BoardofGovernorsoftheFederalReserveSystemInternationalFinanceDiscussionPapers

ISSN1073-2500(Print)ISSN2767-4509(Online)

Number1397

October2024

HouseholdExcessSavingsandtheTransmissionofMonetaryPolicy

ThiagoR.T.Ferreira,NilsGornemann,JulioL.Ortiz

Pleasecitethispaperas:

Ferreira,ThiagoR.T.,NilsGornemann,JulioL.Ortiz(2024).“HouseholdEx-cessSavingsandtheTransmissionofMonetaryPolicy,”InternationalFinanceDiscus-sionPapers1397.Washington:BoardofGovernorsoftheFederalReserveSystem,

/10.17016/IFDP.2024.1397

.

NOTE:InternationalFinanceDiscussionPapers(IFDPs)arepreliminarymaterialscirculatedtostimu-latediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstafortheBoardofGovernors.ReferencesinpublicationstotheInternationalFinanceDiscussionPapersSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.RecentIFDPsareavailableontheWebat/pubs/ifdp/.ThispapercanbedownloadedwithoutchargefromtheSocialScienceResearchNetworkelectroniclibraryat.

HouseholdExcessSavingsandthe

TransmissionofMonetaryPolicy*

ThiagoR.T.FerreiratNilsGornemann?JulioL.Ortiz§

October8,2024

Abstract

HouseholdsavingsroseabovetrendinmanydevelopedcountriesaftertheonsetofCOVID-19.Givenitslinktoaggregateconsumption,thepresenceofthese“ex-cesssavings”hasraisedquestionsabouttheirimplicationsforthetransmissionofmonetarypolicy.Usingapanelofeuro-areaeconomiesandhigh-frequencymone-tarypolicyshocks,wedocumentthathouseholdexcesssavingsdampentheeffectsofmonetarypolicyoneconomicactivityandinflation,especiallyduringthepandemicperiod.Torationalizeourempiricalfindings,webuildaNewKeynesianmodelinwhichhouseholdsusesavingstoself-insureagainstcounter-cyclicalunemploymentandconsumptionrisk.

KeyWords:MonetaryPolicy,ExcessSavings,PrecautionarySavings,ConsumptionRisk,Unemployment

JELClassification:E12,E21,E24,E31,E52.

*WearegratefultoMitchLottforoutstandingresearchassistance.WealsothankMatteoIacoviello,PhillipJefferson,StevenOngena,ChristopherWaller,andpresentationattendeesattheFederalReserveBoardandthe2024IJCBconferencefortheircommentsandsuggestions.TheviewsexpressedinthispaperaresolelythoseoftheauthorsandshouldnotbeinterpretedasreflectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystemorofanyotherpersonassociatedwiththeFederalReserve

Sys.eralReserveBoard,InternationalFinanceDivision;Washington,DC,20551,USA;Emailaddress:

thiago.r.teixeiraferreira@.

?FederalReserveBoard,InternationalFinanceDivision;Washington,DC,20551,USA;Emailaddress:nils.m.gornemann@.

§FederalReserveBoard,InternationalFinanceDivision;Washington,DC,20551,USA;Emailaddress:julio.l.ortiz@.

1

1Introduction

DuringtheCOVID-19pandemic,householdsaroundtheworldaccumulatedlargestocksofsavingsthroughacombinationofprecautionarymotives,aninabilitytospendtheirfundsamidwidespreadlockdowns,andincreasedfiscalsupporttotheirincomes.Soonafter,themainconcernofpolicymakersquicklyswitchedfromalleviatingthelackofhouseholdincometofightingdecades-highinflation.Still,householdsmaintainedrobuststocksof“excesssavings”(i.e.,savingsinexcessoftrend),andpolicymakersbegantoquestiontheirpossibleeffectsonthetransmissionofmonetarypolicy.

