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LOUISREVIEWJULY/AUGUST2009187WhatDoWeKnow(AndNotKnow)AboutPotentialOutputSusantoBasuandJohnG.
FernaldPotentialoutputisanimportantconceptineconomics.
Policymakersoftenuseaone-sectorneo-classicalmodeltothinkaboutlong-rungrowth,andtheyoftenassumethatpotentialoutputisasmoothseriesintheshortrun—approximatedbyamedium-orlong-runestimate.
Butinboththeshortandthelongrun,theone-sectormodelfallsshortempirically,reflectingtheimportanceofrapidtechnologicalchangeinproducinginvestmentgoods;andfew,ifany,modernmacroeconomicmodelswouldimplythat,atbusinesscyclefrequencies,potentialoutputisasmoothseries.
Discussingthesepointsallowstheauthorstodiscussarangeofotherissuesthatarelesswellunderstoodandwherefurtherresearchcouldbevaluable.
(JELE32,O41,E60)FederalReserveBankofSt.
LouisReview,July/August2009,91(4),pp.
187-213.
neoclassicalmodel—whereonesectorproducesinvestmentgoodsandtheotherproducescon-sumptiongoods—providesabetterbenchmarkformeasuringpotentialoutputthantheone-sectorgrowthmodel.
Second,intheshortrun,themeas-ureofpotentialoutputthatmattersforpolicy-makersislikelytofluctuatesubstantiallyovertime.
Neithermacroeconomictheorynorexistingempiricalevidencesuggeststhatpotentialoutputisasmoothseries.
Policymakers,however,oftenappeartoassumethat,evenintheshortrun,potentialoutputiswellapproximatedbyasmoothtrend.
1Ourmodelandempiricalworkcorrobo-ratethesetwopointsandprovideaframeworktodiscussotheraspectsofwhatweknow,anddonotknow,aboutpotentialoutput.
Aswebegin,cleardefinitionsareimportanttoourdiscussion.
"Potentialoutput"isoftenusedTheconceptofpotentialoutputplaysacentralroleinpolicydiscussions.
Inthelongrun,fastergrowthinpotentialoutputleadstofastergrowthinactualoutputand,forgiventrendsinpopulationandtheworkforce,fastergrowthinincomepercapita.
Intheshortrun,policymakersneedtoassessthedegreetowhichfluctuationsinobservedoutputreflecttheeconomy'soptimalresponsetoshocks,asopposedtoundesirabledeviationsfromthetime-varyingoptimalpathofoutput.
Tokeepthediscussionmanageable,wecon-fineourdiscussionofpotentialoutputtoneo-classicalgrowthmodelswithexogenoustechnicalprogressintheshortandthelongrun;wealsofocusexclusivelyontheUnitedStates.
Wemaketwomainpoints.
First,inboththeshortandthelongrun,rapidtechnologicalchangeinproducingequipmentinvestmentgoodsisimportant.
Thisrapidchangeintheproductiontechnologyforinvestmentgoodsimpliesthatthetwo-sector1See,forexample,CongressionalBudgetOffice(CBO,2001and2004)andOrganisationforEconomicCo-operationandDevelopment(2008).
SusantoBasuisaprofessorinthedepartmentofeconomicsatBostonCollege,aresearchassociateoftheNationalBureauofEconomicResearch,andavisitingscholarattheFederalReserveBankofBoston.
JohnG.
FernaldisavicepresidentandeconomistattheFederalReserveBankofSanFrancisco.
TheauthorsthankAlessandroBarattieriandKyleMatobaforoutstandingresearchassistanceandJonasFisherandMilesKimballforhelpfuldiscussionsandcollaborationonrelatedresearch.
TheyalsothankBartHobijn,ChadJones,JohnWilliams,RodyManuelli,andconferenceparticipantsforhelpfuldiscussionsandcomments.
2009,TheFederalReserveBankofSt.
Louis.
Theviewsexpressedinthisarticlearethoseoftheauthor(s)anddonotnecessarilyreflecttheviewsoftheFederalReserveSystem,theBoardofGovernors,ortheregionalFederalReserveBanks.
