Equilibrium Unemployment: The Role of Discrimination

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Equilibrium Unemployment: The Role of Discrimination Juan C. Co´rdoba, Anni T. Isoj¨arvi, and Haoran Li 2021-080 Please cite this paper as: C´ordoba, Juan C., Anni T. Isoj¨arvi, and Haoran Li (2021). “Equilibrium Unemployment: The Role of Discrimination,” Finance and Economics Discussion Series 2021-080. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2021.080. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Equilibrium Unemployment: The Role of Discrimination.* JuanC.Co´rdoba† AnniT.Isoja¨rvi‡ HaoranLi§ December8,2021 Abstract U.S.labormarketsareincreasinglydiverseandpersistentlyunequalbetweengenders, races and ethnicities, skill levels, and age groups. We use a structural model todecomposetheobserveddifferencesinlabormarketoutcomesacrossdemographic groups in terms of underlying wedges in fundamentals. Of particular interest is the potentialroleofdiscrimination,eithertaste-basedorstatistical.Ourmodelisaversion of the Diamond-Mortensen-Pissarides model extended to include a life cycle, learningbydoing,anonparticipationstate,andinformationalfrictions. Themodelexhibits group-specific wedges in initial human capital, returns to experience, matching efficiencies,andjobseparationrates. Weusethemodeltoreverseengineergroup-specific wedgesthatwethenfeedbackintothemodeltoassessthefractionofvariousdisparities they account for. Applying this methodology to 1998–2018 U.S. data, we show thatdifferencesininitialhumancapital,returnstoexperience,andjobseparationrates accountformostofthedemographicdisparities;wedgesinmatchingefficienciesplay asecondaryrole.Ourresultssuggestaminoraggregateimpactoftaste-baseddiscriminationinhiringandanimportantroleforstatisticaldiscriminationaffectingparticularlyfemalegroupsandBlackmales. Ourapproachismacro,structural,unified,and comprehensive. Keywords: Search; Unemployment; Discrimination; StatisticalDiscrimination; Taste-Based Discrimination;Structural;Decomposition. JELClassification: E2;J6;J7. 1 Introduction TheU.S.populationhasgrownincreasinglydiverseduringthepast40years,anditisexpectedtobecomeevenmorediverseduringthenext40years(Figure1). Atthesametime, there are significant and persistent differences in labor market outcomes between genders,races,andethnicitiesthatconstituteanimportantdimensionofeconomicinequality (Altonji & Blank, 1999; Guryan & Charles, 2012; Lang & Lehmann, 2012; Blau & Kahn, 2017;Cajneretal.,2017). Figure2usesdatafromtheCurrentPopulationSurvey(IPUMS, 2018)fortheyears1998to2018toillustratesomeofthesedisparitiesoverthelifecycle. The figureincludeseightdemographicgroupsandfourlabormarketoutcomes: wages,unemployment, nonparticipation, and job-finding rates.1 Given that the population shares of demographic groups with historically weaker labor market outcomes are predicted to increaseinthefuture,theoveralllabormarketoutcomescouldbeweakenedunlessthelabor marketdisparitiesarereduced. *Wearegratefultonumerouscolleaguesandseminarparticipantsforveryhelpfulcomments. Theviews expressed are those of the authors and not necessarily those of the Federal Reserve Board or the Federal ReserveSystem. †IowaStateUniversity,DepartmentofEconomics.E-mail:cordoba@iastate.edu ‡BoardofGovernorsoftheFederalReserveSystem.Email:anni.t.isojaervi@frb.gov §Corresponding author. School of Applied Economics, Renmin University of China. Email: haoranl@ruc.edu.cn 1SeeSection3fordetails. 1

45.0% 41.7% 40.0% 40.0% 35.0% 31.3% 31.5% 30.0% 25.0% 23.0% 23.0% 20.0% 15.0% 15.0% 15.0% 10.0% 6.8% 9.1% 8.7% 6.2% 7.0% 5.6% 7.0% 4.7% 5.0% 5.0% 5.0% 2.7% 2.9% 3.1% 3.4% 0.8% 0.9% 0.0% White Males White Females Black Males Black Females Hispanic Males Hispanic Females Asian Males Asian Females 1980 2018 2060 Source: U.S.CensusBureau, 2019; U.S.CensusBureau, 2017; NationalCenterforHealthStatistics, 2021 Figure1: CompositionoftheU.S.populationofages25to65: 1980–2060. 1.8 1.6 1.4 1.2 1 0.8 30 40 50 60 ,egaW 52 egA elaM etihW ot evitaleR Average Wages 0.15 0.1 0.05 30 40 50 60 etaR tnemyolpmenU Average Unemployment Rate 0.6 0.4 0.2 30 40 50 60 Age etaR noitapicitrapnoN 0.6 0.5 0.4 0.3 30 40 50 60 Age ,etaR gnidnif-boJ ylretrauQ Age Age Average Nonparticipation Rate Average Job-finding Rate, Unemployed White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female Notes: Theselabormarketstatisticsarebasedontheauthors’calculationsusingIPUMS(2018)data fortheyears1998to2018. Figure 2: Selected labor markets statistics over the life cycle for different demographic groups. 2

Whataretheunderlyingsourcesoftheobservedlabormarketdisparitiesbetweendemographic groups? To what extent could these differences reflect discrimination? The main task of this paper is to disentangle the extent to which differences in human capital versus search frictions, which could include discrimination, account for the observed differencesinlabormarketoutcomesbetweendifferentdemographicgroups. Tomeasure the differences in human capital and search frictions, we use an extended version of the Diamond-Mortensen-Pissarides (DMP) search and matching model to solve for and calibratethehumancapitalandmatchingefficiencytrajectoriesforeachgroup. Asearchand matching model is a natural choice for our exercise, as it can jointly explain differences in both employment and wage outcomes—the variables of our interest—in terms of underlying economic incentives and a costly matching process.2 We include all the major demographic dimensions in the U.S. labor market in our analysis to create a clear picture of the determinants of the aggregate labor market gaps. These dimensions include gender (females and males), race and ethnicity (Asians, Blacks, Hispanics, and Whites), age (25–65-year-olds),andskilllevel(skilledandunskilled). The DMP model offers a unified general equilibrium framework in explaining aggregatelabormarketgaps. Inthemodel,employersputmoreresourcesandeffortintohiring workers with higher expected payoffs, higher chances of a successful search, and lower chances of a match break; each of these elements is captured by either group-specific humancapitalorsearchfrictions. WefurtherextendthestandardDMPframeworkalongthe followinglinestobettermatchtheobservedlabormarketdata. First,weallowworkersto benonparticipatinginadditiontobeingemployedorunemployed. Thisfeatureallowsus to account for the significant differences in participation rates between different genders andraces. Second,weintroducelife-cycleaspectstothemodelbyassumingthatworkers retire deterministically at age 65, which means that the match between a retiring worker and a firm breaks at a finite time. This feature lets us study the labor market outcomes over the life cycle and life-cycle patterns of potential discrimination. Third, we allow for human capital accumulation through learning by doing. Employed workers gain experience that enhances their human capital. Being non-employed—either unemployed or a nonparticipant—is costly since experience and human capital accumulation halts. This is an important channel to consider because labor market attachment varies significantly between demographic groups. The groups that are more likely to move out of the labor force are affected through lost human capital causing stagnation in their wage growth. Firms also care about the labor market attachment of their workers: as posting a vacancy is costly for a firm, the higher likelihood of a match break has a negative effect on the number of vacancies a firm is willing to open, and the wages the firm is willing to pay. Variation in match break probabilities between groups creates an incentive for firms to engageinstatisticaldiscriminationbasedonthegroup-specificjobdestructionrates. 2AlthoughtheDMPmodelhasbeenquestionedinitsabilitytoaccountforunemploymentfluctuations(for example, byShimer, 2005)themodelremainsthestandardforstudyingthenaturalrateofunemployment. Ouranalysiscanberegardedasanexplorationofthedeterminantsofunequalnaturalratesofunemployment amongdemographicgroups. 3

We also study the potential role of discrimination in explaining the aggregate labor marketdisparitiesrelyingonthetwomaintheoriesofdiscrimination,taste-baseddiscrimination (as in Becker, 1957) and statistical discrimination (as in Arrow & Pascal, 1972 and Phelps,1972).3 Wefocusonpotentialdiscriminationinhiringandwagenegotiation4,and discrimination can be present in at least two components of the model. First, taste-based discrimination (or prejudice, which we use interchangeably with taste-based discrimination) in hiring can take the form of a wedge across groups in their matching efficiencies. Inthemodel,variationinmatchingefficienciesbetweendemographicgroupsisnotbased on variation in match values between the groups, but rather captures a residual differenceinjob-findingprobabilitiesthatcannotbeexplainedbythenumberofvacanciesand job seekers.5 Any wedges in matching efficiencies can thus reflect prejudice of employers towards certain groups. For that reason, we measure the potential aggregate role of taste-based discrimination in describing aggregate labor market disparities by using the unexplained wedges in matching efficiencies. Second, statistical discrimination in hiring and wage bargaining can occur if firms utilize group-specific statistics to gauge the longterm prospects of a potential hire. We introduce a parametric formulation into the DMP modeltocontrolthedegreetowhichstatisticaldiscriminationcanoccur. Asingleparameterµ ∈ [0,1]determinesthedegreetowhichindividualsobservegroup-specificstatistics (µ = 1) or just statistics common among groups (µ = 0). The strategy to identify µ is a novelcontributionofthepaper. Weidentifythepotentialroleofstatisticaldiscrimination in explaining labor market gaps by running a counterfactual exercise that prevents firms fromusinggroup-specificstatisticswhenmakinghiringdecisions. Thecoreofthe paper isthecalibrationofthefundamentalmodelparametersfor each demographicgroupandthecounterfactualexercisesassessingtheroleofdifferentwedges inthesefundamentalsinaccountingfortheaggregatelabormarketdisparities. Thespirit of the quantitative exercise is to let the data speak by itself through the lens of the DMP model. As in Chari, Kehoe, and McGrattan (2007)6, we use macro accounting techniques and reverse engineer the underlying parameters—in particular, the implied parametric 3Taste-baseddiscrimination(orprejudice)theoryiscommonlyusedtocharacterizethetypeofdiscrimination that is based on less favorable attitudes and prejudice of either employer, co-workers, or customers towardsworkersbelongingtoacertain,nonpreferredgroup(e.g.,gender,ethnicity,race,religion,etc.). For example,asituationwhereanemployerpreferstohirealess-qualifiedcandidateofthepreferredgroupover amore-qualifiedworkerofthenonpreferredgroupisconsideredtaste-baseddiscrimination. Insuchacase, an employer is willing to accept a financial penalty to avoid interaction with nonpreferred workers, either becauseoftheemployer’sownprejudiceorthatofco-workersorcustomers. Incontrast,statisticaldiscriminationtheoryisbasedontheideathatemployershavelimitedinformationaboutaworker’strueproductivity. Thiscanleademployerstorelyonaccurateorinaccuratestereotypesaboutagroup(e.g.,gender,race,ethnicity,age,etc.) theworkerbelongstowhenmakinghiringdecisions. Forexample,anemployermayassess thatafemalejobapplicantislessattachedtothelaborforceandmorelikelytoleaveajobgiventhatfemale workers,onaverage,haveahigherlikelihoodtoleavethelaborforce. 4Otherpotentialoutcomesinthelabormarketcanbeaffectedbydiscrimination. Forexample,long-term wageoutcomeswilldependonthelikelihoodofgettingpromotions,anditispossiblethatsomedemographic groupsarediscriminatedagainstinpromotions. 5ComparetotheSolowresidualingrowthaccountingliterature. 6Chari,Kehoe,andMcGrattan(2007)usethestandardgrowthmodelastheirprototypemodel,extenditto includefourtime-varyingwedges,andcalibratethemtomatchtheseriesofoutput,labor,consumption,and investment. Theyfindthatefficiencyandlaborwedgesaccountedformostofthepostwarbusinesscycles, whileinvestmentwedgesplayedonlyaminorrole. 4

wedges—neededtoexactlymatchseveraltargetsforthestudieddemographicgroupsduringthe1998–2018period. Specifically, givenestimatedjobseparationratesandtransition flowsbetweenunemploymentandnonparticipation,weusethemodeltocalculategroupspecific initial levels of human capital, age-specific returns to experience, and matching efficienciesfortheunemployedandthenonparticipantsrequiredtoexactlymatchstylized life-cyclepatternsofwagesandjob-findingrates. The extent to which each wedge accounts for observed disparities in wages, employment, lifetime earnings, job-finding rates, and other labor market outcomes is then assessed through counterfactual exercises of closing one wedge at a time. Wedges in initial human capital and returns to experience refer explicitly to differences in the human capitaloftheworkerandcanberegardedaswedgesin“fundamentals.”Wedgesinmatching efficiencies as well as in job separation rates are “search frictions” and may include elementsoftaste-basedandstatisticaldiscrimination.7 Resultsfromanaccountingtechnique ofthistypearehelpfultoidentifythemostandleastpromisinglinesoffutureresearchby suggestingdimensionsalongwhichthemodelwouldneedtobeextended. Thefollowingarethemainresultsofthepaper. First,ourcalibratedhumancapitalseriesdiffersignificantlybetweendemographicgroups.8 However,wefindthathumancapital differences alone cannot explain differences in the key labor market outcomes. Additionalwedgesinsearchfrictions—specifically,inmatchingefficienciesandjobdestruction rates—are required for the model to be able to match the differential wage, employment, andlifetimeearningsoutcomes. Accordingtothecalibratedmodel,humancapitaldifferences account for around 65 percent of the average gap in lifetime earnings, including all groups, while search frictions account for around 32 percent. When we break down the impact of search frictions to the parts potentially coming from taste-based and statistical discrimination, respectively, we find a quantitatively small potential role for taste-based discrimination and a large role for statistical discrimination. We find that around 24 percent of the average lifetime earnings gap is accounted for by statistical discrimination, while taste-based discrimination can explain up to 3 percent of the aggregate gap. We find that there are significant differences in matching efficiencies between different demographic groups. However, as Hispanics have relatively high matching productivities comparedtoWhiteswhilethematchingproductivitiesofAsianandBlackwomenarerelativelylow,thosewedgeslargelycancelout,andthematchingefficienciescannotexplain alargepartofaggregategapsinthelabormarketoutcomes. Thesefindingsemphasizethatitisimportanttoaccountforsearchfrictionswhentry- 7Thereexistotherfactorsthatcangeneratewedgesinmatchingefficiencies.Demographicgroupscansimplydifferintheiraveragesearcheffort,forexample,inthenumberofapplicationstheysendwhilesearching for a job. Differences in geographic locations (e.g., urban vs. rural) can drive differences in matching efficienciesifcertaindemographicgroupsaremorelikelytoliveincertaingeographiclocationsandgeographic locationsvaryintheirmatchingefficiencies. Also, someoccupationsaresubjecttoregulationslikeoccupational licensing, which may impact the matching efficiency. To the extent that some demographic groups aremorelikelytoworkinoccupationssubjecttoregulationsthatimpacthiring,regulationsmayalsocreate matchingefficiencygapsbetweendemographicgroups. 8Ourestimatesareroughlyconsistentwithexistingestimatesintheliterature, particularlywithOaxaca- Blinderdecompositions(seeBlau&Kahn,2017foraliteraturereviewforthecaseofgendergaps). 5

ing to explain the life-cycle labor market disparities. When firms face costs when posting vacancies, the long-term value of the match becomes important. An intuitive example concerns why skilled women have faced difficulties in finding jobs. Hsieh et al. (2019) point out that Justice Sandra Day O’Connor, like many women in the 1950s, had difficultiesfindingajobearlyinhercareer,despitebeingrankedthirdinherclassatStanfordLaw School. Justice Ruth Bader Ginsburg faced similar difficulties. A model of career choice, like the Roy model used by Hsieh et al. (2019), would have problems rationalizing high unemployment rates of high-skilled, willing-to-work women, just like Justices O’Connor andGinsburg. Oursearchmodelwithstatisticaldiscriminationcanrationalizethesesituations. An average skilled woman in the 1950s had a high job separation rate, and a high average job separation rate lowers the expected long-term value of the match for firms. This weakens all labor market outcomes of skilled women, particularly job-finding and employment rates, as firms are less willing to hire workers with a low predicted match value. We separately decompose skill, gender, and racial and ethnic gaps in labor market outcomes. Regardingthegapsinlifetimeearnings,wefindthatwedgesinhumancapital variablesaremoreimportantwhenexplainingskillgaps(74percent),whilesearchfrictions arerelativelymoreimportantinexplaininggendergaps(46percent)whencomparedtothe determinantsofthetotalgaps. Moreover,statisticaldiscriminationaccountsfor15percent oftheskillgap,25percentofthegendergap,and31percentoftheracialandethnicgapin lifetimeearnings,emphasizingthelargerroleofdiscriminationasadeterminantofgender andracialgaps. Our findings suggest that statistical discrimination is potentially a more important source of discrimination than prejudice, although taste-based discrimination remains potentially important for certain groups and certain outcomes, such as for the job-finding rates of Black males and Asian females. This conclusion is consistent with a variety of micro evidence including List (2004), Levitt (2004), and Ewens, Tomlin, and Wang (2014). LangandLehmann(2012)reachasimilarconclusionintheirreviewoftheexistingliterature. Based on the survey and micro-evidence, they argue that any theory of discrimination should rely on “either strong prejudice in only a small portion of the population or widespreadmildprejudice”(p. 970). Separationratesareexogenousinourmodel,anddifferencesinseparationratesamong demographic groups are the underlying source of statistical discrimination. Our findings suggestthatmodelsofstatisticaldiscrimination—suchasthoseinCoateandLoury(1993), Rosen (1997), Moro and Norman (2004), Gayle and Golan (2012), and Jarosch and Pilossoph (2019)—provide promising lines of research for understanding labor market disparities. Asthisliteraturemakesclear,statisticaldiscriminationmaybeindividuallyrational but not necessarily socially optimal. We discuss in more detail other related literature in Section7. The remainder of the paper is organized as follows. Section 2 presents the model, whileSection3describesthedifferencesinlabormarketoutcomesbetweendemographic 6

groups. Section 4 explains the calibration strategy, Section 5 reports the calibration and decompositionresults,andSection6reportsrobustnesschecks. Finally,Section7provides aliteraturereview,andSection8concludes. 2 Model 2.1 ModelSetup ConsideraversionoftheDMPsearchandmatchingmodelextendedtoincludeheterogeneousworkersandsegmentedlabormarkets. Theextendedmodelalsofeaturesalifecycle withafinitehorizon,learningbydoing,andanonparticipationstate. Timeisdiscreteand ageisdenotedbya,wherea ∈ A ≡ [a,a¯]. Themodelfocusesontheworkingyears,which aretheyearsbetweeneducationandretirement. Workers. Individuals enter the labor market at age a, retire at age a , and die at R age a¯, where a¯ > a . We call individuals who have not retired workers. At any point R in time a worker is either employed, E, unemployed, U, or nonparticipating, N. Let (cid:8) (cid:9) s ∈ S ≡ E,U,N denote the labor market status of a worker. Workers enter the labor market without work experience and gain experience by working. Let e ∈ [0,a¯−a] denote years of experience of a worker. Experience increases by one unit during each period of employment, e = e + 1, and each nonworking period keeps experience a+1 a constant, e = e . Workers also belong to a demographic group i defined by gender a+1 a (female,male),skilllevel(skilled,unskilled),andraceandethnicity(non-HispanicAsian, non-Hispanic Black, Hispanic, and non-Hispanic White). We thus combine all workers with Hispanic ethnicity into one group regardless of their race, and the other groups defined by race include the members of the corresponding racial groups who are not Hispanic. For simplicity, we use “race” to refer to these four racial and ethnic groups from now on. As i determines the three dimensions of a worker’s demographics, an example of i could be a skilled Black female. Let I denote the set of demographic groups. A worker is fully identified by her years of experience (e), age (a), labor market status (s), anddemographicgroup(i). Denotebyx = (e,a,s,i)thestate,ortype,ofaworker,where x ∈ [0,a¯−a]×[a,a ]×S×I andletx(cid:48) = (e+1,a+1,s(cid:48),i). Thestateofaretireeisdefined R (cid:0) (cid:1) asx = e,a ,N,i . R R Let m(x) be the mass of workers of type x. The initial mass distribution, ms(0,a) is i taken as given for all s and i. Workers transition into unemployment and nonparticipation at exogenous rates π¯ (x), π¯ (x), π¯ (x), and π¯ (x), and into employment at EU EN UN NU endogenousratesπ¯ (x)andπ¯ (x).Workersseek tomaximize theirexpectedpresent NE UE valueofconsumption. Theyareriskneutralanddiscountthefutureaccordingtothediscountfactorβ ∈ (0,1). Letc(x)andw(x)denoteconsumptionandwagesoftypex,respectively. Therearenosavings,whichimpliesthatc(x)=w(x)foremployedworkers. Wages of employed workers are determined by Nash bargaining between workers and firms, whileconsumptionofnon-employedworkersandretireesaregivenbyc(x),anexogenous parametric form. For completeness, it is convenient to assume that consumption of un- 7