1

Inthispaper,weevaluatetheeffectsofexcesssavingsonmonetarypolicytransmission,bothempiricallyandtheoretically.Wedocumentthatexcesssavingsineuro-areaeconomiesrosetohistoricallyhighlevelsduringthepandemicperiod.Then,usinghigh-frequencymonetarypolicyshocks,weestimatestate-dependenteffectsofmonetarypolicyusinglocalprojections(

Jord`a,

2005

),andwefindthatmonetarypolicytransmissiontobothinflationandeconomicactivityisdampenedinperiodsofhighexcesssavings.Finally,werationalizehowexcesssavingsaffectthetransmissionofmonetarypolicyusingaNewKeynesianmodelinwhichhouseholdsfaceidiosyncratic,countercyclicalunemploymentandconsumptionriskagainstwhichtheycanonlyself-insurethroughsavings.

Webeginbymeasuringthestockofexcesssavingsandmonetarypolicyshocksforeuro-areaeconomies.Inadditiontotheeuro-areaaggregate,ourempiricalanalysisfocusesonthefourlargesteuro-areacountries:Germany,Italy,France,andSpain.Following

deSoyreset

al.

(2023),wedefinehouseholdexcesssavingsastheamountofsavingsarisingfromabove

-trendhouseholdsavingsrates.Toestimatecountry-leveltrendsavingsrates,weemploythe

Hamilton

(2018)filter

.Ourmeasureofexcesssavingsexhibitsvariationacrosstimeandcountries,withthepandemicperiodshowinghistoricallyhighlevels.Tomeasurethemonetarypolicyshocks,weapplythehigh-frequencyapproachof

Buetal.

(

2021

)totheeuroarea,whichaccountsforthemixofpoliciesfromtheEuropeanCentralBank(ECB)focusedonbothpolicyratesandassetpurchases.

Aftermeasuringtheseobjects,weusethemtoestimatetheeffectsofmonetarypolicyonrealandnominaloutcomes.Wefocusontwovariablesofinterest:theunemploymentrateandconsumerpriceinflation.Weestimatetheeffectsofmonetarypolicyontheseoutcomes

ofinterestvialocalprojections.Ourestimatesrevealthattheeffectofacontractionary

1Forinstance,seethe

speech

byChristineLagarde,PresidentoftheEuropeanCentralBank,at“TheECBandItsWatchersXXIII”conference.

2

monetarypolicyshockonrealandnominaloutcomesofinterestisattenuatedwhenstocksofexcesssavingsarelarger.Wefindthatourresultsarerobustto(i)differentmeasuresofeconomicactivity,(ii)controllingforthebalancesheetstrengthofthebankingsystem,and(iii)time-specificchangesaroundtheCOVIDperiod.

Ourempiricalresultscanbesummarizedasfollows.Wefindthatacontractionarymonetarypolicyshockscaledtogeneratea50basispointincreaseinthetwo-yearGermangovernmentyieldraisestheunemploymentratebyabout0.30percentagepointwhenexcesssavingsareclosetozero,butonlybyabout0.15percentagepointwhenexcesssavingsarefixedtotheir2023Q1levels.Additionally,weshowthattwelve-monthheadlineinflationdeclinesbynearly0.40percentagepointwhenexcesssavingsareclosetozero,butonlybyabout0.30percentagepointwhenexcesssavingsareconsistentwiththeirobserved2023Q1levels.Wechoosetoevaluatetheefficacyofmonetarypolicyin2023Q1becauseeuro-areaheadlineinflationpeakedaroundthistime,therebyconstitutingamomentatwhichpolicymakerspaidheightenedattentiontotheeffectivenessofmonetarypolicygoingforward.

Motivatedbyourempiricalfindings,webuildasimpleNewKeynesianmodelwithunemploymentandimperfectinsuranceagainstindividualunemploymentrisk.RelativetothestandardrepresentativeagentNewKeynesiansetting,savingsinourmodelarevaluedbecausetheyallowworkerstoself-insureagainsttheconsumptionriskofbeingunemployed.Unemploymentriskrisesduringcontractions,inducingworkerstocutbackconsumptionfurtheratthestartofadownturntosavemore.Thisresponseamplifiesthedirectimpactofanycontractionaryshock.Highersavingsattheonsetofthedownturnreducethiscon-sumptionresponseandthereforeleadtolessamplification.Asaresult,consistentwithourempiricalfindings,acalibratedversionofourmodelgeneratesdampenedrealandnominalresponsestomonetarypolicyshocksinahigh-savingseconomyrelativetothebaselineeconomy.Intotal,ourempiricalandquantitativeresultspointtoaneconomicallymean-ingfulnonlinearityinthepotencyofmonetarypolicybasedonthelevelofstocksofexcesssavings.

