The Role of Observed and Unobserved Heterogeneity in the Duration of Unemployment Spells

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) The Role of Observed and Unobserved Heterogeneity in the Duration of Unemployment Spells Hie Joo Ahn 2016-063 Please cite this paper as: Ahn, Hie Joo (2022). “The Role of Observed and Unobserved Heterogeneity in the Duration of Unemployment Spells,” Finance and Economics Discussion Series 2016-063r1. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2016.063r1. 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.

The Role of Observed and Unobserved Heterogeneity in the Duration of Unemployment Spells HieJooAhn*† FederalReserveBoard March1,2022 Abstract Thispaperstudiesthedegreetowhichobservableandunobservableworkercharacteristicsaccountforthevariationintheaggregatedurationofunemployment. Imodel thedistributionofunobservedworkerheterogeneityastimevaryingtocapturetheinteractionoflatentattributeswithchangesinlabor-marketconditions. Unobservedheterogeneityisthemainexplanationforthedurationdependenceofunemploymenthazards.Bothcyclicalandlow-frequencyvariationsinthemeandurationofunemployment aremainlydrivenbyonesubgroup: workerswho,forunobservedreasons,stayunemployedforalongtime. Incontrast,changesinthecompositionofobservablecharacteristicsofworkershavenegligibleeffects. Keywords: unemployment duration, disaggregate unemployment, unobserved heterogeneity,genuinedurationdependence,nonlinearstatespacemodel,extendedKalmanfilter *Theviewsinthispaperaresolelytheresponsibilityoftheauthorandshouldnotbeinterpretedasreflecting theviewsoftheBoardofGovernorsoftheFederalReserveSystemorofanyotherpersonassociatedwiththe Federal Reserve System. I thank Gianni Amisano, Travis Berge, Michael Boerman, Marco Del Negro, James Hamilton,AndreaStella,CaitlinHesser,DavidJenkinsandChristopherKarlstenforhelpfulcommentsonan earlierdraftofthispaper. †E-mail:hiejoo.ahn@frb.gov

Introduction Why does the average duration of unemployment rise during an economic downturn? Darbyetal.(1986)arguethatrecessionsareperiodswhenworkerswithlowreemployment prospects lose their jobs, and the increased share of these workers in the unemployment pool raises the mean duration of unemployment. Baker (1992) labels this explanation the "heterogeneityhypothesis."Aquitedifferentviewisthatduringarecession,theindividual duration of unemployment becomes longer due to weak labor demand, regardless of the worker’scharacteristics. Thispaperrevisitsthisdebate—adebatethathasbeenatthecenterofthediscussionon labor market dynamics for decades—using an empirical approach with two novel aspects. First, my approach takes into account worker characteristics that are both observed and unobserved in the data, while previous studies (e.g., Kroft et al. (2016)) only consider observedattributes. Hereafter,Iwillrefertoobservedandunobservedworkercharacteristics asobservedandunobservedheterogeneity,respectively. Second,Imodelthedistributionof unobservedheterogeneitytobetimevarying,whereastheexistingliteratureonlycharacterizesitastimeinvariant(e.g.,Shimeretal.(2015)). The empirical findings in this paper support the "unobserved" heterogeneity hypothesis. We postulate that there is a group of workers who are prone to long-term unemployment due to their unobserved attributes. Such workers make up a larger fraction of those who havebeenunemployedforalongperiodoftimecomparedtoagroupofworkerswhohave been unemployed for a short period of time. This could account for the negative duration dependence of unemployment hazards, which is the observation that the unemploymentexitprobabilitydeclineswithunemploymentduration. Whenthereisanegativeeconomic shock,disproportionatelymoreworkersinthissubgroupflowintotheunemploymentpool than others. As a result, the exit from unemployment as well as the entry into unemployment of this subgroup of workers could be the main driver of cyclical and low-frequency 1

variations in the mean duration of unemployment. The empirical conclusion of this paper isthatthisisindeedwhathappens.1 Whydoweneedtoconsideratime-varyingdistributionforunobservedheterogeneity? Previous studies treat unobserved heterogeneity as a fixed characteristic with constant effects on the individual’s job-finding prospects over time. However, this assumption is not validifunobservedworkercharacteristicsinteractwithchangesinlabor-marketconditions. Consider for example an economy where workers with certain skills become less productive and thus are less in demand because of skill-biased technological changes (Acemoglu (2002)). Workers with those skills tend to have lower job-finding probabilities and experiencelongerunemploymentspells,fatteningtherighttailoftheunemploymentdurationdistribution. During an economic downturn, firms might shed these workers as they become unable to retain less productive workers. The job-finding probabilities of such workers fall further. Therefore,theirshareinunemploymentrises,drivinguplong-termunemployment. Insuchaneconomy,themeandurationofunemploymentgoesupduringtherecessionbecause workers with skills that are in lower demand make up a larger fraction of the pool ofunemployedworkers. Iftheskilldifferencesarenotwellcapturedbyobservablecharacteristics, we would observe a common increase in unemployment duration across workers with the same observable characteristics, incorrectly concluding that worker heterogeneity is unimportant. The role of worker heterogeneity in the aggregate duration of unemploymentwillnotbeaccuratelymeasured,ifwefailtoconsiderthetime-varyingdistributionof unobservedheterogeneity. 1PreviousstudiessuchasKruegeretal.(2014)andKroftetal.(2016)claimthataggregatefactorsthataffect differentworkersinasimilarway,ratherthanchangesinthecompositionoftheunemployed,arethecauseof therecord-highlevelofunemploymentdurationaftertheendoftheGreatRecession. However,thesestudies donotconsiderunobservedworkerheterogeneity. Asfurthersupportfortheconclusionsofthispaper, Gregory et al. (2021) find that a small group of workers with a particular unobserved attribute—what they call "γ-workers"—mainlyaccountsforthesharpriseinunemploymentduringtheGreatRecessionanditsslowrecovery. Fortheidentificationofunobservedtypes, theauthorsapply k-meansclusteringtotheLongitudinal Employer-HouseholdDynamicsdataset,whileIestimateanonlinearstatespacemodelwiththedatasetconstructed from the micro data of Current Population Survey. Gregory et al. (2021) provide a search-theoretic modelthataccountsfortheempiricalfinding,whilethispaperdoesnot. 2

Howdoweidentifyworkerswithunobservedattributes? Supposeunemployedindividualsareoneoftwounobservedtypeswhohavehigh(H)andlow(L)probabilitiesofexiting unemploymentstatusnextmonth. Newlyunemployedindividualsofbothtypesflowinto theunemploymentpooleachmonth. Iwillrefertonewlyunemployedindividualsastheinflows. Supposethattheeconomyisinasteadystate. Usingtheinflowsandtheprobabilities ofcontinuingunemploymentnextmonthforthetwotypes,wecancalculatethenumberof individualsunemployedfornmonths. Thismeansthatgivenfourobservationsoverthefull sample—theaveragenumberofindividualsunemployedfor1month,2to3months,4to6 months,and7to12months—wecanidentifythefourpopulationparameters—inflowsand unemployment-continuationprobabilitiesoftypes H and L. Moregenerally,supposethata worker’s chance of exiting unemployment changes with the length of the worker’s unemploymentspell,whichisoftenreferredtoasgenuinedurationdependence(hereafter,GDD). Forexample,employersmightdiscriminateagainstthelong-termunemployed,orworkers might take a low-paying job as their jobless spells get longer. If GDD is a linear function oftheunemploymentdurationcharacterizedbyoneparameter,wecanfurtheridentifythe GDD parameter together with an additional data point—the number of individuals unemployed for longer than one year. In fact, we observe these five data points every month from January 1976 to December 2019. Ahn and Hamilton (2020) show that with such data, wecanidentifytime-varyinginflowsandunemployment-continuationprobabilitiesoftwo unobserved types at each point in time, while allowing a more flexible functional form for GDD. IapplytheidentificationschemeofAhnandHamilton(2020)tounemploymentdatadisaggregatedonthebasisofobservablecharacteristicstoestimatetheinflowsandunemploymentcontinuation probabilities of workers of unobserved types who share the same observable characteristics. Withtheestimates,Irecoverthedistributionofunemploymentdurationfor 3

each worker type at each point in time.2 I find substantial heterogeneity in unemployment hazardsevenwithinagroupofunemployedindividualswhosharethesamereportedreasonforunemployment,whichisthekeyobservablecharacteristicthatseemstoaccountfor differencesinjob-findingratesofunemployedindividuals(FujitaandMoscarini(2017)and Hall and Schulhofer-Wohl (2018)). I also find unobserved heterogeneity is crucial among a group of workers with the same demographic characteristics or level of education. This result implies that the long-term unemployed mostly represent workers with some unobserved attributes, and their inflows and unemployment-continuation probability drive the variationinlong-termunemployment. Unobservedheterogeneityiscrucialinunderstandingchangesintheaggregateduration ofunemployment. Usingashift-shareanalysis,IshowthatfromDecember2007toDecember 2011—the period during which the mean duration of unemployment registers its most dramaticincrease—theriseinunemploymentdurationoftype Lworkersisresponsiblefor about 80% of the observed hike in the mean duration. The remaining 20% is explained by theincreasedshareoftypeLworkersintheunemploymentpool. Thecompositionalshiftof workers with observable characteristics is essentially irrelevant in this period. It is further notable that during the Great Recession, aggregate unemployment duration rises mainly due to the increased share of type L workers. During the recovery, however, the share of type L workers starts to slowly decline, while their unemployment duration continues to riseanddrivesuptheaggregatedurationofunemployment. TypeLworkersarealsoimportantinsecularchangesintheaggregatedurationofunemployment. BetweenJanuary1980andDecember2019,themeandurationofunemployment doubledfrom10.4weeksto20.8weeks.3 ThecompositionalshiftoftypeLworkersexplains 2This paper is closely related to Ahn and Hamilton (2020). The key differences are that while Ahn and Hamilton(2020)focusoncyclicalunemploymentvariationsanddonotconsidertheobservablecharacteristics of workers, this paper concentrates on the determinants of unemployment duration and explicitly considers the observable characteristics as potential drivers. Ahn and Hamilton (2020) cite this paper in framing their discussionontheassociationbetweenreasonsforunemploymentandunobservedtypes. 3Thedifferencebetweenthetwolevelsislikelytorepresentthetrend,asthetwodatesrepresentbusiness- 4

