美聯(lián)儲(chǔ)-政府債務(wù)、有限的遠(yuǎn)見和長(zhǎng)期利率 Government Debt,Limited Foresight,and Longer-term Interest Rates

FinanceandEconomicsDiscussionSeries

FederalReserveBoard,Washington,D.C.

ISSN1936-2854(Print)

ISSN2767-3898(Online)

GovernmentDebt,LimitedForesight,andLonger-termInterestRates

ChristopherGustandArseniosSkaperdas

2024-027

Pleasecitethispaperas:

Gust,Christopher,andArseniosSkaperdas(2024).“GovernmentDebt,LimitedForesight,andLonger-termInterestRates,”FinanceandEconomicsDiscussionSe-ries2024-027.Washington:BoardofGovernorsoftheFederalReserveSystem,

/10.17016/FEDS.2024.027

.

NOTE:StafworkingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminarymaterialscirculatedtostimulatediscussionandcriticalcomment.TheanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstafortheBoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.

GovernmentDebt,LimitedForesight,andLonger-termInterestRates

ChristopherGustandArseniosSkaperdas1

April23,2024

Abstract

Westudytherelationshipbetweengovernmentdebtandinterestratesinanenvironmentwherefinancialmarketparticipantshavelimitedforesightaboutthefuturepathofgovernmentdebt.Weshowthatlimitedforesightsubstantiallyattenuatesestimatesoftheeffectof

governmentdebtonlonger-termyieldsrelativetothebenchmarkofrationalexpectationsoftenusedinempiricalanalysis.

JELClassification:E7,E4,G1

Keywords:governmentdebt,longer-terminterestrates,termpremiums,limitedforesight

1BoardofGovernorsoftheFederalReserveSystem,christopher.j.gust@and

arsenios.skaperdas@.TheauthorswouldliketothankDavidBowman,JimClouse,RochelleEdge,Eric

Engen,CanlinLi,DavidLopez-Salido,WillPeterman,BerndSchlusche,andZeynepSenyuzforhelpfulcommentsandLucyCordes,EllieNewman,andJamesTrevinoforexcellentresearchandtechnicalassistance.Theviews

expressedinthispaperaresolelyourownandshouldnotbeinterpretedasreflectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystem,orofanyoneelseassociatedwiththeFederalReserveSystem.

1

1Introduction

WiththeissuanceofU.S.Treasurydebthavingrisensubstantiallyinrecentyears,the

effectofgovernmentdebtissuanceonlonger-terminterestrateshascomeunderrenewed

attention.Whilegovernmentdebtcanaffecteconomicoutcomesinavarietyofways,itseffectoninterestratesisanimportantdeterminantoftheconsumptionandsavingsdecisionsof

householdsaswellastheinvestmentdecisionsoffirmsandhenceofmacroeconomicactivity.

Inthisnote,westudytheroleofexpectationsformationininfluencingtherelationship

betweengovernmentdebtandlonger-terminterestrates.Whileitiscommontoanalyzethe

effectsofgovernmentdebtoninterestratesinadynamicsettingundertheassumptionoffull

information,rationalexpectations,therealismofthisassumptionisquestionable.Inparticular,

thisassumptionimpliesthateconomicdecisionmakersknowallpossiblefuturesituationsthat

willariseandcanusethatknowledgetoformulatecompletestate-contingentplansintothe

distantfuture.Akeycontributionthatwemakeinthispaperistodepartfromthisassumption

andstudytheeffectsofgovernmentdebtoninterestrateswheneconomicdecisionmakersare

‘boundedlyrational’andonlyhavelimitedforesightaboutfutureevents.2Inparticular,weadopttheapproachofWoodford(2018)inwhichagentscanonlyengageinsophisticatedforecasting

andplanningouttoafinitehorizon.3WeembedthisapproachintothemodelofLiandWei

(2013),asitprovidesasimplerelationshiplinkingthefuturepathofgovernmentdebttolonger-termyieldsandisanempiricallyrelevantmodelfortheeffectsofthesupplyofgovernmentdebtonlonger-terminterestrates.4Weillustratehowlimitedforesightattenuatestheeffectofthe

supplyofgovernmentdebtonlonger-terminterestrates.Calibratingthemodeltorecent

empiricalevidenceimpliesthatlimitedforesightdiminishestheeffectsofgovernmentdebtsubstantiallyrelativetothebenchmarkofrationalexpectations.