employed workers equals consumption of nonparticipating workers, cU¯ (e,a) = cN¯ (e,a), i i which allows us to use a concise notation when describing the solution for wages. For simplicity, we do not explicitly describe the domain of each function whenever it is clear. Forexample,w(x)referstothewagesoftheemployedworkersonly,x = (cid:0) e,a,E¯,i (cid:1) .9 Human capital: Human capital of a worker, h(x), is of the general type. There is no firm-specifichumancapital. Weassumethefollowingfunctionalformforthehumancapital: h(x) = y exp(r(x)e), (1) i where y is the baseline level of human capital that a member of a group i has when eni teringthelabormarket,andr(x)aretype-specificreturnstoexperience. Bothy andr(x) i are exogenous. We interpret y as education-related human capital, the human capital of i a new worker for whom e = 0. Differences in baseline human capital, y , and returns i to experience, r(x), across types can then capture differences in the quality and quantity of education between demographic groups, differences in occupations and industries in which a representative worker of each type works, and discrimination. Central to our accountingexerciseistocalibrateparametersy andr(x)forallx. i The chosen functional form of human capital assumes that the post-schooling human capital formation is of the learning-by-doing type as in Barlevy (2008), Yamaguchi (2010), andBaggeretal.(2014). Thehumancapitalofaworkerincreasesautomaticallywhenever she is employed and producing. We could instead assume that the investment in human capital and working are competing, mutually exclusive activities as in models using the Ben-Porathtypeofhumancapitalaccumulation. However,Heckman,Lochner,andCossa (2003) argue that it is difficult to distinguish between learning-by-doing and on-the-job training (Ben-Porath) human capital accumulation based on empirical evidence, so we choosetomodelthehumancapitalaccumulationbasedonalearning-by-doingapproach. Learning-by-doing human capital accumulation is also supported by the empirical evidenceshowingthescarringeffectsofnon-employmentperiodsonwages(seemoreonthe literaturereviewinSection7). Firms and labor markets: There is a continuum of infinitely lived firms that seek to maximizetheirexpectedpresentvalueofprofitsnetofhiringcosts. Firmsareriskneutral and discount the future at the same rate as workers do. Labor markets are assumed to be perfectly segmented across worker types. Firms can freely enter any of the segmented markets. Firms post vacancies for long-term positions at a cost κ(x) per vacancy, a cost that may depend on a worker’s type. Once a firm is matched with a worker, a worker produces h(x) units of output per period, while gross per-period profits of the firm are h(x)−w(x). Amatchisdestroyedexogenouslyatarated(x). The assumption about segmented labor markets requires some discussion, as it may seem strong at first glance. First, segmentation is needed for the model to match key fea- 9WemaintainvariousconvenientassumptionsofthecanonicalDMPmodelsuchaszerosavings,exogenousjobseparationrates, andexogenousconsumptionofthenon-employed. Thefocusofthemodelison determiningemploymentandunemploymentrates,wages,andjob-findingandlabormarkettightnessrates foralltypesofworkers,asdefinedbyx. 8

turesofthedata,suchasdifferentialjob-findingratesbetweendemographicgroups,aswe willshow. Second,whilevariouslaws(e.g.,theCivilRightsActandtheEmploymentAct) forbid differential treatment of workers in the U.S. labor markets based on, for example, workers’ race, gender, and age, discriminatory behavior is hard to prove in practice. The evidencesuggeststhatanti-discriminatorylawshavehadlimitedsuccess(Valfort,2018).10 Third, in the absence of discrimination, segmentation would still be required for allocations to be efficient. Last but not least, allowing for segmentation of labor markets in the model does not create discrimination—it merely makes discrimination possible. Workers with similar characteristics facing nonprejudiced employers should display similar labor market outcomes even if markets are segmented. For these reasons, and because we are specificallyinterestedinstudyingwhetherdiscriminationisneededforthemodeltomatch theobservedlabormarketgaps,wechoosetostudysegmentedlabormarkets. Matching technology: A worker and a firm with a vacant position are randomly matchedineachofthesubmarketsaccordingtothematchingtechnologyM (u(x),v(x);x), whereu(x)andv(x)arethemassesofworkersandfirms,respectively,searchinginaparticular labor market. We assume that all unemployed workers search for a job, employed workersdonotsearch,andafractionψ(x) < 1ofnonparticipantssearch.11 Thus, the mass of workers searching at a given employment status can be defined as follows:   m(x), ifs = U,     u(x) ≡ ψ(x)m(x), ifs = N, (2)    0otherwise.  WeassumethatthematchingtechnologyadoptsastandardCobb-DouglasformM(u,v;x) = A(x)uαv(1−α), whereA(x)representstheefficiencyofthematchingtechnologyandisallowedtodependonaworker’stype. Differencesinmatchingefficiencyacrosstypesreflect searchfrictionsassociatedwithparticularlabormarkets. Onceamatchisformed,theoutputofthematchisdistributedaccordingtoaNashbargainingsolutioninwhichaworker’s bargainingpowerisgivenbyφ(x). v(x) Let θ(x) ≡ denote the tightness of a particular labor market, the number of u(x) vacancies per job seeker. A firm’s probability of filling a vacancy is given by q(x) = M (u(x),v(x);x)/v(x) = A(x)(θ(x))−α , and a non-employed worker’s probability of findingajobisf(x) = M (u(x),v(x);x)/u(x) = A(x)(θ(x))1−α . Theseexpressionsmake it clear that job-finding rates are solely the functions of labor market tightness rates and theefficienciesofthematchingfunction. The following assumption will guarantee that each match generates a strictly positive surplus: Assumption1 h(x) > c¯(x)andc(x )increases(weakly)withexperience. R This first part of the assumption is standard. The human capital of a worker is strictly 10As noted by Lang and Lehmann (2012, p. 970), almost all models they review implicitly assume such illegalpractices. 11Job-to-jobsearchissuboptimalinthemodelgiventhatthereisnoexpectedgainfromamatchbreak. 9

greater than the consumption during non-employment for any given type x. The second part reinforces the benefit of remaining in a match as pensions (weakly) increase with experience. Bothpartsoftheassumptionarerequiredtoguaranteethatamatchgenerates apositivesurplus. Statistical discrimination: The notion that employers use statistics specific to a demographic group when assessing a worker’s prospects is present in the model through the job destruction rates d(x). Firms in a given market x can perfectly forecast the human capital of the worker they are looking to hire conditional on the worker staying in thematch, buttheexpecteddurationofthematchdependsonjobdestructionrates, d(x), specific to that market. Statistical discrimination arises if d(x) is a function of i, the demographic identifier. In that case, job destruction rates may vary based on i, creating variation in the long-term values of the matches between a worker and a firm. To assess the extent to which statistical discrimination is prevalent in labor markets from the point of view of the model, we assume that firms and workers observe only a noisy signal of the true job destruction rate of a group x. The true job destruction rate is determined as d¯(x) ≡ π¯ (x) + π¯ (x), where π¯ (x) is the transition probability of a worker from EU EN EU employment to unemployment, and π¯ (x) is the transition probability from employ- EN ment to nonparticipation. Firms and workers observe d(x)=µd¯(x)+(1−µ)dˆ(x), where µ ∈ [0,1] is a parameter and dˆ(x) is a reference job destruction rate common among all groups. For example, dˆ(x) could be the average job destruction rate across demographic groupsoritcouldbethejobdestructionrateofareferencegroupsuchasWhitemales. The same holds true for workers. Workers observe π (x) ≡ µπ¯ (x)+(1−µ)πˆ (x) and EU EU EU π (x) ≡ µπ¯ (x)+(1−µ)πˆ (x),whereπˆ (x)andπˆ (x)aredefinedanalogously EN EN EN EU EU to dˆ(x). At one extreme, firms can engage in perfect statistical discrimination based on workers’demographicgroupiwhenµ = 1. Firmscanpostvacanciesandnegotiatewages basedonaverage,group-specificjobdestructionratesand,consequently,basedontheaccuratelong-termvaluesofthematches. Attheotherextreme,ifµ = 0,firmscanonlyuse jobdestructionratesofthereferencegroup,commonforalldemographicgroups. Parameterµwillbecalibrated.12 Gaps in the reverse-engineered parameters and taste-based discrimination: Before moving to the recursive formulation of the model, it is convenient to briefly explain the main goal of the paper in light of the setup just described. We use the model’s solution to calibrate and reverse engineer the key model parameters: µ, y , r(x), κ(x), A(x), φ(x), i and ψ(x). Reverse engineering is a step further from calibration in the sense that it seeks to match complete sequences of wages and job-finding rates of different groups over the entirelifecycle,notonlysomeselectedmomentsorstylizedfacts. Thereverse-engineering resultsarethenusedtocalculateandinterpretgapsinparametersacrossgender,race,age, and skill. Finally, using the obtained gaps in the parameters, we perform counterfactual 12Onecaninterpret1−µasthedegreeoffirms’compliancewithanti-discriminationlaws. Forexample, whenµ=0,firmsarestillabletopostvacanciesandnegotiatewagescontingentonworkers’humancapital butareunabletodifferentiateworkersintermsoftheirexpectedmatchlength.Thiswouldeliminatestatistical discriminationbasedon,forexample,women’shigherlikelihoodofexitingthelaborforcebecauseoffamily reasons. 10

exercises to quantify the importance of each gap in explaining the distinct labor market outcomesofdemographicgroups. Thereverse-engineeredandcalibratedgapsrepresenttheunderlyingfundamentalsources of unequal labor market outcomes among demographic groups, according to the model. By separating human capital differentials from other gaps in the underlying parameters, themodelsuggestspotentialdiscriminatorybehaviorunderlyinganumberoftheseparametricgaps. Taste-baseddiscriminationduringthehiringprocesscouldbelinkedtogaps in matching efficiencies, search efficiencies of nonparticipants, and in vacancy posting costs(parametersA(x),κ(x),andψ(x)),whiletaste-baseddiscriminationduringemploymentcouldbelinkedtogapsinparametersr(x)andφ(x),parametersrepresentingreturns toexperience,andthebargainingpowerofworkers. 2.2 RecursiveFormulation 2.2.1 AFirm’sProblem LetV¯ bethevalueofafirmwithoutaworkerandJ(x)bethevalueofafirmwithaworker (cid:2) (cid:3) oftypex = e,a,E,i . Then  h(x)−w(x)+β (cid:2) d(x)V¯ +(1−d(x))J(x(cid:48)) (cid:3)      J(x) = ifa ≤ a < a −1, . R   h(x)−w(x)+βV¯ ifa = a −1   R The first part of the expression states that the value of a firm with a worker is the flow of grossprofitsplusthediscountedcontinuationvalueofthematch. Thecontinuationvalue consistsofthevalueofpostinganewvacancy,V¯ , ifthematchisdestroyed, whichoccurs withprobabilityd(x),andthevalueofremaininginthematch,J (e+1,a+1),whichoccurs i withprobability1−d(x). Thesecondpartoftheexpressionstatesthatafirmwithaworker whoisabouttoretirewillbecomeafirmwithoutaworkerinthefollowingperiod. Thevalueofafirmpostingavacancyinmarketxis V (x) = max (cid:8) −κ(x)+β (cid:2) q(x)J (e,a+1)+(1−q(x))V¯(cid:3) ,0 (cid:9) . i Themaximumvalueofpostingavacancyinanylabormarketisthengivenby V¯ = max{V (x),0}. x Freeentryoffirmsintoanylabormarketguaranteesthatthevaluesofunfilledvacanciesmustallbeequaltozero: V (x) = 0forallfeasiblex. Asaresult,themaximumvalue ofpostingavacancymustbezeroaswell,V¯ = 0. Activefirmsarethusindifferentinwhich typeofaworkertohireandinwhichofthesegmentedmarketstooperateifthefreeentry conditionholds.13 13Potentialprejudicedemployersmaystilloperateinmarketstheydonotpreferif,forexample,negotiated wagesinthatmarketaresufficientlylowforfirmstobreakeven. 11

Theproblemofafirmwithaworkerthensimplifiesto   h(x)−w(x)+β(1−d(x))J(x(cid:48))     J(x) = ifa ≤ a < a −1, , (3) R    h(x)−w(x) ifa = a −1  R whileforfirmspostingvacanciessimplifiesto κ(x) = βq(x)J (e,a+1) = βf(x)θ(x)−1J (e,a+1) fora ≤ a < a −1. (4) i i R The last equation states that the expected present value of filling a vacancy must be just enoughtorecoverthecostsofpostingthevacancy. 2.2.2 AWorker’sProblem Considernowthe(maximum)expectedpresentvalueofearningsofanemployedworker, E,anunemployedworker,U,anonparticipatingworker,N,andaretiredworker,R. The expectedpresentvalueofconsumptionofanewlyretireesimplysatisfies (cid:88) a 1−βa−aR−1 R(x ) = βi−aRc(x ) = c(x ), (5) R R R 1−β i=aR wherec¯(x )isconsumptionofaretireeoftypex . Likefirms,workersdonotnecessarily R R knowtheirtruematchbreakprobabilitiesandusetheweightedaveragematchbreakprobabilities π (x) and π (x) in their value functions. The corresponding value functions EU EN E,U,andN canthenbewrittenrecursivelyas  (cid:34) (cid:35)     w(x)+β π EU (x)U(x(cid:48))+π EN (x)N(x(cid:48))      +(1−π (x)−π (x))E(x(cid:48))   EU EN E(x) = , (6)   ifa ≤ a < a R −1     (cid:0) (cid:1)    w(x)+βR e+1,a ,N ifa = a −1  i R R  (cid:34) (cid:35)     c(x)+β f(x)E i (e,a+1)+π¯ UN (x)N i (e,a+1)       +(1−f(x)−π¯ (x)U (e,a+1)  UN i U(x) = , (7)   ifa ≤ a < a R −1     (cid:0) (cid:1)    c(x)+βR e,a ,N ifa = a −1  i R R  (cid:34) (cid:35)     c(x)+β f(x)E i (e,a+1)+π¯ NU (x)U i (e,a+1)       +(1−f(x)−π¯ (x))N (e,a+1)  NU i N(x) = , (8)   ifa ≤ a < a R −1     (cid:0) (cid:1)    c(x)+βR e,a ,N ifa = a −1  i R R The interpretation of these functionals is intuitive. An employed worker consumes her wage w(x) each period. A match between a worker and a firm can be destroyed in two ways: with (perceived) probability π (x), a worker becomes unemployed, and with EU 12

probabilityπ (x), theworkerbecomesanonparticipant. Theworkercontinuesproduc- EN ing with probability 1−π (x)−π (x) and stays in the employment state. At the be- EU EN ginningofeachperiod,anunemployedworkerconsumesc(x)=cU¯ (e,a). Nextperiod,she i findsajobwithprobabilityf(x) = f (e,a,U¯),inwhichcaseshemovestotheemployment i state. A worker may also move to nonparticipation with probability π¯ (x); otherwise, UN she will stay unemployed. A similar interpretation holds for the value function of a nonparticipatingworker. It is convenient to define the present value of lifetime earnings, or consumption, of a workerxas W (x) = mE¯ (e,a)E(x)+mU¯ (e,a)U(x)+mN¯ (e,a)N(x), (9) i i i where mE¯ (e,a), mU¯ (e,a), and mN¯ (e,a) determine the masses of workers in each of i i i theselabormarketstatesforanygivenexperienceandage. 2.2.3 NashBargaining Wages in the model are negotiated through Nash bargaining. A firm and a worker share thematchsurplusS(x) = E(x)−U(x)+J(x), giventhebargainingweightsφ(x)forthe workerand1−φ(x)forthefirm,inthefollowingway:14 max(E −U)φ(x)J1−φ(x) subjecttoS(x) = E −U +J, E−U,J andthesolutionforeachlabormarketsatisfies 1−φ(x) J(x) = Θ(x)×(E(x)−U(x))whereΘ(x) = . (10) φ(x) 2.3 AggregateLaborFlows Given the initial distribution of workers, ms(0,a), and job-finding rates f(x) for all x, i the subsequent distribution of workers m(x) can be calculated assuming a law of large numbers. Themassofindividualswithnoexperienceatagea ∈ [a,a −2]isdetermined R as mE¯ (0,a+1) = fU¯ (0,a)×mU¯ (0,a)+fN¯ (0,a)×mN¯ (0,a); i i i i i mU¯ (0,a+1) = (1−π¯ (x)−fU¯ (0,a))×mU¯ (0,a)+π¯ (x)×mN¯ (0,a); (11) i UN i i NU i mN¯ (0,a+1) = (1−π¯ (x)−fN¯ (0,a))×mN¯ (0,a)+π¯ (x)×mU¯ (0,a). i NU i i UN i 14Weassumethattheoutsideoptionofaworkerduringwagebargainingisalwaysunemployment,U. An alternativespecificationistoallowtheoutsideoptionoftheworkertobenonparticipationoramixbetween unemploymentandnonparticipation. AsdiscussedinCo´rdoba,Isoja¨rvi,andLi(2021),theefficiencyofthe solution requires the surplus of a new worker to be defined relative to the worker’s previous state, before becomingemployed,whichcouldbeeitherunemploymentornonparticipation.However,efficiencydoesnot restrict how the surplus of production is divided between a firm and a worker with tenure in the job. For tractability, weassumeasimpleoutsideoption, unemployment. Thisreducesthevectorxbutalsoimplies thatallocationsinthemodelarenotfullyefficient. 13

Moreover,themassofindividualswithexperiencee ∈ [1,a]atagea ∈ [a,a −2]isdeter- R minedas mE¯ (e,a+1) = (1−π¯ (x)−π¯ (x))×mE¯ (e−1,a)+fU¯ (e,a)×mU¯ (e,a) i EU EN i i i +fN¯ (e,a)×mN¯ (e,a); i i mU¯ (e,a+1) = (1−π¯ (x)−fU¯ (e,a))×mU¯ (e,a)+π¯ (x)×mN¯ (e,a) i UN i i NU i (12) +π¯ (x)×mE¯ (e−1,a); EU i mN¯ (e,a+1) = (1−π¯ (x)−fN¯ (e,a))×mN¯ (e,a)+π¯ (x)×mU¯ (e,a) i NU i i UN i +π¯i (x)×mE¯ (e−1,a). EN i Notice that while the firms and the workers may not be sure about the accurate match breakprobabilities,π¯ andπ¯ ,theactualflowsintoemployment,unemployment,and EU EN nonparticipationevolveaccordingtotheactualprobabilities. 2.4 CharacterizationoftheSolution Wenowcharacterizethesolutionforwages,labormarkettightnessrates,andjob-finding ratesusingbackwardinduction. Inparticular,wefirstobtainclosed-formsolutionsforthe last period of working life (see Appendix A for the solution), which we then use to find solutionsforthepreviousperiods. 2.4.1 Solutionfora < a −1 R Thesolutionsforperiodsa < a −1canbeexpressedintermsofworkers’surplusesand R valuechangesdefinedas S (x) ≡ E(x)−U(xU¯ (e,a)); S (x) ≡ E(x)−N(xN¯ (e,a)); (13) EU i EN i S (x) ≡ N(x)−U(xU¯ (e,a)); S (x) ≡ U(x)−N(xN¯ (e,a)); NU i UN i ∆U(x) ≡ U(x)−U (e−1,a); ∆N(x) = N(e,a)−N (e−1,a). i i Thefollowingpropositionprovidesapartialcharacterizationofthesolutionforwages, tightnessrates,andjob-findingrates. Proposition 1Thesolutionsforw(x),θ(x),andf(x),for0 ≤ a < a −1,satisfy R h(x)+Θ(x)[c¯(x)+βΩ(x)] w(x) = , (14) 1+Θ(x) (cid:20) (cid:21)1 βA(x)J i (e,a+1) α θ(x) = , and (15) κ(x) A(x) f(x)α = (βJ (e,a+1))1−α ,where (16) κ(x)1−α i 14

