speeches · February 10, 2022

Regional President Speech

James Bullard · President

A TWO-TRANCHE VIEW OF NATIONAL DEBT DavidAndolfatto,JamesBullard,Riccardo DiCecioandGuillaumeVandenbroucke FederalReserveBankofSt. Louis UniversityofTexasatAustin Feb. 11,2022 Austin,Texas AnyopinionsexpressedhereareourownanddonotnecessarilyreflectthoseoftheFOMC. 1 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS Introduction 2 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS RETHINKING NATIONAL DEBT Observeddebt-to-GDPratiosintheU.S.,Japanandsomelarge Europeaneconomiesclearlyexceedrecommendationsgivena generationagointheMaastrichtTreaty. Thisisoftenconsideredunsustainable,yetthedemandforthis debtremainsrobust. Weexplorearesolutiontothispuzzleinastylizedmodelin whichtheequilibriumlevelofthedebt-to-GDPratiois considerablyhigherthanwhatisrecommendedinthe MaastrichtTreaty. 3 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS WHAT WE DO Astylizedgeneralequilibrium“large”life-cyclemodelwith interest-bearinggovernmentdebtheldaspartofthefirst-best equilibrium. Nogovernmentspendingortaxes: Theonlyroleofthefiscal authorityistoissueinterest-bearingpapereachperiod. The federaldebtisthereforenotbackedbyfuturetaxes. Importantprivatecreditmarket: Theyoungborrowfromthe middle-aged,whoaresavingforwhentheyareold. Enoughrealisticfeaturestoprovideaninterestingcalibrated benchmark. Substantialinequalityinincomeandfinancialwealth—enough togenerateGinicoefficientsclosetothoseobservedinU.S.data. 4 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS MAIN FINDING Mainresult: Theoptimalfederaldebt-to-GDPratiointhe benchmarkcalibratedequilibriumofthiseconomyis100%,a substantialshareofthecurrentU.S.federaldebt-to-GDPratio. Intuition: Ourmodelprovidesademandforgovernmentdebtas atypeof“interest-bearingmoney,”andtheamountneededto supportthefirst-bestallocationofresourcesturnsouttobelarge. Theresultsinthispaperarebestthoughtofasapplyingtolarge stableeconomieswithhighfiscalandmonetarypolicycredibility. WhethertheseresultswouldapplytocountrieswithintheEMU isanopenquestion. 5 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS REMARKS Completecharacterizationofoptimalmonetary/fiscalpolicy. Thefiscalauthorityissuesone-periodnominaldebtattheexpected rateofnominaloutputgrowth. Themonetaryauthoritysetsthepriceleveltoensurethatthereal rateofreturnonthisdebtandotherassetsisequaltothestochastic rateofrealoutputgrowth. Theoptimalfiscal-monetarymixworksequallywellwhether interestratesarehighorlow. Monetarypolicyprovidesaformofinsurancetoinvestorsby makingtherealreturnongovernmentdebtappropriately state-contingentinaneconomywithnon-state-contingent nominalcontracting. 6 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS MORE REMARKS Intheequilibriumwedescribe,federalgovernmentdebtcoexists withcapitalandwithprivatelyissueddebt,whichcanbe interpretedasmortgage-backedsecurities. Wefocusonone-perioddebt,butthemodelcanprice many-perioddebt. Weabstractfrominternationalconsiderations,butthisisan importantareaforfutureresearch. 7 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS BOTTOM LINE EXAMPLE TheU.S.federaldebt-to-GDPratiois122.5%(Q32021). Standardmacroeconomicswouldconsiderthisentirelyas Barro-Ricardiandebtthatmustbebackedbyfuturetaxation. Also,levelsinexcessof60%(accordingtotheMaastrichtTreaty) areexcessiveandsuggestafuturecrisis. Thispapercalibratesafirsttrancheof100%,whichis “interest-bearingmoney”andnotbackedbyfuturetaxation. Thiswouldleave22.5%asBarro-Ricardiandebt(notmodeled) thatmustbebackedbyfuturetaxes—alevelthatwould normallybeconsideredeasilysustainable. Thepaperprovideswidescopeforinterpretinghowlargethe twotranchesmaybe—thecasewithafirsttrancheof100% presentedhereprovidesoneillustrationthatthefirsttranche maybequitelarge. 