Monetary Policy Shocks: Data or Methods?

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Monetary Policy Shocks: Data or Methods? Connor M. Brennan, Margaret M. Jacobson, Christian Matthes, Todd B. Walker 2024-011 Please cite this paper as: Brennan, Connor M., Margaret M. Jacobson, Christian Matthes, and Todd B. Walker (2024). “Monetary Policy Shocks: Data or Methods?,” Finance and Economics Discussion Series 2024-011r1. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2024.011r1. 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.

MONETARY POLICY SHOCKS: DATA OR METHODS?* ConnorM.Brennan† MargaretM.Jacobson‡ ChristianMatthes§ ToddB.Walker¶ October2024 Abstract Differentseriesofhigh-frequencymonetaryshockscanhaveacorrelationcoefficientaslowas0.3 andthesamesigninonlyonehalfofobservations. Bothdataandmethodsdrivethesedifferences, which are starkest when the federal funds rate is at its effective lower bound. After documenting differencesinmonetaryshockseries,weexploretheirconsequenceforinferenceinseveralspecifications. Wefindthatempiricalestimatesofmonetarypolicytransmissionhavefewqualitativedifferences. Wecautionthatinferencemaynotbeentirelyrobusttoallshockconstructionsbecause qualitativedifferencescanemergewhenweinterchangedataandmethods. Keywords: high-frequencymonetarypolicyshocks;monetarypolicytransmission;empiricalmonetaryeconomics. JELCodes:E52,E58,E31,E32. *ThismaterialreflectstheviewsoftheauthorsandnotthoseoftheFederalReserveBoardofGovernors.Theauthorsthank AeimitLakdawalaforanexcellentdiscussion. TheauthorsalsothankMiguelAcosta,BenJohannsen,EllisTallman,andaudiencesattheFederalReserveBoard,MidwestMacroSpringMeetings,theBarcelonaSummerForum,theNorthAmerican EconometricSociety,theSocietyforEconomicDynamics,andtheWakeForestUniversityEmpiricalMacroWorkshopforhelpfulcomments. FinallytheauthorsthankMiguelAcostaforhelpextendingtheNakamuraandSteinsson(2018)shockseries, JennyTangandRicardoNunesforhelpwiththeFF4shockseries,andJohnRogersandWenbinWuforhelpreconstructing theirBRW shockseries. †UniversityofChicago;cmbrennan@uchicago.edu.5757SUniversityAve,Chicago,IL60637. ‡FederalReserveBoard;Margaret.M.Jacobson@frb.gov. 20thandConstitution;Washington,DC20551. Corresponding author. §DepartmentofEconomics,IndianaUniversity,matthesc@iu.edu.100SWoodlawnAve;Bloomington,IN47405. ¶DepartmentofEconomics,IndianaUniversity,walkertb@indiana.edu.100SWoodlawnAve;Bloomington,IN47405

1 INTRODUCTION Because monetary policy simultaneously affects and responds to economic conditions, identifying its exogenousvariationisanongoingchallenge. Anyinstrumentthatestimatesmonetaryshocksmustbe orthogonaltoeconomicconditionsandcontrolforallavailableinformationtoisolateunanticipateddecisionsfromanticipated.SinceatleastKuttner(2001),high-frequencyenvironmentshaveprovenuseful tofine-tuneinformationsetstoextractmarketsurprises.Assetpricesobservedminutesbeforeamonetarypolicydecisionpresumablycontainallavailableinformationandhencecontrolforanyanticipated decision. Assetpricesobservedminutesafteramonetarypolicydecisionreflectthemarketreactionto thedecision. Becauseonlymonetarynewsisreleasedinthenarrowtimewindowsurroundingadecision,researcherscanpresumablyisolatemonetarysurprisesfromnon-monetarynews. Given that various high-frequency monetary shock series are constructed from highly correlated changes in asset prices in similar narrow time windows around the same monetary policy announcements,onecouldexpecttheseriestohavesimilarmagnitudesandsignsevenifunderlyingdataorstatisticalmethodsdiffer.Wefindthatdifferencesemergeinpractice,especiallywhenthefederalfundsrate isatitseffectivelowerbound(ELB).Weaskifdataormethodsdrivethesedifferencesinhigh-frequency monetary shock series for the United States. For researchers studying the transmission of monetary policytoeitherfinancialmarketsorthemacroeconomy,differencesinmonetaryshockseriescouldbe particularlytroublingif theyleadtodifferencesinestimatesoftheeffectofmonetarypolicy.Inpractice, wefindthatdifferencesinmonetaryshockseriesaffectthemagnitudesofpointestimatesbutonlyaffect thesignincertainspecifications. Thisfindingisonlyrobusttocommonlyusedmonetarypolicyshock series,asconstructionsthatinterchangedataandmethods—i.e.takethedatafromoneseriesanduseit inthemethodofanother—havedifferentsignsoftheirpointestimates. The first contribution of this paper is to construct and compare commonly used monetary shock seriesfromhigh-frequencytradessothatreaderswithoutaccesstotheunderlyingintradaytick-by-tick datacanbetterunderstandthedifferences.Althoughhigh-frequencyconstructsarewidelyused,limited dataavailabilityoftenprecludesconstructionfromscratch[seeNakamuraandSteinsson(2018),Acosta (2023),BoehmandKroner(2023)andNunesetal.(2023)fornotableexceptions]. Amongallofthenumerous high-frequency series, we focus on six: four that are commonly used—Kuttner (2001), Gertler andKaradi(2015),NakamuraandSteinsson(2018),andBuetal.(2021)—andtwothatinterchangedata andmethods. LikeSwanson(2023)andBuetal.(2021),wefindthatassetpriceswithlongermaturities canbeadriverofdifferences, especiallysincecentralbanktoolkitsexpandedbeyondthemaintoolof targetingshort-terminterestratesinrecentdecades. Infact,shockseriesconstructedfromtheshortest andlongestmaturitiesofdata—Kuttner(2001)andBuetal.(2021),respectively—arethemostdifferent withonlya0.3correlationcoefficientandthesamesignforonlyonehalfofobservations. Intheircomparisonoftheforwardguidancecomponentsofhigh-frequencymonetarypolicyshocks, Bundickand Smith(2020,AppendixA.4)similarlyfindlowcorrelationsanddifferencesinsigns. Thesecondcontributionofthispaperistodocumentthatmonetaryshockseriesbecomeevenmore differentwhenthefederalfundsrateisatitseffectivelowerbound(ELB)duetodata. Monetaryshock seriescalculatedfromassetpriceswithmaturitiesofayearorless—thoseofKuttner(2001),Gertlerand

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? Karadi(2015),andNakamuraandSteinsson(2018)—yieldestimatesthatarerelativelysmallerinmagnitudeattheELB.Bycontrast,estimatesbasedonassetpriceswithlongermaturities—thoseofBuetal. (2021)—yieldmonetaryshocksseriesthathavesimilarmagnitudesinELBandnon-ELBperiods. While thefederalfundsrateaffectsshorterratesmorestrongly,forwardguidanceandLSAPsspecificallytarget longerrates. Therefore, high-frequencymonetaryshockseriesconstructedfromonlyshort-termrates maybelessequippedtocapturetheeffectsofthesenewerpolicytools. Wenotethatdataonlong-termratesarenottheonlydeterminantofdifferencesinmonetaryshock series: methodsarealsoimportantforcapturingtheeffectsofthe21st-centurymonetarypolicytoolkit. Weshowthatexpandingthemethodsdevelopedinthe2000s,whenthefederalfundsratewastheprimarypolicytool,tosimplyincludelong-termratestargetedbynewerpolicytoolsmaybeineffectiveat exploitingadditionalinformation. Bycontrast,wearguethattheFama-MacBethregressionusedbyBu etal.(2021)iseffectiveatexploitingadditionalinformationfromlong-termratesbecauseitreliesonthe differentialresponsivenessofshort-andlong-termratestomonetarypolicy. Giventhatlong-termrates arelessresponsive,onaverage,tomonetarypolicythanshort-termrates,methodssuchastheprincipal component analysis of Nakamura and Steinsson (2018) that weight by the averages across the sample arelessequippedtoextractinformationfromlong-termrates. Thispaper’sthirdcontributionistoanalyzehowdifferencesindataandmethodsaffectestimatesof monetarypolicytransmission. Wefindthatdifferencesaffectthesignofestimatesofmonetarypolicy transmissioninspecificationsthatrelyonforecastrevisions. Bycontrast, insomeVARsandlocalprojections the signs are similar across shock series while the magnitudes may differ. We only find these similaritiesforcommonlyusedshockseries.Qualitativedifferencesinestimatesemergewhenweinterchangedataandmethodssuggestingthatsomeconstructionsmayresultinnon-robustinference. Becausemanycommonlyusedmonetaryshockserieshavebeenshowntobepredictableandhence notentirelyexogenous,wecarryoutseveralpredictabilitytestsstandardintheliteratureandfindthat only a subset of shock series constructed from short-term asset prices are predictable [see Karnaukh andVokata(2022),BauerandSwanson(2022,2023),CaldaraandHerbst(2019),Sastry(2021),Miranda- AgrippinoandRicco(2021)]. However, inourstudyofmonetarypolicytransmission, wefindthatthe predictable shocks series do not have drastically different impulse responses than those that are unpredictable. While predictability is inherently undesirable, we find that its practical consequences for inferencemaydependonthespecification. Next,weestimatemonetarytransmissionusingthespecificationofCampbelletal.(2012)andNakamuraandSteinsson(2018)thatpredictsforecastrevisionsfrommonetarypolicyshockseries.Thisspecification yields transmission estimates with signs and magnitudes affected by the choice of monetary shockseries. WhilethemonetaryshockseriesofBuetal.(2021)isthemostlikelytodeliversignsand magnitudesinlinewiththeoreticalpredictions,theshockseriesofKuttner(2001)isthenextbest. Ofall of the shock series studied, these two are some of the simplest to construct in terms of both data and methodsbutthemostdifferentintermsofcorrelationcoefficientsandsigns. Apotentialreasonforthe lackofanopposite-signedresponsefoundintheotherseriesdespitetheirdifferencesmaybethatthey aretheleastlikelytocontaincentralbanksignalsaboutthefuturestateoftheeconomy,i.e.theso-called 2

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? “Fedinformationeffect"or“Fedresponsetonews"channel[BauerandSwanson(2022)]. Finally, we find thatestimates ofmonetary transmissionfromlocal projections and vector autoregressions(VARs)aremoresimilaracrossshockseriesthantheircounterpartsestimatedviaforecastrevisions.ThedailylocalprojectionsspecificationofJacobsonetal.(2022)controlsfortemporalaggregation bymatchingthefrequencyofshocksandresponsevariables, anddeliversimpulseresponsefunctions withanegativesignpredictedbytheoryinthefourmainshockseriesstudied. Positiveresponsesthat contradicttheoreticalpredictionsareneitherstatisticallysignificantnorlong-lived. VARspecifications can yield similar findings: impulse response functions vary in magnitude across the four main shock series,butallhavesignsconsistentwiththeoreticalpredictions. Accordingly,differencesinshockseries arelesslikelytoaffecttransmissionestimatesindynamicspecificationslikeVARsrelativetomorestatic treatments. Therefore,whetherornotdifferencesincommonlyusedmonetaryshockseriesmattersfor estimatesofmonetarypolicytransmissiondependsonthespecificationusedbytheresearcher. Qualitativedifferencesinestimatesofmonetarytransmissiondoemergewhenusingmonetarypolicyshock seriesthatinterchangedataandmethods,asthesetendtobequitedifferentfromthecommonlyused series. Assuch,wesuggestthatresearchersproceedwithcautionwhenvaryingcertaincomponentsof shockconstructionasitcouldleadtonon-robustinference. 1.1 CONNECTION TO THE LITERATURE While there are numerous approaches to identifying exogenousvariationinmonetarypolicy,wefocusonfourcommonlyusedhigh-frequencyseriesandtwothat interchange data and methods. All six series rely on asset price data that are either at an intraday or a daily frequency and are constructed either directly from raw data or from simple statistical procedures.Thedatausedinconstructionconsistofshort-termfuturesandthefulltermstructureofTreasury yields. Althoughtherearecomplementarynon-highfrequencyapproachesandadd-ontechniquesthat furtherpurgehigh-frequencyseriesfromcontamination,wefocusonfourcoreseriestohighlighttheir differencesandsimilaritiesassimplyaspossible. Inasimilarappealtosimplicity,wefollowBauerand Swanson(2022)andfocusonshockseriesthatsummarizemonetarypolicyinasingleseriesratherthan multipledimensions. AsBauerandSwanson(2022)explain,asingleseriescanoftenbeinterpretedasa weightedaverageofmultipledimensionthatparsimoniouslycapturescertainaspectsofthedimensions. Complementingourstudyoftheimplicationofdifferenceswithinhigh-frequencymonetarypolicy shockseriesarethosethatcompareacrosstypesofshockseries.Rudebusch(1998)comparesmonetary shockseriesestimatedasaVARresidual[Christianoetal.(1996,2005)]tohigh-frequencyshockseries andfindsthattheseseriesarequitedifferent.Similarly,EttmeierandKriwoluzky(2019)comparetheperformanceofnarrativeidentificationachievedbyparsingFOMCpolicydocumentsforintendedchanges inthefederalfundsrate[RomerandRomer(1989),RomerandRomer(2004),WielandandYang(2020), AruobaandDrechsel(2023)]tohigh-frequencyshocksandfinddifferencesininference. Finally,Ramey (2016)alsodocumentsdifferenceswithinandacrosstypesofshocks. McKayandWolf(2023)appealto Sims’s(1998)argumentthatmonetarypolicyshocksneednotnecessarilybecorrelatedacrossdifferent typesofidentificationastheycouldbecapturingdifferentsourcesofexogenousvariationinmonetary policy. However,withinhigh-frequencymonetarypolicyshocks,onecouldexpectsimilaritygiventhat theyareconstructedfromhighlycorrelatedassetprices. 3

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? Because high-frequency identification explicitly relies on monetary policy announcements, most researchers are limited to starting their sample in 1994 when the Federal Reserve’s Federal Open MarketCommittee(FOMC)beganregularlyannouncingitsmonetarypolicydecisions(exceptionsinclude Bauer and Swanson (2022) and Bu et al. (2021)). Other approaches typically extract longer monetary shockseriesbecausetheyarenotconstrainedtoexplicitlyannouncedFOMCdecisions. However,judgment plays a larger role in determining the time and date of a monetary shock in the absence of an explicit announcement. Therefore, relying on explicitly announced decisions may lend to greater reproducibility,asitisstraightforwardforresearcherstolookupthedateandtimeoftheannouncement and calculate a fixed time window around that announcement. See Appendix D for details on FOMC announcementdatesandtimes. Researchershavefocusedonrefininghigh-frequencymonetaryshockserieswithadd-ontechniques becauseestimatesofmonetarytransmissionoftenhavesignsthatareoppositeofwhattheorypredicts.1 By controlling for information mismatches between central banks and private agents, high-frequency monetaryshockseriesandtheirassociatedmonetarytransmissionestimatescanbepurgedofthissocalled “Fed information effect" [see Miranda-Agrippino and Ricco (2021), Bauer and Swanson (2023, 2022),JarocinskiandKaradi(2020),Nunesetal.(2023),Zhu(2023),andothers].Becausetherearemany solutions to control for potentially endogeneity, we leave our monetary shock series in their simplest formwithoutanyadditionalrefinements,permittingmorestraightforwardandtransparentcomparisons acrossdataandmethods. Because today’s monetary policy has many tools in addition to the federal funds rate, researchers haveoftenextractedmulti-dimensionalhigh-frequencymonetaryshockseries[Gürkaynaketal.(2005), Lewis(2023), Swanson(2021,2023), Acosta(2023), Jarocin´ski(2024)andothers]. WefollowBauerand Swanson (2022) and focus on single monetary shock series for easier comparisons, especially for exercises that interchange data and methods.2 Furthermore, a single series allows us to parsimoniously identifythejointeffectsofmonetarypolicytoolsandmaycombinedifferentdimensionsofmonetary policythatarenotnecessarilyindependent,likethoseidentifiedbyJarocin´ski(2024). Although we focus on high-frequency monetary shock series for the United States, the data and methods described in this paper can be extended to other settings. Altavilla et al. (2019), Cieslak and Schrimpf(2019),AndradeandFerroni(2021),Buetal.(2021),andothersconstructshockseriesforEurope while Braun et al. (2024) and Cieslak and Schrimpf (2019) construct shock series for the United Kingdom. Like us, these researchers start from raw data to highlight the choices faced by researchers andhowthesechoicesaffectestimatesofmonetarytransmission. 1BauerandSwanson(2023)andJacobsonetal.(2022)arenotableexceptionsthatinsteadexplorefeaturesofresponsevariablesthatmayexplainopposite-signedresponses. 2BauerandSwanson(2022)explain,“Ratherthanfocusontwodimensionsofmonetarypolicy,asinGürkaynaketal.(2005), wefollowNakamuraandSteinsson(2018)andtakejustthefirstprincipalcomponentofthechangesinED1–ED4aroundFOMC announcements...Gürkaynaketal.(2005)showedthatFOMCannouncementscausesurprisesaboutboththecurrentfederal fundsratetargetandtheexpectedpathofthefederalfundsrateforthenextseveralmonths(i.e.,their“target"and“path" factors). Becausethefirstprincipalcomponentisessentiallyequaltoaweightedaverageofthetargetandpathfactors, it parsimoniouslycapturessomeofthemainfeaturesofbothtypesofmonetarypolicysurprises." 4