Articlesmaybereprinted,reproduced,published,distributed,displayed,andtransmittedintheirentiretyifcopyrightnotice,authorname(s),andfullcitationareincluded.
Abstracts,synopses,andotherderivativeworksmaybemadeonlywithpriorwrittenpermissionoftheFederalReserveBankofSt.
Louis.
todescriberelated,butlogicallydistinct,concepts.
First,peopleoftenmeansomethingakintoa"forecast"foroutputanditsgrowthrateinthelongerrun(say,10yearsout).
Wewilloftenrefertothisfirstconceptasa"steady-statemeasure,"althoughadecade-longforecastcanalsoincorpo-ratetransitiondynamicstowardthesteadystate.
2Intheshortrun,however,asteady-statenotionislessrelevantforpolicymakerswhowishtostabilizeoutputorinflationathighfrequencies.
Thisleadstoasecondconcept,explicitinNewKeynesiandynamicstochasticgeneralequilib-rium(DSGE)models:Potentialoutputistherateofoutputtheeconomywouldhaveiftherewerenonominalrigiditiesbutallother(real)frictionsandshocksremainedunchanged.
3Inaflexiblepricerealbusinesscyclemodel,wherepricesadjustinstantaneously,potentialoutputisequiva-lenttoactual,equilibriumoutput.
Incontrasttothefirstdefinitionofpotentialoutputasexclu-sivelyalong-termphenomenon,thesecondmean-ingdefinesitasrelevantfortheshortrunaswell,whenshockspushtheeconomytemporarilyawayfromsteadystate.
InNewKeynesianmodels,wherepricesand/orwagesmightadjustslowlytowardtheirlong-runequilibriumvalues,actualoutputmightwelldeviatefromtheshort-termmeasureofpoten-tialoutput.
Inmanyofthesemodels,the"outputgap"—thedifferencebetweenactualandpotentialoutput—isthekeyvariableindeterminingtheevolutionofinflation.
Thus,thisseconddefinitionalsocorrespondstotheolderKeynesiannotionthatpotentialoutputisthe"maximumproduc-tionwithoutinflationarypressure"(Okun,1970,p.
133)—thatis,thelevelofoutputatwhichthereisnopressureforinflationtoeitherincreaseordecrease.
Inmost,ifnotall,macroeconomicmodels,thesecond(flexibleprice)definitionconvergesinthelongruntothefirststeady-statedefinition.
Yetathirddefinitionconsiderspotentialout-putasthecurrentoptimalrateofoutput.
Withdistortionarytaxesandothermarketimperfec-tions(suchasmonopolisticcompetition),neithersteady-stateoutputnortheflexiblepriceequilib-riumlevelofoutputneedstobeoptimaloreffi-cient.
Likethefirsttwoconcepts,thisthirdmeaningisofinteresttopolicymakerswhomightseektoimprovetheefficiencyoftheeconomy.
4(However,decadesofresearchontimeinconsis-tencysuggestthatsuchpoliciesshouldbeimple-mentedbyfiscalorregulatoryauthorities,whocantargettheimperfectionsdirectly,butnotbythecentralbank,whichtypicallymusttaketheseimperfectionsasgiven.
See,forexample,theseminalpaperbyKydlandandPrescott,1977.
)Thisarticlefocusesonthefirsttwodefinitions.
Thefirstpartofourarticlefocusesonlong-termgrowth,whichisclearlyanissueofgreatimpor-tancefortheeconomy,especiallyindiscussionsoffiscalpolicy.
Forexample,whetherpromisedentitlementspendingisfeasibledependsalmostentirelyonlong-rungrowth.
Weshowthatthepre-dictionsoftwo-sectormodelsleadustobemoreoptimisticabouttheeconomy'slong-rungrowthpotential.
Thispartofourarticle,whichcorre-spondstothefirstdefinitionofpotentialoutput,willthusbeofinteresttofiscalpolicymakers.
