美联储-双重惯性、泰勒规则与货币政策渐进主义 Double Inertia,Taylor Rules,and Monetary Policy Gradualism

FinanceandEconomicsDiscussionSeries

FederalReserveBoard,Washington,D.C.

ISSN1936-2854(Print)

ISSN2767-3898(Online)

DoubleInertia,TaylorRules,andMonetaryPolicyGradualism

EdmundCrawley,WilliamGoodwin,MargaretM.Jacobson,FabianWinkler

2026-036

Pleasecitethispaperas:

Crawley,Edmund,WilliamGoodwin,MargaretM.Jacobson,andFabianWinkler(2026).“DoubleInertia,TaylorRules,andMonetaryPolicyGradualism,”FinanceandEconomicsDiscussionSeries2026-036.Washington:BoardofGovernorsoftheFederalReserveSystem,

/10.17016/FEDS.2026.036

.

NOTE:Sta优workingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminarymaterialscirculatedtostimulatediscussionandcriticalcomment.Theanalysisandconclusionssetfortharethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchsta优ortheBoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthanacknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.

1

DoubleInertia,TaylorRules,andMonetaryPolicy

Gradualism

∗

EdmundCrawleyWilliamGoodwinMargaretM.JacobsonFabianWinkler

May26,2026

Abstract

Inrecentdecades,anempiricallyestimateddouble-inertialrulefitsthepathofchangesinthefederalfundsratebetterthanastandardinertialTaylorrule.InertialTaylorrulesaimtocapturemonetarypolicygradualismviaslowadjustmentsinthelevelofthepolicyrate.Double-inertialrulesbuildonthisspecificationbyalsograduallyadjustingthepaceofchangeinthepolicyrate.Becauseadouble-inertialruleexplainsmorethantwicethevariationofchangesinthepolicyratethanitsstandardinertialcounterpart,wearguethatpractitionersshouldconsideradouble-inertialrulewhencharacterizingU.S.monetarypolicy.

Keywords:Monetarypolicy,Taylorrules,gradualism,interestratesmoothing,in-ertia,federalfundsrate,effectivelowerbound.

JELCodes:E52,E58,E43.

∗AllauthorsareattheFederalReserveBoard.WethankStephenVasilijevicforhisexcellentdis-cussionandBenjaminJohannsenforhelpfulcomments.Thismaterialreflectstheviewsoftheau-thorsandnotthoseoftheFederalReserveBoardofGovernors.E-mails:

Edmund.S.Crawley@

,

Liam.M.Goodwin@

,

Margaret.M.Jacobson@

,

Fabian.Winkler@

.

2

1Introduction

“Indeed,FOMCparticipantshavebuilt[...]agradualpathofratehikesintotheirprojectionsforthenextcoupleofyears.”

—JanetYellen,October15,2017,SpeechasFedChairattheGroupof30InternationalBankingSeminarinWashington,DC.

1

“Atsomepoint,asthestanceofmonetarypolicytightensfurther,itlikelywillbecomeappropriatetoslowthepaceofincreases.”

—JeromePowell,August26,2022,SpeechasFedChairataneconomicsymposiuminJacksonHole,Wyoming.

2

ThelasttwodecadesprovideanespeciallyusefulsettingforstudyingthebehaviorofU.S.monetarypolicy.Inthewakeofthe2008financialcrisis,thefederalfundsratewasheldattheeffectivelowerbound(ELB)foranextendedperiod.Afterabriefnormaliza-tion,theCOVID-19pandemicbroughtaboutareturntotheELB,followedbyaboutofhighinflation,arapidhikingcyclefrom2022to2024,andasubsequenteasingtowardsmoremoderatelevels.Understandingthefactorsthatexplainthisvariationinthefederalfundsrate,itsdeparturesfromtheELB,anditsrelationshipwitheconomicfundamentalsisanongoingchallengeinmonetaryeconomics.

Sincetheirinceptionintheearly1990s,Taylorrules(

Taylor

,

1993

)havebeenwidelyemployedasaframeworkfordescribingthemovementsofthepolicyratethroughasmallsetofmacroeconomicaggregates.Despitetheirsimplicity,theserulesperformremarkablywellandremainamongthemostinfluentialframeworksfordescribingmonetarypolicy.Alargesubsequentliteraturehasestablishedthataddingthelaggedpolicyratetotheserulessubstantiallyimprovesfit,particularlyinthepost-Volckerera(

Claridaetal.

