The Federal Reserve's Large-Scale Asset Purchase Programs: Rationale and Effects

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Federal Reserve’s Large-Scale Asset Purchase Programs: Rationale and Effects Stefania D’Amico, William English, David Lopez-Salido, and Edward Nelson 2012-85 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

TheFederalReserve’sLarge-ScaleAssetPurchasePrograms:RationaleandEffects StefaniaD’Amico,WilliamEnglish,DavidLópez-Salido,andEdwardNelson(*) Firstdraft:March2011 Thisdraft:October 31,2012 Abstract Weprovideempiricalestimatesoftheeffectoflarge-scaleassetpurchase(LSAP)-styleoperations onlonger-termU.S.Treasuryyieldswithinaframeworkthatneststhealternativetheoretical perspectivesonLSAPs. AstheprincipalchannelsthroughwhichLSAPsmightmatterforlongerterm interestrates,weconcentrateon(i)thescarcity(availablelocalsupply)channelassociated withthetraditionalpreferredhabitatliterature,and(ii)thedurationchannelassociatedwiththe generalnotionofinterestraterisk. WealsoclarifyLSAPs’roleinthebroadercontextofmonetary policystrategy,bringingouttheconnectionsbetweenpurchasesoflonger-termassetsandhistorical FederalReservepolicyapproaches. OurresultsindicatethattheimpactofLSAP-styleoperations onlonger-terminterestratesismainlyfeltonthenominalterm-premiumcomponent;moreover, withinthenominaltermpremium,itistherealtermpremiumthatexperiencesthegreatestresponse. Theestimatessuggestthatthescarcityanddurationchannelshavebothbeenofconsiderable importanceforthetransmissionofpurchasestolonger-termTreasuryyields. Finally,byisolating thedegreetowhichscarcityanddurationimpingeontermpremiums,ourestimatesindicatethe directioninwhichmacroeconomicmodelsshoulddevelopinordertoencompassthetransmission channelsassociatedwithLSAPs. (*)FederalReserveBoard. Emailsofauthors:Stefania.D’Amico@frb.gov; William.B.English@frb.gov;David.J.Lopez-Salido@frb.gov;Edward.Nelson@frb.gov. For helpfulcommentsonearlierversionsofthispaper,wethankJane Ihrig, MikeJoyce,ThomasKing, Elizabeth Klee, CanlinLi,ElmarMertens,DimitriVayanos, Andrew Scott,MinWei,Jonathan Wright,andparticipantsattheEuropeanCentralBankworkshop,“MacroeconomicImpactof NonstandardMonetaryPolicyMeasures”(March2011),attheSeventhMeetingofCentralBank MonetaryPolicyManagers,RiodeJaneiro(April2011),andattheBankofEnglandconferenceon “QEandOtherUnconventionalMonetaryPolicies”(November2011). Wealsothankseminar participantsattheBankofEnglandandtheIMF,aswellasnumerouscolleaguesattheFederal ReserveBoard. D’AmicoalsoacknowledgesthehospitalityoftheMacrofinancialAnalysis DivisionattheBankofEngland. BenjaminBrookins,George Fenton, ChristineGarnier,Andrew Giffin,ShenjeHshieh, and John Searsprovidedresearchassistance. Theviewsexpressedinthis paperarethoseoftheauthorsaloneanddonotnecessarilyreflecttheviewsoftheBoardof GovernorsoftheFederalReserveSystemoritsstaff. 0

1. Introduction Sincelate2008,havingbroughtthenominalfederalfundsratedowntoitseffectivelowerbound, theFederalOpenMarketCommittee(FOMC)hastakenstepstoprovidefurthermonetarypolicy stimulus. OnemeasureundertakenhasbeentheprovisionofCommitteeguidanceaboutthelikely futurepathofthepolicyrate;forexample,theCommittee’sstatementsfromMarch2009through June2011indicatedthateconomicconditionswere“likelytowarrantexceptionallylowlevelsof thefederalfundsrateforanextendedperiod”(see,forexample,FOMC,2009).1TheFOMChas, however,alsomadeuseofmonetarypolicytoolsotherthanforwardguidance. In particular, the CommitteehasprovidedfurthermonetarypolicyaccommodationbyauthorizingaseriesofFederal Reservepurchasesoflonger-termsecurities,apolicyknownas“large-scaleassetpurchases” (LSAPs). ThefirstprogramofLSAPswasannouncedinlateNovember2008,fromwhichtimetheFederal Reservepurchasedagencydebtandagency-guaranteedmortgage-backedsecurities(MBS). In March2009,thepurchaseprogramwassteppedupandwasalsobroadenedtoincludelonger-term Treasurysecurities. ThefirstroundofpurchaseswascompletedinMarch2010. Thenext developmentintheFederalReserve’spurchasespolicywastheFOMC’sannouncementinAugust 2010ofreinvestmentarrangements,underwhichtheFederalReserve—byredeployingintolongertermTreasuryinvestmentstheprincipalpaymentsfromagencysecuritiesheldintheSystemOpen MarketAccount(SOMA)portfolio—wouldmaintaintheelevatedlevelofholdingsoflonger-term securitiesbroughtaboutbythefirstseriesofLSAPs. FromNovember2010totheendofJune2011, theFederalReserveundertookasecondLSAPprograminvolvingthepurchaseof$600billionin longer-termTreasuries. TheFOMCdecidedtocontinuetomaintainthelevelofsecuritiesholdings attainedundertheLSAPs,andinSeptember2011theCommitteemadefurtheradjustmentstoits investmentpolicyincludingan extension of theaveragematurityofitsTreasurysecurities portfolio,andreinvestingprincipalpaymentsfromagencysecuritiesinMBSratherthanlongertermTreasuries. FOMCmembers(forexample,Bernanke,2011a,Kohn,2009,Williams,2011,andYellen,2011) haveemphasizedthatLSAPsaredesignedtoaffecttheterm-premiumcomponentoflonger-term interestrates. Thus,whileLSAPsdifferfromfederalfundsratepolicy,whichexertsitsinfluenceon longer-termratesprincipallyviaanimpactontheexpectationscomponentoftheserates,theyshare ————————————————————————————————————— 1 Prior to adopting this statement language, the FOMC had referred for several months to its expectation that an exceptionally low funds rate would be in force “for some time.” In August 2011, the FOMC changed the statement language from “for an extended period” to “at least through mid-2013” and then in January 2012 it changed this to “at least through late 2014.” 1

withfunds-rateactionstheintentionofaffectingthelonger-terminterestratesthatbearimportantly onspendingdecisions. InoutliningtheeffectofLSAPsontermpremiums,Kohn(2009)andYellen (2011)appealtothepreferred-habitatliterature. Thisliterature,developedatanearlystageby Tobin(1961,1963)andModiglianiandSutch(1966,1967),hasreceivedamodernformalizationin theworkofVayanosandVila(2009). Thepreferred-habitatapproachis,however,oneofseveraltheoreticalperspectivescapableof rationalizingtheeffectsonlonger-termratesofLSAP-styleoperations. Amajoraimofthepresent paperistoprovideempiricalestimatesoftheeffectofLSAP-styleoperationsonlonger-termU.S. TreasuryrateswithinaframeworkthatneststhealternativetheoreticalperspectivesonLSAPs. As theprincipalchannelsthroughwhichLSAPsmightmatterforthelongrate,weconcentrateon(i) the“availablelocalsupply,”or“scarcity,”channelassociatedwiththetraditionalpreferred-habitat literature—amechanismunderwhichthepurchasebytheFederalReserveofassetswithaspecific maturityleadstohigherprices(andloweryields)ofsecuritieswithsimilarmaturities;(ii)the “durationchannel”—amechanismunderwhichtheremoval,bymeansofFederalReserve purchases,ofaggregatedurationfromtheoutstandingstockofTreasurydebtreducesterm premiumsonsecuritiesacrossmaturities;2and(iii)the“signaling,”or“expectations,”channel mentionedabove,whichoperatestotheextentthatLSAPshaveanimpactonmarketexpectations oftheshort-termpolicyrate.3 Thepresentpaperalsoadvancesonexistingempiricalwork,suchasGreenwoodandVayanos (2010),Gagnon,Raskin,Remache,andSack(2011),D’AmicoandKing(2012),andHamiltonand Wu(2012),inseveralways.4First,byusingCUSIP-level(i.e.,security-specific)data,wecan disaggregatebondsupplybymaturityclassandtherebymeasurelocalsupplyorscarcity. Second, byanalyzingSOMAholdingsattheCUSIPlevel,wecanmeasuremoreaccuratelythestockof privatelyheldlonger-termTreasurysecurities5topindowntheresponsestoLSAP-styleoperations. Wearethereforebetterequippedtoaddressthekeypolicyquestionempirically. Finally,by harnessingthisfinerdegreeofdisaggregation,wecanmoredefinitivelyinferspecificaggregate characteristicsoftheTreasurysupply,suchastheaveragedurationofprivately-heldTreasury securities. ComparedwithstudiessuchasD’AmicoandKing(2012)thatalsomakeuseofCUSIP- ————————————————————————————————————— 2 In the context of LSAPs, this channel was first highlighted by Gagnon, Raskin, Remache, and Sack (2011). 3 We will also have occasion to comment on the typology of channels offered by Krishnamurthy and Vissing- Jorgensen (2011), and to discuss why we omit (or condense) a number of channels that these authors list. 4 The magnitude of the effect of LSAPs on longer-term policy rates that is assumed in macroeconomic model simulations such as those in Chung, Laforte, Reifschneider, and Williams (2012) has been informed by these studies. 5 That is, held by private households and private financial and nonfinancial firms (including foreign entities), rather than by the public sector (where “public sector” includes the Federal Reserve). 2

leveldata,wefleshoutthetransmissionchannelsinvolvedinLSAPs,consideradifferentsample period,andfocusouranalysisonadecompositionoflonger-termTreasuryyields. Ourapproach thusseekstodisentanglethechannelsthroughwhichLSAPsworkratherthansimplyascertainthe magnitudeoftheoverallresponseofyieldstotheoperations. WealsoclarifyLSAPs’roleinthebroadercontextofmonetarypolicystrategy. Wehighlightthe connectionsbetweenlonger-termassetpurchasesandhistoricalFederalReserveapproachesto monetarypolicy. Thishistoricaloverviewbringsoutepisodesandinstitutionalfeaturesthat supportourviewthatthetheoreticalargumentsagainsttheeffectivenessofLSAPsareoflimited applicability. Ourresultscanbesummarizedbriefly. Theestimatesindicatethatlocalsupplyandaggregate durationofTreasurysecuritiesarepositivelyandsignificantlyrelatedtolonger-termTreasury yieldsandtermpremiums. Accordingtoourestimates,asizableportionoftheimpactofvariations inscarcityandaggregatedurationonlonger-termTreasuryyieldshasbeentransmittedviathe nominalterm-premiumcomponent. Moreover,withintheoveralltermpremium,itistherealterm premiumcomponentthatexhibitsthegreatestresponsetothesetwovariables;theinflationrisk premium’sresponse,incontrast,isquitesmallandisnotuniformlystatisticallysignificantacross differentspecifications. Thesefindingsarerobusttotheadditionofasetofexplanatoryvariables, includingaflight-to-qualityproxy,tothebaselineregression. Finally,ourestimatessuggestthat boththelocalsupplyandaggregatedurationchannelshavebeenofconsiderableimportancein deliveringeffectsofpurchasesonlonger-termTreasuryyields. Thispaperproceedsasfollows. Section2provideshistoricalperspectiveontheFederalReserve’s longer-termsecuritiesmarketoperations. Section3discussestheoreticalperspectivesonLSAPs andourmeansofdiscriminatingbetweenthem. Section4showsthataspecificsequenceofevents in2010providesacasestudythatcastslightonthemainchannelsthroughwhichLSAPsmay operate. Section5describesindetailtheconstructionofthevariables,aheadofthepresentationof themainresultsinSection6. Section7concludesbysuggestingsomeimplicationsofourresultsfor thespecificationofmacroeconomicmodels. 2. LSAPsinhistoricalperspective Section14oftheFederalReserveActdescribesinthesetermstheopenmarketoperationswhichthe FederalReservemayconduct:“anybonds,notes,orotherobligationswhicharedirectobligations oftheUnitedStatesorwhicharefullyguaranteedbytheUnitedStatesastotheprincipaland 3

interestmaybeboughtandsoldwithoutregardtomaturitiesbutonlyintheopenmarket.”6The law’swording,“withoutregardtomaturities,”helpsputtherecentpurchaseprogramintoproper perspective. Comparedwiththepreviousdecades’focusonshort-terminterestratepolicy,LSAPs domarkabreakwithconvention. ButviewedintermsofthetoolsthattheFederalReservehas historicallyhadatitsdisposal,andhashadoccasiontodeploy,LSAPsdonotamounttoan altogetherunconventionalpolicy. Rather,theycanbeseenasthelatestinaseriesofFederal Reserveoperationsinlonger-termsecuritiesmarkets. And,incommonwithshort-terminterestrate policy,theaimoftheseoperationshasbeentoaffectaggregatedemandbyinfluencinglonger-term interestrates. WeputLSAPsinhistoricalcontextbyreviewing,inSection2.1,FederalReserve operationsinlong-termmarketsinthepostwarperiod. ThenSection2.2brieflyreviewsthe chronologyoftherecentLSAPs. 2.1Operationsinlonger-termsecuritiesmarketsinthepostwarperiodbefore2008 TheFederalReserve’speggingofbondpricesduringandafterWorldWarIIisdiscussedin Bernanke(2002),whocitesthisexperienceasdemonstrationofcentralbanks’capacitytoaffect longer-termratesdirectlyiftheytransactinlonger-termsecuritiesmarkets. Aspartofthe“cheap money”policyinstitutedduringthewar,theFederalReservefixedamaximumvalueforverylongterminterestratesof2.5percent,withtheFederalReservestandingreadytotradeinlonger-term Treasuriestoenforcetheceiling. Thebondpricepeglastedfrom1942to1951. Overpartofthisperiod,from1942to1947,the peggingpolicywasundertakeninconjunctionwiththepeggingoftwootherTreasurysecurity rates:thoseonninety-daybillsandone-yearnotes.7ItissignificantthattheFederalReserve’s policyamountedforseveralyearstoenforcingvaluesforasetofTreasuryratesofdifferent maturities. Accordingtothepureexpectationstheoryofthetermstructure,targetingthreeseparate interestratesshouldsucceedifandonlyiftheprivatesector’sexpectationsofthepathoftheshort rateisalignedinawaythatpreciselygeneratesthetargetedconfigurationofrates. Inthis environment,foragivenexpectedpathfortheshort-termrate,directinterventioninlongermaturityTreasurymarketscouldnotcontributetoachievingthepeg. Moreover,theslightest fluctuationinexpectationsoftheshort-ratepathwouldimmediatelyimperilthepeg. Thepicture paintedbythiswell-knowntheoreticalbenchmarkcontrastswiththeactualpracticeofthepegging policy. TheperiodofbondratepeggingwitnesseddirectFederalReserveinterventioninlonger- ————————————————————————————————————— 6 See http://www.federalreserve.gov/aboutthefed/section14.htm 7 The targets for the shorter-maturity rates were dropped in July-August 1947. See Friedman and Schwartz (1963, pp. 577579) and Romer and Romer (1993, p. 81). 4

termmarketswhichsucceededindeliveringthethreetargetedrates. Thissuggeststhatcentralbank interventioninthelonger-termTreasurymarketsprovidedanextradegreeoffreedomforthe managementofrates. Equivalently,foreachsecuritypricetargeted,theFederalReservehadtwo instrumentsforhittingthetarget:itsinfluenceonexpectationsoftheshortrateanditstransactions inthemarketforthatsecurity. Viadirectintervention,themonetaryauthoritiescouldachievea configurationofinterest-ratetargetswithouthavingtorelyoncontinuouslymaintainingaspecific patternofmarketexpectationsoffutureshort-termrates. SoonafterWorldWarII,seniorstaffattheFederalReserveBoardvoicedtheirreservations publiclyabouttheimplicationsofthebondpeg. Theseconcernsaboutthepeggingpolicytypically didnotimplyadenialofthetechnicalfeasibilityofpeggingasetofratesacrossthematurity spectrum;onthecontrary,theobservedstabilityofthemarketyieldsonthetargetedsecurities seemedtoconfirmthefeasibilityofthatpolicy.8TheFederalReserve’sdoubtsaboutthepegging policywereinsteadgroundedintheconcernthatitperpetuatedaninterest-ratestructurethatwas incompatiblewithmonetarystability. WiththeoutbreakoftheKoreanWarin1950,continuousupwardpressureonaggregatedemand emerged,andtheincompatibilityofthepeggingpolicywithinflationcontrolbecamemanifest. The FederalReservesteppedawayfromthepeggingpolicyin1951,withtheadventofthe Treasury/FederalReserveAccord. TheAccordmarkedanimportantstepinrestoringcentralbank independenceintheUnitedStates,andtheaccompanyingabandonmentofbondpricepeggingwas importantinachievingthegoalofpricestability. Forthepresentdiscussion,however,the experiencewiththepeggingpolicyprovidesanimportantcasestudy. Althoughthelackofdetailed marketdataonexpectationsoftheshort-termpolicyrateworksagainstaclear-cutconclusion,the widely-takenlessonofthiscasestudyappearstobethattheFederalReserve’slonger-termbond purchasesdidindeedstimulateaggregatedemandandkeep,forseveralyears,thereal-interest-rate componentoflonger-termrateslowerthanwouldhavebeenthecasewithoutthepurchases. FollowingtheAccord,theFederalReserveshiftedtoapolicyofadjustabletargetsforshort-term interestrates. Aspartofthisframework,theFederalReserveadopteda“bills-only”policywhich restrictedtoshort-termTreasurysecuritiestheclassofassetstradedinopenmarketoperations. Bills-only,adoptedin1953,prevailedforthebalanceofthedecade,interruptedbyabriefperiodof FederalReservepurchasesofcouponTreasuriesinresponsetobondmarketdisruptionsinlate1955 andmid-1958(seeCooper,1967,pp.1415). Holdingsoflong-termbondsranofftheFederal ————————————————————————————————————— 8 Consistent with this, Thomas (1947, p. 210) considered the consequences of a scenario in which “long-term rates were permitted to rise” (emphasis added), thereby accepting that the authorities could have prevented such a rise. 5

