失业率之外：结构性劳动力市场指标（英）

FinanceandEconomicsDiscussionSeries

BeyondtheUnemploymentRate:AStructuralLaborMarket

Indicator

IsabelCairo,HessChung,FrancescoFerrante,CristinaFuentes-Albero,Camilo

Morales-Jimenez,DamjanPfajfar

2026-058

Pleasecitethispaperas:

Cairo,Isabel,HessChung,FrancescoFerrante,CristinaFuentes-Albero,CamiloMorales-Jimenez,andDamjanPfajfar(2026).“BeyondtheUnemploymentRate:AStructuralLaborMarketIndicator,”FinanceandEconomicsDiscussionSeries2026-058.Washington:BoardofGovernorsoftheFederalReserveSystem,

/10.17016/FEDS.2026.058

.

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

BeyondtheUnemploymentRate:AStructuralLaborMarketIndicator*

IsabelCair´o‡HessChung‡FrancescoFerrante‡CristinaFuentes-Albero‡

CamiloMorales-Jim´enez‡DamjanPfajfar§

July2026

Abstract

Labormarketvariablesfrequentlysendconflictingsignalsaboutthedegreeofslackortightness,oftencomplicatingpolicyassessmentsatcriticaljunctures.ThispaperdevelopsaStructuralLaborMarketIndicator(SLMI)fortheU.S.economythataddressesthelimitationsofexistingunivariatemeasuresoratheoreticalstatisticalapproachesthatsynthesizemultiplelabormarketindicatorsbutcannotdistinguishbetweensupplyanddemanddrivingforces.WeconstructtheSLMIusingamedium-scaleNewKeynesianDSGEmodelfeaturingsearchandmatchingfrictions,endogenouslaborforceparticipation,andvariablehours.Themodelisdisciplinedbyacomprehensivedatasetthatincludesnotonlylabormarketvariablesbutalsoothermacroeconomicaggregates.TheSLMIsynthesizesmodel-impliedgapsacrossmultiplelabormarketdimensionsusingprincipalcomponentanalysis.WeshowthatGDPgrowthandinflationprovidesubstantialinformationaboutlabormarketslackbeyondwhatlabormarketvariablescontain,validatingourmulti-variablestructuralapproach.Relativetoalternativemeasures,theSLMIoftenprovidesearlierwarningsofdeterioratingconditionsatrecessiononsetbutrecoversmoregraduallyduringexpansions.

JELClassification:E32,J64,J20,E37.

Keywords:Searchandmatching,labormarket,labormarketslack.

*TheviewsexpressedinthispaperaresolelytheresponsibilityoftheauthorsandshouldnotbeinterpretedasreflectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystem,FederalReserveBankofCleveland,orofanyoneelseassociatedwiththeFederalReserveSystem.

‡Address:BoardofGovernorsoftheFederalReserveSystem,20thStreetandConstitutionAvenueNW,Washington,D.C.20551,USAEmailaddresses:

isabel.cairo@

(I.Cair),

hess.t.chung@

(H.Chung),

francesco.ferrante@

(F.Ferrante),

cristina.fuentes-albero@

(C.Fuentes-Albero),

camilo.moralesjimenez@

(C.Morales-Jimnez).

§Address:FederalReserveBankofCleveland,1455E6thStr.,Cleveland,OH44114,USA.Emailaddress:

dam-

jan.pfajfar@

(D.Pfajfar).