8 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS Environment 9 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS MACROECONOMY WITH HETEROGENEOUS AGENTS Ateachdatet,anewcontinuumofhouseholdsentersthe economy,makeseconomicdecisionsoverT+1=241dates, thenexitstheeconomy. Thiscorrespondstoanagententeringtheeconomyasa decision-makeratage20andexitingasadecision-makeratage 80,inclusiveofendpoints,andmakingeconomicdecisionsata quarterlyfrequency. ResultsareperfectlygeneralforthechoiceofT,withhigher valuescorrespondingtodecision-makingatmorefrequent intervals. Thisclassofmodelshasa“paper-and-pencil”equilibrium solution,andsoitprovidesasimplebenchmarkmodelfor heterogeneous-agentmacroeconomieswithaggregateshocks. 10 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS RISK FACED BY HOUSEHOLDS Thereisbothaggregateriskandidiosyncraticrisk. Allidiosyncraticriskisborneastheagententerstheeconomy. Macroeconomicpolicymakersprovideaformofinsurance againsttheaggregaterisk. Awelfaretheoremdescribesthesenseinwhichtheequilibrium studiedhererepresentsafirst-bestallocationofresources. 11 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS ASSETS AND NOMINAL CONTRACTING Therearethreenominallydenominatedassets: privatelyissued debt,publiclyissueddebtandcapital. WethinkoftheseasrepresentingU.S.datacounterparts: (1) mortgage-backedsecurities,(2)federallyissueddebtand(3) physicalcapital,respectively. IntheU.S.data,MBSnetout,butfederallyissueddebtand physicalcapitalareinpositivenetsupplyandwetargetavalue ofassets-to-GDPequalto1.00+3.32=4.32. Thecreditmarketfrictionisnon-statecontingentnominal contracting(NSCNC):Alldebtcontractsarestatedinnominal terms,withastatednominalinterestrate,andrepaymentisnot state-contingent. Theroleofmonetarypolicyistoadjustthepriceleveleach periodinordertoconvertthesenominal,non-statecontingent contractsintoreal,state-contingentcontractsinordertoachieve thefirst-bestallocationofresources. 12 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS HOUSEHOLD TYPES Therearetwohouseholdtypes: “lifecycle”and “hand-to-mouth.” Thelife-cyclehouseholdsareassignedahump-shaped productivityprofileatthebeginningoftheirlifecycle. Accordingly,theyneedtousecreditmarkets(holdassets)to smoothlife-cycleconsumption. Thehand-to-mouthhouseholdsareassignedaperfectlyflat productivityprofileastheyentertheeconomy. Accordingly,they neverneedtousecreditmarketsandinsteadconsumetheir laborincomeeachperiod. Theeconomywithalllife-cyclehouseholdswantstoholdassets worth5.71timesthesizeofGDP,higherthanwhatweseeinthe data. TheeconomywithallHTMhouseholdswouldbe“Spartan,” andwouldholdnoassetsatall. WewilladjustthefractionofHTMhouseholdsinordertomatch theassets-to-GDPratiointheU.S.data. 13 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS PREFERENCES Eachhouseholdi (0,1)enteringtheeconomyatdatethas 2 preferences(bothtypes) T ∑ U = [ηlnc˜ (t+s)+(1 η)ln` (t+s)]. t,i t,i t,i (cid:0) s=0 Wedefinec˜ (t+s) =D(t+s)c (t+s),whereD(t+s)isthe t,i t,i stateofaggregatedemandatdatet+s.Thestateofdemand evolvesas D = δ(t 1,t)D , t t 1 (cid:0) (cid:0) whereδ(t 1,t)isthegrossgrowthrateofdemand,which (cid:0) followsanappropriatestochasticprocessthatkeepsD(t) >0 t. 8 FollowingBai,Ríos-RullandStoresletten(unpublished,2019), weallowthestateofaggregatedemandtoinfluenceproductive activityintheeconomy. 14 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS LIFE-CYCLE PRODUCTIVITY PROFILES Life-cyclehouseholdsenteringtheeconomydrawascaling factorxfromalognormaldistributionandreceivealife-cycle productivityprofilethatisascaledversionofthebaseline profile,e : s e =x e , s,i s (cid:1) 4 wheree s =1+p 1 exp (cid:0) s (cid:0) p3 p2 ,andwherep 1 ,p 2 andp 3 are chosentomatchcalibr (cid:20) atio(cid:16)ntarg(cid:17)et (cid:21) sgivenbelow. Huggett,VenturaandYaron(AER,2011)arguethatdifferencesin initialconditionsaremoreimportantthandifferencesinshocks. Wealsoincludeameasureofhand-to-mouthagentsineach cohort. Theyhaveaperfectlyflatendowmentprofile,scaledup ordownbyasimilarscalingfactor. 