Arnau - WageandEmploymentGapsovertheLifecycle– TheCaseofBlackandWhiteMalesintheUS · 2019. 4....

Wage and Employment Gaps over the Lifecycle –The Case of Black and White Males in the US

Christopher Rauh∗

University of Montreal, CIREQ

Arnau Valladares-Esteban∗

University of St.Gallen

April, 2018

Abstract

In the US economy, black males on average receive lower wages than their white counterparts.This difference in wages increases over the working life. At the same time, the probability of beingemployed is lower for black than for equally educated white males. Notably, the black-white gap inemployment is almost constant over the lifecycle. These two facts suggest that the determinationof the earnings gap is related to on-the-job human capital accumulation. We propose a modelof on-the-job human capital accumulation with labor market frictions to quantitatively assesshow much of the black-white earnings gap can be accounted for by differences in employmentprobabilities versus pre-market factors. Conditional on education, we find that differences inemployment probabilities between blacks and whites account for 26% of the aggregate laborearnings gap over the working life. Together with differences in the education distribution,employment probabilities can explain almost half the gap.

Keywords : Inequality; Lifecycle; Racial gap; Human capital; Wage gap; Incarceration.

JEL Codes : J15, J24, J31, J64.∗E-mail: [email protected] and [email protected]. We thank Jan Grobovšek, Nezih

Guner, Rafael Lopes de Melo, Brendon McConnell, José V. Rodríguez Mora, Ludo Visschers, and conference andseminar participants at the SAEe Bilbao, EEA Lisbon, Swiss Macro Workshop, Banco de España, University ofGlasgow and University of St.Gallen for their comments and suggestions. All errors are ours.

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1 Introduction

Inequality is a major concern across the globe in general as well as in the US more specifically.1

Today, 50 years after the civil-rights movement, the racial earnings gap remains. Also the gender gaphas proven resilient to 100 years of female suffrage. However, a less studied fact is that both the racialand gender gap do not only exist in terms of earnings, but also in terms of employment. An even lessstudied fact is the combination of the two, i.e., how the employment gap might be feeding into theearnings gap. In this paper, we propose a model with on-the-job human capital accumulation andlabor frictions, which we apply to the case of the racial gaps amongst males in the US.

In the US economy, black men receive lower wages than their white counterparts even withineducational categories. For instance, using tax records, Chetty, Hendren, Jones, and Porter (2018)document that even when conditioning on parental income and neighborhood fixed effects, i.e. precisecharacteristics of socio-economic conditions during childhood, black males earn less than white malesduring adulthood. A large part of the literature has tried to assess whether the gap can be accountedfor by other observable characteristics which include proxies for ability and schooling quality. Theconsensus tends to be that there is a significant proportion of the gap in wages that cannot beexplained by observables.2 Another relevant difference in labor market outcomes between black andwhite men is the disparity in employment rates. Black men present a lower employment rate than theirwhite counterparts for all levels of education. This gap cannot be fully accounted for by observableseither.3

When looking at earnings and employment gaps over the lifecycle, the differences present a strikingpattern. While the gap in earnings increases over the lifecycle, the gap in employment is almostconstant. These two facts suggest that the evolution of the earnings gap could be related to on-the-job human capital accumulation. At the beginning of the working life, after formal education iscompleted, the gap in employment implies that white men have more opportunities to accumulatehuman capital on the job than black men. Hence, the gap in earnings increases with age. On topof the lack of opportunities to learn on the job, the gap in employment during the working life alsoimplies that black men have less chances to reap the payoff of any given investment in human capital,thereby reducing incentives to invest. Hence, the optimal decision for a forward looking individual isto invest less in human capital.

In this paper, we assess how much of the black-white earnings gap can be accounted for bydifferences in employment probabilities versus pre-market factors. The model relies on the Ben-Porath (1967) structure of human capital accumulation as in Huggett, Ventura, and Yaron (2006,

1For instance, a recent opinion poll by the Pew Research Center documents that nearly half of Americans considerinequality to be a ‘very big problem’, while concerns in Europe tend to be even higher. See http://www.pewresearch.org/fact-tank/2013/11/15/the-global-consensus-inequality-is-a-major-problem/.

2See Neal and Johnson (1996) and Lang and Manove (2011) for discussions.3See Ritter and Taylor (2011).

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2011), while adding labor market frictions that allow us to assess which labor market transitionsare relevant for the gap in earnings.4 We calibrate the model to replicate average earnings of blackand white males disaggregated by level of education over the lifecycle. We perform counterfactualsimulations to determine how much of the gap in earnings can be accounted for by differences inemployment probabilities between blacks and whites. We find that, conditional on the educationdistribution observed in the data, differences in employment transition probabilities account for nearlyone fifth of the total earnings gap over the working life. Amongst transition probabilities, we findthat in particular differences in transitions from employment to out of the labor force are the largestcontributor to the racial earnings gap. From a policy perspective, assuming we are concerned aboutthe racial earnings gap, the implication is that we should not only focus on disparities in hiring, whichattract most of the public interest, but maybe in particular on differences in separation rates.

The on-the-job human capital accumulation mechanism of our paper also creates a link to thegrowing literature looking at scarring effects of non-employment.5 Using administrative tax records,Guvenen, Karahan, Ozkan, and Song (2017) document that one year of non-employment is associatedwith a 50 to 120 log points reduction in earnings the following year. The average earnings lossesgenerated by our model one year after a full year of non-employment are between 60 and 120 logpoints and also exhibit a similar pattern by previous earnings, that is, earnings losses are greatest atthe bottom of the earnings distribution.6 Moreover, the setting of our model allows us to disentanglethe role of opportunities versus incentives to invest in human capital on-the-job, i.e. somebody withouta job cannot learn on-the-job and somebody without a job in the future will not want to invest inlearning in the present. We find that incentives and opportunities are complements when it comesto explaining the racial wage gap, namely, the sum of the two experiments individually explainsless of the gap than an experiment in which both are equalized. In general, opportunities play aquantitatively more important role than incentives. Finally, in accordance with the Micro- (e.g.,Cunha, Heckman, and Schennach 2010) and Macro-literature (e.g, Huggett, Ventura, and Yaron2006, 2011) emphasizing the importance of skill accumulation before entering the labor market in

4While Jarosch (2015) creates a model with search and matching dynamics to model frictions, our model exogenouslyimposes all labour market states and prison. However, in his model human capital evolves stochastically while in oursit develops according to investment decisions of optimizing agents.

5There is also a large literature looking at the scarring effect of entering the labor market during a recession (e.g.,Oreopoulos, Von Wachter, and Heisz 2012) or mass lay-offs (e.g., Jacobson, LaLonde, and Sullivan 1993, Couch andPlaczek 2010). However, the aforementioned literature is more concerned with cyclical patterns, while we take alifecycle perspective of different demographic groups in order to gain a better understanding of average patterns.