Ourpaperproceedsasfollows.Section2presentsanoverviewoftheliteratureon

governmentdebtandinterestrateswhichwelaterusetocalibratethedegreeoflimited

foresight.Section3presentstheimplicationsoflimitedforesightfortherelationshipbetween

governmentdebtandlonger-terminterestrates,ourcalibration,andresults.Section4concludes.

2Theliteratureonfinitehorizonplanninghaslargelyfocusedonitsmonetarypolicyimplications.An

importantexceptionisWoodfordandXie(2022).Theyemphasizetheabilityofcountercyclicalfiscalpolicyto

providestimulusinsituationswherethenominalinterestrateisconstrainedbyalowerbound,whilewefocusontherelationshipbetweengovernmentdebtandinterestrates.

3Ourapproachisconsistentwithotherpapers,suchasGabaix(2020),thatdeviatefromrationalexpectationsbyintroducingmyopicbehaviorofeconomicagentsintomacroeconomicmodels.

4WhileweusetheLi-Weimodeltoillustratehowexpectationsformationcanaffecttherelationship

betweengovernmentdebtandinterestrates,BoardstaffregularlyusethismodeltoassesstheeffectsofchangesintheFederalReserve’ssecuritiesholdingsonlonger-terminterestrates(e.g.,Bonis,Ihrig,andWei,2017).

2

2AReviewoftheLiteratureonGovernmentDebtandInterestRates

Determiningtheempiricaleffectofgovernmentdebtoninterestratesisachallenging

task,andthevoluminousliteratureestimatingthiseffecthasproducedawiderangeofestimates.Thisliteraturehasemphasizedthattherelationshipbetweendebtandinterestratesisendogenousandcanvarydependingonavarietyoffactors,includingthetypeoffiscalaction—taxes,

transfers,orspending—associatedwiththechangeindebt.Theliteraturehasalsopointedto

severalchannelsthroughwhichissuanceofgovernmentdebtcanaffectinterestratesinthelongrun.5Inmodelsinwhichfinancialmarketsareincompleteandriskisuninsurable,apermanentincreaseingovernmentdebtcanincreasethesupplyoffinancialassetsintheeconomyandraisethelong-runleveloftheshort-termrealinterestrate(hereafterreferredtoasr*),crowdingout

privatecapital.6Inaddition,KrishnamurthyandVissing-Jorgensen(2012)havedocumentedthattherearesafetyandliquiditybenefitsassociatedwithgovernmentsecurities,andinmodelssuchasMianetal.(2022)apermanentincreaseingovernmentdebtcanincreaser*byreducingthe

conveniencevalueassociatedwiththesebenefits.Issuanceoflonger-termgovernmentsecuritiescanalsoraisetheexposurethatinvestorshavetointerest-rateriskonthevalueoflonger-term

securitiesinpreferredhabitatmodelsoftheyieldcurve(e.g.,VayanosandVila,2021,

GreenwoodandStein,2014).Asaconsequence,anincreaseinthesupplyoflonger-termdebtcanreducebondspricesthroughanincreaseinthetermpremiumcomponentofyields.7

Table1presentsselectedestimatesfromtheliteraturethatfocusonthelonger-run

relationshipbetweenthesevariables.StudiessuchasEngenandHubbard(2004)andLaubach

(2009)takeareduced-formapproachanddonotimposeeconomictheoryinestimatingtheeffectofgovernmentdebtoninterestrates.Inordertoabstractfrombusinesscycledynamicsthat

mightinfluencetheshorter-runrelationshipsbetweenthesevariables,thesepapersusedataonlonger-termdebtprojectionsandtheleveloflonger-runrealinterestrates.Forthesepapers,theeffectofgovernmentdebtonlonger-runinterestratescouldariseeitherthroughmovementsinthetermpremiumorthroughr*.Otherresearcherstakeamorestructuralapproachinordertoestimateorcalibratemodelsthatuseeconomictheorytohelpdeterminetheeffectofa

permanentchangeingovernmentdebt.Forinstance,Mianetal.(2022)studytheissueofdebtsustainabilityinamodelinwhichhigherlevelsoflonger-rundebtcanincreaser*andcalibratethiseffecttobeconsistentwithempiricalestimatesintheliterature.Inaddition,LiandWei

(2013)estimateatermstructuremodelthatbuildsontheoreticalmodelsinwhichthepreferred

5Whilewefocusontheempiricalliteraturestudyingthelonger-runrelationshipbetweendebtandinterestrates,Coenenet.al.(2012)provideadiscussionofshortandmedium-rundeterminantsofthisrelationship,

includingtheroleofmonetarypolicy.