30%ofthesecularriseandtypeLdurationexplains65%. Bothfactorspreventthemeanduration of unemployment from recovering to pre-recession levels after each recession ends, therebydrivingtheuptrendintheaveragedurationofunemployment. This paper is composed of five sections. Section 1 discusses the data used for the empirical analysis. Section 2 illustrates the need to consider unobserved heterogeneity in understandingthedistributionofunemploymentduration. Section3introducestheempirical methodology,andSection4discussestheempiricalresults. Section5analyzesthecontributionofworkerheterogeneitytotheevolutionofaggregateunemploymentduration. Section 6exploresthesourceoflow-frequencyvariationinthemeandurationofunemployment. 1 Data Theempiricalexerciseisbasedonthenumbersofpeoplewhohaveobservedcharacteristic j and have been unemployed for 1 month (less than 5 weeks), 2-3 months (5-14 weeks), 4- 6 months (15-26 weeks), 7-12 months (27-52 weeks), and longer than 1 year (53 weeks and over)ineachmontht.4IdenotethesefivenumbersbyU1,U2.3,U4.6,U7.12,andU13.+ ,respecjt jt jt jt jt tively. Eachvalueofjsummarizestheobservablecharacteristicsofunemployedindividuals including demographic characteristics, education level, previous industry and occupation, and reason for unemployment. In particular, I consider five reasons for unemployment: temporarylayoffs,permanentseparation,jobleavers,reentrantstothelaborforce,andnew entrantstothelaborforce.5 Fortheaggregatedata,thenotation jissuppressed. Iconstruct cyclepeaks. 4TheBureauofLaborStatistics(BLS)reportsthenumberunemployedforlessthan5weeks,5-14weeks,15- 26weeks,and27weeksandovertominimizemeasurementerrors(e.g.,digitpreference)byaveragingwithin broaddurationgroups. Withinlong-termunemployment,theBLSoftenfurtherbreaksdownthenumberunemployedfor27weeksandoverintothoseunemployedfor27-52weeksandthosewithadurationlongerthan 52weeks.Becausethemainfocusofthispaperishowunemployedindividuals’laborforcetransitionsbetween monthsaffectthedistributionofunemploymentduration,Iuse"months"astheunitofunemploymentduration insteadof"weeks." 5The Current Population Survey (CPS) asks unemployed individuals in which circumstance they become unemployed. TherearefivereasonsforunemploymentintheCPSthataretemporarylayoffs,permanentjob loss, jobleavers, reentrantstothelaborforce, andnewentrantstothelaborforce. Permanentjoblosscanbe 5

thedatasetusingtheCPSmicrodata.6 ThesampleperiodisJanuary1976–December2019. 2 Why study heterogeneity within an observed category? Whyisitimportanttoconsiderheterogeneitywithinanobservedcategorywhenanalyzing thedurationofunemployment? Thissectionillustratesthatamodelthatdoesnotconsider unobserved heterogeneity or GDD is limited in its ability to predict the distribution of unemploymentdurationinthedata. Consider an economy in which unemployed individuals have the same probability of exiting unemployment at t conditional on being unemployed at t−1. Let U denote the t totalnumberofunemployedindividualsandU1 denotethenumberofnewlyunemployed t individuals with the duration of unemployment one month in month t. The probability of continuingtobeunemployedattconditionalonbeingunemployedatt−1, p ,iscalculated t from U −U1 p = t t . t U t−1 In this economy, the number of those unemployed for n months at t, denoted Uˆn, is det termined by how many people become newly unemployed at t−n+1 and by the history between t−n+1 and t of the probability of staying unemployed next month conditional onbeingunemployedinthecurrentmonth.Then,Uˆn iswrittenintothefollowing: t Uˆ1 = U1 t t n Uˆn = U1 ∏ p for n ≥ 2. (1) t t−n+1 t−n+h h=2 Suppose that the maximum duration of unemployment is 48 months.7 With Uˆn with n = t furtherdividedintotemporaryjobendedandotherseparation,butthiscategorizationisavailableafter1994. Therefore,Iusethefive-waybreakdownfortheempiricalexercise,asthesampleperiodis1976-2019. 6Furtherdetailsonthedataconstructionarefoundintheonlineappendix. 7IntheCPS,themaximumdurationofunemploymentwas2yearsbeforeJanuary2011butwasextendedto 6

1,2,...,48, we can predict the mean and standard deviation of unemployment duration in agg agg progress in each month in this economy. Let M denote the mean, and S denote the t t standarddeviation. ∑48 Uˆnn M agg = n=1 t t ∑48 Uˆn n=1 t (cid:115) ∑48 Uˆn(n−M agg)2 S agg = n=1 t t (2) t ∑48 Uˆn n=1 t agg InFigure1,PanelAshows M (redline)andtheactualmeandurationcomputedfromthe t agg CPSmicrodata(blueline);PanelBplotsS (redline)andtheactualstandarddeviationof t unemploymentduration(blueline)fromJanuary1980toDecember2019.8 Onaverage,the predictedmeanis65%oftheactualmean,andthepredictedstandarddeviationis40%ofthe actualstandarddeviation. Thisresultsuggeststhatthedistributionofunemploymentdurationanditsvariationovertimecannotbecorrectlydescribedwithouttakingheterogeneity inunemploymenthazardsintoaccount. Nowsupposethatworkersdifferonlybyobservablecharacteristics. Iwillrefertoindividuals who have observable characteristic j as group j for j = 1,2,3,...,J with J being the numberofworkercharacteristics. Let p denotetheunemployment-continuationprobabiljt ityattofindividualsingroup j. Theprobability, p ,iscalculatedas jt U −U1 jt jt p = , jt U j,t−1 where U is the total number of unemployed individuals and U1 is the number of newly jt jt 5yearsfrom2011. Before2011,anyresponseofunemploymentdurationgreaterthan2yearswasenteredas2 years. Inspiteoftheincreasedupperboundfrom2011,thenumberofindividualsreportingadurationlonger than4yearsislow.Therefore,settingtheupperboundtobe4yearsisnotrestrictive.Assuming2or3yearsas themaximumdurationdoesnotchangethemainresultofthispaper. Hornstein(2012)alsoassumesthatthe maximumdurationofunemploymentis4yearsinhismodelofunemploymentaccountingidentity. 8Originally,thesampleperiodofmicrodataisfromJanuary1976toDecember2019. Thedatafromthefirst fouryearsareusedtocomputethefulldistributionofunemploymentdurationinprogressforthefirstmonth inthesample,January1980. 7

PanelA PanelB 12 12 No heterogeneity No heterogeneity Observed heterogeneity Observed heterogeneity 10 Data 10 Data 8 8 6 6 4 4 2 2 0 0 1980 1985 1990 1995 2000 2005 2010 2015 1980 1985 1990 1995 2000 2005 2010 2015 Note: Unitsareinmonths. TheactualmeanandstandarddeviationarecomputedfromtheCPSmicrodata, andarenotseasonallyadjusted.ShadedareasdenoteNBERrecessions. Source:Author’scalculationbasedupontheCPSmicrodata. Figure1: Mean(PanelA)andstandarddeviation(PanelB)ofthedistributionofunemploymentdurationinprogresspredictedfromequations(2)and(3) unemployed individuals in group j at t. Similar to equation (1), the number of individuals who have been unemployed for n months in group j, denoted by Uˆn, is written into the jt following: Uˆ1 = U1 jt jt n Uˆn = U1 ∏ p for n ≥ 2. jt j,t−n+1 j,t−n+h h=2 Themeandurationofunemploymentinprogressofgroup jiscalculatedfrom ∑48 Uˆnn n=1 jt M = . jt ∑48 Uˆn n=1 jt In this economy, the aggregate mean and standard deviation of unemployment duration, 8

disagg disagg denotedby M andS ,respectively,arecalculatedasfollows: t t J U M disagg = ∑ ( jt )M t ∑J U jt j=1 j=1 jt (cid:118) S disagg = (cid:117) (cid:117) (cid:116) ∑ J ( U jt ) ∑4 n 8 =1 Uˆ j n t (n−M jt )2 . (3) t ∑J U ∑48 Uˆn j=1 j=1 jt n=1 jt For illustrative purposes, I take the reason for unemployment as the observed category. disagg As shown by Figure 1, M (dotted fuchsia line in Panel A) is 70% of the actual mean, t disagg and S (dotted fuchsia line in Panel B) is 50% of the actual standard deviation. The t predicted mean and standard deviation are slightly larger than those simulated under the assumption that all workers are homogeneous.9 Although we consider different observed characteristicsinvaryinglevelsofdetail,meaningfulimprovementisnotachievedinfitting thedistributionofunemploymentdurationinprogresstowhatisobservedinthedata. In the remainder of the section, I argue that it is crucial to consider the duration dependence in unemployment hazards to match the observable distribution of unemployment duration among individuals who share the same detailed observable characteristics. Consider an economy in which unemployed individuals who share the same observable characteristicshavedifferentunemployment-continuationprobabilities. Ipostulatethatthe unemployment-continuation probability of workers in group j is a function of duration, τ, to characterize changes in unemployment hazards over the duration of unemployment. Supposethattheprobability,denotedby p (τ),iswrittenintothefollowingform: jt p (τ) = exp(−exp(dτ)), (4) jt jt 9ByJensen’sinequality,themeanandstandarddeviationbecomeequalorlarger,asweconsiderfinergradationsofheterogeneityinthemodel. 9

