【世界银行】主权风险下的扩张性财政整合-2025.6

PublicDisclosureAuthorizedPublicDisclosureAuthorized

PolicyResearchWorkingPaper11156

ExpansionaryFiscalConsolidationUnderSovereignRisk

CarlosEsquivel

AgustinSamano

WORLDBANKGROUP

DevelopmentEconomics

DevelopmentResearchGroupJune2025

PolicyResearchWorkingPaper11156

Abstract

Thispaperdevelopsasovereigndefaultmodelwithcapitalaccumulation,long-termdebt,andfiscalruleswithtwodis-tortions:debtdilutionandprivateunderinvestment.Fiscalrulesgeneratealong-runeconomicexpansionbecausetheymitigatedefaultriskcausedbydilution,whichincreasescapitalaccumulation.Intheshortrun,however,theecon-omygoesthroughacostlytransitionwhereconsumptionandinvestmentdroptofinancedebtreduction.Thesedynamictrade-offsarequantified,andthewelfaregainsoffiscalrulesarecomputedusingacalibrationforArgentina.

Adebtlimitof44percentofgrossdomesticproductattainsthemaximalwelfaregainof0.5percent.Implementationofthedebtlimitgeneratesshort-liveddropsinconsump-tionandinvestmentof5and7percent,respectively,andalong-rungrossdomesticproductexpansionof1.4percent.Thepaperrelaxestheassumptionofcommitmenttotheruleanddiscusseshowthethreatofexclusionfromimple-mentingfuturerulesprovidesenoughincentivestoavoiddeviations.Welfaregainsmorethandoubleinthiscase.

ThispaperisaproductoftheDevelopmentResearchGroup,DevelopmentEconomics.ItispartofalargereffortbytheWorldBanktoprovideopenaccesstoitsresearchandmakeacontributiontodevelopmentpolicydiscussionsaroundtheworld.PolicyResearchWorkingPapersarealsopostedontheWebat

/prwp.Theauthorsmay

becontactedatasamanopenaloza@

;andcarlos.esquivel@.

ThePolicyResearchWorkingPaperSeriesdisseminatesthefindingsofworkinprogresstoencouragetheexchangeofideasaboutdevelopmentissues.Anobjectiveoftheseriesistogetthefindingsoutquickly,evenifthepresentationsarelessthanfullypolished.Thepaperscarrythenamesoftheauthorsandshouldbecitedaccordingly.Thefindings,interpretations,andconclusionsexpressedinthispaperareentirelythoseoftheauthors.TheydonotnecessarilyrepresenttheviewsoftheInternationalBankforReconstructionandDevelopment/WorldBankanditsaffiliatedorganizations,orthoseoftheExecutiveDirectorsoftheWorldBankorthegovernmentstheyrepresent.

ProducedbytheResearchSupportTeam

ExpansionaryFiscalConsolidationUnderSovereignRisk*

CarlosEsquivel†AgustinSamano‡

Keywords:Fiscalrules,Sovereignrisk,Expansionaryfiscalconsolidation.

JELCodes:F34,F41

*Thefindings,interpretations,andconclusionsexpressedinthispaperareentirelythoseoftheauthors.TheydonotnecessarilyrepresenttheviewsoftheWorldBankGroup,itsExecutiveDirectors,orthegovernmentstheyrepresent.ForcommentswethankManuelAmador,JavierBianchi,TobeyKass,TimKehoe,HyunjuLee,LeonardoMartínez,JuanPabloNicolini,VegardNygaard,PabloOttonello,RadekPaluszynski,FaustoPatiño,RongQian,HabibRab,FranciscoRoch,JohnShea,LuminitaStevens,MiguelZerecero,andseminarparticipantsatU.AlbertoHurtado,theMinneapolisFed,UniversityofHouston,UCIrvine,UniversityofMaryland,SED2023,andthe2023ITAMAlumniConference.Allerrorsareourown.