1

1Introduction

Thelabormarketoftenconfrontspolicymakerswithconflictingsignalsaboutlabormarketslack,com-plicatingtheassessmentofappropriatepolicy.Forexample,inDecember2015,theunemploymentratehadfallento5percent,nearmostcontemporaryestimatesoffullemployment,yetparticipationhadde-clinednearlytwopercentagepointssincetherecoverybegan,andnominalwagegrowthremainedbelow3percent,shortoflevelsconsistentwithatightlabormarket.In2021-2022,unemploymentreturnedtoitspre-pandemiclevelofroughly4percentevenasthevacancy-to-unemploymentratioexceeded2andaverageweeklyhourssatbelowtrend.Thepuzzleisagainlivetoday:through2025-2026unemploymenthashoveredaround4percentwhilevacancieshavefallensharplyfromtheirpost-pandemicpeaks,leavingopenwhetherlabormarketsaregenuinelylooseningorwhethertheearliervacancysurgereflectedtransi-torypost-pandemicdistortionsratherthantruetightness.Theseepisodesshareacommonfeature:labormarketindicatorsdisagree,andthecostofmisreadingtheunderlyingslackishighforpolicymakers.Thispaperdevelopsastructuralapproachtosynthesizinginformationacrosslabormarketmargins,alongsidekeymacroeconomicaggregates,intoasinglemodel-consistentmeasureofslack.

Measuringslackisadifficulttaskthatextendsbeyondsimplyobservingconflictingindicatorsinadashboard;itisaconceptualandidentificationproblem.Laborsupplyanddemandadjustalongmulti-plemarginssimultaneously:extensive(employment,unemployment,participation),intensive(hoursperworker),vacancyposting,andwagedetermination.Nosingleindicatorcapturesthismulti-dimensionality.Unemploymentabstractsfromparticipationandhours;thevacancy-to-unemploymentratio,thoughin-formativeabouttightness,omitsemployedworkers’desiredhours;wagegrowthconflatessupplyanddemandshifts,makingitanambiguoussignalofslackabsentfurtherstructure.Evenobservingeverymarginpresentsthreekeychallenges.First,howtoaggregatethismultidimensionalinformation?Second,shouldtheassessmentdrawonlabordataalone,ordootheraggregatessignalwhetherlaborresourcesarefullyutilized?Forinstance,strongGDPgrowthwithsubduedinflationsuggestslackatagivenunemploymentrate,whileweakgrowthandelevatedinflationsuggesttightness.Third,thesourceoffluctuationsmatters:unemploymentdrivenbyadversesupplyshockscallsforadifferentmonetarypol-icyresponsethanunemploymentdrivenbydeficientaggregatedemand.Adashboardofindicatorsreadthroughsubjectivejudgmentoffersnosystematicwaytoconfrontaggregation,informationextraction,oridentification,leavingpolicymakerswithoutguidancepreciselywhenlabormarketsaremostconfounding.

WeaddressthesechallengesbyconstructingaStructuralLaborMarketSlack(SLMI)indicatorgroundedinamedium-scaleNewKeynesianDSGEmodelwithsearchandmatchingfrictions,endoge-nouslaborforceparticipation,andvariablehoursworked,featuringnominalpriceandwagerigidities.Themodelbuildson

Cair´oetal.

(

2026

),whichweextendbyintroducingwealthintohouseholdutil-ity.Thisformoftheutilityfunctiondecouplesthesteady-statefederalfundsratefromlonger-runrealGDPgrowth,asobservedinthedata.Definingslackbycomparingactualoutcomesrelativetotheirflexible-price-and-wageequilibriumcounterparts,wecomputemodel-impliedgapsforninelabormarketvariables—employment,unemployment(boththerateandlevel),laborforceparticipation,totalhours,averageworkweek,vacancies,labormarkettightness,andrealwages—andextracttheircommoncyclical

2

componentviaprincipalcomponentanalysis.WelabelthatcomponenttheSLMI.Becausethemodel

isestimatedonacomprehensivedatasetspanningnotonlylabormarketvariablesbutalsoaggregateoutput,consumption,investment,inflation,interestrates,andcreditspreads,thegapsinheritinforma-tionfrombroadermacroeconomicconditions,andthestructuralframeworkisbetterabletoidentifythesupplyanddemanddisturbancesbehindlabormarketfluctuations.WevalidatethemodelagainstU.S.datafrom1987–2026,showingthatitreproduceskeycyclicalmovementsand,inparticular,thedynamicco-movementsandlead-lagrelationshipsamonglabormarketandmacrovariablesobservedinthedata.

