The Long-Lived Cyclicality of the Labor Force Participation Rate

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Long-Lived Cyclicality of the Labor Force Participation Rate Tomaz Cajner, John Coglianese, and Joshua Montes 2021-047 Please cite this paper as: Cajner, Tomaz , John Coglianese, and Joshua Montes (2021). “The Long-Lived Cyclicality of the Labor Force Participation Rate,” Finance and Economics Discussion Series 2021-047. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2021.047. 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 Long-Lived Cyclicality of the Labor Force Participation Rate* Tomaz Cajner John Coglianese Joshua Montes July 6, 2021 Abstract HowcyclicalistheU.S.laborforceparticipationrate(LFPR)?Weexamineitsresponse to exogenous state-level business cycle shocks, finding that the LFPR is highly cyclical, but with a significantly longer-lived response than the unemployment rate. The LFPRdeclinesafteranegativeshockforaboutfouryears—wellbeyondwhentheunemployment rate has begun to recover—and takes about eight years to fully recover after the shock. The decline and recovery of the LFPR is largely driven by individualswithhomeandfamilyresponsibilities,aswellasbyyoungerindividualsspending time in school. Our main specifications measure cyclicality from the response of the age-adjusted LFPR, and we show that it is problematic to use the unadjusted LFPR when estimating cyclicality because local shocks spur changes in the population of high-LFPRagegroupsthroughmigration. LFPRcyclicalityvariesacrossgroups,with largerandlonger-livedresponsesamongmen, youngerworkers, less-educatedworkers,andBlackworkers. Keywords: laborforceparticipation,laborsupply,laborforcecomposition,laborforce demographics, full employment, Okun’s law, geographic mobility, labor mobility, regionalmigration JELClassification: E24,J21,J22,J61,J64 *All authors are at the Federal Reserve Board of Governors. We thank our discussants Bruce Fallick, Laura Giuliano, and Eliana Viviano, as well as Andrew Figura, Brendan Price, and seminar participants at the Federal Reserve Board of Governors, WALES 2020, SOLE 2020, UIUC, FAU Nuremberg, ASSA 2021, the 4th IZA Labor Statistics Workshop, and the Federal Reserve System AppliedMicroeconomicsConferenceforhelpfulcommentsandsuggestions. Theanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersofthe researchstaffortheBoardofGovernors.

Forpolicymakers,thekeyquestionis: Whatportionofthe declineinlaborforceparticipationreflectsstructuralshiftsand whatportionreflectscyclicalweaknessinthelabormarket? JanetYellen(2014) 1 Introduction How cyclical is the U.S. labor force participation rate? Many observers have noted that the labor force participation rate (LFPR)—the share of population 16 years or olderthatiseitherworkingorlookingforwork—exhibitssomedegreeofcyclicality (see,forexample,Aaronsonetal.,2014b;CouncilofEconomicAdvisers,2014;Erceg and Levin, 2014; Montes, 2018). Measuring the degree of cyclicality in the LFPR is complicated, though, by the presence of trend movements reflecting structural changes in the labor market that are unrelated to the business cycle, including the prolific entry of women into the workforce through at least the 1990s and the aging of the baby boom generation since the late 1990s. Observers often disagree about themagnitudesofthesetrends,whichresultsinsubstantialdisagreementaboutthe extent of cyclicality in labor force participation. Those disagreements can be particularly acute following recessions, such as the period following the Great Recession in which estimates of the cyclical portion of the LFPR shortfall varied from 20-60 percent(CouncilofEconomicAdvisers,2014). We estimate LFPR cyclicality using state-level business cycles, which sidesteps the need to identify trend changes in labor force participation at the national level. We use the local projections method introduced by Jordà (2005) to estimate the response of the state-level, age-adjusted LFPR to changes in state-level output. By usingthisapproach,weareabletoidentifytheresponseoftheLFPRtounexpected declinesinoutputwithoutimposingstrictparametricassumptionsorassumingthat the effects of business cycle shocks dissipate in the long run. To avoid endogeneity between output and the labor market, we instrument for changes in state-level output with a shift-share instrument exploiting variation in local exposure to national changesinoutputacrossindustries(Bartik,1991). We show that labor force participation is cyclical, but that its response to an exogenous output shock is long-lived. In response to a negative 1 percentage point output growth shock, the LFPR declines slowly yet persistently and does not reach its trough until 4 years later—at about 0.2 percentage point below its initial value. 1

TheLFPRthengraduallyrecoversandeventuallyreturnstoitspre-shocklevel,but notuntilabout8yearsaftertheinitialshock. The cyclical response of the LFPR substantially lags behind the unemployment rate. Following a negative 1 percentage point output growth shock, the unemployment rate spikes quickly and peaks a year later, with a peak response that is about 0.4percentagepoint.1 Bythetimethattheunemploymentratefullyrecovers6years aftertheshock,theLFPRisstillintheearlystagesofitscyclicalrecovery. Thedelay in recovery between the LFPR and the unemployment rate suggests that observers whofocusonlyontheunemploymentrateunderestimatetheextentofslackremaining in the labor market after a recession, particularly in the period approximately 6 yearsormoreaftertheinitialshock. These results shed light on the extent of slack in the post-Great-Recession labor market, which was hotly debated by policymakers at the time. By 2014, the unemployment rate had nearly returned to its pre-recession level, but the LFPR had continued to decline, reaching about 3 percentage point below its pre-recession level. This led to substantial disagreement about whether the shortfall in participation reflected cyclical factors, which could later rebound, or structural factors, which would keep the LFPR depressed (Council of Economic Advisers, 2014; Aaronson etal.,2014b;ErcegandLevin,2014;Krueger,2017). The actual path of the LFPR following the Great Recession lines up closely with ourestimates,implyingthatmuchofthisshortfallreflectedcyclicalfactors. Wescale our estimates to a Great-Recession-sized shock and compare them to the national age-adjusted LFPR from 2007 through 2019.2 The two are remarkably close: the predicted LFPR declines slowly yet persistently through 2014 and then rebounds over the subsequent several years, the same as the actual path. By the end of 2019, only a small portion of the national age-adjusted LFPR is left unexplained by our cyclical model, implying that the response of the LFPR after the Great Recession largely did not reflect any unusual features of this recession and instead was in line withthetypicalbusinesscyclepattern. Why does the LFPR typically take so long to recover? We distinguish between two possible explanations. The first, which we term “shadow unemployment”, refers to nonparticipants who are effectively unemployed. The distinction between unemployment and nonparticipation is notoriously subjective, and many people 1ThisestimatedcoefficientontheunemploymentrateisatthelowendoftherangeofOkun’slaw coefficientsestimatedintheliterature(Ball,LeighandLoungani,2017),supportingthatourmethod measurescyclicalityaccurately. 2AswediscussinSection4,thenationalage-adjustedLFPRisthecorrectbenchmarktocompare ourestimatesto,andthiscontrolsfortheagingofthebabyboomgenerationoverthisperiod. 2

may want work in any given month even though they are not currently searching, and then can end up misclassified as nonparticipating (Abowd and Zellner, 1985; Elsby, Hobijn and S¸ahin, 2015). The second explanation we term “persistent nonmarket-workactivities”,whichincludesindividualsenrolledinschool,athometaking care of family, or other similar activities. Although, many of these individuals transition into employment in any given month, those transitions may not respond quickly to changes in labor market conditions, since these activities may take time toenterorexit. We find that changes in shadow unemployment do not explain the delayed recovery of the LFPR. Although shocks do lead to increases in nonparticipants who self-report that they “want a job”, this type of nonparticipation returns to its preshocklevelatthesametimeastheunemploymentrateandwellbeforetheLFPRhas fully recovered. Similarly, we also find that shocks lead to an increase in churn betweenunemploymentandnonparticipation,whichwetakeasameasureofshadow unemployment,butthistoosubsidesbeforetheLFPRisfullyrecovered. Instead, the delayed cyclical recovery is driven by persistent non-market-work activities,whichbuildinresponsetoashockbuttakesometimetounwind. Initially following a negative shock, the increase in persistent non-market-work activities is mainly driven by people either taking care of the home and family or going to school. Theseincreasesonlystarttodissipateseveralyearsaftertheshock,reflecting thestickinessofthesechoicestoleavethelaborforceoncetheyaremade. Onlyafter the labor market is well on its way to recovery do these types of nonparticipation returntopre-shocklevels. Thisisalsoconsistentwiththepatternswedocumentfor flows from nonparticipation to employment: these flows drop initially in response to the shock and then surge only after the unemployment rate has fully recovered, drivingthedelayedrecoveryoftheLFPR. Our main approach controls for changes in the composition of state-level populations through age adjustment. This approach removes any mechanical effect on the LFPR from changes in the age structure of the population following local-level shocks,whichmayoccurduetoeitherin-migrationorout-migrationamongparticularagegroups. Inourbaselinespecification,weadjustforagebyresidualizingthe individual-level LFPR on single-year-age-by-sex fixed effects; we use the state-year average of these age-adjusted outcomes as the dependent variable in our local projections regressions. In this way, our estimates isolate the true cyclical response of theLFPRtoanoutputshockwithouttheinfluenceofcompositionalchanges. This age-adjustment is necessary, since we show that shocks lead to structural changes in the population of high-LFPR ages. Following a negative 1 percentage 3

point shock to output growth, the population of 25 to 39 year olds gradually decreases over 10 years, eventually falling up to 4 percent below the pre-shock level, while other age groups see slight increases in population over the same period. Since 25 to 39 year olds tend to have higher LFPRs than other age groups, this response mechanically lowers the unadjusted state-level LFPR in the long run by about 0.2 percentage point in the long run. We explore whether the population changesalongotherdemographicdimensions—suchaseducationalattainment,race, andmaritalstatus—butfindlittlefurthereffectsbeyondage. Ourfindingthatthelocal LFPR is persistently altered by changes in the population among young, primeage people adds to the understanding of the migratory adjustment mechanism of localshocksdocumentedbyBlanchardandKatz(1992),Dao,FurceriandLoungani (2017),andAmiorandManning(2018). We also document that the long-lived cyclicality of the LFPR is especially pronounced for less-advantaged groups in the labor market. Younger workers (ages 16 to 24) exhibit a much larger cyclical response of the LFPR than do prime age workers (ages 25 to 54), while older workers (ages 55+) show a lower degree of cyclicality. Our estimates show a sharp difference by education level with lesseducated prime-age workers experiencing a large decrease in LFPR after a shock, while more-educated workers experience no significant change in labor force participation. We also find substantial inequality in long-lived cyclicality across racial and ethnic groups, with the prime-age Black LFPR exhibiting larger, longer-lived cyclicalitythantheprime-agewhiteLFPR. Our paper contributes to the literature studying LFPR cyclicality. Several recent papers take a national-level approach, estimating a structural trend for the LFPR and using deviations from this trend to estimate LFPR cyclicality (Aaronson et al., 2014b,a; Council of Economic Advisers, 2014; Krueger, 2017; Montes, 2018; Hornstein and Kudlyak, 2019). This approach requires specifying the structural supply and demand forces that affect participation decisions (see the reviews by Abraham and Kearney (2020) and Juhn and Potter (2006) for a discussion of these forces). Another approach, used by Aaronson et al. (2014b); Erceg and Levin (2014); Balakrishnanetal.(2015),ittorelyonstate-levelvariationaswedoinouranalysis. While some of these papers do argue that the cyclical response of LFPR can be delayed, one of the main contributions of our paper is to use a method that is particularly well-suited for causally estimating long lags in LFPR cyclicality. More precisely, unlike the previous papers in this literature, we estimate the dynamic response of LFPR to output shocks by using local projections, which allow for the possibility of very persistent effects on LFPR. Moreover, by using a shift-share instrumental vari- 4

