美联储-失业保险与宏观金融稳定Unemployment Insurance and Macro-Financial (In)Stability 2024

FinanceandEconomicsDiscussionSeries

FederalReserveBoard,Washington,D.C.

ISSN1936-2854(Print)

ISSN2767-3898(Online)

UnemploymentInsuranceandMacro-Financial(In)Stability

YavuzArslan,AhmetDegerli,BulentGuler,GaziKabas,BurhanKuruscu

2024-087

Pleasecitethispaperas:

Arslan,Yavuz,AhmetDegerli,BulentGuler,GaziKabas,andBurhanKuruscu(2024).“UnemploymentInsuranceandMacro-Financial(In)Stability,”FinanceandEconomicsDis-cussionSeries2024-087.Washington:BoardofGovernorsoftheFederalReserveSystem,

/10.17016/FEDS.2024.087

.

NOTE:StafworkingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminarymaterialscirculatedtostimulatediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstafortheBoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.

UnemploymentInsuranceandMacro-Financial

(In)Stability*t

YavuzArslanAhmetDegerliBulentGulerGaziKabasBurhanKuruscu

Abstract

Weidentifyandstudytwomechanismsthatcanoverturnthestabilizingeffectsofunem-ploymentinsurance(UI)policies.First,householdsineconomieswithmoregenerousUIreducetheirprecautionarysavingsandincreasetheirmortgagedebt.Second,theshareofmortgages,especiallythosewithhigherloan-to-incomeratios,increasesonbankbalancesheets.Asaresult,bothbankandhouseholdbalancesheetsbecomemorevulnerabletoadverseshocks,whichdeepensrecessions.Wedemonstratetheimportanceofthesechannelsbyemployingaquantitativeheterogeneous-agentgeneralequilibriummodelandbyprovidingcounty-levelempiricalevidencefromtheU.S.housingandmortgagemarkets.

Keywords:Automaticstabilizers,unemploymentinsurance,householdandbankbalancesheets,housingmarket,mortgagedebt,foreclosures.

J.E.L.Classification:E21,E32,E44,E60,G20,G51

*WethankMichaelBoutros,WilliamLastrapes,MichalZator,andAndreiZlatefortheirvaluablediscussionsofourpaper.WealsothankMarcoBassetto,SatyajitChatterjee,OliverDeGroot,PabloD’Erasmo,BurcuEyigungor,AlexeyGorn,FatihGuvenen,LoukasKarabarbounis,IlleninKondo,AlisdairMcKay,MakotoNakajima,FabrizioPerri,VincenzoQuadrini,RicardoReis,JuanSanchez,PedroSilos,seminarparticipantsattheBankforInternationalSettlements,GhentUniversity,IndianaUniversity,LancasterUniversity,MinneapolisFed,PhillyFed,St.LouisFed,UniversityofZurich,UniversityofLiverpool,andparticipantsatvariousconferencesforusefulcommentsandsuggestions.KuruscuthankstheSocialSciencesandHumanitiesResearchCouncilofCanadaforfinancialsupport.TheauthorsacknowledgetheIndianaUniversityPervasiveTechnologyInstituteforprovidingcomputingresourcesthathavecontributedtotheresearchresultsreportedwithinthispaper.Arslan:UniversityofLiverpoolManagementSchool,yavuz.arslan@liverpool.ac.uk;Degerli:FederalReserveBoard,ahmet.degerli@;Guler:IndianaUniversity,bguler@;Kabas:TilburgUniversity,g.kabas@;Kuruscu:UniversityofToronto,burhan.kuruscu@utoronto.ca.TheviewsexpressedherearethoseoftheauthorsandnotnecessarilyreflectthoseoftheFederalReserveBoard.

tThisversion:September2024.