Thesecondpartofourarticle,ofinteresttomonetarypolicymakers,focusesonatime-varyingmeasureofpotentialoutput—thesecondusageabove.
Potentialoutputplaysacentral,ifoftenimplicit,roleinmonetarypolicydecisions.
TheFederalReservehasadualmandatetopursuelowandstableinflationandmaximumsustainableemployment.
"Maximumsustainableemploy-ment"isusuallyinterpretedtoimplythattheFederalReserveshouldstrive,subjecttoitsothermandate,tostabilizetherealeconomyarounditsflexiblepriceequilibriumlevel—whichitselfischanginginresponsetorealshocks—toavoidinefficientfluctuationsinemployment.
InNewKeynesianmodels,deviationsofactualfrompotentialoutputputpressureoninflation,soinBasuandFernald188JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEW2Insomemodels,transitiondynamicscanbeverylong-lived.
Forexample,Jones(2002)interpretsthepastcenturyasatimewhengrowthinoutputpercapitawasrelativelyconstantatarateabovesteadystate.
3SeeWoodford(2003)forthetheory.
NeissandNelson(2005)con-structanoutputgapfromasmall,one-sectorDSGEmodel.
4JustinianoandPrimiceri(2008)define"potentialoutput"asthisthirdmeasure,withnomarketimperfections;theyusetheterm"naturaloutput"tomeanoursecond,flexible-wage/pricemeasure.
thesimplestsuchmodels,outputstabilizationandinflationstabilizationgohandinhand.
Thefirstsectionofthisarticlecomparesthesteady-stateimplicationsofone-andtwo-sectorneoclassicalmodelswithexogenoustechnologicalprogress.
Thatis,wefocusonthelong-runeffectsofgiventrendsintechnology,ratherthantryingtounderstandthesourcesofthistechnologicalprogress.
5Policymakersmustunderstandthenatureoftechnologicalprogresstodevisepoliciestopromotelong-rungrowth,butitisbeyondthescopeofourarticle.
Inthenextsection,weusethetwo-sectormodeltopresentarangeofpossi-blescenariosforlong-termproductivitygrowthanddiscusssomeofthequestionsthesedifferentscenariospose.
Wethenturntoshort-termimplicationsandaskwhetheritisplausibletothinkofpotentialoutputasasmoothprocessandcomparetheimplicationsofasimpleone-sectorversustwo-sectormodel.
Thesubsequentsectionturnstothecurrentsituation(asoflate2008):Howdoesshort-runpotentialoutputgrowthcomparewithitssteady-statelevelThisdiscussionsuggestsanumberofadditionalissuesthatareunknownordifficulttoquantify.
Thefinalsectionsummarizesourfindingsandconclusions.
THELONGRUN:WHATSIMPLEMODELMATCHESTHEDATAAcommon,andfairlysensible,approachforestimatingsteady-stateoutputgrowthistoesti-mategrowthinfull-employmentlaborproductiv-ityandthenallowfordemographicstodeterminetheevolutionofthelaborforce.
Thisapproachmotivatesthissection'sassessmentofsteady-statelaborproductivitygrowth.
Wegenerallythinkthat,inthelongrun,dif-ferentforcesexplainlaborproductivityandtotalhoursworked—technologyalongwithinducedcapitaldeepeningexplainstheformeranddemo-graphicsexplainsthelatter.
Theassumptionthatlaborproductivityevolvesseparatelyfromhoursworkedismotivatedbytheobservationthatlaborproductivityhasrisendramaticallyoverthepasttwocenturies,whereaslaborsupplyhaschangedbymuchless.
6Evenifproductivitygrowthandlaborsupplyarerelatedinthelongrun,assug-gestedbyElsbyandShapiro(2008)andJones(1995),theanalysisthatfollowswillcapturethekeypropertiesoftheendogenousresponseofcapitaldeepeningtotechnologicalchange.
Areasonablewaytoestimatesteady-statelaborproductivitygrowthistoestimateunderly-ingtechnologygrowthandthenuseamodeltocalculatetheimplicationsforcapitaldeepening.
