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1、INTERNATIONA1.MONETARYFUNDCostlyIncreasesinPublicDebtwhenrgYongquanCao,VitorGaspar,andAdrianPeralta-AlvaWP/24/10IMFWorkingPapersdescriberesearchinprogressbytheauthor(三)andarepublishedtoelicitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheauthor(三)anddonotnecessarilyrepr
2、esenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.WoRK-NGPAPER2024JANWP/24/102024InternationalMonetaryFundIMFWorkingPaperFiscalAffairsDepartmentCostlyIncreasesinPublicDebtwhenrgPreparedbyYongquanCao,VitorGaspar,andAdrianPeralta-Alva*AuthorizedfordistributionbyMarcosPoplawski-RibeiroJanuary2024
3、IMFWorkingPapersdescriberesearchinprogressbytheauthor(三)andarepublishedtoelicitcommentsandtoencouragedebate.TheviewsexpressedinIMFWorkingPapersarethoseoftheathor(三)anddonotnecessarilyrepresenttheviewsoftheIMF,itsExecutiveBoard,orIMFmanagement.ABSTRACT:Thispaperquantifiesthecostsofapermanentincreasei
4、ndebttoGDP.Weemployadeterministic,overlappinggenerationsmodelwithtwoassetsandnoriskofdefault.Thetwoassetsarepublicdebtandprivate(productive)capital.Weassumethatthereturnonprivatecapitalequalstheinterestrateonpublicdebtplusanexogenouslygivenspread.Employingaanalyticalversionofthemodelweshowanexamplei
5、nwhichapermanentriseinthepublicdebtratioleadstoasignificantreductioninsteady-stateGDPevenasrg.FollowingMcGrattanandPrescott(2017)weconsideracalibratedmodeloftheUSeconomyincludingarichsetoffeaturesofnationalaccounts,fixedassets,distributionofhouseholdincomesanddemographics.Theintuition(andeventheorde
6、rsofmagnitude)fromthesimpleanalyticalmodelcarriesovertothisricherenvironment:theincreaseinthedebtratio,from60to120percentofGDP,isassociatedwithareductioninthecapitalstockofabout15percentandareductioninsteadystateGDPofabout8percent.RECOMMENDEDCITATION:Cao,Yongquan1VitorGasparandAdrianPeralta-Alva.202
7、4.CostlyIncreasesinPublicDebtwhenrg1IMFWorkingPaperNo.2024/10.JE1.ClassificationNumbers:E43,E62,H63Keywords:Crowdingout;publicdebtAuthorsE-MailAddress:YCao2imf.org,APeralta-Alvaimf.organdVGasparimf.orgIMFWORKINGPAPERSCostlyIncreasesinPublicDebtwhenrgWORKINGPAPERSCostlyIncreasesinPublicDebtwhenrgPrep
8、aredbyYongquanCao,VitorGaspar,andAdrianPeralta-Alva1INTERNATIONA1.MONETARYFUNDI.IntroductionIn2020,acuriousanomalywasapparentinglobalfinancialmarkets:despiterisingandhistoricallyhighdebt-to-GDPratios,sovereignbondyieldsweredecliningtoverylowlevels(even,insomecases,turningnegativeinrealterms).Thisled
9、tothecoincidenceofrecordlevelsofdebtwithverylowdebtservicingcosts.OlivierBlanchardcharacterizesthislandscapeaszunusual,inhisbookFiscalPolicyunder1.owInterestRates,whereheextensivelyexplorestheassociatedfactsandpolicyimplications.Whileonemightbetemptedtodismisstheselow-interestratesasahistoricalaberr
10、ationespeciallyinlightofrecentinflationarypressuresandhighnominalratessuchadismissalmaybepremature.PriortotheCOVID-19pandemic,bothrealandnominalneutralinterestrateshadbeenonadecliningtrajectoryfordecades.Variousstructuralfactors,fromsluggisheconomicgrowthanddemographicchanges,asoutlinedbytheIMF(2023
11、),toaglobalscarcityofsafeassets,asdiscussedbyCaballeroetal.(2017),contributedtothisenduringtrend.Manyofthesefactorsareexpectedtoremainoperatinggoingforward.Hence,asinflationreduces,lowinterestratesarelikelytoreturn.Other,moretemporaryfactors,mighthavealsopayedaroleinkeepinginterestrateslow,including
12、quantitativeeasingpoliciesimplementedbymajorcentralbanks.Determiningtheoverallquantitativeeffectsoftheinterplayofalltheseforcesisbeyondthescopeofthispaper.ThenegativedifferentialbetweeninterestratesandgrowthhasledscholarslikeBlanchard(2023)andBlanchard(2019)toarguethatelevatedlevelsofpublicdebtmayin