1

1Introduction

Automaticstabilizersaregovernmentpoliciesthatautomaticallyadjusttaxrates,andtransferpaymentstostabilizeincomeandconsumptionwithoutrequiringavotefromlegislators.Unemploymentinsurance(hereafterUI)isoneofthetextbookexamplesofautomaticstabilizers.ThepredominantviewisthatUIpoliciesstabilizeeconomicdownturnsbyreducingincomeriskandtransferringincometohouseholdswithahighmarginalpropensitytoconsume(MPC)

.1

Inthispaper,weidentifytwonovelmechanismsstrongenoughtooverturnthestabilizingeffectsofUI.First,duetothedeclineinleft-tailincomeriskasUIbecomesmoregenerous,householdsreducetheirprecautionarysavings(liquidassets)andtakeonmoremortgagedebt,leadingtohigherleverage.Second,thedeclineinhouseholds’left-tailincomeriskalsoreducestheirdefaultrisk,inducingbankstoofferloosercredittermsandincreasingtheshareofmortgages(especiallythosewithhigherloan-to-incomeratios)ontheirbalancesheets.Asaresult,bothhouseholdandbankbalancesheetsbecomemorevulnerabletoadverseshocks.Consequently,aneconomywithUI-inducedvulnerabilitiesinhouseholdandbankbalancesheetsmayexperiencedeepercontractionsinresponsetoadverseshocks,despitethecushioningeffectsofUIbenefits.WedemonstratetheimportanceofthesechannelsusingaquantitativegeneralequilibriummodelandempiricalevidencefromUShouseholdandcounty-leveldatafromhousingandmortgagemarkets.

Ourmodelcombines(i)households,withanoverlapping-generationsstructure,whofaceidiosyncraticincomeandunemploymentrisksunderincompletemarketsandmakehousingandmortgagedecisions;(ii)banksthatissueshort-termloanstofirmsandlong-termmortgagestohouseholds,andaresubjecttocapitalconstraints;(iii)firmsthatproduceoutputusingcapitalandlaborbutneedtofinanceaportionoftheirworkingcapitalthroughshort-termloansfrombanks;(iv)realestatecompaniesthatownapartofthehousingstock,whichtheyrenttothehouseholds;and(v)thegovernmentthatmanagestheUIpolicy.

Householdscandefaultontheirmortgagesinanyperiodthroughoutthelifeofthemortgage.Mortgagecontractsinternalizethedefaultprobabilityofhouseholds,henceeach

1See,forexample,

Brown

(1955),

Blinder

(1975),

McKayandReis

(2016),and

McKayandReis

(2021)

forearlierandmorerecentdiscussionsofthesemechanisms.

2

mortgageisindividual-specific,andborrowinglimitsendogenouslyariseduetolimitedcommitmentbyhouseholds.AnimplicationisthatahigherUIreduceshouseholds’defaultrisk,ceterisparibus,andallowsthemtoaccessbettercreditterms,leadingtoincreasedborrowinginthemortgagemarket.

Banksprovideshort-termrisk-freeloanstofirmsandlong-termdefaultablemortgagestohouseholds.Theyfundtheseloansthroughbankequityandshort-termborrowingatanexogenouslygiveninterestrate.Asiscommonintheliterature,weassumethatbankerscandefaultandkeepafractionoftheirassets

.2

Topreventsuchbehaviorinequilibrium,bankcreditorsconditiontheirfundingtobankequity.Therefore,bankcreditsupplydependsonbankequity.Consequently,anylossesinbankbalancesheetsleadbankstoreducecreditsupply,causinganincreaseintheequilibriumbanklendingrate.This,inturn,resultsinhigherborrowingcostsforhouseholdsandfirms.

WecalibratethesteadystateofthemodeltomatchUSdatamoments,mostimportantlythoseregardinghouseholdandbankbalancesheets,unemploymentriskbyearnings,andunemploymentduration.Wefirstanalyzethesteady-stateeffectsofUI:astheUIreplacementrateincreasesfrom20to60percent,themortgagedebt-to-GDPratioincreasesfrom76.4percentto82.6percent,anddownpayments(onaverage)declinefrom10.4percentto8.4percent,increasinghouseholdleverage.Moreover,householdsreducetheirfinancialassetsby3.3percent,whichincreasesthefractionofhand-to-mouthhouseholds.Inparallel,theshareofmortgagesamongbankassetsincreasesfrom45.7percentto47.7percent.