,

2000

;

Sack

andWieland

,

2000

).Thissuccessiscommonlyinterpretedasevidenceofmonetarypolicy“gradualism”—thepracticeofavoidinglarge,abruptadjustmentsofthelevelofthepolicyrateandinsteadadjustthepolicyrategraduallyinresponsetoeconomicfundamentals.

However,large,abruptadjustmentsofthepaceofpolicyratechangesarealsorareandpolicymakersoftencommunicatetheirpolicydecisionsintermsofthepaceofchanges,asouropeningquotesmakeclear.

CarlstromandFuerst

(

2014

)arguethatsuchaviewofgradualismcannotbecapturedwithasinglelaginapolicyruleandintroducedtheterm“doubleinertia”tocapturethesmoothpathofpolicyratechanges.Usingdataupto2008,

CarlstromandFuerst

(

2014

)and

CoibionandGorodnichenko

(

2012

)documentthatadouble-inertialTaylorrulefitsthepathofthefederalfundsratebetterthanasingle-inertialrule.

Thispaperprovidesasystematicempiricalevaluationofthedouble-inertialTaylorrulethrough2025,therebydoublingthesamplelengthofpreviouswork.Thesampleincludestwoepisodesduringwhichthepolicyratehititseffectivelowerbound(ELB),whichmaybeparticularlyimportantforunderstandinggradualism.Thatis,gradual

1

/newsevents/speech/yellen20171015a.htm

.

2

/newsevents/speech/powell20220826a.htm

.

3

post-liftoffincreasesinthepolicyratecanactasapartialcommitmentdevice,helping

policymakerskeeprateslowerforlongerwhentheriskofreturningtotheELBremainselevated(

Evansetal.

,

2015

;

Nakata

,

2017

;

Nakov

,

2008

).TheDecember2015ELBdeparturewasfollowedbysmallincreasesof0.25percentagepoints,butthe2022exitwasoneofthemostrapidtighteningcyclesin40years.Takingintoaccountthepaceofpolicyrateincreasesfeaturedinthedouble-inertialrulehelpsexplainthebehaviorofthefederalfundsrateinbothepisodes.

Wefindstrongevidencethatthedouble-inertialrulecanexplainthepathofthefederalfundsrate.AtanR2of0.57,thedouble-inertialruleisabletoexplainmorethantwicethevariationinquarterlychangestothefederalfundsrateacrosstherelevantsamplethanthebestsingle-inertialrule.Furthermore,thisresultisrobusttoalternativedatasubsets,theuseofshadowrateestimatesduringeffectivelowerboundperiods,substitutionofanoutputgapmeasurefortheunemploymentgap,andtheuseofreal-timeratherthanrealizeddatainthespiritof

Orphanides

(

2001

).Becauseasingle-inertialrulecapturesonlypartofthegradualismevidentinthedata,itsuseinestimatedNew-Keynesianmodelsrisksmisspecification.Adouble-inertialspecificationoffersasharperbenchmarkforthepolicyanalysisandforecastingcarriedoutincentralbanksandtheprivatesector.

Thesuccessofinertialrulesmaysimplyreflectthefactthatfirst-orderautoregres-sivemodelsareoftenthebestpredictorofmacroeconomictimeseries,includinginterestrates.Indeed,simpleautoregressivemodelsdovirtuallyjustaswellinpredictingone-quarter-aheadchangesinthefederalfundsrateassingle-inertialTaylorrules,asnotedby

Nakamuraetal.

(

2025

).However,whenpredictingthepolicyrateatlongerhorizons,rulesrelyingoneconomicfundamentalsoutperformsimpleautoregressivebenchmarks.Economicfundamentalsthuscontributelittletoshort-runpredictionsofthepolicyratebutareessentialforpredictingthepathofthepolicyrateoverlongerhorizons.