wheredτ isacubicfunctionofτ, jt dτ = δa +δbτ+δcτ2+δdτ3.10 (5) jt jt jt jt jt The double-exponential function is a convenient way of implementing a proportional hazard specification to guarantee a well-defined probability between 0 and 1 (e.g., Katz and Meyer(1990)). Suppose,forsimplicity,thattheeconomyisinasteadystate. Then,thenumberofindividualsunemployedfornmonthsingroup j,Uˆn,iswrittenasfollows: j Un = U1p (1)....p (n−1). (6) j j j j Notethattherearefourunknownparameters—δa,δb,δcandδd. Withtheobserveddata—U1, j j j j j U2.3,U4.6,U7.12, and U13.+ —we can solve for the four unknown parameters with the four j j j j equationsforU2.3,U4.6,U7.12,andU13.+ . j j j j 2003m01−2007m11 2003m01−2007m11 2007m12−2013m12 2007m12−2013m12 0.5 0.6 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 Men,25-44,Somecollege/associatedegree Women,16-24,Highschoolorless Source:Author’scalculation. Figure 2: Duration profile of exit probability from unemployment, 1− p (τ). Horizontal j axis: duration of unemployment in months. Vertical axis: probability that an individual leavestheunemploymentstatusthefollowingmonth. 10Acubicfunctioncanflexiblycharacterizebothlinearandnonlinearfunctions. Iadoptacubicfunctionto capturepossiblenonlinearityinthedurationprofileofunemploymenthazardsforillustrativepurposes. 10

I estimate the model, equations (4)-(6), for two different groups—men aged 25-44 with some college education or an associate degree and women aged 16-24 with a high school education or less—and for two different periods—January 2003-November 2007 and December 2007-December 2013.11 Figure 2 plots the average exit probability from unemployment over unemployment duration, 1− p (τ), for each group and for each period of time. j The duration profile of unemployment hazards is different over business cycle phases and betweendifferentgroups. There are three important observations. First, the unemployment-exit probabilities exhibit a non-monotonic U-shape along the duration of unemployment, decreasing for the first year of duration in unemployment and increasing afterward. Deterioration in unemploymenthazardsovertheduration—thenegativedurationdependence—iscommonlyobserved in the two groups and in the two different time periods during the first year of unemployment. There are two explanations for the negative duration dependence. One theory claims workers with low re-employment prospects due to their unobserved attributes are dynamically sorted into the long-term unemployment pool, creating the observed deterioration in unemployment hazards. Another theory suggests workers’ re-employment prospectsdeclineduringtheirjoblessspells,becausepotentialemployersdiscriminateagainst the long-term unemployed or their human capital depreciates over time. This theory is called the negative GDD. Though these two theories explain the negative duration dependence, the rising exit probabilities after one year in unemployment suggest that workers are exposed to a different type of GDD. The long-term unemployed might become more likelytoleavethelaborforceoutofdiscouragementortotakealow-payingjobduetotheir 11Iconsiderthetwogroupstoillustratethatthedurationdependenceisageneralphenomenoncommonly observedacrossindividualsaftercontrollingfordemographicandeducationcharacteristics.Inaddition,Ifocus onthetwoperiodsoftimewithdifferentaverageunemploymentrates(5.2%in2003:M01-2007:M11and8.2% in2007:M12-2013:M12)toillustratethatthepatternofdurationdependencecanchangedependingonthelevel oftheunemploymentrate. ThenonlinearstatespacemodelintroducedinSection3takesthispossibilityinto accountassumingtworegimesforGDD.Thetwoperiodsconsideredinthesteady-stateexerciseareinlinewith thetworegimesinthenonlinearstatespacemodel. 11

liquidityconstraintsastheystayunemployedlonger. ThistheoryiscalledthepositiveGDD. Second, the exit probabilities were, on average, lower after the Great Recession began (bluedashedline)thantheywereduringthepre-recessionperiod(redline). Thisevidence suggests that either the average exit probability falls or the share of those who have low job-findingratesamongnewlyunemployedworkersrisesduringtheeconomicdownturn. Finally, substantial differences exist in the shape of unemployment-exit probabilities over the duration of unemployment between groups. Specifically, between December 2007 andDecember2013,theunemploymenthazardsofwomenaged16to24withahigh-school diploma or less increase after one year in unemployment (blue dashed line in the right panel), while those of men aged 25 to 54 with some college or an associate degree do not (blue dashed line in the left panel). This observation indicates the importance of consideringdifferentdistributionsofunobservedheterogeneityanddifferentpatternsofGDDfor eachobservable-characteristicgroupinordertoaccuratelyunderstandthefactorsthataffect thedurationdistributionofaparticulargroup. 3 Model and Estimation This section portrays the key empirical analysis. Section 3.1 discusses the identification of the inflows and unemployment-continuation probabilities of workers who have the same observable characteristics but have different unobserved types based on the model of dynamic accounting identity. Section 3.2 introduces the nonlinear state space model that estimatesthedynamiclatentvariables. 12

3.1 Identification: Dynamicaccountingidentityforgroup j Suppose that there are unemployed individuals with two unobserved types—H and L—in groupj.12 Inmontht,typeHworkershaveahighprobabilityofexitingunemploymentnext month,denotedby pH,andtypeLworkershavealowprobabilityofexitingunemployment jt nextmonth,denotedby pL. Eachmonth,therearenewinflowsoftype H and Lworkersin jt group j,denotedby wH and wL,respectively. Inaddition,type H and L workers’probabiljt jt itiesofexitingunemploymentchangeoverthedurationofunemploymentreflectingGDD. We assume that GDD has limited time-variations, and that the two types of workers are exposedtothesameGDDbuttheGDDmaydifferby j. Giventhissetofassumptions,wecanidentifytheinflows,theunemployment-continuation probabilities of workers with two unobserved types, and the parameters governing GDD withU1,U2.3,U4.6,U7.12, andU13.+ . Toprovidetheintuitionofidentification, supposethat jt jt jt jt jt theeconomyisinasteadystate. Isuppressthetimesubscript, t, accordingly. Assumefirst thatthereisnoGDD.ThesumofwL andwH isU1. Thenumberofindividualsunemployed j j j for two months, U2, equals the number of newly unemployed type H and L individuals j whocontinuetostayunemployedforonemoremonth. Likewise,U3 equalsthenumberof j newlyunemployedtype H and L workerswhocontinuetostayunemployedfortwomore months. The sum of U2 and U3 is U2.3. By the same token, we can express U4.6 and U7.12 j j j j j asthefunctionsofthetwoinflowsandtwounemployment-continuationprobabilities. This suggeststhatwecansolveforthefourunknowns,wL,wH,pL,and pH,ifweobservethefour j j j j datapoints,U1,U2.3,U4.6 andU7.12. j j j j 12Becauseweestimatetheinflowsandunemployment-continuationprobabilitiesofeachtype,onlytwotypes canbeidentifiedfromthefivedatapointsinmontht. Consideringjustthetwounobservedtypesinagiven groupisarestriction,andincorporatingmoretypesisdesirable.Nonetheless,assumingthetwotypesofworkers is not critical for a few reasons. First, the goal of this analysis is to show that a model with unobserved heterogeneitycangoalongwaytowardexplainingthedistributionofunemploymentduration.Achievingthe goalwithasimplemodelsuggeststhatwewillreachthesameconclusionwithamodelofmoretypes.Second, inaseparatepaperbyAhnandHamilton(Forthcoming),threetypesareconsideredtocharacterizetheweekly durationdata. However, nostatisticallysignificantimprovementinthelikelihoodvalueisachieved, andthe thirdtypetendstoconvergetooneofthetwotypes. 13

GDDcanbejointlyidentifiedwiththeinflowsandunemployment-continuationprobabilitiesoftwotypes. AssumeforsimplicitythatGDDisalinearfunctionofτ characterized by one parameter. Then, we can identify the five unknowns—the GDD parameter along with wL,wH,pL, and pH—using the five values U1,U2.3,U4.6,U7.12, and U13.+ . Now supj j j j j j j j j posethatweobserveU1,U2.3,U4.6,U7.12,andU13.+ intwodifferentperiodsandGDDdoes j j j j j not change over time. We can solve for wL,wH,pL, and pH in each period and use the two j j j j remaining data points to characterize GDD. Note that we can characterize nonlinearity in GDDwiththetwodatapoints. Asweconsiderdatafrommoreperiods,wecanhaveamore general functional form for GDD. In fact, we use U1,U2.3,U4.6,U7.12, and U13.+ for every jt jt jt jt jt monthtduringthesampleperiod. Withsuchdata,wecanevenallowdifferentregimesfor GDDassumingthatGDDdoesnotvaryovertimewithinaregime. Thesesteady-stateexamplesillustratetheintuitionofidentification,butthesimilarlogic applies in a dynamic setting. The four variables, pH, pL, wH, and wL, are dynamic latent jt jt jt jt variables that change every month. Each group j has a different function for GDD. I use a nonlinearfunctionforGDDtocaptureapossiblenon-monotonicpatternofunemploymentexit probabilities over the duration of unemployment. Lastly, following the previous research studying variation in GDD depending on business cycle phases (e.g., Kroft et al. (2013)), I assume that there are two regimes for GDD—low- and high-unemployment-rate regimes—but that the magnitude of GDD does not change within a regime. Given the historyofestimatedinflowsandunemployment-continuationprobabilitiesuptomonth t−1 and the parameters governing GDD, we can estimate the four latent variables in month t that best fit U1,U2.3,U4.6,U7.12, and U13.+ . In this way, we can identify the inflows and jt jt jt jt jt unemployment-continuation probabilities of workers with unobserved types at each point intimejointlywiththeGDDparametersbasedupontheaccountingidentityforthenumber ofunemployedindividualsbythedurationofunemployment.13 13Dataonunemploymentdurationareaffectedbyreportingerrors,suchasthedigitpreferencedocumented inAhnandHamilton(Forthcoming). Intheonlineappendix,Ielaborateonwhythisissueisnotrelevantfor 14