†RutgersUniversity;Email:carlos.esquivel@;Web:

‡TheWorldBankResearchDepartment,EastAsiaandPacificChiefEconomistResearchCenter;Email:asamanopenaloza@;Web:

/

1

1Introduction

SignificantfiscalexpansionsfollowingtheeconomicdownturnfromtheCOVID-19pandemicledtohistoricallyhighlevelsofpublicdebt.Intheaftermath,mosteconomiesfacethechallengeofrestoringtheirfiscalbalancewithouthamperingtheireconomicrecovery.Whilethereissomeevidencethatfiscalconsolidationscanbeexpansionary,thischallengecanbeparticularlydifficultforemergingeconomiesthatpayhighinterestrate

spreads.1

Moreover,mostofthetheoreticalworkthatstudiessuchexpansionsfocusesonadvancedeconomiesforwhichdefaultriskislowanddebtishelddomestically.

2

Withdebtcrisesloomingonthehorizon,highlyindebtedemergingeconomiescannotsolelyrelyonpolicyprescriptionsfromthisliterature.

Weintroduceanovelmechanismthroughwhichfiscalconsolidationcanbeexpansionaryinthepresenceofdefaultrisk.Thekeypolicyprescriptionistoconsolidatefollowingtheintroductionofafiscalrule.Wearguethatthefiscalrulemitigatestwodistortionsthathavebeenstudiedinthesovereigndefaultliterature:dilutionoflong-termdebt(

Hatchondo,Martinez,andSosa-Padilla

(

2016

))andunderinvestment(

Esquivel

(

2024

)).Bymitigatingthesedistortionsfiscaldisciplineinducedbytherulelowersdefaultriskandincreasescapitalaccumulationinthelong-run.Intheshort-run,however,theimplementationofthefiscalrulemayresultinacostlytransitionwithdepressedinvestmentandconsumptiontofinancedebtreduction.

Tostudythistrade-offandformalizethemechanismwedevelopaquantitativesovereigndebtmodelwithcapitalaccumulation,long-termdebt,andfiscalrules.

3

Domestichouseholdsmakeag-gregateinvestmentdecisionsandlackaccesstointernationalfinancialmarkets,whileabenevolentgovernmentmakesoptimalborrowinganddefaultdecisionsontheirbehalf.Wemodeldebtrulesasanupperboundtothedebt-to-GDPratio,followingthebenchmarkanalysisof

Hatchondo,Mar-

tinez,andRoch

(

2022

).Differentfrompreviouswork,afeatureofourmodelisthatwhetherthelimitbindsdependsonthehistoryofcapitalaccumulationandontherealizationofaproductivityshock.Asisstandard,weassumethatwhenthegovernmentdefaultsitisexcludedfromfinancialmarketsforarandomnumberofperiodsandthereisanexogenouscosttoproductivity.Thelatterimpliesthatdefaultrisklowerstheexpectedreturntocapital,whichdepressesinvestment.

1

GiavazziandPagano

(

1990

)documenttwocasesofexpansionaryfiscalconsolidationsinDenmarkandIrelandinthe1980s.

AlesinaandArdagna

(

2009

)documentingsimilarcasesforalargersetofadvancedeconomies

2See

BertolaandDrazen

(

1993

),

Bi

(

2012

),

Bi,Leeper,andLeith

(

2013

),

BarseghyanandBattaglini

(

2016

)

3Themodelbuildsonthequantitativeliteraturefollowingtheseminalworkof

EatonandGersovitz

(

1981

).

2

Debtdilutionandunderinvestmentinteractwitheachother.Asin

Hatchondo,Martinez,and

Sosa-Padilla

(

2016

),dilutionsubstantiallyincreasesdefaultrisk.Highdefaultrisklowerstheex-pectedmarginalreturntocapital,towhichhouseholdsrespondbyinvestingless.

Esquivel

(

2024

)showsthatlowcapitalaccumulationfurtherincreasesdefaultriskandlimitstheabilityofthegov-ernmenttoroll-overitsdebt,whichhouseholdsdonotinternalize.Fiscalrulescontaindebtdilutionbylimitingfuturedebtissuance(see

Hatchondo,Martinez,andRoch

(

2022

)),whichinturnlowersdefaultriskandamelioratesunderinvestmentfromhouseholds.Itisbymitigatingtheinteractionofthesedynamicfrictionsthattheintroductionofafiscalrulegeneratesanexpansionaryfiscalconsolidationinthemodel.