Wealsoevaluatetheempiricalperformanceoftheinertialrulesduringthehistoricalperiodstartingin1960andendingwithVolcker’sresignation.Alargeliteratureindi-catesthatmonetarypolicywasstructurallydifferentbeforethe1980s,exhibitingweakerresponsestoinflationexpectations,morefocusonmonetaryaggregates,lessrelianceonpolicyrules,andlowerinertia(e.g.

Taylor

,

1999

;

Claridaetal.

,

2000

;

Duffee

,

2026

).Inlinewiththisliterature,wecannotrejectthenullthatasingle-inertialruleissufficienttodescribethebehaviorofthefederalfundsratepriorto1987.

Whileweshowthatthesmoothingofthepaceofratechangesisagoodempiri-caldescriptionofmonetarypolicy,ananalysisofwhypolicymakersbehaveinthiswayisbeyondthescopeofourpaper.

Rudebusch

(

2006

)hascontendedthatinterest-ratesmoothingmayjustbeanartifactofpersistentpolicyshocks,but

CoibionandGorod-

nichenko

(

2012

)provideseveralpiecesofevidencerefutingthisinterpretation.Thereistheoreticalworkthatjustifiesinterestratesmoothingasoptimal.Mostprominently,

Woodford

(

1999

)derivestheinterestraterulethatimplementsoptimalmonetarypolicyinastandardNew-Keynesianmodelandshowsthatitisinertial.Infact,itfeaturesexactlytwolagsinthepolicyrate,justlikethedouble-inertialrule.Othernormativeargumentsexplainthatinertiacouldbeanoptimalresponsetoeconomicuncertaintyandfinancialmarketvolatility(

Bernanke

,

2004

;

Woodford

,

1999

;

SackandWieland

,

2000

;

SteinandSunderam

,

2018

;

Levinetal.

,

1999

;

CaballeroandSimsek

,

2022

).

4

OurpapercontributestorecentworkthatassesseshowwellTaylorrulesfitthepathofthefederalfundsrate.

Aastveitetal.

(

2024

)documentahigherdegreeofinterestratesmoothingineconomicexpansionsthanincontractions.

Kakhbodetal.

(

2026

)and

Hofmannetal.

(

2025

)findhigherTaylorrulecoefficientsondemand-driveninflationthansupply-driveninflation.

Nakamuraetal.

(

2025

)compareTaylorrulepredictionsacrosscountriesandfindthestrongestfitfortheUnitedStates,butwiththecaveatthatthequalityofthefitvariesacrossthesample.

CarlstromandJacobson

(

2015

),

Baueretal.

(

2024a

,

b

),

Gonz´alez-AstudilloandTanvir

(

2026

),and

HerbstandPage

(

2026

)studyprofessionalforecastsofinterestratesthroughthelensofTaylorrules.

Tatarand

Wieland

(

2024

)interprettheTaylorrulespublishedintheFederalReserve’sMonetaryPolicyReporttoCongress.

Thestructureoftherestofthepaperisasfollows.

Section2

presentsourTaylorrulesandbenchmarkmodelsusedinestimation.

Section3

describesourdataandmethod-ologicalapproach.

Section4

evaluatesourprimaryresultsandgoodnessoffitmetrics.

Section5

detailsouradditionalrobustnessexercises.

Section6

concludes.

2Monetarypolicyrules

WefirstreviewTaylorrulespecificationswithandwithoutinertia,includingthedouble-inertialruleof

CarlstromandFuerst

(

2014

).

Letitbethenominalpolicyrateattimet.Anon-inertialTaylorruleTRtrelatesthenominalpolicyrateittoinflationandameasureofresourceutilizationintheeconomy.Whenthepolicyrateisnotconstrainedbytheeffectivelowerbound(ELB),thepolicyrateissetaccordingto:

wherer*isthelonger-runneutralrealrate(assumedtobeconstantoveragivendatawindow),πtistheinflationrate,utistheunemploymentrate,π*isthetargetrateof

inflation,anduisthenaturalrateofunemployment.Inestimation,weaccountforthe

effectivelowerboundbyspecifyingtheshadowpolicyrateas:

t=θ0+θ1πt+θ2(ut—u)+εt,(2)

andwethenobserve

~

it=max{i,it},(3)

wherethemaxoperatorcapturestheconstraintthattheinterestratecannotfallbelowtheELB,i.