6See,forexample,AiyagariandMcGrattan(1998)aswellasthediscussionandreferencesinRachelandSummers(2019).

7Inaddition,Mianetal.(2022)andVissing-Jorgensen(2023)emphasizethatlong-termgovernment

securitiescanhavesafetyandliquiditybenefitsseparatefromthatofshort-termsecurities.Asaresult,the

outstandingstockoflong-termgovernmentsecuritiescaninfluencelong-terminterestratesthroughtheconveniencethatthesesecuritiesbring.

3

habitatthatinvestorshavefordifferentmaturitiesofgovernmentdebtgivesrisetoaterm

premiumthatdependsontheamountoflonger-termsecuritiesthatinvestorshold.Reflectingthedifferencesinmethodologies,datasources,andsampleperiods,theeffectofa1percentagepointincreaseinthedebt-to-GDPratioonlonger-runrealinterestratesrangesfrom1to6basispoints.Importantly,theseestimatesarebasedonthehistoricalU.S.relationshipbetweengovernment

debtandinterestratesandwouldnotnecessarilyapply,forinstance,tosituationsinwhichthelevelofgovernmentdebtismuchhigher.8

Table1:SelectedEstimatesoftheEffectofGovernmentDebtonLong-RunRealInterestRates

Source

EstimationPeriod

Effectof1pct.pt.

increaseindebt/GDP(basispoints)

Methodology

TermPremiumorExpectedShort-Rate

EngenandHubbard(2004)

1976-2003

3bps

OLSandVAR

both

GaleandOrszag

(2004)

1976-2004

4-6bps

OLS

both

Kinoshita(2006)

1971-2004,

internationaldata

4-5bps

Panelregression

both

Laubach(2009)

1976-2006

3-4bps

OLS

both

Chadhaetal.(2013)

1986-2008

2bps

OLS

both

GamberandSeliski(2019)

1976-2017

2-3bps

OLS

both

Coenenetal.(2012)

N/A

1bp

Calibrated

structuralmodel

Expectedshort-rate(r*)

Mianetal.(2022)

N/A

1-2bps

Calibrated

structuralmodel

Expectedshort-rate(r*)

LiandWei(2013)*

1994-2007

6bps

Estimatedterm

structuremodel

Termpremium

*ThemodelofLiandWei(2013)usestheoutstandingandprojectedvolumeofTreasuryten-yearequivalents

(TYEs)asinputs.ThevolumeofTYEsinagivenperiodrepresentstheamountofinterestrateriskofthepar

amountofTreasurydebtintermsofanequivalentnumberofTreasurysecuritiesissuedwith10yearstomaturity.InordertomakeestimatesfromLiandWei(2013)comparabletoothersinthetable,wetranslateparvaluesof

governmentdebtsupplytoTYEswithanapproximationusinghistoricalaveragesofTreasuryduration.

8Cechettietal.(2011)provideevidencethatsuggeststhattheremaybethresholdeffectsatwhichahigh

levelofgovernmentdebtisassociatedwithlowereconomicgrowth.Theypostulatethathighlevelsofgovernmentdebtmayconstrainthegovernment’scapacitytoengageincountercyclicalstabilizationpoliciesoractasalenderoflastresortduringfinancialcrises,leadingtolargereconomicdownturnsandloweraveragegrowth.

4

3LimitedForesightandtheTermPremiumEffectofDebtIssuance

Withtheseempiricalestimatesasbackground,wenowturntoshowingtheimportant

influenceexpectationsformationcanhaveontherelationshipbetweendebtandinterestrates.