able approach, we are able to establish a link between exogenous shocks and the dynamic response of LFPR.3 Our approach of using state-level variation to identify LFPRcyclicalityandaggregateuptoanestimateofnationalLFPRcyclicalityfollows thegrowingliteratureusingregionalvariationtostudymacroeconomicphenomena (NakamuraandSteinsson,2014,2018;Fukui,NakamuraandSteinsson,2018;Beraja, HurstandOspina,2019;Chodorow-Reich,2019). Additionally, following the early work of Blanchard and Katz (1992), several papers investigate how employment adjusts in response to economic shocks at the local level (Decressin and Fatas, 1995; Bound and Holzer, 2000; Dao, Furceri and Loungani,2017;AmiorandManning,2018;HornbeckandMoretti,2018;Weinstein, 2018; Yagan, 2019; Hershbein and Stuart, 2020) as well as the relationship between shocksandmigration(CadenaandKovak,2016;Monras,2018;Howard,2020). This literaturehasdocumentedthatlocallabormarketsadjustfollowingshocksthrough changes in migration that return the labor market to equilibrium. We contribute to this literature by showing that this migration channel can have persistent effects on LFPR through altering the composition of the population, primarily among 25 to 39 year olds, which makes it important when studying local shocks to use the age-adjustedLFPR. We also contribute to a literature following Okun (1973) that examines how different demographic groups fare during a long recovery. Some groups of workers may disproportionately benefitfrom a tight labor market, as discussedin Bradbury (2000); Hoynes (2000); Jefferson (2008); Hoynes, Miller and Schaller (2012); Wilson (2015); Cajner et al. (2017); Hotchkiss and Moore (2018); Fallick and Krolikowski (2019) and Aaronson et al. (2019). Some of these differences in the benefits of a tight labor market may stem from delayed recoveries of LFPR, since we estimate that some groups’ LFPRs take substantially longer to recover after a typical recession. These differences in LFPR cyclicality make it necessary to sustain recoveries beyondthepointatwhichunemploymenthasfullyrecoveredifpolicymakerswant toensureallgroupsexperienceafullrecovery. 2 Research Design We measure the cyclicality of labor force participation by estimating its response to state-level business cycles in order to sidestep the issue of trend changes in participation,whichcomplicateidentifyingcyclicalityatthenationallevel. Inthissection, 3Balakrishnanetal.(2015)alsouseasimilarshift-shareinstruments,butforemployment,while ourpaperusesoutput. Usingthelatterhasseveralmethodologicaladvantagesaswearguelateron. 5

weoutlineourresearchdesign,startingwiththeidentificationproblemandourapproach to solve it. We then turn to the issue of inference and the description of the dataweuseinthisanalysis. 2.1 Identification Estimating the dynamic cyclical responses of national outcomes typically requires strict assumptions. For example, time series models usually assume a mean zero cyclical component, which rules out hysteresis by definition. Further, identification in those models relies on a trend component that is smooth and identifiable— a strong assumption for the LFPR, given the sharp and changing nature of LFPR trendsforvarioussubgroupsofthepopulation. To meet these challenges, we use state-level panel data to estimate the dynamic cyclical responses of labor market outcomes to a state-level business cycle shock using the local projections method. In particular, we measure the impulse response functions(IRFs)ofashockbyestimatingthefollowingseriesofregressionsindexed by k: y −y = β (k) Shock +Θ W +(cid:101) (1) s,t+k s,t−1 s,t s,t s,t+k where y represents the labor market dependent variable of interest—for example, s,t the LFPR—of state s in time t; k indexes the regression that measures the effect of the shock at time t on the dependent variable t + k periods ahead; Shock is the s,t measureofthebusinesscycleshock(definedbelow);andW representsavectorof s,t control variables. In our baseline specification, the controls include state and year fixedeffects. Our local projections regressions control for national trends through the inclusionofyearfixedeffects. Thisdoesnotimposestrictassumptionsaboutthesmoothnessoftrends,aswouldbeneededinnational-leveltimeseriesregressions. Nationwidephenomenathataffectlabormarketoutcomesacrossallstatesequally,includingdemographicshifts(suchastheagingofthebabyboomgeneration)andnational policy responses (such as monetary policy shocks), are controlled for nonparametricallybythisapproach. We view local projections regressions as a better alternative in our setting than vectorautoregressions(VARs). StockandWatson(2018)pointoutthatinstrumented versions of VARs and local projections identify the same IRFs under standard conditions, but VARs may not correctly identify IRFs if the true IRFs are not invertible. In terms of efficiency, instrumented local projections have the same properties as VAR models with internal instruments, as documented by Plagborg-Møller and 6

Wolf (2021). Additionally, Olea and Plagborg-Møller (2020) show that local projectionshaveattractivepropertiesforinference.4 Forthesereasons,weuselocalprojections in our main specification, but we return to the question of whether VARs are appropriate for our setting in Section 9.4, where we conduct a test of invertibility fromourestimatedIRFs. Shocks: We measure the business cycle shock using real gross state product (GSP) growth as estimated by the BEA. Specifically, we define Shock ≡ ∆ GSP , s,t s,t ∆ where GSP is the year-over-year percent change in GSP. That is, the shock is a s,t one-time, temporary, one percentage point shock to GSP growth. All else equal, the shockleadstoapermanentlylowerlevelofoutput.5 GSP estimates are based on the factor incomes earned and other costs incurred in production, which is the same concept for measuring output as is used by Gross Domestic Income (GDI) at the national level. For each state, GSP sums labor income, capital income, and business taxes, where each of the three components is estimated by industry. Note that labor income is based on wage and salary accruals (as opposed to disbursements), which implies that retroactive wage payments (bonuses) are counted for the year in which they were earned rather than when theywerereceived. We view our choice to define business cycles based on output as superior to alternative approaches that use employment. Using GSP provides a measure of business cycle fluctuations at the state level that is more comprehensive than only usingemployment,whichomitsfluctuationsinproductivity. Additionally,ifshocks taketimetopropagatetothelabormarket,usingoutputwillcorrectlytimebusiness cycles,whileemployment-basedbusinesscycleswilltendtolagbehindthetruetiming of the shock. Lastly, estimating the response of LFPR to an output shock, rather than an employment shock, makes the results more interpretable in the context of Okun’sLaw,akeyeconomicrelationshipusedamongmanypolicymakers. PotentialEndogeneity: Thecoefficient β (k) givesthek-period-laterresponseof y to a one-time, temporary, one percentage point shock to GSP growth.6 For β (k) to 4Herbst and Johannsen (2020) show that local projections can be biased in small samples when the outcome variable is highly persistent, but this bias is likely to be minimal in our setting. The dependentvariableinourregressions,thestate-levelage-adjustedLFPR,onlyhasanautocorrelation coefficientof0.81,lowerthanthe0.9–0.99rangeinwhichthisbiasbecomesacute. 5We show in Section 8 that the lower level of output in large part reflects a permanently lower levelofoutputperemployee. 6AssumingthattheshockleavesGSPgrowthinotherperiodsunaffected,thisresultsinapermanentonepercentshocktothelevelofGSP. 7

identify a causal effect of the GSP shock on y −y , it must be the case that, s,t+k s,t−1 conditionalonthesetofcontrols,thegrowthrateofGSPinperiod t isuncorrelated withtheerrorterm: E(cid:2)∆ GSP ·(cid:101) |W (cid:3) = 0 s,t s,t+k s,t However, two key concerns suggest this requirement might not be met in practice. One concern is that employment may affect GSP, as lower employment (through higherunemployment,lowerLFPRs,orboth)willlowerGSPifproductivityisheld constant. A second concern is that GSP growth could be autocorrelated, in which case estimates of β (k) may pick up the correlation between y −y and GSP s,t+k s,t−1 growthratesinfuture(orpast)periods. ∆ Instrument: To overcome these issues, we instrument for GSP with a Bartik (1991) shift-share type measure to isolate shocks to demand at the state-level. The first-stageequationisasfollows, ∆ GSP = αZ +γW +ν (2) s,t s,t s,t s,t where Z s,t ≡ ∑∆ GDI q,−s,t ω q,s,t−5 . (3) q Industries are indexed by q, and ω represents the three-year moving average q,s,t−5 of industry q’s share of total GSP in state s five years previously.7 ∆ GDI q,−s,t represents the growth rate of national gross domestic income in industry q for period t using the "leave-one-out" approach—that is, we calculate GDI q,−s,t by summing up GSP acrossallstatesexceptforstate s. q,s,t Thisformulationoftheshift-shareinstrumentreliesonindustryvariationinoutput,ratherthanemployment. Manypreviousstudies,includingBlanchardandKatz (1992), Dao, Furceri and Loungani (2017), Adão, Kolesár and Morales (2019), and Goldsmith-Pinkham,SorkinandSwift(2020),measuretheresponseofemployment to a shift-share instrument that uses industry variation in employment. However, we view industry variation in output as more appropriate for our setting, both becausechangesinoutputarelikely tobemorecloselyalignedtoindustrycyclesand because output is a distinct variable measured separately from our outcomes of interest. 7Duringthefirstfiveyearsofavailableindustrydata,wecalculateω q,s,t−5 fromindustryq’sshare oftotalGSPinthefirstyearofdatainstead. 8

Identifying Assumptions: In order for Z to be a valid instrument, it must s,t meetthefollowingconditions(StockandWatson,2018): E(cid:2) Z ·∆ GSP |W (cid:3) = α (cid:54)= 0 (relevance) (4) s,t s,t s,t E(cid:2) Z ·(cid:101) |W (cid:3) = 0 (contemporaneousexogeneity) (5) s,t s,t s,t E(cid:2) Z ·(cid:101) |W (cid:3) = 0 (cid:41) s,t s,t+k s,t fork (cid:54)= 0 (lead-lagexogeneity) (6) E(cid:2) Z ·∆ GSP |W (cid:3) = 0 s,t s,t+k s,t Z captures predicted GSP growth for a given state, s, in time, t, based on that s,t state’s industry mix in period t −5. We argue that this is likely to meet the relevanceconditionsincelocaloutputinagivenindustryislikelytobecorrelatedwith national output in that industry due to changes in industry technology or relative demand. The contemporaneous exogeneity assumption will hold as long as the national industry shocks used to construct Z are unrelated to local changes in labor s,t market outcomes (where we have removed any mechanical correlation by using a "leave-one-out" approach). Lead-lag exogeneity requires not only that Z is uncors,t related with unobserved forces affecting local labor markets in other periods, but ∆ alsothatitisnotcorrelatedwitheitherofthetwocomponentsof GSP inother s,t+k periods. In Section 8 and Section 9, we show that E[Z ·∆ GSP |W ] ≈ 0 for s,t s,t+k s,t k (cid:54)= 0inoursample,confirmingthisaspectoflead-lagexogeneity.8 There are multiple interpretations of exogeneity for the shift-share instrument. The variation in the shift-share instrument comes from differential exposure to national shocks across regions based on initial industry shares. Goldsmith-Pinkham, Sorkin and Swift (2020) point out that this variation is equivalent to instrumenting with the industry shares directly, and therefore exogeneity of the instrument comes from exogeneity of these shares. Borusyak, Hull and Jaravel (forthcoming) provide analternativeinterpretationinwhichthenationalshocksareexogenous. 2.2 Inference This section describes three important issues for inference in our research design: the role of clustering in computing standard errors, how we weight observations, andtestingforpotentialweakinstruments. 8Iftheshockwerepositivelyautocorrelated, thensomeoftheeffectestimatedby β(k) wouldbe theresultofthepersistenceoftheshock,thusbiasingourestimateupward. Conversely,iftheshock werenegativelyautocorrelated,theeffectsofanoutputshockontheLFPRwouldbestrongerthan whatisestimatedbyβ(k).SincewefindthatautocorrelationinZ isminimal,thisbiasdoesn’taffect s,t ourestimates. 9