Ourmodelconfirmsthat,inthesteadystate,UIachievesitsintendedpurposeofhelpingtheunemployeddespitetheirhigherleverage.Specifically,theunemployedexperiencehigherconsumptionandlowerforeclosuresinmoregeneroussystemssincetheyreceivehigherUIpayments.However,theoppositeistruefortheemployedsincetheyaremoreleveragedbutdonotreceiveUIbenefits.Additionally,theemployedpayhighertaxestofundmoregenerousUI.ThisdifferentialeffectofUI(employedversusunemployed)iscrucialinunderstandingthedestabilizingeffectsofUIinourmodelinresponsetoaggregateshocks.

ToanalyzehowUIaffectstheeconomicdynamicsduringboomsandbusts,weintroducetwounanticipatedandpermanentshockstotheexogenousbankborrowingrateinthemodeleconomy.First,whiletheeconomyisintheinitialsteadystate(representingtheU.S.economy

2See

GertlerandKiyotaki

(2015)

.

3

priorto1997),aboomstartswiththebankfundingcostdecliningfrom1997until2006andisexpectedtostaylowthereafter.Second,thebustperiodstartsin2008,whenthebankborrowingrateunexpectedlyandpermanentlyrevertstoitsinitialsteady-statelevel

.3

Furthermore,toincorporateastabilizingroleforUI,weintroduceanadditionalunem-ploymentshockin2008thatdeclineslinearlyuntil2013—mimickingtheU.S.experiencearound2008.WedemonstrateinthepaperthatthedestabilizingeffectsofUIarelargerintheabsenceofthisshock,strengtheningthemainpointsofthepaper.

Theseshocksgenerateaboom-bustcycleinthehousingmarketandthemacroeconomysimilartotheUSexperience,althoughthesizeoftheboom-bustissmallerinthemodel.Duringtheboom,theequilibriumbanklendingrategraduallyfalls,closelyfollowingthedeclineinthebankfundingcost.Asborrowingcostsforhouseholdsandfirmsdecline,householdsincreasemortgageborrowingandhousingdemand,causinghousepricestoincrease;firmshiremorelabor,leadingtoincreasesinlaborincomeandoutput,whichfurthercontributestotheincreaseinhouseprices.Thecombinationoftheincreasesinhousepricesandlaborincomegeneratesanincreaseinaggregateconsumption.

Inthebustperiod,allaggregatevariablesofinterestfallbelowtheirinitialsteady-statelevelwhilethebankcapitaldeterioratessharplyduetoincreasedforeclosuresandthedeclineinmortgagevaluations.Sincetheamountthatbankscanlenddependsontheircapital,banksareforcedtocutbacklending,whichinequilibriumcausesalargebuttemporaryspikeinthebanklendingrate.Then,duetohighborrowingcosts,firmscutbackemployment,loweringincometohouseholds.Householdscutbackconsumptionduetothecombinationoflowerincomeandhouseprices,andhigherborrowingcosts.

Tounderstandthe(de)stabilizingeffectsofUI,wecomparetheboom-busttransitionsgeneratedbytheshocksaboveineconomieswithpermanentlydifferentlevelsofUIgenerosity.Theresultsofthisexerciseillustratethat,duringthebust,economieswithmoregenerousUIbenefitsexperiencelargerincreasesinforeclosuresandbanklendingrates,aswellasgreaterdeclinesinbanknetworth,houseprices,householddebt,consumption,andoutput.

3Wehavechosenshockstothebankborrowingrateasthedriveroftheboom-bustcycleinthebenchmarkanalysissince,intheempiricalpartofthepaper,weshowthattheeffectsofchangesininterestratesonhousingandmortgagemarketsareamplifiedinmoregeneroussystems.However,wedemonstrateinthepaperthatthedestabilizingeffectsofUIarepresentunderproductivityandhousepriceexpectationshocksaswell.