WecalibratethemodelwithnofiscalruletoArgentina,whichisaneconomythatfaceshighdefaultriskandfrequentdefaultepisodes.Then,weusethemodeltoquantifytheshort-runandlong-runtrade-offsofintroducingafiscalruleandcomputethewelfaregainstakingtheseintoaccount.Thedebtlimitthatmaximizesthesegainsis44.2percentofGDPandgenerateswelfaregainsof0.5percentinconsumptionequivalentunits.

Theaveragetransitionpathfeaturesaninitialdropinconsumptionandinvestmentof5and7percent,respectively,whichfinancethedebtreduction.Thesedropsareshort-livedandconsump-tionishigherafterfourquarters.Inthelong-run,averageconsumptionis1.35percenthigher.Thishighlightstheimportanceofaccountingforthecostlytransitionwhencomputingthewelfaregainsofimplementingtherule(whicharelessthanhalfofthisnumber).Averagespreadsdroponim-pactfrom7to2percentandremainlowinthelong-run.Thislargereductioninspreadsisaresultofthereductioninoutstandingdebtandofashiftinitspriceschedule,reflectingexpectationsoffuturefiscaldisciplineimposedbytherule.Eachofthesechannelsexplainsroughlyhalfofthereductioninspreads.Theaveragedebt-to-GDPratioconvergesto0.42,andGDPinthelong-runisonaverage1.2percentlarger,showingthatthefiscalconsolidationwas,indeed,expansionary.

Inthebenchmarkcase,weassumethatthefiscalruleimposesabalancedbudgetwheneverthelimitbinds,whichiswhyconsumptionandinvestmentdropbysomuchinitially.Weexplorefiscalconsolidationplansthatallowfortheprimarydeficittobepositive,butlimited,whenthedebtlimitbinds.Theseplansposeatrade-offbetweenflexibilityduringthetransitionandunderminingthebenefitsofthedebtlimitinthelong-run.Theoptimaldeficitlimittoimplementthe0.42debtlimitis1.58percentofGDPanddeliversmodestlylargerwelfaregainsof0.52withsimilartransition

3

paths.Thesimilarityonthepathssuggeststhattheshort-runcostsduringthetransitionaremorethancompensatedbythelong-runbenefitsthatresultfromexpectationsoffuturefiscaldiscipline.

Wethenrelaxtheassumptionofcommitmenttothefiscalrule.Thisexerciseisparticularlyvaluableforeconomiesthatmayfacedifficultiesingeneratinginstitutionalguardrailsthatwouldforcethegovernmenttocommittotherulewhenitbinds.Wesupposethat,atthebeginningofeachperiod,thegovernmentcanchoosetodeviatefromtherule.Oncethegovernmentdeviates—eitherbyissuingmoredebtthantheruleallowsorbydefaulting—itisabsorbedintothebenchmarkequilibriumwithnofiscalrule.Interestingly,themodelwithoutcommitmentfeaturessignificantlylowerdefaultrisk,lowerspreads,highercapital,andhigherconsumption,resultinginwelfaregainsof1.2percent,morethandoublethanwithcommitment.Sincedefaultingwouldnowimplylosingthebenefitsofhavingtherule,defaultbecomescostlierthanbeforeandthegovernmentchoosestoavoidit.Theprospectoflosingtheruleprovidesenoughincentivestosupportitandhigherincentivestoavoiddefault,whichsignificantlyincreaseswelfaregains.

Finally,wepresentempiricalevidencethatsupportsthemainmechanismofthemodel.Whiletherelationshipbetweenfiscalrulesandsovereignspreadsiswellestablishedintheliterature,thelinkbetweenrulesandprivateinvestmenthasbeenlessexplored.

4

Wefillthisgapbyestimatingthelong-runandtheshort-runrelationshipbetweendebtrulesandprivateinvestmentforapanelof63emergingeconomies.Usingapanelregression,weestimateasignificantpositiverelationshipbetweenhavingadebtruleinplaceandprivateinvestmentaspercentageofGDP.Weinterpretthisresultaslong-runevidenceofhigherinvestmentincountrieswithadebtrule.Wethenusealocalprojectionsframeworktoestimatechangesininvestmentfollowingtheintroductionofafiscalruleandfindevidenceofatransitionpathsimilartotheonepredictedbythemodel:aninitialdropininvestmentshortlyfollowedbyanexpansion.