Clustering: Toquantifytheuncertaintyaroundourestimatedimpulseresponse functions, we compute heteroskedasticity-robust standard errors clustered at the state-levelinourbaselinespecification. Adão,KolesárandMorales(2019)raiseconcerns that this approach may understate uncertainty in shift-share designs. However,theseconcernsareprimarilyaboutsettingswherevariationcomesfromasubset of industries, while our setting uses the full set of industries.9 We validate this choiceinSection9.3withaplaceboexercise,whichindicatesthatourclusteredstandarderrorsare,ifanything,abitconservativeforthissetting. Weighting: We weight each regression of outcome y for group j by the pops,t j ulation, n of group j in state s at time t. Weighting has two main advantages in st this setting. First, weighting the regressions by population allows us to interpret the estimates in terms of the national LFPR. Second, the smallest states have relatively few respondents in the CPS, which has the potential to generate noise when calculatingstate-levelLFPRsforthosesmallerstatesandyieldimpreciseregression estimates. Thenoiseissuecompoundswhenslicingthedatafurtherintosubgroups of the population, such as prime-age individuals, men and women, and levels of educational attainment. Weighting by state-level population reduces the influence ofnoiseinourestimates. Testing for WeakInstruments: To verify thatour estimates are notaffected by weakinstrumentproblems,weconductfirst-stageF-testsforeachspecification. We compute the first-stage F-statistics under the assumption of homoskedasticity and examine whether they exceed 10 to determine if our instrument is weak, following Staiger and Stock (1997). Although the instrument and endogenous variable are the same in all specifications, the F-statistics may vary across regressions for different demographic groups due to the different state population weights for different groups. 2.3 Data We combine state-level data from multiple sources to form an annual panel. Labor market outcome variables consist of the unemployment rate, the labor force participation rate, and the employment-to-population ratio, each of which is calculated from Current Population Survey microdata. For each rate, we compute the average 9Our analysis is most similar to the results shown in Panel B of Table 6 in Adão, Kolesár and Morales (2019), which shows that more sophisticated approaches to estimate confidence intervals arenotmeaningfullydifferentfromclusteringbylocallabormarket. 10

over the calendar year in each state. Our main specification uses the CPS sample of civiliannoninstitutionalizedpeopleages16andovertocomputeeachoftheserates. Inlatersections,wecomputetheseratesforsubgroupsofthepopulation. Inordertocontrolforshiftingdemographicsunrelatedtothebusinesscycle,we age-sex-adjust each of our labor market outcome variables. That is, for an outcome y forperson i instate s andyear t,weestimatethethefollowingequationonour i,s,t CPSsample: y = θ +y˜ (7) i,s,t age(i),sex(i) i,s,t where θ is a age-by-sex fixed effect. We then compute the average ageage(i),sex(i) adjustedoutcomeforstate s inyear t as ∑ y˜ ≡ y˜ w (8) s,t i,s,t i,s,t i∈(s,t) wherew istheCPSsamplingweightforpersoni. Thisprocedureremoveschanges i,s,t from our outcomes that are due to changes in the age structure of the population suchastheagingofthebabyboomgeneration,whichhasbeenshowntoberesponsible for variation in labor market outcomes over time (see, e.g., Shimer, 1999). We use the age-adjusted rates in all of our main estimates, but return to examine the roleofthisadjustmentcomparedtoalternativeadjustmentsandunadjustedratesin Section6.1. Data on GSP for each state and year are obtained from the BEA. GSP data by industry are from the BEA as well, using SIC-coded industries for 1976–1998 and NAICS-coded industries for 1998–2018. For the purposes of decomposing the variation in the shift-share instrument in Section 8.3, we link a subset of industries between SIC and NAICS that are categorized in essentially the same way in both systems,andtreatallotherindustriesasdistinctbetweenthetwosystems. 3 Cyclicality of Labor Market Outcomes Figure1presentsourestimatesoftheimpulseresponsefunctionsfortheage-adjusted LFPR,unemploymentrate,andemployment-to-populationratio(EPOP)from3years before the shock to 10 years after the shock. For ease of interpretation, we report all ofourestimatesastheresponsetoatemporarynegative1percentagepointshockto GSPgrowth,sothatthecyclicalresponseswillhavethesamesignasinarecession. The unemployment rate, LFPR, and EPOP all respond to cyclical shocks, but with varying timing. For the unemployment rate, a contractionary 1 percenage 11

Figure1: EstimatedCyclicalResponsestoaNegativeOutputShock Percentage points Percentage points 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 -0.6 -0.6 -2 0 2 4 6 8 10 Year relative to output shock Labor force participation rate Unemployment rate Employment-population ratio Note: Each line shows the estimated coefficients from Equation 1 for the associated labor market outcome. The bands around each line show a 95% confidence interval, based on standard errors clusteredbystate. Coefficientsarenormalizedtoshowtheeffectofatemporary-1percentagepoint shocktoGSPgrowthinyear0. Alloutcomesareadjustedforchangesintheage-by-sexcomposition of the population. F-statistic: 149.1. Regressions control for state and year fixed effects and are weightedbypopulation. Source: BLS,BEA,andauthors’calculations. point shock to output growth causes a contemporaneous 0.25 percentage point increaseintheunemploymentrate. Theincreaseintheunemploymentratecontinues in the following year and peaks at 0.4 percentage point one year after the shock. Ourestimateofthetotalincreaseintheunemploymentrateduetoanegative1percentagepointshocktoGSPisatthelowendoftherangeofOkun’slawcoefficients estimated in the literature of -0.5 to -0.4; see, for example, Ball, Leigh and Loungani (2017). Followingthepeakoneyearaftertheshock,theunemploymentratesteadily declinesbyabout0.1percentagepointperyearuntilitreturnstoitspre-shockvalue about six years after the shock and remains there. This asymmetric response of a sharpincreasefollowedbyagradualdecreaseisconsistentwiththe“plucking”dynamicsofbusinesscyclesexaminedbyDupraz,NakamuraandSteinsson(2019). The LFPR also shows a significant response to a negative shock, but with a substantial delay compared to the unemployment rate. Specifically, the LFPR declines bylessthan0.1percentagepointintheyearoftheshock,muchsmallerthantheincrease in the unemployment rate. However, while the unemployment rate quickly 12

peaksandbeginstorecover,theLFPRcontinuestosteadilydeclineforseveralyears after the shock, finally reaching a trough four years later at a level that is 0.2 percentage point below its initial value. After reaching its trough, the LFPR gradually recovers and only attains its pre-shock level eight years after the initial shock, two yearsaftertheunemploymentratehasfullyrecovered. ThedifferentpatternsfortheLFPRandunemploymentratereflectdifferentcyclicalprofiles,whichwecanshowformallywithanonlinearWald-typetest. Wedenote (k) the set of coefficients tracing out the impulse response of the LFPR as {β } and LFPR (k) the set of coefficients for the unemployment rate as {β }. Our null hypothesis is UR thattheLFPRresponsehasthesametimeprofileastheunemploymentratebutper- (k) (k) β haps a different cyclical loading: β ≡ UR for each horizon k. Under this null, LFPR φ (k) β the ratio of coefficients UR is the same at every horizon k. To test this, we stack (k) β LFPR thesamplesusedtoestimatedimpulseresponsesforbothvariablesandre-estimate Equation1,fromwhichweobtainacovariancematrixcontainingallcoefficientsfor both impulse responses.10 We use the delta method to construct a nonlinear Waldtype test statistic for the restriction that the ratio of coefficients is the same at each horizon. For the null hypothesis that lags 1 to 8 share the same ratio, we obtain a test statistic of 31.69 with a p-value of 0.000, enough to strongly reject the null hypothesisthatthetimeprofileisthesameforbothvariables. The combination of the LFPR and unemployment rate responses create cyclicalityintheEPOPthatisbothlargeandlong-lasting. TheEPOPdeclinesrapidlyatthe onsetoftheshock,reflectingtheinitialspikeintheunemploymentrate,andreaches its trough at about -0.4 percentage point two years after the shock. Thereafter, the EPOP steadily recovers by about 5 basis points per year until it is fully recovered seven years after the shock. While the EPOP shortfall in earlier years reflects high unemployment, the remaining EPOP shortfall in years 5 to 7 is almost entirely accountedforbytheLFPR. 4 Implications for National LFPR Cyclicality In this section we lay out a framework for aggregating our results from state-level business cycles to the national level. Using this framework, we show that our estimatescloselymatchtheobserveddynamicsoftheLFPRfollowingtheGreatRecession. In particular, the strength in labor force participation starting in 2014 lines up 10This is equivalent to a seemingly unrelated regression with the same right-hand-side variables ineachequation(DavidsonandMacKinnon,1993). 13

closelywiththedelayedrecoveryoftheLFPRinourestimates. TheaggregateLFPRatthestatelevelisanaverageacrosstheLFPRsofallages,a, withinthepopulation. TheLFPRforeachoftheseagesinturncanbebrokendown into a cyclical component and a secular trend component unrelated to the business cycle. Let C denote the measure of the business cycle in state s and time period s,t t, let β(L) denote the cyclical coefficients tracing out the impulse response, and let α andα bestate-agefixedeffectsandyear-age-specificseculartrendcomponents a,s a,t respectively. Withasetofpopulationweightsforeachagew ,thestate-levelLFPR a,s,t canbewrittenas: ∑ LFPR = (α +α +β(L)C )w s,t a,s a,t s,t a,s,t a Fromthisexpression,thefirst-orderapproximationforchangesinthestate-level LFPRfromperiod t to t+k canbebrokendownintothreecomponents11: ∆ LFPR ≈ ∑ (∆ α w )+β(L)∆ C + ∑ (α +α +β(L)C )∆ w s,t+k,t a,t+k,t a,s,t s,t+k,t a,s a,t t a,s,t+k,t a (cid:124) (cid:123)(cid:122) (cid:125) a (cid:124) (cid:123)(cid:122) (cid:125) Cycle (cid:124) (cid:123)(cid:122) (cid:125) Trend Populationchanges When using our methodology to estimate the cyclical response of the LFPR, the first and third terms drop out. The first term consists of national trends in LFPR, which can be broken down into a purely national component ∑ (∆ α w ) that a a,t+k,t a,t isabsorbedbyourtimefixedeffectsandaresidualcomponent∑ (∆ α (w −w )). a a,t+k,t a,s,t a,t Ouridentificationassumptionimpliesthattheresidualcomponentisequaltozero.12 The third term in the decomposition above is equal to zero in our setting since we usetheage-adjustedLFPRastheoutcome,whichmechanicallyadjustsfor ∆ w .13 a,s,t+k,t Asaresult,ourmethodologyprovidesestimatesforthecyclicalcoefficientsβˆ(L). These coefficients represent the lagged change in LFPR associated with a one unit change in output. Importantly, since we include time fixed effects, the change in ∆ output C is measured relative to nationwide trend output growth, which acs,t+k,t counts for gradual increases in GDP due to population growth and productivity, amongotherforces. 11Theapproximationomitsahigher-orderterminvolvingtheproduct∆α a,t+k,t ·∆w a,s,t+k,t . 12Thereisnoparticularreasonwhytheresidualcomponentwouldnotbeequaltozero,andthis assumptionisconsistentwiththelackofnoticeablepre-trendsinourLFPRestimates. 13Note that even if we had not used the age-adjusted LFPR, our inclusion of time period fixed effectswouldabsorbanyofthevariationin ∆w a,s,t+k,t thatiscommonnationwide,forexamplethe aging of the baby boom population. However, ∆w a,s,t+k,t also includes age-selected migratory responses,whicharenotcontrolledforbytimeperiodfixedeffects,butarecontrolledforbyusingthe age-adjustedLFPR. 14