Ouranalysisyieldstwointerestingfindings.First,andrelativetoalternativeslackmeasures,theSLMIoftendisplaysdistinctcyclicalbehavioratbusinesscycleturningpoints.Ittendstowarnearlierofdeteriorationatrecessiononsetandrecovermoreslowlythereafter,thoughthemagnitudeandtimingofthesedifferencesvaryacrossepisodes.Second,decomposingtheSLMIrevealsthatGDPgrowthandin-flationcarrysubstantialinformationaboutslackbeyondwhatlaborvariablesalonecontain,underscoringthatslackneedstobejudgedinconjunctionwiththebroadermacroeconomiccontext.HistoricalshockdecompositionsattributethebulkofSLMIvariationoverthe1987–2026periodtoriskpremiumandinvestmentefficiencyshocks,whichdrovethedeepslackof2008–2009financialcrisisandtheCOVID-19recession;monetarypolicyshocksplayonlyamodestroleandbecomenegligibleafter2013onceweallowtime-varyingTaylorrulecoefficients.

Thispapermakesthreeimportantcontributions.First,weprovidethefirststructurallabormarketindicatorthatsynthesizesallmajorlabormarketmargins—employment,participation,hours,vacancies,andwages—withinadisciplinedDSGEmodelratherthanapurelystatisticalaggregation.Thestructuraldisciplinepaysoff:thefirstprinciplecomponentofourmodel-impliedgapsexplainsthevastmajorityoftotalvarianceanditistheonlycomponentwithaneigenvalueaboveone,whereasapplyingPCAdirectlytofilteredlabormarketdatayieldsuptothreesuchcomponents,providingadiffusefactorstructurethatobscurestheunderlyingsignal.BecausetheSLMIalsodrawsonoutput,consumption,investment,inflation,interestrates,andcreditspreads,itcanreadthesameunemploymentrateasmoreorlessslackdependingonthemacroeconomiccontext,anditcanseparatesupplyfromdemanddisturbances,supportcounterfactualexperiments,andbedecomposedintocontributionsfromspecificshocksandobservables—noneofwhichisavailabletoapproachesbuiltonlabormarketalone.Second,weincorporatetime-varyingmonetarypolicyrulecoefficientsestimatefromtheFederalOpenMarketCommittee’s(FOMC)SummaryofEconomicProjections(SEP)by

Gonz´alez-AstudilloandTanvir

(

2026

),preventingattributingsystematicshiftsinmonetarypolicymakingtopolicyshocks,whichwoulddistortourinferenceaboutlabormarketslack.Third,weofferapracticaltoolforreal-timeanalysiswithformaluncertaintyquantification:credibleintervalsconstructedviaMonteCarlosimulationovertheparameterdistribution,whichrevealthatuncertaintyaboutslackisespeciallyelevatedduringrecoveries.Notethattheseresultsaremodeldependent,restingonjudgmentsaboutstructuralfeatures,long-runcalibration,andshockspecification.However,weshowthatthemodelsuccessfullyreproduceskeyU.S.businesscyclepropertiesandgeneratesoutputandunemploymentrategapsbroadlyconsistentwithexternalestimates.Thispapercontributestoalargeliteratureonmeasuringunobservableeconomicslackandnatural

3

rates.Theoutputgaphasbeenestimatedwithunivariatefilters,productionfunctionapproachesthat

aggregatefactor-utilizationestimates(

CongressionalBudgetOffice

,

2026

;

Kiley

,

2013

),andmultivariatefiltersexploitingtheoutput-inflationcorrelation(

Blagraveetal.

,

2015

);thenaturalrateofunemploymentwithtime-varyingparametermethods(

Staigeretal.

,

1997

;

Gordon

,

1997

),withattentiontosurrounding(

OrphanidesandWilliams

,

2002

);andthenaturalrateofinterestwithframeworksemphasizingthatequilibriumconceptsthemselvesdriftwithstructuralchange(

LaubachandWilliams

,

2003

;

Holstonet

al.