Reserve’sportfolioanddeclinedsharplyasashareofFederalReserveassetsinthecourseofthe 1950s(seeFigure1). Thethinkingbehindthebills-onlypolicywasoutlinedbyRiefler(1958a,1958b).9Riefleraccepted thatchangesinthematuritycompositionoftheFederalReserve’sbalancesheetcouldaffectlongerterminterestratesforagivenpathofshort-termrates.10ButhearguedthattheFederalReservehad amplescopetoaffectlonger-termratesbyinfluencingmarketexpectationsoftheshort-term interestratepath. Riefler(1958b)accordinglyconcludedthattheFederalReservecould“exertan influenceonlong-terminterestrateswithoutdirectinterventioninthelong-termmarket.” This viewwasechoedinprominentmarketcommentary.11 Outsidecriticismofthebills-onlypolicypersisted,however,andwasbuttressedbytheemerging academicliteratureonimperfectlinksbetweentheshort-andlong-termsecuritiesmarkets(suchas Culbertson,1957,Conard,1959,andAscheim,1961),aliteraturelaterputonafirmertheoretical footingbyTobin’s(1961,1963)workondebtmanagementandthetermstructureandby ModiglianiandSutch’s(1966,1967)layingoutofthepreferred-habitatmodel. Theincoming Administrationin1961wassympathetictothecriticismsofthebills-onlypolicy. TheKennedy Administrationsawmeritinmeasuresthatcouldlowerlonger-terminterestrates—whichwere widelyregardedasmorerelevantforthedeterminationofaggregatedemandthanwereshort-term rates—evenasshort-termrateswereincreased(acourseforthepolicyratedesignedtopromotea greaterrateofinflowofforeigncapital). Theresulting“OperationTwist”policywasratifiedbythe FederalReserve(asreportedinFOMC,1961). Longer-termsecuritiesgrewasshareoftheFederal Reserve’sassets(again,seeFigure1). Initialverdictsonthesuccessofthepolicytendedtobenegative,withMarty(1962,p.208) referringtothe“FederalReserve’sfailure,intheearlymonthsoftheKennedyadministration,to influencetheratestructure.” Theunfavorableassessmentapparentlywasnotdueprimarilytothe behavioroflong-termrates;theseyieldsdidindeedfallslightlyintheearly1960s(seeFigure2), ————————————————————————————————————— 9 Another publication by Board senior staff, Young and Yager (1960), outlined arguments similar to Riefler’s. 10 Consistent with this position, discussions within the Federal Reserve generally accepted that official purchases of longer-term securities could affect bond rates. For example, Cooper (1967, p. 20) notes that while as of the early 1960s there were “divergent and shifting opinions of members and staff throughout the period when operations in coupon issues were being discussed,” it was nevertheless “recognized that System purchases of intermediate- and long-term government securities… would tend to influence prices (and rates) as would any large-scale buying.” 11 For example, the First National City Bank of New York (1959, p. 114) stated: “Sustained movements in bill yields work their way throughout the rate structure and vitally affect the availability of credit, long-term as well as shortterm, without direct Federal Reserve intervention in the long-term market.” 6

(a) Percent 25 Bond Holdings / Total Assets 20 Holdings of Agency Obligations / Total Assets 15 10 5 0 1945 1950 1955 1960 1965 1970 1975 1980 (b) Percent 60 Notes + Bonds / Total Assets Holdings of Agency Obligations / Total Assets 50 40 30 20 10 0 1945 1950 1955 1960 1965 1970 1975 1980 Figure 1. Longer-term securities as a share of Federal Reserve assets, 19451980: (a) “Bonds” as percent of total assets; (b) “Notes and Bonds” as percent of total assets. Source: Federal Reserve balance sheet, Federal Reserve Board, Annual Report, various years. 7

Percent 25 Effective federal funds rate 10-year Treasury bond rate 20 15 10 5 0 1954 1959 1964 1969 1974 1979 1984 1989 1994 1999 2004 2009 Figure 2. Effective federal funds rate and ten-year Treasury bond rate: Monthly averages, July 1954March 2011 Source: FRED portal, Federal Reserve Bank of St. Louis. andwere,astheFederalReserveBoard(1966,p.1747)noted,morestableinthefirsthalfofthe 1960sthantheyhadbeeninprecedingrecoveries. Butitwasfeltthatthispatternoflonger-maturity ratebehaviorwasnotobviouslyduetotheTwistmeasures. Inflationexpectationswerelikely decliningovertheearly1960s,andthishasbeensingledoutasthemainfactordrivingtheobserved declineinlonger-termrates(see,forexample,Meigs,1972,p.271). Notwithstandingtheemerging preferred-habitatliterature,manyeconomistsatthestartofOperationTwistwereskepticalabout portfolioeffectsoflong-termbondpurchases,andexperiencefromtheearly1960sprobably reinforcedthatskepticism.12Fortheirpart,adherentstopreferred-habitatmodelscouldpointout thattheTreasurylengthenedthematurityofitsdebtissuesintheearly1960s,perhapsswampingthe effectoftheFederalReservepurchases.13ArecentstudybySwanson(2011),however,findsthata negativeeffectongovernmentbondyieldsofthe1961FederalReservepurchasescanbediscerned when an event-study approach is taken. After1963,theFederalReservelargelyreturnedtoabills-onlypolicy. Itcontinuedtoholdcoupon ————————————————————————————————————— 12 In a major understatement, a Financial Times article (1960) discussing preparations for Operation Twist noted, “There is, it is true, some difference of opinion about how far it is possible to reduce long-term interest rates, while maintaining short-term rates.” 13 See Meigs (1972, p. 271) and Culbertson (1973, p. 37). The position that Treasury debt-lengthening operations by the Treasury had swamped the effects of Operation Twist held by James Tobin while he served in the Kennedy Administration (see Morris, 1968, p. 23, and Tobin, 1974, pp. 3233) and he reaffirmed it subsequently (see Tobin’s testimony in Joint Economic Committee, 1992, p. 53). Franco Modigliani shared this view (see Brookings Institution, 1978, p. 652). 8

securitiesinitsportfolio;amongthese,holdingsofagencysecuritiesissuesgrewafterthelate1960s astheFederalReservetookupsomeofthecouponissuesofFannieMaeandFreddieMac,which, beinggovernment-guaranteed,wereopen-market-operation-eligibleinstruments. Theendof OperationTwistisnonethelessevidentinFigure1inthediminishingfractionoflonger-term securitiesintheFederalReserve’sportfolioafterthemid-1960s. NotwithstandingtheabsenceofmajorFederalReserveactivityinlonger-termmarkets,long-term interestratebehaviorplayedanimportantpartinFederalReservethinkinginthelate1960sand 1970s. Boardstaffviewedthetransmissionoffederalfundsratestolonger-termratesasakey elementinthetransmissionmechanismformonetarypolicyactions(seePierce,1974). Thetopicof term-structuredeterminationreceivedparticularprominencein1975whenasharpdeclineinthe federalfundsratewasassociatedwithlittledeclineinthebondrate(seeFigure2). Inlightofthe concernthatlonger-terminterestrateswereaberrantlyhigh,aBoardstaffanalysisin1975,quoted inMeltzer(2009,p.1002),consideredthepossibilityofFederalReserveinterventioninthebond market. Thestaffmemojudgedthattheexpectationstheorywastheappropriatebaselinefor thinkingabouttheeffectsofpolicyactionsonlonger-termrates. Insuchaframework,whileterm premiumscouldbeamajorfactordrivingbondyields,FederalReserveassetpurchasesmightnot havereliableeffectsonpremiums. Consequently,theFederalReservestaffpositionin1975was thatlonger-termsecuritiespurchaseswerenotworthwhileasanexpansionarymeasureandthatthe pureexpectationstheoryprovidedthebestbenchmarkforviewingtheconnectionsbetweenFederal Reserveactionsandlong-termrates. Likewise,inacademia,withsomeexceptions(e.g.,B.M.Friedman,1978;Walsh,1982),the expectationstheorypredominatedinthe1970sand1980sastheframeworkthroughwhich macroeconomistsviewedlong-terminterest-ratedetermination,andpreferred-habitat-style approachestoterm-structureanalysisfellintodisfavor. Inparticular,thebaselineterm-structure equationinlinearizedrationalexpectationsmacroeconomicmodelstreatedthelong-termrateas equaltotheefficientforecastofthestreamofpolicyrates,uptoapremiumwhichwastreatedas exogenousorconstant(seeMishkin,1978,andPlosser,1982,forearlyexamples). Bythemid- 1980s,Lucas(1987,p.2)waslookingbackonOperationTwistashavinginvolved“issuesthat seemedsoimportantastheywereoccurringandaresohardtoremembernow.” Theexpectations-theorybenchmarkpredominatedinpolicycirclesinthe1980s. TheFederal Reservekeptsomelonger-termsecuritiesinitsassetportfolio,butofficialsweredoubtfulofthe existenceofportfolioeffects. Asoneofficialputit(Davis,1982,p.56):“Ihavealwaysassumed that,intheUnitedStatesatleast,theevidenceandthetheoryhavestronglyarguedagainstour 9

abilitytohavesignificantandpredictableeffectsontheyieldcurve,throughchangesin[the] maturitycompositionoftheFed’sportfolio.” Likewise, in testimony in early 1992 Federal Reserve Chairman Greenspan emphasized the expectations channel, arguing that it was “only in that context that we believed we could get a significant decline initiated in long-term rates.”14 With theresurgenceofmonetarypolicyanalysisinacademiccirclesaftertheearly1990s,thepure expectationstheorylargely remainedthebaseline for thinking about longer-term interest rates, mostnotablysoinlinearizeddynamicmacroeconomicmodelsoftheNewKeynesiantype. The short-terminterestratepathwasconsideredthecriticalvariableunderthecontrolofmonetary policy,andmonetarypolicyanalysisstressedthecontributionthatforwardguidanceaboutthe fundsratecouldconsequentlymaketostabilizationofaggregatedemandandinflation(see,for example,R.G.King,1994;RotembergandWoodford,1999). Thescopeformonetarypolicytoaffectlonger-termratesviameansotherthanshort-termrate policy wasreconsidered,however,inaliteraturethatemergedoverthelate1990sandearly2000s. ThezerolowerboundhadbeenreachedinJapan,whileintheUnitedStates,thefederalfundsrate targetin2002to2004tooklowvaluesandthelower-boundemergedasapossibility. Mervyn King (1999)andBernanke(2002)suggestedthatcentralbankpurchasesoflong-termbondswerea meansofprovidingmonetarypolicystimuluswhentheshort-termpolicyratewasatitslower bound. Aroundthesametime,theinformationrevealedbytheTreasurybuybackprogram potentiallyofferednewinsightintotheeffectofdebt-managementoperationsontheterm structure.15Inparticular,thebuybackcouldthrowlightonthelikelyimpactofotherpossibledebtmanagementoperationssuchascentralbankpurchasesoflong-termbonds. Bernanke,Reinhart, andSack(2004)inferredfromtheexperienceofthebuybackprogramthatFederalReserve operationsinlong-termdebtcouldhaveappreciableeffectsonthelong-terminterestrateforagiven pathofshort-terminterestrates. Nevertheless,considerabledoubtsaboutthispolicyoption enduredintheliterature,withEggertssonandWoodford(2003)providingawell-knowncritique. 2.2LSAPs,2008to2011 ThebasicchronologyofLSAPswasoutlinedintheintroduction. Theoriginalsequenceof ————————————————————————————————————— 14 From Greenspan’s January 10, 1992 testimony in Committee on Banking, Housing and Urban Affairs (1992, p. 68). In contrast, Paul Samuelson and James Tobin testified during this period in favor of Federal Reserve purchases of longer-term securities to put downward pressure on longer-term rates: see Joint Economic Committee (1992). 15 Treasury debt management operations, like Federal Reserve purchases or sales of longer-term securities, can alter the composition of the outstanding debt, so the former can be informative about the effects of the latter. The fact that either the Treasury or the Federal Reserve can take actions to secure a particular maturity composition for the outstanding stock of Treasury debt was noted by Friedman and Schwartz (1963, pp. 579, 634). 10

purchases,fromNovember2008toMarch2010,beganwithpurchasesofthedebtsecuritiesissued byhousing-relatedgovernment-sponsoredenterprises(GSEs)andagency-guaranteedmortgagebackedsecurities. Asdiscussedpreviously,agencydebtandagency-guaranteedsecuritiesare open-market-operation-eligiblesecurities. TheFederalReserve’sfirstappreciableacquisitionof agency-relatedsecuritieswasintheearly1970s;priortorecentyears,thepeaklevelofholdingswas in1981(seeMeulendyke,1998,pp.4041). TheNovember2008decisiontoundertakelarge-scale FederalReservepurchasesofagency-relatedsecuritiescameinthewakeofawideningspreadof yieldsonthesesecuritiescomparedwiththoseonTreasuries,and itwasmotivatedbythedesireto “reducethecostandincreasetheavailabilityofcreditforthepurchaseofhouses,whichinturn shouldsupporthousingmarketsandfosterimprovedconditionsinfinancialmarketsmore generally”(FederalReserve,2008). ThescaleoftheLSAPswasexpandedattheMarch2009 FOMCmeeting,whentheCommitteedecidedtobringitsmaximumpurchasesofagencyMBSto $1.25trillionandofagencydebtto$200billion(amaximumsubsequentlyloweredto$175billion); inaddition,itdecidedtopurchaseupto$300billionoflonger-termTreasurysecuritiesoverthe followingsixmonths(FOMC,2009). Thepurchasesofagency-relatedsecuritieswerecompleted inMarch2010. InAugust2010,theFOMCadoptedapolicyofreinvestingprincipalpaymentsonholdingsof agencysecuritiesinlonger-termTreasurysecurities. Thepolicythusmaintainedtheaggregate levelofsecuritiesholdings,andtheassociateddegreeofmonetaryaccommodation,inplaceatthat time. Inthefaceofsignsofaslowingrecovery,Bernanke(2010)listedanewLSAPprogramasan optionand,inNovember2010,theCommitteedecidedtopurchaseafurther$600billionoflongertermTreasurysecuritiesbytheendofthesecondquarterof2011,aprogramdulycompletedatthe endofJune2011. Morerecently(September2011),theFederalReservelaunchedtheMaturity ExtensionProgram(MEP). UnlikeLSAPs,MEPoperationsarelargelysterilizedanddonot increasetheFederalReserve’soverallsecuritiesholdings. LikeLSAPs,however,theylengthenthe maturitystructureoftheFederalReserve’ssecuritiesholdings,andthusdependonchannelslike thoseunderlyingtherationaleforLSAPs;inparticular,MEPshouldworkviathe“duration” channeldiscussedbelow. Weturnnowtoadiscussionofthetransmissionchannelsthatmightbe associatedwithLSAPs. 3. TransmissionchannelsforLSAPs InthissectionweoutlinesomeofthemainchannelsthroughwhichLSAPsmightwork. 11

