FinanceandEconomicsDiscussionSeries
DivisionsofResearch&StatisticsandMonetaryAairs
FederalReserveBoard,Washington,D.C.
GDPTrend-cycleDecompositionsUsingState-levelData
ManuelGonzalez-Astudillo
2017-051
Pleasecitethispaperas:
Gonzalez-Astudillo,Manuel(2017).“GDPTrend-cycleDecompositionsUsingState-level
Data,”FinanceandEconomicsDiscussionSeries2017-051.Washington:BoardofGovernors
oftheFederalReserveSystem,https://doi/10.17016/FEDS.2017.051.
NOTE:StaworkingpapersintheFinanceandEconomicsDiscussionSeries(FEDS)arepreliminary
materialscirculatedtostimulatediscussionandcriticalcomment.Theanalysisandconclusionssetforth
arethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstaorthe
BoardofGovernors.ReferencesinpublicationstotheFinanceandEconomicsDiscussionSeries(otherthan
acknowledgement)shouldbeclearedwiththeauthor(s)toprotectthetentativecharacterofthesepapers.
GDPTrend-cycleDecompositionsUsingState-level
Data
ManuelGonzalez-Astudillo
manuel.p.gonzalez-astudillo@frb.gov
FederalReserveBoard
Washington,D.C.,USA
April28,2017
Abstract
ThispaperdevelopsamethodfordecomposingGDPintotrendandcycleexploit-
ingthecross-sectionalvariationofstate-levelrealGDPandunemploymentratedata.
Themodelassumesthattherearecommonoutputandunemploymentratetrendand
cyclecomponents,andthateachstate’soutputandunemploymentratearesubject
toidiosyncratictrendandcycleperturbations.ThemodelisestimatedwithBayesian
methodsusingquarterlydatafrom2005:Q1to2016:Q1forthe50statesandtheDis-
trictofColumbia.ResultsshowthattheU.S.outputgapreachedabout-8%during
theGreatRecessionandisabout0.6%in2016:Q1.
Keywords:Unobservedcomponentsmodel,trend-cycledecomposition,state-levelGDP
data
JELClassicationNumbers:C13,C32,C52
asreectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystem.
1Introduction
Theoutputgap—thedierencebetweenactualandpotentialortrendoutput—isacentral
measureinpolicymaking.Bothmonetaryandscalpolicylookattheoutputgaptogauge
inationarypressuresorthedegreeoflabormarketslack.Becausetheoutputgapisa
nonobservablevariable,severalstatisticalandeconometrictechniqueshavebeenproposed
toestimatethecyclicalpositionoftheeconomy.TheCongressionalBudgetOce(CBO),for
example,oersameasureofpotentialoutputthathelpsforecastfuturefederalrevenueand
spending,andfromwhichtheoutputgapcanbeobtained(seeCongressionalBudgetOce,
2014,forarecentreport).Centralbanksalsoconstructestimatesoftheoutputgapthat
informtheirmonetarypolicydecisions(seeFederalReserveBankofPhiladelphia,2017).
Figure1plotstheCBO-impliedandBoardofGovernors(BOG)oftheFederalReserve
Systemoutputgapsfortheavailableperiods.1
Figure1:CBO-impliedandBOGOutputGaps
1950196019701980199020002010-8
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-4
-226%
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d/p
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CBO-implied Output Gap
1950196019701980199020002010-8
-6
-4
-226%
dev
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BOG Output Gap
Amongthestatisticaltechniquesusedtodiscriminatethepermanentcomponentfrom
thetransitoryorcyclicalcomponentistheBeveridgeandNelson(1981)decompositionof
integratedtimeseries.Othertechniquesinvolveltersofdierentnaturestoseparatethe
cyclefromthetrendorlong-runcomponent,liketheHodrickandPrescott(1997)lter,or
variationsofaband-passlter,asinBaxterandKing(1999)andChristianoandFitzger-
ald(2003),ortheKalmanltertoestimatemodelswithunobservedcomponents(UC),as
inClark(1987).AnotherapproachsuggestedbyStockandWatson(1989)usesmultiple
macroeconomictimeseriestoextractacommoncyclicalcomponentinthespiritofdynamic
factormodels.