4

TheaggregatedestabilizingeffectsofUIaremainlydrivenbyitsinfluenceontheemployed.Whilethebalancesheetvulnerabilitiesaffectboththeemployedandunemployed,theunemployedreceivehigherbenefitsinmoregenerousUIeconomiesduringthebustbuttheemployeddonot.Consequently,theconsumptionoftheunemployedisstabilizedinthebustperiodundermoregeneroussystems.However,theforeclosurerateoftheunemployedfollowsanon-monotonicpattern:itincreaseswithUIforlowUIlevelsandthendeclines.Ontheotherhand,theemployedexperiencelargerdeclinesinconsumptionandagreaterincreaseinforeclosuresundermoregenerousUI,drivingaggregatetrends,astheemployedconstitutethemajority.

TheweakeningeffectsofUIonbothhouseholdandbankbalancesheetsdriveourresults.Onthehouseholdside,first,households’abilitytoinsureagainstincomelossduringthebustislowerduetolowerprecautionarysavingsinhigherUIeconomies.Second,sincehouseholdsaremoreleveragedinhigherUIeconomies,agivendeclineinhousepriceshasalargerwealtheffect.Onthebankingside,thehighershareofmortgagesinbankbalancesheetsandhighermortgagedebt-to-incomeratiosinhigherUIeconomiesmakebanksmorevulnerabletoadverseshocksfortworeasons.First,asmortgagesarelong-termassets,theirmarketvaluedeclinesastheequilibriumbanklendingrateincreases.ThiseffectisamplifiedinmoregenerousUIsystemssincethefractionofmortgagesishigherinbankbalancesheets.Second,highermortgagedebt-to-incomeratiomakesbanksmorepronetoforeclosurelosseswhenanunexpectedbustintheeconomylowershousepricesandincome.Consequently,banknetworthdeclinesmoreduringthebustinmoregenerousUIeconomies,causingalargerdeclineincreditsupplyandalargerincreaseintheequilibriumbanklendingrate,whichincreasesborrowingcostsmoreforbothhouseholdsandfirms,deepeningtherecession.

Tounderstandtheimportanceofhouseholdandbankbalancesheetsinourmodel,westudytheeconomicdynamicsduringthebust,byclosingthegeneralequilibriumfeedbackfrombankbalancesheetstothebanklendingrate.Thisessentiallyeliminatesthesharpincreaseinthebanklendingrateduringthebustresultingfromdeterioratingbankbalancesheets.Wefindthat,inthiscase,higherUInolongerdestabilizesoutputandconsumption.Housepricesandhouseholddebtstilldecreasemore,andforeclosuresstillincreasemoreundermoregeneroussystems,buttheeffectsarerelativelysmaller.Overall,thesefindingshighlightthesignificantrolesofbothhouseholdandbankbalancesheetsinthedestabilizing

5

effectsofUI.

TheimportanceofthegeneralequilibriumfeedbackfrombankbalancesheetstothebanklendingrateinamplifyingthedestabilizingeffectsofUIillustratesthatincreasingUIgenerosityforthewholeeconomycreatesasystemicvulnerabilityinthenationalbankingsystem.Ontheotherhand,whenonestateintheUSincreasesitsUI,itdoesnotgenerateasystemicriskinthenationalbankingsystem.Consequently,empiricalstudiesrelyingoncross-statevariationinUImightunderestimate(overestimate)thedestabilizing(stabilizing)effectsofUIsincetheydonotcapturethesystemicriskcreatedbyincreasingtheUIforthe

wholeeconomy.4

ThedestabilizingeffectsofUIthatwefindarenotana-prioriunambiguousoutcome.Infact,wefindthatunexpectedandtemporaryincreasesinUIstabilizedownturns.However,permanentdifferencesinUIaffecthouseholdandbankbalancesheetsinamannerthatmakesthemvulnerabletodownturns,outweighingitsstabilizingeffects.

