美联储-了解美元的实力（英）-2022.12

BoardofGovernorsoftheFederalReserveSystemInternationalFinanceDiscussionPapersISSN1073-2500(Print)ISSN2767-4509(Online)Number1366UnderstandingtheStrengthoftheDollarZhengyangJiang,RobertRichmond,andTonyZhangPleasecitethispaperas:Jiang,Zhengyang,RobertRichmond,andTonyZhang(2022).“UnderstandingtheStrengthoftheDollar,”InternationalFinanceDiscussionPapers1366.Washington:BoardofGov-ernorsoftheFederalReserveSystem,/10.17016/IFDP.2022.1366.NOTE:InternationalFinanceDiscussionPapers(IFDPs)arepreliminarymaterialscirculatedtostimu-latediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstaffortheBoardofGovernors.ReferencesinpublicationstotheInternationalFinanceDiscussionPapersSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.RecentIFDPsareavailableontheWebat/pubs/ifdp/.ThispapercanbedownloadedwithoutchargefromtheSocialScienceResearchNetworkelectroniclibraryat.gAbstractWelinkthesustainedappreciationoftheU.S.dollarfrom2011to2019tointernationalcapitalflowsdrivenbyprimitiveeconomicfactors.Weshowthatincreasesinforeigninvestors’netsavings,increasesinU.S.monetarypolicyratesrelativetotherestoftheworld,andshiftsininvestordemandforU.S.financialassetscontributedapproximatelyequallytothedollar’sappreciation.WethenquantifytheimpactofpotentialfuturedemandshiftsforU.S.assetsonthevalueofthedollar.KeyWords:Dollar,ExchangeRate,CapitalFlows,AssetDemandSystemJELClassifications:F3,F31,G1,G11,G12*ForcommentsanddiscussionswewouldliketothankRalphKoijen,JuanLondono,AlexiSavovandseminarparticipantsattheFederalReserveBoard,theUniversityofWisconsin,theBankofInternationalSettlements,andNewYorkUniversity.CodyWanprovidedexcellentresearchassistance.TheviewsinthispaperaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasreflectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystemoranyotherpersonassociatedwiththeFederalReserveSystem.tNorthwesternUniversity,KelloggSchoolofManagement,andNBER;E-mail:zhengyang.jiang@.主NewYorkUniversity,SternSchoolofBusiness;E-mail:rrichmon@.?FederalReserveBoard;E-mail:tony.zhang@.1In2022,thedollarreacheditshighestlevelsincetheearly2000s,afterexperiencingadecade-longperiodofsustainedappreciation.Thestrengthofthedollarhasfar-reachingconsequencesforglobalassetprices,economicconditions,andthehealthoftheglobalfi-nancialsector.Assuch,itisimportanttounderstandtheeconomicdriversofthestrengthofthedollar.Inthispaper,weuseaportfolio-basedapproachtoattributethedollar’sap-preciationtovariationsinassetsupplyanddemanddrivenbyprimitiveeconomicfactors.Ourkeyfindingisthatincreasesininvestors’netsavings,risingU.S.monetarypolicyratesrelativetotherestoftheworld,andshiftsininvestordemandforU.S.assetscontributedapproximatelyequallytothedollar’sappreciation.Weemploythedemandsystemapproachtoassetpricing(KoijenandYogo2019a,b;Koijen,Richmond,andYogo2019)byadoptingthespecificationofJiang,Richmond,andZhang(2022).Inthepresenceofdownward-slopingassetdemand,ourapproachtracesouthowthedollar’sexchangeraterespondstovariationsinassetsupplyanddemand.Forexample,anincreaseinforeigners’demandforU.S.assetsleadstoacapitalinflowtotheinthesupplyoftheUSshorttermdebtassetsdilutesthesupplyofdollarassetsandleadstoadollardepreciation.Weestimateourmodelusingacomprehensivedatasetofbilateralequityanddebtport-foliopositionsbetween2011and2019.Wefocusonthetrade-weightedindexofthedollaragainstadvancedforeigneconomies,referredtoasthedollarAFEindex.Inthisperiod,thedollarAFEindexappreciatedby23%,whichrepresentsasubstantialproportionofthe30%appreciationbetweenJanuaryandAugust2022.Wedivideourmodel’sprimitivedemandandsupplyfactorsintothreecategories:(i)ininvestors’demand.Wetreatthesevariablesasexogenous,andtheyjointlyexplaintheendogenousexchangerates,assetprices,andportfolioallocations.Fromoneyeartotheginexogenousvariablesbetweenyearsandrecomputingequilibriumexchangerates,prices,andallocations,weareabletoattributevariationsinthedollartodifferentfactors.nvestmentopportu2veinnancialassetstheyallocatetheirsavingsaccordingtotheirexistingportfolioweights.Then,giventhatassetpricesadjustinresponsetotheadditionaldemand,investorswilladjusttheirportfo-liosbymovingalongtheirdemandcurves.Asaresult,savingsandissuancescanimpactexchangeratesevenwithoutshiftsininvestors’demandcurves.Wefindthattheincreaseinglobalsavingsaccountsforanofthedollar’sappreciationbetween2011and2019.Second,westudytheeffectsofmonetarypolicies.Overthelastdecade,theFederalReserveBank(FRB)raiseddomesticinterestratesfasterthanothercentralbanks.ThisrelativelyhighyieldattractedforeigncapitaltotheU.S.,keepinginvestorsavingsandassetsupplyfixed.TheriseinU.S.short-terminterestratesexplainsanadditional5.8%dollarappreciation.TheFRB’smonetarypolicyisparticularlyimportantforexplainingtheriseofthedollaragainsttheEuroduetotheexpansionarypolicystancetakenbytheEuropeanCentralBank.Interestingly,therelationbetweendollarappreciationandtheU.S.monetarypolicyimpliedbyourmodelalsomatchestheestimatesfromtheliteraturethatuseshigh-frequencyshockstoidentifytheeffectsofmonetarypolicy.afurther9.3%dollarappreciation.Thesedemandshiftsappreciatedthedollarintwoways.creasedThisshiftindemandtowardsUSfinancialassets,particularlytowardsU.S.equity,wasalsoinstrumentalinexplainingthereturnsonU.S.financialassetsasshownbyJiang,Richmond,andZhang(2022).Second,U.S.investors’demandforforeignassetsdeclinedoverthelastdecade,puttingdownwardspressureonforeigncurrenciesrelativetothedollar.Inthefinalpartofthepaper,westudytheconsequencesofhypotheticallarge-scalesalesofU.S.financialassetsonthedollar.WefindthatevenifalargeeconomysuchasChinaunilaterallysellsallofitsholdingsofU.S.assets,theimpactonthedollar’svalueisWealsostudyadeclineinthespecialnessofU.S.assetsandshowthatitwouldleadtoalargerdepreciationofthedollar.Theseresultshighlightthestabilityofthedollarasaglobalcurrency,andthesupporttheliteratureoncoordinationonreservecurrencies.3Ourfocusonthedollarismotivatedbytheliteraturethatshowsthedollarplaysacriticalroleintradeandtheinternationalfinancialsystem(Maggiori,Neiman,andSchreger2020;Jiang,Krishnamurthy,andLustig2020;GopinathandStein2021).Thedollar’sinfluenceonforeigneconomiesdrivestheglobalfinancialcycle(Rey2015;Du2019;Miranda-AgrippinoandRey2020)anditsstrengthisrelatedtofrictionsinfinancialintermediation.Specifically,Avdjiev,Du,Koch,andShin(2019)showthatastrongerdollarcoincideswithlargerdevia-tionsfromcoveredinterestrateparity(CIP)andlesscross-borderlending.GlobalfinancialconditionsalsoaffecttheCIPdeviationandthedemandforsafeassets(DuandSchreger2021;Jiang,Krishnamurthy,andLustig2021).Ourpaperbuildsonworkthatdemonstrateshowexchangeratesareconnectedtoin-ternationalcapitalflows.GabaixandMaggiori(2015)presentsamodelforhowexchangeratesandcapitalflowsarerelatedinsegmentedfinancialmarkets.Lilley,Maggiori,Neiman,andSchreger(2022)documentthataftertheglobalfinancialcrisis,thedollar’svalueissuresofglobalriskappetiteandtoUSforeignbondpurchasesHauandRey(2006)presentanequilibriummodelofexchangeratesandcapitalflowsandshowthathcapitalowsCamanhoHauandReystudymutualfundrebalancingandexchangerates.Ourpapercontributestothisliteraturebyquantifyinghowfactorsthatdrivecapitalflowscanjointlyexplainthedynamicsofthedollar.Finally,ourpapercontributestotheliteratureonreservecurrenciesandthedollar.Maggiori(2017)studiestheemergenceofandpropertiesofareservecurrencyinamodelwithvaryingdegreesofnancialdevelopmentFarhiandMaggioriHeKrishnamurthy,andMilbradt(2019)studyamodeloftheinternationalfinancialsystemandtheimplicationsofsupplyanddemandforreserveassets.Ourstudyhighlightsthestabilityofthedollarregimebasedontheassetsubstitutionpatternsofdifferentinvestors.1APortfolioApproachtoDollarValuationOurmodelfollowsJiang,Richmond,andZhang(2022),whichbuildsonKoijenandYogo(2019b).Therearethreekeyingredients:(1)investors’assetdemandcurves,(2)investors’4wealthdynamics,and(3)marketclearing.Theseingredientsconstituteanassetdemandsystemthatrelatesexchangeratesandassetpricestothedemandandsupplyoffinancial1.1InternationalAssetDemandSystemTimeisdiscrete.ThereareIinvestorcountriesthateachcontainarepresentativeinvestorssetsThesebyb:short-termdebt(b=1),long-termdebt(b=2),andequity(b=3).EachassetclasscontainsN+1assets—oneforeachissuercountryplusan“outside”assetindexedn=0.Thisoutsideassetcontainsholdingsinsmallcountriesthatarenotinourmainsampleduetodatalimitations.Wedenoteinvestorcountryi’sportfolioweightonissuercountryninassetclassbbyti,t(n,b),whichcanbedecomposedas:ti,t(n,b)=ti,t(nIb).ti,t(b),(1)whereti,t(nIb)isinvestorcountryi’sportfolioweightonissuercountrynwithinassetclassb,andti,t(b)isinvestorcountryi’stotalportfolioweightonassetclassb.DemandwithinAssetClass.Withinanassetclassb,theportfolioweightforinvestoriattimerincountrynisalogisticfunction1:ti,t(nIb)=(2)ti,t(nIb)=(2)1+|6i,t(k,b),where6i,t(n,b)capturestherelativedesirabilityofacountry’sassetinthisassetclass:6i,t(n,b)=exp(βeui,t(n,b)+甘xi,t(n)+si,t(n,b)).(3)1Byconstruction,thetotalweightineachassetclassequals1,|=0wi,t(nIl)=1.Theportfolioweightintheoutsideassetinassetclasslisthereforewi,t(0Il)=1/(1+|=16i,t(n,l)).5Thisdesirabilityhasthreecomponents.First,ui,t(n,b)denotestheexpectedreturnattimerforcountryi’sinvestorincountryn’sassetofclassb.Second,xi,t(n)denotesasetofobservableassetcharacteristicsthatcanbecountry-specificorbilateralinnature.TheThird,si,t(n,b),denoteslatentdemandanddescribesadditionalvariationintheportfolioweightsthatisnotcapturedbytheexpectedreturnorobservableassetcharacteristics.ForconcretenessconsidertheUSinvestordecidingonherportfolioweightonGermanlong-termdebt.Thus,iistheU.S.,nisGermany,andb=2representslong-termdebt.ui,t(n,b)capturesthelocalcurrencyreturntheU.S.investorexpectstoearnonGermanlong-termdebt.xi,t(n)capturescharacteristicssuchasthesize(GDP)ofGermanyandthematterforthelong-termbondportfolioallocation.ExpectedReturns.Investorscareaboutexpectedreturnsintheirowncurrency.WeyLetgt+1(n,b)=log(Rt+1(n,b))denotethelogreturnindollarsonassetclassbincountrynfromtimertor+1.Tomeasureexpectedreturns,weuseaforecastingregressionasinKoijengt+1(n,b)-gt+1(Us,1)=oe.pót(n,b)+we.(et(n)-wt(n))+xn,e+5t+1(n,b).