Eventhoughthereareexistingmethodstoestimatethecyclicalpositionoftheeconomy
orofagroupofeconomiesexploitingthevariabilityofmultiplevariables,multiplecross-
1TheBOGoutputgaparereal-timeestimatesandprojectionsoftheoutputgapusedbythestaofthe
BoardofGovernorsoftheFederalReserveSysteminconstructingitsforecast.Theseestimatesarereleased
withalagof5yearsandpublishedbytheFederalReserveBankofPhiladelphia.Hence,theinformation
endsinthefourthquarterof2011,asofthedateofpublicationofthecurrentdraft.sectionalunits,orboth,noneofthesemethodshasexploredtheestimationoftheoutput
gap—denedasthedierencebetweenactualandpotentialoutput—usingmultiplecross-
sectionalunitssuchasgeographicalregionsorindustries.Inthispaper,IproposeaUC
modelthatcombinesinformationaboutoutputandtheunemploymentratefrommany
cross-sectionalunits—theU.S.states—toestimatetheaggregateGDPcycleanditstrend.
Theproposedmodelexploitsthepanelstructureofthestate-leveldataandaddsrichnessto
theconventionalUCapproachinawaythatresemblesthedynamicfactormodelsbutthat
allowsmetomeasuretheoutputgapasthedierencebetweenactualandpotentialGDP.
Thesetupassumesthat(thelogof)eachstate’srealGDPisthesumofstate-specic
trendandcyclecomponents.Eachofthestate-specictrends,inturn,isalinearcombination
ofatrendcommonacrossstatesandanidiosyncratictrend.Likewise,eachofthestate’s
cyclesisalinearcombinationofacyclecommontoallofthestatesandanidiosyncratic
component.Lastly,anOkun’slawatthestatelevelrelatesthecycleofGDPtothecycleof
theunemploymentrate.Hence,informationfrommultiplecrosssectionsandvariablescan
beusedtoestimatetheaggregateoutputcycle.
ThemodelissimilartotheonesuggestedbyStockandWatson(2016)forestimating
trendination,inwhichdierentinationcategoriesareusedasthesourceofcross-sectional
variation.Thedierenceisthatthemodelinthispaperincorporatesabivariateanalysis
withinthecrosssections,includinganotherdimensionofvariationthataddsinformation
totheestimation.Additionally,inthemodelofthispaper,thecyclicalcomponentsare
assumedtohaveautocorrelateddynamics,whileautocorrelationisabsentfromthesetupof
StockandWatson.
TheaimofthepaperissimilarinspirittothatofOwyang,RapachandWall(2009),
whoextractbusinesscyclefactorsusinginformationonincomeandpayrollemploymentat
thestatelevel.Inthepresentpaper,however,IuserealGDPandunemploymentratedata,
soitispossibletointerpretthecyclicalcomponentofGDPasameasureoftheoutputgap.
Iestimatethemodelwithquarterlyinformationforthe50statesandtheDistrictof
Columbiafortheperiodfrom2005:Q1to2016:Q1.Theresultsareobviouslyinuencedand
characterizedbythefeaturesoftheGreatRecession.Inparticular,theestimatedcycleis
verypersistent,withahump-shapedresponseofthecycletoaninnovationinitself.
Theestimatedsmoothedcycleis-7.9%atthetroughoftherecessioninthefourthquarter
of2009,slightlylowerthantheCBO-impliedcycle,whichreachedabout-7.3%twoquarters
before.Themodel’sestimatesimplythatthetrendofGDPdeclinedabout1.9%between
theendof2008andthebeginningof2009,whereastheCBOestimatelowersitsslopemuch
moreslowly.Attheendofthesample,theestimatedoutputgapisabout0.6%andtrend
outputwouldbegrowingatanaverageannualpaceof34percent,comparedto314percent
beforetherecession.
Theproposedmodelalsoallowsonetoexaminethecyclicalfeaturesofthestateeconomies
duringtherecessionandattheendofthesample.Forexample,thestatesthatwerehit
thehardestbytherecessionwerethoseintherustbelt,aswellasArizona,California,
Nevada,andFlorida.Attheendofthesample,stateslikeWestVirginiaandWyomingwere
experiencingnegativeoutputgaps,probablydrivenbylowcommodityprices.
Indthataddingcross-sectionalinformationreducestheuncertaintyaroundtheestima-
torofthecyclecomparedwithamodelthatusesaggregatedataonly.Ialsondthatthe
modelwithmanycrosssectionsoutperformstwocompetingmodelsinpredictingthegrowth。。。以上简介无排版格式，详细内容请下载查看