Inthesecondpartofthepaper,weprovideempiricalevidencefromtheUShousingandmortgagemarkets,consistentwithourmodel’spredictions.WeusetheUIsystemintheU.S.aseachstatesetsitsUIlevel,leadingtosignificantheterogeneityinUIgenerosityacrossstates.First,weexploretherelationshipbetweenUIgenerosityandhouseholdleverage.WeuseHomeMortgageDisclosureAct(HMDA)dataandshowthatUIandloan-to-income(LTI)ratioatmortgageoriginationarehighlypositivelycorrelatedacrossUScounties.Quantitatively,asUIbenefitsincreasefromthe10thpercentiletothe90thpercentile,theLTIratioincreasesby20percentagepoints(equivalenttoaround10percent).Thiseconomicallylargeeffectstillholdswhenweincludeyear,county,andbank-yearfixedeffectstocontrolfortime-invariantcounty-levelcharacteristicsandtime-varyingbankcharacteristics.

Tosupportcausalinterpretation,wealsoexploitanunexpectedcutinUIbenefitsdurationinMissouriin2011(from73weeksto57weeks)(

JohnstonandMas

(

2018

)).AsMissouriistheonlyaffectedunit,weemployasyntheticcontrolapproach(

Karahan,MitmanandMoore

(2019))

.WefindthattheaverageLTIratioinMissouriwouldhavebeen10basispoints(approximately5percent)higheriftherewerenoreductionsintheUIduration,indicatingacausalpositiveeffectofUIontheLTIratio.

4Cross-statevariationinUIwouldcapturetheeffectofhigherUIonbankbalancesheetsonlytotheextendthatbanksarelocalandlocalhouseholdsandfirmsrelyonlocalbanks.

Next,weanalyzethedelinquencybehavioroftheemployedhouseholdsinthedatatotestthemodel’spredictionthattheforeclosurerateamongtheemployedishigherinhigherUIeconomieswhenhousepricesdecline.Indoingso,wecloselyfollow

Hsu,MatsaandMelzer

(2018)andusetheSurveyofIncomeandProgramParticipation(SIPP)data,whichincludes

mortgagedelinquencyinformation,astrongpredictorofforeclosures.WefindthatemployedindividualsinstateswithhigherUIbenefitsexperiencedahigherdelinquencyratewhenhousepricesdeclinedduringthe2008crisis.

Finally,wetestthemodel’spredictionthatUIpoliciesdestabilizethehousingmarket.Inparticular,wefocusonhousepricesandmortgagecreditvolumeandanalyzehowUIbenefitsinteractwiththechangesinlong-terminterestrates—theshockthatweuseinthequantitativemodel.Toensurethatourresultsarenotdrivenbyomittedvariables,weuseborderdiscontinuitydesignandexploittheheterogeneityinUIlevelsacrossstatebordersbycomparingtwoneighboringcountiesthatarelocatedatstateborders,oneofthemlocatedinonestateandtheotherlocatedintheotherstate

.5

OurresultsshowthatcountieswithmoregenerousUIbenefitsexperiencehighermortgageandhousepricegrowthwhenlong-terminterestratesdecline.Inallofourregressionmodels,weincludeotherimportant

macroeconomicvariables,theirinteractionswithUIbenefits,aswellasotherstate-levelsocialwelfarepoliciesandtheirinteractionswithlong-termrates.Overall,theseresultsprovideevidencethatUIbenefitsmightfailtoactasanautomaticstabilizer.

RelatedLiterature:Thereisampleevidencethatsupportsthebalancesheetchannelsthatwehighlightinthispaper.

MianandSufi

(2010)and

Mian,RaoandSufi

(2013)showthatU.S

.countieswithhigherhouseholdleverageasof2006experiencedadeeper2007–09recession.

KaplanandViolante

(2014)highlighttheimportanceof“hand-to-mouth”consumersforthe

responseofaggregateconsumptiontoincome/wealthshocks.Inourmodel,amoregenerousUIincreasesthefractionofhand-to-mouthhouseholds,makingindividualconsumptionmoredependentonindividualincome,increasingtheeconomy’sresponsetoadverseshocks.Onthebankingside,theroleofmortgagesintheGreatRecessioniswelldocumented(

Bernanke

(2018),

GertlerandGilchrist

(

2018a

),and

BrunnermeierandReis

(

2023

)).