6While our model does generate persistence in scarring effects, they are not as long-lasting as documented byGuvenen, Karahan, Ozkan, and Song (2017) and nearly vanish after five years, except for at the bottom and uppertail of the earnings distributions where a mild scar remains. One reason why the model is not able to generate theobserved persistence is that labor market transition rates are independent of human capital or unemployment history,and therefore prolonged unemployment spells do not further reduce job finding probabilities. However, job findingsrate have been shown to depend on duration (e.g., Van den Berg and Van Ours 1996, Ahn and Hamilton 2016, Kroft,Lange, Notowidigdo, and Katz 2016, Morchio 2017).

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general, and its significance for the racial earnings gap specifically (Neal and Johnson 1996; Carneiro,Heckman, and Masterov 2005a,b), we find that the levels of human capital at labor market entry area major factor explaining almost three quarters of the racial earnings gap.

This paper is also related to the extensive literature that looks at possible explanations of theblack-white gap in earnings.7 Eckstein and Wolpin (1999), Bowlus and Eckstein (2002), Fryer, Pager,and Spenkuch (2013), Decreuse and Tarasonis (2016), and Borowczyk-Martins, Bradley, and Taraso-nis (2017) use search and matching frameworks with taste and/statistical discrimination to explain theblack-white gap in earnings and employment.8 More specifically, Decreuse and Tarasonis (2016) andBorowczyk-Martins, Bradley, and Tarasonis (2017) split males into two levels of education, collegesvs. non-college, focus on two states of the labor market, employed and unemployed, and transitionsbetween these states are taken as independent of age. Given that labor force participation is relativelylow amongst black males, we add the third state, i.e. out-of-the labor force, and non-constant tran-sitions by age, two ingredients that are particularly important when taking a lifecycle perspective.Moreover, given that high school completion is considerably lower amongst black males comparedto white males, and labor market transitions and outcomes improve substantially with high schoolgraduation, a more granular view on education allows us to provide deeper insights. Fryer, Pager, andSpenkuch (2013) estimate the extent of statistical discrimination using detailed longitudinal data fromNew Jersey on job search behavior and job offers received. While their approach provides advancedidentification concerning transitions into employment, it ignores potential differences in transitionsout of employment.9 Moreover, their approach requires rich longitudinal information which is rarelyavailable in that form and ignores the lifecycle perspective. Instead, we document how employmentand wage gaps evolve over the working life and assess the role of human capital accumulation onthe job to reconcile the patterns observed in these two outcomes while explicitly taking into accounttransitions in and out of employment.

Wu (2007) estimates a structural model based on the Ben-Porath (1967) structure of humancapital accumulation to address the gender and race gap over the lifecycle. Our approach in additionhas labor market frictions and transitions, which Wu (2007) proxies through the rate at which humancapital dissipates. Therefore, we can isolate the contribution of labor market transitions on earnings

7See Charles and Guryan (2011) and Lang and Lehmann (2012) for comprehensive reviews of the literature. SeeBayer and Charles (2017) for the historic evolution of the earnings gap from 1940 until today.

8In contrast to these approaches we do not posit a theory of discrimination. This does not mean we claim dis-crimination might not play a role. Discrimination could well be a reason behind differential transitions in and outof employment. For instance, Bertrand and Mullainathan (2004) find in a field experiment that applications withtypical names of white males receive 50% more callbacks for interviews than applications with names found relativelymore amongst black males. Non-discrimination related explanations include differences in networks, and consequentlyjob referrals (Holzer 1987, Tenev 2017). See Charles and Guryan (2008, 2011) for the quantitative importance ofdiscriminatory tastes.

9Similarly, Eckstein and Wolpin (1999) focus on differences in (unobserved) offered wages and Bowlus and Eckstein(2002) in the frequency of job offers.

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through counterfactual simulations. Another difference is that we include different levels of educationin our analysis, which has important implications for the decomposition as individuals with differentlevels of education exhibit stark differences in earnings profiles, i.e. the higher the level of educationthe steeper the rise in earnings in the beginning of the lifecycle.

Finally, none of the previously mentioned literature attempting to explain the racial earningsgap takes into account a frequent episode for black males, in particular those with lower levels ofeducation: incarceration. Pettit and Western (2004) document that 21% of black males spend timein prison at some point, while Chetty, Hendren, Jones, and Porter (2018) document that 10.3% ofblack men aged 27-32 and 21% of those born to the lowest-income families are in prison on a givenday. Therefore, in our model individuals transition in and out of a fourth state, prison.10 We findthat in particular for black high school drop outs, incarceration is a considerable factor accountingfor one quarter of the racial earnings gap.11

In summary our aim is two-fold: First, we look at the black-white gaps from a lifecycle perspectiveand provide a set of facts than can shed light on the potential determinants of the gaps. Second, wehighlight a mechanism, namely human capital accumulation on the job, that is quantitatively relevant.The fact that one actually needs a job to learn on the job seems to have been largely overlooked bythe existing literature. More generally speaking, our contribution is a model which allows for thedecomposition of lifecycle earnings gaps under the consideration of labor market frictions. Thisapproach can be easily extended or adapted to study the evolution of other earnings gap, such as thegender gap.

The paper proceeds as follows: In Section 2, we document facts on earnings, and labor marketstocks and transitions. In Section 3. we specify the model with on-the-job human capital accumulationand labor frictions. In Section 4, we present the chosen parameters and model fit. In Section 5, weconduct counterfactual experiments to understand the drivers of the racial earnings gap, while Section6 summarizes our main findings and discusses future venues of research.

2 Empirical Facts

In what follows, we document hourly earnings and labor market rates by race over the lifecycle. Wereport both the within-race averages as well as the figures broken down by level of education. Whenwe segment by education, we consider four exclusive categories of educational attainment: (i) high

10For the sake of completeness, we actually have a fifth state, i.e. death, as black males face higher mortality ratesthan white males even for the same level of education.

11This is consistent with Waldfogel (1994) and Western (2006) who find that incarceration reduces individuals’earnings. In our model the additional impact of anticipated incarceration on earnings is that it exacerbates its negativeeffect as it reduces incentives for human capital investment ex-ante. Michaud and Guler (2018), using a dynamic Macromodel, also find that incarceration reduces subsequent earnings. However, their approach does not address the racialincarceration and earnings gap.

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school dropouts, (ii) high school graduates, (iii) some college but no college degree, and (iv) collegegraduates. In Appendix Table B.1 we present the population distribution across race and education.On average, white males have achieved higher levels of education than black males.

In order to approximate labor market rates and transitions, and lifecycle earnings, we use theCurrent Population Survey (CPS) Merged Outgoing Rotation Group (MORG) from 1994 until 2016.We restrict our sample to black and white non-hispanic, US-born males aged 23 to 60. We thenapproximate life-cycle profiles for each level of education separately using a polynomial of degreethree in age while controlling for state, cohort, and year dummies.12 Moreover, we include a racedummy and interact this dummy with the age polynomial. In the following, we present lifecycleprofiles as predicted by the age polynomial, race and the interaction thereof.

