Hysteresis and the Role of Downward Nominal Wage Rigidity: Evidence from U.S. States

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Hysteresis and the Role of Downward Nominal Wage Rigidity: Evidence from U.S. States Hie Joo Ahn and Yunjong Eo 2025-062 Please cite this paper as: Ahn, Hie Joo, and Yunjong Eo (2025). “Hysteresis and the Role of Downward Nominal Wage Rigidity: Evidence from U.S. States,” Finance and Economics Discussion Series 2025-062r1. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2025.062r1. 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.

Hysteresis and the Role of Downward Nominal Wage Rigidity: Evidence from U.S. States* HieJooAhn† YunjongEo‡ FederalReserveBoard KoreaUniversity December16,2025 Abstract Thispaperempiricallyinvestigatesthesourcesofhysteresis, emphasizingtheroleof downwardnominalwagerigidityusingU.S.state-levelpayrollemploymentgrowth. U.S. statesexhibitheterogeneousrecoveries,withL-shapedandU-shapedrecessionscorrespondingtopersistenthysteresisandfullrecovery.L-shapedrecessionsareimportantlydrivenby demandshocksandreinforcedbydownwardnominalwagerigidity,whichprolongsemploymentlossesbyraisingrealwagesanddeepeningdownturns.Whenwagerigidityisstrong, expansionary policies are particularly effective in mitigating these effects through labor marketadjustment.ThesemechanismsarevalidatedinaNewKeynesianmodelfeaturing bothhysteresisanddownwardnominalwagerigidity. JELclassification:C22;C51;E32;E37. Keywords: Hysteresis,Regionalbusinesscycles;L-shapedrecession;U-shapedrecession; Downwardnominalwagerigidity;Monetarypolicy;Fiscalpolicy. *Thispaper,previouslypublishedunderthetitle“RecessionShapesofRegionalEvolution:FactorsofHysteresis” hasbeenrevised,addingastructuralmodeltosupplementtheempiricalanalysisandfocusingontheroleof downwardnominalwagerigidityinhysteresisbydroppingdiscussionsrelatedtothegenderemploymentgap. WethankTravisBerge,JoonkyuChoi,MasaoFukui,FrancescoFurlanetto,JordiGalí,ManuelGonzález-Astudillo, AdamGulan,JamesHamilton,YoonJooJo,MikaelJuselius,AntoineLepetit,NigelMcClung,MichaelMcCracken, Raven Molloy, Emi Nakamura, Mike Owyang, Damjan Pfajfar, Jeremy Piger, Hannah Rubinton, Jeremy Rudd, ChoongryulYangandseminarparticipantsattheBankofFinland,theFederalReserveBoard,HanyangUniversity, theHitotsubashiSummerInstitute,NorgesBank,theRegionalConferenceoftheFederalReserveSystemfortheir helpfulcomments.LucasMoyonprovidedexcellentresearchassistance. Disclaimer:Theviewsexpressedinthispaperarethoseoftheauthorsanddonotnecessarilyreflecttheviewsand policiesoftheBoardofGovernorsortheFederalReserveSystem. †FederalReserveBoardofGovernors,20thStreetandConstitutionAvenueNW,Washington,DC20551,U.S.A. Email:econ.hjahn@gmail.com ‡DepartmentofEconomics,KoreaUniversity,Seoul02841,SouthKorea;Tel:+82232902212; Email:yunjongeo@korea.ac.kr

1 Introduction Hysteresisreferstoaphenomenonwhererecessionaryshockshavepermanentorlong-lasting effects on the level of economic activity (Cerra et al., 2023). The hysteresis view has gained attentionasanexplanationfortheslowrecoveryaftertheGreatRecessionand,morerecently,as achannelthroughwhichmonetaryandfiscalpolicieshavelong-lastingeffectsontheeconomy (e.g.,Jordáetal.,2020;Antolin-DiazandSurico,2025). Reflectingthisgrowinginterest,recent studieshavediscussedvariousdriversofstagnantrecoveriesorhysteresis,suchaswagerigidity (Shimer, 2012; Schmitt-Grohé and Uribe, 2017), gender convergence (Heathcote et al., 2017; Olsson,2019;Fukuietal.,2023;Albanesi,2025),structuralchanges(JaimovichandSiu,2020), and secular stagnation (Hall, 2016; Benigno and Fornaro, 2018). Despite its importance, the determinantsofhysteresishavebeendifficulttoempiricallyexploreforseveralreasons. First, economicrecessionsarerelativelyrareevents,makingitdifficulttoreliablyidentifyandestimate thedriversofhysteresis. Second,andmorefundamentally,thereisnoconsensusabouthowto measurehysteresis,resultinginrelativelyfewempiricalanalysesofhysteresisbasedonaformal statisticalframework.1 Thispaperempiricallyinvestigatesfactorsofhysteresisandexplorestheirpolicyimplications. To overcome the aforementioned empirical challenges, we exploit regional heterogeneity in business-cycleexperiencesbasedonstate-levelpayrollemployment. Weusepayrollemploymentbecauseitisawidelycitedmonthlycyclicalindicatorwithalongsampleperiodstartingin 1960,availableforallstates,anditcontainsidentifyinginformationabouthysteresis(Furlanetto etal.,2025).2 Adoptingthewidelyacceptednotionofhysteresiswhererecoveryfromaneconomicrecessiondoesnotbringeconomicactivitybacktoitspre-recessiontrend,wedistinguish betweenL-shapedandU-shapedrecessions: anL-shapedrecessionreflectshysteresis,whereas aU-shapedrecessionischaracterizedbyafullreturnoftheeconomytoitspre-recessiongrowth path.3 Wethenestimatethelikelihoodofthetwotypesofrecessionsateachpointintimeforall theU.S.statesbasedonaMarkovswitchingmodelofEoandMorley(2022). 1Previousstudieshaveprimarilyreliedonstructuralmodelstoanalyzethecausesandconsequencesofhysteresis, duetotheempiricalchallengesofidentifyinghysteresisepisodesandtheirstructuraldriversusingaggregatedata. RecentempiricaldevelopmentsincludeFurlanettoetal.(2025)basedonastructuralVARandAntolin-Diazand Surico(2025)basedonaBVARmodel. 2Separately, Dupraz et al. (2025) analyze U-shaped recessions through the lens of plucking theory using a structurallabor-marketmodel. 3Hereafter,thetermshysteresisandL-shapedrecessionareusedinterchangeably. 1

Among the various factors potentially contributing to hysteresis, we focus on downward nominalwagerigidity. Instructuralmodelsofhysteresis,downwardnominalwagerigidityserves asakeymechanismthroughwhichrecessionsinflictlastingdamageonthelabormarket,as downwardnominalwagerigidityputsupwardpressureonrealwagesandhenceexacerbates job destruction during downturns (e.g., Acharya et al., 2022; Alves and Violante, 2024). In ourempiricalanalyses,wecomprehensivelycontrolthestate-levelattributessuchasindustry composition, minimum wages, and labor market outcomes by gender in a comprehensive mannerbybuildingonacoherentempiricalframework.4 WefindthatU.S.statesexhibitbroadlysimilarbutdistinctrecessiondynamicsintermsof shape,timing,andmagnitude. Astate’sbusinesscycledoesnotalwaysalignwiththenational cycleandoftendisplaysnotableidiosyncrasies;justoverhalfofthestatesexperiencerecessions thatcoincidewiththenationalrecessionsidentifiedbytheNBER.Moreover,U-shapedrecessions become less frequent after the 1990s. The emergence of jobless recoveries in the aggregate economy during this period is associated with the reduction in the prevalence of U-shaped recessions across states. Nonetheless, our model classifies the sharp and rapid COVID-19 recessionasaU-shapedrecession. Thetwotypesofrecessionsaredrivenbybothsupplyanddemandshocks,buttheyyield markedlydifferentmacroeconomicoutcomes. Thestatisticallysignificantlinkbetweendemand shocksandL-shapedrecessionssupportsthehysteresishypothesis(e.g.,BlanchardandSummers,1986;Blanchard,2018),whichpositsthatdemandshockscangeneratepersistent,long-run effectsontheeconomicactivity.Moreover,followingL-shapedrecessions,thenegativeeffectson theemployment-to-populationratioandoutputtendtobemorepersistent,whereasU-shaped recessionsarecharacterizedbyaswiftreboundinthesevariablesaftertherecession. Notably,L-shapedrecessionstendtoputupsidepressureoninflation. Thisisbecausethey reducetheeconomy’spotentialoutputorraisethenaturalrateofunemployment. Consequently, theresultingeconomicslackismuchnarrower,andtheeconomy’scyclicalpositionimprovesceterisparibus,exertingupwardpressureonpriceinflation. Incontrast,U-shapedrecessionsexert persistentdownwardpressureoninflationbyworseningthecyclicalpositionoftheeconomy 4Recentempiricalstudiesalsosuggestthathigherfemaleemploymentfacilitatesfasterrecoveries(e.g.,Cortes etal.,2018;Fukuietal.,2023;Bergholtetal.,2024).Thisfactoranddownwardnominalwagerigidityare,infact, correlated:increasedfemaleemploymentraisesdownwardnominalwagerigidity,aswomenaredisproportionately concentratedatthelowerendofthewagedistribution,wherewagesaremorelikelytobedownwardlyrigid(Jo, 2024).Weexplicitlyconsiderlabormarketoutcomesbygenderinourempiricalanalysestocontroleffectsofthe genderevolutioninthelabormarket. 2

withoutpermanentlyalteringitspotentialoutput. Wealsofindthatdownwardnominalwagerigidityraisesthelikelihoodofhysteresis. States withahighershareofzeronominalwagechangesduringeconomicrecessionsaremorelikelyto experienceL-shapedratherthanU-shapedrecessions. Thispatternholdsconsistentlyoverthe fullsampleperiod(1978:Q1–2019:Q4)aswellasinthepost-2000period,duringwhichthegender employmentgapsloweditsnarrowing—onefactorbehindstagnantrecessionrecoveries(Fukui etal.,2023). Thisfindingprovidesempiricalsupportforstructuralmodelswheredownward nominalwagerigidityservesasacrucialmechanismthroughwhichhysteresisarises(Acharya etal.,2022). Finally,weempiricallyexaminetheextenttowhichdemand-sidepolicies—namely,expansionarymonetaryandtaxpolicies—mitigatehysteresis,andtherolesofdownwardnominalwage rigidityinshapingpolicyeffectiveness. Wefindthatexpansionarymonetaryandtaxpolicies are more effective in mitigating hysteresis when downward nominal wage rigidity is greater. Thisfindingalignswiththeconventionalviewthatmonetarypolicyaffectstherealeconomy throughnominalrigidities. Inaddition,whenlaborcostsareinflexibleduetowagerigidity,tax cutseffectivelyreduceproductioncosts,helpingtosustainlabordemandandtherebymitigate hysteresis.ThisisconsistentwithLee(2025),whofindsthatthemultipliereffectsofexpansionary taxpoliciesarelargerwhennominalwagerigidityisgreater. To interpret these empirical findings, we turn to a prototype New Keynesian model. The frameworkbuildsonGalí(2022),inwhichaninsider–outsiderlabormarketstructuregivesrise tohysteresisintheformofL-shapedrecessions. Weextendthismodelbyincorporatingdownwardnominalwagerigiditytoemphasizeitsamplifyingroleinhysteresisandtoevaluatethe effectivenessofmonetarypolicyinterventionsinsuchanenvironment. Theanalysisshowsthat, inthepresenceofdownwardnominalwagerigidity,anegativedemandshockresultsindeeper downturnsinemploymentandoutput,butasmallerreductionininflation,comparedwiththe casewithoutsuchrigidity. Itisbecausedownwardnominalwagerigiditypreventsrealwages fromfalling,whichconstrainsfirms’abilitytoadjustemploymentflexiblyand,consequently, resultsinalargeremploymentreductionthanwouldoccurunderflexibleadjustment. Furthermore,expansionarydemandpolicieseffectivelymitigatehysteresis,withtheirimpact strengthened by the presence of downward nominal wage rigidity. Therefore, our structural modelhighlightsthedualroleofwagerigidity: whileitamplifieshysteresis,italsoenhancesthe effectivenessofmonetarypolicy. Theseresultsunderscoretheimportanceoftimelyandforceful 3

demand-sideinterventionstopreventpersistenteconomicscarring. Thesefindingsalignwithpreviousresearchhighlightingthelong-runeffectsofmonetaryand fiscalpolicies(e.g.,Jordáetal.,2020,Antolin-DiazandSurico,2025)andthehysteresis-mitigating impactoftimelyinterventionsofmonetarypolicy(e.g.,Acharyaetal.,2022). Distinguishingour analysisfrompreviousstudies,wefurtheridentifytheconditionsunderwhichdemand-side policiesaremoreeffective. Ourfindinghighlightsthetwofacesofnominalwagerigidity. Though downwardnominalwagerigidityisthekeymechanismthroughwhichhysteresisismorelikely tobecreated,demand-boostingpoliciesbecomemoreeffectiveinmitigatinghysteresiswhen downwardnominalwagerigidityisgreater. Previousstudiesonfiscalmultipliershavefound thattheeffectsoftaxpolicyorgovernmentspendingarelargerwhennominalwagesaremore downwardlyrigid(e.g.,deRidderandPfajfar,2017;ShenandYang,2018;JoandZubairy,2025; Lee,2025),althoughthesestudiesdonotaccountforhysteresis. Thispaperliesattheintersectionofseveralstrandsofthemacroeconomicandeconometric literatureonbusinesscycles.5 Wecontributetothegrowingbodyofresearchonmacroeconomic hysteresisbylinkingittothelong-standing,yetstillevolving,econometricliteratureonrecession prediction. Tothebestofourknowledge,thisisthefirstempiricalstudytoinvestigatedownward nominalwagerigidityasakeysourceofhysteresiswithinaformalstatisticalmodelofbusiness cycledynamicsusingregionaldata. AfurthercontributionofthepaperistouncoverthestructuralmechanismunderlyingtheempiricalfindingsbydevelopingaNewKeynesianmodelwith aninsider–outsiderlabormarketstructurethatincorporatesdownwardnominalwagerigidity. Unlikethepreviousstudiesonhysteresis,weexplicitlymeasurethelikelihoodofhysteresis using the Markov-switching model developed by Eo and Morley (2022). Previous empirical literatureonhysteresishasreliedontimeseriesmodelsforaggregatedatathatdistinguishthe trendandcyclecomponentsofmacroeconomictimeseriesandexamineseffectsofstructural shocks including supply, demand, and policy shocks on the components of time series (e.g., Furlanettoetal.,2025). Anotherstrandoftheempiricalliteratureemployscross-countrydatato examinecountry-leveldifferencesinlong-rungrowthexperiencesandthelong-runeffectsof monetarypolicy(e.g.,CerraandSaxena,2008;Jordáetal.,2020). Incontrast,wefirstidentifythe likelihoodofhysteresisatthestatelevelbasedonaBayesianMarkovswitchingmodelandthen examinetheeffectsofpolicyshocksandstate-specificstructuralfactorsonhysteresis. Ourpaperalsocontributestotheliteratureontheidentificationofbusinesscyclephases.Pre- 5AdetailedliteraturereviewisprovidedinSectionAppendixA. 4

viousstudiesonregionalbusinesscycleshavetypicallyemployedtwo-regimeMarkov-switching models that distinguish only between expansions and recessions, focusing primarily on the determinantsofbusinesscycleduration(e.g.,Owyangetal.,2005;HamiltonandOwyang,2012; Francis et al., 2018). While Eo and Morley (2022) estimate a three-regime Markov-switching modelwithtworecessiontypesfortheaggregateeconomybasedonGDPgrowth, ourstudy focusesonregionalheterogeneity,inferringrecessionexperiencesfrompayrollemployment growthforeachstate. Thisstate-specificapproacheffectivelyidentifieseachstate’sbusiness cycle phases and recovery shapes, fully capturing regional heterogeneity in business cycles and their determinants in structural factors. To the best of our knowledge, this paper is the firsttoapplyaMarkov-switchingmodelwithtwotypesofrecessionstostate-leveldataandto investigatethesourcesofrecoveryshapes. Thispaperisorganizedasfollows. Section2describesthedatausedintheempiricalanalysis. Section3explainsourstrategyforidentifyingstate-levelrecoveryshapesandpresentsthe empiricalfindingsontheirheterogeneouspatterns. Section4documentsthekeycharacteristicsofthetwotypesofrecessions,withafocusontheirassociationswithkeymacroeconomic variables. Section5examinestheroleofdownwardnominalwagerigidityindrivinghysteresis. Section 6 analyzes how downward nominal wage rigidity influences the effectiveness of policyinterventionsinmitigatinghysteresis. Section7validatesourempiricalfindingswithina NewKeynesianframeworkthatincorporateshysteresisanddownwardnominalwagerigidity. Section8concludes. 2 Data Section2.1discussesstate-levelpayrollemploymentdata. Section2.2outlinesobservedstatelevelattributesincludingthemeasureofnominalwagerigidity. 2.1 State-levelEmploymentData Asameasureofstate-leveleconomicactivity,weusenonfarmpayrollemploymentgrowthby stateforseveralreasons. First,jobgainsareamongthemostfrequentlycitedcyclicalindicators (e.g.,Abrahametal.,2013).6 Second,monthlypayrollemploymentdataareavailablefrom1960. 6Owyangetal.(2015)mentionthatpayrollemploymentisthebroadestmeasureofeconomicactivity. 5