ThestandardwayofaddinggradualismtothisruleistoassumethattheinterestrateissetasaweightedaverageoftheTaylorruleprescription,TRt,andthepreviousperiod’sinterestrate.Wethusintroduceaparameterρthatcapturesgradualismonthelevelof

5

thepolicyrate.Theresultingspecificationisthe“single-inertial”Taylorrule.Awayfrom

theELB,thisruleprescribes:

it=ρit-1+(1—ρ)TRt.(4)

Bysubtractingit-1frombothsides,thisrulecanberewrittenintoapartial-adjustmentspecificationthatrelatesthepaceofchangeininterestratestothedifferencebetweentheprescribedandthepreviouslevelofthepolicyrate:

∆it=(1—ρ)(TRt—it-1),

where(1—ρ)istheproportionofmovementfromthecurrentlevelofthepolicyratetowardstheintermediateratetargetgivenbythenon-inertialTaylorrule.

Expandingthelevelsspecificationofthesingle-inertialruleyieldsthefollowing:

it=ρit-1+(1—ρ)[r*+π*+βπ(πt—π*)+βu(ut—u)].(5)

Werecovertheparametersofthisrulefromtheestimationofthecorrespondinglatentpolicyratespecification:

it=max{i,θ0+θ1πt+θ2(ut—u)+θ3it-1+εt}.(6)

CarlstromandFuerst

(

2014

)advocatedforaTaylorrulewith“doubleinertia”,whichsmoothsnotonlythelevelofthepolicyrate,butalsoitspaceofchange.Themotivatingideaisthatitisuncommonforcentralbankstoabruptlygofromahiketoacutevenwhenthecutissmall,andcentralbankscommonlyadjustthepolicyrateinaseriesofequal-sizeincrements.Theseempiricalregularitiesarecapturedwiththeadditionofaparameterγinthepartial-adjustmentspecification:

∆it=γ∆it-1+(1—ρ)(TRt—it-1).

Expandingandconvertingintolevels,thedouble-inertialTaylorruleawayfromtheELBtakestheform:

it=—γit-2+(ρ+γ)it-1+(1—ρ)[r*+π*+βπ(πt—π*)+βu(ut—u)].(7)

Werecovertheparametersofthisrulebyestimatingthecorrespondinglatentpolicyratespecification:

it=max{i,θ0+θ1πt+θ2(ut—u)+θ3it-1+θ4it-2+εt}.(8)

TounderstandtheextenttowhichthestrongempiricalperformanceofinertialTaylorrulescomessimplyfromanchoringpredictionsforthecurrentinterestratetotheirpreviouslevel,wealsoevaluateAR(1)andAR(2)benchmarkmodelsofthepolicyrate,wherewesetθ1andθ2tozeroin(

6

)and(

8

).

6

3Data

AllofthedatausedinourprimaryestimationprocedureissourcedfromtheFederalReserveBankofSt.Louis’sFREDdatabase.Wefocusonthe2026:Q2datavintage,whichallowsustoestimatealongersamplethanwouldbepossibleusingreal-timedata,asin

Orphanides

(

2001

).

3

Weusedataforthefederalfundseffectiverate(FEDFUNDS),thepersonalconsumptionexpenditurespriceindex(PCEPILFE),theunemploymentrate(UNRATE),andtheCongressionalBudgetOfficeestimateofthenoncyclicalrateofun-employment(NROU)ataquarterlyfrequency.Wethenconstructanunemploymentgapproxybycomputingthedifferencebetweentheunemploymentrateandthenoncyclicalrateofunemploymentineveryquarter.Theinflationtargetπ∗isnotestimatedbutinsteadsettotheFederalReserve’s2percentgoal.Whilethistargetwasnotformallyannounceduntil2012,wetreatitasareasonableproxyforthelowandstableinflationmandatethatguidedpolicyinearlierdecades.