3.2 Nonlinearstatespacemodel Themodelofdynamicaccountingidentityofunemploymentforgroup j iscastintoanonlinear state space model. The measurement equation is the following. In month t, the numberofindividualswithobservablecharacteristic jwhohavebeenunemployedforone month, U1, is the sum of newly unemployed type H and L workers, wH and wL, respecjt jt jt tively. U1 = wH +wL jt jt jt I assume that for unemployed individuals in group j who have already been unemployedforτ monthsasoftimet−1,thefractionofthosewhowillstillbeunemployedatt isgivenby pz(τ) = exp[−exp(xz +d gt)] jt jt jτ for z = H,L.Thenotation xz isatime-varyingparameterdeterminingtheunemploymentjt continuation probability for workers of type z in group j regardless of their duration, and it captures cross-sectional heterogeneity in unemployment-continuation probabilities between the two types. Because type H workers have a higher exit probability from unemployment,Iset xH > xL. jt jt The term d gt captures the effect from GDD. To characterize the possible nonlinearity in jτ the relations between the unemployment-exit probability and the unemployment duration as illustrated in Section 2, I use a linear spline for d gt with breaks at τ = 6 and 12. One jτ source of the nonlinearity is the exhaustion of unemployment insurance (UI) benefits. As shownbyKatzandMeyer(1990),unemployedindividualstendtoexitunemploymentmore rapidly, before they exhaust their UI benefits. This can create positive GDD in the first 6 months in unemployment, considering the maximum duration of UI benefits is 6 months innormaltimes. After6monthsinunemployment, workersmightbecomediscouragedor thepurposeofthepresentstudyandwhichalternativestrategiesmaybeusedinfurtherresearch. 15

discriminated against by potential employers because of their long jobless spells, creating negative GDD. In addition, after having been jobless long enough, unemployed workers mightquitjobsearchortakealow-payingjob, whichcreatesthepositiveGDD.Tocapture thispossibility,Iconsideranotherbreakatτ = 12. In addition, when a state’s unemployment rate is higher than 6.5%, the UI benefits are extendedupto52weeks,suggestingthepatternofGDDcanchangeovertime. Therefore,I allow d gt tohavetworegimesdependingonthelevelofunemploymentrateattime t. Iset jτ g = E(Expansion)formonthtwhentheunemploymentrateislowerthan6.5%and g = R t t (Recession) when the unemployment rate is 6.5% or higher.14 Lastly, I set d gt to be constant jτ forτ ≥ 24,assumingthatthosewhohavebeenunemployedfor2yearsorlongerarelargely thesameintheirprobabilitiesofexitingunemployment. Thefunctionalformofd gt isasfollows: jτ    δ gt(τ−1) forτ < 6  j1      δ gt[(6−1)−1]+δ gt[τ−(6−1))] for6 ≤ τ < 12 d gt = j1 j2 jτ   δ gt[(6−1)−1]+δ gt[(12−1)−(6−1)]+δ gt[τ−(12−1)] for12 ≤ τ < 24   j1 j2 j3     δ gt[(6−1)−1]+δ gt[(12−1)−(6−1)]+δ gt[(24−1)−(12−1)] for24 ≤ τ. j1 j2 j3 Positive values of δ gt for h = 1,2,3 capture positive GDD, while negative values capture jh negativeGDD. Let Pz(k) be the fraction in group j of individuals of type z who were unemployed for jt onemonthasofdatet−kandarestillunemployedatt.Then, Pz(k)iswrittenasaproduct jt ofmonthlyfractions pz (τ)forτ = 1,2,...,kasfollows: j,t−k+τ Pz(k) = pz (1)pz (2)...pz(k). jt j,t−k+1 j,t−k+2 jt 14Forrobustnesschecks, Iadditionallyconsiderthethirdregimewiththethresholdunemploymentrateat 8.0%.Nonetheless,therearenomaterialchangesintheestimates,andthelikelihoodvaluesarenotsubstantially improved. 16

Note that individuals unemployed for two to three months at t include those who become newlyunemployedattimet−1andlookforajobatt,andthosewhobecomenewlyunemployedatt−2andcontinuetolookforajobatt−1andt.Thus,thenumberofindividuals ingroup junemployedfortwotothreemonthsinmontht,U2.3,iswrittenasfollows: jt (cid:104) (cid:105) U2.3 = ∑ wz Pz(1)+wz Pz(2) . jt j,t−1 jt j,t−2 jt z=H,L Likewise,thenumberofthosewhohavebeenunemployedforbetweenm andm months 1 2 attimet(U m 1.m2)is jt U m 1.m2 = ∑ m ∑2 −1 (cid:104) wz Pz(k) (cid:105) . jt j,t−k jt z=H,Lk=m 1 −1 Ifurtherassumethateachdatapoint,U1,U2.3,U4.6,U7.12andU13.+ ,isobservedwithameajt jt jt jt jt surementerror,r1,r2.3,r4.6,r7.12 andr13.+ ,respectively: jt jt jt jt jt U1 = wH +wL +r1 jt jt jt jt (cid:104) (cid:105) U2.3 = ∑ wz Pz(1)+wz Pz(2) +r2.3 jt j,t−1 jt j,t−2 jt jt z=H,L 5 (cid:104) (cid:105) U4.6 = ∑ ∑ wz Ps(k) +r4.6 jt j,t−k jt jt z=H,Lk=3 11 (cid:104) (cid:105) U7.12 = ∑ ∑ wz Pz(k) +r7.12 jt j,t−k jt jt z=H,Lk=6 47 (cid:104) (cid:105) U13.+ = ∑ ∑ wz Pz(k) +r13.+ . jt j,t−k jt jt z=H,Lk=12 I terminate the calculations after 4 years of unemployment. We can define the likelihood functionfortheobserveddataconditionalonstatevariablesbyassumingthatthevectorof measurementerrorsr = [r1,r2.3,r4.6,r7.12,r13.+]′ isindependentNormal, jt jt jt jt jt jt r ∼ N(0,R ) jt j 17

with R = diag((R1)2,(R2.3)2,(R4.6)2,(R7.12)2,(R13.+)2)where R1, R2.3, R4.6, R7.12,and R13.+ j j j j j j j j j j j arethestandarddeviationsofr1,r2.3,r4.6,r7.12,andr13.+ ,respectively. jt jt jt jt jt Let me turn to the state equation. Let ξ be the vector [wL,wH,xL,xH]′, and ϵ be the jt jt jt jt jt jt vector [ϵLw, ϵHw,ϵLx, ϵHx]′. The assumption that the latent factors evolve as random walks jt jt jt jt wouldbewrittenas ξ = ξ +ϵ , ϵ ∼ N(0, Σ ) jt j,t−1 jt jt j with Σ = diag((σw)2,(σw )2,(σx )2,(σx )2)where σw,σw ,σx,and σx arethestandarddej jL jH jL jH jL jH jL jH viationsofϵLw,ϵHw,ϵLx,andϵHx,respectively. jt jt jt jt Becausethemeasurementequationisafunctionof{ξ ,ξ ,...,ξ },thejointdistrijt j,t−1 j,t−47 butionofξ fromt−47totiscapturedbythestateequationasfollows: jt     ϵ  ξ jt   (cid:124)(cid:123) I (cid:122)(cid:125) (cid:124)(cid:123) 0 (cid:122)(cid:125) 0 0 ... 0 0 0   ξ j,t−1    (cid:124)(cid:123) j (cid:122) t (cid:125)      4×4 4×4    4×1           ξ j,t−1     I 0 0 0 ... 0 0 0     ξ j,t−2     (cid:124)(cid:123) 0 (cid:122)(cid:125)           ξ  =   ξ + 4×1   j,t−2   0 I 0 0 ... 0 0 0  j,t−3     .    .   0    . .     . . . . . . . . . . . . ... . . . . . . . . .     . .     .         . .      ξ j,t−47 0 0 0 0 ... 0 I 0 ξ j,t−48   (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) 0 (cid:124) (cid:123)(cid:122) (cid:125) 192×1 192×192 192×1 (cid:124) (cid:123)(cid:122) (cid:125) 192×1 where I and0denotea(4×4)identityandzeromatrix. Themodelisanonlinearstatespacemodelwherethemeasurementequationisnonlinear in the latent variables of interest. Therefore, the extended Kalman filter is used to form the likelihood function for the observed data and make an inference on the dynamic latent variables. Themodelhas15parameterstoestimateforeachgroup j—namely,thediagonal terms in the variance matrices Σ and R , and the parameters governing GDD, δE, δE , δE, j j j1 j2 j3 δR, δR and δR. The system of equations is estimated with maximum likelihood. I report j1 j2 j3 18