Identifyinghysteresisseparatelyfromabounce-backfullrecoveryandestimatingitsevolution requiresmonthlyorquarterlydatawithasampleperiodlongenoughtocapturethesufficient numberoftworecessionepisodes. Giventhateconomicrecessionsarerareevents,losingafew recessionsisfairlycostlyfortheidentificationoftworecessiontypes,andhencealongersample periodenhancestheprecisionofestimates. Inthissense,thestate-levelpayrollemployment dataareidealforourempiricalanalysis. Alternatively,onemightconsiderstate-leveloutputdata orunemploymentratesfromtheLocalAreaUnemploymentStatistics. However,quarterlystatelevelGDPdataareonlyavailablefrom2005,andstate-levelnominaloutputdataareavailable from1963,butonlyatanannualfrequency. Inaddition,state-levelunemploymentandlabor force participation rates are available monthly, but only from1976 onward, omittingseveral importanteconomicrecessionsthatoccurredbetween1960and1975.7 For these reasons, previousresearchonregional businesscycles has frequently reliedon payrollemploymentgrowthtoanalyzestate-levelbusinesscycles(e.g.,HamiltonandOwyang, 2012). We convert the monthly data to a quarterly frequency to align with the time frame commonlyusedinthepreviousliteratureonbusinesscycles. Thesampleperiodspansfrom 1960:Q1to2023:Q4. Figures B1 - B2 in the appendix display nonfarm payroll employment growth (red lines) anditslong-runtrend(blueline)bystate. Panel(a)alsodisplaysthenationalpayrollgrowth. Whilestatesexhibitcommonprocyclicalvariationinthepayrollgrowth,theydifferinboththe magnitudeandtheshapeoftheirrecoveries. Additionally,somestatesexperiencedecelerations inpayrollemploymentnotseenelsewhere. Forinstance,Louisiana(Panel(t)inFigureB1)saw asharpdeclineinitspayrollemploymentin2005duetoHurricaneKatrina. Similarly,dueto theboomandsubsequentbustofshaleoilproduction,NorthDakota(Panel(j)inFigureB2) experiencedarapidpayrollgrowthaftertheGreatRecession,followedbyaprolongeddeclinein itspayrollemployment. 2.2 AttributesofStates: DownwardNominalWageRigidity Thissectionexaminesstate-levelcovariatesthatareincludedinouranalyses. First, as a measure of downward nominal wage rigidity, we employ the fraction of zero 7Employmentdataarerelativelyfreefrommeasurementerrorsthathavecyclicalfeaturesrelativetounemploymentrateandlaborforceparticipationrate(AhnandHamilton,2022),whichisanadditionalbenefitofusingthe employmentdatafortheidentificationofrecessiontypes. 6

nominalwagechangesoutoftotalwagechangesbystateconstructedbyJo(2024). Basedon the Current Population Survey (CPS, 1979–2018), Jo measures the share of workers with no changesinhourlywages,withhourlywagecuts,andwithhourlywageincreasesbystate. These threestatistics,summarizingthenominalwagechangedistribution,showasymmetrybetween wageincreasesandcutsandaspikeatzero,whichtheauthorinterpretstorepresentdownward nominalwagerigidity.8 Thethreesharesshowsufficientvariationacrossstatesandovertimeto permitstate-levelanalysesonthepropagationofpolicyshocksorbusinesscycles(Jo,2024;Lee, 2025). Asadditionalstate-levelattributes,weconsiderfactorsreflectingindustrystructuresuchas oilproductionandtheemploymentsharesofmanufacturing,professionalandbusinessservices, and finance. Specifically, we construct an indicator variable for oil-producing states, which takesthevalueofoneifastatehaspositiveoilproductionandzerootherwise. Fortheother industrymeasures,weusetheindustry’semploymentshareoutofthestate’snonfarmpayroll employment.Forunionmembership,weusethefractionofworkerswhoareunionmembersout ofthestate’snonfarmpayrollemployment.9 Asaproxyformarketcompetitionormonopsony power,weusethefractionofworkersemployedbyfirmswith500ormoreemployees.Inaddition, weincludeindicatorsforCensusregionstoaccountforheterogeneityacrossbroadergeographic areas. Wealsoconsiderthegendergapinlabormarketoutcomes,measuredbythedifferencein theemployment-to-population(EPOP)ratiobetweenmenandwomen. Inaddition,wetakestate-specificpolicyvariablesintoconsideration,includingtheminimum wageandthetax-to-incomeratio(forastate’sminimumwage,weusethehigherofthestate-level minimumwageandthefederalminimumwage). Detailedinformationonthesourcesofthe state-leveldataisprovidedinAppendixB. Forstate-levelinflationinnontradables,tradables,andallcategories,weusetheestimates fromHazelletal.(2022). Wealsoemploythestate-levelmacroeconomicdatasetcompiledby JoandZubairy(2025),whichincludesnominalgrossstateproduct(GSP),employmentlevels, 8Theestimatesarefoundintheauthor’swebsite(https://sites.google.com/view/yoonjoojo/rsearch). 9Fortheemploymentsharesofthethreeindustries,weuseBEA’sannualnonfarmwage-and-salaryemployment anditsindustrybreakdownbasedontheSICclassification(1969–2001).Thesedataexcludeproprietors’employment (self-employment)andthereforeconceptuallyalignwithCES(establishment)employmentmeasures,whichdoes notincludetheself-employed.Forthemorerecentperiod,weusenonfarmpayrollemployment(CESconcept)from theBLS’StateandMetroAreaEmployment,Hours,&Earnings,whichispartoftheCESprogram.Althoughthese dataareavailablebeginningin1990,weusethissourcetocomputetheindustryemploymentsharesonlyfrom2002 onward,correspondingtotheyearsforwhichtheBEAsectoraldataareunavailable.Weaddresspotentialstructural breaksarisingfromthechangeindatasourcebyincludingtimefixedeffects,asdiscussedfurtherinSection5. 7

andtheconsumerpriceindexatanannualfrequencytoconstructstate-levelrealGSPandlabor productivity. For externally identified policy shocks, we use monetary policy shocks from Romer and Romer(2004),asextendedbyWielandandYang(2020),andtaxshocksconstructedbyRomer andRomer(2010).10 3 The Shapes of Recoveries at the State Level Section3.1presentsthemodelandtheidentificationofthetworecessiontypes. Section3.2 describesourestimationprocedure. Section3.3reportsthenational-levelresults,andSection 3.4reportsthestate-levelresults. 3.1 ModelandIdentification ToidentifytheshapesofrecessionrecoveriesacrossU.S.states,weemploytheMarkov-switching model of business cycles from Eo and Morley (2022). The model allows a given recession to eitherpermanentlyalterthelevelofemployment(i.e.,anL-shapedrecession)oronlyhavea temporaryeffect(i.e.,aU-shapedrecession). AnL-shapedrecoveryischaracterizedbyaninitial declineineconomicactivity, followedbyanexpansionthatdoesnotrestoreemploymentto itspre-recessionlevel. Incontrast,aU-shapedrecoveryalsobeginswithasharpdeclinebutis followedbyastrongrebound,duringwhichgrowthtemporarilyexceedsitspre-recessionpace, allowingtheeconomytoreturntoitstrendgrowthpath. IllustrationsofL-shapedandU-shaped recoveriesareprovidedinFigure1. Thechangeinpayrollemploymentatthestatelevelisassumedtofollowafirst-orderMarkovswitchingprocesswiththreeregimes: expansion,U-shapedrecession,andL-shapedrecession. 10Sincemonetarypolicyshocksidentifiedfromhigh-frequencydataareonlyavailablefromthelate1980s,we useRomerandRomer(2004)’sestimates,whichcoveralongersampleperiodstartingin1969.Fortaxshocks,Lee (2025)constructstate-levelaveragemarginaltaxshockestimatesandcorrespondinginstrumentalvariablesfor theperiod1980–2000.However,theseseriesareannualandthusnotdirectlyapplicabletoourempiricalanalysis withoutstrongassumptionsregardingthefrequencyortimingoftheshocks.Therefore,forthesakeoftransparency, wedirectlyemployaggregatetaxshockestimatesfromRomerandRomer(2010). 8

Figure1:ILLUSTRATIONOFL-SHAPEDANDU-SHAPEDRECOVERIES U-shape L-shape -6 -4 -2 0 2 4 6 8 10 12 Notestofigure:TheX-axisdenotesperiodsafterrecession.Theblackdottedlineindicatesthehypothetical employmentlevelifarecessionhadnotoccurred.Theshadedarearepresentsperiodsofrecession. Source:Authors’calculation. Forthegeographicstatei, ∆y −µ˜ =µ + µ ·χ ·1(S =L) i,t i,t i,E i,L i,t i,t m (cid:88) + µ i,U ·χ i,t ·1(S i,t =U)+λ i · χ i,t−k ·1(S i,t−k =U) k=1 + χ ·e , e ∼i.i.d.N (cid:161) 0,σ2(cid:162) (3.1) i,t i,t i,t i where∆y isthequarterlygrowthrateofpayrollemploymentforstatei, S =E,L,U isthe i,t i,t regimeindicator,withS =E correspondingtotheexpansionregime,S =LtotheL-shaped i,t i,t recoveryregime,andS =U totheU-shapedrecoveryregime,1(·)isanindicatorfunction,and i,t µ ,µ ,andµ aretheconditionalmeansfortherespectiveregimes. Thebouncebackeffect i,E i,L i,U λ represents the strong recovery over m quarters for t+1,...,t+m following the U-shaped i recessionshock,µ ,attimet,suchthatλ ·m+µ =0. Therefore,λ iscalibratedasaformof i,U i i,U i therestrictionwithoutestimation. Toaccountforstate-specificchangesinlong-runtrendemploymentgrowth,weuse“dynamicdemeaning”foremploymentgrowth.11 Dynamicdemeaning isessentiallythe10-yearmovingaverageofemploymentgrowth: µ˜ i,t ≡ 4 1 0 (cid:80)3 j 9 =0 ∆y i,t−j .12 11EoandMorley(2022)considerthistreatmentintheirrobustnessanalysis.Relatedly,seeEoandKim(2016)for adiscussionoftheimportanceofallowingfortimevariationinlong-runtrendgrowthwhenestimatingMarkovswitchingmodelsofthebusinesscycle. 12Kamberetal.(2018)providesin-depthdiscussionontheusefulnessofdynamicdemeaningandthechoiceof10 9

Moreover,toaddressextremeoutliersarisingfromtheCOVID-19pandemic,asshownin Figure2,weadoptadecayfunctionfollowingLenzaandPrimiceri(2022)andEoandMorley (2023). Thescalingparameterχ isspecifiedasfollows. Fortheperiodpriortotheonsetof i,t the COVID-19 pandemic (t ∗ =2020Q2), we set χ =1 for all t <2020Q2. After this period, i,t weemployascalingfactordefinedasχ i,t∗+j =c i +(1−c i )ρ i j ,where j denotesthenumberof periodssincethepandemicbegan,reflectingthegradualdeclineinthesizeofCOVID-19shocks. We estimate these parameters without imposing any restrictions on their values and do not preassignthemtoanyparticulartypeofrecessionexante.Thedecayparameterρ isconstrained i toliebetween0and1duringestimation. Foremploymentgrowthduringcontractionaryregimes,wesettheconditionalmeanstoµ i,L andµ forL-shapedandU-shapedrecessions,respectively,whent <2020Q2,andto(χ µ ) i,U i,t i,L and(χ µ )otherwise.Accordingly,thebouncebackeffectfortheU-shapedrecoveryisdefined i,t i,U asλ i,t−k =−µ i,U /m fort <2020Q2,andλ i,t−k =−χ i,t µ i,U /m otherwise. The indicator S is a latent Markov-switching reggime variable governed by transition i,t probabilitieswheretheprobabilityofmovingfromregimek attime t−1toregime j attime t isPr[S i,t = j |S i,t−1 =k]=p i,kj fork,j ∈{E,L,U}. Inaddition,weruleoutdirecttransitions betweenL-shapedandU-shapedrecessionregimes,requiringthatanymovementbetweenthem passesthroughanexpansionaryregime. Thisrestrictionisimposedas p i,LU =Pr[S i,t =U |S i,t−1 =L]=0, p i,UL =Pr[S i,t =L|S i,t−1 =U]=0. Therefore,theregimetransitionmatrixforstatei isgivenby   1−p −p p p i,EL i,EU i,EL i,EU   Π i =  1−p i,LL p i,LL 0   ,   1−p 0 p i,UU i,UU wherethesumofelementsinthekthrowsatisfies (cid:80) j∈{E,L,U} p i,kj =1. Forexample, the(1,1) elementofthematrixisp =1−p −p . i,EE i,EL i,EU yearswindow. 10

Figure2:NONFARMPAYROLLEMPLOYMENTGROWTHATTHENATIONALLEVELANDINVIRGINIA PanelA.NationalLevel 5 0 -5 -10 -15 1960 1970 1980 1990 2000 2010 2020 PanelB.Virginia 5 0 -5 -10 1960 1970 1980 1990 2000 2010 2020 Notestofigure:Thefiguresplotnonfarmpayrollemploymentgrowthatthenationallevel(PanelA)andinVirginia (PanelB).Theredlinerepresentsthepayrollemploymentgrowth,whilethebluedashedlineshowsthelong-run growthrate,calculatedusinga40-quarterrollingaverage. Source:BLS,Haver,andauthors’calculation 3.2 BayesianEstimation Thelengthofthepost-recessionbounce-backperiodwassettom=5quartersfollowing Eo andMorley(2022).13 ThemodelparametersareestimatedusingaBayesianapproach,which accommodates the irregular likelihood function inherent in regime-switching models. This estimation strategy is selected for its robustness in capturing parameter uncertainty and its capacitytoincorporatepriorinformation(Owyangetal.,2005). 3.2.1 Priors (cid:161) (cid:162) Thepriordistributionforthetransitionprobabilitiesfromtheexpansionregime p ,p ,p E,E E,L E,U followsaDirichletdistributionwithparametersDirichlet(36,1,1),whilethosefortheL-shaped 13Asarobustnesscheck,weconsideralternativevaluesform,andtheresultsremainrobusttothesealternative values. 11

andU-shapedrecessionregimes (cid:161) p ,p (cid:162) followaBetadistributionwithparametersBeta(5,1).14 L,L U,U Thepriordistributionsfortheconditionalmeans (cid:161)µ ,µ ,µ (cid:162) aregivenbyNormal(1,1),Normal(−2,1), E L U and Normal(−2,1), respectively. The prior distributions for the scaling parameters (cid:161) c,ρ(cid:162) are Normal(5,1) and Beta(8,2), respectively. Finally, the prior distribution for the error variance σ2isgivenbyInverseGamma(10,5). Thesepriorsarerelativelydiffusetoallowforflexibilityin estimation. 3.2.2 MCMCProcedure ForBayesianestimation,weemployMarkovChainMonteCarlo(MCMC)samplingtechniques toestimatethemodelparametersineachstate. Fornotationalconvenience,wesuppressthe stateindicatori fromtheparameters. Specifically,Metropolis-Hastingssamplingwitharandom walk proposal is utilized for the COVID-19 scaling parameters, denoted as c and ρ. For the remainingparameters,Gibbssamplingisimplemented. Thepriorsforallparametersareset according to established and standard values found in the literature. The MCMC procedure involvesgenerating10,000draws,withtheinitial5,000drawsdiscardedasburn-instoensurethe convergenceofthesamplingprocess. Thissamplingapproachallowsforefficientexplorationof theposteriordistributionsoftheparameters,particularlygiventhehighdimensionalityofthe modelandthecomplexityintroducedbytheCOVID-19scalingparameters.LetY=(cid:169)∆y (cid:170)T ,Θ≡ t t=1 (cid:161)µ ,µ ,µ ,σ2(cid:162) ,P≡(cid:161) p ,p ,p ,p (cid:162) ,S={S }T ,andΓ=(cid:161) c,ρ(cid:162) . Thefollowingsummarizes E L U E,L E,U L,L U,U t t=1 theposteriorsamplingalgorithm. MCMCSamplingProcedure • Step1: GibbsSamplingΘ|Y,S,Γ • Step2: GibbsSamplingS|Y,Θ,Γ,P • Step3: GibbsSamplingP|S • Step4: Metropolis-HastingsSamplingΓ|Y,S,Θ IntheMetropolis–Hastingsalgorithm,weaimforanacceptancerateforthescalingparameters (cid:161) c,ρ(cid:162) between0.15and0.40.15 14Thesepriorsimplythattheexpecteddurationofexpansionsis19quarters,whiletheexpecteddurationsof L-shapedandU-shapedrecessionsareboth6quarters. 15Gelmanetal.(1997)suggestanoptimalacceptancerateof0.234witharandomwalkproposal. 12