Relatedliterature.—Wemainlycontributetothequantitativesovereigndefaultliterature(

Eato

n

andGersovitz

(

1981

);

Arellano

(

2008

);

AguiarandGopinath

(

2006

))withconstraintstofiscalpolicy(

AlfaroandKanczuk

(

2017

);

Hatchondo,Martinez,andRoch

(

2020

);

Bianchi,Ottonello,

andPresno

(

2023

));

DengandLiu

(

2023

);

AzzimontiandMitra

(

2023a

);

AzzimontiandMitra

(

2023b

)).Ourmodelextendsthemodelin

Hatchondo,Martinez,andSosa-Padilla

(

2016

)toincor-

4See

IaraandWolff

(

2010

),

Kalan,Popescu,andReynaud

(

2018

),

Davoodietal.

(

2022

),and

Islamaj,Samano,and

Sommers

(

2024

)).

4

porateprivatecapitalaccumulationasstudiedby

Esquivel

(

2024

)andfiscalrulessimilartothosein

Hatchondo,Martinez,andRoch

(

2022

).Ourmaincontributionistoshowhowusingafiscalruletomitigatethedynamicinteractionsbetweendebtdilutionandunderinvestmentcangenerateanexpansionaryfiscalconsolidation,especiallyineconomieswithsubstantialdefaultrisk.

Thispaperisalsorelatedtotheliteratureonrulesversusdiscretion.

Angeletos,Amador,and

Werning

(

2006

)studythetrade-offbetweencommitmentandflexibilityinaconsumptionsavingsmodelwithtasteshocksprivatelyobservedbyanagent.

HalacandYared

(

2014

),

HalacandYared

(

2018

),and

HalacandYared

(

2022

)studydebtlimitsundersimilarenvironments.Atthecoreoftheconflictstudiedinthesepapersisadisagreementbetweenanagent(thegovernment)andaprincipal(incumbentcitizens)overpreferencesforintertemporalconsumption.Debtlimitsemergeasanefficientmechanismthroughwhichcitizensprovideincentivestothegovernmentexante.Wecontributebyshowingthatwithcapitalaccumulationanddefaultriskfiscalrulesmaybesustainedevenwithoutacommitmenttechnologytoenforcethem.

Finally,thispaperrelatestotheliteraturethatstudieswhetherfiscalconsolidationisexpansion-aryorcontractionary.Thisliteraturehasfocusedonatensionbetweena"Keynesian"argumentthatstatesthatfiscalconsolidationislikelytocontractaggregatedemanda"Ricardian"onethatclaimsthatifprivateagentsexpectfiscaldisciplineinthefuture,theywillreviseupwardstheirestimateoftheirpermanentincome,whichwillinturnincreasecurrentandplannedconsumption,resultinginaneconomicexpansion.

GiavazziandPagano

(

1990

)presentevidenceoflarge-scalefiscalcontractionsinDenmarkandIrelandassociatedwithastrongoutputexpansion.Inadiscus-sionoftheirwork,

Blanchard

(

1990

)developsasimplemodeltoreconcilebothideas.Similarly,othertheoreticalworksuchas

BertolaandDrazen

(

1993

),

Bi

(

2012

),and

Bi,Leeper,andLeith

(

2013

)hasstudiedmechanismsforsuchexpansionsinadvancedeconomies.Wepresentanovelchannelthroughwhichfiscalconsolidationgeneratesanexpansioninemergingeconomiesfacinghighdefaultrisk.

Layout.—Section

2

presentsthemodelenvironmentanddiscussesthemainmechanismandtrade-offsindetail.Section

3

presentsthequantitativeanalysisandthemainresults.Section

4

presentstheempiricalanalysis.Section

5

concludes.

5

2Model

Wedevelopasovereigndefaultmodelwithprivatecapitalaccumulationandfiscalrules.Thereisasmall-openeconomypopulatedbyalargenumberofidenticalhouseholds,acompetitivefirm,andabenevolentgovernment.Productionofthefinalconsumptiongoodiscarriedoutbythefirm,whichrentscapitalfromhouseholds.Householdsownthefirmandallthecapitalintheeconomybutdonothaveaccesstointernationalfinancialmarkets.Thebenevolentgovernmentborrowsonbehalfofthehouseholdsbyissuinglong-termdebtthatispurchasedbyrisk-neutralforeignlenders.Thegovernmentmakeslump-sumtransfers(orlevieslump-sumtaxes)tothehouseholdsandcannotcommittorepayingitsdebt.