Ω(x) = fU¯ (e,a)Si (e,a+1)+π¯ (x)Si (e,a+1) (17) i EU UN NU +π (x) (cid:2) S (cid:0) x(cid:48)(cid:1) −S (x(cid:48)) (cid:3) −∆Ui(e+1,a+1), EN EN EU J (e,a+1) = Θ(x)Si (e,a+1), and i EU   (1−π (x))S (x(cid:48))−π (x)S (x(cid:48)) EU EU EN EN S (x) = w(x)−c¯U¯ (e,a)+β −π¯ (x)Si (e,a+1) . EU i  UN NU  −fU¯ (e,a)Si (e,a+1)+∆U (x(cid:48)) i EU Proof. SeeAppendixA. The term βΩ(x) in equation (14) collects all net losses of remaining employed. Wages increasewithΩ(x)tocompensateworkersforthoselossestoanextentdeterminedbythe workers’ bargaining power. In particular, a higher job-finding probability, fU¯ , increases i wagessinceSi (e,a+1) > 0.Intuitively,thehigherthechancesoffindinganewjob,the EU higherthelossesassociatedwithremaininginthecurrentjob. Furthermore,thewageofa workerequalsaworker’shumancapitalifΘ(x) = 0,whileattheotherextreme,thewage equalsc¯U¯ (e,a)+βΩ(x)whenΘ(x) = ∞. Accordingtotheseexpressions,unequalwages i among workers with identical human capital only arise if firms have some bargaining power, Θ(x) > 0, andworkershavedifferentoutsideoptionsorprospects. Workerswith betteroutsideoptions, asreflectedbyc¯U¯ (e,a)+βΩ(x), arepaidmore. Unequalpayforan i equal job, the idea that w(x ) (cid:54)= w(x ) even when h(x ) = h(x ), arises naturally due to A B A B searchfrictionspresentinthemodel. Equation (16) shows that a job-finding rate of a worker is a direct function of the economic value of the worker to the firm, J (e,a + 1). In general, it states that job-finding i ratesarehigherinmarketswithmoreefficientmatching,lowercostsofpostingvacancies, and higher values of active firms. Discrimination in hiring could arise through the term A(x) : a particularly low matching efficiency for type x workers or an unusually high κ(x)1−α cost of hiring type x workers would lead to job-finding rates lower than what is justified bytheeconomicvalueoftheworkertothefirm. The key role of job separation rates and statistical discrimination can also be gauged fromtheseexpressions. Considertheeffectofπ (x)onwagesandjob-findingrates. For EU a given sequence of wages, an inspection of the formulas reveals that a higher π (x) EU reduces workers’ surplus S (x) at state x but also at all states leading to state x. This EU reduces firms’ incentives to post vacancies for those types of workers. Lower surpluses also lower wages, according to (14), but only of wages in previous periods leading up to statex. Currentandfuturewagesarenotaffectedbyahigherdestructionrateatstatex. To gain some further intuition about the determination of wages, consider the determinationofwagestwoperiodsbeforeretirement. Denotebyx = x(e,a −2,E¯,i)and R−2 R assumethatc¯(x) = c¯forallx. AsshowninAppendixA.3,thewagesthenare (cid:104) (cid:105) h(x )+Θ(x ) c¯+βfU¯ (e,a −2)(w(x )−c¯) R−2 R−2 i R R−1 w(x ) = . R−2 1+Θ(x ) R−2 15

Thisexpressionillustratesthedeterminationofwagesand,inparticular,theroleofthejobfinding rate. A higher current job-finding rate tends to increase current wages if workers have some bargaining power. If Θ(x ) = 0, then w(a ) = h(a ). At the other R−2 R−2 R−2 extreme,ifΘ(x ) = ∞,then R−2 w(x ) = c¯+βfU¯ (e,a −2)(w(x )−c¯), R−2 i R R−1 a minimum wage that reflects the value of the outside option. In conclusion, in the presence of search frictions, wages do not reflect only the underlying true productivity of the worker. As a result, simple Mincer wage regressions will not provide a correct estimate oftheunderlyinghumancapitaltrajectoriesofworkersoverthelifecycleinthepresence of search frictions and unemployment. In Section 4, we reverse engineer human capital trajectories of workers in different markets over the life cycle using the structure of the model. Asexpectedfromthepreviousdiscussion,ourestimatedhumancapitalpathsdiffernotablyfromwagesforcertaingroups. 3 Stylized Facts and Basic Counterfactuals 3.1 StylizedFacts We now highlight stylized features of the data regarding different demographic groups. Table 1 provides averages of the various labor market outcomes for the studied demographic groups, calculated using IPUMS (2018) data for individuals between the ages 25 and 65. Figure 2, presented in the Introduction, and Figure 3 portray corresponding lifecycleprofilesoftheoutcomes. Table 1 documents some well-known facts. Whites, males, and the skilled tend to exhibit better labor market outcomes compared to minority15 groups, females, and the unskilled. They have higher wages and higher employment and job-finding rates, lower unemployment and job separation rates, and, overall, higher average lifetime earnings. Therearesomeimportantexceptionstothischaracterization. SkilledAsianmalesoutperformothergroupsinwagesandearnings,whileHispanicmales,skilledandunskilled,do particularly well compared to the other groups in terms of employment and job-finding rates. Labor market outcomes of Black males are problematic: they have the highest unemploymentrate,bothamongtheskilledandtheunskilled,thehighestseparationrateto unemployment,andunusuallyhighnonparticipationratesamongmales. Blackmalesalso havethesecond-lowestjob-findingrateoftheunskilled,andthethird-lowestwagerateof theskilled. Considernextthefulllife-cycleprofiles. Figure2showspersistentwagegapsbetween groupsovertheentirelifecyclewithafewbutimportantexceptions. Foreachgender-race pair,life-cyclewagegrowthshowsthewell-knownpattern: wagesgrowrapidlyforyoung workers,flatten,thenstarttodecreaselaterinthecareer. WagesforbothAsianmalesand 15Forthesakeofsimplicity,werefertoracialgroupsotherthannon-HispanicWhitesasminorities. 16

Table1: Descriptivestatisticsandbasiccounterfactuals(IPUMS,2018). Groups Pop. Wage Employ. Unemp. Non-Part. π UE π EU π EN Earnings share ($/hour) rate rate rate (W) Whitemale 31.0% 30.1 80.3% 3.5% 16.2% 49.7% 2.1% 4.0% 89.3 Skilled 19.2% 34.5 84.9% 2.9% 12.2% 49.4% 1.7% 3.3% 106.0 Unskilled 11.9% 21.8 73.0% 4.5% 22.5% 49.8% 3.0% 5.3% 60.1 Whitefemale 31.2% 23.3 67.8% 2.7% 29.6% 44.8% 1.6% 6.9% 62.0 Skilled 20.3% 26.4 72.6% 2.4% 25.0% 47.3% 1.5% 6.3% 73.3 Unskilled 10.9% 16.4 58.6% 3.3% 38.2% 40.3% 2.1% 8.5% 42.1 Blackmale 6.2% 21.7 65.1% 6.6% 28.3% 38.9% 3.9% 7.6% 58.5 Skilled 2.9% 25.6 73.6% 5.7% 20.7% 41.5% 3.2% 5.9% 73.6 Unskilled 3.2% 17.2 57.0% 7.7% 35.3% 36.8% 4.9% 9.6% 44.0 Blackfemale 6.7% 19.5 62.7% 5.2% 32.1% 35.4% 2.9% 8.6% 51.5 Skilled 3.6% 22.8 70.6% 4.6% 24.8% 39.1% 2.4% 7.2% 64.3 Unskilled 3.1% 14.5 52.9% 6.2% 40.9% 31.9% 3.7% 10.8% 35.9 Asianmale 3.5% 32.6 81.1% 3.6% 15.3% 42.0% 1.8% 4.9% 92.8 Skilled 2.2% 37.3 82.7% 3.4% 13.9% 40.7% 1.5% 4.5% 109.1 Unskilled 1.3% 18.5 77.1% 4.7% 18.2% 42.6% 2.7% 5.8% 52.4 Asianfemale 3.7% 25.3 64.1% 2.7% 33.2% 35.3% 1.5% 8.6% 64.6 Skilled 2.4% 29.4 67.4% 2.8% 29.8% 34.6% 1.4% 7.9% 78.1 Unskilled 1.3% 14.6 58.7% 2.7% 38.6% 36.8% 1.6% 11.3% 37.6 Hispanicmale 9.0% 20.7 78.4% 4.9% 16.7% 56.0% 3.6% 5.6% 59.3 Skilled 3.0% 28.0 81.5% 4.3% 14.3% 48.5% 2.5% 4.5% 83.0 Unskilled 6.1% 16.9 76.6% 5.4% 18.0% 58.2% 4.1% 6.1% 47.1 Hispanicfemale 8.6% 17.7 56.1% 4.0% 39.9% 38.8% 2.6% 11.7% 44.7 Skilled 3.3% 22.9 68.0% 3.7% 28.3% 40.2% 2.0% 8.0% 63.0 Unskilled 5.4% 13.6 49.2% 4.3% 46.5% 37.8% 3.2% 14.6% 33.4 Ratio Skillratio 0.76 0.60 0.83 1.48 1.58 0.96 1.75 1.55 0.55 Genderratio 1.01 0.80 0.83 0.79 1.80 0.86 0.77 1.70 0.73 Raceratio 0.61 0.79 0.91 1.55 1.23 0.89 1.57 1.50 0.76 Averagegainsfromeliminatingdemographicgaps(%increase) Skillgap 20.9% 7.9% -17.2% -20.1% 1.8% -24.6% -19.1% 24.4% Gendergap 11.5% 9.3% 12.1% -28.7% 7.6% 13.1% -26.1% 15.6% Racegap 8.5% 3.7% -17.1% -7.9% 4.3% -17.8% -15.7% 10.0% Allgaps 42.4% 18.9% -23.2% -50.7% 9.3% -29.1% -49.5% 54.7% Notes:Displayedaverageoutcomesarebasedonauthors’calculationsusingCurrentPopulationSurveydata (IPUMS,2018)fortheyears1998to2018andindividualsbetweentheages25and65. The2018population shares in the second column are calculated using data from U.S. Census Bureau (2019) and IPUMS (2018). Inadditiontopopulationshares, thetableshowsthehourlywagerates; employment, unemployment, and nonparticipationrates; quarterlyjob-findingratesfortheunemployed(π UE); jobseparationratestounemployment (π EU) and nonparticipation (π EN); and present value of lifetime earnings (W). W is calculated using equation (9). The displayed ratios are calculated as follows: Skill ratio = population-weighted average of outcomes of the unskilled/ population-weighted average of outcomes of the skilled; Gender ratio = population-weighted average of female outcomes / population-weighted average of male outcomes; Race ratio = population-weighted average of non-White (minority) outcomes / population-weighted average of Whiteoutcomes. 17

females have slightly different patterns in the CPS data compared to other groups: their wages peak earlier, around age 40, and start to decrease after that. The between-group wagegapsarefairlysmallforyoungworkers,butasthewagegrowthratesdifferbetween groups, the wage gaps increase over the life cycle. Within race, males have higher wage growthratescomparedtofemales,andAsianshavethehighestwagegrowthrateamong eachgender,followedbyWhitesandBlacks. AnaverageWhitefemalehasaverysimilar wagegrowthpatternasaverageHispanicandBlackmales. Interestingly,Asianmalesand females have the highest wage growth rates early in life, along with White males, which partlyarisebecauseofthehigherschoolinglevelofanaverageAsianbutalsofromhigher initialreturnstoschooling,particularforAsianmales.16 Figure 2 also shows the average unemployment and nonparticipation rates as well as job-finding rates for the unemployed for each gender-race pair. Unemployment rates are higher for younger workers, but decrease up to age 35 and stay fairly constant after that. White and Asian males and females have the lowest unemployment rates, while Black malesandfemaleshavesignificantlyhigherunemploymentratesoverthewholelifecycle, andespeciallywhentheyareyoung. Hispanicsdobetterintermsofunemploymentrates compared to Blacks, but their rates are still high compared to Whites and Asians. Within race, Hispanic females have higher unemployment rates and Black females have lower unemploymentratescomparedtomales,whiletheunemploymentratesarefairlysimilar betweenWhiteandAsianmalesandfemales. Figure 2 reveals variation in life-cycle nonparticipation rates between groups. In general, nonparticipation rates are lower for younger workers but start to increase rapidly afterage55forallgroups. Femalesaremorelikelytobenonparticipatingoverthewhole lifecycleandespeciallybeforeage45. Withinmalegroups,nonparticipationratesarequite similaroverthewholelifecycle,theonlyexceptionbeingBlackmales: theyaremorelikely tobenonparticipatingoverthewholelifecyclecomparedtoothermalegroups,andtheir nonparticipation rate starts to increase earlier, around age 45. The nonparticipation rates of Black males are closer to the nonparticipation rates of female groups than other male groupsafterage45. ItisnotclearwhythenonparticipationpatternsforBlackmalesdiffer fromthepatternsofothermalegroups. Anexplanationcouldbehighertheincarceration rateforBlackmales,butasCPSdatatypicallyexcludeinstitutionalizedpeople,thehigher incarcerationratecannotsolelyexplainthisdifference. Thereismorevariationinthenonparticipation rates for within-female groups compared to within-male groups, Hispanic andAsianfemalesbeingmorelikelytobenonparticipatingcomparedtoBlackandWhite females,especiallybeforeage45. To conclude the patterns in the labor market outcomes shown in Figure 2, we see that unemployment and wage outcomes seem to be negatively correlated: the lower the unemployment rates, the higher the levels and growth rates of wages tend to be. However, whileHispanicmalesandfemaleshavelowerunemploymentratesandhigherjob-finding ratescomparedtoBlackmalesandfemales,theirwagesarelower. Thus,itseemsthateven 16WecanconfirmthesestylizedfactsforAsiangroupsusingPanelStudyofIncomeDynamics(PSID)data, although,duetothesmallsamplesize,theresultsarenoisy. 18

though Hispanics have relatively better employment outcomes compared to Blacks, their wagesdonotseemtoreflectthat. Figure3presentstheaveragequarterlytransitionflowsbetweenemploymentandunemployment, and employment and nonparticipation for each gender-race pair.17 We observe large disparities in the job-finding rates between gender and racial groups. In general,job-findingratesarethehighestfortheyoungandprime-ageworkers,whiletherates start to decline after ages 40 to 45. Overall, males tend to have higher job-finding rates comparedtofemales,especiallyduringtheprimeworkingyears,butthejob-findingrates of Black males are closer to the rates of female groups than other male groups. Hispanic maleshavenotablyhighjob-findingratesoverthewholelifecyclecomparedtoanyother group. While Asian females have very strong labor market outcomes in terms of wages and unemployment, their job-finding rates are surprisingly the lowest of all the groups, alongwithBlackfemales. Thegreatestdifferencebetweenjob-findingratesofmalesandfemaleswithineachrace occursbetweenages25and45: whilemales’job-findingratesareattheirhighestlevelfor everygroup,females’job-findingratesslightlydecrease. AsianandBlackfemaleshaveespeciallylowjob-findingratesbetweenages30and40. Ingeneral,job-findingprobabilities fortheunemployedareoverallhigherforallgroupswhencomparingtojob-findingprobabilitiesfornonparticipants,whichdemonstratesthatthesetwogroupsshouldbetreated separately. Figure 3 shows that job destruction rates to unemployment and nonparticipation differ greatly with gender. While females are typically more likely to leave employment to nonparticipation, especially during the prime working years, this result reverses when lookingatthejobdestructionratestounemployment. Malesaremorelikelytomovefrom employment to unemployment when comparing the rates within a race. Job destruction rates to unemployment are higher early in the life cycle but stay relatively constant from ages35to55forallthegroups,exceptforBlacks,whosejobdestructionprobabilitiesshow a decreasing trend over the whole life cycle. Both Black males and females are the most likely groups to move from employment to unemployment within gender, followed by Hispanics. Young Blacks have an especially high likelihood of moving from employment tounemploymentcomparedtoanyothergroup. Also,Blackmalesarenotablymorelikely tomovetononparticipationcomparedtoothermalegroups, whichisconsistentwiththe higher nonparticipation rate for Black males shown in Figure 2. Black males are almost twice as likely to move from employment to nonparticipation during the prime working ages compared to White males, and the flows from employment to nonparticipation for Black males seem to be somewhat closer to the ones of Black and White females than the onesofothermales. Toconclude,femalesaremorelikelytomovetononparticipationover thelifecyclecomparedtomales,andBlackshaveconsiderablyhigherjobdestructionrates comparedtootherraces. 17Asmentioned,wealsoestimatethetransitionflowsseparatelyforbothskilledandunskilledgroups,and weusethoseflowsinthemodelcalibration. 19

0.6 0.5 0.4 0.3 60 etaR ylretrauQ Job-Finding Rate, Unemployed 0.4 0.3 0.2 0.1 30 40 50 60 etaR ylretrauQ Job-Finding Rate, Nonparticipants 0.06 0.04 0.02 30 40 50 60 Age etaR ylretrauQ Job Separation Rate to Unemployment 0.15 0.1 0.05 30 40 50 60 Age White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female etaR ylretrauQ 30 40 50 Age Age Job Separation Rate to Nonparticipation Notes:Thesejob-findingandjobseparationratesarebasedontheauthors’calculationsusingIPUMS (2018)datafortheyears1998to2018. Figure 3: Average quarterly job-finding and job separation rates over the life cycle for differentdemographicgroups. 3.2 SkillPremium,GenderGaps,andRacialGapsinLaborMarketOutcomes Table1alsoreportsskill,gender,andraceratiosinthelabormarketoutcomes. Skillratios arecalculatedasthepopulation-weightedaverageoftheoutcomesoftheunskilledrelative totheskilled. Forexample,thewageratioof0.60signifiesthattheunskilledaveragewage is 60 percent of the skilled average wage. Gender ratios similarly refer to the average outcomes of females relative to the average outcomes of males, while race ratios refer to the average outcomes of minorities relative to those of Whites. These ratios provide concise evidence of the large gaps between various demographic groups in a variety of labor market outcomes. In terms of average lifetime earnings (W), the unskilled earn 45 percent less than the skilled, females earn 27 percent less than males, and minorities earn 24 percent less than Whites. Gaps in lifetime earnings are due to gaps in both wages and employment. The unemployment rate is 48 percent higher for the unskilled, 21 percent lowerforfemales,and55percenthigherforminorities. The last part of Table 1 reports simple counterfactual effects of eliminating skill, gender, and racial gaps, one by one, on the economy-wide averages of various labor market outcomes. The counterfactual that eliminates gender gaps assumes that females achieve the same labor market outcomes as their male counterparts of the same skill, age, and race. The counterfactual eliminating the racial gaps assumes that minority groups have thesamelabormarketoutcomesastheirWhitecounterpartsofthesamegender,age,and skill. Finally, the counterfactual that eliminates skill gaps assumes that unskilled individualsachievethesameoutcomesastheirskilledcounterpartsofthesameage,gender,and 20

race. The potential aggregate impacts of eliminating these gaps in the labor market outcomesaresignificant. Forexample,averagelifetimeearningscouldincreaseby24percent ifskillgapswereeliminated,16percentifgendergapswereeliminated,and10percentif racial gaps were eliminated. These simple counterfactual results indicate that the aggregatebenefitsofclosingorreducingthesegapscouldbesignificant. 4 Calibration and Reverse Engineering of Model Parameters 4.1 StandardParameters Wesetthemodeltimeperiodtobeaquarterandthediscountratetobeβ = 0.9902,which implies that the real interest rate equals 4 percent annually. We concentrate on workers between ages 25 and 65 and assume that people live until age 80. Thus, a = 0 (age 25), a = 163(age65), anda¯ = 319(age80). Weassumethatatage25, theinitialmassoneof R workers,ms(0,a),isdividedbetweenemployment,unemployment,andnonparticipation i so that the values match the average values for each group i observed in the CPS data between 1998 and 2018. We calibrate the model for 24 types of i: we first calibrate the model for eight different gender (male and female) and race (non-Hispanic Asian, non- Hispanic Black, Hispanic, and non-Hispanic White) groups and then separately for 16 differentgender-race-skillgroups,wherethelevelofskillcanbeeitherskilledorunskilled, asdefinedintheprevioussections. Wesettheelasticityofthematchingfunction,α,tobe equalto0.5,acommonvalueusedinthesearchliterature(e.g.,Shimer(2005)). The parameter capturing the degree of statistical discrimination, µ, is calibrated such that the White/Black male ratio of vacancies per unemployed equals 1.5, consistent with the findings of Bertrand and Mullainathan (2004). We find that matching that calibration targetrequiressettingµ = 1,whichimpliesthat,inthemodel,firmsneedtobeallowedto accuratelyusethegroup-specificjobdestructionratessothatthecalibrationtargetcanbe matched. Our baseline model specification then allows for full statistical discrimination. Section 6.1 provides a comparison with the alternative case, µ = 0, and explains in detail whyfullstatisticaldiscriminationbetterdescribesthedatainthelightofthemodel. 4.2 MatchingProductivitiesandHumanCapital The main stylized facts that we require the model to exactly replicate are the life-cycle profiles of wages and job-finding rates for each group i, as illustrated in the first panel of Figure 2 and panels 1 and 2 of Figure 3. The key equations for this purpose are (3), (16), (21), and (14). Given a value of J (e,a + 1), which can be obtained by backward i inductionstartingattheretirementage,equation(16)providesaconnectionbetweenjobfinding rates and the ratio A(x)/(κ(x))1−α . Given the series of job-finding rates, only partialidentificationofthisratioispossible. Itisnotpossibletodetermine,forexample,if an unusually low job-finding rate—one that is below what is justified by the value of the matchtothefirm, J—isduetoaparticularly lowmatchingproductivityoraparticularly 21