3.1Expectations/signalingchannel ThesignalingorexpectationeffectcapturesthosechangesintheexpectedpathoffutureshorttermratesthatarisefromperceivednewinformationthatLSAPmeasuresmightrelayaboutthe stateoftheeconomyandtheFederalReserve’sshort-terminterest-ratereactionfunction. This effectworksthrough,andrelieson,thestandardexpectationhypothesisconcerningtheconnection betweenshort-andlonger-terminterestrates. 3.2Traditionalpreferred-habitat/scarcitychannel Whiletheexpectationschanneliswidelyacknowledgedasonemeansthroughwhichmonetary policyaffectslonger-terminterestrates,itsexistencedoesnotprecludethepossibilitythatdirect purchasesoflonger-termsecuritiesactontheterm-premiumcomponentoflonger-termratesby settinginmotionaportfoliobalancemechanism. Deviationsoflonger-terminterestratesfromthe predictionsofthestrictexpectationstheoryhavebeenrepeatedlydocumentedintheliterature,and thepreferred-habitatapproachadvancestheviewthatsomeofthesedeviationsare attributable to variationsintherelativesuppliesofoutstandingstocksofdebt. Thepositionthatlonger-termyields dependinpartontherelativequantitiesoutstandingoflonger-termassetsinthehandsoftheprivate sector(includingcommercialbanks)wasthesubjectofasubstantialliteratureinthe1950sandthe 1960s(seeCulbertson,1957,ModiglianiandSutch,1966,Wallace,1967,andthereferences discussedinSection2). Recently,VayanosandVila(2009)haveofferedmorerigorousfoundations forthisapproachwithinaterm-structuremodelwithtwotypesofinvestors. Thepreferred-habitat investorsinthisframeworkaredisposedtopurchasingsecuritiesofcertainmaturities,while arbitrageurscanprofitbytradingacrossmaturities,butriskaversionpreventstheseagentsfrom takingcompleteadvantageofprofitopportunities.16 Thepreferred-habitatapproachprovidesarationaleforassetpriceadjustmentsinthewakeofashift inthequantitiesofspecificmaturitiesofgovernmentdebtheldbyprivateagents. Underlyingthe viewthatthematuritycompositionbearsonassetpricesisthepremisethatapermanentdemand existsfromaclassofinvestorsformarketable,fixed-incomesecurities. Thus,insegmented-market modelsfeaturingimperfectassetsubstitution,areductioninthestockofsecuritiesofaparticular maturityinthehandsofprivateinvestorscreatesashortageofthoseassetsthatcannotbewholly relieved,atexistingassetprices,bysubstitutionintoothersecurities. Theshortagethuspromptsan ————————————————————————————————————— 16 Gagnon, Raskin, Remache, and Sack (2011) and Hamilton and Wu (2012) use Vayanos-Vila as their baseline. 12

adjustmentoffinancialmarketprices. Suchascarcityeffectmaybespreadovertime,anditcould bemanifestedinbondratesforaparticularmaturity. Anofficialpurchaseprogramthatmakeslonger-termTreasuriesscarceristhenlikelytogenerate downwardpressureonlonger-termTreasuryyields. Sucha“localsupply”(orscarcity)effectof LSAPscanbethoughtofaswithdrawinglonger-termsecuritiesfromthehandsoftheprivatesector andtherebycreatingaprospectiveexcessofdemandoversupplyforfixed-incomeassets. Asa result,themarketforlong-termsecuritiesclearsatalowerequilibriumquantityandahigherprice, thatis,aloweryield. Thisyieldadjustmentwouldnotoccurinsimplerepresentative-agent frameworksbutbecomespartoftheadjustmentprocessinanenvironmentthatallowsfor heterogeneityamongprivateinvestors. Thus,whenaclassofinvestorsunderpinsthedemandfor longer-termsecurities,conditionsarecreatedthatbreakthepureexpectationstheoryoftheterm structureandmakethetermpremiumafunctionoftheratioofshort-termtolonger-termsecurities outstanding. Itisthisdeparturefromtherepresentativeagentframeworkthatimpliesthattheresult ofEggertssonandWoodford(2003),accordingtowhichmonetarypolicy’seffectonlonger-term ratesislimitedtotheexpectationschannel,nolongerholds. 3.3Durationchannel TheVayanos-Vila(2009)preferred-habitatframeworkreferredtoabove,inadditiontofeaturing localsupplyeffects,alsoimpliesadirectrelationshipbetweenthetermpremiumandtheaverage durationriskfacedbyinvestors,inparticularbythearbitrageurs.17TotheextentthatLSAP-style measuresremovedurationriskfromthemarketbywithdrawingaportionoflong-termsecurities, theriskpremiumbuiltintothepriceofsuchassetsshoulddecline. Theremovalofdurationrisk shouldgeneratereactionsofyieldsacrossmuchofthematurityspectrum—notjustontheyieldsof purchasedsecuritiesandthoseofadjacentmaturities. 3.4Comparisonwithanothertypologyofchannels Theprecedingcataloguehasallowedforthreechannelsthroughwhichmonetarypolicymight affectlonger-terminterestrates:theexpectationsorsignalingchannel,thescarcityorlocalsupply channel,andthedurationchannel. KrishnamurthyandVissing-Jorgensen(2011, p. 216)endeavor tooutline“theprincipaltheoreticalchannelsthroughwhichQE[quantitativeeasing]mayoperate,” andwenowbrieflycompareourowntypologywiththeirs. ————————————————————————————————————— 17 The model shares this feature with a class of models of the impact of second moments on term-structure behavior. 13

Somechannelsarecommontobothtypologies:KrishnamurthyandVissing-Jorgensenconsider durationandsignalingchannels,alsoincludedinourownlist,whiletheir“safetypremium channel”—underwhichasegmenteddemandforlong-termsafeassetstendstoloweryieldson thosesecurities—issubsumedwithinthescarcitychannelofthepreferred-habitatliterature. KrishnamurthyandVissing-Jorgensenalsorefertothe“liquiditychannel,”underwhichdownward pressureonlong-termratesemergesasreservesbecomeplentifulrelativetolong-termbonds. We donottreatthisasadistinctchannelhere;wefocusonchannelsthatremaininoperationwhenshortterminterestratesareattheirlowerbound. Inthevicinityofthezeroboundonshort-terminterest rates,commercialbankreservesandshort-termTreasuriesarelargelyequivalent;operationsthat exchangebillsforlonger-termsecuritiesbecomeanalyticallysimilartothosethatexchange reservesforlonger-termsecurities,andthesupplyeffectofeitheroperationdependsonascarcity channel. Finally,KrishnamurthyandVissing-Jorgensenclassifythe“inflationchannel,”under whichLSAPschangeinflationexpectations,asaseparatechannel. Thereactionofinflation expectations,however,canbeviewedasaconsequenceoftheoperationoftheprecedingchannels, ratherthanasachannelinitsownright. Thus,webelievethatourtypologyofchannels,though listingfewertransmissionmechanismsthanthosegiveninKrishnamurthyandVissing-Jorgensen (2011),coversallthechannelslikelytoberelevantfortheanalysisofLSAPs. Ourestimatesin Section6belowprovideawayofdeterminingtheimportanceofeachchannelgivenabove. Ahead ofthat,webrieflyconsideracasestudy. 4. Someinitialempiricalevidence:acasestudy ThesequenceofeventsfollowingtheFOMCmeetingofAugust10,2010,throwsconsiderablelight ontheimpactofLSAP-styleoperationsonlonger-termTreasuryyields. Initsstatementafterthat meeting,theFOMCannounced(at2.15p.m.)thatprincipalpaymentsfromagencysecuritieswould bereinvestedinlonger-termTreasurysecurities. Soonthereafter,at2.45p.m.,theFederalReserve BankofNewYork(FRBNY)issuedastatementindicatingthatthepurchasesunderlyingthe reinvestmentpolicywouldbeconcentratedinthetwo-toten-yearsectorofthenominalTreasury yieldcurve. Changesoverthishalf-hourintervalinmarketexpectations(asascertainedfrom observedyieldbehavior)arerevealingabouttherespectiverolesofthescarcityandduration channelsindeterminingTreasuryyields. Ouranalysisofthisepisodeconsidersthepricesoffourpreviously-issuedthirty-yearTreasury bondswithremainingmaturitiesjustaroundtenyearsorjustabovefourteenyears,showninFigure 14

Figure3:CUSIP-levelintradaypricesonAugust10,2010: Verticallinesindicatetimeofannouncements. Source:ThomsonReutersTickHistorydatabase. 3.18Basedonthe2:15p.m.announcement,theseclassesofsecuritiesmaywellhavebeenperceived asequallylikelycandidatesforpurchasebytheFederalReserve. Followingthereleaseofthe statementbytheFRBNY,however,investorsshouldhaveassignedasmallerprobabilitytothe FederalReservepurchasingsecuritieswithremainingmaturitiesabove10 years.19Wetherefore wouldexpectthesecondannouncementtohavenomaterialimpactonthepricesofTreasury securitieswithtwo-toten-yearmaturities(thetwo solid linesinFigure3),buttoexertapotentially sizablepriceimpactonsecuritieswithmaturitiesbeyondtenyears(thetwo broken lines). ThefirsttworowsofTable1establishthat,inresponsetotheFRBNYstatement,thetwosecurities ————————————————————————————————————— 18 We restrict the analysis to seasoned thirty-year bonds in order for all the securities considered to feature similar characteristics on the dimension of their liquidity (using that term in its financial-market sense of “marketability”). 19 The Federal Reserve Bank of New York release stated: “The Desk will concentrate its purchases in the two- to ten-year sector of the nominal Treasury curve, although purchases will occur across the nominal Treasury coupon and TIPS yield curves.” 15

withmaturitiesclosetoorbelowtenyearsexperiencedareversalofonlyabouttwentypercentof thepriceincreasesthathadcomeinthewakeoftheFOMCannouncement.20Incontrast,forthetwo securitieswithmaturitiesabovefourteenyears,abouttwo-thirdsoftheinitialpriceincreasewas reversedinthewakeoftheFRBNYannouncement. Thecontrastingextentofpricereversalsacross thetwomaturitygroupssuggeststhatroughlytwo-thirdsofthedeclineinthefourteen-year Treasuryyieldisattributabletotheanticipationofareductioninsupplyaroundthatmaturity— whichistosay,thescarcitychannel.21Thepart of the price movement that endured in the wake of both announcements likely reflected the anticipation of reduction in aggregate duration. Furthermore,inthewakeofthesecondannouncement,theon-the-runthirty-yearTreasuryyield morethanreverseditsearlierdecline,suggestingthatthepriceactionatthismaturitywasalmost entirelydrivenbychangingperceptionsofthelikelihoodofpurchasesbeingconductedinthis sectorratherthanbyexpectedchangesinduration. Althoughwecannotruleoutthepossibilitythat afractionofthesevariationswasduetorevisionstofunds-rateexpectations,itseemsreasonableto assumethatthosewouldlikelyonlyhaveaminorimpactonyieldssofaralongtheyieldcurve. 5. Datadescriptionandvariableconstruction Inthissection,wediscussourdatasourcesandtheseriesthatweconstructfromthedata. Inorderto generateaccuratemeasuresoflocalTreasurysupply(thatis,thesupplyofthesecurityinquestion andthatofsecuritieswithnearbymaturities)andtodiscerntheaggregatecharacteristicsof Treasurydebtheldbyprivateinvestors,westartfromCUSIP-leveldata(thatis,datadelineatedby theidentificationnumberoftheissuedTreasurysecurity). ForeachCUSIPwehaveavailablethe totalamountoutstanding(TAO),theamountheldintheFederalReserve’sSOMAportfolio (SOMA),andthecumulativeamountofanyTreasurybuyback(TB),allofwhicharemeasuredatpar value. TheavailabilityofthesethreecomponentsallowsustoderiveforeachCUSIPtheamount heldbyprivateinvestors(thatis,investorsnotincludingtheFederalReserve). Thisisacentral variableinouranalysisbecauseitcanbealteredbyFederalReservepurchasesoflonger-term Treasurysecurities,andbecauseitisapossibleinfluenceonthebehavioroflonger-termTreasury yields. ————————————————————————————————————— 20 Part of this reversal likely reflects investors’ marking-down of the probability that ten-year Treasury securities would be among the bonds purchased. Investors may have initially interpreted the FOMC reference to “longer-term Treasury securities” as pertaining to maturities beyond seven years. 21 As in the case of the ten-year rate, a minor part of this retracement may be attributable to the expectation that a smaller amount of duration would be withdrawn from the market, this expectation arising from the realization that the Federal Reserve purchases would be concentrated in maturities under ten years. The likelihood that the patterns of the ten- and fourteen-year rates are driven by the same factors is reinforced by the fact that the two securities considered are more similar to each other in duration than in maturity. 16

PreviousstudiessuchasGreenwoodandVayanos(2010)andHamiltonandWu(2012) documentedtheimportanceofcertainaggregatecharacteristicsoftheTreasurydebtforthe determinationofthetermstructure. Owingtodatalimitations,thesestudiesdidnot,however, excludeactualFederalReservesecuritiesholdingsfromthetotalsofTreasurydebtoutstanding. Consequently,theholdings-aggregatesusedinthesestudiessufferfromtheshortcomingthatthey arenotidealforaddressingtheimpactofLSAP-stylepurchases. Furthermore,tocomputecorrectlytheaveragematurityordurationremaininginthemarketinthe wakeofFederalReservepurchases,itiscrucialtoemploytheshareofeachCUSIPheldbythe privateinvestors,asthosesharesdeterminetheappropriateweightsintheaggregation. Itisalso importanttohavedatarecordedathighfrequency,sincequantitiesoutstandingexperiencefrequent changesasaresultofTreasuryauctionsandFederalReserveoperations. Thisfinerlevelofdata disaggregationdoes,however,comewiththecostthatwearelimitedtoashortersampleperiodin ourestimation,asdataonSOMAholdingsattheCUSIPlevelareavailableonlyfromDecember 2002. 5.1Constructingourvariables Weusethesedatatoconstructourproxiesforscarcityandduration. Consistentwithaconceptof scarcitythatcorrespondstothelocalavailabilityofsecuritiesofaparticularmaturity,wesplitthe availableCUSIPsintodistinct“buckets”accordingtomaturity. Foreachofthesebucketsb ,we mn computeprivately-heldnominalTreasuries(PHNT)asafractionoftotalTreasurydebtoutstanding (TDO):22 (cid:1842)(cid:1834)(cid:1840)(cid:1846)(cid:4666)(cid:1865)(cid:3398)(cid:1866)(cid:4667) (cid:3404) ∑ (cid:4666)(cid:1846)(cid:1827)(cid:1841) (cid:3398)(cid:1845)(cid:1841)(cid:1839)(cid:1827) (cid:3398)(cid:1846)(cid:1828) (cid:4667)/(cid:1846)(cid:1830)(cid:1841) (cid:3040)(cid:3000)(cid:3036)(cid:2996)(cid:3041) (cid:3036) (cid:3036) (cid:3036) , whereiistheindexfortheCUSIP,andmandnaretheindexesforthematurities. Weexclude indexedTreasurybonds(TIPS)andTreasurybillsfromourcomputations. Ourproxyforthe aggregatedurationrisk(ADR)remaininginthemarketiscomputedasaweightedaverageofthe modifiedduration(MD)ineachbucket(thethinnerthebucket,themoreaccurateisthemeasure, promptingourchoicethateachbucketcontainsonlyoneCUSIP,i.e.,b =(cid:1861) ): mn (cid:3040) ————————————————————————————————————— 22 As indicated earlier, “privately held” here refers to holdings outside the federal government and the Federal Reserve. It includes the holdings of both the nonbank private sector (including foreign entities and state and local governments) and commercial banks. 17