,

2017

).Mostofthiswork,however,treatssingle-variablegapsandissilentonsynthesizinginformationacrosslabormarketmargins.

Chungetal.

(

2014

)and

HakkioandWillis

(

2014

)takeastepinthatdirectionbyapplyingprincipalcomponentanalysistolabormarketindicators,butapurelystatisticalsummaryofco-movementcannotdistinguishsupplyfromdemand,offersnoroutetoincorporatenon-labordata,andsupportsnocounterfactualorshockdecomposition.Wealsobuildonworkstudyingendogenouslaborsupplyalongtheextensive(e.g.

Cair´oetal.

,

2022

,

Kruselletal.

,

2017

,

2020

,

CampolmiandGnocchi

,

2016

and

NucciandRiggi

,

2018

)andintensive(e.g.

Cacciatoreetal.

,

2020

)margins,andhowitshapescyclicallabormarketdynamics(e.g.

Elsbyetal.

,

2015

,

Christianoetal.

,

2015

and

Christianoetal.

,

2021

).

Theremainderofthepaperproceedsasfollows:Section

2

describesthemodelstructureandcalibra-tionstrategy;Section

3

validatesthemodel’sabilitytomatchU.S.businesscycleproperties;Section

4

constructstheSLMIandexaminesitshistoricalevolution;Section

5

comparestheSLMItoalternativeslackmeasures;andSection

6

quantifiesuncertaintyaroundtheindicatorandcomparesthetwo-sidedwiththeone-sidedfilteredindicator,moresuitableforpracticalpolicyanalysis.Finally,Section

7

concludes.

2ModelDescriptionandCalibration

Weadoptthemedium-scaleNewKeynesianmodelof

Cair´oetal.

(

2026

)asourbaselineframework.The

Cair´oetal.

(

2026

)modelincorporatessearchandmatchingfrictionsalongsideendogenouslaborforceparticipationandhoursworkeddecisions.Therefore,thismodelincludesthemultiplemarginsofadjustmentthatacomprehensivelabormarketindicatormustcapture.Wethenintroducethreetargetedmodificationstoadopttheirframeworktoourpurposes:(i)weaugmenthouseholdpreferenceswithawealth-in-the-utilitytermthatdecouplesthesteady-staterealinterestratefromlonger-runGDPgrowth;(ii)weupdatethecalibrationoflonger-runvaluestoreflectthemostrecentassessmentsfromtheCongressionalBudgetOffice(CBO)andtheFOMC’sSEP;and(iii)weincorporatetime-varyingcoefficientsinthemonetarypolicyrule,estimatedusingmedianSEPdata,topreventsystematicchangesinmonetarypolicyfrombeingattributedtomonetarypolicyshocks.Thissectionprovidesaconciseoverviewofthebaselinemodel,withaparticularemphasisonthedifferentlabormarketmarginsofadjustment,andthendiscusseseachmodification.DetailedmodelderivationsandadditionalmodelspecificationsareprovidedinAppendix

A

.

4

2.1BaselineFramework

Households

Theeconomyispopulatedbyarepresentativehouseholdwithacontinuumofmemberswhomakela-borsupplydecisionsalongboththeextensiveandintensivemargins.Eachhouseholdmembercanbeemployed,unemployedandsearchingforajob,oroutofthelaborforce.Thehouseholdchoosescon-sumption,bondholdings,laborforceparticipation,andhoursworkedtomaximizeexpectedlifetimeutility.Preferencesfollow

JaimovichandRebelo

(

2009

)specification,allowingforflexibleparameteriza-tionofwealtheffectsonbothlaborsupplymarginswhilemaintainingconsistencywithbalancedgrowth.Perfectconsumptioninsuranceacrosshouseholdmembersensuresthatallmembersconsumeidenticalbundlesregardlessoftheiremploymentstatus,andthehousehold’sstochasticdiscountfactorgovernsallintertemporaldecisions.