Lethatsoveravariablerepresentlogchanges.
Asamatterofidentities,wecanwriteoutputgrowth,y,aslabor-productivitygrowthplusgrowthinhoursworked,h:Wefocushereonfull-employmentlaborproductivity.
Supposewedefinegrowthintotalfactorproductivity(TFP),ortheSolowresidual,aswhereαiscapital'sshareofincomeand1–αislabor'sshareofincome.
Definingwhereislabor"quality"(composition)growth,7wecanrewriteoutputperhourgrowthasfollows:(1)Asanidentity,growthinoutputperhourworkedreflectsTFPgrowth;thecontributionofyyhh=()+.
tfpykl=()αα1,lqlhlq≡+,yhtfpkllq()=+()+α.
BasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST20091895Ofcourse,totalfactorproductivity(TFP)canchangeforreasonsbroaderthantechnologicalchangealone;improvedinstitutions,deregulation,andlessdistortionarytaxesareonlysomeofthereasons.
Webelieve,however,thatlong-runtrendsinTFPindevelopedcountriesliketheUnitedStatesaredrivenprimarilybytechnologicalchange.
Forevidencesupportingthisview,seeBasuandFernald(2002).
6King,Plosser,andRebelo(1988)suggestafirstapproximationshouldmodelhourspercapitaasindependentoftheleveloftech-nologyandprovidenecessaryandsufficientconditionsontheutilityfunctionforthisresulttohold.
BasuandKimball(2002)showthattheparticularnon-separabilitybetweenconsumptionandhoursworkedthatisgenerallyimpliedbytheKing-Plosser-RebeloutilityfunctionhelpsexplaintheevolutionofconsumptioninpostwarU.
S.
dataandresolvesseveralconsumptionpuzzles.
7Seefootnote7onp.
190.
capitaldeepening,definedasαk–l;andincreasesinlaborquality.
Economicmodelssug-gestmappingsbetweenfundamentalsandthetermsinthisidentitythataresometimestrivialandsometimesnot.
TheOne-SectorModelPerhapsthesimplestmodelthatcouldreason-ablybeappliedtothelong-rundataistheone-sectorneoclassicalgrowthmodel.
Technologicalprogressandlaborforcegrowthareexogenousandcapitaldeepeningisendogenous.
WecanderivethekeyimplicationsfromthetextbookSolowversionofthemodel.
ConsideranaggregateproductionfunctionY=KαAL1–α,wheretechnologyAgrowsatrategandlaborinputL(whichcapturesbothrawhours,H,andlaborquality,LQ—henceforth,wedonotgener-allydifferentiatebetweenthetwo)growsatraten.
Expressingallvariablesintermsof"effectivelabor,"AL,yields(2)wherey=Y/ALandk=K/AL.
Capitalaccumulationtakesplaceaccordingtotheperpetual-inventoryformula.
Ifsisthesavingrate,sothatsyisinvestmentpereffectiveworker,theninsteadystate(3)Becauseofdiminishingreturnstocapital,theeconomyconvergestoasteadystatewhereyandkareconstant.
Atthatpoint,investmentpereffec-tiveworkerisjustenoughtooffsettheeffectsofyk=α,syngk=++()δ.
depreciation,populationgrowth,andtechnologi-calchangeoncapitalpereffectiveworker.
Insteadystate,theunscaledlevelsofYandKgrowattherateg+n;capitaldeepening,K/L,growsatrateg.
LaborproductivityY/L(i.
e.
,outputperunitoflaborinput)alsogrowsatrateg.
Fromtheproductionfunction,measuredTFPgrowthisrelatedtolabor-augmentingtech-nologygrowthbyThemodelmapsdirectlytoequation(1).
Inparticular,theendogenouscontributionofcapitaldeepeningtolabor-productivitygrowthisOutputperunitoflaborinputgrowsatrateg,whichequalsthesumofstandardTFPgrowth,1–αg,andinducedcapitaldeepening,αg.