15 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS TECHNOLOGY AggregaterealoutputY(t)isgivenby Y(t) = [D(t)Q(t)N(t)]1 (cid:0) αK(t)α[L(t)]1 (cid:0) α , (1) whereK(t)istherealvalueofthephysicalcapitalstock,L(t)is theaggregateeffectivehumancapitalsupply(hours (cid:2) productivityofvarioushouseholds),Q(t)isaproductivity index,N(t)indexesthesizeofthelaborforce,andD(t)isthe stateofaggregatedemand. Q,NandDgrowatstochasticgrossratesλ,νandδrespectively. Theseassumptionsmeanthatrealoutputgrowsatthestochastic rateλνδeachperiod. TheaggregatedemandassumptionisasimpleversionofBai, Ríos-RullandStoresletten(unpublished,2019). Thelaborforcegrowthassumptionaffectsallcohorts proportionatelyandcanbeinterpretedas“immigration.” 16 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS NOMINAL CONTRACTING AND TIMING PROTOCOL Undertheassumptionsoutlined,thecontractnominalinterest rateisgivenby c˜ (t) P(t) Rn(t,t+1) (cid:0) 1 =E t c˜ t ( , t i +1)P(t+1) . (2) (cid:20) t,i (cid:21) Thetimingprotocolis: (1)Natureassignsnewentrant productivityprofilesandalsodrawsaggregateshocks;(2)The fiscalauthorityissuesnominaldebt;(3)Themonetaryauthority setsthepricelevel;(4)Householdschoosedatetconsumption, hoursworkedandnetassetholding. Householdswillbeabletomakedatetdecisionswithout referencetofutureuncertainty,asthemonetarypolicymakeris providingatypeofperfectinsurance. 17 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS THE FISCAL AUTHORITY Thefullycrediblenominaldebtissuanceprocessisgivenby B(t) =Rn(t 1,t)B(t 1), (3) (cid:0) (cid:0) whereB(t)isthenominallevelofdebtandB(0) >0. Thefiscalauthorityisissuingenoughnewdebttopayoff existinginvestorswithinterest. Therearenotaxesorgovernmentexpendituresofanykind,so thereisnoreferencetofutureprimarysurpluses. Thespiritofthemodelisthatdebtaboveandbeyondthat indicatedby(3)wouldbeBarro-Ricardiandebt(notmodeled), backedbyafuturestreamoftaxes. 18 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS THE MONETARY AUTHORITY Themonetaryauthoritycontrolsthepriceleveldirectlyand implementsapricelevelpathcriterion Rn(t 1,t) P(t) = (cid:0) P(t 1). (4) δ(t 1,t)λ(t 1,t)ν(t 1,t) (cid:0) (cid:0) (cid:0) (cid:0) Thiscriterionimplementscountercyclicalpricelevelmovements relativetotheexpectationembodiedinthecontractrate Rn(t 1,t).SeeKoenig(IJCB,2013)andSheedy(BPEA,2014). (cid:0) Seeourpaper(p. 14)foradiscussionofhowthiscriterionrelates toasimilarNewKeynesiancriteriondevelopedbyGiannoniand Woodford(2004,pp. 101-2). Thismonetarypolicyachievesthe“Wickselliannaturalrealrate ofinterest”forthiseconomy. 19 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS COMPETITIVE EQUILIBRIUM AND SOCIAL WELFARE Solution: Guessandverifythatthereisacompetitive equilibriuminwhichtherealrateofinterestisalwaysequalto thestochasticrateofrealoutputgrowth. Asocialplannerwouldconcludethattheallocationofresources isasocialoptimumprovided(i)theplannerplacesequalweight onallhouseholdsforalltime,(ii)theplannerdiscounts backwardandforwardintimeatthestochasticrealrateof interest,(iii)theplannercannotalterthedistributionof productivityprofileswithinthecohort,whicharedecidedby natureatthebeginningofthelifecycle. 20 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS Mapping to Data 21 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS MAPPING TO THE DATA AdjustcohortsizebasedondatafromtheU.S.CensusBureau. Setthebaselinehump-shapedlife-cycleproductivityprofilesuch thathouseholdsendogenouslychoosetoworkthehoursworked byageintheU.S.data. Chooseηtomatchaveragetimedevotedtomarketworkacross theeconomy. SetthefractionhofHTMhouseholds(whodonotholdassets) suchthattheaggregatelevelofassetstooutput,A/Y,matches theU.S.data(4.32),withnetassetsdefinedascapital (K/Y=3.32)plusgovernment-issueddebt(B/Y=1.00). Wechoosethewithin-cohortstandarddeviationsofproductivity forlife-cycleandhand-to-mouthhouseholds,σ andσ , lc htm respectively,toapproachthepre-taxes-and-transfersGini coefficientsforincomeandfinancialwealthintheU.S.data. 22 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS BASELINE LIFE-CYCLE PRODUCTIVITY 1.5 1 0.5 0 60 120 180 240 quarters FIGURE: Baselineendowmentprofileoflife-cycleagents. 23 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS THE MASS OF LIFE-CYCLE PRODUCTIVITY 3 2 1 0 0 60 120 180 240 quarters FIGURE: Themassofendowmentprofiles:life-cycleagents(blue)and hand-to-mouthagentsforh=0.5(red).Thedashedlinesdenotethe25thand the75thpercentileoftheendowmentdistributions. 