Production

Ontheproductionside,therearefivetypesoffirms.Afinalgoodsproducerpurchasesdifferentiatedproductsfromretailersandaggregatesthemintoafinalconsumptiongoodthatissoldinaperfectlycompetitivemarket.Retailersoperateinamonopolisticallycompetitivemarketandfacenominalpricerigidities`alaCalvo:eachperiod,onlyafractionofretailerscanre-optimizetheirprices,whiletheremain-derindextheirpricestopastinflation.Retailersproduceusinganintermediategood,whichtheypurchaseinaperfectlycompetitivemarket.IntermediategoodsproducersoperateinacompetitivemarketandproduceoutputusingcapitalandlaborviaaCobb-Douglastechnology.Thelabormarketischaracterizedbysearchandmatchingfrictions:firmspostvacanciesandmatchwithjobsearchersaccordingtoastan-dardmatchingfunction,andwagesaredeterminedthroughstaggeredNashbargaining,whichintroducesnominalwagerigidities.Hiringiscostly,withageneralizedrecruitingcostfunctionthatdistinguishesbetweenpre-matchcosts(vacancyposting)andpost-matchcosts(workertraining).Capitalisproducedbycompetitivecapitalproducerswhofaceinvestmentadjustmentcosts.Entrepreneurspurchasecapitalusingacombinationofnetworthandexternalfinance,andtheyrentcapitalservicestointermediategoodsproducers.Following

Bernankeetal.

(

1999

),financialfrictionsarisefromacostlystateverificationproblem,generatinganendogenousspreadbetweenthereturnoncapitalandtherisk-freerate.

MonetaryPolicyRule

Finally,monetarypolicyfollowsaninertialTaylor-typerule,withthenominalinterestraterespondingtodeviationsofinflationfromitstarget,theoutputgap,andoutputgapgrowth,subjecttoaneffectivelowerboundconstraint.

5

2.2ModificationstotheBaselineFramework

Wecalibratethestructuralparametersgoverningpreferences,technology,andrigiditiesattheposteriorestimatesreportedin

Cair´oetal.

(

2026

)andlistedinAppendix

A

.InSection

3

,weshowthatthebaselineparameterization,combinedwiththethreemodificationsdescribedbelow,deliversstrongempiricalper-formance,closelymatchingkeybusinesscyclemomentsinthedataandproducingrealisticlabormarketdynamicsacrossmultiplemargins.

WealthintheUtilityFunction

Inthebaselinemodelof

Cair´oetal.

(

2026

),standardEuler-equationlogictiesthesteady-staterealinterestratetotherateoftimepreferenceandtheconsumptiongrowthrate.Whilestandardintheliterature,thistightlinkisnotsupportedbythedata:overrecentdecades,realinterestratesandGDPgrowthhavedivergedsubstantially.Tobreakthisconnection,weaugmentthehouseholdutilityfunctionwithalinearwealthterm,χtBt,whereχtgrowswithtechnologytoguaranteeabalancedgrowthpathandBtrepresentsbondholdings.Thismodificationaltersthehousehold’sEulerequation,providinganadditionaldegreeoffreedomthatallowsthesteady-staterealinterestratetobecalibratedindependentlyoftheconsumptiongrowthrate.Withthewealth-in-utilityterm,wecansetthesteady-statefederalfundsrateto3.0percentandGDPgrowthto2.0percent,whichisconsistentwiththeFOMC’sSEP,withoutthesevaluesbeingmechanicallylinked.