(cid:1827)(cid:1830)(cid:1844) (cid:3404) (cid:3533)(cid:1842)(cid:1834)(cid:1840)(cid:1846)(cid:4666)(cid:1861) (cid:4667)(cid:1499)(cid:1839)(cid:1830)(cid:4666)(cid:1861) (cid:4667), (cid:3040) (cid:3040) (cid:3036)(cid:3288) foreveryavailablematuritymupto30years. Wefaceapossiblesimultaneityproblemarisingfrom thefactthataloweryieldwouldimplyalengtheningofthedurationofanyTreasurycoupon security. Tomitigatethissimultaneityproblem,wecomputethedifferencebetweenADRandthe durationofon-the-runten-yearTreasurynotes(D10y).23Wedefinethedurationgap(DG)as: DG=ADRD10y. Asboththevariablesontheright-handsideoftheprecedingexpressionareaffectedbythe mechanicalelementofthechangeinduration,afocusonfluctuationsinthedifferencebetweenthe twoseriesislikelytopinpointthemoremeaningfulmovementsinduration. Itisusefultonote,incomparingourresultswithexistingstudies,thatthederivationofourproxyfor theaggregatedurationriskremaininginthemarketsimplyamountstoanalternativemeansof weightingtheTreasurysecuritiescontainedineachmaturitybucketb . Ontheotherhand,taking mn intoconsiderationthefactthatourseriesincludesonlythoseTreasurysecuritiesheldbyprivate investors,andthefactthatthesensitivitytointerest-rateriskofabondofaparticularmaturity dependsonitsduration,wecontendthatourADR(andhenceDG)seriesarecloserinspirittothe conceptofaggregateriskofthearbitrageurs’portfoliounderlyingthe Vayanos-Vila (2009) analysis. Totheextentthatinvestorsareprincipallyconcernedwiththedurationriskoftheirportfolio,ADR providesthemostconvenientsummaryofthedegreeofinterest-rateriskinthemarket. Itshould thereforecontributetotheexplanationofthebehaviorofbondriskpremiums. If,however,this constitutedtheonlyrelevantchannelconnectingFederalReservebondpurchasestolonger-term Treasuryyields,wewouldobserveyieldchangesthatweremonotonicintheamountofduration. Thus,ifFederalReserveoperationstendedtoreducetheamountofdurationthatprivateinvestors wererequiredtoabsorb,theimpactonthethirty-yearTreasuryyieldwouldconsiderablyoutweigh theimpactontheten-yearyield. TheavailableempiricalevidenceontheeffectofLSAPs,aswellas ontheannouncementsconcerningreinvestmentsofproceedsfromagencysecurities,suggeststhat thisisnotthecase(see,forexample,D’AmicoandKing,2012,Figure2,andKrishnamurthyand Vissing-Jorgensen,2011,Table1). Thislendsweighttotheviewthatadditionalchannelsmightbe important. Moreover,theoccurrenceoflargerimpactsinsectorsinwhichmostofthepurchases ————————————————————————————————————— 23 We are grateful to Canlin Li for this suggestion. 18

Figure 4. Privately held nominal Treasuries and average duration wereconcentratedpointstowardlocalsupplyanddemandeffects. Withthisinmind,we constructedourscarcityproxyinthemannerdescribedabove. Figure4displaysthetimeseriesofPHNTandADR,asconstructedfromweeklyCUSIP-leveldata fromDecember2002toAugust2011. TheperiodsofthefirstandsecondLSAPprogramsare indicatedbyshadedregionsinthefigure. Asexpected,intheseperiodstheshareofTreasury securitiesheldbyprivateinvestorsexhibitedalargedecline,reflectingthesecuritiesaddedtothe SOMAportfolio. Incontrast,ADR,whichismeasuredinunitsofyears,recordedonlyamodest declineduringthefirstandsecondLSAPs,asmostofthepurchaseswereconcentratedinthetwo-to ten-yearsector. CounterfactualcomputationsindicatethatduringthefirstLSAPstheaverage durationofprivatelyheldTreasurydebtoutstandingwasreducedfrom4.42to4.30years,andwas 19

reducedbyasimilarextentinthecourseofthesecondLSAPprogram. Thesepatternsindicatethat verylargepolicyinterventionsinthesectorbeyondtheten-yearmaturityarerequiredtoremovea significantamountofdurationfromthemarket. 5.2Alookatthedatacorrelations HereweillustratehowourdecompositionofPHNTintothinbucketshighlightskeyaspectsofthe correlationstructurebetweenlonger-termTreasuryyieldsandtheavailablesupplyforeachbucket. Table2displayscorrelationsbetweenconstant-maturityyieldsandlocalTreasurysecuritysupply asmeasuredbytherelevantPHNTs, where (here and below) the notation PHNT(m: ab) denotes the bucket covering maturities from a years up to, but not including, b years. Thecorrelation structureforDecember2002toOctober2008—asamplethatprecedestheinceptionofLSAPs—is suggestiveofaroleforimperfectsubstitutionacrosssectorsoftheyieldcurve. Treasuryyieldsat maturitiesbetweentwoandtenyearsarepositivelycorrelatedonlywithTreasurysupplywitha maturitybetweentwoandtwelveyears,andtheyarenegativelycorrelatedwiththesupplywith maturitybetweentwelveandtwenty-eightyears. Incontrast,Treasuryyieldswithamaturityof fifteenyearsandbeyondarepositivelycorrelatedonlywiththesupplyconcentratedinmaturity bucketsbeyondtwelveyears. ThiscorrelationpatternisfullyreversedinthesampleperiodcoveringthetwoLSAPs(seeTable2, lower panel). It may bethatFederalReserveactions inlonger-termTreasurymarketsarethemain factordrivingthesign-change. If the bucket combinations used here imply that Treasuries with similar yield behavior are grouped together, and if it were the case that theFederalReserve boughtlargeamountsofsecuritieswhoseyields showed thestrongestupwardtrend,thenwewould observeacombinationofrisingyieldsonthosesecuritiesanddecreasingquantitiesavailableto privateinvestors. Suchapatternshouldbemoreevidentforthematuritysectorsinwhichthe FederalReserveconcentratedpurchases,namely,thetwo-tofifteen-yearsectors. Thisresultpointstothelikelihoodthatthepurchasesstrategyoversampleperiodsthatinclude LSAPsisafactorthathindersattemptstodeterminebystatisticalmethodsthestructural relationshipbetweenyieldsandquantities. Thisendogeneityproblem,whichisstressedin D’AmicoandKing(2012),underscorestheimportanceofoursubsampleanalysisforbringingout theunderlyingrelationshipbetweenlonger-termTreasuryyieldsandthesecuritiessupplyavailable toprivateinvestors. Thepreliminarydataanalysisalsoindicatesthatyieldsandquantitiesare highlycorrelatedinsomeofthebuckets,anditsuggeststhatitwouldbepreferabletogroupthe bucketsaccordingtocommoncorrelationpatterns. Inparticular,wecangrouptogetherPHNTfrom 20

two-toten-yearmaturitybucketsandPHNTfromtwelve-totwenty-eight-yearmaturitybuckets withoutlosingmuchoftheinformationcontainedinthedata. Finally,itisimportanttonotethat onlyinthefirstsubsampledoweobserveamonotonicpatternofthekindwewouldexpectforthe correlationbetweenlonger-termTreasuryyieldsandthedurationgap,thecorrelationbeing,by contrast,quiteflatinthesecondsubsample. 6. Empiricalspecificationandresults Thissectionprovidesourestimatedspecifications. Weinitiallyconsiderthelevelsofnominal Treasuryyieldsatdifferentmaturities,obtainedviaSvensson’s(1995)yield-curveapproximation, andpresentresultsthatarelargelymodel-independent,inthesensethatonlyquitegeneral assumptionsarerequiredtogeneratethedependentvariables. Then,usingdifferentspecifications ofaGaussianthree-factormodelofthetermstructure,wefocusontheterm-premiumcomponentof longer-termTreasuryyields.24Wealsoconsiderwhethertheseresultsarerobusttoalternative specifications. Finally,usingtheaffinetermstructuremodelaugmentedwithTIPS—themodelfor whichwehavethegreatestconfidencewhenitcomestothedecompositionofnominalterm premiums—weestimateimpactsontherealtermpremiumandtheinflationriskpremium.25 Table3reportsestimatesthatresultfromregressingnominalTreasuryyieldsatdifferentmaturities onourproxiesforscarcityandaggregatedurationaftercontrollingfortheslopeoftheterm structure,whichismeasuredbythespreadbetweenthetwo-andten-yearyields. Theslopevariable hasbeenwidelyfoundtobeapredictorofbotheconomicactivityandTreasuryreturns.26 Accordingly,weregarditsinclusionasimportantforestablishingwhetherourproxies(scarcityand aggregateduration)areimportantintheirownrightinaccountingforthebehavioroflonger-term rates.27Wenotethatourequations,likethoseinallpreviousstudiesofLSAPs,arespecifiedin termsofactualscarcityanddurationproxiesratherthantheexpectedpathofthesevariables. This specificationmightnotbewhollyappropriatefortheLSAPperiod,asLSAPprogramsconsisted largelyofpurchasesannouncedsometimeinadvance,andannouncementsoffutureeffectson scarcityanddurationlikelyfiguredinthereactionoflonger-termrates. Thisissue,however,isless problematicforourestimatedspecifications,since—inlightoftheanalysisofthepreceding section—ourestimationperiodpredatestheLSAPprograms. ————————————————————————————————————— 24 See Kim and Wright (2005) and Kim and Orphanides (2005). 25 See D’Amico, Kim, and Wei (2008). 26 See, for example, Fama and Bliss (1987) and Estrella and Hardouvelis (1991). 27 It will turn out that the inclusion of the slope term in the regression improves the explanatory power of the regression but has little effect on the estimated impact of the scarcity and duration regressors. See Table 8, which reports results without the slope as an explanatory variable. 21

Weconsideronlysecuritieswithatleastsevenyearstomaturity(seven-tothirty-yearnominal yields);shorter-termyieldsforoursampleappeartoexhibitclearlynonstationarytimeseries behavior,reflectingboththefactthatoursamplefeaturesonlytwofunds-rate“cycles”—one tighteningandoneeasing—andthefactthatshorter-termyields,presumablybeingdominatedby theexpectationscomponentratherthantermpremiumbehavior,tendtomimicfundsratebehavior moreclosely. ThetoppanelofFigure5confirmsthatthemaindriverofshorteryieldsisthe expectationscomponent. Incontrast,theterm-premiumcomponentseemstobethedominant sourceoffluctuationsinyieldswhenlonger-termratesareconsidered—ascanbeseeninthelower halfofFigure5. Thelatterpatternimpliesmorestationarybehaviorofinterestrates,asthetermpremiumcomponentinthissampleislesspersistentthantheexpectationscomponent. Afurtherconsiderationthatreinforcesthedesirabilityofconcentratingonpre-crisisbehaviorwhen ascertainingtheeffectofLSAP-styleoperationsisthattheresidualor“fittingerror”forthetermstructurespecificationusedtodecomposelonger-termratesbecameunusuallylargeinlate2008 andearly2009. Thus,overthisperiod,ourscopetomakejudgmentsaboutoveralllonger-term interestratebehaviorbasedonthedecompositionisreduced. Sinceoureconometricwork concentratesonthedeterminationofthesesystematicterms,itseemsallthemoreappropriateto confineourestimationsampleperiodstothepre-crisisperiod. Thespecificationofthenominalyieldequationis(neglectingtheerrorterms): (cid:1877) (cid:4666)(cid:1865)(cid:4667) (cid:3404) (cid:1853)(cid:3397)(cid:1854) (cid:1842)(cid:1834)(cid:1840)(cid:1846) (cid:4666)(cid:1865):2(cid:3398)10(cid:4667)(cid:3397)(cid:1854) (cid:1830)(cid:1833) (cid:3397)(cid:1854) (cid:3435)(cid:1877) (cid:4666)(cid:1865)(cid:4667)(cid:3398)(cid:1877) (cid:4666)2(cid:4667)(cid:3439), (cid:3047) (cid:2869) (cid:3047) (cid:2870) (cid:3047) (cid:2871) (cid:3047)(cid:2879)(cid:2869) (cid:3047)(cid:2879)(cid:2869) for(cid:1865) (cid:3409) 10(cid:1877),and (cid:1877) (cid:4666)(cid:1865)(cid:4667) (cid:3404) (cid:1853)(cid:3397)(cid:1854) (cid:1842)(cid:1834)(cid:1840)(cid:1846) (cid:4666)(cid:1865):14(cid:3398)30(cid:4667)(cid:3397)(cid:1854) (cid:1830)(cid:1833) (cid:3397)(cid:1854) (cid:3435)(cid:1877) (cid:4666)10(cid:4667)(cid:3398)(cid:1877) (cid:4666)2(cid:4667)(cid:3439), (cid:3047) (cid:2869) (cid:3047) (cid:2870) (cid:3047) (cid:2871) (cid:3047)(cid:2879)(cid:2869) (cid:3047)(cid:2879)(cid:2869) for(cid:1865) (cid:3408) 10(cid:1877),whereallthevariablesareobservedweekly. Sinceweareconsideringpersistent variables,andsomeofthedata’spersistencemightcarrythroughtothebehavioroftheestimated residuals,thet-statisticsarecomputedusingNewey-West(1987)standarderrors,allowingfora four-weekwindow. Theestimatedcoefficientsforourmeasuresofscarcityandaggregateduration arebothpositiveandstatisticallysignificantacrossallmaturitiesevenaftercontrollingfortheslope oftheyieldcurve,withtheadjustedR2’svaryingfrom0.46to0.70.28Thesignsoftheestimated ————————————————————————————————————— 28 We caution against direct comparison of the coefficient on duration in these estimated specifications with those in studies such as Greenwood and Vayanos (2010) and Hamilton and Wu (2012), as we are using a gap variable rather than the level of aggregate duration or average maturity. 22