Preferencesandtechnology.—Householdshavepreferencesforconsumptionofatradablegoodctineachperiodrepresentedby.Theydiscountthefutureatarateβandarerelativelymoreimpatientthanforeignlenders.Thatis,β(1+r*)<1wherer*istheinternationalrisk-freeinterestrate.Householdsownallthecapitalintheeconomyandrentittothefirmforrt.Capitaldepreciatesatarateδandhouseholdsfaceaquadraticcapitaladjustmentcostwhereφ>0.Thebudgetconstraintofarepresentativehouseholdis:

whereik,t=kt+1−(1−δ)ktisinvestment,Πtareprofitsfromthefirm,andTtisalump-sumtransferfromthegovernment.

Theconsumptiongoodisproducedbythecompetitivefirmusingtechnologyyt=ztk,where

ktisthecapitalrentedbythefirm,αisthecapitalshareofincome,andztisaproductivityshock.

5

TheproductivityshockfollowsanAR(1)process:

logzt+1=plog(zt)+∈t,

5Implicitly,weareassumingthatthereisaunitoflaborthatissuppliedinelasticallybythehouseholds.Weabstractfromendogenouslaborsupplyforsimplicity.

6

logzt+1=(1−P)log(μz)+Plog(zt)+∈t

E[logzt]=log(μz)

wherePisthepersistenceparameter,∈t∼N(0,σ),andμzismeanproductivityinthelong-run.

Governmentdebtanddefault.—Thegovernmentisbenevolentandmakesborrowingdeci-sionsonbehalfofthehouseholds.Itissueslong-term,non-contingentdebtBtthatmaturesatarateYandpaysacouponKonunmatureddebt.ThelawofmotionofdebtisBt+1=(1−Y)Bt+ib,t,whereib,tisnetdebtissuanceinperiodt.Thegovernment’sbudgetconstraintwhenitisingoodfinancialstandingis:

Tt+(Y+K(1−Y))Bt=qtib,t,(2)

whereqtisthemarketpriceofgovernmentdebt.

Atthebeginningofeachperiodthegovernmentcandecidetodefault.Ifitdoes,thenitisexcludedfromfinancialmarketsforastochasticnumberofperiods,andtheproductivityintheeconomydropstozD(zt)=zt−max{0,ξ0z+ξ1z2},whereξ0<0<ξ1.

6

ThegovernmentgetsreadmittedtofinancialmarketswithaprobabilityθandalldebtforgivenB=0.Thedebtispurchasedbyalargenumberofrisk-neutralinvestorswithdeeppockets.Investorspayapriceqtforthegovernmentdebtandhaveaccesstoaone-periodrisk-freebondthatpaystherisk-freeinterestrater∗.

Fiscalrules.—Ingeneral,afiscalruleisacorrespondenceFthatmapsthestatespaceoftheeconomyintothepowersetofgovernmentpolicyinstruments.Westudydebtlimitswherethefiscalruleisoftheform:

F(zt,kt,Bt)={Bt+1|Bt+1≤max{xbztk,(1−Y)Bt}}(3)

wherexb∈(0,1).Thisformulationimposesthatthedebt-to-GDPratiocannotexceedxb.IfoutstandingdebtBtisalreadyhigherthanthislimitforagivenrealizationofzt,thenitmust

6Weusethequadraticformulationintroducedby

ChatterjeeandEyigungor

(

2012

)forapureexchangeeconomy.

Asdiscussedby

Arellano

(

2008

),anasymmetriccostofdefaultthatisincreasinginzt(suchasthisone)allowsthemodeltogenerateacounter-cyclicalcurrentaccountandspreads,anddefaultepisodes“inbadtimes”,allofwhicharefeaturesofthedataforemergingeconomies.

MendozaandYue

(

2012

)showthatthesetypesofcostsfromdefaultcanbetheresultofaricherproductionstructureinwhichsomeimportedmaterialsrequireworkingcapitalfinancing.Forsimplicity,weassumethisexogenousforminstead.