full-samplesmoothedinferences,denotedbyξˆ .15 jt|T 4 Empirical results Thissectionreportstheestimationresults. Idiscusstheunemployment-continuationprobabilitiesoftypesHandLinSection4.1andthetwoinflowsinSection4.2. Amongthevarious workercharacteristicsIconsider—gender,age,education,industry,occupation,andreason for unemployment—I particularly focus on "reason for unemployment" for two reasons. First, theestimatesindicate thatthe singleobserved workercharacteristic thatis mostsimilartothetype L attributeispermanentseparation—oneofthereasonsforunemployment. Second,previousstudiessuchasFujitaandMoscarini(2017)andHallandSchulhofer-Wohl (2018) also argue that the reason for unemployment is the key worker characteristic determiningdifferencesinthejob-searchoutcomesofunemployedindividuals.16 4.1 Theunemployment-continuationprobabilitiesoftwounobservedtypes In this section, I first show the unemployment-continuation probabilities of type H and L workers without GDD to examine the magnitude of difference in unemployment hazards between two unobserved types at each point in time. Next, I report GDD parameters and analyze the role of GDD in the duration dependence of unemployment hazards. Last, I explorewhattheseestimatestellusaboutchangesinlong-termunemployment. The unemployment-continuation probabilities of newly unemployed type H and L individuals are reported in Figure 3. Note that these probabilities are not affected by GDD. It is commonly observed across the five groups that the difference in probabilities between thetwotypesissubstantial. AveragetypeLcontinuationprobabilitiesarebetween0.69and 15Moredetailsabouttheestimationalgorithmarefoundintheonlineappendix. 16Theestimationresultsforthegroupsofotherobservablecharacteristicsaredocumentedintheonlineappendix.Consistently,thevarianceofunemploymentattributedbytheinflowsandunemployment-continuation probabilitiesexhibitsthelargestdifferenceacrossgroups,whenthedataaredisaggregatedbyreasonforunemployment. 19

0.95, while average type H continuation probabilities are between 0.34 and 0.56 as summarized in Table 1. The gap between type H and L probabilities ranges between 0.35 and 0.46. Temporary layoffs Permanent separation Job leavers 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 p (1) p (1) p (1) p (1) p (1) p (1) L,t H,t L,t H,t L,t H,t 0 0 0 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 Reentrants to the labor force New entrants to the labor force 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 p (1) p (1) p (1) p (1) L,t H,t L,t H,t 0 0 1980 1990 2000 2010 1980 1990 2000 2010 Note:ShadedareasdenoteNBERrecessions.Thedashedlinesdenote90%confidenceintervals. Source:Author’scalculation. Figure3: Probabilitythatanewlyunemployedworkerofeachtypewillstillbeunemployed thefollowingmonthbyreasonforunemployment. TL PS JL RE NE Type Lcontinuationprobability 0.69 0.95 0.90 0.91 0.93 Type H continuationprobability 0.34 0.56 0.44 0.47 0.49 Type Lshareininflows 0.19 0.31 0.15 0.17 0.12 Note: TL,PS,JL,RE,andNEstandfortemporarylayoffs,permanentseparations,jobleavers,reentrantstothe laborforce,andnewentrantstothelaborforce,respectively. Table 1: Average inflows and unemployment-continuation probabilities by reason for unemployment(1980-2019) Theunemployment-continuationprobabilitiesofbothtypes H and Ltendtogoupduring an economic downturn. During the Great Recession and its aftermath, the two proba- 20

bilitiesreachthehighestorclosetothehighestlevelssince1980inallgroups. Temporary layoffs Permanent separation Job leavers Reentrants New entrants 1 1 1 E 1 1 0.9 0.9 0.9 R 0.9 0.9 0.8 0.7 E 0.8 E 0.8 0.8 E 0.8 E R R R R 0 10 20 0.7 0 10 20 0.7 0 10 20 0.7 0 10 20 0.7 0 10 20 Temporary layoffs Permanent separation Job leavers Reentrants New entrants 1 1 1 1 1 0.5 0.5 0.5 0.5 0.5 0 0 10 20 0 0 10 20 0 0 10 20 0 0 10 20 0 0 10 20 Note: Intheupperpanels,thevariationintypeLunemployment-continuationprobabilityreflectseffectsfrom GDD.Thesolidlinedenotesregime"E"andthedashedlinedenotesregime"R." Source:Author’scalculation. Figure4: Averagetype Lunemployment-continuationprobability(upperpanels)andaveragetype Lshare(lowerpanels)overthedurationofunemployment Overall,GDDparametersarepositiveforthefirst6monthsofunemployment,negative between 7 and 12 months, and positive again after 1 year as shown in the upper panels of Figure 4.17 GDD parameters are largely statistically significant.18 The lower panels of Figure 4 show that type L share increases rapidly as the unemployment duration progresses up to 6 months. The positive GDD and the rapid rise in type L share in the range of duration with 6 months or less indicate that unobserved heterogeneity is the main explanation for the negative duration dependence, considering that a large part of the deterioration in unemploymenthazardstakesplaceinthefirst6monthsofunemployment.1920 17Iplottheunemployment-continuationprobabilityoftypeLworkersoverunemploymentdurationbecause the share of type H workers becomes close to zero after 6 months in unemployment, as shown by the lower panels of Figure 4. The positive GDD in long-term unemployment might reflect that unemployed workers become more likely to quit looking for a job due, for instance, to discouragement from an unsuccessful job search. MeanwhilethenegativeGDDmightreflectfirms’discriminationagainstthelong-termunemployed. It ispossiblethatnegativeGDDisprevalentintransitionsfromunemploymenttoemployment, whilepositive GDDisineffectintransitionsfromunemploymenttononparticipation. 18Theparameterestimatesaredocumentedintheonlineappendix. 19Kroftetal.(2013)showthatthenegativedurationdependenceisobservedinthefirsteightmonthsofthe job search, and Jarosch and Pilossoph (2018) argue that this pattern can be explained by unobserved worker heterogeneity. 20TherisingtypeLshareoverthedurationofunemploymentcapturesthedynamicsortingthatarisesfrom 21

In addition, GDD has a small effect on the mean duration of unemployment. In shortterm unemployment with duration 6 months or less, the positive GDD lowers the mean durationby0.3month,onaverage. Inlong-termunemploymentwithdurationlongerthan 6 months, the negative GDD pushes up the mean duration by 2.5 months and the positive GDD lowers the average duration by 2.2 months, raising the mean duration of unemployment by 0.3 months on net.21 Changes in the regime of GDD do not significantly alter the contributionofGDDtothemeanduration,either.22 Whatdo theresults implyabout long-termunemployment? The estimatessuggest that type Lworkers’unemployment-continuationprobabilitiesareanimportantdeterminantof changes in long-term unemployment, as type L workers mainly constitute long-term unemployment. In fact, the unemployment-continuation probabilities of long-term type L workers stay at high levels for a few years after the Great Recession as shown in Figure 5, coinciding with the period when the mean duration of unemployment continues to rise toarecord-highlevel. Inaddition,thelimitedrecoveriesinthemeandurationofunemployment after the 2001 and 2007 recessions are also closely associated with type L permanent thedifferenceinunemploymenthazardsbetweenthetwotypes. Type Lworkerstakealargershareinlongtermunemployment, astheyarelesslikelytoleaveunemploymentstatus. Figure4showsthatthedynamic sortingisthekeycontributortothenegativedurationdependenceinunemploymenthazards. However,this findingdoesnotnecessarilymeanthatthecompositionalshiftoftype Lworkersshouldbeadominantfactor intheriseofthemeandurationofunemployment. Notethattwocircumstancescanraisethemeanduration of unemployment: when type L workers stay unemployed longer than before and when the type L share in theunemploymentpoolrisesbecausemoretypeLworkerslosejobsthanthantypeHworkersdo. Whentype L workers’ unemployment duration becomes longer during a recession, the type L duration can be the key factorintheriseofthemeandurationandthedynamicsortingcanstillbethekeycontributortothenegative durationdependence.Therefore,thepotentiallygreaterimportanceoftypeLdurationinaccountingfortherise inthemeandurationofunemploymentdoesnotcontradicttheimportanceofdynamicsortinginthenegative durationdependenceofunemploymenthazards. 21ThecontributionofpositiveGDDintheshort-termunemploymentiscomputedfromthedifferencebetween themeandurationwhered gt =d gt forτ<6andthatwiththefullpathofGDD(thebaseline).Thecontribution jτ j5 ofnegativeGDDiscomputedfromthedifferencebetweenthemeandurationwhereonlythenegativeGDDis inactioninthelong-termunemploymentandtheaveragedurationwhereGDDdoesnotchangefromτ ≥ 6. Theformeriscalculatedbyfixingd gt forτ≥12atd gt ,andthelatteriscomputedbyfixingd gt forτ≥6atd gt. jτ j,11 jτ j5 ThedifferencebetweenthebaselineandtheformercounterfactualisthecontributionfrompositiveGDDinthe long-termunemployment. 22Onaverage,GDDraisesthemeandurationby0.3monthonnetintheEregime,andlowersitby0.2month onnetintheRregime. 22