Figure 5. Decomposition of Treasury yields coefficientsareinthepredicteddirection:theloweristhevolumeofprivately-heldTreasury securitiesinaspecificmaturitysector,thelowertheyieldprevailinginthatsector;likewise,the smallertheamountofaggregatedurationleftinthemarket,thelowershouldbetheyields. Table4displaysresultsforasetofregressionssimilartothebaseline,butinsteadofaggregating PHNTintoonlytwobroadmaturitybuckets,weconsidertwo-year-widebucketswithmaturities 23

withinfewyearsoftheyield’smaturity. Thatis,weseektotestfurthertheimpactofscarcity,or localsupply. Inparticular,werestrictattentiontothebucketcenteredontheyield’smaturity,andto thetwobucketswithmaturitiesjustaboveandbelowit.29Forthemajorityoftheyields,theresults appeartosuggestthatthePHNTbucketswiththeclosestmaturitytotheyieldtendtoexhibithigher positivecorrelationsand/orstrongerstatisticalsignificance. Wenowconsiderresultsforthenominalterm-premium(TP)componentoflonger-termTreasury yields. TheupperpanelofTable5reportstheresultsforthefollowingregression: (cid:1846)(cid:1842) (cid:4666)(cid:1865)(cid:4667) (cid:3404) (cid:1853)(cid:3397)(cid:1854) (cid:1842)(cid:1834)(cid:1840)(cid:1846) (cid:4666)(cid:1865):2(cid:3398)10(cid:4667)(cid:3397)(cid:1854) (cid:1830)(cid:1833) (cid:3397)(cid:1854) (cid:3435)(cid:1877) (cid:4666)(cid:1865)(cid:4667)(cid:3398)(cid:1877) (cid:4666)2(cid:4667)(cid:3439), (cid:3047) (cid:2869) (cid:3047) (cid:2870) (cid:3047) (cid:2871) (cid:3047)(cid:2879)(cid:2869) (cid:3047)(cid:2879)(cid:2869) wheretheTPserieshasbeenderivedusinganaffinetermstructuremodel(ATSM)withTIPS.30 In lightofthefactthat,overthissample,theTPcomponentofmedium-termyieldsappearstobe stationary,wealsoconsiderresultsusingthetwo-andfive-yeartermpremiumsasthedependent variable. Thefirstnotablefeatureoftheresults,previouslyfoundforournominalyieldregressions,isthatthe coefficientsonourmeasuresofscarcityandaggregatedurationarepositiveandstatistically significant. Anothernotablefeatureisthatthemagnitudeofthecoefficientsseemstoindicatethata largepartoftheimpactofscarcityandaggregatedurationonlonger-termTreasuryyieldshasbeen transmittedviatheterm-premiumcomponent. Putanotherway,theeffectsonthetermpremiums foundherearesimilarinsizetothoseontheentireyields. Finally,forbothvariables,beyondthe two-yearmaturity,thecoefficientestimatesarefairlysimilaracrossthedifferentmaturities. Thepresenceofsignificantimpactsofscarcityanddurationinthetermpremiumregressions stronglysuggeststhatthesignificanceofthesevariablesforlong-terminterestratevariationisnot arisingfromtheircorrelationwithexpectedfuturepolicyrates. LSAP-styleoperationswould appeartoexertadistinctimpactonlonger-terminterestratesforagivenpathoftheshort-term policyrate. Thesignalingchannel,whilepresent,isevidentlynotthemainmeansbywhichLSAPs canreducelonger-terminterestrates.31 ————————————————————————————————————— 29 An exception is the thirty-year yield, for which the buckets of interest are empty for the bulk of the sample period. 30 We also considered specifications based on an ATSM without TIPS. The resulting estimates of the key coefficients were very similar. 31 Our finding of effects of LSAP-style operations on longer-term interest rates, though based on estimates from the pre-LSAP period, is consistent with several studies noted above that focus on the periods of the LSAPs. An exception, which emphasizes the signaling channel, is Bauer and Rudebusch (2011). 24

Percent 4.05 3.80 3.55 3.30 3.05 2.80 2.55 2.30 2.05 1.80 1.55 1.30 1.05 0.80 2-year 5-year 7-year 10-year Oct. 29, 2009 Duration Effect Dur+Scar Effect Scarcity Effect Figure6. Counterfactualyieldcurves ToillustratethescarcityanddurationeffectofLSAP-styleoperations,weconstructcounterfactual yieldcurvesobtainedusingtheresultsinTable5forthenominaltermpremium. Theresultingyield curvesareshowninFigure6. Forsimplicity,thecounterfactualexercisestartsfromtheactualyield curveasofOctober29,2009—attheconclusionofthefirstTreasuryLSAPprogram—andtreatsall purchases($300billion)asconcentratedinthetwo-toten-yearsector. Inadditiontotheactual yieldcurve(solidline)thatincorporatestheeffectofthefirstTreasuryLSAPprogram,thefigure plotstheestimatedyieldcurvesthatwouldhaveprevailedwithoutthescarcityeffectofLSAP (dottedline),withouttheaggregatedurationeffect(dashedline),andwithouteitherofthese effects—i.e.,theno-LSAPcase(the combined dashed/dottedline). Thescarcityeffectisthelargest forthefive-yearyieldatabout23basispointsandisslightlysmallerforthetwo-andten-yearyield atabout18and20basispoints,respectively. Theaggregatedurationeffectis larger for longer maturities: it is about6.5basispointsfor thetwo-yearyield;about8.7basispointsfortheten-year yield. ThemiddleandbottompanelsofTable5provideresultsfortherealtermpremium(RTP)andthe inflationriskpremium(IRP)componentsoflonger-termyields. Theestimatedregression specificationstaketheform: 25

(cid:1844)(cid:1846)(cid:1842) (cid:4666)(cid:1865)(cid:4667) (cid:3404) (cid:1853)(cid:3397)(cid:1854) (cid:1842)(cid:1834)(cid:1840)(cid:1846) (cid:4666)(cid:1865):2(cid:3398)10(cid:4667)(cid:3397)(cid:1854) (cid:1830)(cid:1833) (cid:3397)(cid:1854) (cid:3435)(cid:1877) (cid:4666)(cid:1865)(cid:4667)(cid:3398)(cid:1877) (cid:4666)2(cid:4667)(cid:3439), (cid:3047) (cid:2869) (cid:3047) (cid:2870) (cid:3047) (cid:2871) (cid:3047)(cid:2879)(cid:2869) (cid:3047)(cid:2879)(cid:2869) and: (cid:1835)(cid:1844)(cid:1842) (cid:4666)(cid:1865)(cid:4667) (cid:3404) (cid:1853)(cid:3397)(cid:1854) (cid:1842)(cid:1834)(cid:1840)(cid:1846) (cid:4666)(cid:1865):2(cid:3398)10(cid:4667)(cid:3397)(cid:1854) (cid:1830)(cid:1833) (cid:3397)(cid:1854) (cid:3435)(cid:1877) (cid:4666)(cid:1865)(cid:4667)(cid:3398)(cid:1877) (cid:4666)2(cid:4667)(cid:3439). (cid:3047) (cid:2869) (cid:3047) (cid:2870) (cid:3047) (cid:2871) (cid:3047)(cid:2879)(cid:2869) (cid:3047)(cid:2879)(cid:2869) InthespecificationwithRTPasthedependentvariable,thecoefficientsonbothscarcityand aggregatedurationarepositiveandstatisticallysignificantacrossallmaturities. Forthe specificationswiththeinflationriskpremiumasthedependentvariable,onlyaggregateduration seemstobeconsistentlysignificantacrossthedifferentmaturities. Further,comparisonofthe coefficientestimatesacrosstheregressionsrevealstheextenttowhichPHNTandDGimpactTP, thusconfirmingthatthebulkoftheresponseisintheRTPcomponent—asonewouldexpectif preferred-habitatmechanismsareoperative. InTable6,weshowthatourresultsarerobusttocontrollingforadditionalexplanatoryvariables. Theresultsinthetablealsoreflectourattempttoaddressapotentialsimultaneityproblem. Ifthe aggregatecharacteristicsofPHNT,suchasaveragematurityandduration,areinpartdrivenby macroeconomicvariables,thentheywouldlikelyhavepredictivecontentforlonger-termTreasury yieldsandtermpremiumsevenintheabsenceofastructuralrelationship. Inlightofthis consideration,weestimateregressionswithPHNTandDGasregressorsalongsidethefollowing variables:theAruoba-Diebold-Scotti(2009)index(whoseinclusionisameansofcontrollingfor real-timebusinessconditionsattheweeklyfrequency),32theweeklyaverageofintradaycorrelation betweenstockreturnsandchangesintheten-yearbondyield(so as tocontrolfor“flight-to-quality” episodes),33andTreasuryoption-impliedvolatility(tocontrolforinterest-rateuncertainty).34 Table 6presentsestimatesofthespecification (cid:1846)(cid:1842) (cid:4666)(cid:1865)(cid:4667) (cid:3404) (cid:1853)(cid:3397)(cid:1854) (cid:1842)(cid:1834)(cid:1840)(cid:1846) (cid:4666)(cid:1865):2(cid:3398)10(cid:4667)(cid:3397)(cid:1854) (cid:1830)(cid:1833) (cid:3397)(cid:1854) (cid:3435)(cid:1877) (cid:4666)(cid:1865)(cid:4667)(cid:3398)(cid:1877) (cid:4666)2(cid:4667)(cid:3439)(cid:3397)(cid:1854) (cid:1850) , (cid:3047) (cid:2869) (cid:3047) (cid:2870) (cid:3047) (cid:2871) (cid:3047)(cid:2879)(cid:2869) (cid:3047)(cid:2879)(cid:2869) (cid:2872) (cid:3047) whereX variesacrossspecificationsdependingonwhichofthethreecandidateadditional t explanatoryvariablesisbeingemployed. Theregressionresultsforthenominaltermpremiumandtherealtermpremiumindicatethatthe ————————————————————————————————————— 32 Inclusion of this variable amounts to an attempt to control for macroeconomic developments that are not already proxied by variation in the yield-slope regressor. 33 The rationale for this variable is that a “flight to quality” should feature falling equity prices and a marking-up of prices of Treasury securities, in response to investors’ shift from more risky assets into Treasury securities. This process should lead to a positive correlation between equity returns and Treasury yields. 34 This is measured by Merrill Lynch’s weighted average of implied volatilities of the two-year (20 percent), fiveyear (20 percent), ten-year (40 percent), and thirty-year (20 percent) Treasury securities. 26

coefficientsonscarcityanddurationremainpositiveandstatisticallysignificantafterincluding eachofthenewexplanatoryvariables. Moreover,thekeyestimatedcoefficientsarelittlealtered,as isclearbyacomparisonacrossthethreecolumnsforeachyield(witheachcolumncorrespondingto aspecificationwithaparticularadditionalexplanatoryvariable). Alsonoteworthyisthatthe specificationthatincludestheflight-to-qualityproxyistheequationwiththehighestexplanatory power. Thus,flight-to-qualityconsiderationswouldappeartobeanimportantfactorinthe determinationoflonger-termTreasuryrates. Moreimportantly,scarcityanddurationremainhighlysignificantevenaftercontrollingforthe flight-to-qualityproxy. KrishnamurthyandVissing-Jorgensen(2012)pointtotheflight-to-quality episodesasoccasionsonwhichthereisasharpincreaseintheutilityderivedfromthe “convenience”-stylevehiclessuchaslonger-termTreasurysecurities. Thisobservationmight suggestthatcontrollingforflighttoqualitycouldrenderinsignificantthevariablesdesignedto standinforpreferred-habitat-typeeffects,butthatisnotthecaseinourresults. Ourresultsalso suggest,consequently,thatforTreasurysecurities,absenceofdefaultriskisnotthemainsourceof preferred-habitatbehaviorormarketsegmentation.35 Inthecaseoftheregressionswiththeinflationriskpremiumasthedependentvariable,theresults aremoresensitivetotheinclusionoftheadditionalexplanatoryvariables. Inparticular,whenwe controlforTreasuryoption-impliedvolatility(seethefirstcolumnofeachtable),DGisnolonger statisticallysignificant,perhapsbecauseasinglevariableisanadequatestand-inforinterest-rate risk. Moreover,fortheseven-andten-yearyields,whenwecontrolfortheflight-to-qualityvariable orthebusinessconditionsindex,PHNTisnotsignificant. Finally,when,inthethirdcolumn,we controlforbusinessconditions,DGisnolongersignificantinexplaininglonger-termyield behavior. Moreimportantly,whenweintroduceadditionalexplanatoryvariables,theestimated coefficientonDGbecomesconsiderablysmallerwhilethatonPHNTisnotaffected. The sensitivityoftheseresultsfortheinflationriskpremiumsupportsthepositionthatthemainmeans throughwhichLSAPsimpactlonger-termyieldsisviatherealtermpremium. Onedifficultywiththeinterpretationofourbaselineregressionsisthatvariationsintheslopeofthe yieldcurveshouldpartlyreflecttheimpactofchangesinPHNTandDG. Thus,ourinclusionofa proxyforthisexplanatoryvariableintheregressionscouldbereducingtheestimatedeffectsof scarcityandduration,leadingtoanunderstatementoftheeffectsonlonger-termyieldsthatarise ————————————————————————————————————— 35 As stressed above, in preferred-habitat models, it is features other than the absence of default risk that make investment in longer-term securities attractive to certain investors. In particular, institutional investors tend to favor a fixed income stream that helps match the maturity of assets and liabilities. 27

fromLSAP-styleactions. Toaddressthisdifficulty,weattempttocontrolfortheinfluenceofthe slopefactorbyincludingavariablethatisnotdirectlyalteredbypurchasesoflonger-termTreasury securities. Inparticular,weemploytheslopeoftheswaptermstructureratherthanthatofTreasury yields.36AstheupperpanelofTable7shows,resultsarenotsubstantiallychangedbythe employmentofthisalternativemeasure;theestimatedcoefficientsonscarcityandonaggregate durationbothbecomemodestlysmaller.37 In a separate appendix, we present supplementary results that establish the robustness of our baseline estimates to variations in the specification and that also show that our proxies for scarcity and duration are important in accounting for the observed variations in fixed-income securities other than Treasury bonds. The appendix also presents estimated impact of our scarcity and duration variables on corporate bond rates, measured as zero-coupon yields obtained via the Nelson-Siegel (1987) yield curve approximation. Finally,thelowerpanelofTable7showstheresultsofourpreferredspecification: (cid:1846)(cid:1842) (cid:4666)(cid:1865)(cid:4667) (cid:3404) (cid:1853)(cid:3397)(cid:1854) (cid:1842)(cid:1834)(cid:1840)(cid:1846) (cid:4666)(cid:1865):2(cid:3398)10(cid:4667)(cid:3397)(cid:1854) (cid:1830)(cid:1833) (cid:3397)(cid:1854) (cid:3435)(cid:1871) (cid:4666)(cid:1865)(cid:4667)(cid:3398)(cid:1871) (cid:4666)2(cid:4667)(cid:3439)(cid:3397)(cid:1854) (cid:1850) . (cid:3047) (cid:2869) (cid:3047) (cid:2870) (cid:3047) (cid:2871) (cid:3047)(cid:2879)(cid:2869) (cid:3047)(cid:2879)(cid:2869) (cid:2872) (cid:3047)(cid:2879)(cid:2869) Thisspecificationincludesboththeslopeoftheswapyieldcurveand(astheX variable)theflightt to-qualityproxy,whichistheonlyotherexplanatoryvariablethatisstatisticallysignificantacross allmaturitiesandwhichgreatlyincreasestheexplanatorypoweroftheregression. 38 The magnitudeofthecoefficientestimatessuggeststhatpurchaseswithamaturitybetweentwoandten yearsthatreducePHNTbyonepercent—which,attheendofthefirstLSAPprogram,amountedto roughly$64billion—wouldbeassociatedonaveragewithaboutafivebasispointdecreasein yieldsofcomparablematurity. Thisestimateimpliesthatthescarcityeffectfromthefirstofthe TreasuryLSAPs(whichtotaled$300billion)wasabout23basispoints. Inaddition,aone-yeardecreaseintheaggregatedurationofTreasurysecuritiesheldbythepublicis estimatedtopushthefive-toten-yearyieldsabout100basispointslower. Asindicatedinsection ————————————————————————————————————— 36 On the other hand, we might expect the reaction of swap rates to changes in aggregate duration to be similar to that of longer-term Treasury securities. 37 The similarity to the previous estimates might be a result of transmission to other interest rates of responses of longer-term Treasury yields to LSAP-style operations. 38 The significance of the key parameter estimates is robust to the choice of length of the Newey-West lag window. The final regression in Table 7 has a coefficient on PHNT of 5.79 with standard error 1.45. This standard error only rises to 1.78 if instead fifty-two lags are used in calculating the Newey-West standard errors. Likewise, the standard error for the coefficient on the duration gap term rises from 15.8 to 18.4 if the Newey-West lag window becomes 52 weeks; this standard error is still small in relation to the coefficient estimate of 107.4. 28