7

bereducedbyatleastthefractionYthatmatured.Thisimplicitlyimposesthatwhendebtisabovethelimittherecannotbeaprimarydeficit(debtissuanceib,tcannotbepositive).Welaterrelaxthisassumptionandallowforpositive(butlimited)primarydeficitswhendebtisaboveitslimit.Animportantcontributionofourmodelisthatcapitalaccumulationrelaxesthefiscalruleinsubsequentperiods.Aswediscussextensivelyinthefollowingsection,thisfeatureincreasesthevalueofsustaininghigherlevelsofcapitalunderafiscalrule.

Timing.—Atthebeginningofaperiod,thegovernmentobserves(zt,kt,Bt)andmakesitsde-faultandborrowingdecisions.Then,thehouseholdsobservethegovernment’schoicesandmaketheirconsumptionandinvestmentdecisions.Finally,attheendoftheperiod,lendersobserveallchoicesandpricethedebtaccordingly.Weassumethatthegovernmentcancommittopol-icywithinthesameperiod.Thatis,ifatthebeginningoftheperiodthegovernmentannouncesrepaymentandadebtissuanceib,t,thenitissuesthatamountattheendoftheperiodandpays(Y+K(1−Y))Bttothelenders.Theseassumptionsallowustoruleoutthemultiplicityofequi-libriastudiedby

ColeandKehoe

(

2000

)becauselenderspricethedebtafterthegovernmentan-nouncesitspolicyandcommitstoitwithinthesameperiod.Thistimingassumptionsalsoruleoutthemultiplicitystudiedby

Galli

(

2021

)becauselenderspricethedebtafterthecapitalallocationhasbeenchosen.

2.1Recursiveformulationandequilibrium

Theaggregatestateoftheeconomyis(z,x),wherex=(k,B)istheendogenousaggregatestate.Letg=(T,B′)bethevectoroffiscalpolicyinagivenperiod,andletd=0denotethatthegovern-mentisingoodfinancialstandingandd=1thatthegovernmentisindefault.

8

Households.—Thevalueofarepresentativehouseholdwhend=0is

+βE[d′HD(z′,k′,K′)]}

i=k′−(1−δ)k

x′=Γ(z,x,g),gp=Γ(z′,x′),d′=Γd(z′,x′)

whereΓisthehousehold’sbeliefaboutthelawofmotionoftheendogenousaggregatestatexinrepayment,Γisthehousehold’sbeliefoffiscalpolicyinrepayment,Γdthehousehold’sbeliefaboutthegovernment’sdefaultdecisions,therentalrateofcapitalisr(z,K)=zαKα−1,andfirmprofitsareΠ(z,K)=z(1−α)Kα.Thevalueofthehouseholdwhend=1is

+βE[(1−θ+θd′)HD(z′,k′,K′)]}

i=k′−(1−δ)k

x′=Γ(z,K),gp=Γ(z′,x′),d′=Γd(z′,x′)

whereΓisthehousehold’sbeliefaboutthelawofmotionoftheendogenousstatexindefault.

Government.—Atthebeginningofaperiodinwhichthegovernmentisingoodfinancial

standing,itsvalueis

v(z,x)=max{dvD(z,K)+(1−d)vp(z,x)}(6)

d∈{0,1}

9

wheredisitsdefaultdecision.Thevalueofrepayingthedebtis

s.t.T+(Y+K(1−Y))B=q(Z,x′)[B′−(1−Y)B]

K′=kp(Z,K,x,g),g=(T,B′)

whereCpandkparethehousehold’spolicyfunctionsforconsumptionandcapitalinrepayment,respectively.ThegovernmentchoosesitsfiscalpolicygsubjecttotheconstraintsimpliedbythefiscalruleFandtoitsbudgetconstraint;andtakesintoaccounthowfiscalpolicyaffectsaggregatehousehold’sdecisions.Thevalueofdefaultingis

VD(Z,K)=u(CD(Z,K,K))+βE[θVD(Z′,K′)+(1−θ)V(Z′,x′)](8)

whereK′=kD(Z,K,K),andCDandkDarethehousehold’spolicyfunctionsforconsumptionandcapitalindefault.

