production function (here, reserva-tion wage function), and a determinant of the shape parameter for the one-sidederror term. This model requires less assumptions and allows for more flexibilitythan those listed above. 19

While not presented in the context of stochastic frontier analysis, Abadie(2003) proposes a method to correct for endogenous binary treatment regres-sors through the creation of observation-specific weights that can be used toweight observations in a maximum likelihood model. The resulting weights arenot typical weights (i.e., not proportional or frequency weights), and, in fact,often take on negative values. While Abadie (2003) shows that the presence ofnegative weights does not prevent the existence of a solution to the maximiza-tion problem, it is nonetheless computationally difficult. Chen, Hsu, and Wang(2014) use this method in the context of a stochastic frontier model with endoge-nous selection. They find it computationally easier to estimate an equivalentGMM model based on the first order conditions of the likelihood function. Thismethod requires the existence of a binary instrumental variable correspondingto the binary treatment variable. While such a binary variable is theoreticallyeasy to construct with the continuous instrument at my disposal 20, the result-ing binary instrument is quite weak. My attempts at estimating a weighted

19Karakaplan and Kutlu have made their model available as a Stata command. Estimatingthe model is computationally difficult and has yet to yield results for my model and data.

20E.G., Zi = 1 if potential UI benefit duration is longer than average potential benefitlengths for individual i, 0 otherwise.

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version of my model, both via ML and GMM failed.It should be noted that the context for the original paper, Abadie (2003) ,

was to correct for an endogenous regressor, Chen et al. (2014) use the weights inthe context of endogenous selection, estimating the two treatment statuses sep-arately. This corresponds to the endogenous regime switching model presentedearlier in this paper. This allows for the effects of the various determinants ofthe model to vary by treatment status. Endogenous switching in the contextof stochastic frontier analysis is also discussed in Lai (2015) . His paper uses amethodology similar to the FIML version of a Heckman selection model. 21

Others have proposed Bayesian methods and copula approaches. Such tech-niques have not (yet) been explored. Unfortunately, for all the methods outlinedabove, estimates have been elusive. Thus far, none of the outlined techniqueshave yielded estimation results. Exploring the use of a stochastic frontier modelboth with endogenous regressors, and endogenous selection remains an area forfuture exploration.

6 Conclusion

The purpose of this paper is to determine the effect of long-term joblessnesson rehiring wages. I estimated many versions of a wage determination func-tion. Under the assumption that the duration of nonemployment is exogenous,models that assumed that nonemployment duration only caused an interceptshift in the wage determination model resulted in an 8% wage penalty for thelong-term nonemployed. Under the assumption that long-term nonemploymentrepresented a regime change in the wage determination model, the effect wasalso found to be around -8%. For models that assumed that the duration ofjoblessness was endogenous, the estimations resulted in both positive and neg-ative effects, but were never statistically significant. As such, while it’s clearfrom the data that the long-term nonemployed do have lower rehiring wagesthan those who are jobless for shorter periods of time, we cannot say with muchcertainty if the duration of nonemployment has any affect on rehiring wages, orif the observed differences are instead the results of observed and unobserveddifferences between the two groups of job-seekers.

A more complicated model of wage determination that separated the wagedetermination process into a function of the job-searcher’s reservation wage,their expected productivity, and a negotiation process between the two was alsopresented. Estimation of this model in full is problematic due to the identifi-cation difficulties of these various influences. I explored the use of a stochasticfrontier model as a way to capture salient features of this wage determinationmodel. While I discussed many potential methods one could use when the du-ration of nonemployment is endogenous, the computational difficulties of thesenew techniques made results elusive. Estimation was done under the assump-tion of the exogeneity of nonemployment duration. This estimation was shown

21Dr. Lai was gracious enough to share his estimation code with me. Unfortunately, dueto computational and technical difficulties, I was unable to estimate the model.

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to be sensitive to the parametric assumptions of the model. Common to allparametric assumptions was the negative effect of nonemployment on the real-ized rehiring wage. This effect was smaller than in the linear models, typicallyaround 1% +/- .5%. Results for the components of the rehiring wage, withregard to the effects on the reservation wage, or the amount of the wage surpluscaptured during negotiation were inconsistent across parametric assumptions.

Overall, it is difficult to say with much certainty what, if any, effect long-term nonemployment has on the rehiring wages of those re-entering employment.While the majority of evidence suggests that a negative effect is more likely, theevidence is not compelling, nor can one rule out the possibility of no effect, oreven a positive effect. As long-term nonemployment remains a concern in theeconomy, and as re-hiring wages may potentially put workers on certain wagegrowth paths with potential long-run effects, it remains a worthwhile topic forfuture research.

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