UpdatedLonger-RunCalibration

Table

1

reportsthekeycalibratedparametersthatanchorthemodel’ssteadystatetocurrentassessmentsoflonger-runeconomicfundamentals.Thesecalibrationsareimportantforensuringthatthemodel’simplicationsforlabormarketslackareevaluatedrelativetoarecentempiricallyplausiblelonger-runequilibrium.Forthesteady-stateunemploymentrate,wecalibrateitto4.3percent,consistentwiththeCBOestimatesofthenaturalrateofunemploymentbasedonrecentdata.Thelaborforceparticipationrate(LFPR)issetto61.3percent,reflectingthestructuraldeclineinparticipationdrivenbydemographicshifts.ThisvaluealignswithCBOlonger-runprojectionsthataccountforpopulationagingandchanginglaborforceattachmentpatterns.Longer-runGDPgrowthiscalibratedto1.8percent(annualized),andthefederalfundsrateto3.0percent(annualized),bothvaluesconsistentwiththemedianlonger-runprojectionsfromtheDecember2025FOMC’sSEP.Thesevaluescapturepolicymakers’assessmentsofequilibriumconditionsthatwillprevailoncecyclicalforcesdissipate.Wesetthepersistenceparameterofmarkupshocksto0.15,reflectingourassessmentthatmarkupdisturbancesinrecentyearshavebeenrelativelyshort-lived.

Time-VaryingMonetaryPolicyRule

Ourthirdmodificationtothemodelin

Cair´oetal.

(

2026

)concernsthemonetarypolicyrule.Asubstantialbodyofempiricalevidencedocumentssignificantchangesintheconductofmonetarypolicyoverrecent

6

Table1:CalibratedParametersandLonger-RunValues

Parameter/Variable

Symbol

Value

PanelA:Longer-runvalues(inpercent)

Federalfundsrate(annualized)

i

3.0

Unemploymentrate

u

-

4.3

Laborforceparticipationrate

L

61.3

GDPgrowth(annualized)

γ

2.0

PanelB:Structuralparameters

Persistencemarkupshocks

ρϵp

0.15

Notes:Long-runsteady-statevaluesforthefederalfundsrate,unemployment

rate,laborforceparticipationrate,andGDPgrowthreflectourassessmentof

longer-runequilibriumvaluesbasedondatathrough2026.

decades.Forexample,

Claridaetal.

(

2000

)showthattheFederalReserve’ssystematicresponsetoinflationandoutputchangedmarkedlybetweenthepre-andpost-Volckerperiods,while

Boivin

(

2006

)and

BoivinandGiannoni

(

2006

)provideevidenceofevolvingpolicyeffectiveness.

Primiceri

(

2005

)estimatestime-varyingcoefficientsinmonetarypolicyrulesusingBayesianmethods,findingsubstantialdriftinpolicyparametersovertime.

Baueretal.

(

2024

)estimatemeaningfulfluctuationsinperceivedpolicyruleformonetarypolicyintheUS,inparticularoverthemonetarypolicycycle.Morerecently,

Gonz´alez-

AstudilloandTanvir

(

2026

)developandestimateaforward-guidanceTaylorrulewithtime-varyingcoefficientsshowingmeaningfulfluctuationsintheestimatedparameters.Beyondthisempiricalevidence,incorporatingtimevariationinthemonetarypolicyruleiscrucialforouranalysisbecausechangesinmonetarypolicy,iftreatedasconstant,wouldbeincorrectlyattributedtomonetarypolicyshocks.Forinstance,iftheFederalReserve’sresponsetoinflationincreasedovertimebutourmodelassumedarulewithconstantparameters,periodsoftighterpolicyduetoasystematichigherresponsetoinflationwouldbeinterpretedassequencesofcontractionarymonetarypolicyshocks.Thismisspecificationwoulddistortourestimatesofflexible-pricegapsand,consequently,ourassessmentoflabormarketslack.

Toaddressthisissue,weincorporatetime-varyingcoefficientsintheTaylorruleasin

Gonz´alez-

AstudilloandTanvir

(

2026

)whoestimatethemusingmedianSEPprojectionssince2013.Specifically,threekeyTaylorrulecoefficientsareallowedtovaryovertime:thedegreeofinterestratesmoothing(ρi);theresponsecoefficienttoinflationdeviationsfromtarget(κπ);andtheresponsecoefficienttotheoutputgap(κy).