Ourpaperrelatestotherecentliteraturemeasuringexcesssavingsandstudyingtheiraggregateimplications.Ourmethodformeasuringexcesssavingsfollows

deSoyresetal.

(2023)

.Alternativeapproachestomeasuringexcesssavingsinclude

Aladangadyetal.

(2022)

and

AbdelrahmanandOliveira

(2023)

.Wetakeatime-varyingfilteringapproachbecauseitbestsuitsourpurposeofestimatingtheeffectsofmonetarypolicyshocksinapanelofeuro-areaeconomieswitharichtimedimension.Additionally,thereareotherrecent

3

studiesevaluatingtheeffectsofexcesssavingsaccumulatedduringCOVID-19.

Auclert

etal.

(2023)analyzestheprocessbywhichhouseholdexcesssavingsaffectthelevelof

aggregatedemand,andhowthisprocessvariesbasedonthedistributionofexcesssavings.

Aggarwaletal.

(2023)studydebt-financedfiscaltransfersinamodeloftheworldeconomy

thatreproduceslargefiscaldeficits,largeincreasesinprivatesavings,andpersistentcurrentaccountdeficits.Wecontributetothisliteraturebyempiricallyandquantitativelylinkingaggregateexcesssavingstomonetarypolicyeffectivenessinthecontextoftheeuroarea.

Ourpaperalsorelatestotheliteratureonthehowmonetarypolicytransmitstohouseholds.Recentcontributions,suchasthosemadeby

Cloyneetal.

(2020),findthat

mortgagorsaremoresensitivetomonetarypolicythanoutrightownersbecausethefor-merhavelittleliquidwealth.Inaddition,

HardingandKlein

(2022)and

Alpandaetal.

(2021)findempiricallythatmonetarypolicyismoreeffectiveinaffectingthemacroecon

-omywhenhouseholddebtisrisingorhigh

.2

Onthemodelingsideourpaperrelatestohouseholdmodelsofprecautionarysavingsdemandinthepresenceofcountercyclicalid-iosyncraticrisk,suchas

AcharyaandDogra

(2020),

Bilbiie

(2018),

Challeetal.

(2017),

Cho

(2023),

DenHaanetal.

(2018),

Gornemannetal.

(

2016

),and

RavnandSterk

(

2017

).Theempiricalstatedependencewedocumentcanbeviewedassupportiveofthemechanismsinthesepapers.Ourpaperissimilartothem,thoughitstudiesstatedependenthouseholdresponsivenesstomonetarypolicyacrossmajoreuro-areacountriesandinthecontextofexcesssavingsratherthanhouseholddebtornetworth.Ourmeasureofexcesssavings,particularlyaroundCOVID-19,likelyreflectsaninfluxofliquidsavingsthatallowedmanyEuropeanhouseholdstoremainclearofborrowingconstraintsduringtherecenttighteningcycle.

Therestofthepaperisorganizedasfollows.Section

2

discussesthedatausedforourempiricalanalysis–particularlyourmeasuresofexcesssavingsandeuro-areamonetarypolicyshocks.Section

3

reportsourempiricalresults,whichshowthattheeffectsofmon-etarypolicyaredampenedwhenstocksofhouseholdexcesssavingsarehigh.Section

4

explorestheeconomicmechanismthroughwhichexcesssavingsaffectthetransmissionofmonetarypolicyinasimpleNewKeynesianmodelandpresentssimulationsrationalizingourempiricalresults.Section

5

concludes.