Figure3:NATIONALLEVELRECESSIONPROBABILITIES PanelA.NonfarmPayrollEmploymentGrowth 1 0.8 0.6 0.4 0.2 0 1960 1970 1980 1990 2000 2010 2020 PanelB.GDPGrowth Notestofigure:ThefiguresdisplaytheprobabilitiesofL-shapedandU-shapedrecessionsatthenationallevel, estimatedusingnonfarmpayrollemploymentgrowth(PanelA)andrealGDPgrowth(PanelB).Thebluelines representtheprobabilityofaU-shapedrecession,whiletheredlinesrepresenttheprobabilityofanL-shaped recession.TheY-axisindicatestheprobability,andtheX-axisrepresentscalendartimeinquarter. Source:Authors’calculation 3.3 NationalLevel Figure 3 presents the national-level recession probabilities estimated based on the payroll employmentgrowth(PanelA)andtherealGDPgrowth(PanelB).Wecomparethetwonationallevel estimates to investigate the extent to which payroll employment and real GDP provide consistentsignalsaboutbusiness-cyclephases. Afewimportantpointsareworthnoting. First,theemployment-basedestimatescloselyalignwiththeNBERrecessiondates,highlightingtheirtimelinessandeffectivenessinidentifyingphasesofthebusinesscycle. Oneexception isthesecondwaveofCOVID-19. AlthoughbothestimatesandtheNBERrecessionchronology agreeonthepandemicrecessionitself,theemployment-basedestimateinterpretsthesecond waveasanotherU-shapedrecessionthatislessseverethanthepandemicrecession. Incontrast, theGDP-basedestimateandtheNBERrecessionchronologybothclassifythesecondwaveas 13

partofexpansion. Indeed,consistentwiththeemployment-basedestimate,initialunemploymentclaimsincreasedbetweenNovember2020andJanuary2021. Thisdiscrepancyunderscores theusefulnessofpayrollemploymentinassessingthecyclicalpositionoftheeconomy. Second,overall,L-shapedrecessionsaremorepronouncedinemploymentgrowththanin realGDPgrowth,possiblyreflectingthephenomenonofjoblessrecoveries,apatternthatbecomesincreasinglyevidentsincethe1990s.16 Notably,theemployment-basedestimateclassifies theGreatRecessionasanL-shapedrecession,whiletheGDP-basedestimatecategorizesitas aprolongedU-shapedrecession. FollowingtheGreatRecession,bothoverallandlong-term unemploymentrecoveredslowly,takingnearlyadecadetoreturntopre-recessionlevels. AlthoughtheGDP-basedestimatelabelstherecessionasU-shaped,itstillindicatesarecovery durationofapproximatelyfiveyears,thelongestonrecord.17 Incontrast,theemployment-based estimateclassifiesitasL-shaped,capturingnear-permanentemploymentlossesthatalignwith theprolongedweaknessinbothlabormarketandoutputrecoveryintheyearsthatfollowed. 3.4 StateLevel Figure4presentsheatmapsillustratingtheevolutionofrecessionprobabilitiesacrossallstates.18 Thefigurehighlightsvariationinthetypesofrecessionsacrossstatesandovertime,revealing severalnotablepatterns. First,roughlyhalfofthestatesexhibitrecessionpatternsthatarebroadlyconsistentwiththe nationalrecessionsidentifiedbytheNBER,whileothersshowdeviations,eithermissingsome national recessions or experiencing additional episodes not recognized at the national level. Statesalsodifferinboththeshapeandtimingoftheireconomicdownturns. Asanexample, Figure5showstheestimatedrecessionprobabilitiesfortwostates: NewYorkandWisconsin. NewYorkdidnotexperiencerecessionsduringthe1980s,whereasWisconsin,astatewithalarge manufacturingsector,underwentpronouncedL-shapedrecessions. Incontrast,NewYorkfaced anL-shapedrecessionintheearly1990s,whileWisconsindidnotexperienceadownturnduring thatperiod.19 Moreover,somestatesundergoindependenteconomicdownturnsnotsharedby 16JaimovichandSiu(2020)showthatthedecliningemploymentshareofroutineoccupationshasdrivenjobless recoveries. 17ForestimatesofpotentialoutputandtheirimplicationsforassessingtheimpactoftheGreatRecession,see CoibionandUlate(2018). 18Thefullsetofstate-levelrecessionprobabilityestimatesisprovidedinFiguresC3andC4intheappendix. 19BothNewYorkandWisconsinexperiencedU-shapedrecessionsduringtheCOVID-19pandemic. In2021, NewYorkunderwentapronouncedL-shapedrecession,reflectingseveredamageinsectorssuchashospitality, 14

Figure4:PROBABILITIESOFL-ANDU-SHAPERECESSIONSACROSSSTATESOVERTIME PanelA.L-shape PanelB.U-shape Notestofigure:ThefiguresshowtheestimatedprobabilitiesofstatesexperiencingL-shapedrecessions(PanelA) andU-shapedrecessions(PanelB).TheY-axisrepresentsthestates,whiletheX-axisgivescalendartime.Darker colorsineachheatmapindicatehigherrecessionprobabilities,asshowninthecolorlegends. Source:Authors’calculation 15

Figure5:L-SHAPEDANDU-SHAPEDRECESSIONPROBABILITIES: NEWYORKANDWISCONSIN PanelA.NewYork 1 0.8 0.6 0.4 0.2 0 1960 1970 1980 1990 2000 2010 2020 PanelB.Wisconsin 1 0.8 0.6 0.4 0.2 0 1960 1970 1980 1990 2000 2010 2020 Notestofigure:ThefiguresdisplaytheestimatedprobabilitiesofL-shapedandU-shapedrecessionsforNewYork state(PanelA)andWisconsin(PanelB).ThebluelinesrepresenttheprobabilityofaU-shapedrecession,whilethe redlinesrepresenttheprobabilityofanL-shapedrecession.TheY-axisindicatestheprobability,andtheX-axis representscalendartimeinquarter.TheshadedareasdenotetheNBERrecessions. Source:Authors’calculation others,asshownbyisolateddarkdotsinbothheatmaps(Figure4). Forexample,NorthDakota experiencedanL-shapedrecessionin2015duetoasharpdeclineinoilprices,whileLouisiana facedaU-shapedrecessionin2005duetoHurricaneKatrina. Overall,thesepatternshighlight substantialheterogeneityintheincidenceandnatureofrecessionsacrossstates,indicatingthat regionalbusinesscyclesdonotalwayscoincidewiththenationalones. Second,U-shapedrecessionsbecamelessfrequentafterthe1990s,apatternthatiswidespread acrossstates(PanelBofFigure4).Thispatterncoincideswiththeincreasedprevalenceofjobless recoveriesinthelabormarket. Nevertheless,itisimportanttonotethatourmodelidentifies theCOVID-19recessionasaU-shapedrecessionratherthananL-shapedoneformoststates, effectivelycapturingthesharp,short-lived,andrapidlyevolvingnatureofthepandemic-induced tourism,retail,andcommercialrealestate.Meanwhile,WisconsinexperiencedamilderU-shapedrecessionafter thepandemicrecession. 16

downturn. Insum,thestate-levelrecessionprobabilitieshighlightsignificantheterogeneityinbusinesscycleexperiencesandhysteresisacrossstates. Buildingonthisvariation,weexplorethedrivers ofhysteresisusingobservablestate-levelcharacteristicsinthesubsequentsections 4 Features of U- and L- Shaped Recessions Thissectiondiscussesthecharacteristicsofthetwotypesofrecessions. Section4.1exploresthe rolesofsupplyanddemandfactorsinshapingU-andL-shapedrecessions,whileSection4.2 analyzestheireffectsonlabormarketoutcomesandbroadermacroeconomicvariables. 4.1 SupplyandDemandShocks To examine the extent to which supply and demand factors drive each type of recession, we considerthefollowingmodel: p j =βj Is +βj Id +γjg +αj +ϵj for j ∈{l,u}, (4.1) it s it d it it i it wherepl andpu aretheprobabilitiesthatstatei experiencesL-shapedandU-shapedrecessions it it inquartert,respectively,obtainedfromtheestimatesdescribedinSection3. Thesupplyfactor indicator,Is ,equalsoneifboththeunemploymentrateandpriceinflationinstatei increasein it quartert,andzerootherwise. Thedemandfactorindicator,Id,equalsoneiftheunemployment it rateincreaseswhilepriceinflationdecreasesinstatei duringquartert,andzerootherwise. We usestate-leveltotalinflation,includingpricesofbothtradablesandnontradables,fromHazell etal.(2022). Theparametersβj andβj denotethecoefficientsofIs andId,respectively. We s d it it further examine the magnitude of the recessionary shock, g , to account for the possibility it thatL-shapedrecessionsaremorelikelytoresultfromlargershocks. Specifically,wemeasure the magnitude of the shock using the absolute value of changes in the unemployment rate, interactedwiththeprobabilityofbeinginarecession(i.e.,thecombinedprobabilityofU-shaped andL-shapedregimes). Theparameterγj isthecoefficientof g . Thesampleperiodspans it 1978:Q1–2017:Q4,consistentwiththeavailabilityofstate-levelCPIdatafromHazelletal.(2022). Table 1 reports the estimated effects of supply and demand factors on recession shapes. Overall,bothsupplyanddemandfactorscontributesignificantlytothelikelihoodofL-shaped 17

Table1:EFFECTSOFSUPPLYANDDEMANDFACTORS (1)pl (2)pu (3)pl (4)pu it it it it [1]βj (Is ) 0.042*** 0.010*** 0.020*** 0.002** s it (0.002) (0.001) (0.002) (0.001) [2]βj (Id) 0.088*** 0.014*** 0.024*** 0.003*** d it (0.004) (0.002) (0.002) (0.001) [3]γj (g ) 0.739*** 0.127*** it (0.006) (0.003) ✓ ✓ ✓ ✓ StateFE No.ofobs. 12,189 12,189 8,925 8,925 R2 0.064 0.029 0.701 0.252 Notestotable:ThistablepresentsthecoefficientestimatesfromEquation(4.1).Thevariablesinparentheses denotetheregressorscorrespondingtoeachcoefficient.StateFEdenotesstatefixedeffects.Thenotation***,**, and*indicatesstatisticalsignificanceatthe1%,5%,and10%levels,respectively.Numbersinparenthesesare standarderrors. Source:Authors’calculation. as well as U-shaped recessions. In addition, L-shaped recessions tend to be associated with largershocks: thecoefficientong fortheL-shapedrecessionprobabilityissubstantiallylarger it thanthatfortheU-shapedrecessionprobability(columns3–4). Itisalsonoteworthythatthe responsivenessoftheL-shapedrecessionprobabilitytothedemandfactor(βl )isthelargest d amongthefourcoefficients(βl ,βl,βu,βu),regardlessofwhetherg isincludedornot. Withg , d s d s it it βl ismarginallylargerthanβl,thesupplyfactor’seffectontheL-shapedrecessionprobability; d s withoutg ,βl isroughlytwiceaslargeasβl.Thispatternisconsistentwiththehysteresistheory it d s of Blanchard (2018), which posits that negative demand shocks can have persistent adverse effectsoneconomicactivity. 4.2 MacroeconomicOutcomesofU-andL-shapedRecessions Thissectionexaminesthepost-recessionmacroeconomicoutcomesofU-shapedandL-shaped recessions,overthefourquarters(oneyear)followingeachrecessionepisode.20 Considerthefollowingmodel: y i,t+4 −y it =β u p i u t +β l p i l t +α i +e i,t+4 , (4.2) where y i,t+4 −y i,t capturesthechangeinstatei’smacrovariableofinterestbetweenquarterst 20Weconsidertheone-yearhorizon, becausethebounce-backphaseofaU-shapedrecessionissettobe5 quarters. 18

Table2:POST-RECESSIONDYNAMICSOFMACROECONOMICVARIABLES y (1)Log (2)EPOP (3)Total (4)Tradables (5)Nontradables it RealGSP Ratio PriceInflation Inflation Inflation β (pu) -0.046*** -1.627*** 1.321*** 1.037*** 1.734*** l it (0.003) (0.098) (0.319) (0.368) (0.386) β (pl ) 0.112*** 3.009** -3.696*** -5.093*** -2.391 u it (0.008) (0.341) (1.253) (1.448) (1.517) ✓ ✓ ✓ ✓ ✓ StateFE No.ofObs. 11,220 8,772 4,479 4,479 4,479 R2 0.057 0.036 0.043 0.022 0.047 Notestotable:ThistablereportsthecoefficientestimatesfromEquation(4.2).Thedependentvariablesarethe annualchangeinlogoutput(yearlydata)andthefour-quarterchangeintheEPOPratioandfour-quarterchanges intheinflationratesoftotal,tradable,andnontradablegoods(quarterlydata)forcolumns(1)–(5),respectively.The notations***,**,and*indicatestatisticalsignificanceatthe1%,5%,and10%levels,respectively.Numbersin parenthesesarestandarderrors. Source:Authors’calculations. andt+4;β andβ arethecoefficientsonpu andpl ,respectively;α isastatefixedeffect;and u l it it i e i,t+4 isthepredictionerror. Ouranalysisfocusesonthepost-recessiondynamicsoflogrealgrossstateproduct(GSP), EPOPratio,andinflationratesoftotal,tradable,andnontradablegoods. TherealGSPismeasuredannually,sothedependentvariableistheannualoutputgrowth(yearlydata). Theother variablesareavailablequarterly,andhenceweconsiderfour-quarterchangesintheEPOPratio andfour-quarterchangesintheinflationratesoftotal,tradable,andnontradablegoods. The state-level inflation, measured in four-quarter percent changes, are taken from Hazell et al. (2022).21 Table2 summarizes the estimatedmacroeconomiceffectsof L-shaped and U-shaped recessions. Itisnotablethatthetwotypesofrecessionsexhibitoppositeeffectsontheoutput growth: anL-shapedrecessionlowersoutputoneyearahead,whereasaU-shapedrecession raisesit(column1). AsimilarpatternemergesfortheEPOPratio(column2),consistentwith thewell-documentedfeaturesofmacroeconomichysteresis(e.g.,Furlanettoetal.,2025).22 In addition,thetwotypesofrecessionsalsodisplaycontrastingeffectsonpriceinflation. While L-shapedrecessionsincreasetotalpriceinflationoneyearahead,U-shapedrecessionslowerit (column3). Thispatternisprimarilydrivenbytradables(column4)and,toalesserextent,by 21Inthisexercise,weconsiderinflationratesratherthanpricelevelsbecausepriorstudiesonthePhillipscurve (e.g.,Hazelletal.,2022)relatetheinflationratetotheleveloftheunemploymentrate(thelevelofeconomicactivity). 22Comparableresultsarefoundforthelaborforceparticipationrate(LFPR),andbothEPOPratioandLFPRby gender(seeAppendixD). 19

nontradables(column5). ThesefindingssuggestthatL-shapedrecessionsarelikelytolowerpotentialoutputorraise structuralunemploymentand,ceterisparibus,widentheoutputgapornarrowtheunemploymentrategap,therebyputtingupwardpressureoninflation. Incontrast,U-shapedrecessions— being less likely to induce structural changes—tend to reduce the output gap or widen the unemploymentrategap,consequentlyexertingdownwardpressureoninflation. 5 Downward Nominal Wage Rigidity and Hysteresis This section examines the role of downward nominal wage rigidity (DNWR) in hysteresis (Lshaped recession). Section 5.1 outlines the econometric methodology for this analysis; Section5.2presentsanddiscussestheestimationresults. 5.1 LinearCompetingRisksModel Inthissection,weexaminetheextenttowhichanobservablestate-levelfactor,suchasDNWR, influence the likelihood of L-shaped relative to U-shaped recessions. In general, when the dependentvariableisanunobservedprobabilityacrossthreeormorecategoricaloutcomes, acompetingrisksframeworkisused,typicallyimplementedasamultinomiallogitmodel. In suchmodels,outcomeprobabilitiesareinferredfromobservedcountsofoutcomes. Inourcase, however,theprobabilitiesofthethreebusinesscyclephasesaredirectlyobserved. Accordingly, weestimatealinearcompetingrisksmodelusingOLS,wherethedependentvariableisdefined asthedifferenceinprobabilitiesofthetwotypesofrecessions.23 ConsiderthefollowingmodelfortherelativeriskofanL-shapedrecessioncomparedtoa U-shapedrecession: (cid:179) (cid:180) pl −pu =β pe +β Zr +Γ X +α +D +ϵ . (5.1) it it e it z it x it i t it 23Whilethemultinomiallogitmodelcanbenumericallychallengingtoestimate,particularlywhenitincludes alargenumberofparameters,thelinearcompetingrisksmodelavoidssuchdifficulties.Forexample,individual fixedeffectscanbereadilyincorporatedintothelinearmodelusingstandardpanelregressiontechniques.Such atreatmentisofteninfeasibleinamultinomiallogitframework,asnumericaloptimizationfrequentlyfailsto convergeinthepresenceofahigh-dimensionalparameterspace.Inthisregard,thelinearcompetingrisksmodel enablesthecomprehensiveinclusionofstate-levelcovariateswithinacoherentstatisticalframework,allowingfor theanalysisofthedeterminantsofhysteresiswithoutimposingsignificantcomputationalburdens. 20