Toillustratethispoint,weusethetermpremiummodelofLiandWei(2013).Table1shows

thatthemagnitudeoftheestimatedeffectfromthatmodelisonthehighendoftheliterature.9

Asweshow,thisresultreflectstheassumptionthatinvestorshaveperfectforesightaboutthe

expectedpathofgovernmentdebtandthatalteringthisassumptiontoallowforlimitedforesightcanreconcileestimatesfromtheLi-WeimodelwiththeotherestimatesshowninTable1.10

InthecontextoftheLi-Weimodel,theassumptionofperfectforesightimpliesthat

investorshaveperfectcertaintyandknowledgeaboutthefuturepathofTreasurydebtandits

effectontermpremiums.Whileperfectforesightmaybereasonablewhenconsideringexpectedchangesinsecuritiesinthenear-term,itismorequestionableforfinancialmarketparticipants’expectationsofthelonger-runpathofTreasurydebtoutstanding,whichishighlyuncertain.Analternative,perhapsmorereasonableassumption,isthatinvestorshavelimitedforesightabout

thefuturepathofTreasurydebt,particularlyforchangesinthatpaththatmayoccurinthedistantfuture.

Tounderstandthedifferencebetweenperfectandlimitedforesight,wereproducethe

equationintheLi-Weimodelrelatingthetermpremiumonalonger-termyieldtothesupplyofgovernmentdebtheldbyfinancialmarketparticipants:

τt=Et

Inthisequation,Etdenotesinvestors’(model-consistent)expectations,bt+idenotestheshockedpathoftheprivatesector’sholdingofgovernmentdebtinperiodt+iintermsofTreasuryten-

yearequivalents(TYEs)asafractionofnominalGDP,andtheparameters,θi,i=0,1,2,…n,are

estimatedcoefficientsfromLiandWei(2013)thatdeterminetheimpacteffectofanexpected

futurechangeindebtatquartert+ionthetermpremiumatdatet.Importantly,therelationshipbetweenthetermpremiumonalonger-termsecuritydependsontheexpectedfuturepathof

governmentdebtoverhorizonn,andforthe10-yearTreasurytermpremium,LiandWei(2013)

9LiandWei(2013)focusonlyonthetermpremiumcomponentofyields,whilemanyoftheotherpapersinthetablefocusontheoveralleffectonlonger-termyields,inclusiveofboththetermpremiumcomponentand

expectedshort-ratecomponent.Ifonetakesintoaccountthatanincreaseindebtissuancecanraisetheexpectedpathofshort-termrates,thenthedifferenceintheestimateofLiandWei(2013)withtheseotherpapersisevenlargerthansuggestedbythenumbersinthetable.

10LiandWei(2013)imposeperfectforesighttoestimatetheeffectsoftheFederalReserve’sasset

purchasesontermpremiums,whereastheestimateinTable1reflectstheassumptionofperfectforesightforthe

effectofanincreaseinTreasuryissuance.Byalteringtheamountoflonger-termTreasurysecuritiesheldbyprivateinvestors,bothTreasuryissuanceandtheFederalReserve’sassetpurchasesaffectthetermpremiumcomponentoflonger-termyields.Assetpurchasescanadditionallyaffectlonger-termyieldsbysignalingmonetarypolicymakers’intentionsregardingthefuturepolicy-ratepath;achannelnotcapturedbytermstructuremodelssuchasLiandWei(2013).Foracomprehensivereviewoftheliteratureonassetpurchases,seeBhattaraiandNeely(2022).

5

setthehorizonntocorrespondtoaperiodof10years.Toevaluatethisexpectedpath,LiandWei(2013)imposethatinvestorshaveperfectforesight,settingEtbt+i=bt+ifori=0,1.2,…n.

Wemodifytheassumptionregardinginvestors’expectationsformationtoallowfor

limitedforesightfollowingtheapproachofWoodford(2018).Underthatapproach,thereare

limitationsontheabilityofinvestorstoforeseeandforecastfutureevents.Wheninvestorsdifferinthehorizonoverwhichtheyuseeconomicrelationshipstomakeforecasts,thisheterogeneitygivesrisetoarelationshipbetweenthetermpremiumandchangesindebtissuanceinwhich

changesindebtissuanceinthefarfuturearediscountedmoreheavilythanthoseoccurringinthenearfuture.Specifically,asshownintheappendix,wheninvestorshavelimitedforesight,the

aggregateeffectonthetermpremiumofthepathofgovernmentdebtisgivenby:

τt=Et.(2)