5.1,thefirstLSAPprogramreducedaveragedurationby0.12years,whichinturntranslatesintoa 12basispointreductioninlonger-termTreasuryyields. Thus,thetotalimpactfromthefirstLSAP programwould,onthiscalculation,beabout35basispoints. Theseestimatesareaboutinlinewith theestimatesofD’AmicoandKing(2012)butlargerthantheestimatesreportedinGagnon,Raskin, Remache,andSack(2011). Similarly,ourresultssuggestthatthescarcityeffectfromthesecond LSAPprogramisabout35basispoints(takingintoaccountthefactthatattheendofthesecond LSAPprogramonepercentofPHNTamountedto$86billion)andthedurationeffectisabout10 basispoints,asthisprogram—althoughlargerindollarsizethanthefirstLSAPforTreasuries— removedonly0.1yearofdurationfromthemarketbecauseallthepurchaseswereconcentratedin thetwo-toten-yearsector. Thus,thetotaleffectonlonger-termTreasuryyieldsofthesecond LSAPprogramisestimatedtobeabout45basispoints. Ourresultsindicatethatthetwochannels werebothquantitativelysignificant,affectinglonger-termTreasuryyieldsinproportionssimilarto thosesuggestedbytheeventstudyinSection4. Itisnotablethatadifferentsampleperiodanda differentmethodologygenerateestimatesquitesimilartoD’AmicoandKing(2012),whoseresults wereobtainedfromdatacoveringtherecentcrisisperiod. Thisfindingsuggeststhatthestrainsin financialmarketscausedbythecrisiswerenotcrucialindeliveringtheeffectivenessofLSAPs. Rather,apictureemergesofsizableeffectsofLSAPsonlonger-termyieldsacrossdifferent samplesandalternativeestimationapproaches. 7. Conclusionsandimplications Forlonger-termTreasurysecurities,thefirstLSAPprogram(undertakenin2009)consistedof$300 billionofFederalReservepurchases,whilethesecondprogram(inlate2010tomid-2011) consistedof$600billionofpurchases. Ourpreferredestimatessuggestthat,takingscarcityand durationtogether,thefirstprogramofLSAPsreducedlonger-termTreasuryyieldsbyabout35 basispoints;thesecondprogram,largerindollaramountbutsmallerinitsimpactonduration, reducedlonger-termTreasuryyieldsbyabout45basispoints. Theseestimatesaresomewhat higherthanmostexistingestimatesintheliterature. Directcomparabilitywithotherestimatesin theliteratureisnotpossiblebecauseofdifferencesinmethodologyandsamplesacrosspapers. SeveralotherstudiesuseeventstudiesofLSAPratherthanregressionprocedures;wefocusonthe Treasurymarket,whilethefirstLSAPcoveredbothagencyandTreasurysecurities;andour estimatesarebasedonthepre-LSAPperiod,whilethepossibilityofstructuralchangesinmarkets, especiallyduringthefinancialcrisis,couldcomplicatethetaskofinferringwithprecisionthe effectsofLSAPsfromresultsbasedonanearliersample. Butanotherimportantreasonwhyour estimatesarehigherthanthoseinotherstudiesisthatweendeavortoestimateboththescarcityand durationeffectsofLSAP-stylepurchases,ratherthanoneortheothereffect. 29

Judgedbyourestimates,eachLSAPprogramamountedtoasubstantialmonetarypolicyeasing. A quantification oftheeasingisprovidedbyconsideringwhatdegreeoffederalfundsratemovement would,inthepre-2008positivefundsrateenvironment,havebeenrequiredtogeneratesucha responseoflonger-termTreasuryyields. Bernanke(2011b)andChung,Laforte,Reifschneider, andWilliams(2012) suggestthata25basispointchangeintheTreasury bondrateisonaverage associatedwitharoughly100basispointchangeinthefederalfundsrate.39Appliedtoour estimates,thisruleofthumbsuggeststhefirstTreasury LSAPprogramwastantamounttoafederal fundsratecutofabout140basispoints;thesecondprogram,toacutofabout180basispoints. OurresultsthusaffirmthepotencyofLSAPsasamonetarypolicytool. Thisinturnhasimportant implicationsforthedirectioninwhichthebuildingofmodelsformonetarypolicyanalysisshould go,especiallywhentakeninconjunctionwithpreviousfindingsfortheUnitedStates(notedinthe introduction)andfortheUnitedKingdom(seeJoyce,Lasaosa,Stevens,andTong,2011). Our empiricalresultssuggestthatLSAPsdonotoperatesolelyorevenprimarilyviatheexpectations channel.40Accordingly,macroeconomicmodelsthatpermitLSAP-styleoperationstomatterfor long-termratesonlytotheextentthattheysignalfutureshort-termpolicyratesdonotadequately encompasstheeffectsofLSAPs. Arethinkingofthespecificationinmacroeconomicmodelsof termstructurebehaviorseemstobecalledfor.41Inparticular,itappearsthatdeparturesfromthe representativeagent/investorframeworkarerequired,sothatmodelsusedformonetarypolicy analysisdevelopinadirectionthatadmitspreferred-habitatelements. Ourestimatessuggestthat therequiredelementscomprisenotonlythescarcitychannelemphasizedinthetraditional preferred-habitatliterature,butthedurationchannelhighlightedbyVayanosandVila(2009). Moreover,itdoesnotappeartobethecasethatsuchmodificationsareonlynecessaryforanalyses inwhichtheshort-termpolicyrateisatthezerolowerbound. Rather,becauseourresultsarisefrom evidencefromdatapointslargelyaccumulatedpriorto2008,preferred-habitatelementsappearto beanecessarymodelingredientinobtainingabetterunderstandingofmonetarypolicy transmission even when short-term rates are away from the zero lower bound. ————————————————————————————————————— 39 See also Rudebusch (2010). This conversion factor is based on an OLS regression of the first difference of the ten-year rate on the first-difference of the funds rate. Such a regression is reported in Chung, Laforte, Reifschneider, and Williams (2012, p. 68). Clearly, this procedure does raise a number of econometric issues and comes with many caveats. We note, however, that the “25 basis point on the longer-term rate for a 100 basis points on the short rate” rule is also implied by Evans and Marshall’s (1998, p. 68) VAR-based estimates of the effect of monetary policy shocks on the term structure of interest rates. 40 Recall that we found significant coefficients on scarcity and duration in our regressions even when conditioning on proxies for expectations of the short-term policy rate. 41 This would also likely entail modifications to the IS function as well as term structure equations. For some suggestions about how to modify the IS equation of dynamic general equilibrium models to allow for an explicit influence of longer-term interest rates on spending decisions, see Andrés, López-Salido, and Nelson (2004), and for a recent extension, see Chen, Cúrdia, and Ferrero (2012). 30

References Andrés,Javier,DavidLópez-Salido,andEdwardNelson(2004). “Tobin’sImperfectAsset SubstitutioninOptimizingGeneralEquilibrium,”JournalofMoney,CreditandBanking,Vol. 36(4),665690. Aruoba,S.Boragan,FrancisX.Diebold,andChiaraScotti(2009). “Real-TimeMeasurementof BusinessConditions,”JournalofBusinessandEconomicStatistics,Vol.27(4),417427. Ascheim,Joseph(1961). TechniquesofMonetaryControl. Baltimore,MD:JohnsHopkins UniversityPress. Bauer,MichaelD.,andGlennD.Rudebusch(2011). “TheSignalingChannelforFederalReserve BondPurchases.” FederalReserveBankofSanFranciscoWorkingPaper201121. Bernanke,BenS.(2002). “Deflation:MakingSure‘It’Doesn’tHappenHere.” RemarksBefore theNationalEconomistsClub,Washington,D.C.,November21. Bernanke,BenS.(2010). “TheEconomicOutlookandMonetaryPolicy.” SpeechatFederal ReserveBankofKansasCitySymposiumon“MacroeconomicChallenges:TheDecadeAhead,” JacksonHole,MO. August28. Bernanke,BenS.(2011a). “Testimony:SemiannualMonetaryPolicyReporttotheCongress beforetheCommitteeonBanking,Housing,andUrbanAffairs,U.S.Senate.” March1. Bernanke,BenS.(2011b). “Testimony:SemiannualMonetaryPolicyReporttotheCongress beforetheCommitteeonFinancialServices,U.S.HouseofRepresentatives.” July13. Bernanke,BenS.,VincentR.Reinhart,andBrianP.Sack(2004). “MonetaryPolicyAlternativesat theZeroBound:AnEmpiricalAssessment,”BrookingsPapersonEconomicActivity,Vol.35(2), 178. BoardofGovernorsoftheFederalReserveSystem(19451980). AnnualReport,variousyears. Washington,D.C.:FederalReserveBoard. BrookingsInstitution(1978). “GeneralDiscussion,”BrookingsPapersonEconomicActivity,Vol. 9(3),650654. Chen,Han,VascoCúrdia,andAndreaFerrero(2012). “TheMacroeconomicEffectsofLarge- ScaleAssetPurchasePrograms,” Economic Journal, Vol. 122(564), F289F315. 31

Chung,Hess,Jean-PhilippeLaforte,DavidReifschneider,andJohnC.Williams(2012). “HaveWe UnderestimatedtheLikelihoodandSeverityofZeroLowerBoundEvents?,”JournalofMoney, CreditandBanking,Vol.44(S1),4782. Committee on Banking, Housing and Urban Affairs, U.S. Senate (1992). United States Trade Policy and the Economy: Hearings. Washington, D.C.: Government Printing Office. Conard,JosephW.(1959). AnIntroductiontotheTheoryofInterest. Berkeley,CA:Universityof CaliforniaPress. Cooper,RobertL.(1967). “TechniquesoftheFederalReserveTradingDeskinthe1960s Contrastedwiththe‘Bills-Preferably’Period.” StaffStudyNo.6, JointTreasury-FederalReserve StudyoftheU.S.GovernmentSecuritiesMarket. Culbertson,JohnM.(1957). “TheTermStructureofInterestRates,”QuarterlyJournalof Economics,Vol.71(4),485517. Culbertson,JohnM.(1973). “AlternativesforDebtManagement:Discussion.” FederalReserve BankofBoston,IssuesinFederalDebtManagement:ProceedingsofaConferenceHeldatMelvin Village,NewHampshire,June,1973. Boston,MA:FederalReserveBankofBoston. 3038. D’Amico, Stefania, and Thomas B. King (2012). “Flow and Stock Effects of Large-Scale Treasury Purchases: Evidence on the Importance of Local Supply,” Journal of Financial Economics, forthcoming. D’Amico,Stefania,DonH.Kim,andMinWei(2008). “TipsfromTIPS:TheInformational ContentofTreasuryInflation-ProtectedSecurityPrices.” FederalReserveBoardFinanceand Economics Discussion Series No. 200830. Davis,RichardG.(1982). “MonetaryTargetingina‘ZeroBalance’World:Commentsbythe Author.” InFederalReserveBankofSanFrancisco,InterestRateDeregulationandMonetary Policy:AsilomarConference. SanFrancisco,CA:FederalReserveBankofSanFrancisco. 5260. Eggertsson,GautiB.,andMichaelWoodford(2003). “TheZeroBoundonInterestRatesand Optimal Monetary Policy,” Brookings Papers on Economic Activity, Vol. 34(1), 139211. Estrella,Arturo,andGikasA.Hardouvelis(1991). “TheTermStructureasaPredictorofReal EconomicActivity,”JournalofFinance,Vol.46(2),555576. 32

Evans,CharlesL.,andDavidA.Marshall(1998). “MonetaryPolicyandtheTermStructureof NominalInterestRates:EvidenceandTheory,”Carnegie-RochesterConferenceSeriesonPublic Policy,Vol.49(1),53111. Fama,EugeneF.,andRobertR.Bliss(1987). “TheInformationinLong-MaturityForwardRates,” AmericanEconomicReview,Vol.77(4),680692. FederalOpenMarketCommittee(1961). “OpenMarketCommitteeAnnouncement[February20, 1961],”FederalReserveBulletin(February),Vol.47(2),p.165. FederalOpenMarketCommittee(2009). “FOMCStatement,March18,2009.” www.federalreserve.gov. Federal Reserve (2008). “Press Release, November 25, 2008.” www.federalreserve.gov. FederalReserveBoard(1966). “TimeDepositsandFinancialFlows,”FederalReserveBulletin (December),Vol.52(12),17381752. FinancialTimes,EconomicCorrespondent(1960). “MenandMeasuresfortheKennedy Administration.” December29. p.6. FirstNationalCityBankofNewYork(1959). MonthlyNewsletter:BusinessandEconomic Conditions. October. Friedman,BenjaminM.(1978). “CrowdingOutorCrowdingIn? EconomicConsequencesof Financing Government Deficits,” Brookings Papers on Economic Activity, Vol. 9(3), 593641. Friedman,Milton,andAnnaJ.Schwartz(1963). AMonetaryHistoryoftheUnitedStates, 18671960. Princeton,N.J.:PrincetonUniversityPress. Gagnon,Joseph,MatthewRaskin,JulieRemache,andBrianSack(2011). “Large-ScaleAsset PurchasesbytheFederalReserve:DidTheyWork?,”FederalReserveBankofNewYorkEconomic PolicyReview,Vol.17(1),4159. Greenwood,Robin,andDimitriVayanos(2010). “BondSupplyandExcessBondReturns.” Manuscript,LondonSchoolofEconomics,August. Hamilton,JamesD.,andJingCynthiaWu(2012). “TheEffectivenessofAlternativeMonetary PolicyToolsinaZeroLowerBoundEnvironment,”JournalofMoney,CreditandBanking,Vol. 44(S1),346. 33

Joint Economic Committee (1992). The 1992 Economic Report of the President: Hearings. Washington, D.C.: Government Printing Office. Joyce,Michael,AnaLasaosa,IbrahimStevens,andMatthewTong(2011). “TheFinancialMarket ImpactofQuantitativeEasing,”InternationalJournalofCentralBanking,Vol.6(3),113161. Kim,DonH.,andAthanasiosOrphanides(2005). “TermStructureEstimationwithSurveyDataon InterestRateForecasts.” FederalReserveBoardFinanceandEconomicsDiscussionSeriesNo. 200548. Kim,DonH.,andJonathanH.Wright(2005).“AnArbitrage-FreeThree-FactorTermStructure ModelandtheRecentBehaviorofLong-TermYieldsandDistant-HorizonForwardRates.” FederalReserveBoardFinanceandEconomicsDiscussionSeriesNo.200533. King,MervynA.(1999). “ChallengesforMonetaryPolicy:NewandOld.” InFederalReserve BankofKansasCity,NewChallengesforMonetaryPolicy. KansasCity,MO:FederalReserve BankofKansasCity. 1157. King,RobertG.(1994). “Commenton‘TowardaModernMacroeconomicModelUsablefor Policy Analysis,’” NBER Macroeconomics Annual, Vol. 9(1), 118129. Kohn,DonaldL.(2009). “MonetaryPolicyResearchandtheFinancialCrisis:Strengthsand Shortcomings.” SpeechattheConferenceonKeyDevelopmentsinMonetaryEconomics, Washington,D.C.,October9. Krishnamurthy, Arvind, and Annette Vissing-Jorgensen (2011). “The Effects of Quantitative Easing on Interest Rates: Channels and Implications for Policy,” Brookings Papers on Economic Activity, Vol. 42(2), 215265. Krishnamurthy,Arvind,andAnnetteVissing-Jorgensen(2012). “TheAggregateDemandfor TreasuryDebt,”Journal of Political Economy, Vol. 120(1), 233267. Lucas,RobertE.,Jr.(1987). ModelsofBusinessCycles. Oxford,U.K.:BasilBlackwell. Marty,AlvinL.(1962). “BookReview:TechniquesofMonetaryControl,”JournalofPolitical Economy,Vol.70(2),207208. Meigs,A.James(1972). MoneyMatters:Economics,Markets,Politics. NewYork:Harperand Row. 34