high cost of posting a vacancy. We follow the literature by assuming that κ(x) solely depends on the human capital of the worker, which implies, for example, that it is more costly to hire a skilled worker than an unskilled worker. In particular, we assume that κ(x) = κ¯h(x), where κ¯ is a constant. This formulation precludes any discrimination to be capturedbyκ(x),sincethecostofhiringaworkeronlydependsonthetrueproductivityof theworker. Thisformulationconfersaconvenientscaleinvariance,orabalancedgrowth, propertytothemodel: equilibriumallocationsareinvarianttoscalinghumancapitallevels by a nonnegative factor. This can be seen from equation (16): doubling human capital would double the value of a firm with workers, J, but also the cost of hiring workers, κ(x),leavingthelabormarkettightnessrateunchanged. Equation(16)canbeusedtosolveforA(x)as (cid:18) κ¯h(x) (cid:19)1−α A(x) = f(x)α . (18) βJ (e,a+1) i Accordingtothisexpression,matchingefficiencyreflectsthejob-findingrateandthecost- κ¯h(x) benefit ratio, , of that particular market x. Labor markets with unusually low βJi(e,a+1) job-findingrates, butnormalcost-benefitratios, areparticularlyinefficientwhenitcomes to matching. Any discriminatory behavior in hiring is thus, by construction, captured by theefficiencyparameterA(x)asunusuallylowmatchingproductivity. Similarly,markets withnormaljob-findingratesbutunusuallylowcost-benefitratiosarealsoparticularlyinefficient. AnalternativeformulationwouldbetoassumeA(x) = Aforallx,whileletting κ(x) adjust to match observed job-finding rates according to (16). In that case, unusually lowjob-findingrateswouldbe“explained”byunusuallyhighhiringcosts. Inconclusion, ourestimatedmatchingefficiencyseries,A(x),arebetterinterpretedasmatchingproductivitiesrelativetohiringcosts. The calibration of human capital is based on equation (14).18 Given a value of W(x), whichcanbeobtainedbybackwardinductionstartingattheretirementage,equation(14) 1−φ(x) providesaconnectionbetweenobservedwagesandh(x),Θ(x) ≡ ,andc¯(x). Stud- φ(x) iesbyCard,Cardoso,andKline(2016)andIsoja¨rvi(2018)suggestthatdifferentialbargainingpowershavefairlymodesteffectsonexplainingwagedifferentials. Forthisreason,we assume identical bargaining powers for all groups, and, following the literature, we further assume that the Hosios condition (Hosios, 1990) holds so that φ(x) = α = 0.5 and Θ = 1.19 Usingthisassumptionandequation(20),equation(14)canbewrittenas (1+γ(x))h(x) = 2w(x)−βW (x). (19) This expression is the basis for the reverse engineering of human capital stocks. Similar 18The calibration of human capital for the last period before retirement is based on equation (21) in Appendix1. 19Co´rdoba,Isoja¨rvi,andLi(2021)showthattheHosiosconditionisasufficientconditionfordecentralized markets to be efficient even in the presence of learning by doing and nonparticipation. As mentioned in Footnote14,ourallocationsarenotfullyefficientsinceweassume,fortractability,thatunemploymentisthe onlyoutsideoptionduringbargaining. 22

tothecalibratedmatchingproductivityseries,onlypartialidentificationofhumancapital series is possible since wages depend on the joint term (1+γ(x))h(x), human capital adjustedbyitsnonmarketvalue. Thisimpliesthataparticularlylowwageratemaybedue to particularly low human capital of the worker, but it could also be due to a particularly low nonmarket value of the worker’s human capital that weakens the worker’s position duringwagenegotiations. We adopt a simple and common formulation for the consumption of workers during non-employment. FollowingPostel-VinayandRobin(2002),Burdett,Carrillo-Tudela,and Coles (2011), and Bowlus and Liu (2013), among others, we assume that consumption duringnon-employmentisproportionaltothehumancapitaloftheworker: c¯(x) = γ(x)·h(x) fora < a , R c¯(x ) = γR·h (e,a ) fora ≥ a . (20) R i R−1 R The first row of equation (20) presents the consumption for working-age non-employed, whereγ(x)isthewagereplacementrateforthenon-employed. Thesecondrowshowsthe consumption for the retired workers, γR being the pension replacement rate. This simple formulationcanbejustifiedbythefactthatunemploymentbenefitsandpensionsusually dependonpastearnings,andnonmarketactivitiesalsodependontheproductivityofthe worker. Ourbenchmarkcalibrationassumesγ(x) = γ sothatallwagedifferentialsarefullyattributed to human capital differentials. This choice reflects the traditional view on wages as primarily reflecting the true productivity of the workers. We calibrate γ such that the averageconsumptionduringunemploymentinthemodelisabout40percentoftheaverage consumption for the employed, following Shimer (2005). The calibrated value of γ is foundtobe0.35. WechooseγR = 0.33, whichimpliesthattheaverageconsumptionduring retirement is about 50 percent of the average human capital at the age of retirement. OurresultsarerobusttodifferentplausiblevaluesofγR. Givenγ(x)andobservedseries ofwages,w(x),equation(19)canbeusedtoobtainhumancapitalseries,andequation(1) canbeusedtoobtainy andr(x)asy = h(0,0,i,E)andr(x) = 1lnh(x) . i i e yi An implication of assuming γ(x) = γ is that any discriminatory behavior affecting wageswillnotbeattributedtodiscriminationoutsidethelabormarket. However,discrimination during hiring and in the workplace can be captured by the benchmark. Specifically, any discrimination in hiring would be included as part of the calibrated values of A(x) and affect wages through the term W(x). Discrimination in the workplace would be incorporated as part of the human capital series, particularly in the returns to experience, r(x). The traditional interpretation of differences in returns to experience obtained fromBlinder-Oaxacadecompositionsisthattheyreflectsometypeofdiscrimination(Blau & Kahn, 2017). The robustness section, Section 6, considers an alternative identification approach that allows discrimination outside the labor market to affect wages. It assumes common returns to experience across groups and uses equation (19) to recover series of γ(x)ratherthanseriesofhumancapital. 23

As we only observe average job-finding rates and average wages for every age, but not for every level of experience, we use the model’s analytical averages to match the corresponding data. In practice, the data restrictions imply that we can only recover A(x) = A (a,s)andr(x) = r (a). DetailsofthecalibrationstrategyareprovidedinAppeni i dicesBandC,alongwiththecalibrationalgorithm. Tofurtherclarifytheinterpretationof thedifferencesinjob-findingratesbetweenunemployedandnonparticipant,wecalibrate thesearcheffortofnonparticipants,ψ (a).20 Todothat,weneedanadditionalrestriction. i Weassumethatthegeneralmatchingefficiencyisequalforbothunemployedandnonparticipants,A (a,U¯) = A (a,N¯) = A (a),whichthenimpliesthatψ (a)capturesunexplained i i i i differences in job-finding rates between unemployed and nonparticipants for any given i anda. 4.3 Reverse-EngineeringResults 4.3.1 Life-CycleHumanCapitalProfiles Figure 4 displays average, reverse-engineered human capital and returns to experience profiles as well as average wage and experience profiles over the life cycle for eight demographic groups.21 As described earlier, human capital profiles are obtained such that themodelexactlymatchesaveragelife-cyclewages. Baseline,oreducation-relatedhuman capital levels, y , are depicted by the initial human capital levels at age 25, while the rei turnstoexperience,r (a),arereflectedinthehumancapitalgrowthratesoverthelifecycle. i Wedges in initial human capital levels and returns to experience could reflect differential schooling and occupational choices but also discrimination in the labor market to some extent. They could be interpreted as “occupational wedges”: a representative worker in each demographic group chooses an occupation with a different level of initial skills and futurehumancapitalgrowthrate. Forexample,aworkerwithalowerlevelofeducationis likely predetermined to have a low initial human capital level and human capital growth rateinthefuture. Apartialvalidation ofthecalibratedhumancapital profilesisprovidedbythe results obtained for White males, the case most studied in the literature. The calibrated average humancapitalprofileofWhitemalesiscloselyconnectedtoaveragewagesduringthelife cycle until around age 55. In particular, human capital starts low, grows faster for young workers,andslowsdownoverthelifecycleinthesamewayasthegrowthofwages. Our seriesforWhitemalesisroughlyconsistentwiththeoneobtainedbyothersearchmodels that also find a close association between wages and human capital (Bowlus & Liu, 2013, p.306). Theassociationisnotperfect,however. First,wagesgrowfasterthanhumancapital, until around age 50, reflecting improving labor market conditions over the life cycle, such as decreasing job separation rates and increasing job-finding rates. Second, human capital does not exhibit the clear inverted-U shape of wages. The model predicts a diver- 20Searcheffortofallunemployedgroupsisassumedtobeequalto1. 21SeeAppendixCforthedisaggregatedresultsforskilledandunskilledgroups. Thefindingsdescribedin thissectionaregenerallyrobusttothedisaggregation. 24

1.8 1.6 1.4 1.2 1 0.8 30 40 50 60 egaW 52 egA elaM etihW ot evitaleR Average Wages 120 100 80 60 40 20 30 40 50 60 Age ecneirepxe fo sretrauQ 2 1.5 1 30 40 50 60 Age Average Experience latipac namuH Average Human Capital 15 10 5 30 40 50 60 Age etaR ylretrauQ Age Average Returns to Experience, by age #10-3 White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female Figure4: Averagewage,humancapital,experience,andreturnstoexperienceprofilesover thelifecycle,relativetothewageofanaverage25-year-oldWhitemale. gentpathofwagesandhumancapitalafterage55,withwagesfallingwhilehumancapital isstillincreasing. Thefallingwagesreflecttheeffectofafiniteworkinglifethatgradually reducesthesurplusofthematch,andthereforewages,asaworkerapproachesretirement. This feature is consistent with similar life-cycle search models, such as Hairault, Cheron, andLangot(2007),Cheron,Hairault,andLangot(2013),andMenzio,Telyukova,andVisschers (2016). Rising human capital is needed to partly offset the finite-horizon effect and avoid wages falling too rapidly. The model thus implies that White males are most productivejustbeforeretirement,despitetheirfallingwages.22 Thesignificantbutnotperfect association between wages and human capital signifies that search frictions play an importantbutnotcrucialroleinwagedetermination. Allinall,ourcalibratedhumancapital profileforWhitemalesisconsistentwithexistingresultsintheliterature. Figure 4 also displays human capital estimates for other, less studied demographic groups. We find significant variation in human capital profiles along all demographic dimensions: age, skill, gender, and race. Within race, males have higher levels of human capital over the life cycle compared to females. However, there are two subperiods with markedly different evolution. Early in the life cycle and up to around age 33, the human capital of female groups grows faster than that of males, and in the case of Hispanics, females have higher human capital than males on average. Such convergence in human capital across genders is not reflected in wages, partly because of the slowly weakening femalelabormarketoutcomesasjobseparationratesincrease. Femalesthenfacestagnat- 22Increasinghumancapitalattheendofthelifecycleinourmodelplaysananalogousroletothefallin reservationproductivityconsideredbyCheron,Hairault,andLangot(2013). 25

ing or declining human capital between ages 35 and 50 likely related to career breaks: as manywomenleavethelabormarketduringprimeworkingagesduetofamilyandother reasons, the average human capital for those groups is lower. The opening gap after age 35 is due to an increasing gap in experience but also due to a decline in the returns to experience. Within gender, we also find fairly large differences in human capital profiles for differentraces, andthedifferencesincreaseoverthelifecycle. Asianmaleshavethehighest human capital until age 55, when White males take the lead. Black and Hispanic males have significantly lower human capital levels compared to Asian and White males, with Blacks having somewhat higher human capital compared to Hispanic males, although their wages are similar. Asian females have the highest human capital over the life cycle comparedtootherfemalegroups,followedbyWhitefemales. Again,BlackandHispanic femaleshavefairlysimilarhumancapitallevelsoverthelifecycle,butsignificantlylower levels compared to Asian and White females. The racial gaps in human capital are, however,smallerforwomenthanformen. TheaverageexperienceofBlackmalesisatypically lowformalesanddrivenbytheirunusuallyhighjobseparationratesandlowjob-finding rates. Blackmalesalsohaveunusuallylowreturnstoexperienceearlyinthelifecycle. ItisworthnotingthatthelifecyclehumancapitalprofilesforAsiansaredistinctfrom all other groups. Their human capital starts from a significantly higher level and grows rapidly until age 35 for females and age 40 for males. However, unlike for other groups, theirhumancapitalstartsdecreasingafterthat. Thereareatleasttwopossibleexplanations. First, the shape of the human capital profiles of Asians could capture cohort effects: it is possible that earlier cohorts in skilled Asian groups were choosing different occupations with very different returns to experience. This could show a relative decrease in human capital for older workers: since older workers in the data represent more heavily older cohorts, this cohort effect could explain the pattern. We study this effect by running our results for two different periods: 1989 to 2018 and 1998 to 2018. Our hypothesis is that if thecohorteffectisstrong,theresultsshouldbedifferentbetweenthesetwotimeperiods, as the 1989–2018 period includes older cohorts. However, we do not find this to be the case,whichimpliesthattherearelikelyotherexplanations. Anotherpossiblereasoncould bethatskilledAsiansfacerelativelymoreobstaclesintermsofpromotions,forwhichthere is some evidence. While Asians are the most educated group (50.6 percent of those aged 25 years and older have at least a bachelor’s degree compared to the national average of 30.1 percent), they are the least likely group to be promoted to managerial positions, and they are not well represented in executive positions (Gee & Peck, 2017). An exclusion of Asians from the highest-paid positions could then show up as stagnating wages and humancapitalinthedata. 4.3.2 Life-CycleMatchingEfficiencyProfiles Wenextpresentthereverse-engineeredmatchingefficiencies,A(x). Differencesinmatching efficiencies across labor markets reflect differences in job-finding rates that cannot be 26

explained by the differences in fundamentals: match values and vacancy posting costs. ExamplesoffactorsthatcanaffectA(x)includegeography,hiringpractices,searchintensity, and regulations specific to a type x. Wedges in matching efficiencies can also capture taste-based discrimination or prejudices in the labor market affecting the job-finding rates of different demographic groups. The results in this section are related to those of BarnichonandFigura(2015)andHallandSchulhofer-Wohl(2018),whoalsostudymatchingefficiencyunderheterogeneityandsegmentedmarkets. Whiletheyfocusonaggregate business cycle properties of matching efficiencies, our focus is on life-cycle and demographicfeatures. Figure 5 shows the job-finding rates and the reverse-engineered matching efficiencies of the unemployed. The first thing to notice is that there exists variation in the matching efficiencies, indicatingthattherearedifferencesinthejob-findingratesthatcannotbeexplainedbythedifferencesinfundamentalsbetweendemographicgroups. Atfirstglance, the calibrated efficiency profiles resemble, to a large extent, the profiles of the job-finding rates,animpressionthatislargelyshapedbytheresultsforHispanicmalesand,toalesser extent, Black females. These two groups exhibit the highest and lowest job-finding rates, respectively, and also end up being the ones with the highest and lowest matching efficiencies.23 Thus,thesimplecost-benefitanalysiscannotfullyexplaintheseoutermostjobfinding rates without significant differences in matching efficiencies. A closer look at the calibrated profiles reveals, however, a more complex relationship. In particular, many of thelargesystematicgapsinjob-findingratesdonottranslateintolargesystematicgapsin matchingefficiencies. Wenextsummarizesomesalientfeaturesofthecalibratedmatching efficiencies. First,whilejob-findingratestrenddownwardoverthelifecycleforallgroups,matchingefficienciesareflatterformanyofthegroups. ThisisparticularlyclearforWhitemales and White females, as well as for Hispanic females. In those cases, the falling job-finding rates over the life cycle are explained largely by the declining value of the match as the retirement age of workers gets closer. A strong downward trend in matching efficiency is clear for Hispanic and Asian males after ages 40–45, and less strong but clear for Black males. For these groups, age discrimination in hiring may play an important role and would show up as a decreasing matching efficiency for older workers. Second, despite theirlowerjob-findingrates,matchingefficienciesarerelativelyhighforHispanicfemales andAsianmales. Ourthirdobservationrelatestogendergaps. Similartohumancapitalgaps,malestend to have higher matching efficiencies within race compared to females. This is especially pronounced for younger workers. Gender gaps in matching efficiency increase and then fall over the life cycle. Hispanics have the widest gender gap among races, followed by Asians,Blacks,andWhites. ThegendergapforWhitesissmallanddisappearsataround 23A possible alternative explanation for the high job-finding rates of Hispanics would be that they have weakeroutsideoptionsbecauseoftheirlegalstatusandlanguagebarriers.Althoughaweakeroutsideoption couldexplaintheparticularlylowwageratesofHispanics,highmatchingefficienciesarestillneededinthe modeltomatchtherelativelyhighjob-findingratesofHispanics.SeeSection6fordetails. 27

0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 30 40 50 60 Age A Matching Productivity, Unemployed (A) 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 30 40 50 60 Age etaR ylretrauQ Average Job-finding Rate, Unemployed White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female Figure5: Averagejob-findingrateandmatchingefficiencyprofilesoverthelifecycle. age 40. Finally, when it comes to racial differences in matching efficiency, Hispanics have the highest matching efficiency over the life cycle. Within males, Hispanics have significantly higher A compared to other male groups. They are followed by Asians, Whites, andBlacks,buttheracialdifferencesaremoremodestbetweenthosethreegroups. When itcomestofemales,Whitefemaleshavethesecond-highestmatchingefficienciesoverthe lifecycle,whileAsiansandBlackshavelowerbutfairlysimilarmatchingefficiencies. Thecalibratedmatchingefficienciessuggestmixedresultsforthepotentialroleoftastebaseddiscriminationduringhiring. Ontheonehand, minoritygroupssuchasHispanics and Asian males exhibit particularly high matching efficiencies. On the other hand, there isapersistentbutnarrowefficiencygapbetweenBlackandWhitemalesandalargerand persistent gap between Black and White females and between Asian and White females. Aswillbecomeclearinthecounterfactualexercisesbelow,Whitemalesdonotexhibitparticularlyhighmatchingefficiencydespitetheirobservedhighjob-findingratesbecauseof theirlowerseparationratesandhigherreturnstoexperience. Everythingelsebeingequal, profit-maximizingfirmswouldnaturallypostmorevacanciesforworkerswithlowerseparationratesandhigherreturnstoexperience. We further reverse engineer the search effort of nonparticipants, ψ (a), over the life i cycle, and the detailed results are presented in Appendix C. To summarize the results, the search effort is higher for younger workers and decreases with age for most of the groups,consistentwiththeintuitionthatyoungworkersaremoreactivelyattachedtothe labor market. The search effort is also typically higher for males than females and the lowestforWhites. Thislastresultisneededforthemodeltoaccountforthefactthatjobfindingrates,outofnonparticipation,tendtobelowerforWhiteseveniftheyhavelower separationratesandhigherreturnstoexperience. 28

5 Decomposition of the Labor Market Outcome Gaps In this section, we assess the quantitative role of the recovered parametric wedges in accounting for differences in labor market outcomes as well as their macroeconomic significance. We consider four sets of counterfactuals: one that eliminates all gaps simultaneously, one that only eliminates gender gaps, one that eliminates racial gaps, and one that eliminatesskillgaps. Ineachcounterfactual,weclosethewedgesinexogenousvariables, onebyone,betweenthecomparisongroupandthereferencegroupandcalculatetheeffect onlabormarketoutcomes. Thesedecompositionsinformusabouttherelativeimportance of each exogenous variable in accounting for labor market disparities. Workers can differ along nine dimensions: human capital parameters (y(x), r(x)), matching efficiencies (A(x), ψ(x)), exogenous labor market flows (π¯ (x), π¯ (x), π¯ (x), π¯ (x)), and the EN EU UN NU initialmassdistributionamongeachemploymentstatus,s,atthebeginningofthelifecycle(ms(0,a)). Aggregateimpactsarecalculatedasweightedaveragesofthedisaggregated i impacts using each group’s population share in 2018 as a weight. For more precision, we usethecalibratedparametersfortheskilledandunskilledgroups,asreportedinAppendix C,ratherthanjusttheaggregatecategoriesreportedinSection4.24 Wealsoidentifythequantitativeimportanceofstatisticaldiscriminationbyrunninga counterfactual in which µ is set to 0. This prevents firms and workers from using groupspecificjobdestructionrateswhendecidinghowmanyvacanciestocreateandwhennegotiatingwages. Firmsinsteadusejobseparationratesofthecorrespondingreferencegroup in the counterfactual.25 As A(x) captures unexplained differences in job-finding rates between groups, we use the counterfactual eliminating gaps in A(x) to assess the potential magnitudeoftaste-baseddiscriminationinexplainingaggregatelabormarketgaps. Todealwithgapsthatareclosetozero,wereport“absolutecontributions”ratherthan simple contributions. To illustrate the issue, and the solution, consider the decomposition of the unemployment gap shown in the fourth panel of Figure 6. Since some of the gaps, relative to the reference group, are close to zero, and since some of the underlying explanatoryfactorshaveapositiveimpactwhileothershaveanegativeimpactonthegap, thepercentagecontributionsofindividualfactorscouldresultinfigureslike+150percent, +50percentand-100percent. Valueslikethesesuggesttherelativeimportanceofeachfactor,buttheexactrankingissometimesunclear. Tokeepindividualcontributionsbounded by100percentandaddingupto100percent,wedefinetheabsolutecontributionasthevalue oftherawcontributionrelativetothesumoftherawcontributionsinabsolutevalues. In the example above, the absolute contributions are 150/300=50 percent, 50/300=16.6 percent and -100/300=-33.3 percent. The absolute values of these contributions add up to 100 percent. This methodology is helpful, as it indicates that the first factor is the main 24Theresultsarequalitativelysimilarifonlyaggregatecategories,asdescribedinSection4,areused.Quantitatively,theresultsreportedinthissectionbasedonthemoredisaggregatedcategoriesprovidealargerrole forinitialhumancapitallevelsandalesserroleforjobseparationrates. 25Theexerciseisdifferentfromtheonecarriedoutforthenostatisticaldiscriminationmodel(NSD),described in Section 6. This section uses the calibrated parameters of the SD model (µ = 1) to assess what happensifµissettozerosothatfirmscannotstatisticallydiscriminatebasedonjobseparationprobabilities. 29