2

HardingandKlein

(2022)provideanalternativemechanismtorationalizeourfindings

.Intheirmodel,highersavingswouldrelaxacollateralconstraint,leadingtoadampeningofcontractionaryshockswhenconstrainedagentscutbackonconsumption.Weviewourmechanismascomplementarytotheirs.

4

2DataDescription

Inthissection,wedescribehowwemeasurethestocksofexcesssavingsandmonetarypolicyshocksusedforourempiricalresults.Appendix

A

providesfurtherdetailsonthedatausedinouranalysis.

2.1ExcessSavingsintheEuroArea

Figure1

StockofExcessSavingsintheEuroArea

Note:Figure

1

showstheseriesofstocksofexcesssavingsfortheeuro-areaaggregate(red),France(pink),Germany(blue),Italy(yellow),andSpain(green).

Wefollow

deSoyresetal.

(2023)bydefiningthestockofexcesssavingsastheamount

ofassets,asapercentofGDP,arisingfromabove-trendsavingsrates.First,foreachcountry,weextractatrendofthesavingsrateusingthe

Hamilton

(

2018

)filter

.3

Wethenusethedetrendedsavingsratetocalculatetheflowofexcesssavingsforcountryiinquartert,ineuros,asfollows:

Flowofexcesssavingsit=(DetrendedSavingsRateit)×(DisposableIncomeit).(1)

Toconstructthemeasureofthestockofexcesssavings,wecalculatethecumulativesum3Following

Hamilton

(2018),wedetrendthesavingsratecountrybycountryviaaregressionofthe

savingsrateonlags8to11.Theresidualisthedetrendedsavingsrate.

5

oftheflowsdefinedinequation(

1

)andnormalizeitbynominalGDP:

Stockofexcesssavingsit=×100.(2)

Finally,wedemeantheseriesatthecountrylevelovertheentiresampleperiod,whichspansfrom1999Q1through2023Q2

.4

Byconstruction,thestockofexcesssavingsincreaseswhentheflowofexcesssavingsispositive,whilethestockofexcesssavingsdecreaseswhentheflowofexcesssavingsisnegative.

Thismeasureofaggregateexcesssavingshassomeadvantages.First,itsconstruc-tionrequiresonlyaggregatenominalhouseholdsavings,disposableincome,andnominalGDP,allofwhicharereadilyavailableforavarietyofeuro-areacountries.Second,ourmethodologyproducesafulltimeseriesofestimatedexcesssavings,allowingustoexploititsvariationovertimeinouranalysis.Finally,despiteusingnominalhouseholdsavingsasaninput,ourmeasuredoesnotrelyontheassumptionthatpricesremainattheirtrends.

Ourmeasureofthestockofexcesssavingsfortheeuroareaexhibitsconsiderablevariation,bothinthetimeseriesandacrosscountries.Figure

1

showsthatinthelead-uptothe2008–2009GlobalFinancialCrisis,differenteconomieshaddifferenttrajectories,withItalyincreasingitsexcesssavings,FranceandGermanymaintainingtheirexcesssavings,andSpainandtheeuro-areaaggregatedecreasingtheirsavings.Incontrast,from2012to2020,mostoftheseeconomiesrandowntheirexcesssavings,withtheexceptionofFrance.Finally,amidtheCOVID-19pandemic,alloftheseeconomiessawtheirstocksofexcesssavingssharplyincrease.

2.2Euro-AreaHigh-FrequencyMonetaryPolicyShocks

Weapplythemethodologyof

Buetal.

(2021)tocalculatehigh-frequencymonetarypolicy

shocksfortheeuroarea.Specifically,weusedailydatafromtheGermanTreasuryyieldcurveforthemonetarypolicymeetingsoftheECBfortheperiodbetweenJanuary1999throughSeptember2022inourapplication.Figure

2

displaysthemonetarypolicyshocksthatarecalculatedusingthismethodology.Forourregressions,weaggregatetheseshocks

4Wedemeanthestockofexcesssavingswithincountrytoensurethatourempiricalresults,whichwedescribeinSection

3

,arenotdrivenbypermanentheterogeneityinexcesssavingsstemmingfrominitialconditionswhenaccumulatingthesavingsflowsovertime.