Intheaboveequation,weincludepe ,theestimatedprobabilityofbeinginanexpansion,to it controlforbusinesscyclephases,asthedependentvariabletendstoapproachzerobothduring expansionsandduringeconomicdownturnswhentheprobabilitiesofthetworecessiontypes canbesimilar.24 Thecoefficientonpe isdenotedbyβ . it e OurmainfocusisonDNWR.ToevaluatetheeffectofDNWRontherelativerisk,weconstruct anindicatorofgreaterDNWR,denoted Zr ,asfollows. Wefirstconstruct Z ,anindicatorof it it greaternominalwagerigidity,whichequalsoneifthechangeintheshareofzeronominalwage inflation at time t exceeds the cross-state average at t, and zero otherwise. This state-level indicatorcaptureslargernominalwagerigidityrelativetothecross-stateaverage. SinceDNWR is primarily relevant during economic downturns, we interact Z with the state’s recession it probability(1−pe )toproduceZr ,anindicatorofgreaterdownwardnominalwagerigidity.25 it it ThevectorX containscontrolvariablescapturingstate-specificattributes,andΓ denotes it x the vector of corresponding coefficients. Additional control variables are listed in the panel labeled“Controls”inTable3,withdetailsoneachmeasureprovidedinSection2.2.26 Theterm α representsthestatefixedeffect,D thetimefixedeffect,andϵ theresidual. i t it Thesampleperiodspans1978:Q1–2019:Q4,basedontheavailabilityoflarge-firmsharedata beginningin1978:Q1. Weexcludethepandemicperiodfromtheanalysis,asthecorrelations betweentheregressorsandrecessionprobabilitiesduringthattimecansubstantiallydifferfrom pre-pandemicpatterns. 5.2 EstimationResults Table3summarizestheestimationresultsforthemodel’sabilitytodistinguishbetweenL-shaped andU-shapedrecessions. Tobeginwith,themodeleffectivelycapturestherelativeprobability ofanL-shapedrecessioncomparedtoanU-shapedrecession,withanR2around0.8. ItisnotablethatgreaterDNWR(Zr )significantlyincreasesthelikelihoodofanL-shaped it recession relative to a U-shaped one. This relationship is robust across both the full sample andthepost-2000subsample. Weconsiderthepost-2000periodtoexaminetheroleofDNWR 24Onemightconsiderconstructingavariablebydividingthedependentvariablebype .However,thismeasureis it undefinedwhenpe iszeroornearzero.Toaddressthisissueandaccountforbusiness-cycleeffects,weinstead it includepe asaregressorinthemodel. it 25Wedonotincludetheindicatorofnominalwagerigidityduringeconomicexpansions,asanincreasedshareof zerowagechangesinexpansionsmayalsoreflectupwardnominalwagerigidity. 26Weincludethestate-levelgendergapinthelabormarketasitisconsideredasanimportantfactorforthe macroeconomichysteresis(e.g.,Fukuietal.,2023). 21

Table3:EFFECTSOFDNWRONTHERELATIVERISKSOFRECESSIONS (1)All (2)2000-2019 IndicatorofDNWR 0.062*** 0.052*** (Zr ) (0.009) (0.009) it (Controls) pe ✓ ✓ it ✓ ✓ gendergap ✓ ✓ oil-producing ✓ ✓ minimumwage ✓ ✓ union ✓ ✓ manufacturing ✓ ✓ prof. services ✓ ✓ finance ✓ ✓ large-firmshare ✓ ✓ tax-incomeshare ✓ ✓ Statefixedeffect ✓ ✓ Timefixedeffect No. ofObs. 8,256 3,856 R2 0.796 0.867 Notestotable:ThistablepresentsthecoefficientestimatesfromEquation(5.1).Thenotations***,**,and*indicate statisticalsignificanceatthe1%,5%,and10%levels,respectively.Numbersinparenthesesarestandarderrors.The panellabeled‘(Controls)’liststhecontrolvariablesincludedintheregressionmodel. Source:Authors’calculation. 22

duringtheperiodofslowedgenderconvergence,giventhatgenderconvergenceissignificantly associatedwiththestagnantrecessionrecoveriesinthelabormarket(e.g.,Fukuietal.,2023).27 The finding supports the central premise of previous research that DNWR constitutes a key mechanismthroughwhichhysteresiseffectsemerge. Taken together, the state-level evidence suggests that DNWR is an important source of hysteresisineconomicactivity.28 6 Effectiveness of Policy Interventions in Mitigating Hysteresis ThissectionevaluatestheextenttowhichDNWRaffectstheeffectivenessofmonetaryandfiscal policiesinmitigatinghysteresis. Section6.1providesanempiricalmodelforthisanalysisand Section6.2discussestheestimationresults. 6.1 Model WeexaminetheeffectsofmonetaryandtaxshocksontherelativelikelihoodofanL-shaped versus a U-shaped recession, depending on the degree of DNWR. To do so, we estimate the followingnonlinearlocalprojection: y i,t+h −y i,t−1 = αh i +βh 1 (s i,t−1 )z t +βh 2 (1−s i,t−1 )z t + (γh 1 ) ′ (s i,t−1 )x it +(γh 2 ) ′ (1−s i,t−1 )x it +ϵ i,t+h for h=1,2,3,···H,(6.1) where y i,t =(p i l t −p i u t )andhence(y i,t+h −y i,t−1 )captureschangesbetween t−1and t+h in therelativeprobabilityofanL-shapedrecessionoveraU-shapedrecession. Thenotationαh i capturesthestatefixedeffectathorizonh,s i,t−1 capturestheprobabilitythatstatei isinregime 1attimet−1,and(1−s i,t−1 )correspondstotheprobabilityofbeinginregime2attimet−1, which we will define below. The externally identified policy shock is denoted by z . We use t monetarymonetarypolicyshocksconstructedbyRomerandRomer(2004)andextendedby 27Wefindthatalargermale-femaleemploymentgapispositivelyassociatedwiththeriskofhysteresiswith statisticallysignificant.ThisresultisreportedinAppendixD. 28Asarobustnesscheck,were-estimatethemodelexcludingallcontrolsexceptforstateandtimefixedeffects, usingthesamesampleperiod.Overall,theresultsremainconsistent,withtheexceptionofthegendergapcoefficient, whichbecomesstatisticallyinsignificantforthe1978–2019period. However,thiscoefficientregainsstatistical significancewhenweincludetheemploymentsharesofthemanufacturingandprofessionalservicesindustries, suggestingthatgenderdifferencesarecorrelatedwiththeindustrycompositionofemployment. 23

WielandandYang(2020),alongwithtaxshocksfromRomerandRomer(2010). Sincethefocus isontheeffectsofexpansionarydemandpolicyshocks,weretainonlynegativerealizationsof monetaryandtaxshocks. Thecoefficientsβh andβh captureeffectsofanunexpectedpolicy 1 2 shock on the dependent variable h-quarter ahead after the shock’s impact in regimes 1 and 2,respectively. Negativevaluesofβh andβh indicatethatademandpolicyhelpstomitigate 1 2 hysteresis,whilepositivevaluesindicatethatitdoesnot. WesetH =12quarters. WeconstructtheregimeindicatorforDNWR(s )inamanneranalogoustotheindicator it used in equation (5.1). Specifically, we interact Z —the indicator of greater nominal wage it rigidity—with state i’s binary recession indicator at t. The recession indicator equals one if (1−pe )>0.2,andzerootherwise,forthemonetarypolicyexperiment. Fortheexperimentwith i,t taxshocks,weadoptathresholdof(1−pe )>0.15fortherecessionindicatortoequalone,and i,t zerootherwise.29 Accordingly,theDNWRindicatorisbinary: itequals1inregime1(s =1), it whenstatei exhibitsnominalwagerigidityabovethecross-stateaverageandisinrecessionin quartert,and0otherwise,denotingregime2(s =0).30 it Forthevectorofcontrolsx ,weincludeeightquarterlylagsofvariablescapturingstate-level it characteristics. Specifically,thesecontrolscomprisetheemploymentsharesinmanufacturing, finance,andprofessionalandbusinessservices;thetax-to-incomeratio;theemploymentshare of unionized workers; and the indicator of oil production. In addition, we include state i’s probabilityofbeinginanexpansionattime t toaccountforthescalingeffectofthecurrent business-cycle phase on the relative likelihood of recessions, in line with our treatment in equation(5.1).Asourprimaryinterestliesintheeffectsofmonetarypolicyshocksontherelative likelihoodofanL-shapedversusaU-shapedrecessionoutsideofexpansions,wecontrolfor eachstate’sconcurrentprobabilityofexpansion.31 Notethatwealsointeractx ,thevectorofstate-levelcontrolsatt,withthelaggedregime it 29ThepurposeofinteractingthetwoindicatorsistocharacterizeDNWR,whichisprevalentduringarecession, whileexcludingupwardnominalwagerigidity—alesslikelyoccurrenceduringaneconomicdownturn.Becausethe state-levelwagedataareannual,weusefour-quartermovingaveragesoftheexpansionprobabilitytoconstruct theDNWRindicatorforthisexperiment.Althoughthesethresholdsyieldthelargestdifferencesbetweenthetwo regimes,imposingthesamethreshold(0.85)tobothexperiments. 30Forthisempiricalanalysis,weconsidertheDNWRindicatortobebinaryforthecleanidentificationofmonetary policypass-through. 31WefurtherconsiderthemagnitudeofshocksmeasuredwiththenegativechangesintheEPOPratiotocontrol foreffectsoflargeshocksindeterminingtheinteractionbetweenpolicyeffectivenessanddownwardnominalwage rigidity(asconsideredbyJoandZubairy,2025),forrobustnessanalyses.Weconsiderboththecontemporaneous valuealoneandthecombinationofcontemporaneousandlaggedvaluesoftheseshockmeasures.Theestimated impulseresponsesremainrobusttothesespecifications. 24

indicatorss i,t−1 and(1−s i,t−1 )tocomprehensivelyaccountforthestate-dependentunderlying dynamicsofeachstate’seconomy,inlinewithAuerbachandGorodnichenko(2012). Thecoefficientsγh andγh,arethevectorofcoefficientsonthecontrolsinregimes1and2,respectively. 1 2 Thesampleperiodforthisexperimentspansfrom1980:Q1to2007:Q4. Thestartdatereflects theavailabilityofstate-levellarge-firmsharedatabeginningin1978:Q1,combinedwiththeuse ofeightlagsofthecontrolvariables. Theenddatecorrespondstotheavailabilityofmonetary policyshocksfromWielandandYang(2020),whichextendsthrough2007. Forconsistencyand comparability,weusethesamesampleperiodintheanalysisoftaxshocks. 6.2 EstimationResults Thissectiondiscussestheestimationresults. UpperpanelsinFigure6showtheresponseofthe relativeprobabilityofanL-shapedrecessioncomparedwithaU-shapedrecessionfollowinga one-unitexpansionarymonetarypolicyshock: PanelApresentsestimatesundergreaterDNWR (regime 1), and Panel B under lower DNWR (regime 2). Negative values indicate that such a policyshocksignificantlyreducesthelikelihoodofanL-shapedrecessionrelativetoaU-shaped one,therebymitigatinghysteresis,whilepositivevaluesindicatetheopposite. Intheregimeof greaterDNWR,anexpansionarymonetarypolicyreducestherelativeprobabilityofanL-shaped recessionwithstatisticalsignificanceapproximatelyfourquartersaftertheshock,witheffects thatpersistovertime.Incontrast,thesehysteresis-mitigatingeffectsareweakerandshorter-lived intheregimeoflesserDNWR.Thisfindingunderscoresthelong-runeffectivenessofmonetary policyinmitigatinghysteresisandhighlightsthatitsimpactisstrongerwhennominalwagesare moredownwardlyrigid. Next,weexaminetheeffectsofexpansionarytaxshocksinmitigatinghysteresis(lowerpanels ofFigure6). Taxcutsexhibitsubstantialhysteresis-reducingeffects,whennominalwagesare moredownwardlyrigid(PanelC),asreflectedbytheirstatisticallysignificantnegativeeffects ontherelativeprobabilityofanL-shapedrecessionoveraU-shapedrecession. Incontrast,the expansionarytaxshocksarenotstatisticallysignificantandshorter-livedunderlesserDNWR (Panel D). These findings indicate that tax cuts are more effective at mitigating hysteresis in environmentswithgreaterDNWR. Insummary,bothexpansionarymonetarypolicyandtaxshocksaremoreeffectiveatalleviatinghysteresiswhenDNWRisgreater. Thisfindingisconsistentwiththeconventionalview thatrealeffectsofmonetarypolicystemfromnominalrigidities. Inaddition,taxcutscanalso 25

Figure6:EFFECTSOFEXPANSIONARYDEMANDPOLICIESONTHERELATIVERISKOFL-SHAPEDRECESSION OVERU-SHAPEDRECESSION (MonetaryPolicy) PanelA.Regime1(greaterDNWR) PanelB.Regime2(lesserDNWR) Shock on U over L probability Shock on U over L probability 0.025 0.4 0.000 0.0 −0.025 −0.050 −0.4 −0.075 2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16 (TaxPolicy) PanelC.Regime1(greaterDNWR) PanelD.Regime2(lesserDNWR) Shock on U over L probability Shock on U over L probability 0.00 0.000 −0.05 −0.025 −0.10 −0.050 −0.15 −0.075 −0.20 −0.100 2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16 Notestofigure:ThisfiguredisplaystheestimatedresponsesofrelativeriskofanL-shapedrecessionovera U-shapedrecessiontoaone-unitdecreaseinmonetarypolicyshock(PanelsAandB)andintaxshock(PanelsC andD).PanelsAandCshowtheresponsesintheregimeofgreaterDNWR,andPanelsBandDshowthoseinthe regimeoflesserDNWR.MonetarypolicyshockestimatesarefromRomerandRomer(2004)extendedbyWieland andYang(2020).TaxshocksarefromRomerandRomer(2010).TheX-axisshowsquartersaftertheshock,andthe Y-axisindicatesthepolicyshock’spass-throughtorelativerisk.Theshadedareacaptures95percentconfidence intervalsbasedonNewey-Weststandarderrors. Source:Authors’calculation mitigatehysteresisbyreducingproductioncostswhenlaborcostsareinflexibleduetoDNWRor helpmaintainlabordemand.32 32ThisresultalignswithLee(2025),whofindsthatmacroeconomicvariablesrespondnearlytwiceasstrongly andmorepersistentlyinstateswithhighernominalwagerigiditycomparedtothosewithmoreflexiblewages.Our analysisdiffersfromLee’sinthatwefocusspecificallyontheresponseofhysteresis,whereasLeeexaminesthe effectsongeneralmacroeconomicvariablesgenerallyfollowingamarginaltaxshock. 26