Table1showshowthismodelperformsrela-tivetothedata.
Itusesthemultifactorproductiv-ityreleasefromtheBureauofLaborStatistics(BLS),whichprovidesdataforTFPgrowthaswellascapitaldeepeningfortheU.
S.
businesseconomy.
Thesedataareshowninthefirsttwocolumns.
Notethatinthemodelabove,standardTFPgrowthreflectstechnologyalone.
Inpractice,alargesegmentoftheliteraturesuggestsreasonswhynontechnologicalfactorsmightaffectmeas-uredTFPgrowth.
Forexample,therearehard-to-measureshort-runmovementsinlaboreffortandcapital'sworkweek,whichcausemeasured(althoughnotactual)TFPtofluctuateintheshortrun.
Nonconstantreturnstoscaleandmarkupsalsointerferewiththemappingfromtechnologi-calchangetomeasuredaggregateTFP.
ButthedeviationsbetweentechnologyandmeasuredTFParelikelytobemoreimportantintheshortrunthaninthelongrun,consistentwiththefindingsofBasu,Fernald,andKimball(2006)andBasuetal.
(2008).
Hence,fortheselonger-termcom-parisons,weassumeaverageTFPgrowthreflectsaveragetechnologygrowth.
Column3showsthepredictionsoftheone-sectorneoclassicalmodelforα=0.
32(theaveragevalueintheBLSmulti-factordataset).
tfpYKLg=()=()ααα11.
αααgtfp=()/1.
BasuandFernald190JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEW7Laborquality/compositionreflectsthemixofhoursacrossworkerswithdifferentlevelsofeducation,experience,andsoforth.
Forthepurposesofthisdiscussion,whichsofarhasfocusedondefini-tions,supposetherewereJtypesofworkerswithfactorsharesofincomeβj,whereThenareasonabledefinitionofTFPwouldbeGrowthaccountingasdonebytheBureauofLaborStatisticsorbyDaleJorgensonandhiscollaborators(see,forexample,Jorgenson,Gollop,andFraumeni,1987)definesβαjj=()∑1.
tfpykhjjj=∑αβ.
lhhdHqljjjjj=∑∑βα1,ln,andhh.
Acomparisonofcolumns2and3showsthemodeldoesnotperformparticularlywell.
Itslightlyunderestimatesthecontributionofcapitaldeepeningovertheentire1948-2007period,butitdoesaparticularlypoorjobofmatchingthelow-frequencyvariationinthatcontribution.
Inpartic-ular,itsomewhatoverpredictscapitaldeepeningforthepre-1973periodbutsubstantiallyunder-predictsforthe1973-95period.
Thatis,giventheslowdowninTFPgrowth,themodelpredictsamuchlargerslowdowninthecontributionofcapitaldeepening.
8Onewaytovisualizetheproblemwiththeone-sectormodelistoobservethatthemodelpre-dictsaconstantcapital-to-outputratioinsteadystate—incontrasttothedata.
Figure1showsthesharpriseinthebusinesssectorcapital-to-outputratiosincethemid-1960s.
TheTwo-SectorModel:ABetterMatchAgrowingliteratureoninvestment-specifictechnicalchangesuggestsaneasyfixforthisfailure:CapitaldeepeningdoesnotdependonoverallTFPbutonTFPintheinvestmentsector.
Akeymotivationforthisbodyofliteratureisthepriceofbusinessinvestmentgoods,especiallyequipmentandsoftware,relativetothepriceofothergoods(suchasconsumption).
TherelativepriceofinvestmentanditsmaincomponentsareshowninFigure2.
WhydoweseethissteadyrelativepricedeclineThemostnaturalinterpretationisthatthereisamorerapidpaceoftechnologicalchangeinproducinginvestmentgoods(especiallyhigh-techequipment).
9Torealizetheimplicationsofatwo-sectormodel,considerasimpletwo-sectorSolow-typemodel,wheresistheshareofnominaloutputthatisinvestedeachperiod.