6

Figure2

MonetaryPolicyShocksfromtheEuropeanCentralBank

.2

.1

0

-.1

-.2

MonetaryPolicyShocksinPercentagePoints

20002005201020152020

Note:Figure

2

showsthetimeseriesofmonetarypolicyshockscalculatedusingGermanTreasuryyieldcurveforthemonetarypolicymeetingsoftheEuropeanCentralBankfortheperiodbetweenJanuary1999toSeptember2022.

bysummingthemtoamonthlyfrequency.

5

Ourchosenapproachtomeasuringmonetarypolicyshockscombinesthreeimportantfeaturesthataddressissuesextensivelydiscussedintheliterature.First,theshocksbridgeperiodsofconventionalandunconventionalmonetarypolicybyusinginterestratemove-mentsfromtheentireTreasuryyieldcurve.Second,

Buetal.

(

2021

)provideevidencethatthismethodologyremovesthecentralbankinformationeffectfortheUnitedStates:mon-etarypolicyannouncementsmayrevealinformationaboutthestateofthemacroeconomy,insteadofrepresentingonlygenuinemonetarypolicysurprises.Third,

Buetal.

(

2021

)documentthattheirU.S.monetarypolicyshocksarenotpredictedbyavailableinforma-tionontheeconomy,suchasBlueChipforecasts,newsreleases,andconsumersentiment

.6

Followingthesameapproach,inAppendix

B.1

weprovideevidencethatoureuroareamonetarypolicyshocksarenotpredictedbyinformationavailableinrealtime.

5WhenanalyzingtheconsumptionresponsetomonetarypolicyinAppendix

B.2

,weaggregatethemonetarypolicyshockstoaquarterlyfrequency.

6Formorediscussionoftheseissues,see

Miranda-Agrippino

(2016)and

BauerandSwanson

(2020)

.

7

3EmpiricalResults

Inthissection,weuseourmeasuresofexcesssavingsandeuro-areamonetarypolicyshockstodocumentthatexcesssavingsdampenthetransmissionofmonetarypolicytobotheconomicactivityandinflation.

3.1RegressionSpecifications

OursamplerunsfromJanuary1999throughSeptember2022andcoversfiveeconomies:theeuro-areaaggregate,Germany,France,Italy,andSpain.Werepresentaneconomywith

iandagivenmonthwitht.Theeuro-areamonetarypolicyshockisdenotedbyεand

isscaledsuchthattheshockgeneratesa50basispointincreaseinthetwo-yearGermangovernmentbondyield.Forallregressions,wealsospecifyasetofcountry-specificandeuro-area-specificcontrolsdenotedbyZit.Thecountry-specificcontrolsare12lagsofinflationrates,unemploymentrates,industrialproduction,GDPgrowth,andaninteractionofGDPgrowthwiththemonetarypolicyshocktoaccountforstate-dependenteffectsofmonetarypolicyoneconomicactivity(

TenreyroandThwaites,

2016)

.7

Theeuro-areacontrolsinclude12lagsofinflation,theunemploymentrate,andthespreadbetweenthefive-yearBBB-ratedbondyieldandthefive-yearGermangovernmentbondyield.

Weestimatethetransmissionofmonetarypolicytomeasuresofeconomicactivityandinflationunconditionallyandconditionalontheexantestockofexcesssavings.Specifically,weestimatethefollowinglocalprojections(

Jord`a,

2005

)atamonthlyfrequencyforaseriesofhorizonsh:

Yit+h?Yit?1=β+βε+β(ExcessSavingsStockit?1)×ε+γhZit?1+eit+h,(3)

whereYitisthemeasureofeconomicactivityandinflation.

Whilewefocusontheunemploymentrateasameasureofeconomicactivity,Appendix

B

documentsthatourresultsarerobusttousingbothaggregateconsumptionandindus-trialproductioninstead.Inaddition,wealsoshowthatourresultsarerobusttocontrollingfortheCOVIDperiodaswellasbankbalancesheetstrength,respectively.