PanelA PanelB Note:Refertotheleftaxisforthebluelineandtherightaxisfortheblackandredlines. Source:Author’scalculation. Figure 5: Unemployment-continuation probability of type L individuals unemployed for longerthan6monthsbyreasonforunemployment job losers and reentrants to the labor force. Their long-term unemployment-continuation probabilities did not return to the pre-recession levels after the two recessions as shown in PanelAofFigure5.23 4.2 Theinflowsoftwounobservedtypes Inthissection,Ifirstreporttheestimatedinflowsoftype H and L workers. Next,Iexplore whichgroupconstitutesthemajorityoftotaltype Linflowsandmainlydrivesthecountercyclicality of aggregate type L inflows to identify the observable worker characteristic that ismostcloselyassociatedwiththetype Lattribute. Lastly,Ibrieflydiscussthetrendsinthe inflows. The smoothed estimates of type H and L newly unemployed individuals are displayed in Figure 6. Type L individuals make up a small portion of the inflows and represent, on 23Section6exploresthedriversofthetrendsinprobabilityestimatesinmoredetail. 23

average,13%to28%ofnewlyunemployedindividualsacrossallgroups(Table1). Notably, permanentjoblosershavethelargesttype Lshareamongthenewlyunemployed.24 Temporary layoffs Permanent separation Job leavers 1 W L W H 1 W L W H 1 W L W H 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 1 0 9 80 1990 2000 2010 1 0 9 80 1990 2000 2010 1 0 9 80 1990 2000 2010 Reentrants to the labor force New entrants to the labor force W W W W 1 L H 1 L H 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 1 0 9 80 1990 2000 2010 1 0 9 80 1990 2000 2010 Note: Units are in hundred thousand individuals. Shaded areas denote NBER recessions. The dashed lines denote90%confidenceintervals. Source:Author’scalculation. Figure6: Numberofnewlyunemployedworkersofeachtypebyreasonforunemployment. The dynamic features of the inflows are quite different both between the unobserved typesandacrossthefivegroups. Theinflowsofjoblosersarecountercyclical. Notably,type L inflows of permanent job losers exhibit the strongest countercyclicality among all the inflowsandessentiallydrivethecountercyclicalvariationintotaltype Linflows.25 However, the inflows of those who did not indicate job loss as their reason for unemployment show mixed cyclicality. The inflows of type L reentrants to the labor force exhibit weak counter- 24Thereareunemployedindividualswhoindicatetemporarylayoffsastheirreasonforunemploymentbut changetheiranswerstopermanentseparationinthesubsequentmonths.Themodeldoesnottakethesetransitionsintoaccount.Intheonlineappendix,Iexplainindetailwhythisproblemdoesnotaffecttheresultsofmy analysis. 25ThispointissummarizedinPanelAofFigure7.Nogroupswithotherobservablecharacteristicsdrivethe riseoftypeLinflowsduringarecessionasmuchaspermanentjoblosersdo. FiguresanalogoustoFigure7for otherworkercharacteristicsaredocumentedintheonlineappendix. 24

cyclicality,thoseoftype H jobleaversareprocyclical,andtherestarelargelyacyclical. Duemainlytotype Lpermanentjoblosers,thecountercyclicalityoftotaltype Linflows is greater than that of total type H inflows. This observation indicates that disproportionately more workers with low reemployment prospects flow into the unemployment pool duringaneconomicdownturn. PanelA PanelB Type L inflows by reason for unemployment Share in type L inflows by reason for unemployment 1 Temporary Layoffs Temporary Layoffs Permanent Separations 0.9 Permanent Separations Job Leavers Job Leavers 1 Reentrants 0.8 Reentrants New Entrants New Entrants Sum 0.7 0.8 0.6 0.6 0.5 0.4 0.4 0.3 0.2 0.2 0.1 0 0 1980 1985 1990 1995 2000 2005 2010 1980 1985 1990 1995 2000 2005 2010 Note: TL,PS,JL,RE,andNEstandfortemporarylayoffs,permanentseparations,jobleavers,reentrantstothe laborforce,andnewentrantstothelaborforce,respectively.ForPanelA,unitsareinmillionindividuals. Source:Author’scalculation. Figure7: Compositionoftype Linflowsbyreasonforunemployment. More importantly, all these observations indicate that permanent separation is likely the observable characteristic that is most closely associated with the type L attribute.26 As showninthecompositionoftype Linflowsbyreasonforunemployment(PanelBofFigure 7), permanent job losers take the largest share, 45%, among type L inflows. At the same time, the share of type L workers in the inflows is the largest among permanent job losers (Table1). 26Notethattheresultsshouldbeinterpretedwithcaution. IdonotclaimthattypeLworkersarepermanent joblosersorpermanentjoblosersaretypeL. AmongworkercharacteristicsobservableintheCPS,permanent joblossistheobservableworkercharacteristicthatismostcloselycorrelatedwiththetypeLattribute.Asshown inFigure3,therestillexistasignificantdifferenceintheunemployment-exitprobabilitiesamongpermanentjob losers,whichisthemainthemeofthepaper. 25

Lastly, it is notable that type H inflows of job leavers and reentrants to the labor force trend down throughout the sample period, while their type L inflows and the inflows of other groups do not exhibit any particular trend.27 This observation suggests the compositionofinflowsgraduallyshiftstowardtypeL,whichmayhavedrivenupthemeanduration ofunemploymentovertime.28 5 Contribution of worker heterogeneity to the evolution of unemployment duration Using the model’s estimates, this section analyzes how much the compositional shift of workerswithobservableandunobservableattributes,aswellaschangesintheunemployment duration of each type in each group, accounts for the evolution of the aggregate durationofunemployment. IfocusontheperiodfromDecember2007toDecember2011,and the entire sample period from January 1980 to December 2019 to examine the role of each factorinthecyclicalandlow-frequencyvariationsinthemeandurationofunemployment. Let Dz denote the mean duration of unemployment of workers in group j with type z jt forz = H,L. Theobject, Dz,iscomputedfromthefollowing: jt 48 (cid:104) (cid:105) ∑ wz Pz(k−1) k j,t−k+1 jt Dz = k=1 , jt 48 (cid:104) (cid:105) ∑ wz Pz(k−1) j,t−k+1 jt k=1 wherekdenotesthenumberofmonthsinunemploymentand Pz(0) = 1. jt 27TypeHinflowsofnewentrantstothelaborforcestepdownin1994duemainlytotheCPSredesignin1994 thatbroadenstherangeofindividualswhoareclassifiedasreentrantstothelaborforceandnarrowstherange ofnewentrantstothelaborforce. PolivkaandMiller(1998)provideadjustmentfactorsfortheunemployment ratesofthetwogroupsthataremethodologicallyconsistentbutdonotprovidefactorsfortheirdistributionof unemploymentduration. Therefore,Idonotadjustthedurationdistributionofnewentrantsandreentrantsto thelaborforceafter1994. EvenifIincreasethetypeHinflowsofnewentrantswiththeadjustmentfactorsfor theunemploymentrates,theinflowsdonotexhibitanyparticulartrend. 28MoredetailedanalysesonthetrendsininflowsareprovidedinSection6. 26

Let fz denotethefractionoftypezworkersintheunemploymentofgroup j. Theobject, jt fz,iscalculatedfrom jt 48 (cid:104) (cid:105) ∑ wz Pz(k−1) j,t−k+1 jt fz = k=1 . jt 48 (cid:104) (cid:105) ∑ ∑ wz Pz(k−1) j,t−k+1 jt z=H,Lk=1 full Themeandurationofunemployment,denotedas D ,iswrittenintothefollowing: t J D full = ∑ F (fHDH + fLDL), t jt jt jt jt jt j=1 where F isthefractionofgroup jintheaggregateunemployment. jt Thecontributionfromacompositionalshiftofworkerswithobservablecharacteristicsis calculatedbylettingonlyF varyovertime,whilefixingDz and fz atthevaluesobservedat jt jt jt the beginning of the period of analysis, t . Let Dz and fz be the unemployment duration 0 jt0 jt0 and the fraction of type z workers in group j in month t , respectively. Then the mean 0 durationofunemploymentexplainedbyshiftsinthecompositionofgroupswithobservable characteristics,denotedas Do,is t J Do = ∑ F (fHDH + fL DL ). t jt jt0 jt0 jt0 jt0 j=1 The contribution from the compositional shift of workers with unobserved types is calculated by letting fH and fL vary over time while fixing the other components at the values jt jt oft .Thenthemeandurationofunemploymentaccountedforbythecompositionalshiftof 0 workerswithunobservedtypes,denotedas Du,is t J Du = ∑ F (fHDH + fLDL ). t jt0 jt jt0 jt jt0 j=1 Next, consider the case in which only the duration of type L workers in group j is al- 27

lowed to vary over time. Then the predicted mean duration of unemployment, denoted as D ,iswritteninto Lt J D = ∑ F (fHDH + fL DL). Lt jt0 jt0 jt0 jt0 jt j=1 Likewise, by allowingonly DH tochange, thepredicted meanduration, denotedas D , is jt Ht expressedasfollows: J D = ∑ F (fHDH + fL DL ). Ht jt0 jt0 jt jt0 jt0 j=1 Changes in the regime of GDD affect D and D through DH and DL, respectively.29 Ht Lt jt jt Let DE (DE)denotethepredictedmeandurationattdrivenonlybychangesintype H (L) Ht Lt duration,whentheGDDparametersareinregimeE. Theeffectofchangesintheregimeon themeandurationofunemployment,denotedasG ,iscalculatedfromthefollowing: t G = (D −DE )+(D −DE). t Ht Ht Lt Lt Figure8plotsthepathsof Do(blackline), Du(redline), DE(bluedashedline), DE (pink t t Lt Ht line with x’s), and G (black dashed line) between December 2007 and December 2011.30 t Note that the values in December 2007 are set to zero.31 The unemployment duration of type L workers(bluedashedline)isthemostimportantcontributortotheriseinthemean durationofunemployment,accountingforabout80%oftherise. Thisfactorbeginstoraise the mean duration in the latter part of the Great Recession, and continues to drive it upward to the unprecedentedly high level in 2011. The remaining increase in mean duration is explained by the compositional shift of unobserved types. The increased share of type L 29NotethattheGDDparametersaretime-invariantwithinaregime.Therefore,changesinthedistributionof unemploymentdurationaredrivenbytype H and Linflows,theirunemployment-continuationprobabilities, orchangesinGDD. 30In 2011, the predictedmean duration, D full , isabout onemonth shorterthan inthe data. The modelatt tributesthedifferencetomeasurementerrorsinthedurationdata. Farberetal.(2015)andAhnandHamilton (Forthcoming)showevidencethatmeasurementerrorsinlong-termunemploymentlikelybecomesubstantially largerduringthisperiod.ThemodelfitsthedataverywellbeforetheGreatRecession. 31Morespecifically,D t f 0 ull issubtractedfromD t o,D t u,D L E t ,D H E t ,andGt. 28