Wage Gap 20 10 0 -10 W M W S M US WF W S F US B M B S M US BFS BF US A M A S M US AFS AF US H M H S M US HFS HF US ruoh rep sralloD Employment Gap 0.3 0.2 0.1 0 W M W S M US WF W S F US B M B S M US BFS BF US A M A S M US AFS AF US H M H S M US HFS HF US / deyolpmE ecrof robaL Life-time Earnings (W) Gap 60 40 20 0 -20 W M W S M US WF W S F US B M B S M US BFS BF US A M A S M US AFS AF US H M H S M US HFS HF US ecnereffiD Unemployment Gap 0.04 0.02 0 -0.02 -0.04 W M W S M US WF W S F US B M B S M US BFS BF US A M A S M US AFS AF US H M H S M US HFS HF US / deyolpmenU ecrof robaL Labor Market Tightness for the Unemployed Gap 0.4 0.2 0 W M W S M US WF W S F US B M B S M US BFS BF US A M A S M US AFS AF US H M H S M US HFS HF US ecnereffiD Job-Finding Rate for the Unemployed Gap 0.2 0 -0.2 W M W S M US WF W S F US B M B S M US BFS BF US A M A S M US AFS AF US H M H S M US HFS HF US y A+A r : : : +: +m EU EN UN NU 0 / srednif boJ deyolpmenU Notes: Thedotsinthegraphsdemonstratetheobservedgaps. Eachbarrepresentsademographic group. The first letter of each acronym denotes race/ethnicity (A=Asian, B=Black, H=Hispanic, W=White), the second letter gender (M=Male, F=Female), and the third skill level (US=Unskilled, S=Skilled). Figure6: DecompositionoftheskilledWhitemalepremium. determinant of the gap, while the third factor is the second-most important determinant, although its contribution is negative. The proposed methodology has a bigger impact on how accounting results are reported for variables such as unemployment, tightness, and job-findingrates, butonlyaminorimpactonothervariablessuchaswages, employment rate,andlifetimeearnings. Forcompleteness,thedetailedtablesincludedinAppendixD alsoreporttherawvalues. 5.1 DecompositionofSkilledWhiteMalePremium Our first counterfactual exercise uses skilled White males as the reference group. We equate,onebyone,alltheparametersofothergroupstothevaluesofthereferencegroup within age and assess the individual impact of each parameter in generating labor market gaps. This exercise eliminates skill, gender, and racial gaps simultaneously. It also providesanupperboundforthepotentialaggregategainsofeliminatingalltypesoflabor marketdisparities,frictions,anddiscrimination. Figure6showsthedecompositionresults between the reference group and each remaining individual demographic group and for six different labor market gaps. The dots in the graphs demonstrate the observed gaps. Tables 2 and 3 report the corresponding aggregate decomposition results for selected labormarketvariables. ThefirstcolumnshowsthedecompositionoftheskilledWhitemale premium. 30

Consider first the determinants of wage gaps. Figure 6 and Table 2 show that wage gaps arise primarily from the differences in human capital parameters, y(x) and r(x). Differences in these two parameters account for around three-fourths of the average explained wage gap, with differences in initial human capital accounting for around half of the explained wage gap. Search frictions account for the remaining one-fourth of the explained wage gap. This split is similar to other findings in the search literature. For example, Bowlus and Liu (2013, p. 305) find that “human capital accumulation accounts for50percentoftotalearningsgrowth,jobsearchaccountsfor20percent,andtheremaining 30 percent is due to the interactions of the two.” Our corresponding decomposition, considering that the explained gap is 78 percent of the actual wage gap, are 47 percent, 23 percent, and 27 percent, respectively (see Table D3.1 in Appendix D). The similarity of thesplitisperhapsreassuringgiventhatBowlusandLiu(2013)focusonwagegrowthof Whitemalesratherthanwagedispersionamongdemographicgroups,useadifferenthumancapitalmechanism(Ben-Porath)ratherthanlearningbydoing,andemployNational Longitudinal Survey of Youth 1979 data rather than CPS data. The key role of human capital variables reflects the fact that the reference group, skilled White males, generally displays higher education levels and higher average returns to experience compared to other demographic groups, except Asian groups, which exhibit significantly larger initial humancapitalbutalsosignificantlyloweraveragereturnstoexperiencethanthereference group. Wefocusourcommentsonthedecompositionoftheexplainedcomponents,asthe explained components consist of 80 percent of the total gaps (see Table D3.1 in Appendix Dfordetails). The third-most important wedge accounting for the explained wage gaps is in the job destructionratetononparticipation(π¯ ). Thiswedgealoneaccountsforaround19per- EN cent of the explained wage gap. Part of this effect comes from the fact that a high π¯ EN is directly related to career interruptions, lower experience, and slower accumulation of humancapital. Surprisingly,themajorityoftheeffectcomesfromthefactthatahighπ¯ EN weakensaworker’soutsideoptioninwagebargaining,leadingtoalowerwage. Wewill returntothisresultwhenanalyzingtheroleofstatisticaldiscriminationbelow. Considernextthedeterminantsofotherlabormarketoutcomes. Gapsinemployment rates reported in Table 3 are largely driven by the wedges in job separation rates, mainly inπ¯ ,althoughwedgesinπ¯ alsoplayasignificantrole. Highseparationratesdirectly EN EU lead to lower employment but they are also the major determinants of the differences in theprobabilityofmovingbacktoemployment,asseenwhenlookingatthedecomposition forthejob-findingratesoftheunemployedπ¯ . Returnstoexperience,r(x),havealarge UE effect on job-finding rates, as they determine the expected long-term value of a match. Noticethatwhiledifferencesininitialhumancapitalarethekeydeterminantofthewage gaps,theyplaynoroleinexplaininggapsinotherlaborvariablessuchasemploymentor job-findingrates. Thereasonisthat,asdiscussedinSection3,themodelisscale-invariant inhumancapitallevels. Interestingly, equating the matching efficiencies A(x) of all groups to that of the ref- 31

Table2: Decompositionofthewageandlifetimeearningsgaps. PanelA.Absolutecontributions,wages Allgaps Skillgaps Gendergaps Racegaps Humancapital Initialhumancapital(y) 46.9% 59.8% 38.4% 24.2% Returnstoexperience(r) 26.9% 23.5% 15.4% 36.5% Total 73.8% 83.3% 53.8% 60.7% Searchfrictions Matchingefficiency(A) -0.7% -2.1% 4.7% 0.2% Searcheffort,nonparticipants(ψ) 2.2% 1.7% 5.2% -6.7% Separationrates(d) Tounemployment(π EU) 2.8% 3.9% -3.3% 8.5% Tononparticipation(π EN) 18.7% 8.2% 29.4% 21.9% Total 23.0% 11.7% 36.0% 23.9% Statisticaldiscrimination 15.1% 9.3% 16.0% 22.6% PanelB.Absolutecontributions,lifetimeearningsW Allgaps Skillgaps Gendergaps Racegaps Humancapital Initialhumancapital(y) 35.4% 48.8% 27.6% 16.5% Returnstoexperience(r) 29.7% 25.2% 18.2% 31.4% Total 65.1% 74.0% 45.8% 47.9% Searchfrictions Matchingefficiency(A) -0.9% -2.8% 4.2% 1.3% Searcheffort,nonparticipants(ψ) 4.0% 4.9% 7.7% -14.0% Separationrates(d) Tounemployment(π EU) 2.9% 4.3% -3.3% 8.4% Tononparticipation(π EN) 25.7% 13.1% 36.2% 26.6% Total 31.9% 19.5% 44.8% 22.3% Statisticaldiscrimination 24.0% 15.2% 25.3% 30.7% Notes: Theroleofstatisticaldiscriminationisobtainedbysettingµ=0, whichimpliesthatfirmscannotobservethetruedforeachdemographicgroupwhenpostingvacanciesandbargainingoverwages. Thetotal contributionofdcanbedividedintotwoparts:statisticaldiscriminationanddirecteffect,contributionofd= statisticaldiscrimination+directeffect. 32

Table3: Decompositionoftheemploymentandjob-findingrategaps. PanelA.Absolutecontributions,employment Allgaps Skillgaps Gendergaps Racegaps Humancapital Initialhumancapital(y) 0.0% 0.0% 0.0% 0.0% Returnstoexperience(r) 7.4% 8.5% 2.7% 4.5% Total 7.4% 8.5% 2.7% 4.5% Searchfrictions Matchingefficiency(A) -3.2% -10.2% 10.8% -3.1% Searcheffort,nonparticipants(ψ) 12.6% 17.7% 14.5% -29.3% Separationrates(d) Tounemployment(π EU) 8.2% 13.5% -6.2% 13.3% Tononparticipation(π EN) 64.0% 47.0% 59.0% 46.7% Total 81.6% 68.0% 78.1% 27.6% Statisticaldiscrimination 14.6% 13.4% 10.2% 13.7% PanelB.Absolutecontributions,job-findingrate,unemployed Allgaps Skillgaps Gendergaps Racegaps Humancapital Initialhumancapital(y) 0.0% 0.0% 0.0% 0.0% Returnstoexperience(r) 26.2% 25.9% 8.9% 17.4% Total 26.2% 25.9% 8.9% 17.4% Searchfrictions Matchingefficiency(A) -14.6% -30.4% 29.6% -22.2% Searcheffort,nonparticipants(ψ) -6.0% -6.0% -8.0% 13.5% Separationrates(d) Tounemployment(π EU) 4.4% 7.0% -3.9% 9.2% Tononparticipation(π EN) 37.7% 23.6% 36.1% 28.4% Total 21.5% -5.8% 53.8% 28.9% Statisticaldiscrimination 46.7% 34.2% 32.6% 40.7% Notes: Theroleofstatisticaldiscriminationisobtainedbysettingµ=0, whichimpliesthatfirmscannotobservethetruedforeachdemographicgroupwhenpostingvacanciesandbargainingoverwages. Thetotal contributionofdcanbedividedintotwoparts:statisticaldiscriminationanddirecteffect,contributionofd= statisticaldiscrimination+directeffect. 33

erence group would further increase most labor market gaps. The reason is that the calibratedmatchingefficiencyforskilledWhitemalesismoreontheaveragelevel,whilesome groups, such as Hispanics and the unskilled, tend to exhibit higher matching efficiencies. The role of taste-based discrimination in hiring thus seems limited when considering the unemployed. Thekeylabormarketoutcomeofthemodelistheaveragelifetimeearningsofworkers, W(x),asdefinedbyequation(9). Thisaveragewelfaremeasuretakesintoaccountallthe wageandemploymentinformationofaworker.26 Thedecompositionresultsfortheaverage W reported in Table 2 follow somewhat closely the decomposition results for wages, emphasizing the roles of human capital parameters and π¯ . However, as W depends EN closelyonbothlife-cyclewagesandemployment,theroleofπ¯ isgreaterandtheroleof EN y is smaller in generating these gaps compared to the wage gap decomposition. We find i that, from the point of view of average lifetime earnings, W, human capital differences account for 65 percent of the total earnings disparities, while search frictions account for about32percent. Finally,weinvestigatetheroleofstatisticaldiscriminationingeneratingthegaps. For thispurpose,wesetµ = 0,whichequatestheseparationratesofallgroupstothereference group, but only for a job posting and wage bargaining decisions. Actual separation rates arestillusedwhencalculatingjobflowsintounemploymentandnonparticipation—what we call the direct channel. We find that statistical discrimination explains the majority of theimpactthatcomesthroughjobseparationrateswhenlookingatthewage,job-finding rate,andearningsgaps. Around70percentoftheroleofπ¯ andπ¯ ingeneratingwage EU EN gapsarisesfromfirms’differentialtreatmentofgroupsbasedontheirjobdestructionrates accounting for 15 percent of the total wage gaps, while the rest is coming through the directchannel. Accordingtothemodel,higherjobdestructionprobabilitiesloweraworker’s outside option in the wage negotiation, leading to lower wages. Around half of the gaps injob-findingratescanbeexplainedbystatisticaldiscrimination,accordingtothemodel. Firms post fewer vacancies to workers with higher job destruction rates. Around 24 percentoftheoverallwelfaregapsoverthelifecyclearecomingthroughthisdiscrimination channel. The contribution of statistical discrimination is smaller when looking at the employment outcome, as this outcome depends closely on the direct channel affecting the employmentmasses. Therestoftheimpactiscomingthroughthediscriminationchannel affectingaworker’sjob-findingrate. In contrast to the role of taste-based discrimination, we find a potentially significant role for statistical discrimination in explaining the aggregate outcome gaps between differentskillgroups,genders,andraces. AccordingtoTables2and3,statisticaldiscriminationalonecanexplainaround15percentofbothwageandemploymentgapsandaround half the gaps in job-finding rates. The impacts on life-cycle welfare gaps are also large, at around24percent. 26Sinceaperiodinthemodelisaquarter,W ismeasuredinquartersofearnings. 34

Wage Gap 20 10 0 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US ruoh rep sralloD Employment Gap 0.2 0.1 0 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US / deyolpmE ecrof robaL Life-time Earnings (W) Gap 60 40 20 0 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US ecnereffiD Unemployment Gap 0.02 0 -0.02 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US / deyolpmenU ecrof robaL Labor Market Tightness for the Unemployed Gap 0.2 0 -0.2 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US ecnereffiD Job-Finding Rate for the Unemployed Gap 0.1 0 -0.1 -0.2 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US y A+A r : EU : EN : UN +: NU +m 0 / srednif boJ deyolpmenU Notes: Thedotsinthegraphsdemonstratetheobservedgaps. Eachbarrepresentsademographic group. The first letter of each acronym denotes race/ethnicity (A=Asian, B=Black, H=Hispanic, W=White), the second letter gender (M=Male, F=Female), and the third skill level (US=Unskilled, S=Skilled). Figure7: Decompositionofskillgaps. 5.2 DecompositionofSkillGapsandSkillPremium Oursecondexercisedecomposesthesourcesofskillgaps,orskillpremium. Thesearegaps in labor market outcomes between skilled and unskilled individuals of the same gender, race, andage. AsshowninTable1, theoutcomegapbetweentheskilledandunskilledis thelargestcomponentofthetotalgaps. Skillgapsrepresent49percentofthetotalgainsof eliminatingallgapsinwagesand42percentand45percentoftheoverallexplainedgaps inlifetimeearningsandemployment,respectively. Thedecompositionexerciseusesskilledindividualsofthesamegender, race, andage as the reference group, and the results are shown in Figure 7 and Tables 2 and 3. As expected,thetwohumancapitalvariables,initialhumancapitalandreturnstoexperience, account for most of the skill premium in wages and lifetime earnings (83 percent and 74 percent, respectively) and less of the corresponding premiums in employment and jobfindingrates(9percentand26percent,respectively). Initialhumancapitalisthedominant factor,accountingforaround60percentoftheskillwagepremiumandforaroundhalfof thepremiuminlifetimeearnings. While a predominant share of the skill premium can be explained by human capital differences,animportantshareoftheskillpremiumsareexplainedbysearchfrictions—in particular, by wedges in separation rates. The lower separation rates of skilled workers accountfor12percent,61percent,and17percentofthepremiumsinwages,employment, 35

and lifetime earnings, respectively. According to the model, statistical discrimination accounts for between 9 and 15 percent of the skill premiums in wages, employment, and lifetime earnings, and 34 percent of the skill premiums in job-finding rates. While statistical discrimination is moderately important in generating skill premiums, the higher average A(x) of the unskilled improves the labor market outcomes of the unskilled and decreasesskillgapslimitingthepotentialroleoftaste-baseddiscriminationingenerating theskillpremiums. These accounting results indicate that higher human capital—the ability of a worker to generate output—is the main reason why skilled workers enjoy labor market premiums. But it is not the only reason. Skill premiums also reflect lower separation rates and statisticaldiscriminationthatfavorskilledworkers. 5.3 DecompositionofGenderGapsandMalePremium Thegendergapisthesecond-largestcomponentofthetotalgaps. AccordingtoTable1,it accountsfor27percent,29percent,and49percentoftheoverallexplainedgapsinwages, lifetime earnings, and employment, respectively. The decomposition results, shown in Figure 8 and Tables 2 and 3, suggest fairly equal roles for human capital and search frictionsinexplaininggendergapsinwages(54percentand36percent)andlifetimeearnings (46 percent and 45 percent), but a minimal role for human capital variables in explaining the significant gender gaps in employment and job-finding rates. The gender gap in job separation rates to nonparticipation (π¯ ) is either the main or a major factor explaining EN gendergapsinoutcomes,andthemajorityoftheimpactentersthroughstatisticaldiscrimination. The respective contributions of π¯ and statistical discrimination are 29 percent EN and16percentforwagegaps,36percentand25percentforlife-timeearningsgaps,59percent and 10 percent for employment gaps, and 36 percent and 32 percent for job-finding ratesoftheunemployed. Highjobseparationratesoffemalesleadtosignificantlyweaker labormarketoutcomes,reflectedparticularlyinjob-findingandemploymentrates. Taste-based discrimination can potentially explain a small share of male premiums in outcomes, and the role of taste-based discrimination is the largest in explaining gender gapscomparedtotheothergaps. Taste-baseddiscriminationcanpotentiallyexplainupto 4 to 5 percent of the gaps in wages and lifetime earnings, 11 percent of the employment gaps,andalmost30percentofthegapsinjob-findingrates. WhenlookingatFigure8,the roleofA(x)isparticularlylargeforunskilledfemalegroups. 5.4 DecompositionofRacialGapsandWhitePremium The racial gaps are the third largest of all gaps. According to Table 1, they account for around 18 to 20 percent of the overall gaps in wages, lifetime earnings, and employment rates. The decomposition results, shown in Figure 9 and Tables 2 and 3, suggest a strong roleforhumancapitaldifferentials,particularlyinreturnstoexperienceandjobseparation ratesinexplainingracialgaps. Humancapitaldeviationsexplain,respectively,61percent and48percentofthewageandlifetimeearningsgapsand5percentand17percentofthe 36

Wage Gap 10 5 0 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US ruoh rep sralloD Employment Gap 0.4 0.2 0 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US / deyolpmE ecrof robaL Life-time Earnings (W) Gap 30 20 10 0 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US ecnereffiD Unemployment Gap 0.04 0.02 0 -0.02 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US / deyolpmenU ecrof robaL Labor Market Tightness for the Unemployed Gap 0.3 0.2 0.1 0 -0.1 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US ecnereffiD Job-Finding Rate for the Unemployed Gap 0.2 0.1 0 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US / srednif boJ deyolpmenU y A+A r : EU : EN : UN +: NU +m 0 Notes: Thedotsinthegraphsdemonstratetheobservedgaps. Eachbarrepresentsademographic group. The first letter of each acronym denotes race/ethnicity (A=Asian, B=Black, H=Hispanic, W=White), the second letter gender (M=Male, F=Female), and the third skill level (US=Unskilled, S=Skilled). Figure8: Decompositionofgendergaps. racialgapsinemploymentandjob-findingratesoftheunemployed. Wedgesinseparation rates and statistical discrimination explain, respectively, 30 percent and 23 percent of the racial wage gap, 35 percent and 31 percent of the racial lifetime earnings gap, 60 percent and14percentoftheracialemploymentgap, and38percentand41percentofthegapin thejob-findingsrateoftheunemployed. These aggregate results hide some important differences between racial groups. As shown in Figure 9, a lower matching efficiency is an important contributor to the lower job-finding rate of the unemployed and other gaps in employment variables, particularly for unskilled Black males and skilled Asian females. The decomposition thus suggests that prejudice in hiring may be an important determinant of employment gaps for these groups. However, Hispanic groups, except for skilled Hispanic females and unskilled Asian females, exhibit particularly high matching efficiencies relative to the comparison group—an average White worker of the same age, gender, and skill. These results suggestreverse-prejudice, asemployersmayprefercertainminoritygroupsforcertaintasks. The overall potential effect of prejudice in hiring is relatively secondary according to our decomposition. Bertrand and Mullainathan (2004) provide compelling evidence that race matters for hiring decisions. In their field experiment, job applicants with White-sounding names received around 50 percent more callbacks for interviews compared to otherwise similar candidateswithBlack-soundingnames. Whatcouldbethesourcesofthisdifference? Our 37