Figure2: ActualandPredictedLFPRaftertheGreatRecession Percentage points Percentage points 67 67 66 66 65 65 64 64 63 63 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 Age-adjusted LFPR Implied by local estimate Note: The blue line shows the LFPR adjusted for changes in the age composition of the population since2007.TheorangelineusesourmainestimatesofEquation1scaledbythe-8.1%declineinGDP relative to its estimated trend during the Great Recession (CBO, 2007). The bands around this line showa95%confidenceinterval,basedonstandarderrorsclusteredbystate. Source: BLS,BEA,andauthors’calculations. The national LFPR is an average of state LFPRs, and can be decomposed similarly. Averaging over states and dropping the state subscripts, the decomposition abovebecomes: ∆ LFPR ≈ ∑ (∆ α w )+β(L)∆ C + ∑ (α +β(L)C )∆ w t+k,t a,t+k,t a,t t+k,t a,t t a,t+k,t a (cid:124) (cid:123)(cid:122) (cid:125) a (cid:124) (cid:123)(cid:122) (cid:125) Cycle (cid:124) (cid:123)(cid:122) (cid:125) Trend Populationchanges Fromthisdecomposition,weuseourestimatedcoefficients βˆ(L) totraceoutthe predictedchangeinthenationalage-adjustedLFPRtoarecessionaryshock,namely the Great Recession. Using the age-adjusted LFPR removes the third term, and we pick a time period (2007–2019) over which trends within age groups are estimated to have been close to zero on net (Montes, 2018), removing the first term. Additionally, by using the age-adjusted LFPR, we remove any contribution of migratory responses to shocks on the LFPR. While we find significant migratory responses affecting the LFPR at the state level, as we will discuss in detail in Section 6.2, those migratoryresponsesareunlikelytohaveaneffectonthenationalLFPRtotheextent 15

thatthisreflectsonlyinterstatemigrationandnotinternationalmigration. Figure2plotsourmainestimatesofthecyclicalresponseofLFPRappliedtothe GreatRecessionshockalongwiththeactualage-adjustedLFPRforthistimeperiod. For the Great Recession shock, we compute the decline from 2007:Q4 to 2009:Q2 in real GDP from BEA, minus the expected increase in real potential output over the sameperiodfromCBO’sAugust2007projections(CBO,2007).14 Weusethechange relative to trend in order to align with our estimates, which control for trends in potential output through year fixed effects. The predicted path of the LFPR from our estimates in Figure 1 is −8.1× βˆ(k) for each horizon k, and we plot this against theactualpathoftheLFPRinFigure2. Thepredictionfromourestimatesisremarkablyclosetotheactualage-adjusted LFPR over this period, featuring a similar slow decline over 2009–2014 and subsequent rebound in later years. By 2019, only a small portion of the LFPR recovery is left unexplained by our model. This similarity suggests that the LFPR largely followeditsusualcyclicaldynamicsoverthisperiodwithlittledeviation. 5 What Drives the Long-Lived Cyclicality of Labor Force Participation? In this section, we draw on two additional features of the CPS data to understand whytheLFPRexhibitslong-livedcyclicality. First,weuseindividuals’self-reported reasonsfornonparticipationtoexaminethecyclicalityof“discouraged”individuals— thosewhoreportwantingajobbutremainoutofthelaborforce—comparedtoindividualsengagedinnon-market-workactivities,suchashomeproductionorschooling. Second, we examine the cyclicality of flows into and out of the labor force to understand whether the shortfall of participation is caused more by a lack of individualsjoiningthelaborforceorasurplusofindividualsleavingthelaborforce. 5.1 Reasons for Labor Force Nonparticipation Business cycle shocks may lead people to make decisions that have persistent effects on their labor supply, which could account for the long-lived cyclicality in the LFPR. Such decisions may include enrolling in school, staying at home and taking care for a family member, applying for disability benefits, or retiring. Alternatively, 14WeusetheAugust2007projectionsinordertoensurethatthepotentialoutputestimatesarenot affectedbythedownturninLFPRthatoccurredaftertherecession. 16

thelong-livedcyclicalityintheLFPRmayreflectindividualsbecomingdiscouraged and stopping their search for work, even though they would still prefer to be employed. To determine the extent to which each of these explanations may account for long-lived cyclicality, we use questions in the CPS that ask nonparticipants about their reason for being out of the labor force. Throughout the sample period, nonparticipants were asked whether they want a job, which provides an indication of desired labor supply. Additionally, from 1989 onward nonparticipants were asked to categorize their main reason for being out of the labor force between being ill or disabled,inschool,takingcareofhomeorfamily,retired,orother,andthisquestion is a full partition of the not-in-the-labor-force group.15 For each of these questions, we compute the share of the population in each state-year that is made up by nonparticipants in each category, and estimate Equation 1 using these outcomes. The estimatedimpulseresponsesareshowninFigure3. WeshowtheIRFsonlythrough eight years following the shock, since the estimates around lag eight become extremelynoisyduetothelimitedsample. Increases in schooling, staying at home due to family responsibilities, and rising self-reported disability all play important roles in shaping the cyclical response of aggregate labor force participation.16 Initially, nonparticipants taking care of home/family constitute the largest response, with schooling close behind. However, nonparticipants reporting illness or disability grow steadily in response from yeartwoonward,andcomprisealargerportionoftheresponseinyears5to7than peopletakingcareofhomeorfamily. Peopleinschoolgrowsteadilyaswell,before fallingrapidlyinyears7and8whentheoverallLFPRisreachingitspre-shocklevel. Interestingly, the cyclical response of labor force participation does not seem to be driven by retirement decisions. If anything, retirements appear to exert an upward pressure on the LFPR. This could indicate that recessions induce individuals topostponeretirements,perhapsduetoafallinthevalueoftheirretirementsavings or to potentially offset income losses of their household members who may lose a job. Separately, we also look at the cyclicality of labor force nonparticipants who say 15Forbothofthesequestions,surveysbefore1994onlyaskedthesequestionstotheroughly 1 of 4 nonparticipantswhoarepartoftheOutgoingRotationGroupsinmonths4and8insample.Further, the“wantajob”questionisseparatefromthe“mainreasonforbeingoutofthelaborforce”question (e.g. some respondents who report being in school may also report wanting a job, while others in schoolmayreportnotwantingajob). 16Inunreportedresultswefindthatincreasesinschoolingaremostprominentforyoungpeople, butalsonotableforprime-ageindividuals. Risingdisabilityismostlypresentforindividualsaged 55yearsandover. 17

Figure3: CyclicalitybySelf-ReportedReasonforLaborForceNonparticipation Percentage points Percentage points 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 -2 0 2 4 6 8 Year relative to output shock Want job Any main reason Ill/disabled School Home/family Retired Other Note:EachlineandsetofbarsshowstheestimatedcoefficientsfromEquation1usingastheoutcome theshareofthepopulationoutofthelaborforceandreportingthespecifiedreason.Thebandaround the orange solid line shows a 95% confidence interval, based on standard errors clustered by state. Reporting“wantjob”isnotexclusivewithreportinganyofthemainreasons. Thebluedashedline is equal to the sum of the bars in each period. Coefficients are normalized to show the effect of a temporary-1percentagepointshocktoGSPgrowthinyear0. Alloutcomesareadjustedforchanges intheage-by-sexcompositionofthepopulation. F-statistic: 149.1. Regressionscontrolforstateand yearfixedeffectsandareweightedbypopulation. Standarderrorsclusteredbystate. Source: BLS,BEA,andauthors’calculations. they want a job, which can represent labor market slack. Although nonparticipants who want a job drive essentially all of the early rise in nonparticipation, their participation recovers faster than nonparticipation as a whole, reaching its pre-shock levelaroundthesametimeastheoverallunemploymentratedoes(years4–5). This suggests that expansive definitions of the unemployment rate that include nonparticipants who want a job—BLS’ U-5 measure includes some of them—are able to captureadditionalcyclicalitybeyondthemainunemploymentrate,butdonotcapturethelong-livedcyclicalityofparticipation. 5.2 Labor Market Flows Additionally, the panel structure of the CPS allows us to examine the contributions of inflows and outflows to the long-lived cyclicality of the LFPR. Examining the flows provides more insight into the cyclicality of stocks, as demonstrated in pre- 18

vious work including Elsby, Hobijn and S¸ahin (2015), Elsby et al. (2019), and Cairó, Fujita and Morales-Jiménez (2021). We calculate annual labor market transitions by matching individuals in the CPS over 12-month horizons, and express those flows as shares by dividing by population 16 years and over. To be consistent with our baselineresults,wealsoadjustforagebyresidualizingtheflowratesusingpersonlevel data to net out the composition component explained by the age distribution ofthepeopleineachstate. Three aspects of the response of flows (shown in Figure 4) are worth noting.17 First, at the onset of a negative output shock, labor force entry drops, driven by a large decline in the flow from nonparticipation to employment, which could reflect decisionstoprolongschoolingortostayhomeandtakecareoffamily,asdiscussed intheprevioussubsection. Second,fromyears1to2aftertheshock,flowsbetween unemployment and nonparticipation in both directions rise notably. In particular, negative business cycle shocks lead to an increase of “in-and-outs”, that is individuals who temporary leave the labor force, perhaps due to discouragement.18 Flows betweenunemploymentandnonparticipationremainelevateduntilroughlyyear6, whichisalsohowlongtheunemploymentrateremainselevated(recallFigure1). Finally, flows from nonparticipation to employment eventually surge around 8 years after the shock, which leads to the recovery of the LFPR. In terms of magnitudes, outflows are elevated by 2 to 3 basis points after a negative shocks, while inflows aredepressedbyabout5basispoints. Cumulatively,theneteffectforflowsissimilartotheoneestimatedforthestockoflaborforceparticipantsshowninFigure1. 6 The Role of Changing Demographic Composition In addition to changes in the age-adjusted LFPR, shocks may lead to changes at the state level in the age structure of the population or other demographics. In this section, we examine how the demographic composition of the state-level population responds to output shocks, finding evidence that shocks induce permanent, structuralcompositionshiftsawayhigh-LFPRsubgroupsinaffectedstates. We start by showing that the unadjusted LFPR experiences a persistent shortfall 17For brevity, we do not report flows between employment and unemployment, since these are neutralwithrespecttotheLFPR. 18Note that while the hazard rate of U → N flows (U → N flow divided by the stock of unemployment)declinesinrecessions,inpartdrivenbycompositionalchangesofunemployedandtheir highereligibilityforunemploymentinsurance,thestockofunemployedrisesevenmoreduringrecessions, leading to an increase of U → N flows as a share of the population (Elsby, Hobijn and S¸ahin,2015). 19