Accordingly,thelimitedforesightoffinancialmarketparticipantsintroducesanadditional

parameter,Y,intotherelationshipbetweengovernmentdebtandthetermpremiumrelativetothecaseofperfectforesight.TheparameterYcorrespondstohowfarinthefuturetheaveragefinancialmarketparticipantusesinformationongovernmentdebttoformbeliefsaboutthetermpremium.AsYapproaches1,equation(2)impliesthesametermpremiumeffectsasunder

perfectforesight.However,forY<1,futureprojectionsofgovernmentarediscountedmoreheavilyunderequation(2)thanequation(1),implyingsmallertermpremiumeffectsunder

limitedforesightthanunderperfectforesight.

3.1Calibration

WecalibrateYsothatthetermpremiumeffectimpliedbyequation(2)isconsistentwithrecentevidence.InanupdateoftheanalysisofLaubach(2009),GamberandSeliski(2019)

studytheeffectsofchangesinlonger-runforecastsofTreasurydebtonlonger-terminterest

rates.AsindicatedinTable1,GamberandSeliski(2019)findthateach1percentagepoint

increaseinthe5-year-aheaddebt-to-GDPratioisassociatedwitha2to3basispointincreasein5-year-ahead,10-yearforwardrealinterestrates.11

BecausetheestimateofGamberandSeliski(2019)appliestoalonger-termrateratherthanthetermpremium,weinfertheeffectofgovernmentdebtonthetermpremiumusing

estimatesoftheeffectonr*fromtheliterature.Fortheseestimates,weturntoMianetal.

(2022),whopresentanoverviewofestimatesfromtheliterature.12Whilenotinguncertaintysurroundingtheseestimates,theevidenceinMianetal.(2022)spansarangeofabout1to

2basispointsfortheeffectonr*ofa1percentagepointincreaseinthedebt-to-GDPratio.

Inourbenchmarkcalibration,wetakethemidpointsoftherangesfromGamberand

Seliski(2019)andMianetal.(2022)andsubtractthepredictedeffectonr*of1?basispoints

11Incomparison,Laubach(2009)estimatedaneffectof3-4basispointsusingdatathrough2006.

12Foranextendeddiscussionandoverviewoftheliteratureregardingtheeffectofgovernmentdebtonr*,seeappendixEofMianetal.(2022).

6

fromMianetal.(2022)fromthepredictedeffectonlonger-termforwardratesof2?basispointsfromGamberandSeliski(2019).Thisyieldsatermpremiumeffectof1basispointfora5-year-ahead10-yearTreasurybond.

Becauseourcalibrationinvolvesusinginformationonaforwardrateona10-yearbond

ratherthanthecurrentrate,weneedtotakeintoaccountthatinvestors’beliefsunderlimited

foresightaboutaforwardratecandifferfromtheirbeliefsregardingaspotinterestrate.In

particular,theexpectedpathofdebtaffectingaforwardtermpremiumoccursfurtherinthe

futurethanthepathnecessarytoformbeliefsaboutthecurrenttermpremium,and,asaresult,aninvestorunderlimitedforesightwilldiscounttheexpectedpathofdebtassociatedwiththe

forwardtermpremiumevenmoreheavilythanimpliedbyequation(2).Wetakethisintoaccountusingtheanaloguetoequation(2)foratermpremiumona10-yearbond,5yearsforward,whichasshownintheappendix,isgivenby:

τt+20,t=EtθiYi+20bt+i+20.(3)

Weuseequation(3)tocalibrateY,keepingtheparametersθi,i=0,1,2,..,n,fixedatthe

valuesestimatedbyLiandWei(2013).Settingτt+20,ttobeconsistentwitha1basispointtermpremiumeffectona10-yearbond,5-yearsahead,asimpliedbytheempiricalliterature,yields

Y=0.942,whichcorrespondstoanaverageforesighthorizonofalittlemorethan4years.13

AlthoughourcalibrationdoesnotinvolvethejointdeterminationofYandθi,weseetwobenefitstoourapproach.First,theLiandWei(2013)modelisestimatedondatafrom1994-

2007.BecauseourcalibrationofYtargetsempiricalmomentsthatuserecentdata,ithelps

capturechangesintherelationshipbetweendebtandinterestratesthatmayhaveoccurredsincethefinancialcrisis.Second,ourcalibrationstrategyusesinformationaboutthelonger-run

relationshipbetweenexpecteddebtandinterestratesandthusislesspronetobeingconfoundedbyfactorsthataffectthisrelationshipintheshorterrun.