OurpapercontributestotheliteratureontheautomaticstabilizationeffectsofUI.

McKay

5Dube,LesterandReich(2010),Hagedornetal.(2013),Hagedorn,ManovskiiandMitman(2015),and

Arslan,DegerliandKabas(2024)alsousestateborderdiscontinuitydesign.

6

7

andReis

(2016,

2021

)mergethestandardincomplete-marketsmodelofconsumptionwiththe

NewKeynesianmodelofnominalrigiditiesandbusinesscyclesandfindthattax-and-transferprogramsreduceaggregatevolatility.

DiMaggioandKermani

(2016)usecross-sectional

variationinbenefitreplacementratestoshowthathigherUIattenuatestheimpactofadverseshocksonemployment.

Hsu,MatsaandMelzer

(2018)findthatUIbenefitswerebeneficial

insmoothingthehousingmarketbyloweringmortgagedefaultsoftheunemployed.Wealsofindsimilareffectsontheunemployedbothinourquantitativemodelandinmicrodata.Wedifferfrom

Hsu,MatsaandMelzer

(2018)byanalyzingthedestabilizingeffectsofUIonthe

employed,whichconstitutethemajority.Sincetheemployedconstitutethemajority,theaggregatesaredominatedbytheirresponses.Overall,wecontributetothisliteraturebyidentifyingnewchannelsthatoverturnthestabilizingeffectsofUI,whichwedemonstratetobeimportantbothquantitativelyandempirically.

WealsocontributetotheliteraturethatinvestigatesthecostsandbenefitsofUIbenefits.MoststudieshavefocusedonthenegativeimpactofUIonthelabormarket.While

Chodorow-

Reich,CoglianeseandKarabarbounis

(2018)reportsmalleffects,

Hagedornetal.

(2013),

Hagedorn,ManovskiiandMitman

(2015),and

Nakajima

(2012)findsignificantadverseeffects

onemployment.Recently,

Arslan,DegerliandKabas

(2024)studiesthenegativeimpactof

UIonbankfunding.TheyfindthatmoregenerousUIlowersbankdeposits,banks’safestandmoststablefundingsource,reducingtheirlendingtofirms.ThereisalsoavastliteraturethatstudiesthemoralhazardaspectsofUI,whichweabstractfrominthispaper(

Shavell

andWeiss

(1979),

HansenandImrohoroglu

(1992),

AtkesonandLucas

(1995),

Hopenhayn

andNicolini

(1997),and

Abdulkadiroglu,KuruscuandSahin

(2002))

.Wedonotmodeljobsearchand/orjobcreation,moralhazardorbankfundingchoice,whichhavebeenthemainmechanismsconsideredinthesestudies,andhavealreadybeenshowntohindertherisk-sharingbenefitsorthestabilizingeffectsofUI.Instead,wecomplementthesestudiesbystudyingthenegativeeffectsofUIonhouseholdandbankbalancesheets.

Ourpapersharessimilaritieswith

Hubbard,SkinnerandZeldes

(1995),

Athreyaand

Simpson

(2006),and

BornsteinandIndarte

(2023)thatexaminetherelationshipbetween

precautionarysavings,creditmarkets,andpublicinsurance.Consistentwithoursteady-statefindings,

Hubbard,SkinnerandZeldes

(1995)findthatprecautionarysavingsdecline

significantlywiththepresenceofsocialinsurance.

AthreyaandSimpson

(2006)findthat

8

increasesinpublicinsurancegenerositymightleadtomoreunsecuredhouseholddebt.

BornsteinandIndarte

(

2023

),leveragingzipcodeheterogeneityinstaggeredexpansionsofMedicaid,findthattheexpansionledtoasignificantincreaseinhouseholddebt.WecomplementthesestudiesbystudyingtheeffectsofUIonmortgagedebt.Inaddition,weanalyzethedestabilizingeffectsofUIonmortgageissuanceandhouseprices.