Figure4: EstimatedCyclicalResponsesofFlowstoaNegativeOutputShock Share of population (p.p.) Outflows Inflows Share of population (p.p.) 0.20 0.20 0.20 0.20 0.10 0.10 0.10 0.10 0.00 0.00 0.00 0.00 -0.10 -0.10 -0.10 -0.10 -0.20 -0.20 -0.20 -0.20 -2 0 2 4 6 8 10 -2 0 2 4 6 8 10 Year relative to output shock Year relative to output shock Efi N Ufi N Total Nfi E Nfi U Total Note: Each line shows the estimated coefficients from Equation 1 for the associated labor market flow. Flowsaremeasuredastheshareofthepopulationexperiencingthespecifiedtypeofflowfrom thebeginningofa12-monthperiodtotheend. Thebandsaroundeachlineshowa95%confidence interval,basedonstandarderrorsclusteredbystate. Coefficientsarenormalizedtoshowtheeffect of a temporary -1 percentage point shock to GSP growth in year 0. All outcomes are adjusted for changesintheage-by-sexcompositionofthepopulation. F-statistic: 149.1. Regressionscontrolfor stateandyearfixedeffectsandareweightedbypopulation. Source: BLS,BEA,andauthors’calculations. after output shocks. However, this persistent effect is not the result of hysteresis but instead reflects changes in the demographic composition of the population at the state level, primarily the age distribution. We find little to no contribution from changesineducation,race,ethnicity,andmaritalstatus. Next, we examine how the state-level population in each single-year age group changesinresponsetooutputshocks,findingthatdeclinesareconcentratedamong 25 to 39 year olds. Since this age group tends to have higher LFPRs than other age groups,declinesinitspopulationpulldowntheunadjustedoverallLFPRmechanicallyafteranoutputshock. Wecautionthatthisphenomenonraisestheimportance of using age-adjusted LFPRs to examine questions about cyclicality and hysteresis inresponsetolocalshocks. 6.1 Cyclicality of Adjusted and Unadjusted LFPRs ToinvestigatehowdemographicsaffectthecyclicalityoftheLFPR,wecompareour age-adjustedbaselineestimatestotwoalternativebenchmarks. 20

First, we estimate Equation 1 using the unadjusted LFPR. Figure 5 shows that theunadjustedLFPRsteadilydeclinestoitstroughinyearfour,withsimilartiming but a steeper decline compared to the age-adjusted LFPR. However, while the ageadjusted LFPR subsequently recovers back to its pre-shock level, the unadjusted LFPR merely edges up a bit, but remains well below its pre-shock level even ten yearsaftertheshock. While a persistent shortfall of the unadjusted LFPR after a shock might be interpreted as evidence of hysteresis, we caution that this is not the case in our setting. By hysteresis, it is commonly meant that people become persistently less likely to participate in the labor market as a result of the shock. However, our estimates do not suggest that people experience persistently lower participation conditional on their demographics, as the age-adjusted LFPR fully recovers on average by 8 years afterashock. Figure5: CyclicalitybyDemographicAdjustment Percentage points Percentage points 0.1 0.1 0.0 0.0 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 -2 0 2 4 6 8 10 Year relative to output shock Unadjusted Age-sex-adjusted Age-sex-educ.-race-married-adj. Fitted values: Age-sex Age-sex-educ.-race-married Note: Each line shows the estimated coefficients from Equation 1 using the specified adjusted, unadjusted, and fitted-value LFPR as the outcome. The band around the orange solid line shows a 95%confidenceinterval,basedonstandarderrorsclusteredbystate. Coefficientsarenormalizedto showtheeffectofatemporary-1percentagepointshocktoGSPgrowthinyear0. F-statistic: 149.1. Regressionscontrolforstateandyearfixedeffectsandareweightedbypopulation. Source: BLS,BEA,owncalculations. For our second benchmark, we consider a broader adjustment for multiple demographic characteristics. Using person-level data from the CPS, we regress a person’s labor force participation indicator on demographic characteristics using the 21

followinglinear-probabilitymodel: Y = ψ +Ψi,m,tD +Ψs,m,tW +η (9) i,s,m,t 0 i,m,t s,m,t i,s,t whereY isaindicatorvariableindicatingwhetherpersoniinstateswaspartici,s,m,t ipatinginthelaborforceinmonthmofyeart; D isavectorofindicatorvariables i,m,t over the demographic characteristics of person i in month m of year t that include age, gender, educational attainment, race/ethnicity, and marital status; and W s,m,t is a vector of state, month, year fixed effects. The age variables are single-year age indicatorsforages16to79andaindicatorvariableforages80yearsandolder. The educationalattainmentindicatorspartitionattainmentintofivecategories: lessthan ahighschooldegree,ahighschooldegree,somecollege,afour-yearcollegedegree, and more than a college degree. The race/ethnicity indicators partition the populationintofourgroups: non-Hispanicwhite,non-HispanicBlack,Hispanic,andother. Marital status is a single indicator indicating whether an individual is married. We includemonth-of-yearindicatorvariablestoaccountforseasonality. Using the estimated coefficients from Equation 9, we predict whether a person is participating in the labor force based on their demographic characteristics and denote this by Y(cid:100)D . With this fitted value, we calculate the demographicallyi,s,m,t (cid:100)D.adj adjustedLFPRastheresidual,Y . Wethenaggregatetheperson-levelfittedand i,s,m,t residual components to calculate monthly rates for the fitted and demographicallyadjusted labor market variables in each state s, and then average across months withinyearttocreateafittedvaluecomponent,y(cid:99)D,andademographically-adjusted s,t (cid:100)D.adj component,y . Finally,weusethosefittedvaluesanddemographically-adjusted s,t state-levelvariablesasthedependentvariableinEquation1. The additional demographic controls beyond age make little to no difference in estimating LFPR cyclicality. Figure 5 shows that the addition of adjustments for education, race/ethnicity, and marital status results in nearly the same estimated impulse response as our baseline estimates, which adjust for age and sex only. The similarity of adjusted values is mirrored in the fitted values, which both decline steadily in response to the shock. This pattern points to the age structure of the state-level population changing persistently in a way which would mechanically pulldowntheLFPRabsentadjustment. In Appendix Figure A.1 we repeat this exercise for the unemployment rate. In contrast to the LFPR, we find that demographics explain essentially none of the response of unemployment, both immediately following the shock and in the longrunafterwards. 22

6.2 Response of Population Composition to Cyclical Shocks Why does the age-composition of the state-level population change in response to a business cycle shock? Blanchard and Katz (1992) provide empirical evidence that economic shocks at the state level trigger adjustments not only through unemployment, but also by triggering cross-state migration. More recently, Dao, Furceri and Loungani (2017) show that it still remains the case that net migration across states responds to spatial disparities in labor market conditions and especially so during recessions, though the effect has weakened somewhat over time. However, Amior and Manning (2018) show that long-term adjustment in regional populations tends to differ across demographic groups, and if the migration response to business cyclessimilarlydiffersacrossgroups,thenthecompositionofthepopulationcouldbe altered by these shocks. For example, if shocks lead to higher migration responses among prime-age people, who tend to have higher LFPRs, then these shocks could alterthecompositionofthepopulationresultinginapermanentlylowerLFPR. In this section, we examine how the age composition of a state’s population across single-year-age groups responds to a business cycle shock. Understanding the changes in the age structure are essential not only for understanding how the population changes but also for understanding how national LFPR cyclicality may be related to local LFPR cyclicality. If shocks induce out-migration of selected groups, the response of the local LFPR, absent any demographic adjustments, may include both the direct cyclical effect as well as the effect of the migration response. However, national LFPR cyclicality would only contain the first effect, assuming that shocks do not induce sizeable migration out of the country. The response of the age-adjusted LFPR, though, would be comparable to national LFPR cyclicality, sinceitwouldnotbeaffectedbythemigrationchannel. To estimate the effect of a business-cycle shock on the composition of the state’s population,weestimateEquation1withtheoutcomey beingthelogpopulation s,t+k of a single-year-age group in state s in period t + k.19 We estimate this equation for each single-year-age group from ages 16 through 80. The interpretation of the estimated equation for single-year-age group 25 in period k = 10 would be, for example, the percent change in the level of the total 25 year old population in state s betweenperiods t+10and t−1causedbythebusiness-cycleshock.20 19RelativetoAmiorandManning(2018),ouranalysisfocusesonsingle-year-agegroupsinsteadof coarseagegroups,estimatesannualdynamicresponsesinsteadofdecadalresponses,andestimate theresponsetooutputshocks. 20Weusestate-leveldataforthecovered-areapopulationforsingle-year-agegroupsfromtheU.S. CensusBureau. Thesepopulationestimatesusethemostrecentdecennialcensuspopulationcounts asabaseandthenaddbirths,subtractdeaths,andaddnetmigration(bothinternationalanddomes- 23