10Onesectorproducesinvestmentgoods,I,thatareusedtocreatecapital;theothersectorproducesconsumptiongoods,C.
ThetwosectorsusethesameCobb-Douglaspro-ductionfunctionbutwithpotentiallydifferenttechnologylevels:BasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST20091918Notethatoutputperunitofquality-adjustedlaboristhesumofTFPplusthecapitaldeepeningcontribution,whichinthebusinesssectoraveraged1.
39+0.
76=2.
15percentperyearoverthefullsample.
Morecommonly,laborproductivityisreportedasoutputperhourworked.
Overthesample,laborqualityintheBLSmulti-factorproductivitydatasetrose0.
36percentperyear,sooutputperhourrose2.
51percentperyear.
Table1One-SectorGrowthModelPredictionsfortheU.
S.
BusinessSectorPredictedcapitalActualcapitaldeepeningcontributionPeriodTotalTFPdeepeningcontributioninone-sectormodel1948-20071.
390.
760.
651948-19732.
170.
851.
021973-19950.
520.
620.
251995-20071.
340.
840.
631995-20001.
291.
010.
612000-20071.
370.
720.
65NOTE:Dataforcolumns1and2arebusinesssectorestimatesfromtheBLSmultifactorproductivitydatabase(downloadedviaHaveronAugust19,2008).
Capitalandlaborareadjustedforchangesincomposition.
Actualcapitaldeepeningisα(k–l),andpredictedcapitaldeepeningis.
αα()tfp/19Onthegrowthaccountingside,see,forexample,Jorgenson(2001)orOlinerandSichel(2000);seealsoGreenwood,Hercowitz,andKrusell(1997).
10Thismodelisafixed–savingrateversionofthetwo-sectorneo-classicalgrowthmodelinWhelan(2003)andisisomorphictotheoneinGreenwood,Hercowitz,andKrusell(1997),whochooseadifferentnormalizationofthetwotechnologyshocksintheirmodel.
Intheconsumptionequation,wehaveimplic-itlydefinedlabor-augmentingtechnologicalchangeasAC=Q1/1–αAItodecomposeconsumptiontechnologyintotheproductofinvestmenttech-nology,AI,anda"consumption-specific"piece,Q1/1–α.
Letinvestmenttechnology,AI,growatrategIandtheconsumption-specificpiece,Q,growatrateq.
Perfectcompetitionandcostmini-mizationimplythatpriceequalsmarginalcost.
Ifthesectorsfacethesamefactorprices(andthesamerateofindirectbusinesstaxes),thenIKALCQKALIIICIC=()=()αααα11.
PPMCMCQICCI==.
Thesectorsalsochoosetoproducewiththesamecapital-to-laborratios,implyingthatKI/AILI=KC/AILC=K/AIL.
Wecanthenwritetheproduc-tionfunctionsasWecannowwritetheeconomy'sbudgetcon-straintinasimplemanner:(4)"Output"hereisexpressedininvestmentunits,and"effectivelabor"isintermsoftech-nologyintheinvestmentsector.
Theeconomymechanicallyinvestsasharesofnominalinvest-IALKALCQALKALIIIICI=()=()αα.
YICQALLKALyIICIInv.
UnitsIn,or+[]=+()()αvv.
UnitsInv.
UnitsInv.
Uni,where==kyYαttsand.
ALkKALII=BasuandFernald192JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEW1.
71.
61.
51.
41.
31.
21.
11.
0RatioScaleIndex,1948=11950196019701980199020001.
8Figure1Capital-to-OutputRatiointheUnitedStates(equipmentandstructures)SOURCE:BLSmultisectorproductivitydatabase.
Equipmentandstructures(i.
e.
,fixedreproducibletangiblecapital)iscalculatedasaTornquistindexofthetwocategories.
StandardIndustrialClassificationdata(fromwww.
bls.
gov/mfp/historicalsic.
htm)aresplicedtoNorthAmericanIndustryClassificationSystemdata(fromwww.
bls.
gov/mfp/mprdload.
htm)startingat1988(datadownloadedOctober13,2008).
ment,whichimpliesthatinvestmentpereffectiveunitoflaborisi=s.
yInv.