Equilibrium.—Anequilibriumisvalueandpolicyfunctionsforthegovernment,value,policyandbeliefsfunctionsforthehouseholds,andapricescheduleforgovernmentdebtqsuchthat:(i)givenqandthepolicyfunctionsforthehouseholds,thevalueandpolicyfunctionsofthegovernmentsolvetheproblemsin(

6

)through(

8

);(ii)givenallpricesandbeliefs,thevalueandpolicyfunctionsforthehouseholdssolvetheproblemsin(

4

)and(

5

);(iii)household’sbeliefsareconsistentwithgovernmentpolicyfunctionsandhousehold’spolicyfunctionsevaluatedattheaggregatestate;and(iv)thepricescheduleofdebtsatisfies

wherex′′=(kp(Z′,K′,x′,Γ(Z′,x′)),B(Z′,x′)).

2.2Debtdilutionandunderinvestment

Twodynamicfrictionsarisefromthegovernment’sinabilitytocommittofuturepolicy:debtdilutionfromnotbeingabletocommittofuturedebtissuance,andunderinvestmentfromthe

10

privatesectorfromnotbeingabletocommittofuturedebtpayments.

Inthepresenceoflong-termdebt,theissuanceofnewdebtreducesthevalueofexistingout-standingdebt.Thegovernmentdoesnotinternalizethislossinvaluebecauseoutstandingdebtisheldbyforeignlenders.Lendersthenofferalowerpriceforcurrentlyissuedbondsinantic-ipationoffutureborrowingincreasingdefaultriskanddilutingthefuturemarketvalueoftheselong-termbonds.

Hatchondo,Martinez,andSosa-Padilla

(

2016

)findthatthisnegativeexternalityfromcurrentdebtissuanceonpastgovernmentssubstantiallyincreasesdefaultrisk.

Underinvestmentarisesbecausehouseholdsdonotinternalizehowtheaggregatecapitalal-locationaffectsfuturedefaultincentives.Theydorespond,however,todefaultriskbecausethemarginalproductofcapitalislowerindefault.TheEulerequationofarepresentativehouseholdis

u′(c)pk,t=βE[(1−dt+1)u′(c1)R+dtu′(c1)R](10)

istheshadowpriceofinvestmentintandthereturntocapitalis

inrepaymentand

indefault.Astheprobabilityofdefaultincreases,theexpectedreturntocapitaldecreasesduetozD(zt+1)≤zt+1,whichlowershousehold’sincentivestoinvest.Inadditiontodefaultriskdepress-inginvestment,householdsdonotinternalizehowtheirinvestmentdecisionaffectsdefaultriskand,thus,thepriceofnewlyissueddebt.Toillustratethis,considerthecaseinwhichthegovern-mentcandirectlychoosetheaggregatecapitalallocation.Then,theEulerequationforcapitalinrepaymentwouldbe:

showsthatthegovernmentunderstandshowitschoiceofkt+1affectsitstheborrowingtermsand,inturn,theresourceconstraintint.

Esquivel

(

2024

)showsthatunder

11

theassumptionswehavemadeforZDdefaultincentivesaredecreasingincapitalandthederivative ≥0.

7

Thisimpliesthathouseholdsunderinvestinperiodswhereborrowingneedsarepositiveib,t≥0.Moreover,thisinefficiencyvanisheswithouthdefaultrisk(qwouldbeconstant)andismoresevereinstatesforwhichqis“steeper”,which,asweshowinthequantitativeanalysisinSection(

3

),isthecaseinperiodsofdistress.

Insummary,governmentoverborrowingduetodebtdilutionexacerbatesdefaultrisk,whichdepresseslong-runlevelsofcapital.Inaddition,underinvestmentinperiodsofdistressfurtherincreasesdefaultriskandtheexantepenaltythatforward-lookinglendersimposeonthepriceofgovernmentdebt.Fiscalrulescanmitigatethecostsfromdebtdilution(

Hatchondo,Martinez,and

Roch

(

2022

))andlowerdefaultrisk.Moreover,inourenvironmentlowerdefaultriskmitigatesunderinvestmentandtheeconomysustainshigherlevelsofcapital,output,andconsumptioninth