Figure6: PercentChangeinSingle-AgePopulationinResponsetoaBusinessCycle Shock -2 years after the shock 0 years after the shock Percent Percent 6 6 6 6 4 4 4 4 2 2 2 2 0 0 0 0 -2 -2 -2 -2 -4 -4 -4 -4 -6 -6 -6 -6 -8 -8 -8 -8 20 25 30 35 40 45 50 55 60 65 70 20 25 30 35 40 45 50 55 60 65 70 Age Age 2 years after the shock 5 years after the shock Percent Percent 6 6 6 6 4 4 4 4 2 2 2 2 0 0 0 0 -2 -2 -2 -2 -4 -4 -4 -4 -6 -6 -6 -6 -8 -8 -8 -8 20 25 30 35 40 45 50 55 60 65 70 20 25 30 35 40 45 50 55 60 65 70 Age Age 7 years after the shock 10 years after the shock Percent Percent 6 6 6 6 4 4 4 4 2 2 2 2 0 0 0 0 -2 -2 -2 -2 -4 -4 -4 -4 -6 -6 -6 -6 -8 -8 -8 -8 20 25 30 35 40 45 50 55 60 65 70 20 25 30 35 40 45 50 55 60 65 70 Age Age Note: Thedependentvariableisthepercentchangeinthepopulationofasingle-agegroupinperiod t+krelativetoperiodt−1. Thebandsaroundeachlineshowa95%confidenceinterval,basedon standarderrorsclusteredbystate. Regressionsareweightedbypopulation. Source: BLS,BEA,andauthors’calculations. A negative business cycle shock causes the population between the ages of 25 and 40 to persistently decline in states exposed to the shock relative to those states withoutashock(seeFigure6,whichshowsthepopulationresponsetoashockat-2, 0,2,5,7,and10yearsaftertheshock). Twoyearspriortotheshock,thereislimited evidencethatchangesinthepopulationarecorrelatedwiththebusinesscycleshock, as essentially all age groups have point estimates that are precisely estimated at 0 percent. Upon impact of the shock, the migration response is still small, with essentially tic)toproduceyearlypopulationestimatesforeachageineachstate.Thecovered-areapopulationis slightlydifferentfromtheciviliannoninstitutionalpopulation,whichisusedtocalculateLFPRand EPOP. The covered-area population includes active members of the armed forces as well as those in institutions (e.g. penal, mental facilities, and homes for the aged), whereas the civilian noninstitutional population does not include these groups. This distinction is not likely to matter in our analysis. 24

all point estimates at 0 percent, but as time goes by, changes in the composition of the population become apparent. Two years after the shock, the population levels of 23 to 35 year olds are all about 2 percent below their levels immediately prior to the shock. Five years after the shock, the population of 27 to 33 year olds falls to 3 percentbelowitspre-shocklevel,whereasthepopulationsof24to26yearoldsand 34 to 27 year olds are 2 percent below their pre-shock levels. Seven years after the shock, the population levels of 28 to 31 year olds fall to 4 percent below their preshocklevels,whereasthepopulationlevels24to27yearoldsand32to39yearolds are all significantly lower, ranging between 1 and 3 percent below their pre-shock levels. Tenyearsaftertheshock,thepopulationlevelsof29to31yearoldsdeclineto about5percentbelowtheirpre-shocklevels,andthepopulationlevelsofallsingleyear-age groups between 25 and 39 years olds are at least 2 percent below their pre-shock values. Though not reported, the population responses 10 years after the shocktendtoholdinyears11through15,suggestingthatanegativebusinesscycle shockpermanentlylowersthepopulationof25to39yearoldsinexposedstates. This pattern suggests that the changes in a state’s population caused by a negativebusinesscycleshockareentirelydrivenbypeoplebetweentheagesof25and39 years old. Since 25 to 39 year olds are among the highest in LFPRs relative to other age groups, permanent declines in a state’s population that are concentrated in this age range will also permanently lower its LFPR through compositional effects, all elseequal. There are several plausible reasons why the net-population response might be concentratedinindividualsages25to39,althoughformallytestingthesetheoriesis outsidethescopeofourpaper. First,peopleinthisagerangemaybelesslikelytobe homeowners, on average, so it might be easier for them to move to a different state in response to a negative shock. Additionally, if a state has been hit by a negative business cycle shock, people from others states that are finishing school may be less likely to move to such a state. As a result, if a state experiences a recession, it could have a “missing generation” of recent graduates. This is consistent with the responses shown in Figure 6, as initially, the largest response is for people in their mid-20s. However, as time goes by and people get older, the response shifts to the rightoftheagedistribution.21 21Ourresultsalsoshowasmallincreaseinthepopulation17to22yearolds. Althoughtestingthe reasonsbehindtheincreaseforthiscollege-agegroupisbeyondthescopeofthispaper,oneplausible mechanismisthatrecessionscausereductionsinincomeandwealththatmakeyoungpeoplemore likelytostayinstatefortheircollegeeducationwithmoreaffordabletuition. 25

7 Differences in Long-Lived Cyclicality Across Groups Business cycles can have different effects on different demographic groups. In this section, we examine how the cyclicality of the LFPR varies across the age, gender, education, and race/ethnicity distributions. Comparing young workers to older workers, men to women, and less-educated people to more-educated people, we findtheLFPRforeachformergroupisbothmorecyclicalandfeatureslonger-lived cyclicality. These differences in long-lived cyclicality may create differential benefits for these groups from “running the economy hot” in years 5 to 7 after a shock, when the unemployment rate has fully recovered but the LFPR is still recovering (Aaronsonetal.,2019). 7.1 Age The labor market performance of prime-age people (ages 25 to 54) is often used as a benchmark for the cyclical state of the labor market as a whole. Understanding the cyclical response for the prime-age group is of considerable interest, as primeage people make up about 50 percent of the 16 and over civilian non-institutional population and roughly 60 percent of the labor force. Further, much work has focusedonthestructuralfactorscontributingtothelong-runandsteadydeclineofthe trend prime-age LFPR and EPOP (see, for example, Abraham and Kearney (2020) and Coglianese (2018)), but there has been relatively less work on identifying the cyclicalresponseofthosevariablesfromtheirlong-rundecliningtrends.22 The cyclical response of the prime-age LFPR is similar to the overall response, albeitabitsmallerinmagnitude. Figure7showstheestimatedimpulseresponsefor theprime-ageLFPR,alongwithunemploymentrateandEPOP.23TheLFPRdeclines steadilyaftertheshockuntilitreachesitstroughfouryearsaftertheinitialshock— well after the unemployment rate peaks—at about 0.14 percentage point below its pre-shocklevel,beforegraduallyrecoveringandreachingitspre-shocklevelinyear eight. Compared to prime-age people, the LFPR for younger people (ages 16 to 24) 22AlthoughthemainpurposeofAaronsonetal.(2014b)andMontes(2018)istobuildaforecasting modeloftheoverallLFPR,bothpapersprovidesomeevidenceonthecyclicalityofprime-ageLFPR. Ourworkcomplementsthosepapersinthatweestablishacausalresponsetooutputshocks,whereas thoseestimateswerelargelybasedoncorrelationswithchangesintheunemploymentrate. 23Unlikeourbaselineresults,wedonotuseage-adjustedparticipationratesforthesesubgroups. However, the results are very similar if we age-adjust the LFPRs within each age range. This is a consequence of the fact that changes in the demographic composition of the population mainly reflectchangesacrosstheseagegroups,ratherthanchangeswithinthem. 26

Figure7: CyclicalityforAges25to54 Percentage points Percentage points 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 -0.6 -0.6 -2 0 2 4 6 8 10 Year relative to output shock Labor force participation rate Unemployment rate Employment-population ratio Note: Each line shows the estimated coefficients from Equation 1 for the associated labor market outcome. The bands around each line show a 95% confidence interval, based on standard errors clusteredbystate. Coefficientsarenormalizedtoshowtheeffectofatemporary-1percentagepoint shocktoGSPgrowthinyear0. F-statistic: 151.6. Regressionscontrolforstateandyearfixedeffects andareweightedbypopulation. Source: BLS,BEA,owncalculations. respondsmorequicklyandwithalargeramplitude—reachingatroughofabout-0.5 percentagepoint—butremainsnearitstroughformanyyearsandbeginsrecovering later (Figure 8, left panel). The point estimate of the LFPR of younger people never fully recovers, as it settles at about 0.2 percentage point below its pre-shock value, althoughtheupperendoftheconfidenceintervalsuggestswecannotruleoutafull recovery. The delayed recovery of the LFPR for younger people likely reflects the increaseintimespentinschoolingdocumentedinSection5. TheLFPRresponseforolderpeopleissimilartotheresponseoftheoverallpopulation, reaching its trough at about 0.2 percentage point four years after the shock (Figure 8, right panel). The LFPR for older people then begins to steadily recover 5 years after the shock and does not fully recovery until 9 years after the shock. For thisagegroup,theshortfallofparticipationatitstroughislikelyduetohigherrates ofillnessanddisability,withnoincreaseinretirements. 27

Figure8: CyclicalityforAges16-24and55+ 16-24 55+ Percentage points Percentage points 1.0 1.0 0.5 0.5 0.0 0.0 -0.5 -0.5 -1.0 -1.0 -1.5 -1.5 -2 0 2 4 6 8 10 -2 0 2 4 6 8 10 Year relative to output shock Year relative to output shock Labor force participation rate Unemployment rate Employment-population ratio Note: Each line shows the estimated coefficients from Equation 1 for the associated labor market outcome. The bands around each line show a 95% confidence interval, based on standard errors clusteredbystate. Coefficientsarenormalizedtoshowtheeffectofatemporary-1percentagepoint shocktoGSPgrowthinyear0. F-statistic:179.1for16–24,162.6for55+. Regressionscontrolforstate andyearfixedeffectsandareweightedbypopulation. Source: BLS,BEA,owncalculations. 7.2 Gender Digging deeper into the prime-age LFPR responses, our results suggest that while both men and women have strong cyclicality, the magnitudes and timing of their responses are quite different. For men, the initial point estimate response shown in the left panel of Figure 9 is small, and subsequent year-over-year declines are also small. However, even though those yearly declines are small, they compound for many years after the shock, cumulating to a total decline in the LFPR of about 0.15 percentage point at its trough 6 years after the shock. Although the confidence bands around those estimates are large due the smaller sample sizes from splitting the prime-age group by gender, the decline in the prime-age LFPR for men is large enoughinyear6fortheconfidencebandtonotincludezero. TheresponseofLFPRforprime-agewomenisconsiderablydelayed. Infact,the LFPRofprime-agewomendoesnotstarttodeclineuntil2yearsaftertheshockand reachesitstrough3to4yearsaftertheshockatabout0.1percentagepointbelowits initial value. This rate fully recovers by about 6 years after the shock and settles at rate slightly above its pre-shock value. Of course, the confidence bands around the 28

Figure9: CyclicalityforAges25to54bySex Men Women Percentage points Percentage points 0.8 0.8 0.4 0.4 0.0 0.0 -0.4 -0.4 -0.8 -0.8 -2 0 2 4 6 8 10 -2 0 2 4 6 8 10 Year relative to output shock Year relative to output shock Labor force participation rate Unemployment rate Employment-population ratio Note: Each line shows the estimated coefficients from Equation 1 for the associated labor market outcome. The bands around each line show a 95% confidence interval, based on standard errors clusteredbystate. Coefficientsarenormalizedtoshowtheeffectofatemporary-1percentagepoint shocktoGSPgrowthinyear0. F-statistic: 151.1formen, 152.1forwomen. Regressionscontrolfor stateandyearfixedeffectsandareweightedbypopulation. Source: BLS,BEA,owncalculations. estimates for prime-age women are quite large, possibly due to large non-cyclical variationintheLFPRforprime-agewomen,andsoonecannotrejectthepossibility thattheLFPRofprime-agewomendoesnotrespondtotheshockatall. 7.3 Education Labor market outcomes over at least the past 40 years have been quite different for less- and more-educated people. Indeed, the levels of the unemployment rates, LFPRs, and EPOPs for prime-age workers vary significantly across levels of educational attainment for both men and women. Additionally, the prime-age LFPR and EPOP for less-educated people have been declining steadily over the past several decades,whiletheLFPRandEPOPformore-educatedprime-agepeoplewererelativelyflat. Thosetrendshaveledtoagrowingdivergenceinlabormarketoutcomes betweenthemostandleasteducatedindividuals. Thisdivergencemay,atleastinpart,beduetoalong-termdeclineinthedemand for lower-educated workers that is unrelated to the business cycle and caused, per- 29