(4)Thisregressionprojectstheexcessreturnattimer+1foraU.S.investorontoitslogmarket-etweencountrynandthedollars.Thebookvalueinthemarket-to-bookratioisequitybookvalueforequityandparvaluefordebt.Thelogrealexchangerateisthedifferencebetweenthelognominalexchangerateet(n)=logEt(n)andthelogconsumerpriceindexwt(n).Theexchangerate,Et(n),isindollarsperunitofforeigncurrency.Theregressioncoefficientsoeandwearespecifictoeachassetclassb.Basedonthisregression,theexpectedlogexcessreturnon6assetnininvestori’scurrencyisui,t(n,b)=Et[gt+1(n,b)-gt+1(i,1)]=oepót(n,b)+we(et(n)-wt(n))+xn,e-o1pót(i,1)-w1(et(i)-wt(i))-xi,1.(5)DemandAcrossAssetClasses.Toallowforsubstitutionacrossassetclasses,theassetclassportfolioweightisspecifiedasanestedlogit.Theportfolioweightforinvestoriatmerinassetclassbis|=1(1+|6i,t(k,m))λmexp(am+Ti,t(m)),ti,t(b)|=1(1+|6i,t(k,m))λmexp(am+Ti,t(m)),whereaecapturesassetclassfixedeffectsandTi,t(b)capturesassetclasslatentdemand.Theterms(1+|6i,t(n,b))arereferredtoasinclusivevaluesforagivenassetclassb,ingineachassetclassForexamplewhenableleandinvestorsmaysubstituteawayfromtheassetclassaccordinglyCentralBanks.Wedifferentiatebetweendemandofprivateinvestorsandcentralbanks.WeuseBi,t(n,b)todenotethequantityofcountryn’sassetsheldbycountryi’scentralbankurrencybookvaluewhichwetakeasexogenousInvestorWealthDynamics.Investorwealthadjustsaccordingtothereturnsontheassetstheinvestorholds.Thelawofmotionfortheassetsundermanagement(AUM)forinvestoriindollarsis:3NAi,t=Ai,t冷1LLti,t冷1(b)ti,t冷1(nIb)Rt(n,b)+Fi,t,e=1n=0whereRt(n,b)isthecapitalgainsonassetninassetclassbintimerindollars,andFi,tisinvestori’snetfinancialsavingsindollars,includingdividendyield.22Wespecifycapitalgainsasafunctionofthemarket-to-bookratioofassetsandtheexchangerateinAppendixA.1.7MarketClearing.Let○t(n,b)denotethebookquantitysuppliedbycountryninassetclassbinitslocalcurrency.Specifically,○t(n,b)isthetotalbookvalueinlocalcurrencyforrmandshorttermdebtWeassumethequantityofassetsoutstandingineachperiodisexogenouslydetermined.Nevertheless,thedollarbookvalue,Et(n)○t(n,b),andthedollarmarketvalue,PBt(n,b)Et(n)○t(n,b),ofanydetermined.Themarketclearingconditionforasset(n,b)indollarsisNNPBt(n,b)Et(n)○t(n,b)=LAi,tti,t(b)ti,t(nIb)+PBt(n,b)Et(n)LBi,t(n,b).(8)i=1i=1Theleft-handsideisthetotalmarketvalue,andtheright-handsideisthesumofthedollarvalueofinvestors’portfolioholdingsoftheassetplusthesumofthedollarvalueofcentralExchangeRateDetermination.Exchangeratesaredeterminedbymarketclearingforshort-termdebt.Demandforequityandlong-termdebtalsoaffectexchangeratesduetohcountry’smonetaryauthoritysoitspricePBt(n,1)isexogenous.Whenthereisashocktoinvestordemandontheright-handsideofequation(8),theexchangerateEt(n)adjusts.3Intuitively,ifdemandforcountrynshort-termdebtincreasesindollarterms,thecountryncurrencyappreciatesinvaluetocleartheshort-termdebtmarket(Et(n)increases).Insum,thereare3assetclasseswithNassetseach,whichleadsto3Nmarketclearingconditions.Takingshort-termbondpricesasgiven,thereareNlong-termbondprices,Nequityprices,N-1exchangerateswithrespecttothedollar,andtheU.S.short-termbondsupply.Thisleadstoanexactlydeterminedsystem.3Peggedexchangeratesareclearedbyassumingthatthecountry’scentralbankmaintainsthepegbyadjustingthesupplyofshort-termdebt.81.2Dataythreetypesofdatacrosscountrybilateralportfolioholdingsassetcountrycharacteristics,and(3)assetreturns.Ateachstageofourdataconstruction,wecombinethebestavailabledatatogetanaccuraterepresentationofcross-borderportfolioholdingsandassetreturns.ThedataweuseinthispaperarethesameasinJiang,Richmond,andZhang(2022).WesummarizeourdatahereandprovidedetailsinAppendixB.1.Weimprovethequalityofthecross-borderholdingsandreturnsdatainthreeways.First,weusethereallocationmatricesfromCoppola,Maggiori,Neiman,andSchreger(2020)tovestmentsinoshorenancialcentersSecondweestimatethereserveholdingsofspecificcentralbankstodisaggregatethequantitiesattributedtoofficialassetpurchasesattheregionlevel.Third,weusedetailedestimatesofassetreturnsfromtheTICdatatoconstructreliableestimatesofcapitalgainsandnetsavings.Wemeasureassetcharacteristics,xi,t(n),thatinvestorslikelyusetoproxyforexpectedreturnsandtheirriskiness.Thesecharacteristicsincludethemarket-to-bookvalueofequityandtheyieldsonshort-termandlong-termdebt.Weuseyieldson3-monthgovernmentdebttocapturetheyieldonshort-termdebt,andtheyieldon10-yeargovernmentdebtforlong-termdebt.TheissuercountrycharacteristicsareitslogGDP,logpopulation,tradenetworkcentrality(Richmond2016),sovereigndefaultrisk,volatility,realexchangerate,andinflation.Bilateralcharacteristicsareimportandexportexposuresanddistance.Wealsoincludeindicatorvariablesfordomesticinvestment,U.S.issuer,investorcountry,andctsOursamplerunsfrom2011to2019,andconsistsof35investorcountriesand32issuercountries.Holdingsinissuercountriesforwhichwedonotobserveacompletepanelofses91.3EstimationandIdentificationWenowdescribehowweestimateinvestor’sdemandcurves.Equations(2)and(3)implylog╱、=βeui,t(n,b)+甘xi,t(n)+si,t(n,b).(9)Thisequationdeterminesthewithin-asset-classdemand,whichweestimateseparatelyforeachassetclassb.Weobtaintheestimationequationforacross-asset-classdemandbydividingequation(6)forshort-term(b=1)andlong-termdebt(b=2)bytheequationforequity(b=3):log╱、=Aelog!1+6i,t(n,b)!-A3log!1+6i,t(n,3)!+ae+Ti,t(b).(10)Themainchallengetoestimatingequations(9)and(10)isthatexpectedreturnsmaybeendogenoustolatentdemand.Considertheestimationofthewithin-asset-classdemandcurves,equation(9).Ifinvestorshavehighlatentdemandforaparticularissuer’sasset,thepriceofthisassetwillbehigher,whichwillimpactthisasset’sexpectedreturnandbiastheestimateddemandcoefficientβeduetothecorrelationbetweentheregressor,ui,t(n,b),andtheresidual,si,t(n,b).Similarlyfortheacrossassetdemandcurvesinequation(10)—Ifaparticularassetclasshashighlatentdemand,thiswillincreasethepriceofthisassetclassandpotentiallybiastheestimationsincetheinclusivevalue,1+|=16i,t(n,b),containstheprice.Toaddresstheseendogeneityconcernsweconstructinstrumentsforbothestimationequations,buildingontheidentificationstrategyinKoijenandYogo(2019b).Toconstructinstrumentsweneedcross-sectionalvariationincountry-levelexpectedre-turnsthatisuncorrelatedwithlatentdemand.Country-levelexpectedreturnsarerelatedtodreturns.Toobtainsuchvariation,weuseourmodeltoconstructinstrumentsforpricesundertheassumptionthatinvestorportfoliosaredeterminedbyexogenouscharacteristics.Formally,ouridentifyingassumptionisthatassetcharacteristics,assetsupply,andin-vestmentinoutsideassetsinvestorwealthareexogenoustolatentdemand:ExtQt,Ot,=0,(11)wherextisamatrixofcharacteristicsforallcountries,Qtisthevectorofassetsupplies,andOtisthevectorofholdingsofoutsideassets.Webeginbyconstructingexogenousportfolioweightsbyestimatingasimplifiedversiondemandlog╱、=甘xi,t(n)+si,t(n,b).