7 A New Keynesian Model of Hysteresis with DNWR In this section, we use a prototype New Keynesian model to validate our empirical findings. BuildingonGalí(2022),whodevelopsaninsider–outsiderlabormarketframeworkthatgenerates hysteresisintheformofL-shapedrecessions,weextendthemodelbyincorporatingDNWR. In this model, wage bargaining is conducted by unions that represent only last period’s employedworkers(theinsiders). Becausetheseunionssetwagestoprotectinsiders’jobswhile disregardingtheunemployed(theoutsiders),theiremploymenttargetsbecomeanchoredtopast employmentlevels,endogenouslygeneratingpersistenceinbothunemploymentandoutput. As a result, employment losses caused by temporary shocks become persistent, giving rise to hysteresis. Downward nominal wage rigidity further amplifies these hysteresis effects by hinderingwageadjustmentinthelabormarket. OurquantitativeanalysisismotivatedbytheempiricalresultsinSections4–6.Inthisanalysis, wefocussolelyontheinteractionbetweenmonetarypolicyshocksandDNWR.Fiscalpolicy shockscanindependentlygeneratepermanentdistortionsandlong-runeffectsontheeconomy evenintheabsenceofnominalwagerigidity(Burnsideetal.,2004;FatásandSummers,2018). Incontrast,monetarypolicyshocksaretypicallytransitory,butourempiricalresultsshowthat theireffectsbecomemoreeffectiveatmitigatinghysteresiswhentheyinteractwithDNWR.To ensureacleanidentificationofthismechanism,wethereforefocusonmonetarypolicy. WemodelhysteresisasdrivenbythecontractionarydemandshockdocumentedinSection4, calibratingthesizeoftheshocktomatchthemagnitudeoftheemploymenthysteresisobserved atthenationallevelinSection3. Thequantitativeexperimentaimsto: (1)showthatDNWR amplifieshysteresis,producinglargernegativeeffectsonemploymentandoutputandsmaller declines in inflation; (2) evaluate the effectiveness of monetary policy in mitigating these effects;and(3)assesshowthiseffectivenessstrengthenswithgreaterDNWR.Thesemechanisms, documentedinSections5and6,highlighttheamplifyingroleofDNWRandtheconditional effectivenessofmonetarypolicyinterventions. 27

7.1 Model 7.1.1 Households Weconsideralargenumberofidenticalhouseholds. Eachhouseholdcontainsacontinuumof members,uniformlydistributedovertheunitsquare. Eachmemberisidentifiedbyapair(j,s)∈ [0,1]×[0,1]. Thefirstcoordinate, j,denotesthetypeoflaborservice(or“occupation”)inwhich thememberisspecialized,whilethesecondcoordinate,s,capturesherdisutilityfromwork.This disutilityisgivenby Θ tχs ϕ ifsheisemployedandzerootherwisewithpreferenceparameters Ct χ>0andϕ>0. Eachemployedworkersuppliesafixednumberofhours,normalizedtoone unitoftime. Foreachoccupation j,employmentN (j)∈[0,1]isdeterminedbylabordemand t andistakenasgivenbythehousehold. Employmentslotsareassignedtothememberswiththe lowestdisutilityfromwork,thatis,thosewiths∈[0,N (j)]. Weassumeseparablepreferences t withlogarithmicutilityinconsumptionandcompleterisksharingwithinthehousehold(i.e., C (i,j)=C for all (j,s)∈[0,1]×[0,1]). As a result, all members consume the same amount, t t regardlessoftheiroccupationoremploymentstatus. Thispreferencespecificationimpliesthateachhouseholdmaximizesitslifetimeutility: E (cid:88) ∞ βt (cid:181) logC − Θ tχ (cid:90) 1 N t (j)1+ϕ dj (cid:182) Z , 0 t=0 t C t 0 1+ϕ t subjecttothebudgetconstraint (cid:90) 1 (cid:90) 1 P t (i)C t (i)di+Q t B t ≤B t−1 + W t (j)N t (j)dj+D t , 0 0 whereC = (cid:179) (cid:82)1 C (i)1−1/ϵ pdi (cid:180)ϵ p/(ϵ p −1) istheDixit–Stiglitzconsumptionindex,ϵ istheelasticity t 0 t p of substitution across differentiated goods, β∈(0,1) is the household’s discount factor, P (i) t denotes the price of variety i, W (j) the nominal wage for occupation j, B the household’s t t holdingsofanominalrisklessone-perioddiscountbond,Q itsprice,andD dividendsfrom t t firmownership. FollowingGalíetal.(2012),thepreferenceshifterΘ isdefinedas t Θ =Θ1−ν C ν , t t−1 t 28

whereC denotesaggregateconsumption,treatedasexogenousfromthehousehold’sperspect tive. We interpret Θ as a smoothed consumption measure that affects labor supply: when t actualconsumptionexceedsΘ ,themarginaldisutilityoflaborfalls. Consequently,theratio Θ t t Ct determinesthestrengthofthehousehold’swealtheffect. Alowerνimpliesaweakershort-run wealtheffect,allowingthemodeltobettercapturetheobservedcomovementoflaborandreal wages. Forseparableutility,thismodificationfollowsGalíetal.(2012),buildingonJaimovich andRebelo(2009). FurtherimplicationsarediscussedinSection7.2inthecontextofthelabor supplyequation. Whenlowercaselettersdenotelogs,thedemandshockz ≡logZ followsanAR(1)process: t t z t =ρ z z t−1 +εz t , (7.1) whereρ ∈[0,1)andεz iswhitenoise. z t Thehousehold’soptimizationproblemyieldstheintertemporalEulerequation,whichin logsiswrittenas: c t =E t {c t+1 }−(i t −E t {i t+1 }−ρ)+(1−ρ z )z t . (7.2) Let L (j) denote the marginal participant in occupation j. The labor supply optimality t conditionis 1 W (j) Θ t = tχL (j) ϕ . t C P C t t t Takinglogsandaggregatingacrossoccupationsgivestheaveragerealwageandpreferenceshifter equations: ω =θ +ϕl +logχ, (7.3) t t t θ t =(1−ν)θ t−1 +νc t , (7.4) whereω =w −p istheaveragelogrealwage,w =(cid:82)1 w (j)dj istheaveragelognominalwage, t t t t 0 t andl =(cid:82)1 l (j)dj istheloglaborforce. t 0 t Then,unemploymentisdefinedas u =l −n , (7.5) t t t wheren =(cid:82)1 n (j)dj isthelogofaggregateemployment,determinedbyfirms’labordemand. t 0 t 29

7.1.2 Firms Amonopolisticallycompetitiveintermediategoods-producingfirmi ∈[0,1]producesoutput accordingto Y (i)=N (i)1−α , t t where0<α<1. PricesaresetfollowingCalvostickiness: afractionθ offirmscannotadjusttheirpriceseach p ∗ period. Attimet,afirmthatcanreoptimizechoosestheresetpriceP (i)tomaximizeexpected t discountedprofits: ∞ E t (cid:88) (βθ p )kΛ t,t+k (cid:163)(cid:161) P t ∗ (i)−MC t+k (cid:162) Y t+k|t (i) (cid:164) , k=0 subjecttothedemandfunction (cid:181) ∗ (cid:182)−ϵ P (i) p Y t+k|t (i)= t Y t+k , P t+k whereΛ t,t+k isthestochasticdiscountfactor,ϵ p istheelasticityofsubstitutionbetweenintermediategoods,andP t+k istheaggregatepricelevelattimet+k. Firms’profit-maximizationproblemyieldstheNewKeynesianPhillipscurveinlogs: πp =βE πp +χ y˜ +λ ω˜ , (7.6) t t t+1 p t p t wheretheoutputgapy˜ =y −yn andtherealwagegapω˜ =ω −ωn arelogdeviationsfromtheir t t t t t t naturallevelsunderflexiblepricesandwages,whicharedefinedinthewage-settingsection. Theparametersaredefinedasχ = αλ p andλ = (1−θ p)(1−βθ p) 1−α . p 1−α p θ p 1−α+αϵ p Finally,inequilibrium,thelogofemploymentsatisfies (1−α)n =y , (7.7) t t andgoodsmarketclearingrequires y =c . (7.8) t t 30

7.1.3 WageSetting WhereasinastandardNewKeynesianmodelunionssetnominalwagestobeequaltoaweighted averageofexpectedmarkups,theinsider–outsidermodelassumesthattheyinsteadsetwages toensurethattheweightedaverageofexpectedemploymentequalsthemeasureofinsiders. A constantfraction1−θ ofoccupations(ortheirunions)areallowedtoresettheirwageinany w ∗ period. WhensettingW (j),aunionrepresentingoccupation j considersthelabordemandfor t itsmembers: fork=1,2,3,..., (cid:181) ∗ (cid:182)−ϵ W (j) w N t+k|t (j)= t N t+k . W t+k Theevolutionoftheaveragelognominalwageis w t =θ w w t−1 +(1−θ w )w t ∗ , ∗ wherew denotesthelogoftheaveragenewlysetwageinperiodt. t FollowingGalí(2022),unionssetwageoptimallysothataweightedaverageofexpected(log) employmentequalsthetargetinsideremploymentlevel: ∞ (1−βθ w ) (cid:88) (βθ w )kE t {n t+k|t (j)}=n t ∗ (j) k=0 wherethetargetinsiderstockevolvesas n t ∗ (j)=γn t−1 (j)+(1−γ)n ∗ . ∗ Here,n denotestheunion’slong-runemploymenttarget,commonacrossoccupations,and γ∈[0,1]capturesthepersistenceofthetargetinsiders,thatis,theextenttowhichcurrentem- ∗ ploymentshapesfutureemploymenttargetsandgeneratehysteresis. Thetargetn (j)represents t themeasureofinsidersinoccupation j withhigherγimplyingstrongerhysteresiseffects. Under fullyflexiblewages,theequilibriumconditionreducestonn=n ∗ forallt. Ifinitialemployment t t equalsitstarget,n =n ∗ ,thennn=n ∗ . Consequently,thenaturallevelofemploymentequals 0 t ∗ thetargetn ,andthecorrespondingnaturallevelofoutputandwageare yn=(1−α)n ∗ , (7.9) t 31

ωn=log(1−α)−αn ∗−µ −log(1−τ), (7.10) t p ϵ whereµ =log p isthenaturalwagemarkup,andτisaconstantwagesubsidy. p ϵ p −1 Withstickiness,wagesettingruleisgivenby ∞ (cid:183) (cid:184) w t ∗ (j)=− ϵ 1 n t ∗ (j)+(1−βθ w ) (cid:88) (βθ w )kE t w t+k + ϵ 1 n t+k . w k=0 w Averagingoverunionsresettingint gives ∞ (cid:183) (cid:184) w t ∗=− ϵ 1 n t ∗+(1−βθ w ) (cid:88) (βθ w )kE t w t+k + ϵ 1 n t+k w k=0 w n t ∗=γn t−1 +(1−γ)n ∗ . Combiningtheequationsabovewithwageevolutionequation,weobtainthewagePhillips curve: πw =βE {πw }+(1−γ)λ (1−βθ )nˆ +γλ ∆n (7.11) t t t+1 n w t n t wherenˆ ≡n −n ∗ denotesthedeviationofemploymentfromtheunion’slong-runtarget,and t t λ ≡ 1−θ w measuresthesensitivityofwageinflationtoemploymentdeviationanditsgaps. n θ ϵ w w ThewagePhillipscurveaboveimpliesthatwhenγishigh(i.e.,hysteresisisstrong),wage inflationrespondslesstotoemploymentgaps,sopersistentdeviationsfromthetargetarenot self-correcting. Wageinflation,priceinflation,andtherealwagesatisfytheidentity ω t =ω t−1 +πw t −πp t . (7.12) Inaddition,followingSchmitt-GrohéandUribe(2022),weincorporateDNWRbyimposing theconstraint,forallfirms j ∈[0,1], W t (j)≥W t−1 (j), whichisequivalentto πw ≥0. (7.13) t 32

Table4:CALIBRATEDPARAMETERS Parameter Description Value ϕ Curvatureoflabordisutility 3.4 β Discountfactor 0.99 α Decreasingreturnstolabor 0.25 ϵ Elasticityofsubstitution(goods) 3.8 p ϵ Elasticityofsubstitution(labor) 4.3 w θ Pricestickiness 0.75 p θ Wagestickiness 0.10 w φ Interestraterulelag 0.9 i φ π Interestresponsetoinflation 1.5 φ Interestresponsetooutputgrowth 0.1 y ρ DemandshockAR(1) 0.90 z γ Persistenceofthetargetinsiders 0.99 ν Wealtheffectparameter 0.02 7.1.4 MonetaryPolicy MonetarypolicyismodeledusingaTaylor-typeinterestraterule,inwhichthecentralbankadjuststhenominalinterestrateinresponsetodeviationsofinflationandoutputgrowthfromtheir respectivetargets. Theruleincludesinterestratesmoothingtoreflectthegradualadjustment behaviorcommonlyobservedinpractice: i t =φ i i t−1 +(1−φ i ) (cid:163)ρ+φ π πp t +φ y ∆y t (cid:164)+εm t (7.14) wherei isthenominalinterestrate,ρisthesteady-staterealinterestrate,πp istheinflationrate t t ofprices,and∆y t denotesoutputgrowth. Theparametersφ πandφ y governtheresponsiveness of policy to inflation and output growth, respectively, while φ ∈[0,1] captures the degree of i interestratesmoothing. Thetermεm representsanexogenousmonetarypolicyshock. t 7.2 Calibration Simulationsusethelog-linearizedstructuralequations(7.2)–(7.12)and(7.14), incorporating thedemandshockprocess(7.1)andmonetarypolicyshock(7.14)underdownwardnominal wage rigidity constraint (7.13). We solve the model under this constraint using the OccBin methodologyofGuerrieriandIacoviello(2015). 33

Table 4 presents the calibrated parameter values used in the simulations. The model is calibratedataquarterlyfrequency. MostparametervaluesaretakenfromGalí(2022),exceptfor thewagestickinessparameterθ andthepreferenceshiftersmoothnessparameterν. Webriefly w discusstheimplicationsoftheseparameterchoices,alongwithotherparameters,below. For furtherdetailsonthecalibration,seeGalí(2022). Inourframework,weincorporatedownwardnominalwagerigidityinadditiontostandard nominalwagerigidity. Specifically,whenashockputsdownwardpressureonnominalwages,all workersreceiveunchangedwages. Withupwardpressure,onlyafractionθ receiveunchanged w wages.Wesetθ =0.10sothatthislowerwagerigidityparameteralignswiththemodelfeaturing w onlydownwardnominalwagerigidity,asinDalyandHobijn(2014)andJoandZubairy(2025). Thepricerigidityparameterissettoθ =0.75,sotheaveragedurationofpricesisfourquarters. p Wealsoconsiderasmallwealtheffectinlaborsupplytomatchtheempiricalevidenceonthe effectsofmonetarypolicyshocksreportedbyChristianoetal.(2021). TheirVARresultsshow thatlaborsupplyincreasesinresponsetoexpansionarymonetarypolicyshocks. However,the conventionalKing-Plosser-Rebelo(1988)(KPR,henceforth)preferences,whichimplyastrong wealtheffectthroughw −p −c =ϕl ,couldgenerateadeclineinlaborsupplyfollowingan t t t t expansionarymonetarypolicyshock,whichiscounterfactual. Toaddressthis,followingGalí et al. (2012), we set ν=0.02, a value close to Greenwood-Hercowitz-Huffman (1988) (GHH, henceforth) preferences (see Jo and Zubairy 2025).33 A smaller wealth effect (i.e., lower ν) strengthenstheprocyclicalresponseoflaborsupplytomonetarypolicyshocksthroughthelabor supplycondition w t −p t −θ t =ϕl t , θ t =(1−ν)θ t−1 +νc t . Theelasticitiesofsubstitutionforgoodsandlaboraresettoϵ =3.8andϵ =4.3,corresponding p w tosteady-statemarkupsof35%and30%,respectively.Thecurvatureparameteroflabordisutility is set to 3.4, which implies a steady-state unemployment rate of approximately 7.8%. The discountfactorisfixedat0.99,followingstandardpracticeintheliterature. Thelaborincome shareiscalibratedtoα=0.25. Themonetarypolicyruleparametersaresettoφ π =1.5,φ y =0.5, and φ = 0.9. The persistence of the demand shock is given by ρ = 0.9. The sizes of the i z demandandmonetarypolicyshockswillbediscussedintheexercisebasedonimpulseresponse functions. 33Theparametervalueν=1correspondstoKPRpreferences. 34