Meltzer,AllanH.(2009). AHistoryoftheFederalReserve,Volume2,Book2. Chicago:University ofChicagoPress. Meulendyke,Ann-Marie(1998). U.S.MonetaryPolicyandFinancialMarkets. NewYork: FederalReserveBankofNewYork. Mishkin,FredericS.(1978). “Efficient-MarketsTheory:ImplicationsforMonetaryPolicy,” BrookingsPapersonEconomicActivity,Vol.9(3),707752. Modigliani,Franco,andRichardC.Sutch(1966). “InnovationsinInterest RatePolicy,”American EconomicReview,Vol.56(1),178197. Modigliani,Franco,andRichardC.Sutch(1967). “DebtManagementandtheTermStructureof InterestRates:AnEmpiricalAnalysisofRecentExperience,”JournalofPoliticalEconomy,Vol. 75(4)(Supplement),569589. Morris,FrankE.(1968). “TheChicagoSchoolAsViewedfromBoston,”BusinessEconomics, Vol.3(2),2326. Nelson,CharlesR.,andAndrewF.Siegel(1987). “ParsimoniousModelingofYieldCurves,” JournalofBusiness,Vol.60(4),473489. Newey,WhitneyK.,andKennethD.West(1987).“ASimple,PositiveSemi-Definite, HeteroskedasticityandAutocorrelationConsistentCovarianceMatrix,”Econometrica,Vol.55(3), 703708. Pierce,JamesL.(1974). “QuantitativeAnalysisforDecisionsattheFederalReserve,”Annalsof EconomicandSocialMeasurement,Vol.3(1),1120. Plosser,CharlesI.(1982). “GovernmentFinancingDecisionsandAssetReturns,”Journalof MonetaryEconomics,Vol.9(3),325352. Riefler,WinfieldW.(1958a). “OpenMarketOperationsinLong-TermSecurities,”Federal ReserveBulletin,Vol.44(11),12601274. Riefler,WinfieldW.(1958b). “ShouldtheFederalReserveBuyLong-TermSecurities?” Manuscript,FederalReserveBoard;presentedattheFederalReserveBankofMinneapolisMoney andBankingWorkshop,May3. 35

Romer,ChristinaD.,andDavidH.Romer(1993). “CreditChannelsorCreditActions?: An InterpretationofthePostwarTransmissionMechanism.” InFederalReserveBankofKansasCity, ChangingCapitalMarkets:ImplicationsforMonetaryPolicy. KansasCity,MO:FederalReserve BankofKansasCity.71116. Rotemberg,JulioJ.,andMichaelWoodford(1999). “InterestRateRulesinanEstimatedSticky PriceModel.” InJ.B.Taylor(ed.),MonetaryPolicyRules. Chicago:UniversityofChicagoPress. 57119. Rudebusch, Glenn D. (2010). “The Fed’s Exit Strategy for Monetary Policy,” Federal Reserve Bank of San Francisco Weekly Letter, June 14. Svensson,LarsE.O.(1995). “EstimatingForwardInterestRateswiththeExtendedNelsonand SiegelMethod,”SverigesRiksbankQuarterlyReview,Vol.17(3),1326. Swanson, Eric T. (2011). “Let’s Twist Again: A High Frequency Event-Study Analysis of Operation Twist and Its Implications for QE2,” Brookings Papers on Economic Activity, Vol. 42(1),151188. Thomas,Woodlief(1947). “TheHeritageofWarFinance,”AmericanEconomicReview(Papers andProceedings),Vol.37(2),205215. Tobin,James(1961). “Money,Capital,andOtherStoresofValue,”AmericanEconomicReview (PapersandProceedings),Vol.51(2),2637. Tobin,James(1963). “AnEssayonthePrinciplesofDebtManagement.” InCommissionon MoneyandCredit,FiscalandDebtManagementPolicies. EnglewoodCliffs,N.J.:PrenticeHall. 143218. Tobin,James(1974). The New Economics One Decade Older. Princeton, N.J.: Princeton University Press. Vayanos,Dimitri,andJean-LucVila(2009). “APreferred-HabitatModeloftheTermStructureof InterestRates.” NBERWorkingPaperNo.15487. Wallace,NeilA.(1967). “TheTermStructureofInterestRatesandtheMaturityCompositionof theFederalDebt,”JournalofFinance,Vol.22(2),301312. Walsh,CarlE.(1982). “AssetSubstitutabilityandMonetaryPolicy:AnAlternative Characterization,”JournalofMonetaryEconomics,Vol.9(1),5971. 36

Williams,JohnL.(2011). “UnconventionalMonetaryPolicy:LessonsfromthePastThreeYears.” PresentationtotheSwissNationalBankResearchConference,Zurich,September23. Yellen,Janet(2011). “UnconventionalMonetaryPolicyandCentralBankCommunications.” SpeechattheU.S.MonetaryPolicyForum,NewYork,February25. Young,RalphA.,andCharlesA.Yager(1960). “TheEconomicsof‘BillsPreferably,’”Quarterly JournalofEconomics,Vol.74(3),341373. 37

Table1.Behaviorofselectedlonger-termyieldsonAugust10,2010 Simple returns (%) (1) 1.55p.m. (2) 2.35 p.m. Years to maturity Maturity date 2.35 p.m. 3.35 p.m. (2)/(1) (1) 9.51 2/15/2020 0.44 0.08 18.9% (2) 10.01 8/15/2020 0.45 0.09 20.1% (3) 14.26 11/15/2024 0.64 0.42 65.7% (4) 14.52 2/15/2025 0.65 0.43 66.2% 38

Table 2. Correlation matrix for nominal yields, maturity buckets, and duration Sample Period: 2002:122008:10 Buckets/Yields 2-yr. 5-yr. 7-yr. 10-yr. 15-yr. 20-yr. 25-yr. 30-yr. PHNT(m: 24) t 0.92 0.85 0.75      PHNT(m: 68) t 0.53 0.42 0.35      PHNT(m: 810) t 0.60 0.51 0.42      PHNT(m: 1012) t 0.58 0.47 0.34      PHNT(m: 1214) t 0.61 0.55 0.44      PHNT(m: 1618) t 0.48 0.37 0.31      PHNT(m: 1820) t 0.75 0.66 0.54      PHNT(m: 2224) t 0.29 0.18 0.12      PHNT(m: 2426) t 0.55 0.42 0.34      PHNT(m: 2628) t 0.87 0.78 0.67      Duration Gap t 0.15 0.01 0.13      Sample Period: 2008:112011:2 PHNT(m: 24) t         PHNT(m: 68) t         PHNT(m: 810) t         PHNT(m: 1012) t         PHNT(m: 1214) t         PHNT(m: 1618) t         PHNT(m: 1820) t         PHNT(m: 2224) t         PHNT(m: 2426) t         PHNT(m: ) t         Duration Gap t         Note: The buckets contain privately-held nominal Treasury securities outstanding grouped by maturity class, and the Treasury yields are zero-coupon rates obtained by fitting the Svensson (1995) yield curve approximation. 39

Table3.Baselinespecification Regressors 7-year 10-year 15-year 20-year 25-year 30-year PHNT(m: 210) t     Duration Gap t     [y(m)  y(2)] t1     PHNT(m: 1430) t         Duration Gap t         [y(10)y(2)]     t1     Adjusted R2       Note: The regressions estimated take the form: y(m) t = a + b·PHNT(m: 210) t + c·DurationGap t + d·[y(m) y(2)] t1 The dependent variable is the nominal yield of maturity m (obtained by fitting the Svensson (1995) yield curve approximation). The regressors are two policy-related variables, privately-held nominal Treasuries (PHNT) as percentage of total Treasury debt outstanding (TDO) and the duration gap defined as the difference between aggregate duration risk (ADR) and the duration of the on-the-run 10-year Treasury notes. Finally the yield spread is included to proxy the slope of the yield curve. The sample period consists of weekly data from December 2002 until October 2008. Standard errors are computed using Newey-West (1987) procedure allowing for four lags. 40

Table4.Extensionsofthebaselinespecification Regressors 7-year 10-year 15-year 20-year 25-year PHNT(m: 46) t   PHNT(m: 68) t     PHNT(m: 810) t     PHNT(m: 1012) t   Duration Gap t     [y(m) y(2)] t     PHNT(m: 1214) t   PHNT(m: 1416) t   PHNT(m: 1618) t   PHNT(m: 1820) t   PHNT(m: 2022) t   PHNT(m: 2224) t     PHNT(m: 2426) t   PHNT(m: 2628) t   Duration Gap t        [y(10) y(2)] t1       Adjusted R2      Note: See notes for Table 3 for further details on the estimated specifications. 41

Table5.Estimatesoftermpremiumspecification Dependent variable: Nominal term premium for maturity: Regressors 2-year 5-year 7-year 10-year PHNT(m: 210) t 3.98 5.11 4.63 4.34 (1.05) (1.32) (1.44) (1.48) Duration Gap t 93.15 120.32 122.59 123.47 (16.51) (17.34) (18.75) (19.41) [y(m) y(2)] t1 0.21 0.32 0.26 0.24 (0.04) (0.06) (0.04) (0.03) R2 0.35 0.45 0.51 0.60 Dependent variable: Real term premium for maturity: 2-year 5-year 7-year 10-year PHNT(m: 210) t 2.64 3.78 3.73 3.63 (0.58) (0.81) (0.87) (0.92) Duration Gap t 62.76 93.17 97.89 99.93 (7.09) (10.06) (11.19) (12.06) [y(m)  y(2)] t1 0.11 0.11 0.09 0.11 (0.02) (0.03) (0.02) (0.02) Adjusted R2 0.45 0.44 0.44 0.48 Dependent variable: Inflation risk premium for maturity: 2-year 5-year 7-year 10-year PHNT(m: 210) t 1.33 1.33 0.90 0.71 (0.58) (0.67) (0.73) (0.75) Duration Gap t 30.38 27.14 24.69 23.54 (12.19) (11.69) (12.15) (12.16) [y(m) y(2)] t1 0.11 0.21 0.16 0.14 (0.03) (0.03) (0.03) (0.02) Adjusted R2 0.21 0.51 0.59 0.66 Note: The regressions are of the form: z(m) t = a + b·PHNT(m: 210) t + c·DurationGap t + d·[y(m) y(2)] t where the dependent variable, z(m) t , is equal to the nominal term premium, the real term premium, and the inflation risk premium, respectively. The decomposition of the yields among real term premium and inflation risk premium is based on a Gaussian three factors model described in D’Amico, Kim, and Wei (2008) using TIPS. See Table 1 for further description of the regressors and the specification. In the case of the two-year term premium, the slope regressor is defined in relation to the one-year yield. 42

Table 6. Term premium regression: sensitivity analysis (additional explanatory variables) Term Premium, Scarcity, and Duration Left-hand side variable: Nominal Term Premium 2-year 5-year 7-year 10-year (1) (2) 3) 1) 2) 3) 1) 2) 3) 1) 2) 3) PHNT t 4.35 3.07 4.37 5.89 4.02 5.38 5.24 3.65 4.78 4.63 3.49 4.40 (1.07) (1.08) (1.11) (1.37) 1.33) 1.40) (1.52) (1.37) 1.50) (1.57) (1.35) (1.51) DG t 49.96 73.15 63.98 81.88 97.99 91.55 91.40 101.30 96.23 99.78 104.60 100.60 14.19) 14.12) 16.18) 15.81) 16.17) 18.37) 17.23) (16.85) 18.96) 17.92) (16.83) (18.74) y(m)y(2) 0.27 0.10 0.15 0.53 0.32 0.36 0.42 0.31 0.33 0.37 0.31 0.32 0.07) 0.05) 0.06) 0.09) 0.06) 0.07) 0.07) 0.04) 0.05) 0.05) 0.03) 0.04) Adj. R2 0.35 0.40 0.29 0.47 0.52 0.43 0.59 0.65 0.57 0.71 0.76 0.71 Left-hand side variable: Real Term Premium PHNT t 2.84 2.46 3.00 4.03 3.54 4.09 3.88 3.56 4.04 3.57 3.50 3.89 0.58) 0.52) 0.54) 0.87) 0.77) 0.79) 0.97) 0.83) 0.87) 1.04) 0.88) 0.93) DG t 55.93 60.36 56.68 88.84 90.48 88.17 96.05 95.85 93.85 100.40 98.43 96.92 7.23) 6.32) 6.97) 9.78) 9.53) 9.93) 10.94) 10.64) 11.03) 11.88) 11.56) 11.91) y(m)y(2) 0.15 0.12 0.14 0.15 0.12 0.13 0.11 0.11 0.11 0.10 0.12 0.12 0.04) 0.02) 0.03) 0.05) 0.03) 0.04) 0.04) 0.02) 0.03) 0.03) 0.02) 0.02) Adj. R2 0.47 0.55 0.49 0.44 0.50 0.45 0.43 0.49 0.45 0.47 0.52 0.48 43

Table 6 (continued). term premium regression: sensitivity analysis (additional explanatory variables) Term Premium, Scarcity, and Duration Left-hand side variable: Inflation Risk Premium 2-year 5-year 7-year 10-year 1) 2) 3) 1) 2) 3) 1) 2) 3) 1) 2) 3) PHNT t 1.92 1.08 1.54 2.16 1.05 1.58 1.79 0.70 1.17 1.54 0.56 0.99 0.53) 0.51) 0.58) 0.59) 0.59) 0.66) 0.69) 0.67) 0.75) 0.74) 0.68) 0.77) DG t 10.57 26.97 26.88 12.88 23.93 23.15 13.99 22.29 21.18 15.82 21.75 20.37 9.80) 10.76) 12.49) 9.32) 10.28) 11.86) 10.11) 10.69) 12.24) 10.55) 10.71) 12.19) y(m)y(2) 0.24 0.12 0.12 0.36 0.22 0.23 0.26 0.17 0.18 0.21 0.15 0.15 0.04) (0.03) (0.03) 0.05) (0.03) (0.04) (0.03) 0.02) 0.03) 0.03) 0.02) 0.02) Adj. R2 0.36 0.37 0.22 0.60 0.61 0.53 0.64 0.67 0.59 0.69 0.72 0.66 Note: The regressions are of the form: z(m) t = a + b·PHNT(m: 210) t + c·DurationGap t + d[y(m)y(2)] t1 + δ·X t1 + u t where the dependent variable, z(m) t , is equal to the nominal term premium, the real term premium, and the inflation risk premium, respectively. In column (1) the variable X is the Treasury option implied volatility, in column (2) the variable X is the weekly average of the intraday correlation between the ten-year yield changes and the returns on the S&P500, and in column (3) the variable X is the Auroba, Diebold, and Schotti index of business conditions. See Table 3 for details. 44

Table7.Termpremiumspecificationswithadditionalregressors Dependent variable: Nominal term premium for maturity: Regressors 2-year 5-year 7-year 10-year PHNT(m: 2-10) t 3.99 5.43 5.89 6.19 (1.45) (1.61) (1.60) (1.55) Duration Gap t 91.51 113.46 115.17 112.31 (18.04) (18.70) (18.47) (17.67) [s(m)  s(2)] t1 0.12 0.21 0.27 0.34 (0.05) (0.05) (0.05) (0.05) Adjusted R2 0.22 0.39 0.55 0.60 Dependent variable: Nominal term premium for maturity: PHNT(m: 2-10) t 3.56 4.98 5.45 5.79 (1.31) (1.48) (1.49) (1.45) Duration Gap t 86.30 107.97 109.88 107.43 (15.75) (16.44) (16.37) (15.84) [s(m)  s(2)] t1 0.14 0.22 0.28 0.36 (0.04) (0.04) (0.04) (0.04) [corr(d10y, S&P500ret] t1     (0.05) (0.06) (0.06) (0.05) Adjusted R2 0.43 0.52 0.60 0.69 Note: The regressions are of the form: z(m) t = a + b·PHNT(m: 210) t + c·DurationGap t + d·[s(m) s(2)] t1 + δ·[corr(d10y, S&P500ret] t1 where the dependent variable, z(m) t , is the nominal term premium. In the upper part of the table, we control only for the slope of the swap yield curve, setting  = 0. In the lower part of the table, we allow for nonzero  by entering the weekly average of the intraday correlation between ten-year yield changes and S&P500 returns as a proxy for flight to quality. 45