7WeconvertGDPfromaquarterlyfrequencytoamonthlyfrequencybyassigningthevalueofrealizedGDPinagivenquartertoeverymonthofthatquarter.

8

Figure3

EffectofaContractionaryMonetaryPolicyShockonEuro-AreaUnemploymentRate

(a)AverageEffect(b)DampeningEffect

Note:Figure

3

depictstheresponseoftheunemploymentratetoamonetarypolicyshocknormalizedto

increase2-yearratesby50basispoints.Panel

3a

plotstheunconditionaleffect,β,fromlocalprojections

(3),whilePanel

3b

plotstheeffectconditionalonthelevelofexcesssavings,β.Theshadedareareflects

the68percentand90percentconfidenceintervalsusingstandarderrorsfrom

DriscollandKraay

(1998)

.

3.2ExcessSavingsDampenMonetaryPolicyEffectsonActivity

Usingtheunemploymentrateasameasureofeconomicactivity,wefindthateuro-areamonetarypolicyshocksincreasetheunemploymentratebutlesssowhenexcesssavingsarehigh.Figure

3a

plotstheunconditionaleffectsofmonetarypolicyshocks,withtheunemploymentraterisingovertime,reachingitspeakeffectafter15to20months,and

increasingby30basispoints.Figure

3b

plotstheestimateofβ,whichcapturesthenon-

linearityinmonetarytransmissionwithrespecttoexcesssavings.Moreprecisely,whenthestockofexcesssavingsofaeuro-areaeconomyincreasesbyonepercentagepointofGDPrelativetothehistoricalaverage,wefindthattheeffectofthemonetarypolicyshockontheunemploymentrateisdampenedbyroughlyone-half.Overall,ourestimatedeffectsofmonetarypolicyshocksoneconomicactivityarecomparableinmagnitudetothosefromotherpapers(e.g.,

BadingerandSchiman,

2023)

.

9

Figure4

EffectofaContractionaryMonetaryPolicyShockonEuro-AreaInflation

(a)AverageEffect(b)DampeningEffect

Note:Figure

4

plotstheresponseofinflationtoamonetarypolicyshocknormalizedtoincrease2-year

ratesby50basispoints.Panel

4a

plotstheunconditionaleffect,β,fromlocalprojections(

3

),whilePanel

4b

plotstheeffectconditionalonthelevelofexcesssavings,β.Theshadedareareflectsthe68percent

and90percentconfidenceintervalsusingstandarderrorsfrom

DriscollandKraay

(1998)

.

3.3ExcessSavingsDampenMonetaryPolicyEffectsonInflation

Inadditiontodampeningtheresponseofrealoutcomes,wefindevidencethatexcesssavingsalsodampentheresponseofprices.Weestimateequation(

3

)fortwelve-monthheadlineinflationandplottheresultsinFigure

4.

Theunconditionaleffect(Figure

4a

)showsthatinflationdeclinesby40basispointsinresponsetoacontractionarymonetarypolicyshock.Whenthestockofexcesssavingsofaeuro-areaeconomyisonepercentagepointofGDPrelativetoitshistoricalaverage(Figure

4b

),thedeclineininflationisdampenedbyaround10basispoints.Ourresultsareconsistentwiththeliteraturedocumentingthatusingahigh-frequencymeasurementofshockshelpstoshowthatinflationdecreasesaftercontractionarymonetarypolicyshocks(e.g.,

Ramey,

2016,

Jaroci′nskiandKaradi,

2020)

.