Figure7:THEROLEOFDNWRINAMPLIFYINGTHEHYSTERESISEFFECT (a) Output (b) Employment (c) Unemployment 0 0 2 -1 -1 1 No DNWR DNWR -2 -2 0 0 5 10 15 0 5 10 15 0 5 10 15 (d) Wage Inflation (e) Nominal Wage (f) Real Wage 1 0 0 0 -1 -1 -1 -2 -2 -2 0 5 10 15 0 5 10 15 0 5 10 15 (g) Inflation (h) Real Rate (i) Nominal Interest Rate 0 0.02 0 0 -0.1 -0.02 -0.05 -0.04 -0.06 -0.2 -0.1 0 5 10 15 0 5 10 15 0 5 10 15 Notestofigure:Thisfigureshowstheimpulseresponsefunctionstoacontractionarydemandshockundertwo scenarios:withtheDNWRconstraint(redsolidline)andwithoutit(bluedashedline). Source:Authors’calculation 7.3 QuantitativeAnalysis WeexaminehowDNWRamplifieshysteresisinoutput,employment,andunemploymentduringrecessionstriggeredbycontractionarydemandshocks,confirmingtheempiricalpatterns documentedearlier. Figure7presentstheeffectsofDNWRbycomparingtheimpulseresponsestoacontractionarydemandshockunderscenarioswithandwithouttherigidityconstraint. Thesizeofthe demandshockiscalibratedtomatchtheestimatednational-levelemploymentgrowthratefor anL-shapedrecession(i.e.,arecessionaccompanyinghysteresis),µ . Employmentonimpact L declinesby1.20percentwithoutDNWRandby1.92percentwithDNWR,yieldinganaverageof µˆ =1.56. Seetheestimatedvalueofµ reportedinTableC1ofSectionAppendixC.Theimpulse L L responsesofemploymentandoutputshowthathysteresiseffectsarehighlypersistentandthat DNWRamplifiestheimpactoftheshock,leadingtodeclinesinemploymentandoutputthatare approximately60percentlarger,consistentwithstrongerhysteresiseffects. UnemploymentrisesunderDNWRbecausehigherrealwagesincreaselaborsupply,butalso suppresslabordemand. IntheNewKeynesianPhillipscurve,inflationisdrivenbyoutputand realwagegaps. Theupwardpressureonrealwagesoutweighstherecessionaryeffectonoutput, 35

Figure8:HYSTERESISANDEXPANSIONARYMONETARYPOLICYUNDERDNWR Output Employment Unemployment 0 0 2 -0.5 -0.5 1.5 -1 -1 N ex o p p a o n l s ic io y nary MP 1 -1.5 -1.5 0.5 -2 0 -2 0 5 10 15 0 5 10 15 0 5 10 15 Wage Inflation Nominal Wage Real Wage 0.2 0.6 0.6 0.15 0.4 0.4 0.1 0.2 0.2 0.05 0 0 0 0 5 10 15 0 5 10 15 0 5 10 15 Inflation Real Rate Nominal Interest Rate 0 0 0 -0.01 -0.05 -0.05 -0.02 -0.03 -0.1 -0.1 -0.04 0 5 10 15 0 5 10 15 0 5 10 15 Notestofigure:Thefiguredisplaystheimpulseresponsefunctionstoacontractionarydemandshockinthe presenceofDNWR,comparingthecasewithexpansionarymonetaryaccommodation(bluedashedline)tothecase withoutit(redsolidline). Source:Authors’calculation producingasmallerdeclineininflation.Consequently,thelargeroutputcontractionandsmaller inflationdeclinelargelyoffseteachotherinthemonetarypolicyrule,sothenominalinterest ratebehavessimilarlywithorwithoutDNWR.Thisleadstoasubstantiallylargerdeclineinthe realinterestrateunderthisrigidity. Wenowconductacounterfactualanalysisofanexpansionarymonetarypolicyimplemented alongsidehysteresisdrivenbyacontractionarydemandshockunderDNWR.Thisexpansionary policyismodeledasa50basispointsperannum(εm=−0.125%ataquarterlyrate),occurring simultaneouslywiththeonsetofthecontractionarydemandshock. Figure8showsthatthis interventionsubstantiallymitigatestheshock’sadverseeffects. Inparticular,itnearlyoffsetsthe riseinrealwagesinducedbythepricedecline,preventingsharpcontractionsinemployment and output that would otherwise generate persistent hysteresis. Consequently, hysteresis in employmentandoutputislargelyeliminated,underscoringtheimportanceoftimelyandforceful monetaryaccommodationwhenDNWRlimitslabormarketadjustment. Figure9plotsthedifferenceinimpulseresponsestoacontractionarydemandshockwith and without an accompanying expansionary monetary policy, comparing outcomes under DNWR and without the constraint. The shocks are calibrated as in Figures 7 and 8. When 36

Figure9:THEAMPLIFICATIONOFEXPANSIONARYMONETARYPOLICYEFFECTSBYDNWR Output Empoloyment Unemployment 1.8 2.5 0 No DNWR 1.6 DNWR 2 -0.5 1.4 1.2 1.5 -1 1 0.8 1 -1.5 0.6 0.4 0.5 -2 0.2 0 0 -2.5 0 5 10 15 0 5 10 15 0 5 10 15 Notestofigure:Thefigureplotstheeffectsofanexpansionarymonetarypolicyimplementedduringhysteresis, obtainedbytakingthedifferencebetweentheimpulseresponsestoacontractionarydemandshockwithand withoutthemonetarypolicyshock,undertwoscenarios:withtheDNWRconstraint(redsolidline)andwithoutit (bluedashedline). Source:Authors’calculation DNWRbinds,nominalwagescannotfall,causingrealwagestorise,depressinglabordemand, and amplifying the recession. Expansionary monetary policy mitigates this effect by raising the price level, lowering real wages, and restoring labor market equilibrium. Consequently, asshowninFigure9,thesamemonetaryexpansionunderDNWRsubstantiallycushionsthe downturninemploymentandoutputandlowersunemploymentrelativetothecasewithoutit. Overall,DNWRmakesmonetarypolicyroughly1.6timesmoreeffectiveinstabilizingoutput, employment,andunemployment. 8 Conclusion ThispaperexaminestheroleofDNWRinmacroeconomichysteresis,exploitingstate-levelheterogeneityinrecessionexperiences. Tothisend,wefirstestimateaBayesianMarkov-switching modelthatdistinguishesbetweenU-shapedrecessions—characterizedbyfullrecovery—and L-shapedrecessions,whichexhibithysteresis. Ourempiricalfindingscanbesummarizedas follows. First,state-levelbusiness-cycleexperiencesexhibitsubstantialheterogeneity,andthis richvariationallowsustoidentifythekeycontributorstohysteresis. Second,DNWRemergesas animportantandstatisticallysignificantfactorthatmagnifieshysteresis. Third,expansionary monetary and fiscal policies can mitigate hysteresis when implemented in a timely manner. 37

Finally,wedevelopacalibratedNewKeynesianmodelinwhichhysteresisarisesfromacontractionarydemandshock. Thequantitativeresultsreplicatetheempiricalpatternsdocumentedin state-leveldata,underscoringthecentralroleofDNWRinamplifyinghysteresisandvalidating theeffectivenessofpolicyinterventionsinsuchenvironments. 38

References Abbritti,M.,Consolo,A.,andWeber,S.(2021). Endogenousgrowth,downwardwagerigidityand optimalinflation. WorkingPaperSeries2635,EuropeanCentralBank. Abraham,K.G.,Haltiwanger,J.,Sandusky,K.,andSpletzer,J.R.(2013). Exploringdifferences in employment between household and establishment data. Journal of Labor Economics, 31(S1):S129–S172. Acharya,S.,Bengui,J.,Dogra,K.,andWee,S.L.(2022). SlowRecoveriesandUnemployment Traps: MonetaryPolicyinaTimeofHysteresis. TheEconomicJournal,132(646):2007–2047. Ahn,H.J.andHamilton,J.D.(2022). Measuringlabor-forceparticipationandtheincidenceand durationofunemployment. ReviewofEconomicDynamics,44:1–32. Akerlof,G.,Dickens,W.R.,andPerry,G.(1996). Themacroeconomicsoflowinflation. Brookings PapersonEconomicActivity,27(1):1–76. Albanesi,S.(2025). ChangingBusinessCycles: TheRoleofWomen’sEmployment. Opportunity andInclusiveGrowthInstituteWorkingPapers109,FederalReserveBankofMinneapolis. Alves, F. and Violante, G. L. (2024). From Micro to Macro Hysteresis: Long-Run Effects of MonetaryPolicy. StaffWorkingPapers24-39,BankofCanada. Alves,F.andViolante,G.L.(2025). MonetaryPolicyUnderOkun’sHypothesis. NBERWorking Papers33488,NationalBureauofEconomicResearch,Inc. Antolin-Diaz,J.andSurico,P.(2025). Thelong-runeffectsofgovernmentspending. American EconomicReview,115(7):2376–2413. Auerbach,A.J.andGorodnichenko,Y.(2012). Measuringtheoutputresponsestofiscalpolicy. AmericanEconomicJournal: EconomicPolicy,4(2):1–27. Benigno,G.andFornaro,L.(2018).StagnationTraps.TheReviewofEconomicStudies,85(3):1425– 1470. Benigno,P.andRicci,L.A.(2011). Theinflation-outputtrade-offwithdownwardwagerigidities. AmericanEconomicReview,101(4):1436–66. Berge,T.,DeRidder,M.,andPfajfar,D.(2021). Whenisthefiscalmultiplierhigh? acomparison offourbusinesscyclephases. EuropeanEconomicReview,138:103852. Bergholt,D.,Fosso,L.,andFurlanetto,F.(2024). Macroeconomiceffectsofthegenderevolution. mimeo. Bhattarai,S.,Schwartzman,F.,andYang,C.(2021). Localscarsoftheushousingcrisis. Journal ofMonetaryEconomics,119:40–57. Blanchard, O., Cerutti, E., and Summers, L. (2015). Inflation and activity– two explorations andtheirmonetarypolicyimplications. Inthe2015ECBForumonCentralBanking,Sintra, Portugal. Blanchard, O. J. (2018). Should we reject the natural rate hypothesis? Journal of Economic Perspectives,32(1):97–120. 39

Blanchard, O. J. and Quah, D. (1989). The dynamic effects of aggregate demand and supply disturbances. AmericanEconomicReview,79(4):655–673. Blanchard,O.J.andSummers,L.H.(1986).Hysteresisandtheeuropeanunemploymentproblem. InNBERMacroeconomicsAnnual,volume1,pages15–78.MITPress. Burnside,C.,Eichenbaum,M.,andFisher,J.D.(2004). Fiscalshocksandtheirconsequences. JournalofEconomictheory,115(1):89–117. Cajner, T., Coglianese, J., and Montes, J. (2021). The long-lived cyclicality of the labor force participationrate. FinanceandEconomicsDiscussionSeries2021-047,FederalReserveBoard. BoardofGovernorsoftheFederalReserveSystem. Cerra,V.,Fatás,A.,andSaxena,S.C.(2023). Hysteresisandbusinesscycles. JournalofEconomic Literature,61(1):181–225. Cerra,V.andSaxena,S.C.(2008). Growthdynamics: Themythofeconomicrecovery. American EconomicReview,98(1):439–457. Christiano,L.J.,Eichenbaum,M.S.,andTrabandt,M.(2021). Whyisunemploymentsocountercyclical? ReviewofEconomicDynamics,41:4–37. Coibion, Olivier, G. Y. and Ulate, M. (2018). The cyclical sensitivity in estimates of potential output. BrookingsPapersonEconomicActivity. Cortes,G.M.,Jaimovich,N.,andSiu,H.E.(2018). Theendofmenandriseofwomeninthe high-skilledlabormarket. WorkingPaper24274,NationalBureauofEconomicResearch. Daly,M.C.andHobijn,B.(2014). DownwardNominalWageRigiditiesBendthePhillipsCurve. JournalofMoney,CreditandBanking,46(S2):51–93. deRidder,M.andPfajfar,D.(2017). Policyshocksandwagerigidities: Empiricalevidencefrom regionaleffectsofnationalshocks. CambridgeWorkingPapersinEconomics1717,Facultyof Economics,UniversityofCambridge. Dupraz,S.,Nakamura,E.,andSteinsson,J.(2025). Apluckingmodelofbusinesscycles. Journal ofMonetaryEconomics,152:103766. Eo,Y.andKim,C.-J.(2016). Markov-switchingmodelswithevolvingregime-specificparameters: Arepostwarboomsorrecessionsallalike? ReviewofEconomicsandStatistics,98(5):940–949. Eo,Y.andMorley,J.(2022). WhyHastheU.S.EconomyStagnatedsincetheGreatRecession? TheReviewofEconomicsandStatistics,104(2):246–258. Eo,Y.andMorley,J.(2023). Doesthesurveyofprofessionalforecastershelppredicttheshapeof recessionsinrealtime? EconomicsLetters,233:111419. Fatás,A.andSummers,L.H.(2018). Thepermanenteffectsoffiscalconsolidations. Journalof InternationalEconomics,112:238–250. Francis,N.,Jackson,L.E.,andOwyang,M.T.(2018). Countercyclicalpolicyandthespeedof recoveryafterrecessions. JournalofMoney,CreditandBanking,50(4):675–704. Fukui,M.,Nakamura,E.,andSteinsson,J.(2023). Women,wealtheffects,andslowrecoveries. AmericanEconomicJournal: Macroeconomics,15(1):269–313. 40

Furlanetto, F., Lepetit, A., Robstad, Ø., Rubio-Ramírez, J., and Ulvedal, P. (2025). Estimating hysteresiseffects. AmericanEconomicJournal: Macroeconomics,17(1):35–70. Galí,J.(2022). Insider–outsiderlabormarkets,hysteresis,andmonetarypolicy. JournalofMoney, CreditandBanking,54(S1):53–88. Galí,J.,Smets,F.,andWouters,R.(2012). Unemploymentinanestimatednewkeynesianmodel. NBERmacroeconomicsannual,26(1):329–360. Gelman,A.,Gilks,W.R.,andRoberts,G.O.(1997). Weakconvergenceandoptimalscalingof randomwalkmetropolisalgorithms. TheAnnalsofAppliedProbability,7(1):110–120. Greenwood,J.,Hercowitz,Z.,andHuffman,G.W.(1988). Investment,capacityutilization,and therealbusinesscycle. AmericanEconomicReview,78(3):402–417. Guerrieri, L. and Iacoviello, M. (2015). Occbin: A toolkit for solving dynamic models with occasionallybindingconstraintseasily. JournalofMonetaryEconomics,70:22–38. Hall, R.(2016). Macroeconomicsofpersistentslumps. volume2, chapterChapter27, pages 2131–2181.Elsevier. Hamilton,J.D.(1989). Anewapproachtotheeconomicanalysisofnonstationarytimeseries andthebusinesscycle. Econometrica,57(2):357–84. Hamilton,J.D.(2011). HistoricalOilShocks. NBERWorkingPapers16790,NationalBureauof EconomicResearch,Inc. Hamilton,J.D.andOwyang,M.T.(2012). Thepropagationofregionalrecessions. Reviewof EconomicsandStatistics,94(4):935–947. Hazell,J.,Herreno,J.,Nakamura,E.,andSteinsson,J.(2022). Theslopeofthephillipscurve: Evidencefromu.s.states. TheQuarterlyJournalofEconomics,137(3):1299–1344. Heathcote,J.,Storesletten,K.,andViolante,G.L.(2017).Themacroeconomicsofthequietrevolution: Understandingtheimplicationsoftheriseinwomen’sparticipationforeconomicgrowth andinequality. ResearchinEconomics,71(3):521–539. SpecialissueonMacroeconomics. Jaimovich,N.andRebelo,S.(2009).Cannewsaboutthefuturedrivethebusinesscycle? American EconomicReview,99(4):1097–1118. Jaimovich, N. and Siu, H. E. (2020). Job Polarization and Jobless Recoveries. The Review of EconomicsandStatistics,102(1):129–147. Jo,Y.J.(2024). Beyondthespikeatzero: Understandingnominalwagerigiditythroughempirical andmodel-basedapproach. Technicalreport,TexasA&MUniversity. Jo,Y.J.andZubairy,S.(2025). State-dependentgovernmentspendingmultipliers: Downward nominalwagerigidityandsourcesofbusinesscyclefluctuations. AmericanEconomicJournal: Macroeconomics,17(1):379–413. Jordá,O.,Singh,S.R.,andTaylor,A.M.(2020). TheLong-RunEffectsofMonetaryPolicy. Working PaperSeries2020-01,FederalReserveBankofSanFrancisco. Kamber,G.,Morley,J.,andWong,B.(2018). Intuitiveandreliableestimatesoftheoutputgap fromabeveridge-nelsonfilter. ReviewofEconomicsandStatistics,100(3):550–566. 41