24 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS HOURS WORKED BY AGE 0.3 0.2 0.1 Data Model 0 0 60 120 180 240 quarters FIGURE: Hoursworkedbyage:U.S.data(blue)andcalibratedmodel(red). 25 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS POPULATION WEIGHTS 3 10 5 4 3 2 Data Smoothed data 1 0 60 120 180 240 quarters FIGURE: Populationweights:U.S.data(blue)and4thdegreepolynomial smoothed(red). 26 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS ASSETS AND GINI COEFFICIENTS Model U.S.data h 0.25 0.50 0.75 (cid:0) σ 1.19 1.22 1.23 lc (cid:0) σ 1.37 0.98 0.58 htm (cid:0) A/(4Y) 4.32 4.32 4.32 4.32 G 0.75 0.75 0.75 0.78 W G 0.66 0.65 0.65 0.63 Y G 0.62† 0.61† 0.61† 0.32‡ C TABLE: Assets-to-outputratiosandGinicoefficients:modelvs.U.S.data. † Pre-taxes-and-transfersconsumptionGini. ‡ Post-taxes-and-transfersconsumptionGini. 27 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS THE CONSUMPTION GINI Thepre-taxes-and-transfersconsumptionGiniinthemodel equilibriumisG 0.62,0.61,0.61 forthecorresponding c 2 f g economies. IntheU.S.data,thepost-taxes-and-transfersconsumptionGiniis 0.32,abouthalfaslarge. Themodelissayingthattheneteffectoftaxesandtransfersin theU.S.dataisenoughtoreduceconsumptioninequalitybyhalf. UsingGermandata,Haan,Kemptner,andProwse(working paper,2018)usealife-cyclemodeltoestimatethatthe tax-and-transfersystemissufficienttooffset54%ofthe inequalityinlifetimeearnings. 28 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS NOMINAL RETURNS Themodelclaimsequalizednominalreturnsforthreeassets underoptimalmonetarypolicy: capital,MBSandTreasuries. Theseassetsarenotfurtherdifferentiatedinsidethemodel. Tocomparetothedata,weneedanassetrepresentingareturnto capitalinaformatwithriskcharacteristicssimilartoMBSand Treasuries. Onecandidateisacorporatebondindex. Themodelequilibriumstatesthatthenominalreturnonsuchan indexshouldbeequaltonominalconsumptiongrowthin periodsofrelativestabilitywithoptimalmonetarypolicy. 29 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS NOMINAL RETURNS 1997 2006 ANR 2010 2019 ANR Corporatebondindex 100 189 7.3% 100 165 5.7% PCE 100 170 6.1% 100 145 4.2% ServicesPCE 100 174 6.3% 100 148 4.5% TABLE: Totalannualnominalreturns(ANR)onanindexofcorporatebonds vs.nominalconsumptiongrowth. Thetwotimeperiodswererelativelystable,withestablished monetarypolicycredibility. Thedifferencesinthebondindexvs. theconsumptionindex suggestsomedeviationfromoptimalmonetarypolicyduring theseperiods,accordingtothemodel. 30 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS Conclusions 31 INTRODUCTION ENVIRONMENT MAPPINGTODATA CONCLUSIONS HOW LARGE IS THE FIRST TRANCHE? Thispaperarguesthatsomefractionofobservedfederaldebtfor largeeconomieswithsubstantialmacroeconomicpolicy credibilitymaybeofthefirst-tranche,“interest-bearingmoney” type. Thisfractionisnotbackedbyfuturetaxes. Itdoesnotcostanything,nordoesitproducerevenue. Itcanberolledoverinperpetuityatmarketinterestrates;this processisgoingoninthebackgroundmuchasthereplacement ofworncurrencyisgoingoninthebackground. AsecondtrancheofBarro-Ricardiandebt(notmodeled)could existontopofthefirsttranche,andthemarginaldollarof additionaldebtwouldthenhavetobebackedbyfutureprimary surpluses. Thiswouldhelpexplainwhytakingonadditionaldebtisoften politicallycontentious,whileatthesametimeseeminglyhigh rawfederaldebt-to-outputratiosremainsustainableforsome countries. 32

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APA

James Bullard (2022, February 10). Regional President Speech. Speeches, Federal Reserve. https://whenthefedspeaks.com/doc/regional_speeche_20220211_james_bullard

BibTeX

@misc{wtfs_regional_speeche_20220211_james_bullard,
  author = {James Bullard},
  title = {Regional President Speech},
  year = {2022},
  month = {Feb},
  howpublished = {Speeches, Federal Reserve},
  url = {https://whenthefedspeaks.com/doc/regional_speeche_20220211_james_bullard},
  note = {Retrieved via When the Fed Speaks corpus}
}