3.2TermPremiumEffectsofGovernmentDebtUnderLimitedForesight

Usingourbenchmarkcalibration,wecanestimatetheeffectsofanincreasein

governmentdebtoninterestratesunderourrevisedassumptionforexpectationsformation.

Underlimitedforesight,ourcalibrationimpliesthatapermanent1percentagepointincreaseinthedebt-to-GDPratio,allelseequal,increasesthe10-yearTreasurytermpremiumbyonly

13Gustet.al.(2024)usesurveydataoninflationexpectationsinadditiontomacroeconomictimeseriestoestimateamacroeconomicmodelwithfinitehorizonplanningandfindthattheirmodelfitsthisdatawellwitha

planninghorizonofoneyear.Ourbenchmarkcalibrationimpliesalongerhorizon,reflectingdifferencesacrossmodelsaswellastheuseoffinancialmarketdataratherthanmacroeconomicdatatocalibrateY.Totakeintoaccountuncertaintyaboutthedegreeoflimitedforesight,wealsoconsideranalternativecalibrationwhereYissmaller.

7

3basispoints,asopposedto6basispointsintheoriginalmodelwithperfectoversight.14While3basispointsisourbenchmarkestimate,thisestimateissubjecttouncertaintystemmingfromtheeffectsoffiscalpolicyoninterestrates.Tohelpaddressthis,weconsideralternative,

plausiblecalibrationsandcalibratetoaforwardtermpremiumeffectona10-yearbondof

?basispointand1?basispoints,respectively.Withthe?basispointcalibration,thevalueofisabout0.92,theaverageforecasthorizonis2.5years,andthetermpremiumeffectofa

permanent1percentagepointincreaseinthedebt-to-GDPratioisestimatedtobe2?basis

points.Withthe1?basispointscalibration,thevalueofisjustabove0.95,theaverage

forecasthorizonisabout5years,andthetermpremiumeffectfromsuchanincreaseis3?basispoints.ThesemagnitudesliewelloutsidetheconfidenceintervaloftheLi-Weimodelestimatesunderperfectforesight.15

4Conclusion

Researchanalyzingtheeffectsoffiscalactionsonthemacroeconomyhasmainlyworkedundertheassumptionofrationalexpectations.However,economicdecisionmakershavean

imperfectunderstandingoftheeconomy,particularlyaboutrelationshipsthatariseinthedistantfuture.Westudytherelationshipbetweengovernmentdebtandinterestratesinanenvironmentwheredecisionmakersareboundedlyrationalbecausetheyhavelimitedforesightaboutfuture

eventsandshowhowthisattenuatestheeffectofthesupplyofgovernmentdebtonlonger-terminterestrates.Whilewehavefocusedontheeffectsofgovernmentdebtoninterestrates,limitedforesighthasbroaderimplicationsforfiscalpolicythanconsideredinthispaper,andfutureworkanalyzingfiscalpolicywhendecisionmakershavelimitedforesightshouldbeanimportantpartofanagendaincorporatingimperfectexpectationsformationintomacroeconomicmodels.

14UnderpreferredhabitatmodelsoftheyieldcurvethatmotivatetheLiandWei(2013)model,central

bankassetpurchasesarethoughttoaffectlonger-terminterestratesbyalteringtheamountofgovernmentdebtheldbyprivateinvestors.Ifinvestorshaveasimilardegreeoflimitedforesightaboutthefuturesizeandcompositionofthecentralbank’sbalancesheet,ourcalibrationresultswouldalsoapplytotheeffectsofcentralbankasset

purchasesonlonger-terminterestrates.

15Weconstructa95%confidenceintervalunderperfectforesightthatrangesfrom5to7basispointsusinghistoricalaveragesofTreasurydurationandtheuncertaintyofparameterestimatesfromLiandWei(2013).Underlimitedforesight,weobtainarangeofuncertaintyofabout2to4basispointsusingourhighandlowcalibrationsofwhileatthesametimeincorporatingsamplinguncertaintyregardingtheestimatesofθifromLiandWei(2013)

usinga95%confidenceinterval.

8

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