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? 2 SHOCK CONSTRUCTION Wefocusonthecommonlyusedhigh-frequencymonetaryshockseriesthatrelyontick-levelintradayor dailydataofthefederalfundsratefutures,eurodollarfutures,andTreasuryyields. Someoftheseseries arefirst-differencesofraworscaleddatawhileothersrelyonstatisticalprocedureslikeprincipalcomponentanalysisorFama-MacBethregression.Carefulassessmentnecessitatesconstructingtheseshock series by selecting suitable trades from tick data so that we can best understand how various componentsoftheunderlyingassetsandstatisticalmethodologycontributetofinalestimates.Ourunderlying datacloselymatchthoseofAcosta(2023)andAcostaetal.(2024)whicharesimilarlyconstructedfrom tickdata. Comparedtotheoriginal seriesavailableonthe authors’websitesofNakamuraandSteinsson(2018)andBuetal.(2021), ourserieshavea0.99anda0.99correlation, respectively. Thecorrelationis0.98and0.97fortheMP1andFF4series,respectively,availablefromGürkaynaketal.(2024)at (http://www.bilkent.edu.tr/∼refet/replication_GKL.zip). To that end, we first provide a brief description of the financial assets used in the shock construction with notation: superscripts j are the duration of an asset; subscripts s and q are the month and quarter, respectively, of an FOMC announcement; and subscripts t are the time of measurement with ∆t the duration of time between measurements. All intraday data is from CME Group Inc. DataMine (https://datamine.cmegroup.com/)attheFederalReserveBoardwhichisavailablestartingin1995. Althoughitmaybepossibletoconstructmonetarypolicyshockseriesbackto1994or1988withotherdata sources, weprefertotruncateourdatasamplethanmergeitwithdataweareunabletoreplicateand verifyonatrade-by-tradebasis. Our January 1995 to September 2024 sample includes 244 FOMC announcements, 7 of which are unscheduled. We drop intermeeting announcements that are notational votes or about topics not directlyrelatedtomonetarypolicyactionssuchas: swaplines,financialcrisisfacilities,thedebtceiling, the monetary policy framework review, foreign economic crises, the outbreak of war in Iraq, or swap lines. Wedroptheannouncementsfollowing9/11(asiscommonintheliterature)anddroptheMarch 15,2020announcementthatoccurredonaSundaywhichprecludestheavailabilityoftrades. FederalFundsFuturesarefuturescontractstradedontheChicagoMercantileExchangesince1988. The contractindex,followingInternationalMonetaryMarket(IMM)convention,ispricedas ff j =100−R, whereR isthearithmeticaverageofthedailyeffectivefederalfundsratesduringthecontractmonth j for j >0.Forexample,apricequoteof95.75isequivalenttoanaveragedailyrateof4.25overthecourse ofthemonthinwhichthecontractmatures.SeeAppendixA.1foradditionalcontractdetails. AsdocumentedbyBarakchianandCrowe(2013),thefederalfundsfuturesmarketishighlyliquidfor contractsexpiringinthenextthreemonthsandlessliquidforcontractsexpiringinseveralyears.Because thefederalfundsratefuturesaremoreliquidatshorterhorizons,onlyhorizonsuptothreemonthsahead aretypicallyusedintheconstructionofmonetaryshockseries.Tradingvolumewasrelativelylowduring ELBepisodes,buthasroughlytripledfrom2014asshowninAppendixFigure(A.11). Followingtheliterature,wemeasurethechangeinfederalfundsratefuturesaroundmonetarypolicy announcements in month s and time t as ∆ff j = ff j −ff j where ∆t measures the length of the s s,t s,t−∆t 5

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? high-frequency window and j is the duration of the futures contract. For example, if s =March2014 then j = 1 is the contract that expires March 31 2014, j = 2 expires April 30 2014, and so on. In the shockseriesstudiedbelow,asintheliterature,weonlyexamine j =1,2,3,4.Wediscussthelengthofthe high-frequencywindowinmoredetailbelow. Eurodollar Futures were quarterly futures contracts traded on the Chicago Mercantile Exchange from 1981toAprilof2023. EurodollarsisagenerictermtodescribeU.S.dollar-denominateddepositsatforeign banks or at the overseas branches of American banks that are outside of the purview of the U.S. financialregulatoryframework. PriortotheirdiscontinuationinAprilof2023,Eurodollarfutureshada payoutatexpirationbasedonthethree-monthmaturityU.S.dollarLondonInter-BankOfferRate(LI- BOR).SeeAppendixA.1foradditionalcontractdetails. Eurodollarfutureswereoneofthemostactivelytradedfuturescontractsintheworldasmeasuredby openinterest.Theextendeddurationofthecontract,relativetofedfundsfutures,istheprimarybenefit ofusingeurodollarfuturestoidentifyexogenousvariationinmonetarypolicy.Thedurationatwhichthe fedfundsfuturesmarketliquiditybeginstodryupiswhereeurodollarfuturesweremostheavilytraded. Gürkaynaketal.(2007)confirmthatthecombinationoffederalfundsandeurodollarfuturesarethebest financialinstrumentstopredictchangesinthefederalfundsrateoneyearahead. SOFRFuturesbasedontheSecuredOvernightFinancingRate(SOFR)havesuccessfullyreplacedeurodollarfuturesontheChicagoMercantileExchange.TheSOFRrateisbasedonthecosttoborrowUSD overnightusingTreasurysecuritiesascollateral. BecauseSOFRfuturesaredesignedtoreplaceeurodollar futures, they can be spliced into shock construction when they are available. Acosta et al. (2024) recommendJanuary2022asastartdateforSOFRfutures,butalsonotethatthechoiceofstartdatehas littleeffectontheconstructionoffinalestimates. Wemeasurethechangeineurodollar/SOFRfuturesaroundmonetarypolicyannouncementinquarterq attimet as: ∆ED j =ED j −ED j ,where j =2,...,4representthe2nd,3rd,and4thexpiring q q,t q,t−∆t eurodollarcontracts, i.e. six-, nine-, and12-monthsahead. ThecorrespondingcontractsforSOFRfuturesarethe3rd,4th,and5thexpiringcontracts,∆SF j =SF j −SF j for j =3,...,5.3 Asbefore,the q q,t q,t−∆t lengthofthehigh-frequencywindow,∆t,issuchthattindicatesthetimeaftertheFOMCannouncement andt−∆t thetimebefore. USTreasurysecuritieshavematuritiesofoneto30yearsandaresowellknownthattheydonotrequireathoroughdescription.BecauseHansenetal.(2019)andHansonandStein(2015)documentthat Treasuriesreacttomonetarypolicyannouncementswithvaryingdegreesofresponsivenessdepending onthematurity,Treasuriesarewellsuitedtocapturemonetarysurprises. Buetal.(2021)usethedaily changeinzero-couponTreasuryyieldstoconstructahigh-frequencymonetaryshockseries. Thezerocouponyields,ascalculatedbyGürkaynaketal.(2007) (https://www.federalreserve.gov/pubs/feds/2006/200628/200628abs.html), harmonize Treasury yields 3Whileeurodollarfutureswerebasedonexpectedinterestratesoverthreemonthsafterthesettlementdate,SOFRfutures arebasedoninterestratesoverthethreemonthsbefore. Asaresult,thefirst-outstandingEurodollarfutureandthesecondoutstandingSOFRfuturearecalledtheq+1contract. EurodollarandSOFRfuturesarenamedbasedonthequarteroftheir interestrateexposure,theycanbematchedbasedontheircontractnames.Alternatively,onecanmatchthenth-outstanding SOFRcontractwiththe(n-1)st-outstandingeurodollarcontract. 6

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? of various maturities to reflect what the discount would be if interest payments were not made until maturity. WemeasurethechangeinTreasuryyieldsaroundeachmonetarypolicyannouncement s as ∆R j =R j −R j where j =1,...30representsyieldsofmaturitiesrangingfromoneto30years. The s s,t s,t−∆t lengthofthewindowis∆t andt isthetimeaftertheFOMCannouncementandt−∆t thetimebefore. 2.1 KUTTNER (2001), MP1 Kuttner (2001) was one of the first to rely on the federal funds futures markettodisentangleanticipatedfromunanticipatedchangestothefederalfundsrate. ForFOMCannouncementinmonths,Kuttner(2001)usesthescaledchangeinthecurrentmonthfederalfundsfutures(j =1)unlessthemonetarypolicyannouncementisinthefinalsevendaysofthemonth,thenhe usestheunscalednextmonthfederalfundsfutures(j =2). LabelthisinstrumentasMP1andinmonth swehave,    Ds (cid:161) ff1 −ff1 (cid:162) if Ds−ds>7 MP1 = Ds−ds s,t s,t−∆t (1) s  ff2 −ff2 otherwise s,t s,t−∆t Ds is the number of days in month s and ds is the day of the FOMC announcement. Kuttner (2001) notes that because the settlement prices of the federal funds futures are based on the average of the effectiveovernightfederalfundsrateinmonthsratherthanthefederalfundsrateonaspecificday,one mustcorrectforthetimeaveragingandscalebytheinverseoftheshareofdaysremaininginthemonth afteranFOMCannouncementoccurs. Forthisreason,∆ff1isscaledby Ds . Kuttner’s(2001)original s Ds−ds specificationdifferedthreewaysfromthispaper:1)heusedadailywindowsothatt−∆t wasthemarket closethedaybeforeanannouncementandt wasthecloseontheannouncementday,2)heswitchedto theone-monthaheadfutureiftheFOMCannouncementwasinthefinalthreedaysofthemonth,and 3)heincludedFOMCdecisionsbacktothe1970s. Inthispaperweusethemorepopular1)narrow30minutetimewindowputforthbyGürkaynaketal.(2005)wheret−∆t indexesthe10minutesbeforeand FOMCannouncementandt indexes20minutesafter,2)sevendaythresholdfortheswitchtothenext month’sfuture,and3)asamplethatstartsaftertheintroductionofannouncementsofFOMCdecisions inFebruaryof1994.4 Panels (4a) and (5a) show the MP1 shock series from January 1995 to September 2024. Although theMP1shockserieshassomeofthelargestnegativeshocksinoursample,itisclosetozerothroughout both ELB periods. When the federal funds rate is at the ELB—as it was from December 16, 2008 toDecember16,2015andagainfromMarch15,2020toMarch16,2022—theFOMChasuseddate-or threshold-basedforwardguidancetocommunicateexpectedliftoff[seeCarlstromandJacobson(2013) foranoverview]. Anexpectedliftoffdatefarintothefutureormacroeconomicindicatorsfarfromtheir policy thresholds has resulted in market participants perceiving a change in the federal funds rate as unlikelyattheupcomingmeeting. Asaresult,theremaybeeitherlittletradinginfederalfundsfutures contractsexpiringinthecurrentornextmonth,ornomonetarynewsthatsurprisesmarkets.Forexam- 4Gürkaynaketal.(2005)advocateusinganintradayfrequencybecauseadailyfrequencymaynotbeabletopurgemonetary newsfromitsnon-monetarypolicycounterpartondayswhentherearebotheconomicdatareleasesandFOMCannouncements. NakamuraandSteinsson(2018)detectsubstantialbackgroundnoisethatcanbiasinferencewhenusingdailyinstead ofintradaydata. Furthermore,becausefederalfundsfuturescontainlow-frequencyriskpremia,high-frequencychangescan essentiallyremovethispotentiallyconfoundingelement,asshownbyPiazzesiandSwanson(2008). 7

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? ple,panel3oftable(2)showsthatabout40percentofELBobservationsare0fortheMP1shockseries. Moreover,themagnitudesoftheseshocksattheELBareatamaximumofaboutfivebasispoints. WithestimatesoftheMP1shockseriesclosetozerointheELBperiods,estimatesofmonetarytransmissionmaybequitesmallorimprecise,leadingresearcherstoconcludethatthereisnoeffectofmonetary policy on the economy, as shown in Appendix figure (B.18). These findings could be potentially problematicbecauseotherevidencesuchastheworkbySwansonandWilliams(2014)findsthatmonetarypolicycanhaveaneffectattheELB,justthroughlongerhorizonsthantheveryshorthorizonsused tocalculatetheMP1shockseries. Inlightoftheseshortcomings,theMP1shockserieshastheadvantageofreducingbiasfromeither theso-called“Fedinformationeffect"orFedforwardguidance,asnotedbyPaul(2020). Becauseeither ofthesefeaturescouldbeoperatingintheoppositedirectionofdirectchangesinthefederalfundsrate, researchersconcernedaboutcontaminationmayfindtheMP1shockseriesappealing. 2.2 NAKAMURA&STEINSSON(2018),NS NakamuraandSteinsson(2018)usethefirstprincipalcomponentofthefinancialinstrumentsemployedbyGürkaynaketal.(2005)(MP1,MP2,ED2,ED3,ED4)to identifyexogenousvariationinmonetarypolicy.Toexploitinformationbeyondtheimmediatehorizon, Gürkaynak et al. (2005) build off Kuttner’s (2001) work by creating composite measures of changes in interestratefuturesthatspanthefirstyearofthetermstructure. TheyincludeKuttner’scurrent-month surpriseMP1alongwiththesurpriseforthenextFOMCmeetingMP2andEurodollarfutures(ED2,ED3, ED4)whichweupdatewithSOFRfutures(SF3,SF4,SF5)startinginJanuary2022.Asbefore,t indexthe 20minutesafteranFOMCannouncementandt−∆t 10minutesbefore,resultingina30-minutetime window.5 Specifically, the five Gürkaynak et al. (2005)/Nakamura and Steinsson (2018) futures—along with theirSOFRfuturescounterparts—are:  Ds  (ff1 −ff1 ) if Ds−ds>7 MP1 = Ds−ds s,t s,t−∆t (1) s ff s 2 ,t −ff s 2 ,t−∆t otherwise MP2 =   Ds D ′− s′ ds′ (cid:34) (ff s j ′,t −ff s j ′,t−∆t )− D ds s ′ ′ MP1 s (cid:35) if Ds′−ds′>7 (2) s ff j+1−ff j+1 otherwise s′,t s′,t−∆t  ED2 −ED2 if q<2022:Q1 ∆ED2/SF3= q,t q,t−∆t (3) q q SR3 −SR3 otherwise q,t q,t−∆t  ED3 −ED3 if q<2022:Q1 ∆ED3/SF4= q,t q,t−∆t (4) q q SR4 −SR4 otherwise q,t q,t−∆t  ED4 −ED4 if q<2022:Q1 ∆ED4/SF5= q,t q,t−∆t (5) q q SR5 −SR5 otherwise q,t q,t−∆t 5AppendixA.2showsthattimewindowsareoftenlargerthan30minutesduetoalackofsuitabletradesexactly10minutes beforeanFOMCannouncementand20minutesafter. Inpractice,wefindthatthelackoftimewindowuniformityhaslittle materialeffectonshockconstruction. 8