Great Recession and its recovery (Dec.2007−Dec.2011) 4.5 Dfull t 4 Do t 3.5 Du t 3 D L E t DE 2.5 Ht G t 2 1.5 1 0.5 0 −0.5 2008.1 2009.1 2010.1 2011.1 Source:Author’scalculation. Figure 8: Contribution of each factor to changes in the mean duration of unemployment fromthelevelinDecember2007(unitsareinmonths). workers (solid red line) is the key driver of the rise in unemployment duration during the Great Recession, but its role becomes limited in the post-recession period when the mean duration continued to rise. Meanwhile, the shift in the share of workers along observable characteristics (thin black line), the unemployment duration of type H workers (pink line withcircle)andchangesintheregimeofGDD(blackdashedline)providelittlecontribution totheevolutionofunemploymentdurationduringthisperiod.32 I also analyze the contribution of each factor to changes in the mean duration of unemploymentbetweenJanuary1980andDecember2019.33 AsshowninPanelAofFigure9,the averagedurationofunemploymentdoublesfrom10.4weeksinJanuary1980to20.8weeks in December 2019. Panel B displays how much Do, Du, D , and D account for the rise t t Lt Ht duringthefourdecadeswiththevalueinJanuary1980settozero. Overthewholeperiod, the increased share of type L workers (solid red line) accounts for 30% of the rise, and the 32Theresultindicatingthelittleroleinthecompositionalshiftofworkerswithobservablecharacteristicsis consistentwiththefindingsofKruegeretal.(2014)andKroftetal.(2016). 33IdonotseparatelyreportthecontributionfromchangesintheGDD,becausetheestimatedGDDparameters donothavetrends.Tomyknowledge,nopreviousstudiesinvestigatedlow-frequencychangesinGDD. 29

lengthier duration of type L workers (dashed blue line) explains 65%. Both the compositional shift of workers with unobserved types and the unemployment duration of type L workersplaycrucialrolesinthesecularriseinthemeandurationofunemployment. Morespecifically, thetype L share(solidredline)beginstodriveupthemeanduration of unemployment from the 1990s. This is mainly attributed to the downward trends in the type H inflowsofjobleaversandreentrantstothelaborforce. Quitedifferently,thecontribution from type L duration to the rising trend (blue dashed line) emerges from the 2000s. Afterthe2001recession,type Ldurationbeginstoimpedethefullrecoveryofthemeanduration to pre-recession levels. By the end of 2019, 10 years into the recovery after the Great Recession, the mean duration of unemployment predicted solely by type L duration is still higherthanthelevelbeforetherecession. Thisismainlyduetothelimitedrecoveryoftype L unemployment-continuation probabilities of permanent job losers and reentrants to the labor force who constitute about 70% of type L unemployment. Meanwhile, the contributions from type H duration (pink line with circle) and the compositional shift of workers withobservableworkercharacteristics(thinblackline),again,arenotimportant. Alltold,thedurationoftypeLworkersisthemostimportantcontributortobothcyclical and low-frequency variations in the mean duration of unemployment. The compositional shiftofworkerswithunobservedtypesisthesecondaryfactorbutstillexplainsthebulkof variation. Meanwhile, the contributionsfromobserved heterogeneityandtype H duration arenegligible. Theseresultssuggestunobservedheterogeneityiscrucialinthedynamicsof theaggregatedurationofunemployment. 30

PanelA PanelB Whole sample period (Jan.1980−Dec.2019) Whole sample period (Jan.1980−Dec.2019) 12 Mean duration of unemployment 5 D t o 11 Value observed prior to the 2001 recession Du t 4 10 D Lt D 9 Ht 3 8 7 2 6 1 5 4 0 3 2 −1 1980.1 1990.1 2000.1 2010.1 1980.1 1990.1 2000.1 2010.1 Source:Author’scalculation. Figure 9: Contribution of each factor to changes in the mean duration of unemployment fromthelevelinJanuary1980(unitsareinmonths). 6 Whatexplainsthetrendsintype H inflowsandtype Lunemploymentcontinuation probabilities? The empirical results in the previous section show that the secular rise in the mean duration of unemployment is mainly driven by two factors. First, type H inflows of job leavers and reentrants to the labor force trend down, driving the secular decrease in total type H inflows. Second, type L unemployment-continuation probabilities of permanent job losers andreentrantsdonotfullyrecovertothepre-recessionlevelsfromthe2000s.34 Iexplorethe driveroftheformerinSection6.1andthatofthelatterinSection6.2. 31

Jobleavers 1.Education 2. Age 3. Gender Reentrantstothelaborforce 4.Education 5. Age 6. Gender Note: Unitsareinhundredthousandindividuals. TherightaxesinPanels1and4arefortypeHinflows(red dots). Source:Author’scalculation. Figure10: Numberofnewlyunemployedindividualsbyeducation,age,andgenderamong jobleaversandreentrantstothelaborforce. 32

6.1 Thesourceofdowntrendintype H inflowsofjobleaversandreentrants WhatdrivesthedowntrendintypeHinflowsofjobleaversandreentrantstothelaborforce? To answer this question, I decompose newly unemployed job leavers and reentrants to the labor force by gender, age, and educational attainment (Figure 10). Consider job leavers first. Between the 1980s and 2010s, the monthly inflows of type H job leavers drop by 200 thousands per month (Panel 1), while those of type L workers are largely unchanged.35 Similar to the decline in type H job leavers’ inflows, the monthly inflows of job leavers whose educational attainment is less than or equal to high-school graduation drop by 180 thousands, from 300 thousands per month in the 1980s to 120 thousands per month in the 2010s. Meanwhile,thosewithhighereducationstayflat,similartotheinflowsoftype Ljob leavers. However, it is hard to pin down the group whose inflows drop as much as type H inflows do, when decomposed by age and gender (Panels 2 and 3). All told, among job leavers,theseculardecreaseintype H inflowsismainlydrivenbyless-educatedworkers. The association between the type H attribute and lower education is also observed among reentrants to the labor force (lower panels in Figure 10). Between the 1980s and 2010s,thedeclineoftype H inflowsisclosetothatofindividualswhoseeducationalattainmentishigh-schoolgraduationorless(Panel4). Meanwhile, boththeirtype L inflowsand the inflows of reentrants whose education level is higher than high-school graduation are largely flat. Again, the similar dichotomy is not observed when decomposing the data by age and gender (Panels 5 and 6).36 To summarize, among reentrants to the labor force, the downtrendintypeHinflowsisalsoaccountedforbythedecreasedinflowsoflesseducated 34Theunemployment-continuationprobabilitiesoftypeHreentrantsandnewentrantstothelaborforcealso showarisingtrend,whichlikelyreflectstheincreasedlaborforceattachmentofwomen.Asitcontributeslittle tothesecularriseinthemeandurationofunemployment, Idonotdiscusstheuptrendanditssourceinthe maintext.Relateddiscussionisfoundintheonlineappendix. 35Type Linflowsofjobleaversare50thousands(1980-1989),54thousands(1990-1999),62thousands(2000- 2009),and54thousands(2010-2019). 36Type H inflowsofreentrantstothelaborforceare0.94million(1980-1989), 0.82million(1990-1999), 0.61 million(2000-2009),and0.46million(2010-2019). Theirtype Linflowsduringthesameperiodsare0.13,0.14, 0.16,and0.14million. 33