Wage Gap 10 5 0 -5 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US ruoh rep sralloD Employment Gap 0.2 0.1 0 -0.1 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US / deyolpmE ecrof robaL Life-time Earnings (W) Gap 20 0 -20 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US ecnereffiD Unemployment Gap 0.01 0 -0.01 -0.02 -0.03 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US / deyolpmenU ecrof robaL Labor Market Tightness for the Unemployed Gap 0.2 0.1 0 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US ecnereffiD Job-Finding Rate for the Unemployed Gap 0.1 0 -0.1 W M W S M US WFS WF US B MS B M US BFS BF US A MS A M US AFS AF US H MS H M US HFS HF US y A+A r : EU : EN : UN +: NU +m 0 / srednif boJ deyolpmenU Notes: Thedotsinthegraphsdemonstratetheobservedgaps. Eachbarrepresentsademographic group. The first letter of each acronym denotes race/ethnicity (A=Asian, B=Black, H=Hispanic, W=White), the second letter gender (M=Male, F=Female), and the third skill level (US=Unskilled, S=Skilled). Figure9: Decompositionofracegaps. exercise sheds some light. According to our model, there are three reasons why some individuals are more employable than others: (i) higher human capital, (ii) prejudice in hiring, and (iii) statistical discrimination. Our quantitative exercise suggests that human capital differences—particularly in returns to experience—and statistical discrimination explains most of the gap. Prejudice in hiring plays a secondary role, on average, but is potentially important for certain groups. For example, our disaggregated results show thatprejudicecanexplainupto38percentofthelowerjob-findingrateofunskilledBlack malesrelativetounskilledWhitemales. 6 Robustness Checks This section provides further support to the use of the benchmark model by considering two alternative calibrations of the model. The first alternative precludes any statistical discrimination from occurring, while the second alternative allows workers’ outside options—the nonmarket compensations—to vary across demographic groups enough for the model to match the observed wage gaps. We find that these alternative formulations areproblematic. Wehaveperformedfurtherrobustnesschecksnotreportedhere. Wefind thatourmainresultsarerobusttothefollowingalternatives: (i)differentperiodsofanalysis (1976 to 1980, 2003 to 2007, and 2014 to 2018), and (ii) exclusion of part-time workers 38

1.02 1 0.98 0.96 0.94 0.92 0.9 30 40 50 60 Age DS/DSN :latipaC namuH evitaleR Average Human Capital 1.05 1 0.95 0.9 0.85 0.8 0.75 30 40 50 60 Age White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female DS/DSN :ytivitcudorP gnihctaM evitaleR Matching Productivity, Unemployed (A) Figure 10: Human capital profiles: No statistical discrimination (NSD, µ = 0) relative to statisticaldiscrimination(SD,µ = 1). fromthedatasample. 6.1 NoStatisticalDiscrimination Thebenchmarkmodelassumesµ = 1,orfullstatisticaldiscrimination(SD).Inthissection, we report results for an alternative calibration strategy with no statistical discrimination (NSD), where µ is set to be 0. This calibration strategy implies that firms are not able to statisticallydiscriminateagainstworkersbasedongroup-specificjobseparationprobabilities,π¯ andπ¯ . Instead,thecalibrationassumesthatfirmsandworkersonlyobservea EN EU commonsetofjobseparationrates, affectedonlybyskill, age,andexperience, butnotby demographic indicators. For convenience, we choose job separation rates of White males asthecommonratesmainlybecauseWhitemalesarethereferencegrouputilizedinother partsofthepaper. Theresultsinthissectionarerobusttoselectingothernaturalreference groups,suchaspopulationaveragesbyage,experience,andskill.27 Figure 10 shows life-cycle human capital profiles and matching productivities of the NSD model relative to the SD model. A salient feature of these graphs is that the NSD model requires significantly lower human capital stocks of demographic groups, relative toWhitemales,andlowermatchingefficienciesthantheSDmodel. Therequiredpercentagedropinmatchingefficienciesislargerandmorepersistentoverthelife-cyclethanthe requireddropinhumancapital. Thelargedropinmatchingefficienciesofallgroupsrelative to White males suggests that reducing the role of statistical discrimination by setting 27Usingaverageprobabilitieswouldbeamoretransparentexercisebecauseitwouldbeamean-preserving changeindestructionrates. 39

µ = 0 increases the potential role of taste-based discrimination (TBD). In particular, the SD model suggests a relatively small potential role for TBD when it comes to gender and racialdiscriminationsincematchingefficienciesareonlyslightlylowerforWhitefemales and Black males relative to White males. As the NSD model requires significantly lower matchingefficienciesforthesetwogroups,theNSDmodelsuggestsalargerpotentialrole forTBD. The direct effect of eliminating statistical discrimination is an increase in the value of matchesforgroupswithhigherbreakprobabilitiesthanWhitemales,suchaswomenand Blackmales,whichincreasesjobpostingandimprovesjob-findingratesforthosegroups. To counteract this effect and thus match the observed job-finding rates, the NSD model requires lower matching efficiencies for those groups. Eliminating SD would also tend to increase wages of those same groups since their match surpluses increase when separation rates fall to equate to the rates of White males. To offset this effect and thus match observed wages, the NSD model requires lower human capital stocks for those groups. Lowerhumancapitalpartlyreducesmatchsurplusesanddiscouragesjobposting,butthe direct effect of lower separation rates dominates, making it necessary for the NSD model tolowermatchingefficienciessignificantly. These exercises show the difficulties that a pure human capital model has to jointly explain the evidence on wages and job-finding rates. In other words, a model that is free ofanytypeofdiscriminationinthelabormarket,beyondwhatisembodiedinthehuman capitaloftheworker,wouldhavedifficultiesmatchingthedata. Theresultsalsohighlight the importance of utilizing a general equilibrium model rather than a partial equilibrium one. Finally, Figure 11 shows the labor market tightness rates for different groups relative totheratesofWhitemalesfortheSDandNSDmodels. Tightnessratesareclosertoeach otherbetweendifferentgroupsintheNSDmodelsincefirmscannottreatworkersdifferently,ordistinguishamongworkers,basedontheirmatchbreakprobabilities. Theaverage labormarkettightnessrateofWhitemalesis1.12timeshigherthantherateofBlackmales in the NSD model. This small gap generated by the NSD model is problematic since the evidence suggests a larger gap in the number of vacancies per unemployed worker. As mentioned earlier, Bertrand and Mullainathan (2004) find that Whites receive 50 percent morecallbacksperapplicationthanBlacks. Thisalsosuggestsa50percenthighereffective vacancy posting rate for Whites compared to Blacks. The NSD model, which turns out to require significant TBD to match the data, does not produce nearly enough gap in the vacancyrates. Incontrast,theSDmodelgeneratesaWhite-Blackvacancypostingratioof 1.5, consistentwiththefindingsofBertrandandMullainathan(2004). Forthisreason, we choosetheSDmodelasthebenchmarkmodel. 6.2 CalibratedOutsideOptions The calibration of the human capital trajectories in the benchmark model using equation (19)assumesacommonreplacementrate, γ(x),forallgroups. Wenowreportresultsfor 40

1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 30 40 50 60 Age deyolpmenU ,ssenthgiT tekraM boJ selaM etihW ot evitaleR Full Statistical Discrimination 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 30 40 50 60 Age deyolpmenU ,ssenthgiT tekraM boJ selaM etihW ot evitaleR No Statistical Discrimination White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female Figure 11: Labor market tightness rates for the average unemployed individuals of each demographic group relative to the average unemployed White males for the statistical discriminationmodel(µ = 1)andthenostatisticaldiscriminationmodel(µ = 0). an alternative calibration that assumes a common human capital function for all groups, and uses (19) to recover group-specific series of γ(x). The nonmarket value of human capital is then given by γ(x)·h(x), a value that allows the model to match the observed wage rates. The common human capital function used is the one calibrated for White males in the benchmark model. The function allows the initial human capital and the returnstoexperiencetodependontheskilllevel. Figure 12 shows the calibrated series of γ(x) for various groups. The limitations of a calibration that relies on differential outside options as a way to explain wage differentialsareimmediatelyclear. Themostsalientlimitationisthatitwouldrequirethehuman capitalofmostgroupstohaveazeroornegativevalueoutsidethelabormarketforasignificantpartofthelifecycle. Forexample,everyfemalegroupwouldberequiredtohave anegativeoutsideoptionbyages35to40. Twootherquestionableimplicationsarethat(i) Whitemaleswouldhavelowerenteringlevelsofhumancapitalthanallothergroups,and (ii)WhiteandAsianfemaleswouldhaveanincreasinglybetteroutsideoptionthanWhite malesearlyoverthelifecycle. 7 Relation to the Literature Ourpaperrelatestothelargeandactiveliteratureonthelabormarketdisparitiesbetween gender and race and, more specifically, to the literature on labor market discrimination (see literature reviews in Lang and Lehmann (2012) and Blau and Kahn (2017)) and on the impacts of career breaks on labor market outcomes. The literature on discrimination using dynamic, structural approaches is fairly limited. The closest paper to ours is Gayle 41

0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 25 30 35 40 45 50 55 60 Age . Value of the Outside Option White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female Figure 12: Value of the outside option (as a proportion of human capital) required to explainwagegaps. 42

andGolan(2012),whostudygenderdiscriminationandagenderwagegapbybuildinga dynamic general equilibrium model. They find that the difference in labor market experience is the most important channel to explain the gender wage gap over the life cycle, and statistical discrimination can also explain a significant fraction of the gap. Our paperdiffersfromtheirsaswenotonlystudythegenderwagegapanddiscrimination, but a wider group of people. Also, we study specifically labor markets with frictions to be abletostudysimultaneouslynotonlywagedisparities, butalsodisparitiesinotherlabor market outcomes. There exists a very recent literature on identifying the causal impacts of parenthood on gender wage gaps (Angelov, Johansson, & Lindahl, 2016; Chung et al., 2017;Kleven,Landais,&Sogaard,2019;Lundborg,Plug,&Rasmussen,2017),andtheresults show consistently large and long-term impacts of parenthood on the increase in the wagegaps. Moregenerally,thereisaliteratureontheimpactofunemploymentspellson earnings. Forexample,Guvenenetal.(2017)foundthatspendingoneyearormoreoutof workcausedlong-termlossesofearningsforU.S.maleworkerscomparedtoworkerswho stayed employed. Our paper builds on these empirical findings by modeling the relation between non-employment periods and human capital growth, and then uses the general equilibriummodeltoassesshowalargefractionofthenegativeimpactofthenonworking periodsisarisingfromthediscriminatorybehaviorofthefirms. Ourtheoryrelatestotheliteratureonsearchmodelswithhumancapitalgrowth. There are earlier papers that study human capital and wage growth in search frameworks. The literature usually studies the role of human capital investment (either general or firmspecific)versuson-the-jobsearchonwagegrowth. Flinn,Gemici,andLaufer(2017)study how firms and workers choose to invest in general and firm-specific human capital in a partialandgeneralequilibriumsearchmodel,andhowmuchoftheworkers’wagegrowth canbeexplainedbyinvestmentinhumancapitalversussearchingfornew,moreproductiveemploymentopportunities. TheylinktheirresultswiththeMincerequationandfind decreasingreturnstoinvestmentinbothtypesofhumancapital. Burdett,Carrillo-Tudela, andColes(2011)alsobuildasearchmodelwithgeneralhumancapitalaccumulationand on-the-jobsearchtoinvestigatetheroleofeachofthesechannelsinhumancapitalgrowth inthesteady-state, butintheirmodel, generalhumancapitalaccumulatesthroughlearningbydoing. TheyalsoconnecttheirresultswiththeMincerequationtoseeiftheirmodel generatesareasonableconnectionwithMincerliterature. However,theyassumeconstant returnstoexperience, whichdiffersfromtypicaldecreasingreturnsofexperienceinMincerequations. Baggeretal.(2014)buildamodelalongthesamelinesasBurdett,Carrillo- Tudela, and Coles (2011) but allow for an employee and an employer heterogeneity and productivity shocks, and they estimate the life-cycle wage growth patterns. Our paper alsoassumeshumancapitalaccumulationthroughlearningbydoing,butthemaindifferenceinourframeworkisthatwealsorequireourmodeltogeneraterealisticemployment, unemployment, and nonparticipation outcomes over the life cycle, in addition to wage outcomes. Theseotherlabormarketoutcomesaretightlylinkedwiththewageoutcomes through human capital accumulation and the wage bargaining between a worker and a 43

firm. We also study quantitatively how well our framework can explain race and gender differencesinalltheselabormarketoutcomes. This paper also combines the literature on wage gaps with the growing literature on transitionflowsandtheirimportanceonunemploymentandparticipationratesofworkers (Choi,Janiak,&Villena-Roldan,2014;Elsby,Hobijn,&Sahin,2015;Kroft&Notowidigdo, 2016; Menzio, Telyukova, & Visschers, 2016) by studying how much gender and race differences in flow probabilities can explain differences in wage growth patterns and other labor market outcomes. This paper also relates to the literature on finite life-cycle search models (Cheron, Hairault, & Langot, 2013; Esteban-Pretel & Fujimoto, 2014; Fujimoto, 2013;Hairault,Cheron,&Langot,2007;Bowlus&Liu,2013,Menzio,Telyukova,&Visschers,2016)bystudyingwagegrowthandthegenderandracewagegapsinafinitelife-cycle environmentwithhumancapitalgrowthduetoexperience. Finally,RauhandValladares- Esteban (2018) study the wage and employment gaps between Black and White males in a model with endogenous human capital and exogenous separation rates. They find a similar role for separation rates as we do. Our focus is more comprehensive, and unemployment rates are endogenous in our environment, which allows us to discuss issues of statisticalandtaste-baseddiscrimination. 8 Concluding Comments The U.S. labor market is becoming increasingly diverse. At the same time, there are persistent differences in labor market outcomes, such as wages or unemployment rates, betweendemographicgroups. Thispapersoughttounderstandthesourcesofunequallabor market outcomes through the lens of the canonical labor market model: the Diamond- Mortensen-Pissarides (DMP) model. We introduced standard elements into the model to makeitamenableforourexercise: (i)humancapitalaccumulatesthroughlearningbydoing;(ii)workerscanbenonparticipants,inadditiontoemployedorunemployed;and(iii) labormarketsaresegmented. Wereverseengineeredthewedgesneededforthemodeltoexactlymatchtheobserved series of wages and job-finding rates over the life cycle for a comprehensive set of demographic groups. We argue that these wedges provide useful guidance about the underlying sources of labor market disparities and for future research. We selected the DMP model for two main reasons. First, there are persistent differences in the unemployment ratesbetweendemographicgroups. TheDMPmodelisthecanonicalmodelofunemployment and therefore the natural candidate for our accounting exercise. Second, the DMP modelprovidesaunifiedexplanationforthemainlabormarketvariables,suchaswages, employment,unemployment,andlabormarketparticipation,allofwhichvarysystematicallybetweendemographicgroups. Wefoundthatwedgesinthreesetsofparametersareresponsibleformostofthelabor marketdisparities: gapsininitialhumancapital,returnstoexperience,andtheseparation rate to nonparticipation. The importance of each of these wedges varies depending on 44

the specific gap, but the influence of each is notable whether we look at skill, gender, or racial gaps. While human capital wedges are the most important factors explaining the gaps in wages, wedges in parameters determining the long-term value of the match, returnstoexperience,andjobseparationratescanexplainthemajorityofgapsinjob-finding rates. Wealsofoundthatamajorfractionoftheimpactthroughjobseparationratescomes through the discrimination channel, emphasizing the role of statistical discrimination in generatinglabormarketgaps. Wedgesinmatchingefficienciesturnedouttobequantitativelysecondary. Whilewefoundquitealargevariationinmatchingefficienciesbetween individualgroups,someminoritygroupsdobettercomparedtothebaselinegroupswhile some do worse, and at the aggregate level those effects cancel out. This result suggests thattaste-baseddiscriminationinhiringislikelynotamajorexplanatoryvariableoflabor marketgaps. Bertrand and Mullainathan (2004) provide compelling evidence that race matters for hiring decisions. Everything else the same, Whites received around 50 percent more callbacks for interviews compared to Blacks in their field experiment. Our findings indicate thatthisismostlikelybecauseofstatisticaldiscrimination: employersinferthatthelongtermvalueofthematchwithaBlackworkersislower,leadingthemtodiscriminateagainst Blacks in hiring even if they are initially exactly the same as White workers. Taste-based discriminationinhiringseemstobeofsecondaryimportance. Ourresultsabouttheimportanceofstatisticaldiscriminationareconsistentwithalarge body of empirical literature (see, for example, Agan and Starr (2017), Altonji and Pierret (2001), Ayres and Siegelman (1995), Bohren et al. (2019), List (2004), and Zussman (2013)) that find evidence on discrimination in various markets, and that the discrimination is statistical in nature. The reason why returns to experience and job destruction rates play such an important role in wages, employment, and earnings has to do with the search friction: hiringaworkerrequiresafirmtoincurafixedcostforthechancetostartalongtermrelationship. Firmsaremorewillingtohireworkerswithlargersurpluses,although, in equilibrium, firms make no profits, as more entry reduces the chance of a successful hire. Workers with higher returns to experience and lower separation rates produce a higherexpectedsurplus,whichinducesmorejobposting,higherjob-findingrates,abetter bargainingposition,andbetterwagesduringbargaining. The natural next step in this research is to endogenize returns to experience and job separationrates. Thisstepwouldrequireenrichingthemodelconsiderably,orfocusingon amorenarrowsetofdemographicgroups,asisstandardintheliterature. References Agan, A., & Starr, S. (2017). Ban the box, criminal records, and racial discrimination: A fieldexperiment. QuarterlyJournalofEconomics,133,191–235. Altonji, J., & Blank, R. (1999). Race and gender in the labor markets. Amsterdam and Boston: Elsevier,North-Holland. 45

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Shimer, R. (2005). The cyclical behavior of equilibrium unemployment and vacancies. AmericanEconomicReview,95,25–49. Valfort,M. (2018). Doanti-discriminationpolicieswork? IZAWorldofLabor. Yamaguchi, S. (2010). Job search, bargaining, and wage dynamics. Journal of Labor Economics,28,595–631. Zussman,A. (2013). Ethnicdiscrimination: LessonsfromtheIsraelionlinemarketforused cars. EconomicJournal,123,F433–49. Appendix A: Characterization of the Model Solution AppendixA.1: Solutionfora −1 R Workers work until age a − 1. Denote by x ≡ x (cid:0) e,a −1,E¯,i (cid:1) the final state of R R−1 R an employed worker, just before retirement. Using equations (3), (6), and (7), the Nash Bargainingsolution(10)forthefinalstatesimplifiesto (cid:104) (cid:105) h(x )−w(x ) = Θ(x ) w(x )−c¯U¯ (e,a −1)+β∆R (e+1,a ) , R−1 R−1 R−1 R−1 i R i R where∆R (e+1,a ) = R (e+1,a )−R (e,a )istheincreaseinthevalueofretirei R i R i R mentduetoanextrayearofexperienceatthepointofretirement. Thisequationprovides asolutionforthelastperiodwagesas (cid:104) (cid:105) h(x )+Θ(x ) c¯U¯ (e,a −1)−β∆R (e+1,a ) R−1 R−1 i R i R w(x ) = . (21) R−1 1+Θ(x ) R−1 According to this expression, wages are a weighted average between a worker’s human capital and the level of consumption of the unemployed net of gains in the value of retirement. If the worker has all the bargaining power (Θ(x ) = 0), wages equal hu- R−1 man capital. At the other extreme, if the firm holds all the power (Θ(x ) = ∞), wages R−1 equal consumption of the unemployed minus any gains in the value of retirement from theaddedexperienceofbeingemployed. Thesolutionforthefinalvalueofthefirmisthengivenby (cid:104) (cid:105) J(x ) = (1−φ(x )) h(x )−c¯U¯ (e,a −1)+β∆R (e+1,a ) . (22) R−1 R−1 R−1 i R i R Thefinalvalueofthefirmisafractionofthesurplusofthematch,whichincludesproduction plus added value of retirement of a worker minus consumption of an unemployed worker. Assumption1guaranteesthatJ(x )ispositive. Thefinalvalueofthefirmcan R−1 beusedtodeterminethefinallabormarkettightnessrateatagea −2. Usingequation(4) R andthedefinitionofq(x),afirm’sprobabilityoffillingavacancy,wehave vs(e,a −2) (cid:20) βA (e,a −2,s) (cid:21)1/α θs(e,a −2) = i R = i R J(x ) . (23) i R us(e,a −2) κ (e,a −2,s) R−1 i R i R 49

This expression, together with (22), shows that vacancies are more abundant for workers with higher human capital, lower outside consumption, and in more efficient labor markets characterized by a higher A and a lower κ. The model predicts, for example, that experiencedworkersandimmigrantswithloweroutsideoptionswillhavemoreopenvacancies,allelsebeingequal. Thefinaljob-findingratecanbesolvedas A (e,a −2,s) fs(e,a −2)α = i R (J(x ))1−α. (24) i R κ (e,a −2,s)1−α R−1 i R The expression (24) states that job-finding rates are higher in markets with more efficient matching,lowercostsofpostingvacancies,andhighervaluesofactivefirms. AppendixA.2: Proofofproposition1 Using the definitions of surpluses given in (13), equations (3), (4), and (10) can be written as Θ(x)S (x) = h(x)−w(x)+β(1−π (x)−π (x))Θ(x)S (x(cid:48)), (25) EU EU EN EU κ(x) = βA(x)θ(x)−αΘ(x)Si (e,a+1), (26) EU wherex(cid:48) = (e+1,a+1,E¯,i). Moreover,equations(6)and(7)read E(x) = w(x)+β (cid:2) E(x(cid:48))−π (x)S (cid:0) x(cid:48)(cid:1) −π (x)S (cid:0) x(cid:48)(cid:1)(cid:3) ; (27) EU EU EN EN (cid:104) (cid:105) U(x) = cU¯ (e,a)+β U (e,a+1)+fU¯ (e,a)Si (e,a+1)+π¯ (x)Si (e,a+1) i i i EU UN NU (cid:34) U(x(cid:48))−∆U(x(cid:48))+fU¯ (e,a)S (e,a+1) (cid:35) = cU¯ (e,a)+β i EU . i +π¯ (x)S (e,a+1) UN NU Subtractingthesecondequationfromthefirstone, S (x) = w(x)−cU¯ (e,a)+ EU i (cid:34) (1−π (x))S (x(cid:48))+∆U (x(cid:48))−fU¯ (e,a)Si (e,a+1) (cid:35) β EU EU i EU −π (x)S (x(cid:48))−π¯ (x)Si (e,a+1) EN EN UN NU or (cid:104) (cid:105) S EU (x) = w(x)−cU i ¯ (e,a)+βE S(cid:101) E i U (e,a+1) , (28) (cid:104) (cid:105) where E S(cid:101) i (e,a+1) is the expected surplus at age a + 1 of an employed worker in EU state(e,a+1).Itisdefinedas (cid:34) (cid:35) (cid:104) (cid:105) (1−π (x))S (x(cid:48))−π (x)S (x(cid:48))−π¯ (x)Si (e,a+1) E S(cid:101) i (e,a+1) = EU EU EN EN UN NU . EU −fU¯ (e,a)Si (e,a+1)+∆U (x(cid:48)) i EU 50