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? WhereMP1isasbeforeandcapturestheunexpectedchangeinthefederalfundsfuturescontracts expiringattheendofthemonths ofanFOMCannouncement. MP2capturestheunexpectedchange ′ infederalfundsfuturesthatexpireattheendofthemonths whichisthemonthofthenextscheduled FOMCmeeting.6 Forexample,lets=March2014thens ′ =April2014.ThenextscheduledFOMCmeeting maybeinthenextmonthoruptotwomonthsafterthecurrentannouncement, asshownbycolumn 1 of table (1). Column 2 shows that the futures used to calculate MP2 may be as far as three months afterthecurrentannouncementbecauseoftheconventionofusingthefollowingmonth’sfuturewhen anFOMCannouncementisinthefinalsevendaysofamonth. Overall,thetableshowsthatmostofthe meetingsusedtocalculateMP2areeitherone-ortwo-monthsaheadsuchthat j =2,3. Asnotedpreviously,limitedtradinginfederalfundsfuturesathorizonsbeyondfourmonthshasledresearcherstorely oneurodollarfuturestocapturetheremaininghorizonsofthefirstyearofthetermstructure. Because eurodollars/SOFRfuturesarequarterly,q indexesthequarterofthecurrentFOMCannouncement. For example,ifq=2014:Q1,ED2/SF3,ED3/SF4,andED4/SF5inequations(3)-(5)representcontractsexpiringin2014:Q2,2014:Q3,and2014:Q4,respectively. NextscheduledFOMCannouncement (1) (2) Future Percent Number PercentMP2 NumberMP2 FF1 incurrentmonth 1% 3 0% 0 FF2 1-monthahead 50% 122 22% 53 FF3 2-monthsahead 49% 119 76% 185 FF4 3-monthsahead 0% 0 2% 6 Total 244 244 Table1:MonthsaheadofthenextscheduledFOMCmeeting. Note:ThenextscheduledFOMCmeetingoccursinthecurrentmonthwhenanunscheduledmeetingoccursbeforeascheduledmeetingas happenedinJanuary2008whentherewasanunscheduledconferencecallonJanuary21stthatannouncedaninterestratecutandascheduled announcementonJanuary30,2008.1-monthaheadimpliesthatthenextscheduledmeetingisthemonthfollowingthatofthecurrentFOMC meetingand2-monthsaheadimpliestwomonths,etc. ThefuturesusedinMP2(column2)maydifferfromthoseincolumn1becausethe futureforthemonthfollowingthatofthenextscheduledFOMCannouncementisusedwhenthatannouncementisscheduledinthefinal sevendaysofthemonth.Forexample,theannouncementfollowingtheMarch18,2015announcementisonApril29,2015.BecauseApril29 isinthelastsevendaysofApril,FF3insteadofFF2wouldbeusedtorepresentthenextmonth’sFOMCannouncement.Thesampleisfrom January1995toSeptember2024. Whetherornotmonetarypolicyhasmultipledimensionsorcanbesummarizedbyasingleseriesis debated. Gürkaynaketal.(2005)extractandrotatetwofactors—thetargetandpath—fromtheinstrumentset{MP1,MP2,ED2,ED3,ED4}. Thesefactorscorrespondtothelevelandslopeoftheyieldcurve foroneyearaheadinterestratesandexplain80and15percentofthevariation,respectively.Gürkaynak etal.’s(2005)multiplefactorswithsuitablerotationscanidentifytheindependenteffectsofeachmonetarypolicytoolwhichmaybeusefulforresearchersstudyingtheeffectsofforwardguidance,orother policytools,separatefromthatofthefederalfundsrate[seeGürkaynaketal.(2005),Jarocin´ski(2024), 6Gürkaynaketal.(2005)explainthattheequationforthefuturesatthenextscheduledFOMCmeetings ′ canbewrittenas, ′ ′ ′ ff s j ′,t = D ds s ′ E t[rs]+Ds D − s ′ ds E t[r s′]+ρ2t wherersistheexpectedFederalFundsratethecurrentFOMCmeetingands ′ isforthe nextscheduledFOMCmeetingandρ2isanyriskpremium.Differencingthisequationbyt−∆tyieldstheexpressionin(2). 9

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? Swanson(2021,2023)andAcosta(2023)foradditionalmulti-dimensionalexamples]. BycontrastNakamuraandSteinsson(2018)useasinglefactorfromthesameinstrumentset(MP1, MP2,ED2,ED3,ED4)whichcanparsimoniouslycapturethejointeffectsofdifferentpolicytools,which is more advantageous when estimating monetary transmission in more complicated frameworks. We followtheapproachofNakamuraandSteinsson(2018),whichisalsousedbyBauerandSwanson(2022), andfocusonthesingleseriestosimplifythecomparisonofshocksandinterchangingexercises. ThefirstprincipalcomponentoftheGürkaynaketal.(2005)/NakamuraandSteinsson(2018)instrument set updated with SOFR futures (MP1, MP2, ED2/SF3, ED3/SF4, ED4/SF5) explains about 80 percentofthevariation. Theestimatedloadingsarerelativelyequalwhichlikelystemsfromallfutures intheinstrumentsethavingmaturitiesoflessthanayearandmovinginlock-step.Otherwise,onecould expect a particular instrument to be associated with a higher loading if its movements were typically outliersrelativetotheothers. AfinalstepintheconstructionoftheNSshockseriesconsistsofre-scalingthefirstprincipalcomponentofequations(1)-(5)intointerpretableunits.UnliketheMP1shockseriesthatissimplyapercentage pointsurpriseinthefederalfundsrate,aprincipalcomponentisnotsostraightforward.FollowingNakamuraandSteinsson(2018),weusethefittedvaluefromtheregressionofthedailychangeintheone-year zero-couponTreasuryyieldonthefirstprincipalcomponent.7 Thecoefficientsfromthisregressionare quitesmallwithavalueofabout0.02fortheslopeandzerofortheconstant. Witha0.8correlationcoefficient, theNakamuraandSteinsson(2018)shockseriesissimilartothe MP1shockseries,asshowninpanels(4b)and(5b). LiketheMP1shockseries,theNS shockseriesis tightlydistributedaroundzerothroughouttheELBperiods. IncontrasttotheMP1shockserieswhere mostELBobservationswere0,78percentoftheNSshockseriesobservationsarepositiveattheELB,as showninpanel2oftable(2). Theprincipalcomponentanalysisusedtocalculatethe NS shockseries canexplainthisdifference. AttheELB,thefederalfundsratetargetrangeis0to25basispointswitha lowerlimitofzero. Theaverageeffectivefederalfundsrateisnearthemidpointofthisrangeorbelow.8 Therefore, the maximum downward surprise at the ELB is about 12.5 basis while upside surprises are notcensoredtothesamedegree.9 Becauseprincipalcomponentanalysisisalinearcombinationofthe underlying instrument set, and this instrument set is left-censored, it is not surprising that there is a rightwardshiftfromzeroobservedinthedistributionoftheNSshockseriesattheELB. GiventhattheFederalReservehasdeployedrecordmonetarystimulusattheELB,whatistheinterpretationofthe78percentpositiveobservationsoftheNS shockseries? Onecouldinterpretunantici- 7SeeAppendixfigure(A.16a)forcomparisonsoftheNSshockseriesunderdifferentscalingassumptions.Becausetheshock serieshaveacorrelationcoefficientclosetoone,transmissionestimatesarelargelyunaffectedbyscalingchoice. Appendix figure(A.14a)showsthatthecorrelationcoefficientbetweentheNSseriesandversionconstructedfromreal-timeestimatesis alsonearperfect. 8In contrast to other central banks that have had a negative policy rate, it is unclear if it would be legal for the federalfundsratetobenegative. FormerFedChairJanetYellenexplainedinher2016Congressionaltestimonythat,"Iwould say that [a negative federal funds rate] remains a question that we still would need to investigate more thoroughly." See https://www.govinfo.gov/content/pkg/CHRG-114hhrg23566/html/CHRG-114hhrg23566.htm. 9Because it may be optimal for central banks to smooth interest rate increases to safeguard financial stability, upside surprises are not indefinitely large. See a October 14, 2024 speech by Federal Reserve Governor Christopher J. Waller https://www.federalreserve.gov/newsevents/speech/waller20241014a.htm. 10

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? patedcontractionarymonetarynewsasmarketsexpectingalargerstimulusthanwhatwasannounced or implemented. Vissing-Jorgensen and Krishnamurthy (2011) note that the LSAP program known as "QE II" announced on November 3, 2010 was about $150 billion less than market expectations. However,itisunlikelythatmarketsexpectedalargerstimulusinnearlyfouroutoffiveannouncements. 2.3 GERTLER&KARADI(2015),FF4 GertlerandKaradi(2015)findthatthethree-monthaheadfederal fundsfutures,FF4,performstronglyasanexternalinstrumentinVARanalysisovertheJanuary1991to June2012period.Asbefore,t indexthe20minutesafteranFOMCannouncementandt−∆t 10minutes before,resultingina30-minutetimewindow. ∆ff4=ff4 −ff4 (6) s s,t s,t−∆t Forexample,ifthemonthsofanFOMCmeetingisMarch2014,FF4istheexpectedfederalfundsrateat theendofJune2014.IncontrasttotheconstructionoftheMP1andNSshockseries,GertlerandKaradi (2015)donotscaletheFF4shockseriesbyDs/(Ds−ds). BecausetheyusetheFF4shockseriesasan externalinstrumentinamonthlyVAR,theyinsteaduseamovingaveragerepresentation.10 Wereport theunscaledversionoftheFF4shockseriesbecausethescaledversionhasbeenshownbyRamey(2016) andMiranda-AgrippinoandRicco(2021)toinducepredictabilityandserialcorrelation. Because the three-month ahead horizon of FF4 covers the next scheduled FOMC announcement as shown by table (1), the FF4 shock series can be interpreted as capturing the effects of both federal fundsratedecisionsandforwardguidanceinasingleinstrument. Figure(1)showshowFF4coversthe nextFOMCannouncementandcancoveruptothreeFOMCannouncementswhichis thecase about 10percentofthetime. Furthermore,table(1)showsthatFF4isoccasionallyusedinthecalculationof MP2andthereforecontainedintheNSinstrumentset. Jun.30,2014 Jul.31,2014 Aug.31,2014 Sep.30,2014 FF1 FF2 FF3 FF4 Jun.17Announcement Jul.30Announcement Sep.17Announcement FF4coverage Figure1:TimingoffuturesandFOMCannouncements Panels(4c)and(5c)showthattheFF4shockseriesissimilartothe MP1and NS shockseries. AlthoughthedistributionoftheFF4shockseriessimilarlynarrowsattheELB,itismorecenteredatzero thantheNSshockseries.Infact,panel3oftable(2)showsthat45percentoftheFF4shockobservations arezeroattheELBandanother27percentarepositive,whichismuchlessthanthe78percentpositive observationsoftheNSshock.EventhoughtheFF4shockseriesavoidssuggestingmorecontractionary 10Infootnote11theyexplain,“First,foreachdayofthemonth,wecumulatethesurprisesonanyFOMCdaysduringthelast 31days(e.g.,onFebruary15,wecumulatealltheFOMCdaysurprisessinceJanuary15),and,second,weaveragethesemonthly surprisesacrosseachdayofthemonth.Or,equivalently,wecanfirstcreateacumulativedailysurpriseseriesbycumulatingall FOMCdaysurprises(similarlyaswasdonebyRomerandRomer(2004)andBarakchianandCrowe(2013)),then,second,we cantakemonthlyaveragesoftheseseries,and,third,obtainmonthlyaveragesurprisesasthefirstdifferenceofthisseries." 11

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? monetarynewsthanexpectedinatimeofrecordstimulus, thepreponderanceofzeroobservationsat theELBsuggeststhatFF4maystillstruggletocapturemonetarypolicyactionsattheELB. Panel1oftable(2)showsthatthepreviouslydiscussedshockseries—MP1,NS,FF4—aretightlycorrelated with correlation coefficients ranging from about 0.8 to above 0.9. This tight correlation is not surprisinggiventhattheyareallcalculatedoverthesamehigh-frequencyintervalsandrelyonfutures with maturities of year or less. Moreover, sometimes these series even use the same underlying data, whichisespeciallytrueforMP1intheNSinstrumentset. 2.4 BU, ROGERS, & WU (2021), BRW Bu et al. (2021) note the following two shortcomings of the previouslydiscussedhigh-frequencymonetaryshockseriesconstructedfromfutureswithmaturitiesof oneyearorless.First,obtainingfuturesdataatanintradayfrequencycanbedifficultandsecond,shorter maturitiesmaybelesssuitedtocapturingpoliciesdeployedattheELBtoaffectlongermaturityassets. ByconstructingmonetaryshockseriesfromchangesindailyTreasuriesyieldsthatspanthefulloneto30-yeartermstructure,Buetal.(2021)overcomethesechallenges.11 Whileintradaydataassurethe crispestseparationofmonetarynewsfromitsnon-monetarycounterpart,dailydatalikethatoriginally usedbyKuttner(2001)mayonlybeproblematiconallbutafewFOMCmeetingsasexplainedbyGürkaynaketal.(2005). However,becauseNakamuraandSteinsson(2018)findthatchangesinlong-terminterestratescanbeconfoundedbybackgroundnoisewhenusedatdailyfrequency,Buetal.(2021)usea Rigobon(2003)heteroskedasticity-basedestimatorinshockconstructiontoavoidoverstatingstatistical precision. Finally,wenotethatdailydatahavetheadvantageofuniformtimewindowsthroughoutthe sample. AppendixA.2showsthatintradaytimewindowsbracketingFOMCannouncementscanoften belargerthan30minuteswhenthereisashortageofsuitabletrades. NotonlyistheBRW shockseriesconstructedfromdifferentunderlyingdata,italsoreliesonadifferent method than the three shock series previously discussed. The Fama and MacBeth (1973) twostep regression extracts unobserved monetary policy shocks ∆i from the common component of the s changeinzero-couponyields∆R j . Thefirststepestimatestheaverageresponsivenessofeachmaturity s j =1,...,30ondaysofFOMCannouncementss. Thesecondstepobtainsrepeatedcross-sectionalestimatesforeachFOMCannouncementbyregressingthedailychangeinmaturitiesoneto30ontothefirst step’saverageresponsivenesscoefficientsformaturitiesoneto30.Theresultingsecondstepcoefficients aretheBRW monetaryshockseries. Notetheslightchangeinnotationinthatregressioncoefficients willhavematurity j asasubscriptinsteadofasuperscript. 1. Estimateresponsivenessofzero-couponyields∆R j withmaturities j =1,...,J topolicyindicator s ∆i for monetary policy announcement s via time-series regressions. For maturities j =1,...30 s yearstherewillbe30regressions. 11SeriesBRW_fomcofspreadsheetbrw-shock-series.csv(https://www.federalreserve.gov/econres/feds/files/brw-shockseries.csv).Thezero-couponTreasuryyieldsarethosecalculatedbyGürkaynaketal.(2007) (https://www.federalreserve.gov/pubs/feds/2006/200628/200628abs.html) 12

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? ∆R1=α +β ∆i +ϵ1 s 1 1 s s . . . ∆R30=α +β ∆i +ϵ30 s 30 30 s s Thisimplementationassumes∆i isone-to-onewithaparticulartenureofinterestrate. Buetal. s (2021)choosethe2-yearconstantmaturityTreasuryyield∆R2. Foreachmaturity j =1,...J,the s aboveexpressioncanbewrittenas: ∆R j =θ +β ∆R2+ϵj−β ϵ2 (7) s j j s s j s (cid:124) (cid:123)(cid:122) (cid:125) ξj s Theendogeneityarisingfromcorr(∆R j ,ξj )>0stemsfromβ ϵ2beingpartofξj andcanberecons s j s s ciledwithIVortheheteroskedasticity-basedestimatorofRigobon(2003). Thetime-seriesregressionsinstrument∆i s with(−1)×∆i s−7 ,thenegativechangeinthechosenpolicyindicatorseven daysbeforeFOMCannouncement s. Using(−1)×∆i s−7 asaninstrumentshouldcanceloutthe β ϵ2thatwouldexistinanygivendaywithoutmonetarypolicynews. j s 2. Recover monetary policy shock ∆iˆ from s =1,...,T repeated cross-sectional regressions of ∆R j s s ontheresponsivenessindexβˆ foreachFOMCannouncementsestimatedinstep1. j ∆R j =α +∆i βˆ +v j , s=1,...,T FOMCannouncements (8) s j s j s 3. Re-scaletheshockseriesbytheassumednormalizationinstep1,i.e.thedailychangeinthe2-year constantmaturity∆R2Treasuryyieldintheoriginalformulation. s Incontrasttotheotherhigh-frequencymonetaryshockseriespreviouslydescribed,panels(4d)and (5d)showthatthedistributionoftheBRW shockseriesissimilaracrossELBandnon-ELBperiods.Furthermore, panel 3 of table (2) shows that shock estimates are never zero throughout the ELB period andabout66percentarenegativeandhenceexpansionaryinperiodsofrecordmonetarystimulus.The largestnegativeobservationsoccurredwhentheFederalReserveextendedorannouncedLSAPprograms inMarch2009andMarch2020,respectively. BecauseforwardguidanceandLSAPsaffectmaturitieslongerthantheone-yearhorizonofthe NS instrument set, shocks constructed from data with maturities up to 30 years should intuitively better capturetheeffectsofthesepolicies. However, includingdataonlongermaturitiesmaybeinsufficient as these data may be unresponsive to monetary policy on average. Figure (2a) shows the responsivenesscoefficientsfromthefirststepoftheFama-MacBethregressiongivenbyequation(7). Onaverage, Treasurieswithrelativelyshortermaturitiesaremoreresponsivetochangesinthetwo-yearTreasuryon FOMCannouncementdays. Infact, Treasurieswithmaturitiesbeyond15yearsdonothaveastatisticallysignificantaverageresponsiveness. Forthisreason, simplyincludinglongertermratesinthe NS instrument set via principal component analysis does not materially change the final series as shown 13