13、curminimalfiscalandsocialcosts.Thefocusofourresearchistorigorouslyinvestigatetheconditionsunderwhichpublicdebtdoesimposesignificantcosts,settingasideanyconsiderationofthepotentiallyproductiveusesofsuchdebt.Thelimitationsimposedbyresourcescarcityandfiniteproductioncapacityapplytoallsectors,includingg
14、overnmentalactivities.Theseconstraintsbecomeparticularlyapparentwhenweexplicitlyconsidertheendogeneityoftheconditionr-ggrthatis,whentheeconomyisdynamicallyefficientdespiter-g0?Ouranalysisconfirmsthatsurgingpublicdebtindeedcrowdsoutprivatecapital,thussuppressinglong-termoutput.Second,wequantifythemag
15、nitudeofthesedetrimentaleffects.Itiswellunderstoodthathighdebtlevelsexposecountriestomultipleequilibriathatincludeattacksonsovereigndebt(seeforexampleColeandKehoe(2000)andAguiarandAmador(2021),foracomprehensivesurveyonsovereigndebtanddefaultissues).Wewillabstractawayfromtheseconsiderations.Ourpaperf
16、ocusesoncrowdingout.Webuildastandardoverlappinggenerationsmodelofaclosedeconomywherebyhigherdebtmaycrowdoutprivatecapital.Akeyfeatureofourmodelisthatitincludestwoassets.Therateofreturnonprivatecapitalwillbedeterminedinequilibrium.Governmentdebtisassumedtoyieldareturnequaltothatofprivatecapitalminusa
17、nexogenouslydeterminedconvenienceyield.Thisconvenienceyieldrepresentstherewardforholdingpublicdebt.Aguiaretal.(2022),showasimplewaytogenerateawedgebetweenprivatecapitalandgovemnentdebt.Theyalsoshowthatcrowdingoutisacriticalforcetobedealtwithinsuchframework.Ourfocusisnotonexplainingtheconvenienceyiel
18、dbutratheronunderstandingitsimplications.Theexercisewehaveinmindtoaddressourresearchquestionsisstraightforward.Wedepartfromaneconomyonabalancedgrowthpath,andfocusonparameterizationsthatallowforanequilibriumwithr-ggrconditionsandthecrowding-outofprivatecapital.1.ikeReis,weemphasizetheintrinsicfiscalc
19、onstraintsthatgovernmentsface,butweextendtheanalysisbycalibratingourmodelstoU.S.economicconditionstoquantifythelong-termGDPeffectsofhigherpublicdebtlevels.Itisimportanttodelineatethefocusandconstraintsofthisresearch.ThestudyisconstructedtoexaminetheeconomicconsequencesOfincreasinglevelsofpublicdebt,
20、specificallyemphasizingtheassociatedcosts.Weintentionallyabstainfromanalyzingpotentialbeneficialeffectsofpublicspending,suchasinvestmentsininfrastructure,education,orclimatetransition.Moreover,ourmodeldoesnotincorporateforcesthatcouldgeneratelargefiscalmultipliers.Thismethodologicalchoiceisdesignedt
21、oisolatethecostsassociatedwithincreasinglevelsofpublicdebt.Assuch,thepapershouldnotbeconsideredanexhaustiveassessmentofreal-worldfiscalpolicies,includingthoseoftheUnitedStates,asacomprehensiveevaluationwouldnecessitateamodelthataccountsforboththeadvantagesanddisadvantagesofpublicdebt.Apaperwithmecha
22、nismsintimatelylinkedtooursisAguiaretal.(2022).TheauthorsworkwithanincompletemarketsmodelinthespiritofBewley-Huggett-Aiyagariwherebyhouseholdsarefacingidiosyncraticriskandholdprecautionarysavingsintheformofprivatecapitalandgovernmentdebt.Theyshowthatthewelfareeffectofincreasinggovernmentdebtdependsc
23、ruciallyontheaggregatesavingsschedule.Indeed,whenthegovernmentissuesbondstheinterestratecanincrease,reducingprivatecapital.Thesearealsothemechanismsatworkinouranalysis.1.astly,AcharyaandDogra(2022)presentastudythatalignscloselywiththequestionsexploredinourresearch.Theyutilizeanoverlappinggenerations
24、model,muchlikeours,butextendtheirframeworktoincludenominalrigiditiesandidiosyncraticcapitalincomerisk.Importantly,theirmodelfeaturesanendogenousconvenienceyield,incontrasttotheexogenousyieldconsideredinourwork.Thisendogenizationallowsforanuancedanalysisofwelfareimplications.Theauthorspositthatanincr
25、easedsupplyofzsafeassets/primarilyintheformofgovernmentdebt,couldrestoretheefficacyofconventionalmonetarypolicyineconomiesconstrainedbythezerolowerbound(Z1.B).Notably,AcharyaandDograobservethat,eveninmodelswithendogenousconvenienceyields,crowdingouteffectsmirrorourfindings:theyarecostlyandleadtodimi