Wefocusouranalysisonthreedatasamples.Thefirstsamplerunsfrom1987:Q4to2006:Q4,whichcoverstheperiodfollowingPaulVolcker’sresignationasChairoftheFederalReserveBoardbutpriortotheeventsassociatedwiththe2008recession.ThiswindowcorrespondsfairlycloselytothedatausedinpreviousanalysisofTaylorruleswithdoubleinertia,whichalsoendsbeforethe2008crisis.WeestimatetheparametersofourpolicyrulesoverthisperiodusingOLSregressioninlinewith

Carvalhoetal.

(

2021

),whoshowthattheendogeneitybiasissmall.

Thesecondsampleadditionallyincludestheperiodbetween2007:Q1and2025:Q3.Thisextensiondoublesthesamplesizeusedinpreviouswork,allowingustoreassesstheprevalenceofdoubleinertiainrecentdecadeswithgreaterprecision.Duringthisperiod,theFederalReserveheldthepolicyrateattheeffectivelowerbound(ELB)fromDecember16,2008toDecember15,2015,andagainfromMarch15,2020throughMarch16,2022.Asaresult,ourextendedsampleincludes“liftoff”episodes,whichmaybeespeciallyimportantforunderstandinggradualismgiventhatpolicymakersmaywanttoincreasethepolicyrateslowlytomitigatetheriskofreturningtotheELB.BecausechangesinthestanceofmonetarypolicyarenotreflectedinthefederalfundsrateduringELBperiods,weemployTobitregressionstoestimatetheruleparametersinourmodelofthelatentpolicyrate.

Ourthirddatasubsetcoversanearlierperiodfrom1960:Q1to1987:Q3.Thiswindowprovidesavaluablecomparisonthatbothhighlightstheimportanceofdoubleinertiainpredictionandhelpstosupportitsinterpretationinthecontextofmonetarypolicygradualism.TheliteraturehaslongrecognizedthatTaylorrules—particularlythosewithsingleinertia—describemonetarypolicyfarmoreaccuratelyinthepost-Volckerera(e.g.

Claridaetal.

,

2000

,

Taylor

,

1999

).ThisobservationisgenerallyunderstoodasreflectingsubstantialshiftsintheFederalReserve’sapproachtomonetarypolicyinthelateeightiesandearlynineties,includingstrongeradherencetotheTaylorprinciple,greaterconcernwithmarketexpectations,andamoregradualpolicyrateadjustmentprocess.Totheextentthatourestimatessuggestdoubleinertiaismorepronouncedinrecentdecades

3Section

5

showsthatourconclusionsholdwithreal-timedata.

7

thanitwasinthehistoricalsample,thisprovidesevidencethatitmaybeacharacteristicfeatureofgradualistpolicyregimes.

4Results

4.1Ruleparameters

Table

1

reportstheestimatedparametersofeachTaylorrulevariant.

Theinflationgapcoefficientπispositiveandtheunemploymentgapcoefficientu

isnegativeinallmodels,asexpected.Theinflationgapcoefficientisalsolargerthanoneinallmodelsexceptinthefullpost-1987sample,wheretheinflationcoefficientforthenon-inertialTaylorruleissmallwithalargestandarderror.At0.92,theimpliedpolicyresponsetoinflationislessthanone-for-oneovertheperiod,implyingaviolationoftheTaylorprinciple.Wethinkthisreflectsmisspecificationfromthemissinginertiainthisrule:TheFederalReservedidadjusttargetinterestratesmorethanone-for-oneinresponsetoinflation.

Ther∗estimatesgeneratedbytheTaylorrulevariantsareverystableacrossmodelswithinthepre-2007sample,clusteringbetween2.30and2.40.Theestimatesareconsid-erablylowerinthefullsample,rangingfrom0.32forthedouble-inertialmodelto1.27forthenon-inertialrule.Theselevelsarebroadlyconsistentwithr∗estimatesoverrecentdecades,andthedifferencesacrossthesamplesareconsistentwithaseculardeclineinthenaturalrealrate.

Thesingle-inertiaparameterρisestimatedtobelargeandhighlysignificantinthepre-2007sample.Intheabsenceofdoubleinertia,theseestimatesimplypartialadjustmentsof13and20percenttowardtheimpliedintermediateratetargetperquarter.Inthefullsample,theestimatedinertiaisslightlyhigher,implyingpartialadjustmentsoflessthan10percent.Thatis,morethan90percentofthelevelofthecurrentfederalfundsrateinagivenquartercanbeattributedtoitslevelinthepreviousquarter.