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? inAppendixA.4. Infact,augmentingtheNS instrumentsetwithone-,five-,ten-and30-yearintraday Treasuryyieldsresultsinashockseriesthathasa0.95percentcorrelationcoefficientwiththeoriginal NS series. Wenotethatthiscorrelationcoefficientishigherthanquiteafewoftheotherseriesstudied inthispaper. (a)AverageresponsivenessoftheBRW datato2-year (b)AverageresponsivenessoftheBRW datato2-year Treasuries,fullsample Treasuries,ELBandnon-ELBsamples (c)Second-stepFama-MacBethforMar.16,2016, (d)Second-stepFama-MacBethforAug.9,2011, ∆iˆ=−0.08 ∆iˆ=−0.05 Figure2:ConstructionoftheBuetal.(2021)shockseries. Panels(a)and(b)showestimates{βˆ j}3 j 0 =1 fromequation(7),∆R s j=θ j +β j ∆R s 2+ξ s j formaturitiesj=1,...,30yearsareobtained byregressingdailychangesinzero-couponTreasuryyieldsfrommaturities j =1,...,30onthedailychangeintheconstant maturitytwo-yearTreasury.EstimatesareobtainedviaOLSwithrobuststandarderrors.Becauseresponsevariablesarezerocouponandtheindependentvariableisconstantmaturity,thecoefficientβˆ 2 forthetwo-yearwillbeclosetoone,butnot exactly.Theeffectivelowerboundofthefederalfundsrate(ELB)isdefinedasdefinedasDecember16,2008toDecember16, 2015andMarch15,2020toMarch16,2022.Panels(c)and(d)showthesecondstepoftheBRW Fama-MacBethregressionin equation(8),∆R s j =α j +∆is βˆ j +v s j wheres=March16,2016andAugust9,2011,respectively.Thex-axisinpanels(c)and(d) is{βˆ j}3 j 0 =1 ,thecoefficientestimatesfromthefirst-stepinequation(7)forone-to30-yearmaturitiesplottedinpanels(a)and (b).βˆ j closeto1areshort-termyieldsandβˆ j close0arelong-termyields.They-axisinpanels(c)and(d)isthedailychangein zero-couponTreasuryyields{∆R s j }3 j 0 =1 formaturitiesj=1,...,30years.Theestimatedlinearfit∆iˆ sisthemonetaryshock.The sampleisfromJanuary1995toSeptember2024. 14

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? If long-term data alone cannot account for the differences in monetary shock series, what is the roleofmethods? Incontrasttoprincipalcomponentanalysis,Fama-MacBethregressionallowsforthe weights on underlying instruments to be time varying so that long-term rates may matter more than short-termforcertainannouncementsandtheoppositeforothers.Byrelyingonthedifferentialresponsivenessofshort-andlong-termTreasuries, theFama-MacBethregressioncanthereforeexploitinformationfromlong-termratesdespitetheiroverallaveragelowresponsivenessshowninpanel(2a). The secondstepofthemethodprojectsthechangeinTreasuriesforeachmaturityonthedayofanFOMC announcementontotheiraverageresponsivenessshowninfigure(2a).IfthechangesacrossallmaturitiesonFOMCannouncementdays wereequalsuchthat∆R j =∆R j+1 forallmaturities j+1,thenthe s s estimatedmonetaryshock∆iˆ fromequation(8)wouldbeequaltozero.Ontheotherhand,ifthechange s inallmaturitiesequaledtheiraverageresponsiveness,i.e. ∆R j =βˆ forallmaturities j,then∆iˆ =1. A s j s more practical example than either of these two extremes would be one like that shown in panel (2c) wherethechangeinlong-termratesisclosetozero,butshort-termratesfall.TheBRW Fama-MacBeth methodwouldthenestimateanegativeshock∆iˆ <0eventhoughlongratesarelittlechanged. s Furthermore,identifyingmonetaryshocksviathedifferentialresponsivenessofshort-andlong-term ratesisparticularlyusefulwhenthefederalfundsrateisattheELB.Althoughshort-termratesmaybe relativelyunchangedduetoforwardguidancecommunicatingnoexpectedchangeinthefederalfunds rate, medium- to long-term rates may still be adjusting, especially since forward guidance and LSAPs maybetargetingtheserates. Infact,panel(2b)showsthatmedium-termratesbecamerelativelymore responsiveattheELBchangingmorethanone-for-onerelativetoachangeinthetwo-yearrate. Panel (2d)confirmsthesedifferentialchangesbyshowingaparticularFOMCannouncementwherelong-term ratesdropbymorethanshort-termratesandmedium-termratesarethemostresponsive.Withroughly a-0.03percentagepointchange,theone-yearTreasuryistheleastresponsiveonthisparticularFOMC announcementduringanELBepisode. Comparedtoothermethodsofincorporatinginformationfrompolicyactionsthattargetlong-term interestrates, the single-series ofBu etal. (2021) has theadvantage ofparsimony andflexibility inassumptions. Bycontrast,Swanson(2023)definesmultipleindependentdimensionsofmonetarypolicy and only allows for the effect of large-scale asset purchase shocks during certain periods. Jarocin´ski (2024)andLewis(2023)definemultipledimensionsviaadditionalinformationfromfinancialmarkets. Appendix figures (A.14b) and (A.16b) show that the BRW shock is tightly correlated with versions constructedfromreal-timeestimatesanddifferentnormalizations,respectively. 2.5 INTERCHANGING DATA AND METHODS To confirm that both data and methods drive the differencesintheBRW shockseriesrelativetotheothershocksseriesstudied,wefollowBuetal.(2021)and interchangedataandmethodsofthe NS andBRW shockseries. Overall, wefindthatdifferencesbecomemorepronouncedwiththelargestcorrelationcoefficientat0.24andthelowestat−0.40 asshown intable(2). UsingtheNSdata—changesinfiveinterestratefutureswithmaturitiesofayearorless—intheBRW Fama-MacBethmethodproducesshocksthathaveonlyacorrelationcoefficientofonlyabout0.2with eitheroftheoriginalseries,asshownintable(2).Thisserieshasthelowestcorrelationcoefficientinthe 15

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? entiretable,−0.40withtheMP1shockseries. Panels(4e)and(5e)showthattheNSdatawithBRW methodresultsindistributionsthataresimilar in the ELB and non-ELB periods. By contrast shock series based on raw data or principal component analysis have distributions that narrow at the ELB. In support of these findings, figure (3) shows the averageresponsivenessofthefiveNSinterestratefuturestothetwo-yearTreasuryonFOMCdaysisnot significantlydifferentinELBepisodesrelativetonon-ELBepisodes.Wedonotethattheresponsiveness oftheinstrumentswiththeshortestmaturities—MP1andMP2—isrelativelylowerinELBepisodes. Furthermore, like the original BRW shock series, the version with NS data is mostly symmetric around zero at the ELB as shown in panel (5e). Although the underlying short-term data may be leftcensored,becausetheFama-MacBethregressioncalculatesthedifferentialvariationacrossunderlying instruments,itmaynotalwaysprescribeapositiveshockifallratesrise.Infact,table(2)showsthatonly 52%ofobservationsarepositiveattheELBcomparedwith78%usingtheoriginalprincipalcomponent analysis. Finally,figure(3)supportsthefindingsofSwansonandWilliams(2014)thatmonetarypolicy canstillhaveeffectsattheELB. Figure3:AverageresponsivenessoftheNSdatato2-YearTreasuries. Estimatesβˆ j fromequation(7),butwiththeupdatedNSinstrumentset{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}regressed onthedailychangeintheconstantmaturitytwo-yearTreasury. EstimatesareobtainedviaOLSwithrobuststandarderrors. Theeffectivelowerboundofthefederalfundsrate(ELB)isdefinedasdefinedasDecember16,2008toDecember16,2015and March15,2020toMarch16,2022.ThesampleisfromJanuary1995toSeptember2024. Panels(4f)and(5f)showthatusingtheBRW data—changesinone-to30-yearzero-couponTreasury yields—with the NS principal component analysis results in shock series that are not as small in magnitudeastheotherinterchangedshockseriesshowninpanels(4e)and(5e). LiketheNS shockseries,theseinterchangedshockseriesalsohaveapositivemass—68percentofobservations—duringthe ELBperiods.Becausetheprincipalcomponentanalysisisalinearcombinationoftheunderlyinginstruments,itwillprescribepositiveshockifallratesriseinresponsetothemonetarypolicyannouncement. Likethepreviouslydiscussedinterchangedshock,theshockseriesconstructedfromtheBRW datawith NS methodhasarelativelylowcorrelationcoefficientofatmost0.24withthecommonlyusedshocks westudy. 16

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? (a)Kuttner(2001)ShockSeries,MP1 (b)NakamuraandSteinsson(2018)ShockSeries,NS (c)FF4ShockSeries,FF4 (d)Buetal.(2021)ShockSeries,BRW (e)NakamuraandSteinsson(2018)data,Buetal.(2021)method (f)Buetal.(2021)data,NakamuraandSteinsson(2018)method Figure4:Timeseriesofmonetaryshockseries,January1995toSeptember2024. MP1 is the 30-minute change around an FOMC announcement in the current month’s federal funds future if the FOMC announcement is in the first 23 days of the month with an adjustment or the next month’s federal funds future if the FOMC announcement is within the last seven days of the month. FF4 is the change in the three-month ahead federal funds futures within 30-minutes of an FOMC announcement. NS is the first principal component of the instrument set {MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefuturesaroundanFOMCannouncement. BRW isaFama-MacBethregressionofthedailychangeinone-to30-yearconstantmaturityTreasuryyields. NSdata/BRW methodisaFama-MacBethregressionoftheNS data. BRW data/NS methodisthefirstprincipalcomponentoftheBRW data. 17

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? (a)Kuttner(2001)ShockMP1 (b)NakamuraandSteinsson(2018)Shock (c)FF4Shock (d)Buetal.(2021)Shock (e)NakamuraandSteinsson(2018)data,Buetal.(2021)method (f)Buetal.(2021)data,NakamuraandSteinsson(2018)method Figure5:Distributionsofmonetaryshockseries,January1995toSeptember2024 MP1 is the 30-minute change around an FOMC announcement in the current month’s federal funds future if the FOMC announcement is in the first 23 days of the month with an adjustment or the next month’s federal funds future if the FOMC announcement is within the last seven days of the month. FF4 is the change in the three-month ahead federal funds futures within 30-minutes of an FOMC announcement. NS is the first principal component of the instrument set {MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefuturesaroundanFOMCannouncement. BRW atheFama-MacBethregressionofthedailychangeinone-to30-yearconstantmaturityTreasuryyields.NSdata/BRW methodisaFama-MacBethregressionoftheNS data. BRW data/NS methodisthefirstprincipalcomponentoftheBRW data.TheELBisdefinedasDecember16,2008toDecember16,2015andMarch15,2020toMarch16,2022. 18

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? Panel1)CorrelationCoefficient Panel2)SameSign,% NSdata BRWdata NSdata BRWdata Shock MP1 NS FF4 BRW MP1 NS FF4 BRW BRWmeth. NSmeth. BRWmeth. NSmeth. MP1 1.00 100% NS 0.77 1.00 47% 100% FF4 0.80 0.92 1.00 59% 67% 100% BRW 0.27 0.50 0.42 1.00 42% 65% 53% 100% NSdata/BRWmeth. −0.40 0.22 0.02 0.28 1.00 32% 70% 52% 61% 100% BRWdata/NSmeth. −0.03 0.14 0.05 0.22 0.24 1.00 35% 57% 41% 52% 59% 100% Panel3)SignattheELB,% Shock zero negative positive MP1 38% 37% 25% NS 0% 22% 78% FF4 45% 27% 27% BRW 0% 66% 34% NSdata/BRWmeth. 3% 45% 52% BRWdata/NSmeth. 0% 32% 68% Table2:Statisticsofvariousshockseries. Forhigh-frequencymonetarypolicyshockseries,thethreepanelsdisplaytheir1)correlationcoefficient,2)percentageofoccurrenceswhentheshockshavethesamesign,and3)percentageofoccurrenceswhentheyareeitherequaltozero,positive, ornegativeduringtheELBepisodeswhicharedefinedfromDecember16,2008toDecember16,2015andMarch15,2020 toMarch16,2022. MP1isthe30-minutechangearoundanFOMCannouncementinthecurrentmonth’sfederalfundsfutureiftheFOMCannouncementisinthefirst23daysofthemonthwithanadjustmentorthenextmonth’sfederalfunds futureiftheFOMCannouncementwithinthelastsevendaysofthemonth. FF4isthechangeinthethree-monthaheadfederalfundsfutureswithin30-minutesofanFOMCannouncement. NSisthefirstprincipalcomponentoftheinstrumentset {MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefuturesaroundanFOMCannouncement. BRW isaFama-MacBethregressionofthedailychangeinone-to30-yearconstantmaturityTreasuryyields. NSdata/BRW methodisaFama-MacBethregressionoftheNS data. BRW data/NS methodisthefirstprincipalcomponentoftheBRW data.ThesampleisJanuary1995toSeptember2024. 2.6 PREDICTABILITY Because commonly used monetary shock series have been shown to be predictable and hence not entirely exogenous, we include in our discussion of shock construction predictability tests standard in the literature. Karnaukh and Vokata (2022), Sastry (2021), and Bauer and Swanson(2023)haveshownthattheNS shocksseriesispredictablebyobservablesintheformofeconomicnews, andBuetal.(2021)confirmthattheBRW shocksseriesisnot. Wefindthatshocksconstructedfromfederalfundsfuturesarethemostlikelytobepredictablebyeconomicnews. Standardtestsassessifeconomicnewspredictsmonetaryshocksεi.LetT indexmonthsandthigher t frequencies. Followingtheliterature,ϵi isaggregatedtoamonthlyfrequencybysummation,ϵi =(cid:80) ϵi t T t t andallnewsindicatorspre-datetheFOMCannouncementinagivenmonth. εi =α+βnewsk +e (9) T T T (cid:110) newsvariablek= Blue-ChipGDPrevisions,Non-farmpayrolls,ADSindex,Braveet.alIndex (cid:110) shocki = MP1,FF4,NS,BRW,NS−interchange,BRW −interchange Figure(6)showsthepredictabilitycoefficientsβˆ estimatedfromequation(9)forvariousmeasures of economic news along with their 95% confidence intervals. A monetary shock series is predicted by pre-existingeconomicnewsandisthereforenotentirelyexogenoustounderlyingeconomicconditions 19

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? YS Yz9 z AYz9 KTS 77: Mb #`r Mbh0 j #`rh0 j h h #`rhL3j@R0MbhL3j@R0 hhhhhhhhhhhhhhhhhhhhhhh/ j hRNhhIhwhhhhhhhhhhhhhhhhhhhhhh/ j h N0hL3j@hhRhh0hhchhhhhhhhhhhhhhhhBNj3a,@ N<30 #In3h+@CUh;/Th`3qY MRN8 aLhT waRIIc /bhBN03u #FFhBN03u Figure6:Predictabilitycoefficientswith95%confidenceintervals. Estimateofβˆinequation(9)εi t =α+βnews T k +eT areobtainedviaOLSwithrobuststandarderrorsthataresimilarwhen bootstrapped. ThesampleisfromJanuary1995toSeptember2024andexcludesthesecondquarterof2020. SeeAppendix Figure(A.17)forresultsoveradditionalsubsamplesandwithdifferentcontrols.ForthespecificationusingtheBlueChipGDP revisions,wefollowBauerandSwanson(2023)andexcludeobservationswheretheFOMCannouncementisinthefirstthree businessdaysofthemonthfrom1995toDecember2000andthefirsttwobusinessdaysthereaftertoensurethattheBlue ChipSurveywascompletedpriortotheFOMCannouncement. BlueChipGDPrevisionsarethemonthlyrevisionofonequarteraheadGDPgrowthforecasts. Thespecificationusingnon-farmpayrollsassuresthattheFOMCmeetingisafterthe FOMCreleasewhichistypicallythefirstFridayofeverymonth. Non-farmpayrollsarethemonthlychangeinthenonfarm payrollsrelease. TheADSIndexistheAruobaetal.(2009)businessconditionsindex. TheBKKindexistheBraveetal.(2019) BigDataindex. MP1isthe30-minutechangearoundanFOMCannouncementinthecurrentmonth’sfederalfundsfuture iftheFOMCannouncementisinthefirst23daysofthemonthwithanadjustmentorthenextmonth’sfederalfundsfuture iftheFOMCannouncementiswithinthelastsevendaysofthemonth. FF4isthechangeinthethree-monthaheadfederalfundsfutureswithin30-minutesofanFOMCannouncement. NSisthefirstprincipalcomponentoftheinstrumentset {MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefuturesaroundanFOMCannouncement. BRW isaFama-MacBethregressionofthedailychangeinone-to30-yearconstantmaturityTreasuryyields. NSdata/BRW methodisaFama-MacBethregressionoftheNS data. BRW data/NS methodisthefirstprincipalcomponentoftheBRW data. whenconfidenceintervalsdonotencompasszero.Figure(6)showsthattheNSshockseriesappearsto sufferthemostfrompredictability. Theunderlyinginstrumentsetcanaccountforthisfinding,particularlytheeurodollar/SOFRfuturesthatareonlyusedintheconstructionofshockseriesbasedontheNS data. KarnaukhandVokata(2022)findthateurodollarfuturestendtobemorepredictablethanshortterm fed funds futures, which could help explain why the MP1 and FF4 shock series are less likely to be predictable than the NS shock series. In fact, only those shock series constructed from short-term futures—MP1,FF4, NS,andtheNS datainterchangedshockseries—haveanystatisticallysignificant predictabilitycoefficients. Finally, figure (6) confirms that shock series constructed from long-term interest rates—the BRW shockseriesanditsinterchangedcounterpartconstructedfromtheNSprincipalcomponentmethod— areunpredictableaccordingtoseveralstandardtestsintheliterature. Becausetheinterchangedshock 20