Note: Unitsareinmillionindividuals. TherightaxisisfortypeHinflowsofjobleavers(JL),andreentrantsto thelaborforce(RE). Source:Author’scalculation. Figure11: Inflowsoftype H workersandless-educatedindividuals individuals. Atthesametime,theseculardeclineininflowsofless-educatedworkersmainlyshows throughtotypeHjobleaversandreentrantstothelaborforce. Betweenthe1980sand2010s, themonthlyinflowsofindividualswhoseeducationalattainmentishigh-schoolgraduation orlessdeclineby1.2million(blacklineinFigure11). Duringthesameperiod,themonthly inflows of type H job leavers and reentrants drop by 0.7 million, accounting for about 60% of the decline in the inflows of less-educated workers. This observation suggests that the downtrend in the inflows of type H job leavers and reentrants is closely related to the increasededucationalattainmentofthelaborforce.37 Whodotype H jobleaversandreentrantsrepresent? Theyarelikelyjobswitcherswho experience a short intervening jobless spell, as their unemployment has a voluntary aspect and job switchers tend to have an intervening nonparticipation spell (Hall and Kudlyak (2019)). In other words, the joblessness of type H job leavers and reentrants is closely associated with churning in the labor markets.38 Considering that one important symptom 37Asthepopulationbecomesmorehighlyeducated,thenumberofnewlyunemployedworkerswithlower educationhasdeclinedovertime(HornsteinandKudlyak(2019)). 38Lazear and Spletzer (2012) and Weingarden (2020) show that voluntary job leavers are the key piece of 34

of reduced dynamism is decreased churns (Decker et al. (2016), Decker et al. (2017)), the downtrendintheirinflowssuggeststhattheincreasededucationalattainmentoflaborforce is tied together with the decreased dynamism in the labor markets. As the workforce becamemoreeducated,job-specifichumancapitalmighthavebecomemoreimportant,which likelyloweredaworker’sincentivetochangejobs. All told, the empirical analyses imply that the two related structural changes in the labor markets—the increased educational attainment of the labor force and the reduced dynamism—have particularly lowered the inflows of type H workers and shifted newly unemployedindividualstowardthosewhotendtobecomelong-termunemployed,whichhas graduallydrivenupthemeandurationoverthepastdecades.39 6.2 The source of limited recovery of type L unemployment-continuation probabilitiesofpermanentjoblosersandreentrantstothelaborforce Thissectionexploresthesourceofthelimitedpost-recessionrecoveryoftypeLunemploymentcontinuationprobabilitiesofpermanentjoblosersandreentrantstothelaborforcefromthe 2000s. Forthis,Iestimatethetype Lunemployment-continuationprobabilityofpermanent joblosersandreentrantsbygender,age,education,industryandoccupation. Thedifficulty in estimating the nonlinear state space model with further disaggregate data is substantial due to large measurement errors caused by the disaggregation. Therefore, I take a nonparametricapproachtoapproximatethetype Lprobability, pL,fromthefollowing: jt U7.+ pL ≈ ( jt )1 3. (7) jt U4.+ j,t−3 churnsinlabormarkets. 39TherearestudiessuchasDavisetal.(2010)andWeingarden(2017)thatanalyzetheeffectsofreduceddynamismonunemployment. However,Idonotacknowledgeanyresearchthatdiscussestheeffectsofreduced dynamismonlong-termunemploymentorthemeandurationofunemploymentwithunobservedworkerheterogeneitytakenintoaccount. 35

Theright-handsideofequation(7)ismainlydeterminedbytheunemployment-continuation probabilityoftype L workers,becausethemajorityofthoseunemployedfor4monthsand overaretypeLworkersineachgroupj.40 Itakea12-monthmovingaveragetotheestimates tosmoothoutthemeasurementerrors. Source:Author’scalculation. Figure12: Nonparametricestimatesof pL amongpermanentjoblosers jt Figures12and13reporttheestimates.41 Thepatternoflimitedrecoveryisbroad-based, withtheexceptionsofcollegegraduatesandindividualsaged55andover. Inotherwords,it isunclearwhichobservableworkercharacteristicisparticularlyassociatedwiththelimited 40GDDisnotconsideredinthiscalculation. However,abstractingGDDdoesnotinfluencethetrendcomponentintheestimates,asGDDmainlyshiftsthelevelofprobability. 41Amongreentrantstothelaborforce,Igroupworkerswithnon-routinemanualandnon-routinecognitive occupationstogetherduetothesmallnumberofobservationsofbothgroups. 36

Source:Author’scalculation. Figure13: Nonparametricestimatesof pL amongreentrantstothelaborforce jt recovery. Therefore,theworkerattributesthathampertheunemploymentdurationoftype L workers from recovering to pre-recession levels are ultimately unobserved in the CPS, thoughthefactorshavepervasiveeffectsacrossvariousworkers. Meanwhile,recentstudies(e.g.,Macaluso(2019))suggestthatskills,thoughchallenging tomeasure,mightbeanimportantdeterminantoflabormarketoutcomesamongjoblosers. Indeed,thecloseassociationbetweenpermanentjoblosersandtype Lworkersalsoimplies that skills might be the key unobserved factor. Workers who have skills not demanded by firms may lose their jobs permanently and stay unemployed for a longer period of time. Considering some reentrants are permanent job losers who left the labor force and came 37

back, type L reentrants are also likely to be those who experience skill mismatch. In this context,theuptrendinunemployment-continuationprobabilitiesamongtype Lpermanent job losers and reentrants might be driven by skill-biased technological changes. To verify thishypothesis,however,oneneedsnewdatasources. 7 Conclusion This paper demonstrates that a statistical model can capture the existence of unobserved worker heterogeneity and its consequences for changes in the aggregate duration of unemployment. Unobserved heterogeneity is important in not only cyclical but also low frequencyvariationsintheaggregatedurationofunemployment. ThecloselinkbetweenpermanentjoblossandtypeLunemploymentimpliesthechangingdemandforskillsmightbe an important factor that makes a worker stay unemployed for a long time. In this context, it is crucial to think about the distribution of unobserved heterogeneity as a dynamic process. Thisresearchalsosuggestsnewdatasourcesareneededtobetteridentifythegroupof workersthatarecriticalinunderstandinglong-termunemployment. References Acemoglu, Daron, “Technical Change, Inequality, and the Labor Market,” Journal of EconomicLiterature,March2002,40(1),7–72. Ahn, Hie Joo and James D. Hamilton, “Heterogeneity and Unemployment Dynamics,” JournalofBusiness&EconomicStatistics,2020,38(3),554–569. and ,“MeasuringLabor-ForceParticipationandtheIncidenceandDurationofUnemployment,”ReviewofEconomicDynamics,Forthcoming. Baker,Michael,“UnemploymentDuration: CompositionalEffectsandCyclicalVariability,” AmericanEconomicReview,March1992,82(1),313–321. Darby, Michael R., John C. Haltiwanger, and Mark W. Plant, “The Ins and Outs of Unemployment: The Ins Win,” NBER Working Papers 1997, National Bureau of Economic Research,IncAugust1986. 38

Davis,StevenJ.,R.JasonFaberman,JohnHaltiwanger,RonJarmin,andJavierMiranda, “Business Volatility, Job Destruction, and Unemployment,” American Economic Journal: Macroeconomics,April2010,2(2),259–287. Decker, Ryan A., JohnHaltiwanger, RonS.Jarmin, andJavierMiranda, “Declining BusinessDynamism: WhatWeKnowandtheWayForward,”AmericanEconomicReview,May 2016,106(5),203–07. , , , and , “Declining Dynamism, Allocative Efficiency, and the Productivity Slowdown,”AmericanEconomicReview,May2017,107(5),322–326. Farber, Henry S., Jesse Rothstein, and Robert G. Valletta, “The Effect of Extended UnemploymentInsuranceBenefits: Evidencefromthe2012-2013Phase-Out,”AmericanEconomicReview,May2015,105(5),171–176. Fujita,ShigeruandGiuseppeMoscarini,“RecallandUnemployment,”AmericanEconomic Review,December2017,107(12),3875–3916. Gregory, Victoria, Guido Menzio, and David G. Wiczer, “The Alpha Beta Gamma of the LaborMarket,”NBERWorkingPapers28663,NationalBureauofEconomicResearch,Inc April2021. Hall, Robert E. and Marianna Kudlyak, “Job-Finding and Job-Losing: A Comprehensive Model of Heterogeneous Individual Labor-Market Dynamics,” NBER Working Papers 25625,NationalBureauofEconomicResearch,IncFebruary2019. andSamSchulhofer-Wohl,“MeasuringJob-FindingRatesandMatchingEfficiencywith HeterogeneousJob-Seekers,”AmericanEconomicJournal: Macroeconomics,January2018,10 (1),1–32. Hornstein, Andreas, “Accounting for unemployment: the long and short of it,” Technical Report2012. andMariannaKudlyak,“AggregateLaborForceParticipationandUnemploymentand DemographicTrends,”February2019,(2019-7). Jarosch,GregorandLauraPilossoph,“StatisticalDiscriminationandDurationDependence intheJobFindingRate,”TheReviewofEconomicStudies,092018,86(4),1631–1665. Katz,LawrenceF.andBruceD.Meyer,“Theimpactofthepotentialdurationofunemployment benefits on the duration of unemployment,” Journal of Public Economics, February 1990,41(1),45–72. Kroft, Kory, FabianLange, andMatthewJ.Notowidigdo, “DurationDependenceandLabor Market Conditions: Evidence from a Field Experiment,” The Quarterly Journal of Economics,2013,128(3),1123–1167. 39

, , , and Lawrence F. Katz, “Long-Term Unemployment and the Great Recession: The Role of Composition, Duration Dependence, and Nonparticipation,” Journal of Labor Economics,2016,34(S1),7–54. Krueger, Alan B., Judd Cramer, and David Cho, “Are the Long-Term Unemployed on the MarginsoftheLaborMarket?,”BrookingsPapersonEconomicActivity,2014,45(1(Spring), 229–299. Lazear,EdwardP.andJamesR.Spletzer,“Hiring,Churn,andtheBusinessCycle,”AmericanEconomicReview,May2012,102(3),575–579. Macaluso,Claudia,“SkillRemotenessandPost-LayoffLaborMarketOutcomes,”2019. Polivka,AnneE.andStephenM.Miller,TheCPSaftertheRedesign: RefocusingtheEconomic Lens,UniversityofChicagoPress,January Shimer, Robert, KatarinaBorovickova, andFernandoAlvarez, “The Proportional Hazard Model: Estimation and Testing using Price Change and Labor Market Data,” Technical Report2015. Weingarden, Alison, “Job Reallocation and Unemployment in Equilibrium,” FEDS Notes, Washington: BoardofGovernorsoftheFederalReserveSystemApril2017. ,“WorkerChurnatEstablishmentsovertheBusinessCycle,”FEDSNotes,BoardofGovernorsoftheFederalReserveSystemAugust2020. 40