King,R.G.,Plosser,C.I.,andRebelo,S.T.(1988). Production,growthandbusinesscycles: I.the basicneoclassicalmodel. JournalofMonetaryEconomics,21(2–3):195–232. Lee, Y.J.(2025). Effectsofamarginaltaxrateshock: Roleofnominalwagerigidity. Working papers,TexasA&M. Lenza,M.andPrimiceri,G.E.(2022). Howtoestimateavectorautoregressionaftermarch2020. JournalofAppliedEconometrics,37:688–699. Lucas, R.E.(1977). Understandingbusinesscycles. Carnegie-RochesterConferenceSerieson PublicPolicy,5:7–29. Ma, Y.andZimmermann, K.(2023). Monetarypolicyandinnovation. WorkingPaper31698, NationalBureauofEconomicResearch. Olsson, J. (2019). Structural transformation of the labor market and the aggregate economy. Technicalreport. Owyang,M.T.,Piger,J.,andWall,H.J.(2005). BusinesscyclephasesinU.S.states. Reviewof EconomicsandStatistics,87(4):604–616. Owyang,M.T.,Piger,J.,andWall,H.J.(2015). Forecastingnationalrecessionsusingstate-level data. JournalofMoney,CreditandBanking,47(5):847–866. Ramey,V.A.andZubairy,S.(2018). Governmentspendingmultipliersingoodtimesandinbad: Evidencefromushistoricaldata. JournalofPoliticalEconomy,126(2):850–901. Romer, C. D. and Romer, D. H. (2004). A new measure of monetary shocks: Derivation and implications. AmericanEconomicReview,94(4):1055–1084. Romer,C.D.andRomer,D.H.(2010). Themacroeconomiceffectsoftaxchanges: Estimates basedonanewmeasureoffiscalshocks. TechnicalReport3. Schmitt-Grohé, S. and Uribe, M. (2022). Heterogeneous downward nominal wage rigidity: Foundationsofanonlinearphillipscurve. Technicalreport,NationalBureauofEconomic Research. Schmitt-Grohé, S. and Uribe, M. (2017). Liquidity traps and jobless recoveries. American EconomicJournal: Macroeconomics,9(1):165–204. Shen, W. and Yang, S.-J. S. (2018). Downward nominal wage rigidity and state-dependent governmentspendingmultipliers. JournalofMonetaryEconomics,98:11–26. Shimer,R.(2012). Wagerigiditiesandjoblessrecoveries. JournalofMonetaryEconomics,59:S65– S77. Tobin,J.(1972). Inflationandunemployment. AmericanEconomicReview,62(1):1–18. Vaghul,K.andZipperer,B.(2016). Historicalstateandsub-stateminimumwagedata. Washingtoncenterforequitablegrowthworkingpaper,WashingtonCenterforEquitableGrowth. Wieland,J.F.andYang,M.(2020). FinancialDampening. JournalofMoney,CreditandBanking, 52(1):79–113. 42

Online Supplement to “Hysteresis and the Role of Downward Nominal Wage Rigidity: Evidence from U.S. States" Appendix A Additional Literature Review Ourpaperisrelatedtoseveralstrandsoftheliterature. Thefirstistheliteratureonbusiness cyclesandhysteresis.Adominantviewinmacroeconomicshasbeen“theindependenceassumption”whereshockstotrendsorstructuralaspectsoftheeconomyandcyclicalfluctuationsare independentfromeachother(e.g.,Lucas,1977;BlanchardandQuah,1989).34 Inthistraditional framework,innovationstotrendsaretreatedassupplyshocksandthosetocyclicalcomponents areviewedasdemandshocks. Meanwhile,thehysteresisviewallowsforpermanenteffectsofcyclicalshocks.Blanchardand Summers(1986)proposeastructuralmechanismofhysteresisbuildingontheinsider–outsider model to characterize labor market hysteresis and account for sclerosis in European labor markets.Galí(2022)incorporatestheinsider–outsiderframeworkintoaNewKeynesianmodelto showthatthesourceofhysteresisisaninefficientlyhighequilibriumwage. Abbrittietal.(2021) constructaNewKeynesianmodelwithdownwardnominalwagerigidityandendogenousgrowth, demonstrating how cyclical shocks can permanently affect trend growth. Similarly, Acharya etal.(2022)buildastructuralmodelfeaturingasearch-and-matchinglabormarketblockand showthatdownwardnominalwagerigidity,combinedwithskilldepreciationamongdisplaced workers,candrivetheeconomytowardasteady-stateunemploymenttrap. AlvesandViolante (2024, 2025) develop a heterogeneous-agent New Keynesian model with three labor market statesandnominalwagerigidity,illustratinghowarecessionaryshockpersistentlyreducesboth employmentandlaborforceparticipation—particularlyamonglow-skilledworkers—alongwith income. Empirically,recentstudiesanalyzemacrohysteresisbyfocusingonthelong-lastingeffectsof 34Cerraetal.(2023)presentanextensivereviewoftheliteratureonhysteresis. 1

demandshocksormonetarypolicyshocks. ExamplesareCerraandSaxena(2008),Blanchard et al. (2015) and Jordá et al. (2020), who base their analyses on multi-country data. Ma and Zimmermann (2023) estimate effects of monetary policy on R&D investment, interpreting thiseffectasthesourceofhysteresis. Relatedly,Furlanettoetal.(2025)identifyapermanent demandshockbasedonastructuralVARmodel;thisshockhaslonglastingeffectsonlong-term unemploymentandalsoemployment. Cajneretal.(2021)empiricallyshowpersistenteffectsof cyclicalshocksonthelaborforceparticipationratebasedonstate-leveldata. Antolin-Diazand Surico(2025)uncoverlong-runpositiveeffectsofgovernmentspendingusingaBVARframework andanewlyconstructedseriesofmilitaryspendingdisaggregatedbycategory. Bhattaraietal. (2021)examinelocalhysteresiseffectswithaspecificfocusonthehousingcrisisintheU.S. Ourpaperalsointersectswiththeliteratureonnominalwagerigidity. Tobin(1972),Akerlof et al. (1996), and Benigno and Ricci (2011) demonstrate that nominal wage rigidity is an importantsourceofnonlinearityinthebusinesscycle. Duprazetal.(2025)highlightdownward nominalwagerigidityasakeychannelthroughwhichasymmetriesinunemploymentdynamics arise,echoingthepredictionsofthepluckingtheory. Otherstudies—suchasAbbrittietal.(2021) andAcharyaetal. (2022)—alsoemphasizethatdownwardnominalwagerigidity isacritical mechanismbehindthelastingeconomicdamagecausedbyrecessions,asitraisesrealwages duringdownturnsandamplifiestheeffectsofrecessionaryshocks. Empiricallyandtheoretically, DalyandHobijn(2014)showthatdownwardnominalwagerigidityisessentialforunderstanding nonlinearitiesinthePhillipscurveandtheeffectivenessofmonetarypolicy. Jo(2024)develops uniquestate-levelmeasuresofdownwardnominalwagerigidityandinvestigatesitsdeterminants, and Jo and Zubairy (2025) analyze the role of downward nominal wage rigidity in the transmissionofgovernmentspendingshocks. Ourempiricalfindingssuggestthatdownward nominalwagerigidityplaysacriticalroleinunderstandinghysteresisandtheeffectivenessof demand-sidepoliciesinmitigatingit. Ourpaperalsorelatestotheliteratureonregionalbusinesscyclesandrecessionprediction. Inthisliterature,theMarkov-switchingmodelhasbeenwidelyusedtodetectbusinesscycle 2

phases (e.g., Hamilton, 1989). However, as noted by Francis et al. (2018) and Hamilton and Owyang (2012), this standard approach typically assumes that the depth of recessions, the trajectoriesofrecoveries,andthelengthsofrecoveryperiodsarethesameacrossallrecessions. Toprovideamorenuancedcharacterizationofrecoverypatterns—particularlytodistinguish betweenbounce-backrecoveriesandhysteresis—Francisetal.(2018)modelthedurationof recessionsusinganacceleratedfailuretimeframework,whileEoandMorley(2022)developa Markov-switchingmodelthatallowsfortwodistincttypesofrecessions. Theliteratureonrecessionpredictionhasincreasinglyreliedonregionaldatatoinvestigate theeffectivenessofpoliciesinstabilizingbusinesscycles. Francisetal.(2018)andBergeetal. (2021)usestate-leveldatatoexaminethetransmissionofmonetaryandfiscalpolicy,respectively. Thispaperiscloselyrelatedtothatworkinitsuseofstate-leveldatatoanalyzebusinesscycles andpolicyeffectiveness;itdiffersbyfocusingonhysteresisanditsattempttodistinguishbetween U-shapedandL-shapedrecessionsusingaBayesianMarkov-switchingmodel. Appendix B Data B.1 Datasources DatawereamalgamatedfromavarietyofsourcesincludingHAVER,FRED,BLS,andCensus. For severalvariables,datawerecollectedfromonesourcefortheearlierpartofthesample(1960s, 70s,80s)andfromanotherformorerecentyears. 1. State-levelpayrollemployment(1960:M1-2023:M12): retrievedfromHAVER.SeeFigures B1andB2. 2. Employmentshareofmanufacturing,finance,andprofessionalservices(1969-2023,yearly): Haver(BEAEMPL)1969-2001;BLSStateemploymentandunemployment(retrievedfrom FRED,ALFRED)2002-2023. Employmentsharesforthethreeindustriesareavailablein FREDstartingin1990. However,toensureconsistencyinindustrialclassification,weuse 3

datafromHAVERthrough2001andswitchtoFRED/ALFREDdatafrom2002onward. The employmentshareforthefinanceindustryisunavailableinALFREDforNewMexicoand SouthDakota,soweexcludethesetwostatesfromthefinanceseriesstartingin2002. 3. Unemploymentrateandlaborforceparticipationratebygenderandbystate: BLS.The employment-to-populationratioiscalculatedbasedontheunemploymentrateandthe laborforceparticipationrate. (https://www.bls.gov/lau/ex14tables.htm; https://www.bls.gov/opub/geographic-profile/.) 4. Employmentsharebyfirmsize(1978-2021,yearly): CensusBureau’sBusinessDynamics Statistics(BDS) 5. Totaltaxandtotalincome(yearly,1960-2022),AnnualSurveyofStateGovtTaxCollections (Census)andPersonalIncomeByState(BEA)data,respectively. Beyondpubliclyavailabledataprovidedbythestatisticalagencies,someseriesaresourced fromwebsitesmaintainedbyindividualresearchersornon-profitinstitutions. 1. Oilproductionbystate(1960-2022 yearly): EIAandHamilton(2011)35 2. Unionmembership(1964-2021,yearly): BarryHirsch(http://www.unionstats.com/) 3. Fractionofwagecuts,nowagechanges,andwageincreases: YoonJooJo(https://sites. google.com/view/yoonjoojo/rsearch). 4. Minimumwagedata(bystate,andofthefederallevel): VaghulandZipperer(2016)(https: //equitablegrowth.org/working-papers/historical-state-and-sub-state-minimum-wage-data/) 5. MonetarypolicyshocksofRomerandRomer(2004)extendedbyWielandandYang(2020) (https://www.openicpsr.org/openicpsr/project/135741/version/V1/view?path= /openicpsr/135741/fcr:versions/V1/Monetary_shocks.zip&type=file) 35WethankprofessorJamesHamiltonforsharingthedatasetusedinHamilton(2011). 4

TableC1:POSTERIORESTIMATESFORTHEMARKOV-SWITCHINGMODELOFEMPLOYMENTATTHENATIONAL LEVEL Posterior 90% Parameter Mean CredibleInterval p 0.93 [0.85,0.95] 00 p 0.04 [0.00,0.06] 01 p 0.03 [0.00,0.04] 02 p 0.73 [0.28,0.86] 11 p 0.77 [0.24,0.92] 22 µ 0.05 [–0.17,0.12] 0 µ –1.30 [–4.34,–1.06] 1 µ –1.56 [–5.27,–1.18] 2 σ2 0.18 [0.11,0.23] c 7.22 [4.27,8.50] 0 ρ 0.61 [0.37,0.72] AcceptanceRate 0.35 Notetotable:Theposteriorestimatesarebasedontheregime-switchingmodelin(3.1)foremploymentgrowthat thenationallevel.Source:Authors’calculation. 6. MilitaryspendingnewsshockofRameyandZubairy(2018)(https://www.openicpsr. org/openicpsr/project/135741/version/V1/view) Appendix C More Estimation Results C.1 NationalLevel TableC1providestheposteriorestimatesfortheregime-switchingmodelatthenationallevel. The transition probabilities from an expansion regime to L-shaped and U-shaped recession regimes,p andp ,are0.04and0.03,respectively. ThisindicatesthatL-shapedandU-shaped 01 02 recessionsarealmostequallylikelytooccurinemploymentgrowthatthenationallevel. The posterior means for the recession shocks, µ and µ , are estimated at -1.30 and -1.56 for the 1 2 L-shapedandU-shapedregimes,respectively,suggestingthatthemagnitudeoftherecession shocksisquitesimilar. TheCOVID-19scalingparameter,c ,is7.22,indicatingthatCOVID-19 0 hadapproximatelyseventimestherecessionaryimpactonU.S.employmentcomparedtoconventionalrecessions. Thedecayparameter,ρ,isestimatedat0.61,suggestingthattheunusually 5

FigureB1:NONFARMPAYROLLEMPLOYMENTGROWTHBYSTATE(1) 5 5 5 0 0 0 -5 -5 -5 -10 -10 -15 -10 -15 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (a)National (b)AL (c)AK 4 - - 4 2 0 2 -2 0 2 -5 0 -6 -4 -10 -8 -6 -10 -8 -15 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (d)AZ (e)AR (f)CA 5 5 5 0 0 0 -5 -5 -5 -10 -10 -15 -10 -15 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (g)CO (h)CT (i)DE 5 5 0 0 0 -5 -5 -5 -10 -10 -10 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (j)DC (k)FL (l)GA 5 5 0 0 -10 0 -5 -20 -5 -10 -310960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 -1 1 5 960 1970 1980 1990 2000 2010 2020 (m)HI (n)ID (o)IL 5 0 0 0 -5 -5 -5 -10 -10 -10 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (p)IN (q)IA (r)KS 5 5 0 0 0 -5 -5 -5 -10 -10 -10 -15 -15 -15 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (s)KY (t)LA (u)ME 5 5 10 0 0 0 -5 -5 -10 -10 -10 -15 -20 -15 -20 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (v)MD (w)MA (x)MI 5 5 0 0 -5 -5 -10 -10 -15 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (y)MN (z)MS Notestofigure:ThefiguresshownonfaFrigmurep1a:yErmolplloeymmepnltoGyrmowethntacgrroosswsttahtebsy(1s)tate,withthebluedashedline representingthe40-quartermovingaverageofemploymentgrowthforeachstate.Theshadedareasdenotethe NBERrecessions. Sources:BLS,Haver,andauthors’calculation 6