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? series with the BRW data is also unpredictable, including long-term rates in shock construction may helpassurethathigh-frequencyseriesareindeedcontrollingforallavailablepre-existinginformation. However,theshocksconstructedonlyfromfedfundsfutures—theMP1andFF4shockseries—areonly marginallypredictablesuggestingthatpredictabilityismoststronglyassociatedwithseriesconstructed fromtheNSdata. SeeAppendixfigure(A.17)foradditionalresultsoverdifferentsub-samples. 3 MONETARY TRANSMISSION Afterdiscussingtheconstructionofhigh-frequencymonetaryshockseriesandsomeoftheirbasicproperties, wenowexplorehowdataandmethodsaffectestimatesofthetransmissionofmonetarypolicy. WefindthatdifferencesinmonetaryshockseriesaremorelikelytoaffectmonetarytransmissionestimatesfromspecificationsthatrelyonforecastrevisionsthanthosefromlocalprojectionsorVARs. The BRW shocksseriesconstructedfromlonger-termratesandtheFama-MacBethmethoddeliverstransmissionestimatesthatarethesamesignastheoreticalpredictionsinallspecificationsstudied. Bycontrast,theshocksconstructedfromfutureswithmaturitiesofoneyearorlesstendhaveopposite-signed transmissionestimatesintheforecastrevisionspecificationandconventionally-signedresponsesinthe localprojectionsorVARspecifications.Amongtheseshocksconstructedfromfutureswithmaturitiesof oneyearorless,transmissionestimatesusingtheMP1shockseriesaretheclosesttohavingthesame sign across all specifications. This supports the findings of Paul (2020) that the MP1 shock series can potentiallyreducebiasfromeithertheso-called“Fedinformationeffect"orforwardguidancewithout appealingtotheadd-ontechniquesofMiranda-AgrippinoandRicco(2021),BauerandSwanson(2023, 2022),JarocinskiandKaradi(2020),Nunesetal.(2023),Zhu(2023),andothers. 3.1 FORECAST REVISION SPECIFICATION ThemonetarytransmissionspecificationofCampbelletal. (2012) and Nakamura and Steinsson (2018) estimate the response of monthly Blue Chip GDP forecast revisionstohigh-frequencymonetaryshocks. LetT indexmonthsandt higherfrequencies. Following theliterature,ϵi isaggregatedtoamonthlyfrequencybysummation,ϵi =(cid:80) ϵi. t T t t BlueChipGDPRevisions =α+βεi +e (10) T T T Equation(10)canbeestimatedviaOLSbecausethedependentandindependentvariablesarenotsimultaneouslydetermined.IfthechangeinactualGDPwereusedinsteadofthechangeinexpectedGDP, thiswouldnotbethecase. BecausequarterlyGDPstatisticsaretheaccumulationofeconomicoutput overthreemonths,itisimpossibletodisentangletheoutputproducedbeforeanFOMCannouncement— andhencepre-determinedatthetimeoftheannouncement—fromtheoutputproducedaftertheannouncement. BycontrastamonthlyseriesofGDPforecastrevisionsside-stepssimultaneousdetermination by subtracting forecasts made before the announcement from those made after. The resulting forecastrevisionbracketstheFOMCannouncementandcanestimatetheeffectofpolicyonperceptions about economy activity. In fact, researchers exclude monetary shock observations in the first several 21

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? businessdaysofthemonthtoensurethattheBlueChipsurveywascompletedpriortoanFOMCannouncement(seeAppendixBformoredetails). 2 1 0 -1 MP1 FF4 NS BRW NS data BRW data BRW method NS method Data onl y Data and metho d s Interchanged Full sample NS sample Figure7:Forecastrevisioncoefficientsand95%confidenceintervals βˆineq. (10)BlueChipGDPRevisions T =α+βεi T +eT isestimatedviaOLS.Robuststandarderrorsaresimilarwhenbootstrapped. ThefullsampleisfromJanuary1995toSeptember2024andtheNSsampleisfromJanuary1995toAugust2015. FollowingBauerandSwanson(2023),weexcludeobservationswheretheFOMCannouncementisinthefirstthreebusiness daysofthemonthfrom1995toDecember2000andthefirsttwobusinessdaysthereaftertoensurethattheBlueChipSurveywascompletedpriortotheFOMCannouncement. SeeAppendixFigure(B.18)forresultsoveradditionalsubsamplesand withdifferentcontrols. MP1isthe30-minutechangearoundanFOMCannouncementinthecurrentmonth’sfederalfunds futureiftheFOMCannouncementisinthefirst23daysofthemonthwithanadjustmentorthenextmonth’sfederalfunds futureiftheFOMCannouncementiswithinthelastsevendaysofthemonth. FF4isthechangeinthethree-monthahead federalfundsfutureswithin30-minutesofanFOMCannouncement.NSisthefirstprincipalcomponentoftheinstrumentset {MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefuturesaroundanFOMCannouncement. BRW isaFama-MacBethregressionofthedailychangeinone-to30-yearconstantmaturityTreasuryyields. NSdata/BRW methodisaFama-MacBethregressionoftheNS data. BRW data/NS methodisthefirstprincipalcomponentoftheBRW data. The coefficient βˆ from equation (10) estimates monetary transmission and is shown in figure (7) alongwith95%confidenceintervalsforthesixhigh-frequencyshocksstudiedinthispaper. Although NewKeynesiantheorypredictsthattheresponseofGDPtoacontractionarymonetaryshockshouldbe significantandnegative,figure(7)showthatthisisnotthecaseforallshockseries. Estimatesofmonetarytransmissionarepositiveandsignificantforthestandardshocksbasedonshort-terminterestrate futures—theMP1,FF4,andNSshockseries.Campbelletal.(2012)andNakamuraandSteinsson(2018) accountfortheseopposite-signedresponsesasaninformationmismatchbetweenthecentralbankand privateagents. Theyarguethatthisso-called“Fedinformation"effectcanupwardlybiasestimatesand accountforopposite-signedresponsesariseviathemoreinformedcentralbankusingannouncements tosignalinformationtoprivateagentsabouttheunderlyingeconomy.BauerandSwanson(2023)finda 22

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? similarupwardbiasandargueitarisesfromthecentralbankandprivateagentsrespondingtoeconomic news. TheBRW andtheinterchangedshockseriesdonotproducestatisticallysignificantresponsessuggestingthattheopposite-signedresponseisonlyfoundinasubsetofshockseries. Buetal.(2021)attributethelackofopposite-signedresponseintheirshockseriestoacombinationoflonger-termrates and methods. As BRW explain, if there is a differential effect of the Fed Information effect on shortand long-term rates—as shown by Hansen et al. (2019)—, adding long-term rates to the construction ofmonetaryshockseriescanoffsettheinformationeffectfoundinshort-termrates. However,anyinformationeffectinshort-termratesisunlikelytobeoffsetinprincipalcomponentanalysisbecausethe procedureextractslinearcombinationsoftheunderlyinginstrumentsandhencewillpreserveanyinformationeffectintheunderlyingdata. AlthoughMiranda-AgrippinoandRey(2020)andStavrakevaand Tang(2019)findevidenceofinformationeffectsinfactorsconstructedfromlonger-termrates,aslongas thereisadifferentialresponsivenessofshort-andlong-termrates,aFama-MacBethregressionwillnot necessarilyinheritaninformationeffectdetectedinasubsetofrates. Even though the BRW shock series is the only series of the four main shocks that does not result in a positive and significant opposite-signed response, we note that the MP1 shock series of Kuttner (2001)isonlyonthemarginofsignificanceandisonlystatisticallysignificantintheoriginalNSsample from1995to2015.Appendixfigure(B.18)confirmsthefindingsofmarginalsignificanceacrosssamples and controls. For researchers concerned that an opposite-signed response in a shock series indicates contamination from Central Bank information signaling, we argue that the MP1 shock series may be analternativetotheNS shockseries. AlthoughadditionalprocedurestotheNS shockseriescanpurge theseinformationeffects,MP1offerstheadvantageofsimpleconstructionfromrawdata.12 3.2 DAILY LOCAL PROJECTIONS Althoughtheinformationmismatchbetweencentralbanksandprivateagentscanaccountforopposite-signedresponsesofmonetarytransmissionestimates,Jacobsonet al.(2022)presenttheinformationmismatchbetweeneconomicmodelersandprivateagentsasacomplementaryexplanation. Whenresponsevariablesareobservedatalowerfrequencythanexplanatory variables—asisthecasewithmostmacroeconomicresponsevariables—temporalaggregationbiascan affecttransmissionestimates. Jacobsonetal.(2022)showthattimeaggregateddatacanleadtoearlier arriving response coefficients being magnified relative to their later arriving counterparts. When usingthedailyinflationseriesfromtheBillionPricesProject[CavalloandRigobon(2016)]asaresponse variableinsteadofthemonthlyofficialCPI,Jacobsonetal.(2022)findthatinitialpositiveresponsecoefficientsareindeedmagnifiedrelativetolaterarrivingnegativecoefficients.Afterall,theopposite-signed positiveresponseisquitetemporary,ifdetectedatall,whenthedatafrequenciesofexplanatoryandre- 12ThreeexamplesofrigorousprocedurestopurgemonetaryshocksfromcontaminationareworksbyMiranda-Agrippino andRicco(2021),JarocinskiandKaradi(2020),andBauerandSwanson(2022). First,Miranda-AgrippinoandRicco(2021) prescribeprojectingmonetaryshockseriesontotheirlagsandFederalReserveGreenBookforecaststocontrolforthefact thatshockseriesandforecastsarecorrelated. Secondly,JarocinskiandKaradi(2020)exploittheco-movementofstockprices andinterestratestodisentangleinformationshocksfrompuremonetaryshocks.Finally,BauerandSwanson(2022)prescribe orthogonalizingmonetaryshockseriesrelativetoeconomicandfinancialseriesthatarepredatedandcorrelatedwiththe monetaryshockseries. 23

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? sponsevariablesarebettermatched. Additionally,aspecificationwithmatcheddatafrequenciesdoes notrequireresearcherstodiscardFOMCannouncementsthatoccurearlyinthemonthasisnecessary foridentificationwhendatafromtheBlueChipsurveyareusedasaresponsevariable. After showing that the daily inflation series decently approximates the official CPI, Jacobson et al. (2022)computelocalprojectionsandfindconventionally-signedresponseswithonlyashort-livedinitial adverseresponse.Theirlocalprojectionfordayt+histhefollowing, π t+h =α (h) +β (h) εi t +Γ (h) z t +e t (h), e t (h)∼N (0,σ (h) ) (11) Whereπ t+h isdailyinflationatdayt+hcalculatedasthe30-daypercentagechange,z t isthevector ofcontrolswhicharethe30lagsofdailyinflation,andεi isoneofthesixmonetaryshockseriesstudied t in this paper. Estimates are obtained from the Canova and Ferroni (2022) toolbox using instrumental variableswithrobustheteroskedasticityandautocorrelationconsistent(HAC)standarderrorsreported at90percenterrorbands. Figure(8)showstheestimatedimpulseresponsefunctionsβˆ ofthedailyinflationindextoaone- (h) standarddeviationcontractionarymonetaryshockforeachofthesixhigh-frequencyseriesconstructed inthispaper. Theimpulseresponsestoallfourconstructedmonetaryshockseriesestimatestatistically significantconventionally-signedresponses.Ifthereisanopposite-signedresponse,itisshort-livedand ambiguous. In the daily local projections specification with matched frequencies of explanatory and responsevariables,neitherdatanormethodsseemtoimplymuchdifferenceinthesignoftheestimates. Thisfindingcontrastswiththatoftheforecastrevisionspecificationinsection3.1,wherebothdataand methodsdrovedifferencesinestimatesofmonetarytransmission. Panels(8a)and(8b)repeatthemainexerciseofJacobsonetal.(2022)andshowthattheresponses of daily inflation to the NS and BRW shock series are both conventionally-signed. Even though the transmission estimates of the forecast revision specification in section 3.1 are positive and significant fortheNSshockseries,thelocalprojectionestimatesarenegative—andhenceconventionally-signed— for a majority of the 60-day response horizon shown. The only positive—and hence opposite-signed response—is short-lived lasting about 10 days before turning negative. About 30 days after the initial impulse,theresponseisnegativeandsignificant.Infact,theestimatedresponsecoefficientswithanegativesignaretheonlyestimatesthatarestatisticallysignificant. WhenusingtheBRW shockseries,the impulse responses are unambiguously negative about 60-days after a contractionary monetary shock. Unlike the NS shocks series, there are almost no estimated opposite-signed impulse response coefficientsfromtheBRW shockseries. ThepositiveresponsesoftheBRW shocksseriesareconsistentwith thoseoftheforecastrevisionspecificationinsection3.1. 24

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? (a) (b) (c) (d) (e) (f) Figure8:Impulseresponsefunctionsoflocalprojectionstoa1percentagepointmonetaryshock,x-axis isdaysandy-axisispercentagepoints. Estimatesofβˆ (h) inequation(11)π t+h =α (h) +β (h) εi t +Γ (h) zt +e t (h) , e t (h)∼N(0,σ (h) )areobtainedviatheCanovaandFerroni (2022)toolboxwithrobustheteroskedasticityandautocorrelationconsistent(HAC)standarderrorsreportedat90percenterror bands. Thedailyinflationseriesπ t isthe30-daypercentagechangeoftheBillionPricesProjectdailypriceindexwhichis publiclyavailablefromJuly2008toAugust2015viaCavalloandRigobon(2016).Allmonetaryshockseriesshownarecalculated overtheJanuary1995toAugust2015sub-sampleinsteadofthefull1995to2024sample.MP1isthe30-minutechangearound anFOMCannouncementinthecurrentmonth’sfederalfundsfutureiftheFOMCannouncementisinthefirst23daysofthe monthwithanadjustmentorthenextmonth’sfederalfundsfutureiftheFOMCannouncementiswithinthelastsevendaysof themonth.FF4isthechangeinthethree-monthaheadfederalfundsfutureswithin30-minutesofanFOMCannouncement. NSisthefirstprincipalcomponentoftheinstrumentset{MP1,MP2,ED2,ED3,ED4}whichisthe30-minutechangeinthese futuresaroundanFOMCannouncement.BRW isaFama-MacBethregressionofthedailychangeinone-to30-yearconstant maturityTreasuryyields. NSdata/BRW methodisaFama-MacBethregressionoftheNSdata. BRW data/NSmethodisthe firstprincipalcomponentoftheBRW data. 25

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? Turningtothe interchangedshockseries, the NS datawiththeBRW methodshowninpanel (8e) is the only series among the six studied in this paper that has a significant opposite-signed response. Theseshocksarethesmallestinmagnitudesoanylargeswingininflationwillbeascribedtoarelatively tinyimpulseandresultinastatisticallysignificantresponsecoefficient.Forthisreason,theshockseries constructed from the NS data with the BRW method likely estimates a larger initial positive impulse responsethantheNSshockseriesconstructedfromitsstandardprincipalcomponentanalysismethod showninpanel(8a). Because shock series constructed from short-term rates shown in panels (8a), (8c)-(8e) all detect aninitialpositiveimpulseresponse,itmaybetemptingtoascribeopposite-signedresponsestoshorttermrates.However,thepointestimatesoftheimpulseresponsesoftheinterchangedshockseriesconstructedfromtheBRW datawiththe NS methodshowninpanel(8f)aresimilartothoseconstructed withthestandardNS dataandmethodshowninpanel(8a). Methodsmustthereforealsoplayarolein thesimilarityofcoefficientsobservedinpanels(8a),(8c)-(8d),and(8f). Inthecaseoftheinterchanged shockserieswiththeBRW dataandtheNSmethodshowninpanel(8f),theerrorbandsarewiderresultinginnostatisticallysignificantresponsefromzero.Becausethedistributionoftheinterchangedseries islargerthanthatoftheNS seriesoverthe2008to2015period,itislikelythattheadditionalvariation leadstolesspreciseestimates. Overall,differencesinestimatesofmonetarytransmissionfromlocalprojectionswithmatchedfrequencies of explanatory and response variables matter less than in the forecast revision specification withmismatchedfrequencies.Bothdataandmethodsaccountforthisfindingasthepointestimatesare quitesimilarfor1)theNSshockseriesrelyingonshort-termfuturesandprincipalcomponentanalysis, 2)theMP1andFF4shockseriesrelyingonshort-termfutures,and3)thelong-termBRW datainthe principalcomponentanalysis. 3.3 VECTORAUTOREGRESSION Inadditiontospecificationsrelyingonforecastrevisionsorlocalprojections,theeffectofmonetarypolicyonthemacroeconomyisfrequentlyestimatedviaastructuralvectorautoregressionframeworkatamonthlyfrequencybyusinghigh-frequencymonetarypolicyshocks asexternalinstruments. Relativetotheprevioustwospecificationsstudied, theVARspecificationhas disadvantages and advantages. Unlike the daily local projection specification, VAR specifications typically have mismatched data frequencies in the form of high-frequency shocks and low-frequency responsevariables. Ontheotherhand,theVARspecificationhastheadvantageofallowingforfeedback betweenmultiplemacroeconomicvariablesasco-movementsofvariableslikeinflationandoutputare welldocumentedbutabsentfromthespecificationsinsections3.1and3.2. WeusetheVARspecificationofBauerandSwanson(2022)whichisavariantofGertlerandKaradi (2015). Theexternalinstrumentimposesasecondmomentrestrictiontoidentifyshocks,morespecificallyitreplacesonecolumnoftherotationmatrixwithpredictedvaluesfromaregressionofareduced formVARinnovationontheexternalinstrument.13 WefocusontheVARwithexternalinstrumentsasit isthedominantspecificationinempiricalmacroeconomicsasnotedbyMiranda-AgrippinoandRicco 13SeeStockandWatson(2018)foradditionaldocumentationofVARswithexternalinstruments. 26