Similarly,rewrite(8)as (cid:104) (cid:105) N(x) = cN¯ (e,a)+β N (e,a+1)+fN¯ (e,a)Si (e,a+1)+π¯ (x)Si (e,a+1) i i i EN NU UN (cid:104) (cid:105) = cN¯ (e,a)+β N(x(cid:48))−∆N(x(cid:48))+fN¯ (e,a)Si (e,a+1)−π¯ (x)Si (e,a+1) . i i EN NU NU Subtractingthisequationfrom(27)leadsto S (x) = w(x)−cN¯ (e,a)+ EN i (cid:34) S (x(cid:48))+∆N (x(cid:48))−fN¯ (e,a)Si (e,a+1) (cid:35) β EN i EN −π (x)S (x(cid:48))−π (x)S (x(cid:48))+π¯ (x)Si (e,a+1) EU EU EN EN NU NU or (cid:104) (cid:105) S EN (x) = w(x)−cN i ¯ (e,a)+βE S(cid:101) E i N (e,a+1) , (29) where (cid:104) (cid:105) (cid:34) (1−π (x))S (x(cid:48))−fN¯ (e,a)Si (e,a+1) (cid:35) E S(cid:101) i (e,a+1) = EU EN i EN EN −π (x)S (x(cid:48))+π¯ (x)Si (e,a+1)+∆N (x(cid:48)) EU EU NU NU istheexpectedvalueofthefuturesurplus,ata+1,ofanemployedworkeratstate(e,a+1). Equations (3), (25), (26), (28), and (29) form a system of five equations in four unknowns that can be solved for each (i,e,a) state given future values of those same variables: {J(x),S (x),θs(x),w(x),S (x)} . Equation (26) can be used to directly EU EN (i,e,a) solveforθ(x)asafunctionofJ (e,a+1).Tosolveforw(x),use(25)and(28)toobtain i (cid:104) (cid:104) (cid:105)(cid:105) Θ(x) w(x)−cU¯ (e,a)+βE S(cid:101) i (e,a+1) i EU = h(x)−w(x)+β (cid:2) (1−π (x)−π (x))Θ(x)S (x(cid:48)) (cid:3) . EU EN EU Solvingforw(x)gives h(x)+Θ(x)cU¯ (e,a)+βΘ(x)Ω(x) w(x) = i , 1+Θ(x) (cid:104) (cid:105) whereΩ(x) = (1−π EU (x)−π EN (x))S EU (x(cid:48))−E S(cid:101) E i U (e,a+1) . Noticethat (cid:104) (cid:105) Ω(x) = (1−π EU (x)−π EN (x))S EU (x(cid:48))−E S(cid:101) E i U (e,a+1) = (1−π (x)−π (x))S (x(cid:48))−(1−π (x))S (cid:0) x(cid:48)(cid:1) +π (x)S (cid:0) x(cid:48)(cid:1) EU EN EU EU EU EN EN +π¯ (x)Si (e,a+1)+fU¯ (e,a)Si (e,a+1)−∆U (cid:0) x(cid:48)(cid:1) or UN NU i EU Ω(x) = π (x) (cid:2) S (cid:0) x(cid:48)(cid:1) −S (x(cid:48)) (cid:3) +π¯ (x)Si (e,a+1) EN EN EU UN NU +fU¯ (e,a)Si (e,a+1)−∆U (cid:0) x(cid:48)(cid:1) . i EU 51

AppendixA.3: Solutionfora < a −1 R Togainsomefurtherintuitionaboutthedeterminationofwages,considerthedetermination of wages two periods before retirement. Denote by x = x(e,a − 2,E¯,i). First, R−2 R usingthesolutionsalreadyobtainedfora = a −1,thefollowingresultscanbefound: R S (x ) = w(x )−c¯U¯ (e,a −1)+β∆R (e+1,a ), EU R−1 R−1 i R i R S (x ) = w(x )−c¯N¯ (e,a −1)+β∆R (e+1,a ), EN R−1 R−1 i R i R S (x ) = c¯N¯ (e,a −1)−cU¯ (e,a −1), NU R−1 i R i R ∆Ui(e+1,a −1) = c¯U¯ (e+1,a −1)−c¯U¯ (e,a −1)+β∆R (e+1,a ). R i R i R i R Furthermore, suppose just for illustration that c¯(x) = c¯for all x. In that case, we can showthatsurplusescanbewrittenas S (x ) = w(x )−c¯, S (x ) = w(x )−c¯, EU R−1 R−1 EN R−1 R−1 S (x ) = 0, ∆Ui(e+1,a −1) = 0, and NU R−1 R W (x ) = fU¯ (e,a −2)Si (e,a −1). R−2 i R EU R Pluggingtheseresultsinto(14),itfollowsthat (cid:104) (cid:105) h(x )+Θ(x ) c¯+βfU¯ (e,a −2)(w(x )−c¯) R−2 R−2 i R R−1 w(x ) = . R−2 1+Θ(x ) R−2 Appendix B: Identification and calibration strategy The model calibration uses average wages and average job-finding rates at each age to calibratehumancapitalandmatchingefficiencyparametersforanygivenageanddemographicgroup. ThecalibrationofthekeyparametersA (a),ψ (a),r (a),andy comefrom i i i i aniterationprocessthatstartswithaninitialguessofms(e,a)andy whicharerecursively i i reviseduntilconvergence. Defineaveragewages,averagehumancapital,averageoutside consumption,andaveragejob-findingratesatageaas (cid:80) mE¯ (e,a)w (e,a) w (a) = e i i , (30) i (cid:80) mE¯ (e,a ) e i R (cid:80) mE¯ (e,a)h (e,a) h (a) = e i i , (31) i (cid:80) mE¯ (e,a ) e i R (cid:80) mE(e,a)c¯U(e,a) c (a) = e i i , (32) i (cid:80) mE(e,a ) e i R (cid:80) mU¯ (e,a)fU¯ (e,a) fU¯ (a) = e i i , and (33) i (cid:80) mU¯ (e,a) e i 52

(cid:80) mN¯ (e,a)fU¯ (e,a) fN¯ (a) = e i i . (34) i (cid:80) mN¯ (e,a) e i AppendixB.1: Calibrationfora = a −1 R Wearenowreadytodescribethebenchmarkcalibrationofhumancapitalparametersand matchingefficiencies. Thereverseengineeringstartsbackwardsfroma −1.Accordingto R (21),(30),(31),and(32),theaveragewageatagea −1satisfies R (cid:80) mE¯ (e,a −1)w (e,a −1) w (a −1) = e i R i R i R (cid:80) mE¯ (e,a −1) e i R (cid:80) mE¯ (e,a −1) [hi(e,aR−1)+Θi(a)(cU i ¯(e,aR−1)−β∆Ri(e+1,aR))] = e i R 1+Θi(a) (cid:80) mE¯ (e,a −1) e i R h (a −1)+Θ (a)[c (a −1)−β∆R (a )] i R i i R i R = , 1+Θ (a) i where (cid:80) mE¯ (e,a)∆R (e+1,a ) ∆R (a ) = e i i R . (35) i R (cid:80) mE¯ (e,a ) e i R Givendataforw (a −1),thisexpressioncouldbeusedtosolveforh (a −1)as i R i R (cid:16) (cid:17) h (a −1) = w (a −1)(1+Θ (a))−Θ (a) cU¯ (a −1)−β∆R (a ) . (36) i R i R i i i R i R Thecalculatedh (a −1)shouldbeequaltotheanalyticalaveragehumancapitalobtained i R from the assumed functional form h (e,a) =y exp(r (a)e) across experiences at age a = i i i a . Thisprovidesthefollowingequationusedtosolveforr (a −1): R−1 i R (cid:80) mE(e,a −1)exp(r (a −1)e) h (a −1) = y e i R i R . (37) i R i (cid:80) mE(e,a −1) e i R Thecalibratedvalueofr (a −1)isthenusedtocalculatehumancapitalsh (e,a −1)and i R i R wages,notjustaveragewages,accordingto(21)as 1 (cid:104) (cid:16) (cid:17)(cid:105) w (e,a −1) = h (e,a −1)+Θ (a) cU¯ (e,a −1)−β∆R (e+1a ) . i R 1+Θ (a) i R i i R i R i Thesewagescanthenbepluggedinto(3),(6),(7),and(8)tofindJ (e,a −1),E (e,a −1), i R i R U (e,a −1),andN (e,a −1)aswellasthesurplusesdefinedby(13)fora = a −1. i R i R R AppendixB.2: Calibrationfora < a −1. R GiventhevaluesofJ (e,a+1),averagejob-findingratesforageacanbefoundusing(18), i (33),and(34). Inparticular, f i U¯ (a) = A i (a)α 1 (cid:80) e mU i ¯ (e,a)( (cid:80) βJ i m (e U , ¯ a (e + ,a 1 ) )/κ i (e,a)) 1− α α e i 53

orsolvingforA (a): i (cid:34) fU¯ (a) (cid:80) mU¯ (e,a) (cid:35)α A (cid:0) a,U¯(cid:1) = A (a) = i e i . i i (cid:80) e mU i ¯ (e,a)(βJ i (e,a+1)/κ i (e,a)) 1− α α Similarly, (cid:34) fN¯ (a) (cid:80) mN¯ (e,a) (cid:35)α A (cid:0) a,N¯(cid:1) = ψ (a)A (a) = i e i . i i i (cid:80) e mN i ¯ (e,a)(βJ i (e,a+1)/κ i (e,a)) 1− α α These two expressions provide the calibrated values of A (a) and ψ (a) given the data i i on average values of job-finding rates for the unemployed and nonparticipants. These formulas are valid for all ages. Given these parametric values, job-finding rates for all e, not just on average, fU¯ (e,a) and fN¯ (e,a), can then be calculated using (16). One can the i i use these job-finding rates as well as the surpluses already obtained for a+1 to calculate Ω(x)asdefinedby(17). Next,definetheexpressionofΩE¯ (a)as i (cid:80) mE¯ (e,a)ΩE¯ (e,a) ΩE¯ (a) = e i i . i (cid:80) mE¯ (e,a) e i Accordingto(14),averagewagessatisfy (cid:34) (cid:35) 1 (cid:88) mE¯ (e,a) h i (e,a)+ w (a) = i (cid:16) (cid:17) i 1+Θ i (a) e (cid:80) e mE i ¯ (e,a) Θ i (a) cU i ¯ +βΩE i ¯ (e,a) 1 (cid:104) (cid:16) (cid:17)(cid:105) = h (a)+Θ (a) cU¯ +βΩE¯ (a) . 1+Θ (a) i i i i i Givendataforw (a),thisexpressioncouldbeusedtosolveforh (a)as i i (cid:16) (cid:17) h (a) = w (a)(1+Θ (a))−Θ (a) cU¯ +βΩE¯ (a) . (38) i i i i i i Thecalculatedsequenceofh (a)shouldagainbeequaltotheanalyticalaveragehuman i capital obtained from the assumed functional form h (e,a) =y exp(r (a)e). This provides i i i thefollowingsetofequationsthatareusedtosolvefory andr (a): i i (cid:80) mE¯ (e,a)exp(r (a)e) h (0) = y ,h (a) = y e i i . (39) i i i i (cid:80) mE¯ (e,a) e i Given y and r (a), then h (e,a) =y exp(r (a)e) can be obtained for all e as well as wages, i i i i i notjustaveragewages,accordingto(14). Wagescanthenbepluggedinto(3),(6),(7),and (8)tofindJ (e,a),E (e,a),U (e,a),andN (e,a)aswellasthesurplusesdefinedby(13)for i i i i a. The process just described delivers full sequences of value functions, human capital, wages,andjob-findingratesforall(e,a,i,s). Thejob-findingratescanthenbeusedalong withotherexogenousflowstoupdatetheguessedsequenceofms(e,a)using(11)and(12). i 54

1.4 1.2 1 0.8 0.6 30 40 50 60 ,egaW 52 egA elaM etihW ot evitaleR Wages, Unskilled 1.6 1.4 1.2 1 0.8 0.6 30 40 50 60 White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female latipaC namuH Human Capital, Unskilled 2.5 2 1.5 1 30 40 50 60 Age ,egaW 52 egA elaM etihW ot evitaleR Wages, Skilled 2.5 2 1.5 1 30 40 50 60 Age latipaC namuH Age Age Human Capital, Skilled Figure C3.1: Wage and human capital profiles over the life cycle for skilled and unskilled workers,relativetothewageofanaverage25-year-oldWhitemale. Appendix C: Detailed calibration results Appendix C.1: Reverse-engineered human capital profiles for skilled and unskilledworkers We next describe the differences in human capital profiles between different skill groups. Figure C3.1 shows, not surprisingly, that unskilled groups have lower starting levels and growth rates of human capital compared to the skilled. Also, human capital levels vary less between gender and race for unskilled compared to skilled. Within race, males have higherlevelsofhumancapitaloverthelifecycleforbothskilledandunskilledcompared tofemales. Malesalsohavesteepergrowthprofilesofhumancapital: whileformostmale groups human capital is strictly increasing over time, White and Hispanic females face a stagnating human capital growth between ages 35 and 50. The human capital of skilled Blackfemalesfollowsasimilargrowthprofiletomales—itkeepsincreasingoverthewhole life cycle. Stagnating human capital growth for certain female groups is likely related to careerbreaks: as manywomenleavethelabormarketduring prime workingagesdueto familyreasons,averagereturnstoexperienceforthosegroupsarelower. Within gender andskill, we also find fairly largedifferences in human capital profiles for different races, and these differences increase over the life cycle. For the unskilled, Whitemalesandfemaleshavehigherhumancapitallevelsoverthewholelifecyclecomparedtootherraces. Fortheskilled,Asianmaleshavethehighesthumancapitaluntilage 55, when White males take the lead. Black and Hispanic males have significantly lower 55

15 10 5 0 30 40 50 60 Age etaR ylretrauQ #10-3Unskilled 15 10 5 0 30 40 50 60 Age etaR ylretrauQ #10-3 Skilled White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female FigureC3.2: Returnstoexperienceforskilledandunskilledworkers. human capital levels compared to Asian and White males, Hispanics having somewhat higher human capital compared to Black males. Skilled Asian females have the highest human capital over the life cycle compared to other females groups, followed by White females. Again, Black and Hispanic females have similar human capital levels over the lifecycle,butsignificantlylowercomparedtoAsianandWhitefemales. Theracialgapsin humancapitalare,however,smallerforwomenthanformen. Figure C3.2 shows specifically the reverse-engineered returns to experience (r (a)) for i bothskilledandunskilledworkers. Returnstoexperiencegapsdeterminethegapsinthe human capital growth rates. Skilled workers have higher r (a) than unskilled workers, i as can be seen in the human capital profiles. Returns to experience seem to decrease for older workers, and this pattern is especially prominent for the skilled groups. Returns to experience within the unskilled are the highest for White males and females followed by othermalegroupsandBlackfemales. Ingeneral,maleshavehigherreturnstoexperience thanfemaleswithinarace. Figure C3.3 shows wage-to-human capital profiles for different demographic groups, whichrepresentthegrossprofitsoffirmshiringamemberofagivendemographicgroup. Grossprofitsarehigherfordemographicgroupswhohavealowerlong-timevalueofthe match. Theintuitionisthatfirmswillattempttorecovertheirvacancypostingcosts,andif thelong-termvalueofthematchislow,firmsarerequiringahighershareoftheworker’s human capital at the current period to cover the cost. Gross profits have a U-shape for many groups: required profits are higher for younger workers, decreased for the primeageworkers,andthenstartincreasingagaintowardsretirement. Thereisalsogenderand racial variation in the gross profits for both unskilled and skilled workers. Firms require lowergrossprofitsfrommaleswithinarace,astheirlong-termvalueforafirmisexpected 56

0.6 0.5 0.4 0.3 0.2 0.1 30 40 50 60 Age stiforP ssorG Unskilled 0.6 0.5 0.4 0.3 0.2 0.1 30 40 50 60 Age White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female stiforP ssorG Skilled FigureC3.3: Grossprofitsperworker,skilledandunskilled. tobehigher. TheonlyexceptionisBlacks,forwhomthegrossprofitsofmalesaresimilar or even higher than the gross profits of females. Within unskilled workers, Asian and especially Hispanic males have the lowest gross profits, followed by Whites, while the gross profits for Black males are the highest. For females under age 45, Asians have the lowest gross profits, while other female groups have fairly similar levels, but after age 45 the gross profits for every female group converge. The patterns for skilled females are verydifferent: Asianfemaleshavenotablyhighgrossprofits. Thispatternislikelyarising fromthefactthatAsianfemaleshaveveryhighhumancapitaland,asthehiringcostsare assumedtobeincreasinginaworker’shumancapital,thecostsofhiringtheseworkersare high. That,combinedwitharelativelylowlong-termvalueofthematch,leadstoveryhigh grossprofits. Hispanicfemaleshavethesecond-highestgrossprofitsfollowedbyWhites, and skilled Black females have the lowest gross profits. Among males, Black males again havethehighestgrossprofits. ThegrossprofitsofWhiteandHispanicmalesareatsimilar levels over the life cycle. For Asian males, they first have as high or even higher gross profitsthanBlackmales,butafterage45theyconvergetotheonesofHispanicandWhite males. Appendix C.2: Reverse-engineered matching efficiencies for skilled and unskilledworkers Overall, matching efficiencies are higher for unskilled groups than skilled groups (Figure C3.4). Unskilled groups have more variation in the matching efficiencies compared to skilled groups. Also, the As of unskilled males are decreasing relatively more with age compared to women and skilled men, which could reflect the fact that unskilled males are more likely to be working in occupations requiring physical labor and that aging is 57

0.8 0.6 0.4 0.2 30 40 50 60 Age etar ylretrauQ Job-finding Rate for the Unemployed, Unskilled 0.8 0.6 0.4 0.2 60 A Matching Efficiency, Unskilled 0.6 0.5 0.4 0.3 0.2 30 40 50 60 Age etar ylretrauQ Job-finding Rate for the Unemployed, Skilled 0.6 0.5 0.4 0.3 0.2 30 40 50 60 Age A 30 40 50 Matching Efficiency, Skilled White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female FigureC3.4: Job-findingratesforunemployedandmatchingefficienciesoverthelifecycle forskilledandunskilledworkers. reducingproductivitymoreintheseoccupations. Similarly,aswithhumancapital,malestendtohavehighermatchingefficiencieswithin raceandskillcomparedtofemales. Thisisespeciallypronouncedforunskilledandyounger workers. Itislikelythatyoungerfemaleworkerswithlowerskillsmaybepresumedless attachedtothelaborforce,whichthenaffectstheirjob-findingrates. Withinskilledgroups, the gender gap in matching efficiency for Blacks and Whites is quite small, and White females have a higher matching efficiency compared to White males after age 40. Young skilledAsianshavethewidestgendergapcomparedtootherskilledgroups,Asianwomen between ages 25 and 40 having significantly weaker matching efficiency. This gap, however, closes towards the end of the life cycle. Skilled Hispanics also have a wider gender gapcomparedtoBlacksandWhites,butmoremodestthanunskilledHispanics. When it comes to racial differences in matching efficiencies, Hispanics tend to do betterinalmostallgender-skillgroups: Hispanicmaleshavethehighestmatchingefficiencies amongbothskilledandunskilledmales,whilethesameistrueforunskilledHispanicfemales. Withinunskilledfemalesandmales,HispanicsarefollowedbyAsiansandWhites, Blackscominglast. Whenitcomestoskilledmales,theotherthreeraceshavefairlysimilar matching efficiencies over the life cycle. Among skilled females, White females have the highestmatchingefficienciesoverthewholelifecycle,followedbyHispanicsandBlacks. As mentioned before, skilled Asian females have the lowest matching efficiency early in lifebutitstartstocatchupwiththeonesofHispanicsandBlacksafterage40. 58