Figure10: CyclicalityforAges25to54byEducation High school or less College plus Percentage points Percentage points 0.8 0.8 0.4 0.4 0.0 0.0 -0.4 -0.4 -0.8 -0.8 -2 0 2 4 6 8 10 -2 0 2 4 6 8 10 Year relative to output shock Year relative to output shock Labor force participation rate Unemployment rate Employment-population ratio Note: Each line shows the estimated coefficients from Equation 1 for the associated labor market outcome. The bands around each line show a 95% confidence interval, based on standard errors clusteredbystate. Coefficientsarenormalizedtoshowtheeffectofatemporary-1percentagepoint shocktoGSPgrowthinyear0.F-statistic:167.9forhighschooldegreeorless,137.7forcollegedegree or more. Individuals with some college but less than a four year degree are omitted. Regressions controlforstateandyearfixedeffectsandareweightedbypopulation. Source: BLS,BEA,owncalculations. haps, by changes in technology and globalization. Thus, to isolate cyclicality one needs to control for these long-term structural declines. Our approach using statelevel business cycles and controlling for these national and international trends is well suited to isolate the effects of the business cycle and explore how they differ acrosseducationgroups. We find a starkly different evolution of the LFPR after a shock for less-educated prime-age workers compared to those with at least college degrees. For workers with a high school degree or less, the shock leads to a slow decline of the LFPR for about 5 years, reaching a trough of about 0.25 percentage point, before recovering subsequently. In contrast, workers with a college degree experience essentially no variation in LFPR following a shock.24 This disparity is also found in the responses of the unemployment rate and EPOP, each of which respond substantially among theless-educatedgroupbutbarelyatallamongthemore-educatedgroup. 24We omit workers with some college but less than a four year degree for ease of comparison. The labor market response of this group falls in between the two groups shown here, closer to the less-educatedgroupthantothemore-educatedgroup. 30

7.4 Race and Ethnicity We also investigate the inequality of long-lived LFPR cyclicality across race and ethnicity. As has been noted by Cajner et al. (2017) and others, business cycles are more costly for minority groups. We divide prime-age people in the CPS into racial and ethnic groups and estimate Equation 1 for each group, showing the results in Figure11. Figure11: CyclicalityforAges25to54byRace/Ethnicity White Black Hispanic Percentage points Percentage points 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 -0.5 -0.5 -1.0 -1.0 -1.5 -1.5 -2 0 2 4 6 8 10 -2 0 2 4 6 8 10 -2 0 2 4 6 8 10 Year relative to output shock Year relative to output shock Year relative to output shock Labor force participation rate Unemployment rate Employment-population ratio Note: Each line shows the estimated coefficients from Equation 1 for the associated labor market outcome. The bands around each line show a 95% confidence interval, based on standard errors clusteredbystate.Individualsnotreportingeitherwhite,Black,orHispanicareomitted.Coefficients are normalized to show the effect of a temporary -1 percentage point shock to GSP growth in year 0. F-statistic: 186.5forwhite,134.9forBlack,10.4forHispanic. ConfidenceintervalforHispanicnot shownduetolowF-statistic. Regressionscontrolforstateandyearfixedeffectsandareweightedby population. Source: BLS,BEA,owncalculations. We find that shocks lead to larger and more long-lived declines in LFPR among minority groups. While the white LFPR falls by only 0.1 percentage point after a shock, the Black LFPR falls by 0.5 percentage point. The Black LFPR remains depressed for substantially longer, and only fully recovers ten years after the shock, well after the white LFPR has recovered. The responses for Hispanic workers are also large, although our results for this group are much noisier due to a lowerpoweredinstrumentwhenweightingstatesbytheHispanicpopulation. 31

8 What Drives the Shocks? We examine what drives the variation in our output shock. We find similar responses to contractionary and expansionary shocks, suggesting that our effects are not being driven by asymmetries. More of our variation comes from the pre-1994 period, with estimates using only post-1994 data being similar overall but substantially noisier. The variation in the shift-share instrument is driven by a handful of industriesincludingmotorvehicleproduction,oilandgasextraction,securitiesand commoditiesbrokers,andfarms,butourestimatedeffectsaresimilariftheseindustries are excluded. Further, we show that our shocks primarily reflect short-lived shocks to productivity growth, which then spill over to persistent effects on employment. Overall, we find that our results are not being driven by a single source of variation, and instead reflect common responses to shocks in a wide variety of environments. 8.1 Expansions vs. Contractions Our estimated impulse responses are an average of the effects of expansionary and contractionary shocks, which may not be informative if these effects are starkly different. To examine whether expansionary and contractionary shocks have different effects, we divide the distribution of shocks into thirds and estimate the impulse responses separately for each third. In the left panel of Figure 12, we present the effectsofexpansionaryshocks(topthird)andcontractionaryshocks(bottomthird), normalizing both to show the effect of a negative 1 percentage point shock. Both impulse responses have similar patterns, and we cannot reject that the two are the same. This result suggests that our baseline estimates, which combine the response of both expansionary and contractionary shocks, are a reasonable guide for a wide rangeofshocks. 8.2 Differences over Time Our instrument also combines variation over time, including periods with different macroeconomic dynamics. Business cycles since 1990 have been characterized byjoblessrecoveries(JaimovichandSiu,2020),whileearlierperiodsincludedmore rapid recoveries in the labor market. Additionally, our CPS sample includes data both before and after the 1994 redesign, which substantially changed how the surveywascollected. 32

Figure12: CyclicalResponsestoDifferentTypesofShocks Different magnitudes Different eras Percentage points Percentage points 0.8 0.8 0.4 0.4 0.0 0.0 -0.4 -0.4 -0.8 -0.8 -1.2 -1.2 -2 0 2 4 6 8 10 -2 0 2 4 6 8 10 Year relative to output shock Year relative to output shock Bottom third Top third Pre-1994 Post-1994 Note: EachlineshowstheestimatedcoefficientsfromEquation1fortheLFPR,usingonlythespecifiedsampleofshocks. Thebandsaroundeachlineshowa95%confidenceinterval,basedonstandarderrorsclusteredbystate. Coefficientsarenormalizedtoshowtheeffectofatemporary-1percentagepointshocktoGSPgrowthinyear0.Inallspecifications,theLFPRisadjustedforchangesin theage-by-sexcompositionofthepopulation. F-statistics: 51.7(bottom-third),45.7(top-third),146.4 (pre-1994),31.2(post-1994). Regressionscontrolforstateandyearfixedeffectsandareweightedby population. Source: BLS,BEA,andauthors’calculations. TotestwhetherthecyclicalityoftheLFPRhaschangedovertime,wedivideour sampleintopre-andpost-1994periods. Foreachperiod,weseparatelyestimatethe impulseresponseandplottheseestimatesintherightpanelofFigure12. Although the post-1994 estimates are substantially noisier, the two point estimates are similar and we cannot rule out that the two are the same. This suggests that most of the variation in the instrument in our baseline estimates comes from the earlier period, butitdoesnotexclusivelydriveourestimates. 8.3 Decomposing the Shift-Share Instrument To further examine where the variation in our shift-share instrument comes from, wedecomposethevariationusingtheapproachofGoldsmith-Pinkham,Sorkinand Swift (2020). For simplicity, we focus on the response of the LFPR four years after the shock, which is the point that it reaches its trough in our main estimates. To 33

Table1: RotembergweightsinGSPShift-ShareInstrument (a)ByIndustry/Year (b)ByIndustry (c)ByYear Industry Year αkt βkt Industry αk βk Year αt βt Oil&gas 1986 0.13 0.40 Motorvehicles 0.30 0.09 1980 0.22 0.16 Oil&gas 1980 0.12 0.24 Oil&gas 0.28 0.38 1986 0.17 0.35 Securities 2009 0.08 0.10 Securities 0.12 0.11 1983 0.10 0.20 Motorvehicles 2010 0.07 0.07 Farms 0.06 0.13 2009 0.10 -0.02 Motorvehicles 1980 0.05 0.09 Primarymetals 0.03 -0.19 2010 0.07 0.12 Oil&gas 1981 0.04 0.35 Computers&electronics 0.02 0.04 1982 0.07 0.14 Motorvehicles 2009 0.03 -0.05 Trans.eq.excl.motorveh. 0.02 0.20 1992 0.04 0.18 Motorvehicles 1983 0.03 0.07 Federalgovt.-military 0.02 0.60 2001 0.04 0.50 Oil&gas 1983 0.03 0.21 State&localgovt. 0.02 0.29 1994 0.03 0.04 Motorvehicles 1992 0.02 0.45 Chemicals 0.01 0.11 1981 0.03 0.21 Allother Allother 0.38 0.16 Allother 0.12 0.18 Allother 0.14 0.22 Note: TablesshowtheRotembergweightsfortheGSPshift-shareinstrumentusedinourmainestimates. Eachpanelshowsthetop10Rotembergweightsineachcategory,alongwiththetotalamong allnon-top-10entries. OutcomeisthechangeintheLFPRfouryearsaftertheshock;thetotaleffect isequalto0.19inourmainspecificationusingthenon-leave-one-outversionoftheinstrument. Source: BLS,BEA,andauthors’calculations. computetheRotembergweightsforeachindustry-yearpair,wecompute (cid:48) ∆ ⊥ (cid:48) ∆ ⊥ g ζ GSP ζ LFPR αˆ = kt kt t,t−1 , βˆ = kt t+4,t−1 , βˆ = ∑∑ αˆ βˆ (10) kt ∑ k(cid:48) ∑ t(cid:48) g k(cid:48)t(cid:48)ζ k (cid:48) (cid:48)t(cid:48) ∆ GSP ⊥ t,t−1 kt ζ k (cid:48) t ∆ GSP ⊥ t,t−1 k t kt kt ∆ ⊥ ∆ ⊥ where GSP isGSPgrowthand LFPR isthecumulativechangeinLFPR t,t−1 t+4,t−1 (cid:48) by fouryears aftershock, both residualizedon state andyear fixed effects, ζ is the kt lagged industry share for industry k in year t, and g is the national growth rate of kt industry k in year t. We depart from our baseline specification in using the national growth rate for g , instead of the leave-one-out growth rate, in order to align with kt thecalculationofRotembergweights.25 Importantly, we treat each industry and year as a distinct instrument, using the variationfromthesharestoidentifyeacheffect. Ourbaselineestimateisaweighted average of these effects, where the weights are the Rotemberg weights outlined above. An alternative interpretation of the shift-share instrument is that the variation comes from the industry shocks, as outlined in Borusyak, Hull and Jaravel (forthcoming). Much of the variation in the shift-share instrument comes from a small number of industry-year instruments. Panel (a) of Table 1 shows the top 10 industry-year instruments,alongwiththeirweightsαˆ andestimatedeffects βˆ . Theinstruments kt kt 25Ourbaselineresultsarelittlechangedusingthenationalgrowthrateinsteadoftheleave-one-out growthrate. 34