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? (2023). BauerandSwanson(2022)provideadditionalcomparisonsoftheimpulseresponsesoftheNS shockandtheirorthogonalizedvariantinseveralVARspecificationsincludingonewheretheshockseriesisusedaninternalinstrumentorinlocalprojections. Identificationviaanexternalinstrumenthingesonahigh-frequencymonetarypolicyshockseries εi satisfying relevance and exogeneity conditions to be an adequate external instrument for εmp the t t unobservabletruemonetaryshocks. E[εmpεi]̸=0 and E[εiε(cid:8)m (cid:8) p ]=0 t t t t Whereε isanyseriallyuncorrelatedstructuralshocksdrivingtheeconomyandε(cid:8)m (cid:8) p isasubsetofthese t shocksunrelatedtomonetarypolicy. Sincethetruevalueofεmp isunobserved,bothconditionsultimatelymustbejustifiedlogically. All t high-frequency monetary shock series studied in this paper should satisfy the relevance condition as theycapturemonetarynewsconveyedbyFOMCannouncementsbyconstruction.TheexclusionconditionshouldalsobesatisfiedbecauseofthetightwindowsaroundFOMCannouncementsshouldprevent non-monetary newsfrom moving markets. Section 2.6 calls into question the exclusionary restriction byshowingthatseveralcommonlyusedmonetaryshockseries—thoseofMP1,FF4,andNS—maybe contaminatedbyobservablesandhencepredictable.However,othershockserieslikethoseofBRW and MP1havebeenshowntobeunpredictable,suggestingtherearealternativesforconcernedresearchers. Otherwise,wepointresearchersinterestedinrelyingontheFF4orNS shockstotheorthogonalization procedureofBauerandSwanson(2022). Similarly,researchersconcernedaboutaninformationeffect contaminatingtheexogeneityoftheFF4or NS shockseriesshouldexploretheadd-onproceduresof Miranda-AgrippinoandRicco(2021),JarocinskiandKaradi(2020),Nunesetal.(2023),andZhu(2023) thatisolatepureshocksfromtheirinformationcounterparts.However,wenotethattheMP1andBRW shockseriesshownoormarginalevidenceofpredictabilityoradversely-signedresponsesintheprevious sectionsandmayallowresearcherstoside-steptheseadditionalprocedures. ThespecificationforaVARwithexternalinstrumentsisgivenas: Y T =α+B(L)Y T−1 +s 1 Y T 2Y +u˜ T (12) WhereY isavectorcontainingfourmonthlyeconomicvariablesfromJanuary1973toDecember2019: T thelogoftheconsumerpriceindex(CPI),thelogofindustrialproduction(IP),theGilchristandZakrajšek(2012)excessbondpremium,andthetwo-yearzero-couponTreasuryyieldatamonthlyfrequency. Appendix D details the sources of these series, which we match the exact vintage used by Bauer and Swanson(2022)(https://www.michaeldbauer.com/files/FOMC_Bauer_Swanson.xlsx). Wealsonotethat the two-year Treasury yield is the daily change observed at the end of the month as in the previously mentionedexcelspreadsheetusedbyBauerandSwanson(2022).Theexcessbondpremiumcontrolsfor financialfactorsandthetwo-yearTreasuryisameasureofthestanceofmonetarypolicy. Althoughthe originalGertlerandKaradi(2015)specificationusestheone-yearTreasury,thetwo-yearhastheadvantageofbeinglessconstrainedattheELBandisusedbyBauerandSwanson(2022),ourmaincomparison. 27

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? Next,B(L)isthematrixpolynomialinthelagoperator. AlthoughBauerandSwanson(2022)follow GertlerandKaradi(2015)andRamey(2016)inusing12lags,weshortento8lagsduetothesamplesizeof ourhigh-frequencyshocks. BauerandSwanson(2022)constructaversionoftheNS shockseriesfrom 1988 to 2019 while we begin our sample in 1995 which is as close to the 1994 introduction of explicit policystatementsasourintradaydataallowswithoutresortingtosourceswecannotreplicatefromintradaydataonactualtrades.AppendixCconfirmsthatshorteningthelagsdoesnotsubstantiallychange thequalitativeestimatesofmonetarypolicytransmission,butdoesresultinslightlydifferentpointestimates. AsnotedbyRamey(2016), thesetypesofspecificationsarehighlysensitivetotheunderlying data sample and may therefore differ from the original Gertler and Karadi (2015) estimates which are from1991to2012. Finally, ϵi istheinstrumentfor s Y 2y estimatedviatwo-stageleastsquaresandu˜ istheresidual. t 1 T T Thesampleoftheexternalinstrumentεi doesnothavetobethesameasthatoftheeconomicdata. In t fact, the sample used for our six shock series is from January 1995 to December 2019 and the sample fortheeconomicdataisfromJanuary1973toFebruary2020. Furthermore,followingtheliteratureϵi is t aggregatedtoamonthlyfrequencybysummation,ϵi =(cid:80) ϵi. Wedonotmakeanyfurtheradjustments T t t for the timing of shocks within the month as Ramey (2016) and Miranda-Agrippino and Ricco (2021) find that the adjustments proposed by Gertler and Karadi (2015) can induce serial correlation.14 AppendixCconfirmsthatweobtainsimilarresultsusingourconstructedmonetarypolicyshockstothose constructedbyBauerandSwanson(2022)usingthedataavailablefromtheauthor’swebsite.15 Figure (9) plots impulse responses from equation (12) obtained via the Canova and Ferroni (2022) toolbox with 68 percent error bands and 20,000 draws. For the four main shock series studied in this paper,theimpulseresponsestoa25basispointmonetaryshockarequalitativelyinlinewithmacroeconomictheoryandsimilarinsignandshape.Theresponseofthetwo-yearTreasuryshowninthebottom rowofeachpanelrisesonimpactandisnormalizedsothatitsinitialresponseis25basispoints. After initiallyrising,thetwo-yearTreasurydecreasesandreturnstozeroabout10monthsaftertheinitialimpulse.Theexcessbondpremiumdisplayedinthethirdrowrisesonimpacttoabout0.2to0.4percentage pointinallseriesshownandthendeclinestowardszero. TheimpulseresponsesofbothindustrialproductionandCPIshowninrowsoneandtwooffigure(9), respectively,toacontractionarymonetaryshockaresignificantlynegative—asstandardNewKeynesian theorypredicts.Wefindnoevidenceofanopposite-signedresponsesinCPIorindustrialproductionas wasfoundintheforecastrevisionspecificationinsection3.1orelsewhereintheliterature. Differences inpointestimatesamongthefourshockseriesareonlyinmagnituderatherthaninsign.Theresponses ofindustrialproductionshowninthefirstrowarethelargestfortheMP1andFF4shockseriesshown inpanels(9a)and(9b),respectively. TheresponsesofCPIshowninthesecondrowhavesimilarinterpretation to the responses for industrial production. All CPI responses are statistically significant and negativewiththoseoftheMP1andFF4shocksinpanels(9a)and(9b),respectively,beingthelargestin magnitude. However,theresponseofCPItotheBRW shockseriesinpanel(9d)hasaninitialresponse 14Seefootnote10. 15Seehttps://www.michaeldbauer.com/files/FOMC_Bauer_Swanson.xlsx. 28

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? dnoBssecxE raeY-2 PI IPC muimerP yrusaerT MP1 FF4 NS method, NS data BRW method, BRW data 0 0 0 0 -2 -2 -2 -2 -4 -4 -4 -4 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 0 0 0 0 -0.5 -0.5 -0.5 -0.5 -1 -1 -1 -1 -1.5 -1.5 -1.5 -1.5 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0 0 0 0 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0 0 0 0 -0.2 -0.2 -0.2 -0.2 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 (a)MP1Shock (b)FF4Shock (c)NSShock (d)BRW Shock Figure9:Impulseresponsestoa25basispointmonetaryshock,x-axisismonthsandy-axisispercentage points. Impulseresponsesareestimatesfromequation(12)YT =α+B(L)YT−1 +s1Y T 2Y +u˜T obtainedviatheCanovaandFerroni (2022)BayesianVARtoolboxwith68percenterrorbands,20,000draws,and8lags. Thesampleofmonetaryshockseriesis fromJanuary1995toDecember2019whilethesampleofeconomicdataisfromJanuary1973toFebruary2020.MP1isthe30minutechangearoundanFOMCannouncementinthecurrentmonth’sfederalfundsfutureiftheFOMCannouncementisin thefirst23daysofthemonthwithanadjustmentorthenextmonth’sfederalfundsfutureiftheFOMCannouncementiswithin thelastsevendaysofthemonth. FF4isthechangeinthethree-monthaheadfederalfundsfutureswithin30-minutesofan FOMCannouncement. NSisthefirstprincipalcomponentoftheinstrumentset{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5} whichisthe30-minutechangeinthesefuturesaroundanFOMCannouncement. BRW isaFama-MacBethregressionofthe dailychangeinone-to30-yearconstantmaturityTreasuryyields. IPistheindustrialproductionindex,CPIistheconsumer priceindex,excessbondpremiumisfromGilchristandZakrajšek(2012),andthetwo-yearTreasuryistheendofthemonth dailychangeinthezero-couponyield.AllsourcesofseriesaredetailedinAppendixD. thatislargestinmagnitudetheCPI. ThedifferencesbetweentheNSandBRW shockseriesarerelativelyminorwiththeexceptionofthe responseoftheexcessbondpremium,whichcanbeexplainedbyBRW’sshockconstructionincluding thelonger-endoftheyieldcurve. Inferencewithrespecttoothervariables(CPI,industrialproduction and two-year Treasury) would not be substantially different between the BRW and NS series. Conversely,theMP1andFF4shockseriesshowmuchlargerresponsesoftheCPI. Boththesimilarityofimpulseresponsesandtheconventionally-signedestimatesinfigure(9)could suggestthatdifferencesinmonetaryshocksseriesarenegligiblewhenestimatingmonetarytransmissioninaVARwithexternalinstruments. However, figure(10)showsthattheimpulseresponsesofthe interchanged shock series are quite different than their counterparts shown in figure (9) as the inter- 29

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? dnoBssecxE raeY-2 PI IPC muimerP yrusaerT BRW method, NS data NS method, BRW data 4 4 2 2 0 0 10 20 30 40 50 10 20 30 40 50 1 1 0.5 0.5 0 0 -0.5 -0.5 10 20 30 40 50 10 20 30 40 50 0.2 0.2 0 0 -0.2 -0.2 10 20 30 40 50 10 20 30 40 50 0.4 0.4 0.2 0.2 0 0 -0.2 -0.2 10 20 30 40 50 10 20 30 40 50 (a)NSData,BRWMethod (b)BRWData,NSMethod Figure10:Impulseresponsetoa25basispointmonetaryshock,x-axisismonthsandy-axisispercentage points. Impulseresponsesareestimatesfromequation(12)YT =α+B(L)YT−1 +s1Y T 2Y +u˜T obtainedviatheCanovaandFerroni (2022)BayesianVARtoolboxwith68percenterrorbands,20,000draws,and8lags. Thesampleofmonetaryshockseriesis fromJanuary1995toDecember2019whilethesampleofeconomicdataisfromJanuary1973toFebruary2020.NSdata/BRW methodisaFama-MacBethregressionoftheNSdata,theinstrumentset{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichis the30-minutechangeinthesefuturesaroundanFOMCannouncement.BRW data/NSmethodisthefirstprincipalcomponentoftheBRW data,thedailychangeinone-to30-yearconstantmaturityTreasuryyields. IPistheindustrialproduction index,CPIistheconsumerpriceindex,excessbondpremiumisfromGilchristandZakrajšek(2012),andthetwo-yearTreasury istheendofthemonthdailychangeinthezero-couponyield.AllsourcesofseriesaredetailedinAppendixD. changedshockseriesoftenestimateopposite-signedresponses.Interchangingdataandmethodsinthis circumstance will drastically change the inference. Together, these findings suggest that even though differencesinmonetaryshockseriescanaffectVARestimates,theeffectsofthesedifferencesrangefrom quantitativelysmallwhencomparingthefourmainshockseriesstudiedtoqualitativelylargewhenexaminingcombinationsofdataandmethods.Aneconometricianmustproceedcautiouslyasinferenceis notrobusttoallmodernconstructionsofmonetarypolicyshockseries. Appendixtable(3)displaysthe first-stageF-statistics. Although section 2 documents differences in several commonly used monetary policy shocks, we findthattheeffectofthesedifferencesonestimatesofmonetarytransmissioncanbesmalldependingon thespecificationused. SpecificationslikethedailylocalprojectionsandVARwithexternalinstruments insections3.2and3.3,respectively,aremoresimilarintermsofsignsandmagnitudesofestimatesthan 30

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? theforecastrevisionspecificationinsection3.1. 4 CONCLUSION Becausemonetarypolicysimultaneouslyaffectsandrespondstoeconomicconditions,identifyingexogenous monetary instruments is an ongoing challenge for researchers. Since at least Kuttner (2001), high-frequencyenvironmentshaveprovenusefulforovercomingthesechallengesbyextractingunanticipatedmarketsurprisesthatcontrolforallavailableinformationpriortoanFOMCannouncement.To constructmonetaryshockseries,researchersseparatemonetarynewsfromtheirnon-monetarycounterpartsbycalculatingthechangeinassetpricesminutesafteranFOMCannouncementrelativetothe pricesobservedjustbefore. Althoughvarioushigh-frequencymonetaryshockseriesrelyonsimilarnarrowtimewindowsaround thesamemonetarypolicyannouncements,wedocumentthattheirsignsandmagnitudesarequitedifferentfortheUnitedStates.Furthermore,thesedifferencesarestarkestwhenthefederalfundsrateisat itseffectivelowerboundandtheFederalReservehastypicallydeployedanexpansivetoolkit. Because underlyingdataandstatisticalmethodscandifferinshockconstruction,weaskwhatdrivesdifferences inmonetaryshockseries. Wefindthatdataonlong-termratescancontributetodifferences,butmethods are also important. Because the Federal Reserve’s 21st century monetary policy toolkit can affect short- and long-term rates, long-term rates can capture additional information. However, long-term ratesmaybe,onaverage,relativelyunresponsivetomonetarypolicy. Therefore,methodsliketheBuet al.(2021)Fama-MacBethregressionthatrelyonthedifferentialresponsivenessofshortandlong-term ratesaremoreeffectiveatextractingadditionalinformationfromlong-termrates. After constructing commonly used monetary shock series from raw data to highlight the choices facedbyresearchers,weanalyzeifdifferencesinshockseriesmatterforinference.Wefindthatestimates ofmonetarytransmissionfromlocalprojectionsandVARsaremoresimilaracrossshockseriesthantheir counterpartsestimatedviaforecastrevisions.Infact,someoftheshockserieswiththesimplestdataand methods—theBuetal.(2021)BRW andKuttner(2001)MP1shockseries—arethemostlikelytodeliver estimates of monetary transmission that are consistent with predictions from New Keynesian models acrossseveraldifferentspecifications. 31