2.1 Mean hourly wages

In Figure 1, we see mean hourly wages across black (solid line) and white (dotted line) males. Thegap already exists upon entry into the labor market and increases over the following years before itnarrows slightly towards the end of the lifecycle.

Figure 1: Hourly wages over the lifecycle.

25 30 35 40 45 50 55 60

Age

8

10

12

14

16

18

20

22

Notes: CPS MORG 1994-2016. The solid line represents black men, while the dotted line is for white men,23-60 years old. The dollar amounts correspond to real USD in 2017.

12See Appendix A for the details.

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The previously presented gap could merely be an artifact of the differing educational distributionsacross race as white males tend to achieve higher education levels leading to higher average earnings.In order to rule out this argument, we break the hourly wage gap down by level of education andpresent the lifecycle trajectories in Figure 2. What we see is that even within every group defined bylevel of education said pattern holds, i.e. there exists an initial gap which increases upon entry intothe labor market. Moreover, we find that not only wage levels but also wage growth is steeper forboth blacks and whites with higher levels of education.

Figure 2: Hourly wages over the lifecycle by education group.

(a) Less than high school

25 30 35 40 45 50 55 60

Age

8

10

12

14

16

18

20

22

(b) High school graduates

25 30 35 40 45 50 55 60

Age

8

10

12

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20

22

(c) Some college

25 30 35 40 45 50 55 60

Age

8

10

12

14

16

18

20

22

(d) College and beyond

25 30 35 40 45 50 55 60

Age

8

10

12

14

16

18

20

22

Notes: CPS MORG 1994-2016. The solid line represents black men, while the dotted line is for white men,23-60 years old. Gray areas represent 95% confidence intervals. The dollar amounts correspond to real USDin 2017.

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2.2 Labor market and prison

Following the documentation of the wage gap, we now turn our attention to participation in the labormarket. In Figure 3 we show the aggregate employment, participation, unemployment, and prisonlifecycle profiles for black (solid line) and white (dashed line) males. In panel 3a we see that theemployment gap is about 20 percentage points at age 23 and remains fairly stable across the entirelifecycle. We observe a very similar pattern for participation rates in panel 3b. Consequently, the gapin unemployment also has to persist over the lifecycle, as can be seen in panel 3c. However, in relativeterms this gap is most pronounced upon entry into the labor market and narrows continuously overthe course of the lifecycle. Finally, in panel 3d we see the stark difference in terms of incarcerationrates between black and white males. While less than 1% of white males are held behind bars at anygiven age, for black males the incarceration rate peaks at almost 10% around age 30.

Figure 3: Labor market and prison rates.

(a) Employment

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(b) Participation

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

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1

(c) Unemployment

25 30 35 40 45 50 55 60

Age

0

0.2

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1

(d) Prison

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

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1

Notes: CPS MORG 1994-2016. The solid line represents black men, while the dotted line is for white men,23-60 years old. The employment, participation, and unemployment rates are computed according to theirstandard definition. The prison rate displays the share of each race group in prison.

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In order to rule out that these gaps are only driven by differing distributions across levels of edu-cation, we present employment (Figure B.1), participation (Figure B.2), unemployment (Figure B.3),and incarceration (Figure B.4) rates by level of education for each race in the Appendix. While thereare differences both in the levels as well as the evolution of gaps across educational categories, theyexist for all of them.

Transition probabilities

Underlying these differences in stocks, are differences in labor market transitions. In Figure 4 wepresent lifecycle profiles for transition probabilities across employment (E), unemployment (U), andout of the labor force (O) by race. In the top row displays transition probabilities from the state E, inthe middle from U, and in the bottom from O. It becomes apparent that black males are less likely tokeep and find a job. The likelihood ratios of transitions into state O are particularly striking, as blackmales are much more likely to transition into this sticky state. We show in Appendix Figures B.5,B.6, B.7, and B.8 that these relationships tend to hold for each level of education as well. Therefore,the aggregate gap does not only result from differences in the education distributions across race.

In Appendix Figure B.9, we present probabilities for males by race and education to transitioninto prison over the lifecycle, which we compute following a three-step approach similar to Pettitand Western (2004) and discussed in further detail in Caucutt, Guner, and Rauh (2016). Transitionsout of prison are equal across race and education as the average time spent in prison is three years.Therefore, in a given year (month) an individual faces a 66.7% (97.2%) probability of remaining inprison if incarcerated.

Finally, we also include differences in mortality rates by race and education using data fromMasters, Hummer, and Powers (2012), as black males face higher mortality rates and consequentlya shorter expected lifespan might also reduce incentives to invest in human capital. The rates arepresented in Figure B.10 in the Appendix.

Now that we have documented the facts about lifecycle-earnings profiles and labor market tran-sitions and stocks, in the following section we propose a model linking human capital accumulationwith labor market frictions to gauge the importance of different transitions on the racial earningsgap.

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Figure 4: Labor market transitions.

(a) EE

25 30 35 40 45 50 55 60

Age

0.8

0.85

0.9

0.95

1

(b) EU

25 30 35 40 45 50 55 60

Age

0.02

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0.1

(c) EO

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(d) UE

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(e) UU

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(f) UO

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(g) OE

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(h) OU

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(i) OO

25 30 35 40 45 50 55 60

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0.7

0.75

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0.85

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0.95

1

Notes: CPS MORG 1994-2016. The solid line represents black men, while the dotted line is for white men,23-60 years old.

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3 The Model

We modify the Ben-Porath (1967) model in Huggett, Ventura, and Yaron (2006) to introduce hetero-geneity in race and education, as well as to allow for exogenous labor market frictions, imprisonment,and differences in survival probabilities. Time is discrete and the working life of an agent consists ofN periods. At the beginning of his working life, each agent is characterized by his race (g), level of ed-ucation (e), learning ability (a), learning elasticity (α), and initial level of human capital (h1). Whilehuman capital evolves endogenously over the working life, we assume that race, level of education,and learning ability remain constant. In each period j ∈ [1, N ], an agent’s state (s) can be: employed(E), unemployed (U), out of the labor force (O), or in prison (P ). The transition probabilities acrossstates are exogenous and given by the transition matrices:

Πg,ej (s′|s) =

E U O P

E πEEg,ej πEU

g,ej πEO

g,ej πEP

g,ej

U πUEg,ej πUU

g,ej πUO

g,ej πUP

g,ej

O πOEg,ej πOU

g,ej πOO

g,ej πOP

g,ej

P πPEg,ej πPU

g,ej πPO

g,ej πPP

g,ej

(1)

where πss′g,ej denotes the probability of an agent of race g, education level e, alive in period j totransit from life state s ∈ {E,U,O, J} to life state s′ ∈ {E,U,O, J} in the following period.