1

Thesetime-varyingcoefficientsaretreatedasknownsequences(notsubjecttouncertainty)whensolvingthemodel.Figure

A.1

inAppendix

A

displaysthetime-varyingmonetarypolicyrulecoefficientsoveroursampleperiod.Thecoefficientontheoutputgapexhibitsremarkablestability,remainingnearlyconstantthroughoutthesample,whiletheinertiaparametershowsonlyminor

1

Gonzlez-AstudilloandTanvir

(

2026

)estimatestime-varyingTaylorrulecoefficientsusingdatafromtheSEP,which

beganin2013.Consequently,thetime-varyingcoefficientsinourmodelapplyonlyfrom2013:Q1onward.Priorto2013,weuseconstantcoefficientsestimatedoverthepre-2013sampleperiod.Additionally,beginningin2013,wesetthecoefficient

onlaggedoutputgapgrowth(κgy)tozero,asthistermisnotincludedintheanalysisby

Gonzlez-AstudilloandTanvir

(

2026

).

7

variationsovertime.Incontrast,thecoefficientoninflationdisplayssubstantialvariation,risingto

approximately3.5intheyearsprecedingtheCOVID-19pandemicbeforegraduallydecliningtoaround1.0by2025.

WeacknowledgethatourrelianceonSEPdatalimitsthetime-varyingspecificationtothepost-2013period.However,wedonotviewthisasacriticallimitationfortworeasons.First,theconstantmonetarypolicyruleestimatedforthepre-2013periodcapturesreasonablywellthesystematicbehaviorofFederalReservepolicyduringthattime,asevidencedbythemodel’sabilitytomatchkeymomentsinthedata(seeSection

3

).Second,aswedemonstrateinourhistoricaldecompositionsbelow,monetarypolicyshocksaccountforarelativelymodestshareofthevariationinflexible-pricegapspriorto2013,suggestingthatmisspecificationofthepolicyruleduringthisearlierperiodwouldhavelimitedconsequencesforourestimatesoflabormarketslack.

2.3Data,SamplePeriod,andELBEpisodes

Wetakethemodeltothedataovertheperiod1987Q1–2025Q4.Becausethestructuralparametersarefixedtotheposteriorestimatesof

Cair´oetal.

(

2026

)wedonotre-estimatethemodel.Instead,giventheseparametersandthethreemodificationsdescribedabove,weruntheKalmansmootheroverthefullsampletoextractthemodel-impliedlatentstates,includingtheflexible-priceequilibriumcounterpartsofalllabormarketvariables,fromwhichweconstructthegapsthatunderlietheSLMI.Theextendedsampleencompassesseveralsignificanteconomicepisodesbeyondtheoriginalestimationwindow:theprotractedpost-Great-Recessionrecovery,theCOVID-19pandemicanditsaftermath,andthe2021–2023inflationsurge.Themodel’sabilitytoproducesensiblegapestimatesovertheseout-of-estimation-sampleepisodesprovidesaninformalassessmentoftherobustnessoftheoriginalparameterization(seeSection

3

).

TheKalmansmootherisconditionedonfourteenobservablevariables.Thedatasetincludesstandardnationalaccountsaggregates—thegrowthratesofrealpercapitaGDP,consumption,andinvestment—alongwithinflationmeasuredbyboththeGDPdeflatorandcorePCEinflationtoextractacommonsignalofunderlyingpricepressures.Weincludetwomeasuresofwagegrowth—compensationperhourandaveragehourlyearnings—tosimilarlyidentifyalatentwageinflationprocessrobusttomeasurementerrorinindividualseries.Financialconditionsarecapturedthroughthethefederalfundsrateandthecorporatecreditspread,definedasthedifferencebetweentheBaacorporaterateandthe10-yearTreasuryyield.Thelabormarketblockisinformedbyfourkeyvariables:theunemploymentrate,theLFPR,averagehoursworkedperweek(workweek),andvacancies.Forthevacancyandworkweekhoursseries,weapplyanHPfilterwithsmoothi