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BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? A APPENDIX SHOCK CONSTRUCTION A.1 FUTURESCONTRACTSDETAILS Thefederalfundsfuturescontractunitis$4,167×contractindex withaticksizeofone-quarterofonebasispoint(0.0025),or$10.4175(0.0025×$4,167)forthenearest month’scontractandone-halfofonebasispoint(0.005), or$20.835percontractforallothermonths. Contracts are monthly listed for 60 consecutive months and are traded Sunday through Friday from 6:00pmto5:00pmEST.Theeffectivefederalfundsrateiscalculatedasavolume-weightedmedianof overnightfederalfundstransactionsandisreportedbytheFederalReserveBankofNewYorkthenext businessday by 9 A.M.EasternTime inthe FR2420 ReportofSelectedMoney MarketRates. Expiring contractsarecashsettledagainsttheaveragedailyfederalfundsovernightrateforthedeliverymonth, roundedtothenearestone-tenthofonebasispointwithfinalsettlementoccurringonthefirstbusiness dayfollowingthelasttradingday. FigureA.11:Totaldailynumberoftradesoffederalfundsfuturescontracts.Source:CMEGroupInc. Thepricingofeurodollarfuturesfollowsthesame conventionasthe fedfundsfutures: 100-index, withacontractunitof$2,500×contractindex. Ticksizewasone-quarterofonebasispoint(0.0025= $6.25percontract)inthenearestexpiringcontractmonthandone-halfofonebasispoint(0.005=$12.50 percontract)inallothercontractmonths. Contractswerequarterlylisted,maturingduringthemonths ofMarch,June,September,orDecember,plusfourserialmonthsandaspotmonth,extendingoutten years. Contractsweresettledincashonthe2ndLondonbankbusinessdaypriortothe3rdWednesday of the contract month, and here we follow the timing convention of Nakamura and Steinsson (2018) inthatnewquartersbeginonthe15thdayofthemonthoftheprecedingquarter(e.g.,2023:Q1would beginonDecember15,2022).Convergencetoafinalsettlementpricewasforcedby“randomly”polling twelvebanksactivelyparticipatingintheLIBORmarketduringthelast90minutesoftradeandatclose. Of course our use of quotation marks in “randomly” refers to the price fixing that had taken place in thismarket.Highestandlowestpricequotesweredroppedandthearithmeticaverageoftheremaining quotesdeterminedfinalsettlement. 36

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? A.2 APPENDIX: WINDOWSFORSOURCINGINTRADAYTRADES TheMP1,FF4,andNSshockseriesare allconstructedfromintradayfuturesdataobservedminutesbeforeaFOMCannouncementandminutes after. However,duetotheavailabilityoftrades,theminutes"before"and"after"maynotbeasuniform asresearcherswouldlike. FollowingNakamuraandSteinsson(2018)andGürkaynaketal.(2007),researchersconstructintraday shocks by selecting trades of federal funds or eurodollar futures 10 minutes before an FOMC announcement and 20 minutes after. However, there are not always trades at these exact times. Typically, tradesthattakeplace lessthan10minutesbeforeanannouncementor20 minutesafter arenot considered. Tradesthattakeplacemorethan10minutesbeforeanannouncementareconsideredand researchersselecttheclosestpossibletradesince4:00P.M.ontheprecedingday—thetimewhenafterhourstradingofficiallybegins.Similarly,ifthereisnotradeexactly20minutesafteranFOMCannouncementtheclosesttradeistaken,uptonoononthesubsequentday. Ifnosuitabletradesbeforeorafter themonetarypolicyannouncementexistwithintheseconditions,thechangeissetto0. Figures(A.12)and(A.13)showthesizeofthetimewindowsaroundFOMCannouncementsforeach ofthefivefuturesintheNSinstrumentsetandtheFF4series. Figure(A.12)showsthattradesinfederalfundsfuturesmarketsareoftennotavailableinexact30minute windows around FOMC announcements. While a large share of available intraday trades are withinanhourofanannouncement,itisnotuncommonforintradaywindowstobeseveralhourslong. Moreover,widerwindowsareparticularlyprevalentpre-2005andduringELBperiods. Figure(A.13)revealsasimilar,althoughlessextreme,phenomenonintheavailabilityoftradesineurodollarfutures. Overall,wenotethatthelackofuniformityinwindowsizesdoesnotseemtoaffectshockconstruction. Ifwesetwindowstobeoneortwohours,andhenceincreasetheuniformity,shockseriesarestill tightlycorrelatedtotheircounterpartsconstructedfrom30-minutewindows. 37

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? (a)HistogramoftimeoverwhichMP1issourced. (b)TimeoverwhichMP1issourced,overtime. (c)HistogramoftimeoverwhichMP1issourced. (d)TimeoverwhichFF4issourced,overtime. (e)HistogramoftimeoverwhichFF4issourced. (f)TimeoverwhichFF4issourced,overtime. FigureA.12:TimewindowsaroundFOMCannouncementsforfederalfundsratefutures. 38

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? (a)HistogramoftimeoverwhichED2/SF3issourced. (b)TimeoverwhichED2/SF3issourced,overtime. (c)HistogramoftimeoverwhichED3/SF4issourced. (d)TimeoverwhichED3/SF4issourced,overtime. (e)HistogramoftimeoverwhichED4/SF5issourced. (f)TimeoverwhichED4/SF5issourced,overtime. FigureA.13: TimewindowsaroundFOMCannouncementsforeurodollarfutures. SOFRfuturesreplace eurodollarfuturesstartinginJanuary2022. 39

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? A.3 APPENDIX: REAL TIME ESTIMATES TheMP1andFF4shockseriesarebasedonchangesinraw data,withMP1havingasmallscalarmultipleadjustmentbasedonthedaysremaininginthemonthofa meeting.Incontrast,theNakamuraandSteinsson(2018)andBuetal.(2021)shockseriesutilizestatisticalprocedures(PCAandFama-MacBethregression,respectively),whichraiseconcernsofdiscrepancies inshockestimatescomparedtoreal-timeversions. Wecomparetheseshockstotheirso-called"real-time"counterparts—thatis,shocksforwhichthe nthmonetarypolicyannouncement’sshockiscalculatedusingdataforonlythefirstnmonetarypolicy announcements. Webeginthesereal-timeestimatesatthe30thmeetinginoursamplesothatthestatisticalprocedureshavesufficientobservations. Figure(A.14)showsthat,overall,thereisnotmuchdifferencebetweenthereal-timeshockestimatesandestimatestakenoverthewholesample. Bothshocks haveacorrelationclosetoonewiththeirreal-timecounterpart. Somereal-timeobservations,particularlyfortheBRW shockseriesneartheonsetoftheGreatFinancialCrisis,cansubstantiallydiffer,but thesearenotmany. Overall,thesegiveusreassurancethatitdoesnotmuchmatterifaresearcheruses shocksconstructedasreal-timeestimatesorshocksconstructedusingtheentiresample. 40

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? (a)NakamuraandSteinsson(2018)shockseries (b)Buetal.(2021)shockseries FigureA.14:Real-timeversionsofNakamuraandSteinsson(2018)andBuetal.(2021)series. MonetaryshockseriesarecalculatedfromJanuary1995toSeptember2024. Real-timeestimatescalculatetheshocksfrom thefirst30FOMCannouncementsandthenupdatetheestimatesrecursively. Fromthe31stestimateonward, eachshock observationonlycontainsinformationthatwasavailableatthetimeoftheFOMCannouncement. NS isthefirstprincipal componentoftheinstrumentset{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefutures aroundanFOMCannouncement.BRW isaFama-MacBethregressionofthedailychangeinone-to30-yearconstantmaturity Treasuryyields. 41

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? A.4 APPENDIX: NAKAMURA AND STEINSSON (2018) SHOCK SERIES WITH TREASURY YIELDS IN THE IN- STRUMENTSET Figure(A.15)showstheoriginalNSshockseriesalongwithaversionthatisaugmented toincludeone-, five-,ten-,and30-yearTreasuryyieldsintheinstrumentset. Includingthelong-term rateshaslittleeffectontheresultingseriesbecausemonetarypolicyisunresponsivetolonger-termrates onaverage. FigureA.15:NakamuraandSteinsson(2018)serieswithandwithoutlong-termrates. MonetaryshockseriesarecalculatedfromJanuary1995toSeptember2024. NS isthefirstprincipalcomponentoftheinstrumentset{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefuturesaroundanFOMC announcement. NS withlong-termratesaugmentstheoriginalinstrumentsetwithone-,five-,ten-,and30-yearTreasury yields. 42

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? A.5 APPENDIX: SCALINGS OF SHOCKS ThemethodologiesofboththeBuetal.(2021)andNakamura and Steinsson (2018) monetary policy shocks require scaling for interpretation. Both shocks scale to Treasuryyields: theNakamuraandSteinsson(2018)shockscalestotheone-yearzero-couponTreasury yieldwhiletheBuetal.(2021)shockscalestothetwo-yearconstantmaturityTreasuryyield. Totestif thechoiceofscalingmatters,weusedifferentmaturities. Figure(A.16a)showsthatusingthechangeinthetwo-yearzero-couponTreasuryyieldinsteadofthe one-year makes little difference for the Nakamura and Steinsson (2018) shock series: both versions of theseriessharethesamesign100%ofthetimeandtheircorrelationcoefficientisaperfect1.00. This nearlyperfectcorrelationstemsfromthefinalstepoftheshockconstructionwhereonescalesthefirst principlecomponentbythecoefficientestimateofthescalingvariableonthefirstprinciplecomponent. Figure(A.16b)similarlyshowsthatscalingmakeslittledifferencefortheBuetal.(2021)shockseries. The correlation coefficient between the shock series constructed from the original two-year constant maturityscalinganditscounterpartconstructedfromtheone-yearis0.96. Whenthereissomedifferenceinestimates,itisbecausethescalingvariableusedintheBuetal.(2021)Fama-MacBethregression isusedinboththebeginningandendofshockconstruction. Whilethechoiceofscalingattheendis simplyameanstoconvertashockseriestointerpretableunitsinthesamemannerasintheconstructionoftheNakamuraandSteinsson(2018)shockseries,thechoiceofscalingatthebeginningcouldbe lessinnocuous. InthefirststepoftheFama-MacBethregression,thechoiceofscalingvariableisalsoa choiceofnormalizationforwhichtoassessaverageresponsiveness. However,asfigure(A.16b)demonstrates,thischoiceultimatelymakeslittledifferenceintheconstructedmonetaryshockseries. (a)NakamuraandSteinsson(2018)shockseries (b)Buetal.(2021)shockseries FigureA.16:Monetaryshockseriesunderdifferentscalingassumptions. MonetaryshockseriesarecalculatedfromJanuary1995toSeptember2024. NS isthefirstprincipalcomponentoftheinstrumentset{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefuturesaroundanFOMC announcement.BRW isaFama-MacBethregressionofthedailychangeinone-to30-yearconstantmaturityTreasuryyields. 43

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? A.6 APPENDIX: PREDICTABILITYREGRESSIONS Becausehigh-frequencymonetarypolicyshockseries shouldbeexogenous, itisclearlydesirablethattheseriesarenotsignificantlyassociatedwithobservable macroeconomic news. Following the literature, we test if the six series studied in this paper are predictable by economic news. More specifically, we use as measures of economic news the monthly releasesofonequarter-aheadBlueChipEconomicIndicatorsoutputgrowthrevisions,thebusinessconditionsindexofAruobaetal.(2009)(ADSIndex),theChicagoFedBigDataBusinessCycleIndicatorof Brave et al. (2019), or the monthly change in nonfarm payrolls. See Appendix D for sources of these series. ThepredictabilityregressionsareestimatedviaOLSwithHuber-Whiterobuststandarderrors,where the dependent variable is the monetary shock series being tested and the independent variable is the macroeconomicnewsthatmaybeapredictoroftheshock. Monetaryshockseriesareaggregatedtoa monthlyfrequencyandmonthswithoutamonetarypolicyannouncementaredroppedfromthesample. Followingtheliterature,weassurethatnewspre-datesFOMCannouncements. TheBlueChipone quarter-aheadoutputgrowthrevisionsandthenonfarmpayrollsreleasesarenotreleasedonthefirstof themonth,soforspecificationsusingeitherasanindependentvariablemustexcludemonthsinwhich there a monetary policy announcement before the release of the independent variable. For specifications where the independent variable is Blue Chip one quarter-ahead output growth revisions, we exclude months before December 1, 2000 in which a monetary policy announcement is within the first four business days of the month and we drop months after December 1, 2000 for which a monetary policyannouncementiswithinthefirstthreebusinessdaysofthemonth. Forspecificationswherethe independentvariableisthemonthlychangeinnonfarmpayrolls,weexcludemonthsinwhichamonetarypolicyannouncementoccurswithinthefirstsevendaysofthemonthandwithinthefirstbusiness weekofthemonth. 44

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? YS Yzk Yzl Yz9 YzS z z AYzS AYz9 KTS 77: Mb #`r Mbh0 j #`rh0 j KTS 77: Mb #`r Mbh0 j #`rh0 j h h #`rhL3j@R0MbhL3j@R0 h h #`rhL3j@R0MbhL3j@R0 hhhhhhhhhhhhhhhhhhhhhhh/ j hRNhhIhwhhhhhhhhhhhhhhhhhhhhhh/ j h N0hL3j@hhRhh0hhchhhhhhhhhhhhhhhhBNj3a,@ N<30 hhhhhhhhhhhhhhhhhhhhhhh/ j hRNhhIhwhhhhhhhhhhhhhhhhhhhhhh/ j h N0hL3j@hhRhh0hhchhhhhhhhhhhhhhhhBNj3a,@ N<30 #In3h+@CUh;/Th`3qY MRN8 aLhT waRIIc /bhBN03u #FFhBN03u #In3h+@CUh;/Th`3qY MRN8 aLhT waRIIc /bhBN03u #FFhBN03u (a)FullSample (b)FullSampleex.crisis YS Yzk Yzl Yz9 YzS z z AYzS AYz9 KTS 77: Mb #`r Mbh0 j #`rh0 j KTS 77: Mb #`r Mbh0 j #`rh0 j h h #`rhL3j@R0MbhL3j@R0 h h #`rhL3j@R0MbhL3j@R0 hhhhhhhhhhhhhhhhhhhhhhh/ j hRNhhIhwhhhhhhhhhhhhhhhhhhhhhh/ j h N0hL3j@hhRhh0hhchhhhhhhhhhhhhhhhBNj3a,@ N<30 hhhhhhhhhhhhhhhhhhhhhhh/ j hRNhhIhwhhhhhhhhhhhhhhhhhhhhhh/ j h N0hL3j@hhRhh0hhchhhhhhhhhhhhhhhhBNj3a,@ N<30 #In3h+@CUh;/Th`3qY MRN8 aLhT waRIIc /bhBN03u #FFhBN03u #In3h+@CUh;/Th`3qY MRN8 aLhT waRIIc /bhBN03u #FFhBN03u (c)FullSampleex.crisis&Covid (d)NSSample YzS Yl Yzz9 YS z z AYzz9 AYzS AYS KTS 77: Mb #`r Mbh0 j #`rh0 j KTS 77: Mb #`r Mbh0 j #`rh0 j h h #`rhL3j@R0MbhL3j@R0 h h #`rhL3j@R0MbhL3j@R0 hhhhhhhhhhhhhhhhhhhhhhh/ j hRhNhhIhwhhhhhhhhhhhhhhhhhhhhh/ j h N0hL3j@hhRhh0hhchhhhhhhhhhhhhhhhBNj3a,@ N<30 hhhhhhhhhhhhhhhhhhhhhhh/ j hRNhhIhwhhhhhhhhhhhhhhhhhhhhhh/ j h N0hL3j@hRhh0hhchhhhhhhhhhhhhhhhhBNj3a,@ N<30 #In3h+@CUh;/Th`3qY MRN8 aLhT waRIIc /bhBN03u #FFhBN03u #In3h+@CUh;/Th`3qY MRN8 aLhT waRIIc /bhBN03u #FFhBN03u (e)ELBepisodes (f)Non-ELBepisodes FigureA.17:Predictabilityregressions Estimateofβˆineq. (9)εi T =α+βnews T k +eT areOLS.Panel(a)isthefullsamplefromJanuary1995toSeptember2024. Panel(b)isthefullsampleex-crisiswhichexcludesthefirstthreemonthsof2009. Panel(c)isthefullsampleexcrisisand Covidwhichexcludesthefirstthreemonthsof2009andthesecondquarterof2020. Panel(d)istheNSsamplefromJanuary 1995toAugust2015. Panel(e)istheELBsampledefinedasDecember16,2008toDecember16,2015andMarch15,2020to March16,2022. Panel(f)isthenon-ELBsampledefinedasalldatesexceptthoseinpanel(e). Forthespecificationusingthe BlueChipGDPrevisions,wefollowBauerandSwanson(2023)andexcludeobservationswheretheFOMCannouncementis inthefirstthreebusinessdaysofthemonthfrom1995toDecember2000andthefirsttwobusinessdaysthereaftertoensure thattheBlueChipSurveywascompletedpriortotheFOMCannouncement. BlueChipGDPrevisionsarethemonthlyrevisionofone-quarteraheadGDPgrowthforecasts.Thespecificationusingnon-farmpayrollsassuresthattheFOMCmeetingis aftertheFOMCreleasewhichisoftenthefirstFridayofeverymonth. Non-farmpayrollsarethemonthlychangeinthenonfarmpayrollsrelease. TheADSIndexistheAruobaetal.(2009)businessconditionsindex. TheBKKindexistheBraveetal. (2019)BigDataindex. MP1isthe30-minutechangearoundanFOMCannouncementinthecurrentmonth’sfederalfunds futureiftheFOMCannouncementisinthefirst23daysofthemonthwithanadjustmentorthenextmonth’sfederalfunds futureiftheFOMCannouncementiswithinthelastsevendaysofthemonth. FF4isthechangeinthethree-monthahead federalfundsfutureswithin30-minutesofanFOMCannouncement.NSisthefirstprincipalcomponentoftheinstrumentset {MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefuturesaroundanFOMCannouncement. BRW isaFama-MacBethregressionofthedailychangeinone-to30-yearconstantmaturityTreasuryyields. NSdata/BRW methodisaFama-MacBethregressionoftheNS data. BRW data/NS methodisthefirstprincipalcomponentoftheBRW data. 45