Agents seek to maximize the present value of earnings over their working life. The value functionof an alive agent of race r, education level e, at period j, is given by:

V g,ej (h, s; a) = max

l,h′I(s) · wh(1− l) + (1− πDg,ej )

1

1 + r

(∑s′

Πg,ej (s′|s)V g,e

j (·))

(2)

subject to h′ = h(1− δg,e) + a(hl)αg,e

(3)

l ∈ [0, 1] (4)

I(s) =

1 if s = E

0 otherwise.(5)

Equation (2) states that the value of earnings in the current period is given by the product ofthe wage rate (w), the current level of human capital (h), the time allocated to work (1− l), and anindicator function (I(s)) which equals 1 for employed agents and 0 for agents in all other life states.That is, only employed agents are able to sell their human capital in the market and obtain earnings.Note that, given the assumption of linear utility, any transfer to non-employed agents would notaffect the policy functions derived from the maximization problem. Hence, the nature of the problem

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would not change if a unemployment benefits (or similar) would be added to the model.Agents discount the future at rate (1− πDg,ej ) 1

1+r, where r denotes the exogenous interest rate of

the economy and πDg,ej is the exogenous probability of death for an agent of race g, education levele, alive in period j. The accumulation of human capital for the next period is given by equation (3).The amount of time invested in human capital is denoted by l. If an agent invests no time in humancapital (l = 0), his human capital depreciates at a constant rate δ.

In order to increase the stock of human capital next period, the agent needs to choose a levelof investment in human capital that offsets depreciation. The learning ability parameter a and theparameter α control the productivity of investments in human capital. For any level of current humancapital, agents with higher learning ability need to devote less time to human capital accumulationthan agents with lower learning ability to achieve any given increase in human capital next period.Non-employed workers suffer human-capital losses because human capital cannot be acquired withoutemployment. We set the terminal value of working life to zero.

The solution of an agent’s problem can be represented using a policy function which describeshow much time an employed agent devotes to investing in human capital each period, denoted bylg,ej (h, s; a). Given the policy function for time invested in human capital, computing the presentvalue of earnings and the trajectory of the human capital stock over the working life is trivial.

There are two sets of factors that determine the optimal amount of time to invest in human capital.The first set of factors are the parameters that affect the law of motion for human capital definedin equation (3). We refer to this set of factors, plus the initial level of human capital, as pre-marketfactors as they are independent of age. The second set of factors that crucially affect the human capitalinvestment decision are the transition probabilities across life states (πss′g,ej ) and the probability ofdeath (πDg,ej ). In particular, these transition probabilities determine the likelihood that an agentis employed in any given period of his life and his employment prospects in the remaining periods.Employment is both an opportunity and an incentive to invest in human capital. Employment is anopportunity because non-employed agents cannot invest in human capital and only see their humancapital depreciate. Future employment is also an incentive as, in each period of employment, investingin human capital represents a trade-off between current and future earnings. Agents forgo currentearnings in order to receive higher (discounted) earnings in the future. Hence, an agent that iscurrently employed takes into account his employment prospects in the future when deciding howmuch human capital to accumulate. Two agents with the same pre-market parameters might facevery different incentives to invest in human capital if they face different employment probabilities inthe future. Even an agent with a very productive human capital technology does not find it optimalto invest in human capital if his employment prospects are bleak.

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4 Calibration

4.1 Earnings

To calibrate the model, we need to set up race groups and education levels that have a counterpartin the data. We define two race groups, black (b) and white (w) males, and four education levels,less than high school (−HS), high school graduates (HS), some college (SC), and college graduatesand beyond (C+). The model time span is from age 23 to 60. A model period is one month, hence,the lifecycle of an agent in the model consists of 456 periods. We set the yearly interest rate r to 4%and normalize the wage rate to unity. Since the only price in the model, the interest rate, is set upexogenously, this implies that there are no general equilibrium effects.

For each race-education group, the model requires two sets of inputs in order to produce lifecycleprofiles that can be compared with the data. One set of inputs are the transition probabilities acrosslabor market states and the survival probabilities. We compute these probabilities as describedin Section 2 and feed them directly into the model. These probabilities are dependent on race,education group, and age. The other set of inputs are the four parameters (depreciation rate δ,human capital elasticity α, learning ability a, and initial level of human capital h1). In order tochoose these parameters we minimize the distance between the lifecycle earnings profiles generatedby the model for each race-education group and their counterpart in the data. In particular, thecalibration algorithm aims to minimize the sum of the squared log distance between the earningprofiles observed in the data and those produced by the model using simulated method of moments.The resulting calibrated parameters for the benchmark calibration are presented in Table 1.

Table 1: Benchmark parameter values.

Black White-HS HS SC C+ -HS HS SC C+

Depreciation rate δ 0.0004 0.0005 0.0005 0.0005 0.0005 0.0006 0.0020 0.0010Human capital tech. α 0.7120 0.7172 0.6763 0.6650 0.7045 0.6767 0.6852 0.7778Learning ability a 0.0315 0.0216 0.0200 0.0212 0.0214 0.0212 0.0293 0.0157Intial human capital h1 46.6605 57.8048 65.0916 89.0086 56.4295 71.3368 93.8167 115.9459

While the human capital depreciation δ rate is similar for blacks for all levels of education, it ishigher for white males with some college or completed college education. The mechanic explanationof this difference is related to the fact that, for educated whites, the earnings profile at the end ofthe lifecycle presents a more negative slope than for the other groups. This bigger decline in earningscan be considered the mirror image of a steeper positive profile of earnings earlier in the lifecycle.

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A significant proportion of educated whites make it into highly paying jobs. However, it seems thatthis high remuneration does not continue until the end of their working life.

The depreciation rate δ is not the only parameter that plays a role in the magnitude of the declineof the earnings profile at the end of the working life. The human capital technology parameter αaffects the curvature of the earnings profile and, hence, plays a role determining the steepness of theprofile both before and after the highest point. The parameter for each group lies in the usual set ofestimates found in the literature (Huggett, Ventura, and Yaron 2006, 2011).

The learning ability parameter a crucially determines how steep and effective investments inhuman capital are. The calibration exercise attributes a very high learning ability to blacks with thelowest education. This is a consequence of the lack of persistence in the labor market and prisonprobabilities that we feed into the model. In the model, the probability of exiting employment isnot positively associated with employment tenure. In order to replicate the earnings profile of thisgroup in the data, the model needs to assign them a very high capacity to generate human capitalgiven that all of them face a significant probability of long non-employment spells. Finally, in thebottom row of Table 1 we see that for both blacks and whites, initial human capital h1 is increasingin education, which is intuitive, and are found to be greater for whites than for blacks for each levelof education.

4.2 Model Fit

In Figure 5 we present the mean hourly wages of blacks (panel 5a) and whites (panel 5b) as in thedata (solid line) and model (circular marker). We see that in the aggregate the mean hourly wagesgenerated by the model closely trace those we observe in the data. In Appendix Figures C.1 and C.2we show that the fit is similarly close when broken down by level of education for each race.

For employment, we see in panel 5c for blacks and 5d for whites that in the model employmentstocks are slightly lower than what we observe in the data. This slight difference is unrelated toany endogenous factor of the model as transitions are inputed directly from the data. Labor marketand prison stocks are the consequence of iterating the Markov process implied by the transitions.13

In general, these type of approximations exhibit a mismatch for the employment rate, which ispositively correlated with the magnitude of the UE transition, while more accurately replicating theparticipation and unemployment rates (as displayed in Figures C.5a, C.5c, C.5b, and C.5d).14 Forprison, we observe in panel 5e for blacks and 5f for whites that incarceration rates over the lifecycleclosely track those observed in the data.