1 0.9 0.8 0.7 0.6 0.5 0.4 30 40 50 60 Age troffe hcraeS Female 1 0.9 0.8 0.7 0.6 0.5 0.4 30 40 50 60 Age troffe hcraeS Male White Skilled Black Skilled Asian Skilled Hispanic Skilled White Unskilled Black Unskilled Asian Unskilled Hispanic Unskilled FigureC3.5: Searcheffort,ψ (a)ofnonparticipants,skilledandunskilled. i FigureC3.5presentsthereverse-engineeredsearcheffortofnonparticipantsfordifferentgroups. Theidentificationassumptioninthecalibrationwasthat, weassumethatthe matching efficiencies, A, are the same for the unemployed and the nonparticipants, and that the search effort of the unemployed is always 1. Thus, ψ (a) captures the differences i injob-findingratesbetweenunemployedandnonparticipantsforotherwisesimilarworkers. Theinterpretationisthatnonparticipantsaretypicallylessattachedtothelaborforce forvariousreasons,whichisreflectedinthelowerjob-findingratesofnonparticipantsand iscapturedbythelowersearcheffort. Themostobvioustrendinsearcheffortsoverthelifecycleisthatthesearcheffortisthe highest for young workers and starts decreasing for the majority of the groups with age. Thisisnotasurprisingresultsinceolderworkersarelikelytobelessattachedtothelabor force for various reasons: older workers are more likely to have issues related to health affecting their willingness to search for work, and they may also be more discouraged to lookforworkbecausetheprobabilityoffindingajobdecreaseswithage. The skilled have higher search effort compared to the unskilled for all the other races except for Asians. For Asians, the search effort for the skilled and the unskilled are quite similar, but the ranking varies over life. There is also a gender gap in the search effort for all the other groups except unskilled Blacks, but the gender gap decreases or closes afterage40. Thelowersearcheffortoffemalesisthusmostlikelyrelatedtochild-rearing responsibilities. ThesearcheffortsofunskilledBlackmalesandfemalesarealmostequal, which either reflects that the search effort of Black females is atypically high, the search effortofBlackmalesisatypicallylow,oracombinationofboth,comparedtoothergender groups. This result likely reflects the fact that Blacks are less likely to be married (see, for example, Caucutt, Guner,andRauh(2018)andBloomandAng(2020))andBlackwomen are more likely to be single-mothers compared to other races, which then shows up as a 59

0.2 0.15 0.1 0.05 0 30 40 50 60 Age etaR ylretrauQ Flow from Nonparticipation to Unemployment 0.6 0.5 0.4 0.3 0.2 0.1 30 40 50 60 Age etaR ylretrauQ Flow from Unemployment to Nonparticipation White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female Notes: Theselabormarketstatisticsarebasedontheauthors’calculationsusingIPUMS(2018)data foryears1998–2018. FigureC3.6: Averagetransitionflowsbetweennonparticipationandunemployment. higher attachment to the labor force and a higher search effort of Black females. While Blacks have the lowest gender gap also among the skilled, the highest gender gaps are amongAsiansandHispanics. Racial differences in search effort vary between gender. While Asian males have the highest search effort within each skill level, followed by Hispanics and Blacks, Black females have the highest search effort among females. Only among unskilled females do Asians and Hispanics have a higher search effort after age 40 than Blacks. Whites always havethelowestsearcheffortwithinagender-skillgroup. FiguresC3.6andC3.7presenttheaveragetransitionflowsbetweenunemploymentand nonparticipation, andthejobdestructionratesfortheskilledandunskilledworkers, πi EU and πi . Figure C3.6 shows that females are more likely to move from unemployment EN to nonparticipation, and less likely to move back to unemployment compared to males. Figure C3.7 shows significant variation in the job destruction rates within and between skillgroups. 60

0.1 0.05 0 30 40 50 60 etaR ylretrauQ Flow from Employment to Unemployment, Unskilled 0.06 0.04 0.02 0 30 40 50 60 etaR ylretrauQ Flow from Employment to Unemployment, Skilled 0.2 0.15 0.1 0.05 0 30 40 50 60 Age etaR ylretrauQ Flow from Employment to Nonparticipation, Unskilled 0.2 0.15 0.1 0.05 0 30 40 50 60 Age etaR ylretrauQ Age Age Flow from Employment to Nonparticipation, Skilled White Male Black Male Asian Male Hispanic Male White Female Black Female Asian Female Hispanic Female Notes: Theselabormarketstatisticsarebasedontheauthors’calculationsusingIPUMS(2018)data foryears1998–2018. Figure C3.7: Job destruction rates to unemployment and nonparticipation for skilled and unskilledworkers. 61

Appendix D: Detailed decomposition results This section presents the detailed decomposition results for the overall, skill, gender, and race gaps, including various labor market gaps. Table D3.1 shows the decomposition of theoverallgapsinthelabormarketoutcomes,TableD3.2thedecompositionofthegender gaps,TableD3.3thedecompositionoftheskillgaps,andTableD3.4thedecompositionof theracegaps. Theoutcomesforwhichthegapsanddecompositionarecalculatedareaveragehourlywages(Wage),employmentrate(Empl),unemploymentrate(Unemp),labor force participation (Part) and nonparticipation (Non-part) rates, labor market tightness rates for the unemployed (θU) and nonparticipants (θN), job-finding rates for the unemployed(π )andnonparticipants(π ),andlifetimeearnings(W).Thetablesdisplaythe UE NE contributionsofeachindividualvariablesingeneratingthecalculatedgapsaswellasthe absolute contributions of each individual variable. Absolute contributions are calculated bydividinganindividualvariable’scontributionbythesumofabsolutevaluesofindividualcontributions. 62

TableD3.1: Detaileddecompositionoftheoverallgaps Wage Empl Unemp Part Non-part θ U θ N π UE π NE W Average gap (weighted) 10.27 13.5% -0.9% 12.6% -12.6% 19.9% 7.8% 4.2% 1.9% 37.49 Explained gap 7.96 14.7% -0.1% 14.5% -14.5% 19.1% 7.9% 4.3% 2.5% 27.97 Initial human capital (y) 3.78 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 10.08 Matching efficiency (A) -0.05 -0.5% 0.2% -0.4% 0.4% -0.7% -0.1% -1.7% -0.4% -0.25 Search effort, nonparticipants (ψ) 0.18 2.0% 0.0% 2.0% -2.0% -2.3% 2.5% -0.7% 1.9% 1.14 Returns to experience (r) 2.17 1.2% -0.2% 1.0% -1.0% 9.5% 3.0% 3.1% 0.9% 8.45 Separation rate to unempl. (πEU) 0.22 1.3% -0.7% 0.6% -0.6% 1.9% 0.5% 0.5% 0.2% 0.83 Separation rate to non-p. (πEN) 1.51 10.3% -0.5% 9.8% -9.8% 14.7% 3.7% 4.4% 0.5% 7.32 Flow unempl. to non-p. (πUN) 0.11 -0.2% 0.7% 0.5% -0.5% -3.8% -1.4% -1.3% -0.5% 0.11 Flow non-p. to unempl. (πNU) 0.04 0.4% 0.4% 0.8% -0.8% -0.2% -0.2% -0.1% -0.1% 0.25 Initial distribution of pop. (m0) 0.01 0.2% 0.0% 0.1% -0.1% 0.0% 0.0% 0.0% 0.0% 0.05 μ 1.22 2.3% -0.3% 2.0% -2.0% 18.0% 6.1% 5.5% 1.8% 6.84 Absolute contributions Wage Empl Unemp Part Non-part θU θN πUE πNE W Human capital Initial human capital (y) 46.9% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 35.4% Returns to experience (r) 26.9% 7.4% 7.3% 6.4% 6.4% 28.8% 25.8% 26.2% 20.0% 29.7% Matching efficiency Matching efficiency (A) -0.7% -3.2% -6.0% -2.3% -2.3% -2.2% -1.1% -14.6% -9.1% -0.9% Search effort, nonparticipants (ψ) 2.2% 12.6% -0.5% 13.2% 13.2% -6.9% 21.9% -6.0% 42.7% 4.0% Separation rates (d) To unemployment (πEU) 2.8% 8.2% 27.0% 3.9% 3.9% 5.6% 4.7% 4.4% 3.4% 2.9% To nonparticipation (πEN) 18.7% 64.0% 18.3% 64.5% 64.5% 44.4% 32.1% 37.7% 11.5% 25.7% Others π UN 1.3% -1.0% -25.3% 3.3% 3.3% -11.5% -12.1% -10.7% -10.9% 0.4% π UN 0.5% 2.6% -15.4% 5.4% 5.4% -0.6% -1.7% -0.4% -1.7% 0.9% m0 0.1% 1.1% 0.2% 1.0% 1.0% 0.0% -0.4% 0.0% -0.7% 0.2% Sum absolute contributions 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% Statistical discrimination Total contribution 15.1% 14.6% 12.5% 13.4% 13.4% 54.4% 53.4% 46.7% 40.6% 24.0% As share of d 70.5% 20.2% 27.7% 19.7% 19.7% 108.6% 145.1% 111.0% 272.3% 83.9% Notes: Thistabledisplaysthecontributionsofeachvariableingeneratingtheoverallgapinlabor marketoutcomes.Theoverallgapineachoutcomeiscalculatedasadifferencebetweentheaverage outcomeofskilledWhitemalesandthepopulation-weightedaverageofoutcomeofallothergroups. Forexample,theaveragegapinhourlywagerate(Wage)betweentheskilledWhitemalesandother groupsisobservedtobe$10.34inthedata. Thesummedupcontributionoftheindividualmodel variables equals $8.01 (Explained gap), while the remaining part of the wage gap arises from the correlationsbetweenindividualvariables. 63

TableD3.2: Detaileddecompositionofthegendergaps Wage Empl Unemp Part Non-part θ U θ N π UE π NE W Average gap (weighted) 3.01 6.8% 0.4% 7.3% -7.3% 5.1% 2.8% 3.3% 1.7% 11.51 Explained gap 2.83 8.0% 0.7% 8.7% -8.7% 5.8% 3.4% 3.3% 2.1% 10.57 Initial human capital (y) 1.16 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 3.12 Matching efficiency (A) 0.14 1.0% -0.1% 0.9% -0.9% 1.0% 0.3% 2.0% 0.6% 0.48 Search effort, nonparticipants (ψ) 0.16 1.4% 0.0% 1.4% -1.4% -1.8% 1.9% -0.5% 1.5% 0.87 Returns to experience (r) 0.46 0.3% 0.0% 0.2% -0.2% 2.0% 0.6% 0.6% 0.2% 2.06 Separation rate to unempl. (πEU) -0.10 -0.6% 0.2% -0.3% 0.3% -0.7% -0.3% -0.3% -0.1% -0.37 Separation rate to non-p. (πEN) 0.89 5.6% -0.2% 5.3% -5.3% 8.2% 2.0% 2.4% 0.4% 4.10 Flow unempl. to non-p. (πUN) 0.07 -0.1% 0.4% 0.2% -0.2% -2.6% -0.9% -0.8% -0.3% 0.05 Flow non-p. to unempl. (πNU) 0.04 0.4% 0.5% 0.9% -0.9% -0.3% -0.2% -0.1% -0.1% 0.23 Initial distribution of pop. (m0) 0.01 0.1% 0.0% 0.1% -0.1% 0.0% 0.0% 0.0% 0.0% 0.03 μ 0.48 1.0% -0.1% 0.9% -0.9% 7.3% 2.4% 2.2% 0.7% 2.86 Absolute contributions Wage Empl Unemp Part Non-part θU θN π UE π NE W Human capital Initial human capital (y) 38.4% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 27.6% Returns to experience (r) 15.4% 2.7% -2.0% 2.3% 2.3% 12.0% 9.9% 8.9% 6.1% 18.2% Matching efficiency Matching efficiency (A) 4.7% 10.8% -7.9% 9.5% 9.5% 6.2% 4.3% 29.6% 20.0% 4.2% Search effort, nonparticipants (ψ) 5.2% 14.5% -0.5% 14.6% 14.6% -10.5% 30.3% -8.0% 47.0% 7.7% Separation rates (d) To unemployment (πEU) -3.3% -6.2% 16.3% -3.7% -3.7% -4.4% -4.5% -3.9% -2.5% -3.3% To nonparticipation (πEN) 29.4% 59.0% -15.0% 56.9% 56.9% 49.3% 32.4% 36.1% 11.3% 36.2% Others π UN 2.3% -1.5% 24.8% 2.5% 2.5% -15.7% -14.3% -12.3% -9.7% 0.4% π UN 1.2% 4.1% 33.6% 9.3% 9.3% -1.9% -3.8% -1.2% -3.4% 2.0% m0 0.2% 1.2% 0.0% 1.2% 1.2% 0.0% -0.6% 0.0% 0.0% 0.3% Sum absolute contributions 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% Statistical discrimination Total contribution 16.0% 10.2% -7.6% 9.4% 9.4% 43.9% 38.3% 32.6% 22.6% 25.3% As share of d 61.4% 19.3% -586.7% 17.6% 17.6% 97.9% 137.4% 101.6% 255.2% 76.8% Notes: This table displays the contributions of each variable in generating the gender gap in labor market outcomes. The gender gap in each outcome is calculated as a difference between the population-weightedaverageoutcomeofallmalesandthepopulation-weightedaverageoutcome ofallfemales. Forexample,theaveragegapinhourlywagerate(Wage)betweenmalesandfemales isobservedtobe$3.03inthedata. Thesummedupcontributionoftheindividualmodelvariables equals$2.84(Explainedgap),whiletheremainingpartofthewagegaparisesfromthecorrelations betweenindividualvariables. 64

TableD3.3: Detaileddecompositionoftheskillgaps Wage Empl Unemp Part Non-part θ U θ N π UE π NE W Average gap (weighted) 4.73 5.5% -0.5% 5.0% -5.0% 7.4% 4.6% 0.6% 1.5% 15.76 Explained gap 3.92 5.7% -0.3% 5.3% -5.3% 7.4% 4.1% 0.8% 1.5% 12.59 Initial human capital (y) 2.45 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 6.51 Matching efficiency (A) -0.09 -0.7% 0.2% -0.6% 0.6% -0.9% -0.3% -1.9% -0.6% -0.37 Search effort, nonparticipants (ψ) 0.07 1.3% 0.0% 1.3% -1.3% -1.1% 1.7% -0.4% 1.4% 0.66 Returns to experience (r) 0.96 0.6% -0.1% 0.5% -0.5% 4.7% 1.3% 1.6% 0.4% 3.36 Separation rate to unempl. (πEU) 0.16 1.0% -0.5% 0.5% -0.5% 1.4% 0.4% 0.4% 0.1% 0.57 Separation rate to non-p. (πEN) 0.34 3.4% -0.2% 3.2% -3.2% 4.3% 1.2% 1.5% 0.3% 1.75 Flow unempl. to non-p. (πUN) 0.03 0.0% 0.2% 0.1% -0.1% -0.9% -0.3% -0.3% -0.1% 0.03 Flow non-p. to unempl. (πNU) 0.00 0.1% 0.1% 0.2% -0.2% -0.2% 0.0% -0.1% 0.0% 0.06 Initial distribution of pop. (m0) 0.00 0.1% 0.0% 0.1% -0.1% 0.0% 0.0% 0.0% 0.0% 0.02 μ 0.38 1.0% -0.1% 0.8% -0.8% 6.3% 2.0% 2.1% 0.7% 2.02 Absolute contributions Wage Empl Unemp Part Non-part θU θN π UE π NE W Human capital Initial human capital (y) 59.8% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 48.8% Returns to experience (r) 23.5% 8.5% -8.5% 7.7% -7.7% 34.9% 24.4% 25.9% 13.8% 25.2% Matching efficiency Matching efficiency (A) -2.1% -10.2% 13.6% -8.9% 8.9% -6.6% -5.9% -30.4% -21.1% -2.8% Search effort, nonparticipants (ψ) 1.7% 17.7% -0.3% 19.8% -19.8% -8.1% 32.9% -6.0% 46.8% 4.9% Separation rates (d) To unemployment (πEU) 3.9% 13.5% -40.5% 7.3% -7.3% 10.4% 7.5% 7.0% 3.5% 4.3% To nonparticipation (πEN) 8.2% 47.0% -13.8% 49.7% -49.7% 32.0% 23.0% 23.6% 10.4% 13.1% Others π UN 0.6% -0.4% 13.9% 2.3% -2.3% -6.5% -5.6% -4.8% -3.4% 0.2% π UN 0.1% 1.5% 8.8% 3.3% -3.3% -1.6% 0.6% -2.2% 1.1% 0.4% m0 0.1% 1.3% -0.5% 1.0% -1.0% 0.0% -0.2% 0.0% 0.0% 0.1% Sum absolute contributions 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% Statistical discrimination Total contribution 9.3% 13.4% -11.0% 12.9% -12.9% 46.7% 38.2% 34.2% 22.4% 15.2% As share of d 76.7% 22.1% 20.2% 22.6% 22.6% 110.3% 125.3% 111.6% 161.6% 86.9% Notes:Thistabledisplaysthecontributionsofeachvariableingeneratingtheskillgapinlabormarketoutcomes. Theskillgapineachoutcomeiscalculatedasadifferencebetweenthepopulationweightedaverageoutcomeofallskilledindividualsandthepopulation-weightedaverageoutcome ofallunskilledindividuals. Forexample,theaveragegapinhourlywagerate(Wage)betweenthe skilled and the unskilled is observed to be $4.73 in the data. The summed up contribution of the individualmodelvariablesequals$3.92(Explainedgap),whiletheremainingpartofthewagegap arisesfromthecorrelationsbetweenindividualvariables. 65

TableD3.4: Detaileddecompositionoftheracegaps Wage Empl Unemp Part Non-part θU θN π UE π NE W Average gap (weighted) 1.29 1.7% -0.6% 1.2% -1.2% 7.5% -0.4% 1.7% -1.3% 4.24 Explained gap 1.20 1.6% -0.5% 1.0% -1.0% 6.5% -0.2% 1.6% -1.2% 3.96 Initial human capital (y) 0.34 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.93 Matching efficiency (A) 0.00 -0.2% 0.1% -0.1% 0.1% -0.2% 0.1% -0.8% 0.0% 0.07 Search effort, nonparticipants (ψ) -0.09 -1.5% 0.0% -1.5% 1.5% 1.3% -2.0% 0.5% -1.6% -0.79 Returns to experience (r) 0.51 0.2% 0.0% 0.2% -0.2% 1.7% 0.6% 0.6% 0.2% 1.78 Separation rate to unempl. (πEU) 0.12 0.7% -0.4% 0.3% -0.3% 0.9% 0.3% 0.3% 0.1% 0.48 Separation rate to non-p. (πEN) 0.31 2.4% -0.1% 2.2% -2.2% 2.9% 0.9% 1.0% 0.2% 1.51 Flow unempl. to non-p. (πUN) 0.02 0.0% 0.1% 0.1% -0.1% -0.4% -0.2% -0.2% -0.1% 0.03 Flow non-p. to unempl. (πNU) -0.01 -0.1% -0.2% -0.3% 0.3% 0.3% 0.0% 0.1% 0.0% -0.06 Initial distribution of pop. (m0) 0.00 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.02 μ 0.32 0.7% -0.1% 0.6% -0.6% 4.1% 1.7% 1.4% 0.5% 1.74 Absolute contributions Wage Empl Unemp Part Non-part θU θN π UE π NE W Human capital Initial human capital (y) 24.2% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 16.5% Returns to experience (r) 36.5% 4.5% 4.9% 3.7% 3.7% 22.3% -14.8% 17.4% -8.9% 31.4% Matching efficiency Matching efficiency (A) 0.2% -3.1% -7.5% -1.9% -1.9% -2.4% -3.1% -22.2% 1.0% 1.3% Search effort, nonparticipants (ψ) -6.7% -29.3% -2.9% -30.8% -30.8% 17.5% 46.9% 13.5% 73.7% -14.0% Separation rates (d) To unemployment (πEU) 8.5% 13.3% 36.8% 6.6% 6.6% 11.6% -7.8% 9.2% -4.9% 8.4% To nonparticipation (πEN) 21.9% 46.7% 13.8% 47.3% 47.3% 37.1% -21.2% 28.4% -7.8% 26.6% Others πUN 1.2% -0.2% -13.3% 2.5% 2.5% -5.5% 4.8% -5.1% 3.0% 0.5% πUN -0.4% -1.9% 20.3% -6.4% -6.4% 3.5% -1.1% 4.2% -0.5% -1.0% m0 0.3% 0.9% 0.7% 0.8% 0.8% 0.0% 0.3% 0.0% 0.2% 0.3% Sum absolute contributions 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% Statistical discrimination Total contribution 22.6% 13.7% 11.7% 12.6% 12.6% 53.5% -38.5% 40.7% -24.6% 30.7% As share of d 74.4% 22.9% 23.1% 23.4% 23.4% 109.7% 132.9% 108.1% 194.0% 87.4% Notes:Thistabledisplaysthecontributionsofeachvariableingeneratingtheracegapinlabormarketoutcomes. TheracegapineachoutcomeiscalculatedasadifferencebetweenthepopulationweightedaverageoutcomeofWhitesandthepopulation-weightedaverageoutcomeofminorities. Forexample,theaveragegapinhourlywagerate(Wage)betweenWhitesandminoritiesisobserved tobe$1.32inthedata. Thesummedupcontributionoftheindividualmodelvariablesequals$1.23 (Explainedgap),whiletheremainingpartofthewagegaparisesfromthecorrelationsbetweenindividualvariables. 66