26、nishedinvestmentsinphysicalcapital.TheseobservationsholdtrueespeciallyineconomieswherethesafeinterestratecanassumenegativeVcdueswithoutcompromisingdynamicefficiency.Whiletheirstudyoffersvaluabletheoreticalinsights,itremainslargelyqualitative.OurresearchisinsteadcalibratedmeticulouslytoreflectU.S.eco
27、nomicconditionsandpolicies,andhasasobjectivethequantificationoftherepercussionsonGDPofescalatinglevelsofpublicdebt.I1.AsimplifiedmodelA. EconomicEnvironmentTimeisdiscreteandrunstoinfinity.EachindividuallivesforNperiods.Hence,individualsbomattimetlivefordatesf,f+l,.,f+N-1.Preferencesoverconsumption,c
28、anberepresentedbythetimeseparableutilityfunction归户。wherefunctionw：R+Rsatisfiesstandardassumptions,and00,andanexogenouslygivenpopulationsizeatperiod0,1.0.1.t=(1+n)Productionisundertakenbycompetitivefirms.TheaggregateproductionfunctionisFandsatisfiesconstantreturntoscaleandotherstandardassumptionsYt=F
29、(Kt,1.1.etk=K1.rsothatf(k)=F片=FK1).Goingforward,OIPitaIletterswilldenoteaggregateswhilesmallcapswilldenotepercapitavalues.Factormarketsareassumedcompetitive.IndividualscanonlyworkduringN-1periods,andsupplyoneunitoflaborinelasticallyearningthewagerate卬匕Tokeepthemodelsimple,wedonotendOgenizeindividual
30、sassetallocationdecisions.Instead,wefollowBraunandJoines(2014)andassumethatindividualssaveinafundthatallocatesanexogenousfraction1-tofsavingstogovernmentdebtandafractionttofirmscapital(Inequilibrium,thevalueoftwillturnouttobeconsistentwiththelevelsofdebtandprivatecapitalstock).Hence,thegrossrateofre
31、turntosavingisaweightedaverageoftherentalrateofcapitalzfcandtheratepaidbygovernmentbonds/sothat1+zc=/(ki)+1-3+(1-)(1+申Wewillassume1+zb=(1+fc-),withconvenienceyield.Finally,thereisagovernmentwithaninitialdebtlevelB11thatfinancesapredeterminedstreamofexpendituresGJ,GfOforallt=0,2,.Governmentexpenditur
32、esdonotdirectlyaffectthereturnfunctionofanyprivateagentofthiseconomy.Thegovernmentcantaxhouseholdsusingonlyconsumptiontaxes,tAcomprehensiveandrealisticsetofdirectandindirecttaxeswillbeintroducedinthequantitativeversionofthemodel.B. IntertemporaloptimizationTheoptimizationproblemofanindividualbomatti
33、met,ismaxnxiu(ct)=ot+jsubjectto:(1+t+j)c+j+s+j=Rt+jstt+WtI1.j鼠=Ij=。N-2,1%nt=0$3=0Firmswillgeneratezeroprofitso,Wagew=f(kt)-f*,kt=(1-a)f(ki).TheinterestratereceivedbyhouseholdsandthemarginalproductOfcapitalarerelatedinthefollowingway(giventheassumptionsonportfolioholdings)R=(l+Z)+(1-)(1+zfc-7)=/(*)-y
34、(i-)C. EquilibriumTotalsavingsintheeconomyareSt=理7t=0whereNiftarethepopulationweightsinperiodtofallindividualswhosave(theweightedsumofthesavingsofindividualsalivewithage0.N-1).Marketclearingforassets(assuminginthiscasefulldepreciation)requires(1) Kt+x+=St.Consistencyofexpectedandactualreturnsrequire
35、sKt+BtThelawofmotionfordebtisthestandardoneBt+=Gt(1+-TtCtor如产+(i+造.一工心1+11Anequilibrium,foragivensequenceofgovernmentdebt,expenditure,andtaxes,isasequenceofprices(interestratesandwages),andallocations(consumptionsandsavingsforallindividuals)suchthatindividualssolvetheiroptimizationproblems,takingpri
36、cesasgiven,andmarketsclear.D.ComparativeStatistics(steadystate)Wenowstudythelong-runimpactofincreasingpublicdebt.Forsimplicity,weassumeindividualslivefortwoperiodsandpreferencescanberepresentedbythelogutilityu=log.Asteadystateisanequilibriumwherepercapitavariablesareconstantovertime.Exogenousgrowthc
37、anbeeasilyintroducedbutdoesnotchangeanyoftheconclusions(onewouldfocusonabalancedgrowthpathwhereallpercapitavariablesgrowsatanexogenouslygivenconstantrate).Noticethatsincetheonlytaxistheconsumptiontax,andinasteadystatesuchtaxisconstantovertime,taxationdoesnotaffecttheintertemporalEulerequationofindividualofgenerationt,namely六二6Rsolvingforsavingsyields(2) S=簿Forassetmarketstoclear(1+n)k+(1+?)Z?*=s=.,musthold.Thefollowingequationcharacterizesthesteadystateofthemodel(3) (1+九)4*+(1+)b*=:涝k).T