FigureB2:NONFARMPAYROLLEMPLOYMENTGROWTHBYSTATE(2) 5 5 0 0 0 -5 -5 -5 -10 -10 -10 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (a)MO (b)MT (c)NE 10 5 5 0 0 0 -10 -5 -5 -10 -10 -20 -15 -15 -20 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (d)NV (e)NH (f)NJ 5 5 0 0 0 -5 -5 -10 -5 -10 -15 -20 -10 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (g)NM (h)NY (i)NC 4 5 2 0 0 0 -2 -5 -5 -4 -10 -10 - - 8 6 -15 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (j)ND (k)OH (l)OK 5 10 5 5 0 0 0 -5 -5 -5 -10 -10 - - 1 1 5 0 -15 -15 -20 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (m)OR (n)PA (o)RI 5 5 5 0 0 0 -5 -5 -5 -10 -10 -10 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (p)SC (q)SD (r)TN 2 4 5 -1 - - - - 1 8 6 4 2 0 0 960 1970 1980 1990 2000 2010 2020 - - - - 18 6 4 2 0 2 960 1970 1980 1990 2000 2010 2020 - - - 2 1 1 - 1 5 0 0 5 0 960 1970 1980 1990 2000 2010 2020 (s)TX (t)UT (u)VT 5 10 0 0 5 -5 -5 0 -5 -10 -10 -10 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (v)VA (w)WA (x)WV 5 5 0 0 -5 -5 -10 -10 1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020 (y)WI (z)WY Notestofigure:ThefiguresshownonfaFrigmurep2a:yErmolplloeymmepnltoGyrmowethntacgrroosswsttahtebsy(2s)tate,withthebluedashedline representingthe40-quartermovingaverageofemploymentgrowthforeachstate.Theshadedareasdenotethe NBERrecessions. Source:BLS,Haver,andauthors’calculation 7

largeimpactofCOVID-19diminishedrapidly. TheacceptancerateoftheMetropolis–Hastings samplerisapproximately0.35,whichlieswithinthetargetrangeof0.15to0.40suggestedby Gelmanetal.(1997). C.2 State-levelResults FiguresC3andC4presenttheestimatedprobabilitiesofL-shapedandU-shapedrecessionsfor eachstate. ThebluelinesrepresenttheprobabilityofaU-shapedrecession,andtheredlines representthatofanL-shapedrecession. TheY-axisindicatestheprobability,whiletheX-axis showscalendartimeinquarters. TheshadedareasdenoteNBER-datedrecessions. TableC2reportstheestimatedtransitionprobabilitiesandtheexpecteddurationofeach regime for all states, along with the national-level estimates for comparison. The expected durationofregimei iscomputedas1/(1−p ). Acrossallstates,wefindthat(i)eachregimeis ii morelikelytopersistthantotransitiontoanother,indicatingstrongregimepersistence,and(ii) theexpecteddurationofexpansionsismuchlongerthanthatofeitherL-shapedorU-shaped recessions,suggestingthatexpansionsdominatemostsampleperiods. Theexpecteddurationof recessionsisaboutfourquarters(oneyear)onaverage,andinmanystates,U-shapedrecessions tendtolastlongerthanL-shapedones. Appendix D Gender and Hysteresis D.1 OutcomebyGender In this section, we examine effects of U-shaped and L-shaped recessions on the labor force participationrate(LFPR)and EPOPratiointotal andby genderbasedonequation(4.2). TableD3presentstheestimationresults. OnlyL-shapedrecessionsareassociatedwithstatistically significantdeclinesintheLFPRfourquartersahead;incontrast,U-shapedrecessionsshowno statisticallysignificantcorrelationwithchangesinthelaborforceparticipationratefourquarter 8

TableC2:PERSISTENCEOFSTATE-LEVELEXPANSIONSANDRECESSIONS PanelA:StatesA–M TransitionProbabilities ExpectedDurations State pEE pEL pEU pLL pUU Expans. L-shape U-shape National 0.93 0.04 0.03 0.73 0.77 14.69 3.74 4.43 Alabama 0.94 0.04 0.03 0.70 0.76 15.70 3.28 4.10 Alaska 0.95 0.03 0.02 0.64 0.82 18.67 2.74 5.63 Arizona 0.95 0.03 0.02 0.77 0.81 20.27 4.38 5.22 Arkansas 0.95 0.03 0.02 0.76 0.78 19.98 4.09 4.63 California 0.95 0.03 0.02 0.77 0.76 19.50 4.41 4.25 Colorado 0.95 0.03 0.02 0.79 0.80 21.71 4.79 5.07 Connecticut 0.95 0.03 0.02 0.77 0.78 19.35 4.39 4.60 Delaware 0.94 0.03 0.02 0.71 0.75 18.01 3.45 4.05 Florida 0.95 0.03 0.02 0.79 0.80 19.95 4.84 5.04 Georgia 0.95 0.03 0.02 0.76 0.80 19.71 4.17 4.89 Hawaii 0.96 0.02 0.02 0.83 0.76 22.37 5.81 4.18 Idaho 0.94 0.04 0.02 0.70 0.78 15.72 3.31 4.61 Illinois 0.94 0.03 0.03 0.76 0.76 17.77 4.14 4.25 Indiana 0.93 0.04 0.03 0.68 0.77 14.67 3.10 4.32 Iowa 0.94 0.03 0.02 0.69 0.79 17.68 3.25 4.73 Kansas 0.95 0.03 0.03 0.75 0.79 18.19 3.98 4.77 Kentucky 0.94 0.04 0.03 0.69 0.75 15.97 3.22 3.92 Louisiana 0.95 0.03 0.02 0.77 0.75 19.41 4.28 3.97 Maine 0.93 0.03 0.03 0.72 0.70 15.05 3.61 3.35 Maryland 0.95 0.02 0.02 0.78 0.80 21.71 4.47 4.91 Massachusetts 0.95 0.03 0.03 0.78 0.76 18.44 4.46 4.19 Michigan 0.93 0.04 0.03 0.65 0.70 14.72 2.84 3.37 Minnesota 0.94 0.04 0.03 0.74 0.77 15.92 3.83 4.31 Mississippi 0.95 0.03 0.02 0.76 0.77 18.66 4.20 4.40 Missouri 0.94 0.04 0.03 0.68 0.72 16.05 3.12 3.61 Montana 0.95 0.03 0.02 0.74 0.79 20.32 3.81 4.79 PanelB:StatesN–Z TransitionProbabilities ExpectedDurations State pEE pEL pEU pLL pUU Expans. L-shape U-shape Nebraska 0.95 0.03 0.02 0.72 0.80 19.77 3.53 5.05 Nevada 0.95 0.03 0.02 0.79 0.79 21.08 4.73 4.87 NewHampshire 0.95 0.03 0.03 0.81 0.73 18.19 5.23 3.64 NewJersey 0.95 0.03 0.03 0.78 0.75 18.61 4.64 3.98 NewMexico 0.95 0.02 0.02 0.78 0.79 21.45 4.49 4.86 NewYork 0.94 0.04 0.03 0.72 0.77 16.07 3.61 4.42 NorthCarolina 0.95 0.03 0.02 0.75 0.78 19.38 4.06 4.54 NorthDakota 0.95 0.02 0.02 0.79 0.80 22.18 4.82 5.02 Ohio 0.93 0.04 0.03 0.69 0.79 14.08 3.18 4.74 Oklahoma 0.95 0.03 0.02 0.73 0.82 19.87 3.70 5.55 Oregon 0.93 0.04 0.02 0.71 0.80 15.23 3.46 4.88 Pennsylvania 0.95 0.02 0.03 0.79 0.76 19.63 4.70 4.13 RhodeIsland 0.94 0.03 0.03 0.74 0.75 16.88 3.87 3.96 SouthCarolina 0.95 0.03 0.02 0.72 0.80 18.67 3.59 5.00 SouthDakota 0.95 0.03 0.02 0.77 0.80 21.44 4.27 4.92 Tennessee 0.94 0.03 0.03 0.73 0.77 17.56 3.64 4.43 Texas 0.94 0.04 0.02 0.75 0.80 16.64 4.06 5.03 Utah 0.95 0.03 0.02 0.71 0.78 18.54 3.47 4.59 Vermont 0.95 0.02 0.02 0.79 0.77 20.74 4.79 4.41 Virginia 0.95 0.02 0.02 0.78 0.78 21.71 4.64 4.55 Washington 0.95 0.03 0.02 0.76 0.80 19.89 4.23 4.93 WestVirginia 0.95 0.02 0.03 0.83 0.62 19.23 6.04 2.65 Wisconsin 0.93 0.04 0.03 0.66 0.78 13.88 2.91 4.47 Wyoming 0.95 0.03 0.02 0.79 0.84 20.33 4.68 6.22 Washington,DC 0.96 0.02 0.02 0.73 0.84 22.82 3.77 6.16 Notestotable:Estimatesoftransitionprobabilitiesforeachstatecapturethepersistenceandtransitions acrossregimes:p (expansion→expansion),p (expansion→L-shape),p (expansion→U-shape), EE EL EU p (L-shape→L-shape),andp (U-shape→U-shape).Expecteddurationsarecalculatedas(1−p ) −1 LL UU ii fori∈{E,L,U}andaremeasuredinquarters.Source:Authors’calculation. 9

FigureC3:ESTIMATEDRECESSIONPROBABILITIESBYSTATE(1) 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (a)NA (b)AL (c)AK 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (d)AZ (e)AR (f)CA 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (g)CO (h)CT (i)DE 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (j)DC (k)FL (l)GA 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (m)HI (n)ID (o)IL 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (p)IN (q)IA (r)KS 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (s)KY (t)LA (u)ME 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (v)MD (w)MA (x)MI 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (y)MN (z)MS Notestofigure:ThefiguresdisplaystatFei-gluervee3l:rSehcapeesssoiofRnepcersosibonasbaiclriotsisesst.aRteesd(1s)olidlinesindicatetheprobabilityofan L-shapedrecession,bluedashedlinesindicateaU-shapedrecession,andshadedareasdenoteNBERrecessions. Source:Authors’calculation 10

FigureC4:ESTIMATEDRECESSIONPROBABILITIESBYSTATE(2) 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (a)MO (b)MT (c)NE 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (d)NV (e)NH (f)NJ 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (g)NM (h)NY (i)NC 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (j)ND (k)OH (l)OK 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (m)OR (n)PA (o)RI 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (p)SC (q)SD (r)TN 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (s)TX (t)UT (u)VT 1 1 1 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (v)VA (w)WA (x)WV 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 10960 1970 1980 1990 2000 2010 2020 10960 1970 1980 1990 2000 2010 2020 (y)WI (z)WY Notestofigure:ThefiguresdisplaystatFei-gluervee4l:rSehcapeesssoiofRnepcersosibonasbaiclriotsisesst.aRteesd(2s)olidlinesindicatetheprobabilityofan L-shapedrecession,bluedashedlinesindicateaU-shapedrecession,andshadedareasdenoteNBERrecessions. Sources:Authors’calculation 11

TableD3:PREDICTABILITYOFLFPRANDEPOPRATIO LFPR Men Women Total [1]β (pl ) -0.675*** -0.251**-0.476*** l it (0.106) (0.123) (0.070) [2]β (pu) 0.288 -0.080 -0.223 u it (0.370) (0.429) (0.244) ✓ ✓ ✓ Statefixedeffects R2 0.010 0.007 0.019 No. ofobs. 8,772 8,772 8,772 EPOP Men Women Total [1]β (pl ) -2.170***-1.120***-1.627*** l it (0.146) (0.132) (0.098) [2]β (pu) 3.438*** 1.325*** 3.009** u it (0.509) (0.459) (0.341) ✓ ✓ ✓ Statefixedeffects R2 0.027 0.013 0.036 No. ofobs. 8,772 8,772 8,772 Notestotable:ThistablepresentsthecoefficientestimatesfromEquation(5.1),excludingobservationswithzero recessionprobabilities.Thenotations***,**,and*indicatestatisticalsignificanceatthe1%,5%,and10%levels, respectively.Numbersinparenthesesarestandarderrors. Source:Authors’calculation. ahead.36 WealsoseequitedifferenteffectsontheEPOPratio. L-shapedrecessionspredictdeclines intheEPOPratiofourquartersahead,mirroringtheireffectonlaborforceparticipation,while U-shapedrecessionspredictariseintheEPOPratio,primarilydrivenbytheswiftrecoveryof theunemploymentrate. ThesignificantpositiveassociationbetweenU-shapedrecessionsand thefour-quarter-aheadEPOPratio—contrastedwiththesignificantnegativeassociationfor L-shapedrecessions—providesfurtherevidencethatourmethodologyeffectivelydistinguishes betweenthetwodistinctrecessionexperiences. WefurtherexamineheterogeneousresponsesoftheEPOPratioandLFPRbygender. Since thelabordatabygenderareavailableonlyatanannualfrequency,weanalyzeone-yearchanges inthesemeasurestoalignwiththeforecastinghorizonsusedfortheaggregatedata. Overall, the aggregate patterns hold for both gender, though the magnitudes differ. Specifically, L- 36Theresultremainsrobustforh=8. 12

shapedrecessionshavemorenegativeeffectsonmen’sLFPRthanonwomen’s,suggestingthat shocksthattriggerL-shapedrecessionshavepersistentnegativeeffectsonmen’slaborforce participation. Meanwhile,U-shapedrecessionsleadtostrongerpositiveeffectsontheEPOP ratioformenthanforwomen,suggestingthatthereboundofemploymentismoreconcentrated among men. Overall, men’s employment and labor force participation are more cyclically sensitiveandmoreheavilyaffectedbythenatureoftherecoveryinthelabormarket. Thisresult furthersuggeststhatthedisappearanceofU-shapedrecessionsandtheincreasedprevalence ofL-shapedrecessionssincethe1990sarelikelytobeassociatedwiththestagnationofmale employment(Cortesetal.,2018). Alltold,thepersistentnegativeeffectsofL-shapedrecessionsontheLFPRandtheEPOP ratioareconsistentwithpreviousempiricalfindingsonmacroeconomichysteresisdiscussed by Furlanetto et al. (2025) and Alves and Violante (2025). The results validate our empirical methodology’sabilitytodistinguisheffectivelybetweenU-shapedandL-shapedrecessionsand confirmthatL-shapedrecessionseffectivelycapturethephenomenonofhysteresis. D.2 EffectsofGenderGaponHysteresis Table D4 reports the coefficients on the gender gap in the labor market. We consider two measuresofthegendergap: thedifferenceintheEPOPratiobetweenmenandwomen(Gap ), it andanindicatoroftherecessiongendergap(Er ),whichequalsonewhenGap exceedsthe it it cross-state average and is interacted with (1−pe ). The statistically significant and positive it coefficientsindicatethatalargergendergapincreasestherelativeriskofhysteresisoverafull recessionrecovery. 13

TableD4:EFFECTSOFGENDEREMPLOYMENTGAPONTHERELATIVERISKSOFRECESSIONS (1)All(2)2000-2019 (3)All(4)2000-2019 IndicatorofDNWR 0.062*** 0.052***0.050*** 0.039*** (Zr ) (0.009) (0.009) (0.009) (0.009) it Gendergap 0.082** 0.178*** (Gap ) (0.037) (0.043) it Indicatorofrecessiongendergap 0.116*** 0.081*** (Er ) (0.010) (0.015) it (Controls) pe ✓ ✓ ✓ ✓ it ✓ ✓ ✓ ✓ oil-producing ✓ ✓ ✓ ✓ minimumwage ✓ ✓ ✓ ✓ union ✓ ✓ ✓ ✓ manufacturing ✓ ✓ ✓ ✓ prof. services ✓ ✓ ✓ ✓ finance ✓ ✓ ✓ ✓ large-firmshare ✓ ✓ ✓ ✓ tax-incomeshare ✓ ✓ ✓ ✓ Statefixedeffect ✓ ✓ ✓ ✓ Timefixedeffect No. ofObs. 8,256 3,856 8,256 3,856 R2 0.796 0.867 0.799 0.868 Notestotable:ThistablepresentsthecoefficientestimatesfromEquation(5.1)withthezerorecessionprobabilities replacedwiththeminimumofthecorrespondingestimatesandwiththeshareofwagecuts.Thenotations***,**, and*indicatestatisticalsignificanceatthe1%,5%,and10%levels,respectively.Numbersinparenthesesare standarderrors.Panelslabeled“(Controls)”indicatetheinclusionofcontrolvariablesintheregressionmodel. Source:Authors’calculation. 14