Appendix: Robustness checks The estimated specifications presented in the main body of the paper covered different dependent variables (corresponding to different Treasury maturities), but used similar regressor sets. A natural means of ascertaining the robustness of the results of this set of estimates is to reestimate the specifications using the seemingly unrelated regression (SUR) estimation procedure. The error terms of the specifications are likely correlated with each other, and the implied contemporaneous relation between the errors can be exploited in estimation. We can apply the SUR estimator to generate more efficient parameter estimates than those obtained by application of OLS to each equation separately. At the same time, however, the estimates now rest on the assumption that the disturbance term in each equation is conditionally homoskedastic and free of serial correlation—an assumption that may not be valid for the specifications we consider. The results are reported in Table 8 for the most basic specification, which incorporates as regressors only our proxies for scarcity and for aggregate duration, and in Table 9 for the specification in which we also control for the slope of the overnight index swap (OIS) curve. As will become apparent later (in our discussion of Table 12’s results), the OIS slope is likely to be a better stand-in (compared with the swap and Treasury curve slopes) for additional policy and aggregate economic factors that may bear on the determination of Treasury yields (for a given path of LSAP-style purchases).42 When we do not control for any proxy for term structure slope, the estimated coefficients on LSAP-related terms in the regressions for the medium-term Treasury yields are somewhat larger, most likely capturing the impact of the omitted policy and macroeconomic variables. The scarcity term remains positive and significant, with the exception of the regression for the fifteen-year Treasury yield. Duration terms continue to be positive and significant across all maturities, although for both specifications shown in Table 8 and 9, the size of the estimated coefficients for the aggregate duration is much smaller across all maturities. Table 10 displays estimates for a specification very like those reported in Table 4. The results in Table 10 cover two-year-wide buckets with maturities within a few years of the yield’s maturity, though now applying the SUR estimator and using the OIS slope as a regressor. The only major difference from the previous results is that in the regression for fifteen-year Treasury yields, the key coefficient estimates are negative; this anomaly may reflect the difficulty of obtaining reliable estimates on a thinner maturity bucket. ————————————————————————————————————— 42 A caveat about using the OIS slope, however, is that the market underlying this series is less deep than the Treasury market, especially beyond the eighteen-month horizon. 46

We now consider results for the nominal term-premium (TP) component of the Treasury yields, when the scarcity proxy is expressed as a percentage of GDP rather than of total debt outstanding (TDO). Table 11 reports the results for the following regression: TP (m) = a + b (BUCKET(m: 210) / GDP) + b DG + b (s (m) – s (2)) + b X, t 1 t 2 t 3 t1 t1 4 t where BUCKET(m: 210) is the variable that appears as the numerator in the definition of PHNT(m: 210), GDP is quarterly nominal GDP (expressed at an annual rate) interpolated to weekly data, and (cid:1850) is the flight-to-quality proxy. We use this specification to provide an (cid:3047) interpretation of the impact of the first series of LSAPs. Note that the Table 7 results take the policy variable to be Treasury securities outstanding at two-to-ten-year maturities as a share of total government debt, while the Table 11 results instead scale these securities holdings by nominal GDP. A one-point change in the policy variable in Table 7 would imply a decrease in bond yields of about 5 basis points, and a one-point change in the policy variable in Table 11 implies a decrease in bond yields of about 20 basis points. As nominal GDP is roughly double the stock of Treasury debt outstanding,43 the Table 11 results imply a bond yield reaction about double that implied by Table 4, for the same scale of asset purchase. To consider further the importance of our scarcity and aggregate duration proxies, we turn our attention to other fixed-income securities besides Treasury bonds. Tables 12 and 13 provide results for regressions in which the dependent variables are the OIS rates and swap yields, respectively. Specifically, due to data availability and the liquidity of the OIS yields, the first three columns of Table 12 show the estimated coefficients for cases in which the dependent variable corresponds to the two- or five-year yields, while the final two columns show the estimated coefficients in specifications for the two- and five-year Treasury-OIS spread. The estimated coefficients on scarcity are not statistically significant, while those on aggregate duration are both positive and statistically significant. This suggests that the OIS rates are affected by the LSAPs only via the aggregate-duration channel. Results for the spreads, on the other hand, suggest that both our proxies are positive and statistically significant. For the swap yields, both scarcity and duration variables are found to be significant across maturities. Table 14 presents the correlation matrix between A- and BBB-rated corporate bond yields and our proxies for scarcity and aggregate duration. The table shows that all the A-rated corporate yields have a large and positive correlation with the two-to-ten-year bucket, although the ————————————————————————————————————— 43 One percent of 2008’s nominal GDP was about $140 billion, and as noted in the text, one percent of TDO as of the first LSAP was about $66 billion. 47

correlation for the most long-maturity bonds is half that for the medium-term bonds, perhaps suggesting a certain degree of imperfect substitution. A similar pattern is observed in the results for BBB-rated bonds, with the difference that the very long-maturity bonds display an even smaller correlation. However, all series exhibit a negative correlation with the fourteen-to-thirtyyear category, although for the very long-term bond yields it is close to zero. Table 15 reports the results for our preferred specification (used in Table 7) in which the dependent variables are now the A- and Bbb-rated corporate rates at various maturities. The estimated coefficients for PHNT are all positive and statistically significant, suggesting that the t scarcity channel plays an important role in yield determination for this asset class, while the estimated coefficients on DG and the flight-to-quality proxy are not statistically significant. t This might suggest a limited role for the risk channel and safety channel, at least as encapsulated by these variables. If, proceeding as before, we add the lagged (prior-week) value of Treasury interest-rate volatility as a regressor—so as to capture the notion that a generally more risky bond market atmosphere pushes up rates—we obtain significant and positive coefficients on the scarcity and duration terms. This is shown in our final table, Table 16, whose results indicate that the volatility term is also significant. These results indicate, however, that there is certainly room for additional work to improve our understanding of the transmission mechanism to other asset classes. 48

Table 8. Seemingly unrelated regression estimates Dependent variable: Nominal yield on Treasury security for maturity: Regressors 7-year 10-year 15-year 20-year 25-year 30-year PHNT(m: 210) 10.43 5.23 t (0.47) (0.27) PHNT(m: 1430) 0.48 6.11 9.11 10.27 t (0.38) (0.47) (0.58) (0.69) Duration Gap 206.23 157.59 112.48 88.97 89.75 103.25 t (13.61) (10.13) (10.05) (10.97) (11.87) (12.79) Adjusted R2 0.59 0.46 0.33 0.44 0.55 0.60 Note: The estimated specifications take the form: y(m) = a + b·PHNT + c·Duration Gap . t t t The dependent variable is the nominal yield (obtained using yield-curve estimates derived using the Svensson (1995) procedure) on Treasury security of the indicated maturity m. The regressors consist of two policy-related variables: privately-held nominal Treasury securities (PHNT) (for maturities of either 210 or 1430 years), expressed as a percentage of total Treasury debt outstanding (TDO); and the duration gap, defined as the difference between aggregate duration risk (ADR) and the duration of on-therun ten-year Treasury notes. The sample period is weekly, from December 2002 to October 2008. The regressions have been estimated by the seemingly unrelated regression technique in order to take into account correlation among error terms, and we specified in estimation that small-sample statistics be computed. 49

Table 9. Further seemingly unrelated regression estimates Dependent variable: Nominal yield on Treasury security for maturity: Regressors 7-year 10-year 15-year 20-year 25-year 30-year PHNT(m: 210) 6.37 4.68 t (0.45) (0.39) PHNT(m: 1430) 1.73 7.59 10.55 11.64 t (0.72) (0.82) (0.87) (0.93) Duration Gap 179.50 151.33 98.92 72.98 74.18 88.39 t (12.81) (10.67) (12.05) (13.15) (13.82) (14.47) [OIS(5) OIS(1)] 0.19 0.01 t1 (0.01) (0.01) Adjusted R2 0.63 0.45 0.31 0.42 0.53 0.59 Note: The estimated specifications take the form: y(m) = a + b·PHNT + c·DurationGap + d [OIS(5) OIS(1)] t t t t1 The dependent variable is the nominal yield (obtained using yield-curve estimates derived using the Svensson (1995) procedure) on Treasury security of the indicated maturity m. In addition to the two variables described in the notes to Table 2, the regressions for the seven- and ten-year bond rate include the slope of the OIS curve. The sample period is weekly, from December 2002 to October 2008. The regressions have been estimated by the seemingly unrelated regression technique in order to take into account correlation among error terms, and we specified in estimation that small-sample statistics be computed. 50

Table 10. SUR estimates: additional explanatory variables Dependent variable: Nominal Treasury yield for maturity: Regressors 7-year 10-year 15-year 20-year 25-year PHNT(m: 46) 2.98 t (1.24) PHNT(m: 68) 2.07 6.23 t (1.46) (1.13) PHNT(m: 810) 7.62 7.38 t (2.63) (1.67) PHNT(m: 1012) 3.11 t (1.38) Duration Gap 176.38 161.63 141.80 128.61 143.31 t (14.98) (11.86) (10.33) (11.48) (11.38) [OIS(5) OIS(1)] 0.51 0.18 t1 (0.02) (0.02) PHNT(m: 1214) 4.26 t (1.73) PHNT(m: 1416) 5.02 t (2.17) PHNT(m: 1618) 8.71 t (1.61) PHNT(m: 18-20) 9.12 t (1.40) PHNT(m: 2022) 1.57 t (2.39) PHNT(m: 2224) 3.05 3.23 t (2.33) (2.54) PHNT(m: 2426) 3.87 t (1.40) PHNT(m: 2628) 13.19 t (1.50) Adjusted R2 0.53 0.33 0.33 0.48 0.59 51

Table 11. SUR estimates for term premium specifications Dependent variable: Nominal term premium for maturity: 2-year 5-year 7-year 10-year PHNTY(m: 2–10) 17.59 21.68 22.87 22.92 t (4.10) (4.97) (5.11) (5.25) Duration Gap 91.08 108.84 109.04 104.05 t (14.49) (15.04) (15.11) (14.83) [s(m)  s(2)] 0.16 0.23 0.29 0.36 t-1 (0.03) (0.04) (0.04) (0.04) [corr(d10y,S&P500ret)] –0.25 –0.26 –0.25 –0.21 t-1 (0.05) (0.06) (0.06) (0.06) Adjusted R2 0.47 0.54 0.62 0.71 Note: The regressions estimated take the form: z(m) = a + b·(BUCKET(m: 210)/GDP) + c·DurationGap + d[s(m)-s(2)] t t t t1 + e· corr(d10y, S&P500ret) t1 where the dependent variable, z(m), is the nominal term premium. The regressors are privately-held t nominal Treasuries (PHNTY)—i.e., private Treasuries of the indicated maturities, here expressed as a percentage of Nominal GDP rather than of total Treasury debt outstanding—and the duration gap (defined as before), as well as the slope of the swap yield curve, and the weekly average of the intraday correlation between the 10-year yield changes and the S&P500 returns. The sample period is weekly from December 2002 until October 2008. 52

Table 12. OIS regressions Dependent variable: OIS rates or Treasury-OIS spread 1-year 2-year 5-year 2-yr. spread 5-yr. spread PHNTY(m: 210) 10.71 7.51 16.34 1.28 1.98 t (11.35) (11.43) (10.24) (0.24) (0.25) Duration Gap 184.75 216.12 204.83 2.70 9.99 t (39.16) (33.27) (33.39) (11.19) (10.55) [s(m)  s(2)] 1.79 1.37 0.70 0.10 0.11 t1 (0.07) (0.07) (0.06) (0.01) (0.01) [corr(d10y, S&P500ret)] 0.34 0.44 0.38 0.02 0.01 t1 (0.15) (0.13) (0.14) (0.03) (0.03) Adjusted R2 0.95 0.93 0.82 0.65 0.73 Table 13. Swap regressions Dependent variable: Swap yields for maturity: 1-year 2-year 5-year 7-year 10-year PHNTY(m: 210) 4.76 18.01 22.62 20.68 18.01 t (7.08) (8.31) (8.90) (8.60) (8.31) Duration Gap 116.55 167.82 179.64 174.10 167.82 t (34.26) (29.74) (31.12) (30.68) (29.74) [s(m)  s(2)] 1.62 1.24 0.61 0.41 0.27 t1 (0.05) (0.05) (0.06) (0.06) (0.05) [corr(d10y, S&P500ret)] 0.11 0.27 0.29 0.27 0.27 t1 (0.15) (0.13) (0.14) (0.14) (0.13) Adjusted R2 0.95 0.94 0.82 0.72 0.57 53

Table 14. Correlation Matrix: corporate yields and policy-related variables Sample Period: 2002:122008:10 Yields/regressors PHNT(m: 2–10) PHNT(m: 14–30) Duration Gap t t t corp(a2) 0.86 –0.87 –0.48 corp(a5) 0.86 –0.83 –0.50 corp(a7) 0.80 –0.75 –0.48 corp(a10) 0.69 –0.62 –0.42 corp(a20) 0.47 –0.39 –0.29 corp(a30) 0.41 –0.31 –0.25 corp(bbb2) 0.78 –0.79 –0.42 corp(bbb5) 0.73 –0.69 –0.42 corp(bbb7) 0.63 –0.58 –0.36 corp(bbb10) 0.48 –0.41 –0.27 corp(bbb20) 0.19 –0.10 –0.08 corp(bbb30) 0.09 0.00 –0.01 Note: The buckets consist of privately-held nominal Treasury securities outstanding, grouped by maturity class. Corporate bond yields are zero-coupon yields obtained via the Nelson-Siegel (1987) yield curve approximation. 54

Table 15. Corporate bond rate regressions Dependent variable: A-rated corporate bond rate for maturity: Regressors 2-year 5-year 7-year 10-year 20-year 30-year PHNTY(m: 210) 20.47 22.18 22.49 21.79 18.71 17.12 t (4.79) (4.58) (4.58) (4.49) (4.21) (4.07) Duration Gap 34.50 27.88 22.33 22.88 25.31 21.95 t (32.51) (32.31) (32.63) (32.23) (29.43) (27.81) [s(m)  s(2)] 0.59 0.06 0.29 0.46 0.56 0.56 t1 (0.15) (0.15) (0.15) (0.14) (0.13) (0.13) [corr(d10y, S&P500ret)] 0.20 0.22 0.26 0.29 0.29 0.28 t1 (0.17) (0.18) (0.18) (0.18) (0.16) (0.15) Adjusted R2 0.86 0.66 0.54 0.44 0.36 0.35 Dependent variable: BBB-rated corporate bond rate for maturity: 2-year 5-year 7-year 10-year 20-year 30-year PHNTY(m: 210) 11.21 15.48 16.27 15.86 13.32 12.09 t (5.27) (5.16) (5.00) (4.79) (4.34) (4.09) Duration Gap 20.46 8.48 14.45 27.71 42.38 43.20 t (38.47) (39.53) (38.95) (36.74) (30.74) (28.31) [s(m)  s(2)] 0.64 0.03 0.23 0.38 0.50 0.51 t1 (0.17) (0.16) (0.16) (0.15) (0.13) (0.13) [corr(d10y, S&P500ret)] 0.35 0.42 0.44 0.42 0.33 0.29 t1 (0.20) (0.22) (0.22) (0.20) (0.16) (0.15) Adjusted R2 0.74 0.44 0.32 0.24 0.24 0.28 55

Table 16. Corporate bond rate regressions Dependent variable: A-rated corporate bond rate for maturity: Regressors 2-year 5-year 7-year 10-year 20-year 30-year PHNTY(m: 210) 13.42 15.06 15.05 14.36 11.86 10.56 t (2.62) (2.85) (2.80) (2.69) (2.38) (2.22) Duration Gap 137.75 131.70 129.27 128.36 121.49 113.94 t (39.23) (36.15) (35.29) (34.61) (33.38) (32.69) [s(m)  s(2)] 1.20 0.55 0.33 0.16 0.00 0.02 t1 (0.13) (0.14) (0.13) (0.13) (0.11) (0.11) [Treasury IV] 0.02 0.02 0.02 0.02 0.02 0.01 t1 (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) Adjusted R2 0.91 0.79 0.72 0.66 0.61 0.60 Dependent variable: BBB-rated corporate bond rate for maturity: 2-year 5-year 7-year 10-year 20-year 30-year PHNTY(m: 210) 3.34 7.04 7.80 7.75 6.36 5.73 t (3.35) (3.61) (3.44) (3.10) (2.46) (2.24) Duration Gap 130.03 124.33 129.81 138.18 138.45 131.67 t (45.77) (43.86) (41.94) (39.56) (35.66) (33.80) [s(m)  s(2)] 1.29 0.65 0.45 0.27 0.07 0.01 t1 (0.15) (0.16) (0.15) (0.13) (0.11) (0.11) [Treasury IV] 0.02 0.02 0.02 0.02 0.02 0.01 t1 (0.003) (0.003) (0.003) (0.003) (0.003) (0.003) Adjusted R2 0.83 0.65 0.58 0.54 0.54 0.56 56