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? B APPENDIX: FORECAST REVISION SPECIFICATION This section describes the data construction for the forecast revision specifications used to estimated monetarypolicytransmission.ThisspecificationisestimatedviaOLSwithHuber-Whiterobuststandard errors.ThedependentvariableismonthlyGDPrevisionsfortheyear-ahead.Morespecifically,foragiven monthwetaketheaverageoftherevisionsfortheone-, two-, andthree-quarteraheadforecasts. The independentvariableistherespectivemonetarypolicyshockbeingtested,excludingshocksoccurring ineitherthefirsttwo(afterDecember2000)orthree(beforeDecember2000)businessdaysofthemonth, asthisiswhentheBlueChipsurveyisstillbeingcollected.ThesampleisfromJanuary1995toSeptember 2024. THEINDEPENDENTVARIABLE: MONETARYPOLICYSHOCK eachofthesixshockseriesstudiedareaggregatedtoamonthlyfrequencybysummingvaluesacrossthemonth.Thereareparticularstepsnecessary totakebeforeinaggregationthatmustbetakentoensurethattheaggregatedmonetarypolicyshocksof amonthprecedeanyBlueChipoutputgrowthrevision. We dropmeetings occurringbefore thatmonth’s survey collectionofBlueChipisfinished. Before December2000,thiswasthefourthbusinessdayofthemonthbutthereafterwasthethirdbusinessday of the month. This step has several sub-steps. Before December 1, 2000, we also drop any meetings within the first three business days of the month while after December 1, 2000 we drop any meetings withinthefirsttwobusinessdaysofthemonth.BeforeDecember1,2000,thismeansthatwedropmonetarypolicyannouncementsthatoccurbeforethefourthdayofthemonthormeetingsthatareeither onthefifthorfourthdayofthemonthandeitheraMonday, Tuesday, orWednesday. AfterDecember 1, 2000 this means that we drop all meetings that occur before the third day of the month as well as meetingsthatareeitheronthethirdorfourthdayofthemonthandonaMondayoraTuesday.Wethen do a monthly sum of monetary policy shocks by month, excluding months during which there are no applicableFOMCmeetings. THE DEPENDENT VARIABLE: GDP FORECAST REVISIONS The dependent variable is the median GDP forecast revisions for the year ahead from the current month from the Blue Chip Economic Indicators. TheBlueChipreleasesGDPforecastsfromthepreviousmonthwithinthefirstweekofthecurrent month.Forexample,theforecastsforOctoberwouldbereleasedwithinthefirstweekofNovember. Year-aheadforecastrevisionsarecalculatedastheaveragechangeintheone,two,andthreequarteraheadmedianGDPforecastsforthecurrentmonth. Forexample, theyear-aheadoutputgrowthforecastrevisionforDecember2007isobtainedbysubtractingtheGDPforecastsfor2008Q1,2008Q2,and 2008Q3fromtheNovember2007editionoftheBlueChipEconomicIndicatorsfromthosefromtheDecember2007editionoftheBlueChipEconomicIndicators. 46

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? 20 10 0 -10 -20 MP1 FF4 NS BRW NS data BRW data BRW method NS method Data on ly Data and metho d s Interchanged non-ELB sample ELB sample 2 1 0 -1 -2 -3 MP1 FF4 NS BRW NS data BRW data BRW method NS method Data on l y Data and metho d s Interchanged Full Full, crisis controls Full, Covid controls Full, crisis and Covid controls NS Sample non-ELB Sample FigureB.18:Forecastrevisioncoefficientsand95%confidenceintervals Estimatesofβˆineq. (10)BlueChipGDPrevisions T =βεi T +eT areobtainedviaOLS.Therobuststandarderrorsaresimilar whenbootstrapped.ThefullsampleisfromJanuary1995toSeptember2024.Crisiscontrolsareindicatorvariablesforthefirst threemonthsof2009andCovidcontrolsareforthesecondquarterof2020. TheNSsampleisfromJanuary1995toAugust 2015.TheELBisdefinedasDecember16,2008toDecember16,2015andMarch15,2020toMarch16,2022.FollowingBauer andSwanson(2023),weexcludeobservationswheretheFOMCannouncementisinthefirstthreebusinessdaysofthemonth from1995toDecember2000andthefirsttwobusinessdaysthereaftertoensurethattheBlueChipSurveywascompleted priortotheFOMCannouncement. MP1isthe30-minutechangearoundanFOMCannouncementinthecurrentmonth’s federalfundsfutureiftheFOMCannouncementisinthefirst23daysofthemonthwithanadjustmentorthenextmonth’s federalfundsfutureiftheFOMCannouncementiswithinthelastsevendaysofthemonth. FF4isthechangeinthethreemonthaheadfederalfundsfutureswithin30-minutesofanFOMCannouncement.NSisthefirstprincipalcomponentofthe instrumentset{MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefuturesaroundanFOMC announcement.BRW isaFama-MacBethregressionofthedailychangeinone-to30-yearconstantmaturityTreasuryyields. NSdata/BRW methodisaFama-MacBethregressionoftheNSdata.BRW data/NSmethodisthefirstprincipalcomponent oftheBRW data. 47

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? C APPENDIX: VAR UsingtheCanovaandFerroni(2022)toolbox,weestimatetheVARspecificationofBauerandSwanson (2022)usingeachofthesixmonetaryshockseriesstudiedinthispaper. ThemonthlyVARhasfoureconomicvariables: two-yearzero-couponTreasuryyields,industrialproduction(IP),theconsumerprice index (CPI), and the Gilchristand Zakrajšek (2012) excess bond premium, inthat order. The two-year zero-couponTreasuryyieldandGilchristandZakrajšek(2012)excessbondpremiumarebothdivided by100,andthelogoftakenofindustrialproductionandCPI.Thetwo-yearzero-couponTreasuryyield is aggregated from a daily to a monthly frequency by using the last observation for each month. Data series and their sources are described in more detail in Appendix D. Appendix figure (C.19) plots the impulseresponsefunctionsforthefoureconomicvariablestoa25basispointNSshock. First,wereproduceBauerandSwanson’s(2022)resultswithdatafromtheirwebsite (https://www.michaeldbauer.com/files/FOMC_Bauer_Swanson.xlsx).Panel(C.19b)inthemiddleshows thatourreplicationisaclosematchtotheirresultsshowninpanel(C.19a)ontheleft.Differencesinerror bandsariseduetoslightvariationinmethodology.WhileweusetheBayesianVARtoolboxofCanovaand Ferroni(2022),theyusefrequentist90percentbootstrappedstandarderrors.However,thesedifferences inerrorbandsdonotmateriallyaltertheimplicationsoftheestimates. Second, we compare estimates from Bauer and Swanson (2022) to those from our construction of the NS shockseriesinaspecificationwith8lagsinsteadof12. BauerandSwanson’s(2022)versionof theNSshockseriesisfromFebruary1988toDecember2019whileoursisfromJanuary1995toSeptember2024.FollowingSwansonandJayawickrema(2023),theyobtainalongersamplebyconstructingthe NS shock series using the first principal component of the (ED1/SF2, ED2/SF3, ED3/SF3, ED4/SF4) instrumentsetscaledbya1percentagepointchangeintheED4rateinsteadofthe(MP1,MP2,ED2/SF3, ED3/SF4, ED4/SF5) instrument set scaled by the daily change in the one-year zero-coupon Treasury.16 Withourrelativeshortersampleformonetaryshockseriesasanexternalinstrument,wefoundthatusing12lagssacrificestoomanydegreesoffreedomforerrorbandstobeinformative.Weinsteaduse8lags asaremedyandourresultsareshowninpanel(C.19c). Whiletherearequantitativedifferencesinthe magnitudesoftheresponses,suchasimpulseresponsesthatarelarger,theresultsarestillquitesimilar tothoseofBauerandSwanson(2022)shownontheleftinpanel(C.19a). Therefore,weproceedtoimplementourvariousmonetarypolicyshocksasexternalinstrumentsstartingin1995inVARswith8lags. Theincreaseinmagnitudesofimpulseresponsesasthesampleshortenscanbeattributedtotheprevalenceofzeroobservationsinthemonetaryshockseries—afterall,inmostyearstherearefourmonths withoutamonetarypolicyannouncements. Asthesampleshortens,thezerosaremoreprominentand giverisetolargermagnitudes. 16Startingthesampleearlierthan1994requiresrelativelymorejudgementondefiningFOMCannouncementdatesandtimes astheFederalReserveonlybeganofficiallyreleasingFOMCstatementsin1994. 48

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? Seriesname F-stat RobustF-stat MP1 0.77 0.54 FF4 0.78 0.31 NS 1.89 1.24 BRW 0.91 0.83 NSdata,BRW method 0.6 0.46 BRW data,NSmethod 2.51 4.1 Table3:First-stageF-statistics. Estimatesfromequation(12)Y T =α+B(L)Y T−1 +s 1 Y T 2Y+u˜ T obtainedviatheCanovaandFerroni(2022) BayesianVARtoolbox with68 percenterror bands, 20,000 draws, and 8 lags. The sample ofmonetary shock series is from January 1995 to December 2019 while the sample of economic data is from January1973toFebruary2020. MP1isthe30-minutechangearoundanFOMCannouncementinthecurrentmonth’sfederalfundsfutureiftheFOMCannouncementisinthefirst23daysofthemonthwith an adjustment or the next month’s federal funds future if the FOMC announcement is within the last seven days of the month. FF4 is the change in the three-month ahead federal funds futures within 30-minutes of an FOMC announcement. NS is the first principal component of the instrument set {MP1,MP2,ED2/SF3,ED3/SF4,ED4/SF5}whichisthe30-minutechangeinthesefuturesaroundan FOMCannouncement. BRW isaFama-MacBethregressionofthedailychangeinone-to30-yearconstant maturity Treasury yields. NS data/BRW method is a Fama-MacBeth regression of the NS data. BRW data/NSmethodisthefirstprincipalcomponentoftheBRW data.IPistheindustrialproduction index,CPIistheconsumerpriceindex,excessbondpremiumisfromGilchristandZakrajšek(2012),and thetwo-yearTreasuryistheendofthemonthdailychangeinthezero-couponyield.Allsourcesofseries aredetailedinAppendixD. 49

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? BS MPS Non-orthogonalized BS MPS Non-orthogonalized 0 0 -1 -1 -2 -2 10 20 30 40 50 10 20 30 40 50 0 0 -0.5 -0.5 -1 -1 10 20 30 40 50 10 20 30 40 50 0.4 0.4 0.2 0.2 0 0 10 20 30 40 50 10 20 30 40 50 0.2 0.2 0 0 -0.2 -0.2 10 20 30 40 50 10 20 30 40 50 (a)BauerandSwanson(2022) (b)Replicationusingdatafrom (c)Replicationusing8insteadof BauerandSwanson(2022) 12lags FigureC.19: Impulseresponsestoa25basispoint NS shockseries, x-axisismonthsandy-axisispercentagepoints. Panel(a)isfigure(3)inBauerandSwanson(2022).Estimatesinpanels(b)and(c)arefromequation(12)YT =α+B(L)YT−1 + s1Y T 2Y +u˜T obtainedviatheCanovaandFerroni(2022)BayesianVARtoolboxwith68percenterrorbandsand20,000draws. IPistheindustrialproductionindex,CPIistheconsumerpriceindex,excessbondpremiumisfromGilchristandZakrajšek (2012),andthe2-yearTreasuryistheendofthemonthdailychangeinthezero-couponyield.Allsourcesofseriesaredetailed inAppendixD. 50

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? D APPENDIX: DATA Thissectionliststhesourceanddescriptionofeachseriesusedinthispaper. ADS INDEX isadailybusinessconditionsindexfromAruobaetal.(2009)andavailablefordownload fromtheFederalReserveBankofPhiladelphia(https://www.philadelphiafed.org/surveys-and-data/realtime-data-research/ads). BLUE CHIP GDP FORECAST REVISIONS arethemonthlyforecastrevisionofthemedianGDPforecast. TheyareobtainedfromHaverAnalytics’BlueChipEconomicIndicators (http://www.haver.com/our_data.html). BKK INDEX isadailycoincidentindexfromBraveetal.(2019)thatprovidesasummarystatisticfor thestateoftheeconomy. ItisavailablefordownloadfromIndianaUniversityKelleySchoolofBusiness (https://www.ibrc.indiana.edu/bbki/). CONSTANTMATURITYTREASURYYIELDS aredailymarketyieldsonU.S.TreasuriesobtainviatheH.15 SelectedInterestRateReleasefromtheFederalReserveBoard. DAILY CPI The Billion Prices Project publicly available daily CPI can be obtained via Cavallo and Rigobon(2016)forJuly2008throughAugust2015(https://dataverse.harvard.edu/dataset.xhtml? persistentId=doi%3A10.7910%2FDVN%2F6RQCRS).ThisisseriesindexCPIforcountry==USAinspreadsheetpricestats_bpp_arg_usa.csvinfolderall_files_in_csv_format.zip.Alternatively,thedata arealsoavailablefromthepricestats_bpp_ar_usa.dtafileintheRAWDATAfolderonthewebsite https://www.openicpsr.org/openicpsr/project/113968/version/V1/view.Theindexisnotseasonallyadjustedconstructedfromwebscrapedpricesofmultichannelretailersthatsellbothonlineandoffline. EURDOLLARFUTURES areavailableatanintradaytickfrequencyfrom1995toMarch2023viatheCME GroupInc.DataMine(https://datamine.cmegroup.com/)attheFederalReserveBoard. EXCESS BOND PREMIUM isamonthlycreditspreadindexfromGilchristandZakrajšek(2012)andis availablefromtheFederalReserveBoard (https://www.federalreserve.gov/econres/notes/feds-notes/ebp_csv.csv.) FEDERALFUNDSFUTURES areavailableatanintradaytickfrequencyfrom1995topresentviatheCME GroupInc.DataMineattheFederalReserveBoard(https://datamine.cmegroup.com/). FOMCANNOUNCEMENTDATESANDTIMES thedatesofFOMCannouncementsfor1995-2024areobtaineddirectlyfromtheFederalReserve’spublicwebsite (https://www.federalreserve.gov/monetarypolicy/fomccalendars.htm). Forselectingtheexacttimesof theannouncements,wefirstusethereleasetimeasprintedontheFOMC’spublicpressreleaseorotherwiseontheFederalReserve’spublicwebsite. Thisispossibleforthemeetingsof8/7/2007,5/9/2010, 51

BRENNAN,JACOBSON,MATTHES&WALKER: DATAORMETHODS? andfrom2016to2024. WheneveritisnotpossibletousereleasetimefromtheFederalReserve’spublicwebsite, wenexttakereleasetimesasrecordedinthedataofGürkaynaketal.(2005), whichcovers meetingsfrom1995-2004. Finally,weconsiderthetimeofthefirstarticleonBloombergregardingthe FOMCannouncement,whichmainlycoversmeetingsfrom2005to2015. WedropallnotationalmeetingsincludingAugust27,2000,October4,2019,March11,2008,andAugust10,2007. Followingmuch oftheliterature,wedropthemeetingsafter9/11. WedroptheMarch15,2020unscheduledmeetingas itoccurredonaSundayanditisdifficulttosourcetrades. INDUSTRIAL PRODUCTION is the seasonally adjusted monthly Industrial Production Index from the FederalReserveBoard(ALFRED: INDPRO_20200616). CONSUMERPRICEINDEX istheseasonallyadjustedmonthlyConsumerPriceIndexfromtheBureauof LaborStatistics(FRED: CPIAUCSL_20210208). NONFARMPAYROLLS,ALLEMPLOYEES isthemonthlytotalnonfarmpayrollsreleasefromtheBureauof LaborStatistic’sCurrentEmploymentStatisticsEstablishmentSurvey(FRED: PAYEMS). ZERO-COUPONTREASURYYIELDS arecontinuouslycompoundedzero-coupondailyyields(mnemonic: SVENYXX)obtainedfromtheFederalReserveBoard (https://www.federalreserve.gov/data/yield-curve-tables/feds200628_1.htmlorasacsvfile). 52