3.4MonetaryPolicyTransmissionPost-Pandemic

WenextquantifytheeffectoftheriseinexcesssavingsonthetransmissionofmonetarypolicyduringtheCOVID-19recovery.With12-monthheadlineinflationintheeuro-areaaggregatehavingpeakedin2022Q4andexcesssavingsstillremainingelevatedinthesame

10

Figure5

EffectofaContractionaryMonetaryPolicyShockin2023Q1

(a)Unemploymentrate(b)Inflation

Note:Figure

5

plotstheresponseoftheunemploymentrateandinflationtoamonetarypolicyshocknormalizedtoincrease2-yearratesby50basispoints.Panels

5a

and

5b

plotthetotalmonetarypolicy

effectundertwoscenarios:(i)whenexcesssavingsareequaltozero(i.e.,βfromlocalprojections(

3

))

and(ii)whenexcesssavingsaresetequaltotheir2023Q1levelbasedonanaverageofthecountriesinoursample.

period,weuseourestimatestoquantifytheeffectivenessofmonetarypolicyfromtheperspectiveofapolicymakerin2023Q1assheorhestartstoevaluatehowtightpolicywouldneedtobegoingforward.

Figure

5

showsthatexcesssavingsdampenedtheeffectsofmonetarypolicyduringtherecoveryfromthepandemic.Asabaseline,thebluelinesdepicttheaverageresponseoftheunemploymentandinflationratestoamonetarypolicyshockundertheassumptionthatexcesssavingsareattheirhistoricalaverages(thesameasinFigures

3a

and

4a,

respectively).Thesolidblacklinesreflecttheresponseoftheunemploymentandinflationratestoamonetarypolicyshockundertheassumptionthatexcesssavingsareattheir2023Q1levels.Comparingthetwosetsofresponses,weestimatepeak-dampeningeffectsofaboutone-fourthtoone-halfontheefficacyofmonetarypolicyforboththeunemploymentandinflationrates.

11

4ExcessSavingsinaSimpleNewKeynesianModel

Inthissection,webuildamodelthatprovidesaninterpretationofourempiricalresults:higherexcesssavingsflattentheIScurve.OurmodelisasimpleNewKeynesianmodelwithequilibriumunemploymentduetomatchingfrictionsinthelabormarket.Workersfaceidiosyncratic,countercyclicalunemploymentriskagainstwhichtheycanonlybepartiallyinsuredbysavingwhileemployed.Whenunemploymentriskrises,householdswanttocutconsumptiontodaytosavemore,whichthenamplifiestheresponseoftheeconomytotheinitialshock.However,highersavingsdampenthisamplificationbyallowingforbetterrisksharing.Ourexactset-upisasimplifiedversionofthemodelin

Challeetal.

(

2017

)andissimilarto,forexample,

RavnandSterk

(

2017

)and

HeathcoteandPerri

(

2018

).Thesameforcescanalsobefoundinlessstylizedmodelsofprecautionarysavingsoverthebusinesscyclelike

Gornemannetal.

(2016),

DenHaanetal.

(

2018

),and

Cho

(

2023

).

4.1Timeline

Theeconomyispopulatedbyaunitmassofidenticalfamilies.Eachfamilyitselfconsistsofaunitmassofworkers.Atthebeginningoftheperiod,thefamilyredistributesbondsbetweenitsmemberswhowereemployedlastperiod.Unemployedmembersofthefamilyalsomightholdsomebondsordebt,dependingontheirhistory.Importantly,theyarenotabletoshareinthewealthofthefamilyuntiltheyfindajob

.8

Aftertheredistributionofbondstookplace,aggregateshocksrealizeandfirmsannouncehowmanyworkerstheyplantohire.Employedworkersproduceforthefirmstheyworkforandarepaid.Unemployedworkersreceiveunemploymentbenefits.Bothgroupsthendecidehowtosplittheirincomebetweenconsumptionandsavings.Attheendoftheperiodallemployedmembersofafamilymeetandpoolresources,whicharethenre-shuffledbetweenthesefamilymembersforthenextperiod.

8Theassumptionofarepresentativefamilythatcanshareitsresourceswithinasubsetofworkersisclearlyunrealistic.Itismeanttocaptureaworldinwhichworkersself-insurethroughsavingagainstunemploymentrisk.Theassumptionthattheemployedworkersareabletopoolresources,however,stronglysimplifiestheanalysis.Thissimplificationarisesbecauseaworker’sassetpositiononlydependson