13The Markov process implied by the model is an extension of the one in Choi, Janiak, and Villena-Roldán (2015).We add prison transitions and survival probabilities.

14A related discussion can be found in Elsby, Hobijn, and Şahin (2015).

14

Figure 5: Model fit of aggregate outcomes over the lifecycle by race.

(a) Mean hourly wages (blacks)

25 30 35 40 45 50 55 60

Age

0

5

10

15

20

(b) Mean hourly wages (whites)

25 30 35 40 45 50 55 60

Age

0

5

10

15

20

(c) Employment rate (blacks)

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

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1

(d) Employment rate (whites)

25 30 35 40 45 50 55 60

Age

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0.2

0.4

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0.8

1

(e) Incarceration rate (blacks)

25 30 35 40 45 50 55 60

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1

(f) Incarceration rate (whites)

25 30 35 40 45 50 55 60

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1

Notes: The solid line represents the data, while the dotted line with circle markers (©) summarizes modeloutput.

15

4.3 Non-Targeted Moments

Including on-the-job human capital accumulation in combination with labor market frictions has theadditional advantage that the model is able to generate non-employment scars. We follow the wayGuvenen, Karahan, Ozkan, and Song (2017) present non-employment scars by splitting the sampleinto control (employed) and treatment group (on full year of non-employment), and compare howearnings evolve in the years following the non-employment spell across the pre-treatment earningsdistribution.

In Figure 6, we present the earnings percentiles in terms of pre-treatment earnings amongst“young” workers (ages 25 to 34) and “old” workers (ages 35 to 50) on the x-axis while the y-axisexhibits the log difference between the average earnings of the treatment y(e, k) and control y(u, k)

groups after one, two, three, five, and ten years. In order to compute earnings percentiles beforethe shock, we split the sample into the two age groups in order to make percentiles comparable,i.e. within young and old workers. Then we pool everybody. We see that one year after the non-employment spell, the average gap is 60 to 120 log points, with the greatest scar being suffered bythose at the bottom of the income distribution. The scarring effect dissipates from year to year andfinally has nearly vanished after five years. While the magnitude of the scar after one year is similarto the one documented by Guvenen, Karahan, Ozkan, and Song (2017), the longterm persistenceis less severe than what is observed in the data. One reason for this discrepancy is the fact thatlabor market transitions are exogenous to the employment history and to individual’s level of humancapital, but instead are linked to age, race, and education. Therefore, prolonged idleness does nothave the multiplicative effect of lowering job finding probabilities, but only affects future wages.Nonetheless, this highlights the importance of including labor market frictions in models of humancapital accumulation in order to embed scaring effects of non-employment. Labor market detachment,in particular due to fertility, has also been shown to be a major contributor to the gender gap (Kleven,Landais, and Søgaard 2017).

16

Figure 6: Model fit of aggregate outcomes over the lifecycle by race.

0 20 40 60 80 100

Earnings Percentile

-1.5

-1

-0.5

0

0.5

k =1 k =2 k =3 k =5 k =10

Notes: The x-axis shows earnings percentiles in terms of pre-treatment earnings grouped by “young” workers(ages 25 to 34) and “prime-aged” workers (ages 35 to 50), while the y-axis exhibits the log difference betweenthe average earnings of the treatment and control groups k = {1, 2, 3, 5, 10} years after the treatment groupsuffers one full year of non-employment.

5 Counterfactual Exercises

Given that the model provides a reasonable fit across race and education levels, we now use counter-factual experiments to gain an understanding of the contribution of different factors to the lifecyclegaps in earnings and employment. More specifically, we will look into the relative importance of labormarket transitions, prison transitions, and human capital production technologies. When conductingexperiments concerning labor market and prison transitions, we will also separately look at how muchof the effect can be contributed to opportunities versus incentives to invest in human capital.

5.1 Decomposing the Earnings Gap

Black men on average spent less time in employment than white males. How much of the lifecycleearnings gap can this fact explain? In Table 2, we present the ratios of aggregate labor earnings ofblacks over those of whites as a consequence of assigning labor market transitions of white males toblack males. In the first column we present the aggregate ratio, in columns two to five for each levelof education, and in the last column the aggregate under the assumption that black males had thesame educational distribution as white males. Each change caused by a counterfactual simulation is

17

the aggregate of three components, i.e. the changes (i) in aggregate earnings due to the change inperiods with a job, (ii) in incentives to invest because of future employment prospects, and (iii) inpossibilities to invest due to the change in periods with a job.

In the first row, the benchmark case, we can already see that equalizing the education distributionreduces the gap from 26% to 19%, i.e. education accounts for 27% of the racial earnings gap. Labormarket transitions alone reduce the gap to 21% and combined with education to 14%. Therefore, labormarket transitions alone account for (19%) 26% of the earnings gap (un)conditional on education.Together education and labor market transitions explain 46% of the gap. Across levels of education,the effect is most pronounced for those with less than high school for whom the gap reduces from19% to 7%.

For assigning prison transitions of white males to black males we find that this reduces theaggregate earnings gap only by one percentage point. However, for those with less than high schooleducation the effect is more pronounced as the gap actually declines from 19% to 14%. For thiseducational group we actually see a reversal of the wage gap when combining the labor and prisonexperiments, i.e. black males with less than high school education earn 13% more. In the aggregatewe find that combining prison and labor experiments accounts for 35% of the wage gap and whenadditionally assigning the education distribution of white males the gap is closed by 58%.15

While Caucutt, Guner, and Rauh (2016) do find that incarceration of black males is an importantcontributor to the racial marriage gap, our model does not suggest that it is an important culprit ofthe aggregate labor earnings gap. However, given that the model includes no additional labor marketpunishment beyond the lack of incentives or opportunities to invest into human capital due to timespent outside the labor force, the presented model might not be the adequate model to address thequantitative importance of prison for the racial earnings gap in itself. Nonetheless, differences intransitions into prison amongst those with less than high school education accounts for more thanone quarter of the earnings gap.

15In Appendix Table C.1 we present the results when computing the gaps in present discounted value and find thepatterns to be confirmed.

18

Table 2: Black/white ratio of aggregate labor earnings when assigning transitions of white males toblack males.