Themechanismsinourpaperaresimilartothosewiththefinancialfrictionsandpecuniaryexternalitiespresentin

Lorenzoni

(

2008

)and

BrunnermeierandSannikov

(

2014

).Intheirframework,contractsthatimproverisk-sharingmayleadtohigherleverageandamplifiedcrises.Similarly,inourframework,higherUIbenefitsinsurehouseholdsagainstrisk,andhouseholdsrespondbyborrowingmoreformortgages,amplifyingboomsandbusts.

Methodologically,ourequilibriumframeworkcombineskeyelementsfromtwoliteratures.

First,onestrandofliteraturehasmodeledthepricingofhouseholddefaultriskinthemortgagemarketwithoutconsideringitsconsequencesonbankbalancesheets

.6

Second,anotherliteraturehasstudiedtheimportanceofthebankbalancesheetchannelwithouttakingintoaccounttheeffectofhouseholdforeclosuresonbankbalancesheets

.7

Inadditiontostudyingadifferentquestionfromthoseexploredinthesepapers,ourtheoreticalcontributionistocombinehousehold,firm,andbankbalancesheetsintooneframework,asdonein

Arslan,

GulerandKuruscu

(2023),whostudiedthedriversoftheUSboom-bustcyclearound2008

.WeintroduceunemploymentriskandUIbenefitstostudythe(de)stabilizingeffectsofUI.

2QuantitativeAnalysis

2.1TheModel

Themodeliscomposedoffivesectors:(i)finitely-livedhouseholds,(ii)acontinuumofall-identicalbanks,(iii)realestatecompanies,(iv)good-producingfirms,and(v)thegovernment.Thereisnoaggregateuncertainty.Boom-busttransitionsaregeneratedby

unexpectedshocks,whichareperceivedaspermanent.Otherthantheshockperiods,thereis

6See

Jeske,KruegerandMitman

(2013),

CorbaeandQuintin

(2015),

ChatterjeeandEyigungor

(2015),

Arslan,GulerandTaskin

(2015),

Guler

(2015),

Hatchondo,MartinezandSanchez

(2015),

Boar,Goreaand

Midrigan

(2021),

Kaplan,MitmanandViolante

(2020),and

Guren,KrishnamurthyandMcQuade

(2021)

.

7See

MendozaandQuadrini

(2010),

GertlerandKiyotaki

(2010,

2015),

BianchiandBigio

(2022),and

CorbaeandD’Erasmo

(2013,

2021

).

9

perfectforesight.Inthissection,weprovideadescriptionofeachsector.DetailedformulationsofalltheproblemsisprovidedintheAppendix

A.

2.1.1Households

HouseholdsliveuntilageJ,retireatageJr<J,andreceiveutilityfromconsumptionandhousingservices.Therearetwotypesofhouseholds:capitalistsanddepositors,denotedbyi∈{K,D}.Therearetwofundamentaldifferencesbetweencapitalistsanddepositors.First,capitalistssavethroughsharesingood-producingfirmsandrealestatecompanies,whichpaythesamerateofreturnrkinaperfectforesightequilibrium(moreonthislater).Ontheotherhand,depositorssavethroughbankdeposits,whichpayanexogenousinterestrater.Second,weallowthemtodifferintheirdiscountfactors.Withthesedifferencesthemodelcanmatchwealthinequalityandtheshareofhand-to-mouthconsumers,whichallowsustogeneratereasonableconsumptionresponses(seealso

KaplanandViolante

(2014))

.8

IncomeandUnemploymentRisk:Working-agehouseholdscanbeeitheremployedorunemployedexogenously.Whentheyareemployed,theysupplylaborinelastically.Theefficiencyunitofahousehold’slabortakestheformexp(f(j)+z),wheref(j)isthelife-cyclecomponentofthehousehold’sproductivity,kistheemploymentstatus(eforemployedanduforunemployed),andzjfollowsanAR(1)processgivenbyzj=ρzj−1+εj,withεjbeingindependentlyandidenticallydistributedasN(0,σ)

.9