(12)Inthisequation,weomitexpectedreturnsanduseasetofexogenouscharacteristics:bi-lateraldistancebetweencountries,issuercountrypopulation,anowncountrydummy,andinvestorfixedeffects.Byincludinginvestorfixedeffectswecontrolforthecross-sectionalvariationininvestor’sweightsintheoutsideasset,whichusestheassumptionthatoutsideassetholdingsareexogenous.Weusepredictedvaluesfrom(12)toconstructpredicteddesirabilities,6ˆi,t(n,b),whicharedrivenentirelybyvariationinexogenouscharacteristics.whentherelativedesirabilityofallassetsinaparticularassetclasschanges.Forexample,whenequitiesbecomemoredesirablerelativetolong-termdebt,investorsmaysubstitutetowardequityandawayfromlong-termdebt.Theamountofthissubstitutionisdeterminedbytheelasticitiese.Toestimatethisequationweneedexogenousvariationintheoveralltocomputeinstrumentsforthetheoverallassetleveldesirabilities,orinclusivevalues,inequation(10):N1+L6ˆi,t(n,b).n=1mandcurve,equation(10).Thefullestimatesforequation(10)arereportedinAppendixB.2inTableB.5.HerewenotethatallAevaluesarebetween0and1.Thisimpliesthatthereissomesubstitutiondesirabilitiesofindividualassets.WhenAe=1,thesubstitutionbetweenassetclassesonlydependsonthedesirabilitiesofindividualissuercountries’assets,andthedemandsystemcollapsestoonetier.Thenextstepistoestimatethewithin-asset-classdemandcurves,asgivenbyequation(9).Todoso,weusetheestimatedcross-assetdemandparameters,theexogenousdesir-abilities,andmarketclearingtoconstructinstrumentsforpricesandexchangerates.Given e,wecomputethemodelimpliedportfolioweights:i,t(n,b)= i,t(n,b)=1+|=16ˆi,t(n,b)|=1╱╱1+|=16ˆi,t(n,m)、mexp(aˆm)、.TheseexogenousweightsarecalculatedusingEquations(1),(2),(3),and(6),butusingtheexogenousassetdesirabilities.Theseweightscanbethoughtofascounterfactualportfolioweightsforissuercountryn’sassetinclassbifportfoliosweredeterminedbythedistancebetweencountries,issuercountrypopulation,andhomebias.Giventheseexogenousportfolioweights,weusethemarketclearingequation(8)tocalculateimpliedassetpricesandexchangerates,whichwethenuseasinstrumentstoestimatethewithin-asset-classdemandcurve.Specifically,weseteachinvestorcountry’s1-|=1|=1i,t1-|=1|=1i,t(m,k),whereoi,tisinvestori’stotalinvestmentintooutsideassets.Marketclearingintheshort-termdebtmarketyieldsourinstrumentsforexchangerates:N○t(n,1)i=1Eˆt(n)=1LAˆi,ti○t(n,1)i=1andmarketclearinginlong-termbondsandequitiesyieldsourinstrumentsforprices:NPˆBt(n,b)=Aˆi,ti,t(n,b).Intuitively,theaboveprocedureidentifiesdifferencesinexpectedreturnsthatariseduetothefactthatassetpricesarehigherincountriesthataregeographicallyclosertolargeinvestorcountries,andcountriesthattendtoissuefewerassets.Inthisway,weobtaininstrumentsforexchangeratesandassetprices,whichweusetoidentifythewithin-asset-classdemandcurve,equation(9).Forshort-termdebt,weinstrumentexpectedreturnswithEˆt(n).Forlong-termdebtandequityweinstrumentexpectedreturnswithEˆt(n)and Thefullestimatesforwithin-asset-classdemandcurvesarepresentedinAppendixTa-demandelasticitiesof197forshort-termdebt,2.5forlong-termdebt,and1.8forequities.AppendixB.5discussesthedetailsofthisconversion.ThesenumbersarecomparabletothosefoundinKoijenandYogo19b)whichwewouldexpectsinceweemployavariationontheestimationmethodology.Forshort-termdebtwithamaturityof3-monthsthiselas-ticitiesimpliesthata1%increaseinannualizedyieldi