Aggregate −HS HS SC C+ EducationBenchmark 0.74 0.81 0.80 0.81 0.83 0.81Labor market 0.79 0.93 0.88 0.84 0.84 0.86

EE transition 0.74 0.82 0.81 0.81 0.83 0.82EU transition 0.75 0.83 0.82 0.82 0.83 0.82EO transition 0.76 0.85 0.83 0.83 0.84 0.83UE transition 0.75 0.83 0.82 0.82 0.83 0.82UU transition 0.74 0.81 0.80 0.81 0.83 0.81UO transition 0.74 0.82 0.81 0.81 0.83 0.82OE transition 0.74 0.81 0.80 0.81 0.83 0.81OU transition 0.74 0.81 0.80 0.81 0.83 0.81OO transition 0.74 0.81 0.80 0.81 0.83 0.81

Prison 0.75 0.86 0.82 0.81 0.83 0.83Labor market and prison 0.83 1.13 0.92 0.85 0.85 0.89

Next we break the results down by opportunities versus incentives and present the results in Ta-ble 3. We conduct the experiment by assigning the respective transitions of white males to blackmales, while we fix the expected future employment rates to the benchmark case, which we considerthe “opportunity” experiment. We also conduct the converse experiment in which we fix the contem-porary employment transition to the benchmark rates for black males but they expect employmenttransitions of white males, which we consider the “incentives” experiment. So in the former case,individuals do not consider the potential future additional benefits from current investment but enjoyadditional contemporaneous opportunities, while in the latter they experience no current change inopportunities to invest and only expect relative improvements for the future. We find that the gapis closed to a larger extent when they expect to have labor market transitions as in the benchmarkcase, but actually enjoy the ones of white males with equal levels of education, i.e. the “opportunities”experiment dominates.

Moreover, when looking at the aggregate impact we see, for instance, that when considering onlythe labor market, the reductions in the earnings gap induced by the “incentives” and “opportunities”experiment are 1 and 2 percentage points, respectively. The sum of the two (3 percentage points)is less than the reduction when both are equalized jointly (5 percentage points). This suggeststhat incentives and opportunities to invest in human capital act as complements, i.e. the return toopportunities (incentives) are higher when incentives (opportunities) are greater as well.

19

Table 3: Black/white ratio of aggregate labor earnings broken down by opportunities and incentives.


Expect White, Experience Black 0.75 0.83 0.83 0.82 0.83 0.83Expect Black, Experience White 0.76 0.86 0.84 0.83 0.84 0.84

Prison 0.75 0.86 0.82 0.81 0.83 0.83Expect White, Experience Black 0.74 0.82 0.81 0.81 0.83 0.82Expect Black, Experience White 0.75 0.84 0.81 0.81 0.83 0.82

Labor market and prison 0.83 1.13 0.92 0.85 0.85 0.89Expect White, Experience Black 0.76 0.82 0.83 0.83 0.84 0.83Expect Black, Experience White 0.77 0.91 0.85 0.83 0.84 0.84

Decomposing the Hourly Wage Gap

The previous section decomposes the aggregate earnings gap. In this section, we look at how theaverage hourly wage gap evolves over the lifecycle under the different scenarios. In Figure 7, we seethe aggregate average hourly wage over the lifecycle for whites (dashed line), blacks (solid line) in thebenchmark economy, and blacks with white males’ labor transitions (circular marker). We see thatthe initial hourly wage gap actually increases compared to the benchmark, but then narrows overthe lifecycle. This is mainly due to the incentive effect early on in life. In the counterfactual, blackmales spend more time training on the job because they anticipate that they can reap the benefitsin the future. Given these past investments, they then possess more human capital as the lifecycleprogresses, hence narrowing the gap. In Figure 8 we see that the pattern within every educationalcategory holds, albeit to varying extents. The greater the level of education, the smaller the initialdrop and the smaller the subsequent increase for black males.

20

Figure 7: Aggregate mean hourly wages over the lifecycle when black males have the same labortransitions as white males.

25 30 35 40 45 50 55 60

Age

0

5

10

15

20

Notes: The solid line is for black and the dotted line for white agents. The dotted line with circle markers(©) represents counter-factual agents endowed with initial conditions and prison probabilities of blacks butface labour market transitions of whites.

21

Figure 8: Mean hourly wages over the lifecycle by education when black males have the same labortransitions as white males.


25 30 35 40 45 50 55 60

Age

0

5

10

15

20


25 30 35 40 45 50 55 60

Age

0

5

10

15

20

(c) Some college

25 30 35 40 45 50 55 60

Age

0

5

10

15

20


25 30 35 40 45 50 55 60

Age

0

5

10

15

20

Notes: The solid line represents black agents, while the dotted line represents white agents. The dotted linewith circle markers (©) are counter-factual agents endowed with initial conditions and prison probabilitiesof blacks but facing labour market transitions of whites.

22

5.2 Decomposing the Employment Gap

In the previous exercises, we focused on decomposing the earnings gap. However, it is also of interestwhich labor market transitions contribute most to the racial employment gap. Therefore, in thefollowing Table 4 we compute the gap in the employment when assigning transitions of white malesto black males. In the first row we see that the employment gap would drop from 22% to 15%,so by nearly one-third if black males had the same education levels as white males. If black maleswithin educational categories had the same labor market transitions as white males, the employmentgap would be reduced to 5%, so by 77%. Strikingly, the most important transition for the racialemployment gap are the differences in transitions from “E” to “O”, the transition from employment toout of the labor force, which holds for each educational category. In the aggregate these differencesalone account for 41% of the racial employment gap. The facts that contribute to this finding arethat the racial gap in this transition is high and that being out of the labor force is a highly persistentstate.

Table 4: Black/white ratio of employment rates when assigning white male transitions to black males.




5.3 Initial Human Capital and Production Parameters

Now we will turn to whether differences in initial conditions and fundamentals can explain the ag-gregate labor earnings gap. In Table 5 we present the ratios of aggregate labor earnings of blacksto whites when varying parameters of black metals are assigned to white males. The main takeawayfrom this exercise is that differences in the level of initial human capital are the main contributors to

23

the racial earnings gap, i.e. they can explain 73% of the aggregate earnings gap.16 This is consistentwith Neal and Johnson (1996) who find that a large part of the earnings gap can be explained bycontrolling for Armed Force Qualification Test Scores.

Table 5: Black/white ratio of aggregate labor earnings when assigning parameters of white males toblack males.

Aggregate −HS HS SC C+ EducationBenchmark 0.74 0.81 0.80 0.81 0.83 0.81Depreciation rate δ 0.67 0.80 0.79 0.59 0.75 0.73Human capital tech. α 0.78 0.81 0.78 0.82 1.18 0.94Learning ability a 0.76 0.78 0.80 0.96 0.78 0.83Intial human capital h 0.93 0.97 0.98 1.14 1.05 1.04

6 Conclusions

In this paper, we present a model of heterogenous agents differing in terms of education, race, andlifecycle employment and earnings trajectories. The wage gaps are a consequence of differing initialconditions combined with exogenous labor market transitions. The heterogeneity in labor frictionscreates a wedge in two ways: First, in terms of opportunities and second, in terms of incentives toinvest in human capital. Our model allows us to decompose the relative quantitative importance ofthese two channels. Moreover, we can gain insights about the role of transitions into versus out ofemployment.