contributingthemostweightincludeshockstooil&gasextractionduringthe1980s, aswellasshockstomotorvehicleproductionandsecuritiesduringrecessions. Collectively, the top 10 instruments account for about 62 percent of the total weight. Mostoftheshockshaveestimated βsclosetoourmainestimate,includingthetotal ofshocksoutsidethetop10. Inthisway,nosingleshockdrivesourresult. We also aggregate the weights to show the most important industries, pooling acrosstimeperiods,andthemostimportanttimeperiods,poolingacrossindustries. Panel (b) of Table 1 shows that 3/4 of the shift-share instrument variation comes from justfour industries—motor vehicleproduction, oil & gasextraction, securities &commoditiesbrokers,andfarms. Nonetheless,theseindustriesdonotexclusively drive our result, as the estimated effect pooling across all other industries is 0.18, very close to our baseline estimate. Panel (c) of Table 1 shows that our instrument derives a substantial amount of variation from recessions, with the top 10 years including at least one year from each of the five national recessions that took place during our sample period, but also includes variation from non-recessionary years. Almost all years have coefficients close to our baseline estimate, indicating that our estimatesarenotbeingdrivenbyasingleyearorrecession. 8.4 Effects on Productivity Our shocks to output could result either from lower output per worker, or fewer workers, or some combination thereof. We have shown in our baseline estimates that employment declines, but some of the output effect could still be driven by labor productivity—defined here as GSP per employee. Importantly, the potential for our instrument to contain variation in productivity shocks sets it apart from shift-shareinstrumentsthatarebasedpurelyonemployment. Figure 13 shows the estimated impulse response of productivity to a temporary negative 1 percentage point output shock, using the same approach as in Equation 1. The left panel shows the effect on yearly growth rates of productivity, along with the cumulated effect on the level of productivity. Productivity grows by about 0.5percentagepointlessintheyearwhentheshocktakesplace,butgrowssimilarly afterwards. This leads to a level of productivity that is permanently about 0.25–0.5 percentloweraftertheshockthanbefore. Productivityaccountsforabouthalfofthe initial shock to output (shown in the right panel of Figure 13), with the remainder accounted for by employment. As productivity is stable after the initial shock, the further decline in output in year 1 and the subsequent partial recovery entirely reflect employment. This points to output shocks being initially driven by productiv- 35

Figure13: EffectsofShocksonProductivityandOutput Productivity GSP Percentage points Percentage points 0.5 0.5 0.0 0.0 -0.5 -0.5 -1.0 -1.0 -1.5 -1.5 -2.0 -2.0 -2.5 -2.5 -2 0 2 4 6 8 10 -2 0 2 4 6 8 10 Year relative to output shock Year relative to output shock Level Growth rate Note: EachlineshowstheestimatedcoefficientsfromEquation1forthespecifiedoutcome,eitherin levelsrelativetoyear-1oringrowthrates.Thebandsaroundeachlineshowa95%confidenceinterval,basedonstandarderrorsclusteredbystate. Theleftpanelshowstheresponseofrealproductivity,definedasrealGSPperworker. Coefficientsarenormalizedtoshowtheeffectofatemporary-1 percentagepointshocktoGSPgrowthinyear0. F-statistic: 149.1. Regressionscontrolforstateand yearfixedeffectsandareweightedbypopulation. Source: BLS,BEA,andauthors’calculations. ity before employment adjusts in response, with time aggregation leading to some of this response appearing in the same year as the shock. These estimates also indicate that our instrument picks up an important source of variation—productivity shocks—whichwouldbeomittedinanemployment-basedshift-shareinstrument. 9 Robustness Inthissection,weshowseveralrobustnesschecksforourmethodology. 9.1 Lead-Lag Exogeneity One of the conditions required for our research design to identify the impulse responseoftheLFPRisthattheinstrumentsatisfieslead-lagexogeneity,aslaidoutin Equation 6 (Stock and Watson, 2018). A necessary, though not sufficient, condition forlead-lagexogeneityisthattheinstrumentshouldbeuncorrelatedwithleadsand 36

Figure14: RobustnessChecks (b)Additionalrobustnesschecks (a)Leads/lagsofinstrument Percentage points PanelI-Additionalcontrols 1.0 Mainestimate -0.19 (0.062) 0.0 Housepriceindex -0.19 (0.066) -1.0 PanelII-Placebo Mainestimate(reducedform) 0.080 -2.0 (0.014) [0.052,0.108] -3.0 Placebo 0.0098 (0.012) -4.0 [-0.022,0.023] -2 0 2 4 6 8 10 Year relative to output shock PanelIII-Testofinvertibility Teststatistic 750.8 Bartik Instrument p-value 0 Note: In the left panel, the line shows the estimated coefficients from Equation 1 using the shiftshare instrument as the outcome, and the band around the line shows a 95% confidence interval, based on standard errors clustered by state. The right panel shows the estimated response of the age-adjusted LFPR four years after a shock (panels I and II), as well as the results of the Stock and Watson (2018) test of invertibility. Standard errors clustered by state are shown in parentheses. In panel I, coefficients are normalized to show the effect of a temporary -1 percentage point shock to GSPgrowthinyear0. InpanelII,the95%confidenceintervalisshowninbrackets;fortheplacebo specification this is the empirical confidence interval taken from the 2.5th percentile to the 97.5th percentile across placebo estimates. F-statistic: 149.1. Regressions control for state and year fixed effectsandareweightedbypopulation. Source: BLS,BEA,FHFA,andauthors’calculations. lags of itself, which we can test empirically. Given that our instrument is based on industry growth rates and shares, which can be persistent over time, there is some potentialfortheinstrumenttobecorrelatedwithleadsandlagsofitself. To examine whether our instrument is correlated with its leads and lags, we estimate Equation 1 using our shift-share instrument as the outcome variable. This impulse response is reported in the left panel of Figure 14. The coefficient in period 0, 2.71, is the inverse of our first stage coefficient, γ, and is highly statistically significantasaresult. Importantly,though,alloftheothercoefficientsareclosetozero andalmostallofthemarestatisticallyindistinguishablefromzero. 9.2 Controlling for House Price Growth To verify the robustness of our results, we show that they remain unaffected when controlling for local house price growth. Our focus in this paper is on the response ofLFPRtochangesinoutput,whichwetaketorepresentchangesintheproduction process. Analternativereasonthatmeasuredoutputcanchangeisifcapitalincome 37

changes unrelated to current production (for example, through home price appreciation).26 Controlling for home price appreciation as measured by the state-level FHFA price index in the period before the shock addresses this concern. Panel I of Figure14showsthatourestimatesarelittlechangedfromthebaselineifwecontrol forhomepricegrowth. 9.3 Placebo Weclusterourstandarderrorsatthestatelevelinourbaselineestimates,butAdão, Kolesár and Morales (2019) point out that this may be insufficient in some circumstances. Our instrument exploits variation across places with different industry exposure, and the residuals for states with similar industry exposure may be correlated. Our clustering approach does not exactly capture this structure, raising a concernthatourstandarderrorsmaybeincorrect. Weexaminetherelevanceofthiscritiqueforoursettingusingaplaceboexercise similar to the one proposed by Adão, Kolesár and Morales (2019). In place of our shift-shareinstrument,weestimatethereduced-formversionofourmainspecificationusingaplaceboshift-shareinstrument,wherethenationalgrowthratesofeach industry have been replaced with random draws from a normal distribution with thesamemeanandvarianceastheobservedgrowthrates. Werepeatthisprocedure 100times,obtainingaplaceboestimateforeach,andreportthedistributionofthese placebo estimates along with our baseline in panel II of Figure 14. Unlike the cases examined by Adão, Kolesár and Morales (2019), we find that the spread of placebo estimates is similar to or a bit smaller than the confidence intervals obtained from standarderrorsclusteredatthestatelevel. Thisresultsuggeststhatourapproachto inferenceisvalid,andifanythingisabitconservative. 9.4 Local Projections vs. VAR Akeydepartureofourapproachfromtheliteratureistheuseoflocalprojectionsregressions instead of a VAR to estimate impulse response functions. Both Blanchard andKatz(1992)andDao,FurceriandLoungani(2017)useVARmethodstoestimate impulse responses and find roughly similar cyclical timing for the unemployment rate and LFPR. However, VAR methods can fail to identify the correct impulse responses even when the instrument conditions are met if the impulse responses are 26Intheoppositedirection,MianandSufi(2014)showthathousepricedeclinesduringtheGreat Recessionledtoloweremploymentthroughdeterioratinghouseholdbalancesheets. 38

notinvertible,butlocalprojectionsdonotrequirethisassumptionforidentification (StockandWatson,2018). To test whether VAR methods are appropriate for our setting, we conduct a test of invertibility following Stock and Watson (2018). This is a Hausman (1978)-type test, where, under the null hypothesis of invertibility, both methods should deliver similar estimates but with VAR estimates more efficient, while under the alternative they would return different estimates. We report the test statistic in panel III of Figure 14 along with the associated p-value. We are able to strongly reject the null hypothesis of invertibility, implying that local projections are the only suitable methodforexaminingthecyclicalityofLFPRwithourapproach. 10 Conclusion We estimate the effect of a business cycle shock on the LFPR and show that the LFPR is cyclical, but it responds with a smaller elasticity, a more delayed impact, and a longer recovery than the unemployment rate. Our approach uses state-level variation in business cycles to estimate the cyclicality of LFPR and instruments for changes in state output with a shift-share instrument to establish a causal link between business cycle shocks and the dynamic response of LFPR. We estimate this dynamic response of LFPR to an output shock using the local projections regressions. This method is particularly well-suited for estimating LFPR’s cyclicality and itslagstructurecomparedtomoretraditionaltimeseriesmodels,asitsflexibilityallowsforthepossibilityoflong-runeffectsofabusinessshockonLFPR,suchashysteresis, and does not impose strict assumption about the smoothness of trends—a particularconcernforLFPRgiventheagingofthepopulationandotherlonger-term structuralchangesuchastheinflowofwomenintothelaborforce. Our results indicate that measuring labor market slack requires looking beyond the unemployment rate. While traditional views hold that the unemployment rate isasufficientstatisticforslack,thelong-livedcyclicalityoftheLFPRposesproblems for this view. During the period 5 to 7 years after a shock, the unemployment rate has essentially fully recovered, but the LFPR still has room to rise before it returns toitspre-shocklevel. Observerswhofocussolelyontheunemploymentrateduring thisperiodwillincorrectlyconcludethattheeconomyhasreachedfullemployment, wheninfactemploymentisstillbelowpotential. A complete view of labor market slack requires examining the LFPR in additiontotheunemploymentrate,andperhapsmaygofurthertoincludethedifferential cyclicality of different demographic groups. Long-lived cyclicality is especially 39

prone among younger workers, men, less educated workers, and racial and ethnic minorities, each of which is also more exposed to business cycles in the form of unemployment. Our results indicate that these groups have the most to gain from maintaining business cycle recoveries until the LFPR has fully recovered, and also themosttoloseiflong-livedcyclicalityintheLFPRisignored. 40

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A Additional Results FigureA.1: UnemploymentRateCyclicalitybyDemographicAdjustment Percentage points Percentage points 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 -2 0 2 4 6 8 10 Year relative to output shock Unadjusted Age-sex-adjusted Age-sex-educ.-race-married-adj. Fitted values: Age-sex Age-sex-educ.-race-married Note: Each line shows the estimated coefficients from Equation 1 using the specified adjusted/unadjusted LFPR or fitted values as the outcome. The band around the orange solid line shows a95% confidence interval, based on standarderrors clustered bystate. Coefficientsare normalized to show the effect of a temporary -1 percentage point shock to GSP growth in year 0. Fstatistic: 149.1. Regressionscontrolforstateandyearfixedeffectsandareweightedbypopulation. Source: BLS,BEA,owncalculations. 46