Mostnotably,thedouble-inertiacoefficientγisestimatedfairlypreciselyat0.61and0.63inthepre-2007andfullsamples,respectively.Thisimpliesthatabout60percentofthepreviouschangeinthefederalfundsratepassesthroughtotheadjustmentinthecurrentquarter.Bothparameterestimatesarehighlysignificant,easilyrejectingthenullthatsingleinertiaaloneissufficienttodescribethedynamicsofthepolicyrate.

Wealsoestimateda“triple-inertial”Taylorrulethataddsathirdlagofthepolicyratetotherule(notreportedinTable

1

).Theestimatedcoefficientonthisthirdlagissmallandstatisticallyinsignificantacrossallsamples,suggestingthattwolagsofferthebestempiricaldescriptionofthebehaviorofthefederalfundsrateinrecentdecades.

4

Theseresultstogethercorroboratepreviousfindingsthatinertia,andhencegradu-alism,playasignificantroleinmonetarypolicythroughthe1990sandintothe2000s.Inaddition,theyareevidencethatgradualismencompassespersistenceinthepaceof

4Wealsouseinformationcriteriatoevaluatethefitofourtriple-inertialTaylorrule,andfindthatithashigherBICvaluesthanthedouble-inertialruleoverboththefull‘Post-1987’and‘Pre-2007’samples.

8

Table1:RecoveredRuleParametersbySample

Parameter

Pre-2007

Post-1987

(1)Non-inertial

(2)Single-inertial

(3)Double-inertial

(4)Non-inertial

(5)Single-inertial

(6)Double-inertial

*

2.37

2.34

2.37

1.27

0.39

0.32

(0.29)

(0.46)

(0.38)

(0.37)

(1.17)

(0.95)

π

1.68

(0.20)

1.74

(0.32)

1.51

(0.29)

0.92

(0.65)

2.38

(0.98)

1.88

(0.75)

u

-1.73

(0.20)

-2.30

(0.34)

-1.66

(0.46)

-1.62

(0.33)

-4.34

(1.67)

-3.09

(1.12)

0.80

(0.05)

0.87

(0.03)

0.94

(0.03)

0.96

(0.01)

0.61

(0.12)

0.63

(0.08)

N

77

77

77

152

152

152

Note:ThistablepresentsestimatesforthespecificationsdetailedinSection

2

.Therulesareestimatedusingquarterlydatafrom

FRED,asdetailedinSection

3

.Parameters*,π,u,,andarerecoveredfromtheregressioncoefficients,andNewey–West

standarderrorswithalaglengthof4arecomputedviathedeltamethod.OLSestimationwasusedforthe‘Pre-2007’sample,runningfrom1987:Q4to2006:Q4.Tobitregressionwithcensorshipat0wasusedforthefull‘Post-1987’sample,runningfrom

1987:Q4to2025:Q3.

changeofthepolicyrate:policymakerstendtopursueinterestrateadjustmentsofsim-ilarsizeandinthesamedirectionacrossperiods.Thestrongevidenceinfavorofthedouble-inertialruleinthefullsampleunderscorestherelevanceofthepaceofchangesinmodernU.S.monetarypolicy.

4.2Goodnessoffit

Tobetterquantifyandevaluatetheperformanceofeachpolicyruleacrosssubsets,weconstructthreeR2statisticvariants.

Thefirstmeasureisstandard,describingtheexplanatorypowerofeachestimatedrulewithrespecttothelevelofthepolicyrate,givenrealizedvaluesoftheinflationandunemploymentgapsinthenextquarter.Wecanexpressthismeasureformallyasfollows:

_

whereiistheaveragefederalfundsrateoverthesampleandtdenotesthepolicy

ratepredictedbytheestimatedrulerinperiodt.Notethatthesepolicyratepredictionsaretruncatedbelowat0toaccountfortheELB,asdescribedin

Section2

.Becausethe

predictionofthepolicyratetmakesuseoftherealizedvaluesofthepolicyrateupto

timet—1,werefertothismeasureas“one-quarterlevels”R2.