We find that differences in labor market transitions can explain a large part of the aggregateearnings gap. Traditionally, much of the literature has focused on differences in job finding rates, e.g.by attempting to detect discrimination in the selection for job interviews through field experiments(Bertrand and Mullainathan 2004, Pager 2007, Pager, Bonikowski, and Western 2009) or survey dataon job search behavior and job offers (Fryer, Pager, and Spenkuch 2013). However, the transitiongap we single out as the most important is the difference in the transition from employment to out ofthe labor force. This suggests that we need a much better understanding of who are the individualswho move from a job to out of the labor force, why they do so, and why this transition is particularlylikely amongst black males.

Consistent with the early childhood education literature, we also find that gaps in skills uponentry into the labor market and education achievement are large contributors to the racial earningsgap. While one implication for policy would be to foster early childhood programs, we think that

16In Appendix Table C.2 we show that this hold when computing the gaps in net present value as well.

24

our findings suggest that we should be concerned about differences in labor market attachment, evenwhen conditioning on the skills gap.

Two interesting extensions of the model proved to be beyond scope. First, differences in initialconditions and the level of education could be the consequences of past choices, including by par-ents. Second, labor market transitions could be a function of human capital and/or a consequenceof endogenous choices. While on the one hand, this would be desirable as there most likely is anendogenous component to transitions, on the other hand, this might require additional modeling as-sumptions, such as differences in preference parameters, which could prove to be difficult to interpret.These differences, moreover, might not be well identified but could nonetheless receive the blamefor the racial employment, and hence earnings gap. Therefore, given the computational complexityof the model and difficulties of identification and interpretation, these extensions are left for futureresearch.

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A Lifecycle profiles

In the following, we outline how we approximate lifecycle profiles of labor earnings and transitions aswell as labor market stocks and transitions. For the sake of exposition, let us focus on the example oflabor earnings. Using the CPS MORG data obtained from the IPUMS-CPS database (Flood, King,Ruggles, and Warren 2017) as a synthetic panel allows us to estimate lifecycle profiles.17 We computethe averages of hourly wages w by age a, cohort c, race r, state s, and level of education e. Cohortsare defined in terms of decade of birth. In the following step, we fit a polynomial of degree threeusing an OLS regression of the form:18

wa,s,t,r,e = β1,eage+ β2,eage2 + β3,eage

3 + γ1,eblack × age+ γ2,eblack × age2 + γ3,eblack × age3+

+ αs,eS + αt,eT + αc,eC + ε (6)

where black is a dummy for black individuals and S are state, C cohort, and T and time dummiesmultiplied with the associated fixed effects. We estimate this equation separately for each of the fourlevels of education. Then we use the wage profiles predicted by

wa,r,e = β1,eage+ β2,eage2 + β3,eage

3 + γ1,eblack × age+ γ2,eblack × age2 + γ3,eblack × age3

as targets for the calibration. Finally, when we compute aggregate profiles we compute the convexcombination of race and education specific profiles using the population weights in Table B.1, whichare computed using the entire time period.

B Data Tables and Figures

Table B.1: Population distribution within each race

Race −HS HS SC C+Black 0.223 0.398 0.262 0.117White 0.113 0.354 0.304 0.229

17We can use the data to compute monthly labor market transitions, though, as we do observe individuals for up tofour consecutive months.

18For transitions we fit a polynomial of degree four in order to improve the fit while excluding state fixed effects dueto the smaller sample size.

29

Figure B.1: Employment rate by race and education.


25 30 35 40 45 50 55 60

Age

0

0.2

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Notes: CPS MORG 1994-2016. The solid line represents black men, while the dotted line is for white men,23-60 years old. Gray areas represent 95% confidence intervals.

30

Figure B.2: Participation rate by race and education.


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31

Figure B.3: Unemployment rate by race and education.


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32

Figure B.4: Prison rate by race and education.


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Notes: The solid line represents black men, while the dotted line is for white men, 23-60 years old.

33

Figure B.5: Labor market transitions for less than high school.

(a) EE

25 30 35 40 45 50 55 60

Age

0.8

0.85

0.9

0.95

1

(b) EU

25 30 35 40 45 50 55 60

Age

0.02

0.04

0.06

0.08

0.1

(c) EO

25 30 35 40 45 50 55 60

Age

0.01

0.02

0.03

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0.07

(d) UE

25 30 35 40 45 50 55 60

Age

0.1

0.15

0.2

0.25

0.3

0.35

(e) UU

25 30 35 40 45 50 55 60

Age

0.5

0.55

0.6

0.65

0.7

0.75

(f) UO

25 30 35 40 45 50 55 60

Age

0.1

0.15

0.2

0.25

0.3

0.35

(g) OE

25 30 35 40 45 50 55 60

Age

0.05

0.1

0.15

0.2

(h) OU

25 30 35 40 45 50 55 60

Age

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

(i) OO

25 30 35 40 45 50 55 60

Age

0.7

0.75

0.8

0.85

0.9

0.95

1


34

Figure B.6: Labor market transitions for high school graduates.

(a) EE

25 30 35 40 45 50 55 60

Age

0.8

0.85

0.9

0.95

1

(b) EU

25 30 35 40 45 50 55 60

Age

0.02

0.04

0.06

0.08

0.1

(c) EO

25 30 35 40 45 50 55 60

Age

0.01

0.02

0.03

0.04

0.05

0.06

0.07

(d) UE

25 30 35 40 45 50 55 60

Age

0.1

0.15

0.2

0.25

0.3

0.35

(e) UU

25 30 35 40 45 50 55 60

Age

0.5

0.55

0.6

0.65

0.7

0.75

(f) UO

25 30 35 40 45 50 55 60

Age

0.1

0.15

0.2

0.25

0.3

0.35

(g) OE

25 30 35 40 45 50 55 60

Age

0.05

0.1

0.15

0.2

(h) OU

25 30 35 40 45 50 55 60

Age

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

(i) OO

25 30 35 40 45 50 55 60

Age

0.7

0.75

0.8

0.85

0.9

0.95

1


35

Figure B.7: Labor market transitions for some college.

(a) EE

25 30 35 40 45 50 55 60

Age

0.8

0.85

0.9

0.95

1

(b) EU

25 30 35 40 45 50 55 60

Age

0.02

0.04

0.06

0.08

0.1

(c) EO

25 30 35 40 45 50 55 60

Age

0.01

0.02

0.03

0.04

0.05

0.06

0.07

(d) UE

25 30 35 40 45 50 55 60

Age

0.1

0.15

0.2

0.25

0.3

0.35

(e) UU

25 30 35 40 45 50 55 60

Age

0.5

0.55

0.6

0.65

0.7

0.75

(f) UO

25 30 35 40 45 50 55 60

Age

0.1

0.15

0.2

0.25

0.3

0.35

(g) OE

25 30 35 40 45 50 55 60

Age

0.05

0.1

0.15

0.2

(h) OU

25 30 35 40 45 50 55 60

Age

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

(i) OO

25 30 35 40 45 50 55 60

Age

0.7

0.75

0.8

0.85

0.9

0.95

1


36

Figure B.8: Labor market transitions for college graduates and beyond.

(a) EE

25 30 35 40 45 50 55 60

Age

0.8

0.85

0.9

0.95

1

(b) EU

25 30 35 40 45 50 55 60

Age

0.02

0.04

0.06

0.08

0.1

(c) EO

25 30 35 40 45 50 55 60

Age

0.01

0.02

0.03

0.04

0.05

0.06

0.07

(d) UE

25 30 35 40 45 50 55 60

Age

0.1

0.15

0.2

0.25

0.3

0.35

(e) UU

25 30 35 40 45 50 55 60

Age

0.5

0.55

0.6

0.65

0.7

0.75

(f) UO

25 30 35 40 45 50 55 60

Age

0.1

0.15

0.2

0.25

0.3

0.35

(g) OE

25 30 35 40 45 50 55 60

Age

0.05

0.1

0.15

0.2

(h) OU

25 30 35 40 45 50 55 60

Age

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

(i) OO

25 30 35 40 45 50 55 60

Age

0.7

0.75

0.8

0.85

0.9

0.95

1


37

Figure B.9: Probability of transition into prison by race and education.


25 30 35 40 45 50 55 60

Age

2

4

6

8

10

12

14

16

10-3


25 30 35 40 45 50 55 60

Age

2

4

6

8

10

12

14

16

10-3

(c) Some college

25 30 35 40 45 50 55 60

Age

2

4

6

8

10

12

14

16

10-3


25 30 35 40 45 50 55 60

Age

2

4

6

8

10

12

14

16

10-3


38

Figure B.10: Survival probability by race and education.


25 30 35 40 45 50 55 60

Age

0.9982

0.9984

0.9986

0.9988

0.999

0.9992

0.9994

0.9996

0.9998


25 30 35 40 45 50 55 60

Age

0.9982

0.9984

0.9986

0.9988

0.999

0.9992

0.9994

0.9996

0.9998

(c) Some college

25 30 35 40 45 50 55 60

Age

0.9982

0.9984

0.9986

0.9988

0.999

0.9992

0.9994

0.9996

0.9998


25 30 35 40 45 50 55 60

Age

0.9982

0.9984

0.9986

0.9988

0.999

0.9992

0.9994

0.9996

0.9998


39

C Model Fit

Figure C.1: Model fit for mean hourly wages of black males over the lifecycle by education.


25 30 35 40 45 50 55 60

Age

0

5

10

15

20


25 30 35 40 45 50 55 60

Age

0

5

10

15

20

(c) Some college

25 30 35 40 45 50 55 60

Age

0

5

10

15

20


25 30 35 40 45 50 55 60

Age

0

5

10

15

20

Notes: Black men. The solid line represents the data, while the dotted line with circle markers (©) summa-rizes model output.

40

Figure C.2: Model fit for mean hourly wages of white males over the lifecycle by education.


25 30 35 40 45 50 55 60

Age

0

5

10

15

20


25 30 35 40 45 50 55 60

Age

0

5

10

15

20

(c) Some college

25 30 35 40 45 50 55 60

Age

0

5

10

15

20


25 30 35 40 45 50 55 60

Age

0

5

10

15

20


41

Figure C.3: Model fit for employment rates of black males over the lifecycle by education.


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(c) Some college

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


42

Figure C.4: Model fit for employment rates of white males over the lifecycle by education.


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(c) Some college

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


43

Figure C.5: Model fit for aggregate participation and unemployment rates over the lifecycle by race.

(a) Participation (blacks)

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(b) Participation (whites)

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(c) Unemployment (blacks)

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(d) Unemployment (whites)

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

Notes: The solid line represents the data, while the dotted line with circle markers (©) is model output.

44

Figure C.6: Model fit for participation rates of black males over the lifecycle by education.


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(c) Some college

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


45

Figure C.7: Model fit for participation rates of white males over the lifecycle by education.


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(c) Some college

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


46

Figure C.8: Model fit for unemployment rates of black males over the lifecycle by education.


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(c) Some college

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


47

Figure C.9: Model fit for unemployment rates of white males over the lifecycle by education.


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(c) Some college

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


48

Figure C.10: Model fit for incarceration rates of black males over the lifecycle by education.


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(c) Some college

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


49

Figure C.11: Model fit for incarceration rates of white males over the lifecycle by education.


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1

(c) Some college

25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


25 30 35 40 45 50 55 60

Age

0

0.2

0.4

0.6

0.8

1


50

D Counterfactuals

Figure C.12: Black males are assigned white males’ prison transitions.


25 30 35 40 45 50 55 60

Age

0

5

10

15

20


25 30 35 40 45 50 55 60

Age

0

5

10

15

20

(c) Some college

25 30 35 40 45 50 55 60

Age

0

5

10

15

20


25 30 35 40 45 50 55 60

Age

0

5

10

15

20

Notes: The solid line represents black agents, while the dotted line represents white agents. The dottedline with circle markers (©) are counter-factual agents endowed with initial conditions and labour markettransitions of blacks but facing prison probabilities of whites.

51

Table C.1: Black/white ratio of aggregate net present value of labor earnings when assigning transi-tions of white males to black males.




Figure C.13: Opportunities and incentives experiment for prison and labor market transitions.

25 30 35 40 45 50 55 60

Age

0

5

10

15

20

Notes: The solid line represents black agents, while the dotted line represents white agents. The dotted linewith circle markers (©) are counter-factual agents endowed with initial conditions of blacks but facing labormarket transitions and prison probabilities of whites. Dotted line with cross markers (×) are counter-factualagents endowed with initial conditions of blacks, expecting labor market transitions and prison probabilitiesof whites, but experiencing labor market transitions and prison probabilities of blacks.

52

Figure C.14: Black males are assigned white males’ labor market transitions.


25 30 35 40 45 50 55 60

Age

0

5

10

15

20


25 30 35 40 45 50 55 60

Age

0

5

10

15

20

(c) Some college

25 30 35 40 45 50 55 60

Age

0

5

10

15

20


25 30 35 40 45 50 55 60

Age

0

5

10

15

20

Notes: The solid line represents black agents, while the dotted line represents white agents. The dotted linewith circle markers (©) are counter-factual agents endowed with initial conditions of blacks but facing labourmarket transitions and prison probabilities of whites.

53

D.1 Parameters

Table C.2: Black/white ratio in present discounted value of aggregate labor earnings when assigningparameters of white males to black males.

Aggregate −HS HS SC C+ EducationBenchmark 0.74 0.81 0.81 0.81 0.83 0.82Depreciation rate δ 0.69 0.81 0.79 0.63 0.77 0.75Human capital tech. α 0.76 0.81 0.80 0.81 0.96 0.86Learning ability a 0.75 0.80 0.80 0.90 0.80 0.82Intial human capital h 0.95 0.98 0.99 1.15 1.07 1.05

54

Arnau - WageandEmploymentGapsovertheLifecycle– TheCaseofBlackandWhiteMalesintheUS · 2019. 4....

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Transcript of Arnau - WageandEmploymentGapsovertheLifecycle– TheCaseofBlackandWhiteMalesintheUS · 2019. 4....