Acrossbothsamples,theresultsforthismeasure,asreportedintheR2columnsofTable

2

,arebroadlysimilar.Inthepre-2007sample,thenon-inertialruleachievesamoderateR2of0.78,whilethesingle-anddouble-inertialrulesareabletoexplainalmostallofthevariationinthepolicyrate,achievingR2valuesof0.97and0.98,respectively.Inthefullpost-1987sample,thisdisparityisevenmoredrastic:thenon-inertialrule

9

Table2:ModelFitStatisticsbySample

PolicyRule

Pre-2007

Post-1987

R2

R2Δ

R24

AIC

BIC

R2

R2Δ

R24

AIC

BIC

Non-inertial

0.78

-3.62

0.78

182.31

177.62

0.44

-17.44

0.44

458.60

452.55

Single-inertial

0.97

0.30

0.80

38.62

36.28

0.98

0.27

0.82

59.98

56.95

Double-inertial

0.98

0.59

0.81

0.00

0.00

0.99

0.57

0.83

0.00

0.00

AR(1)

0.95

0.02

0.54

61.17

54.14

0.97

-0.07

0.65

115.34

106.27

AR(2)

0.98

0.53

0.70

5.77

1.08

0.98

0.50

0.76

26.05

20.00

Note:ThereportedstatisticsarefortheestimatedmodelsasinTable

1

.Predictionsbelow0aretruncatedforthecalculationofthegoodnessoffitmeasures.R2measuresfitforone-quarter-aheadlevelsoftheFFR,R2Δmeasuresfitforone-quarter-aheadchanges,andR24measuresfitforyear-aheadlevels.ThecomputationproceduresaredetailedinSection

4.2

.AICandBICarecomputedfromthemodellog-likelihoodsandnormalizedtozeroforthedouble-inertialmodel.The‘Pre-2007’samplerunsfrom1987:Q4to2006:Q4,andisestimatedwithOLS.Thefull‘Post-1987’samplerunsfrom1987:Q4to2025:Q3,andisestimatedwithTobitregression.

performsratherpoorlywithanR2ofmerely0.44,whilethesingle-anddouble-inertialrulesachieveR2valuesof0.98and0.99.Clearly,thesingle-anddouble-inertialrulesareabletosubstantiallyimproveexplanatorypowerrelativetothenon-inertialspecification.

TheperformanceofeachruleinlevelsacrosstheextendedsampleisvisualizedinFigure

1

.Allrulesandbenchmarksexceptforthenon-inertialruletrackthelevelofthefederalfundsrateclosely.Onlyuponcarefulinspectiondoesthereducedphaseshiftofthedouble-inertialrulebecomevisible,as

CarlstromandFuerst

(

2014

)highlight,particularlyduringthehikingcyclesofthemid-1990sandmid-2000sandthecuttingcycleassociatedwiththe2001recession.

WethereforeconstructasecondR2variantwhichevaluatestherules’predictionsofchangestothepolicyrate,ratherthanitslevels.WeviewthismetricasespeciallyrelevantforthecommonnarrativesaroundFOMCmeetings,wherepolicymakersandthepublicalikeoftenfocusonpotentialchangestothepolicyrate.Inessence,this“one-quarter

changes”R2measure,whichwedenoteR,comparesrealizedchangesinthepolicyrateto

thechangespredictedbyeachrule.Thepredictedadjustmentistakentobethedifferencebetweentherule-impliedrateandthelaggedrealizedpolicyrate.Formally,

where∆iistheaveragechangeinthefederalfundsrateoverthesample.Becausethismeasureevaluatespredictedchangesrelativetothelaggedrealizedpolicyrate,andthenon-inertialruleisnotanchoredtothatvalue,itsperformanceisfarworsethanarulewhichsimplytakestheaveragechangeasitspredictionineachperiod.

10

Figure1:One-Quarter-AheadFederalFundsRatePredictionsforEstimatedRules

FFR

0

1987199720072017

FederalFundsRateNon-inertialRule

InertialRule

Double-inertialRuleAR(1)Rule

AR(2)Rule

8

6

4

2

10

No