Units.
11Capitalaccumula-tionthentakesthesameformasintheone-sectormodel,exceptthatitisonlygrowthininvestmenttechnology,gI,thatmatters.
Inparticular,insteadystate,(5)Theproductionfunction(4)andcapital-accumulationequation(5)correspondexactlytotheirone-sectorcounterparts.
Hence,thedynamicsofcapitalinthismodelreflecttechnologyintheinvestmentsectoralone.
Insteadystate,capitalperunitoflabor,K/L,growsatrategI,sothecontribu-tionofcapitaldeepeningtolabor-productivitygrowthfromequation(1)issyngkIInv.
Units.
=++()δConsumptiontechnologyinthismodelis"neu-tral"inthatitdoesnotaffectinvestmentorcapitalaccumulation;thesameresultcarriesovertotheRamseyversionofthismodel,withorwithoutvariablelaborsupply.
(Basuetal.
,2008,discusstheideaofconsumption-technologyneutralityingreaterdetail.
12)Toapplythismodeltothedata,weneedtodecomposeaggregateTFPgrowth(calculatedfromαααgtfpII=()1.
BasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST200919311syPIPIPCIPCPALIICCII=+()+()Inv.
Units=IALI.
RatioScale,2000=10020019018017016015014013012011010090801960196519701975198019851990199520002005EquipmentandSoftwareBusinessFixedInvestmentStructuresFigure2PriceofBusinessFixedInvestmentRelativetoOtherGoodsandServicesNOTE:"Othergoodsandservices"constitutesbusinessGDPlessbusinessfixedinvestment.
SOURCE:BureauofEconomicAnalysisandauthors'calculations.
12Notealsothatoutputininvestmentunitsisnotequaltochainout-putinthenationalaccounts.
Chaingrossdomesticproduct(GDP)isIncontrast,inthismodelHence,YsIsC=+()1.
YsIsCsqInv.
Units.
=+()()11YYsq=+()Inv.
Units.
1chainedoutput)intoitsconsumptionandinvest-mentcomponents.
Giventheconditionssofar,thefollowingtwoequationshold:Thesearetwoequationsintwounknowns—Hence,theyallowustodecomposeaggregateTFPgrowthintoinvestmentandconsumptionTFPgrowth.
13Table2showsthatthetwo-sectorgrowthmodeldoes,infact,fitthedatabetter.
Allderiva-tionsaredoneassuminganinvestmentshareof0.
15,aboutequaltothenominalvalueofbusinessfixedinvestmentrelativetothevalueofbusinessoutput.
Forthe1948-73and1973-95periods,acom-parisonofcolumns5and6indicatesthatthemodelfitsquitewell—andmuchbetterthantheone-sectormodel.
TheimprovedfitreflectsthatalthoughoverallTFPgrowthslowedverysharply,investmentTFPgrowth(column3)slowedmuchless.
Hence,theslowdownincapitaldeepeningwasmuchsmaller.
Thesteady-statepredictionsworklesswellfortheperiodsafter1995,whenactualcapitaldeepeningfellshortofthesteady-statepredictionforcapitaldeepening.
Duringtheseperiods,notonlydidoverallTFPaccelerate,buttherelativepricedeclineincolumn2alsoaccelerated.
Hence,impliedinvestmentTFPacceleratedmarkedly(asdidotherTFP).
Ofcourse,thetransitiondynam-icsimplythatcapitaldeepeningconvergesonlyslowlytothenewsteadystate,andadecadeisarelativelyshorttime.
(Inaddition,thepaceofinvestment-sectorTFPwasparticularlyrapidinthelate1990sandhasslowedsomewhatinthe2000s.
)Sothemoreimportantpointisthat,quali-tfpstfpstfpPPtfptfpICCICI=+=()1,.
.
tfptfpICand.
tatively,themodelworksintherightdirectionevenoverthisrelativelyshortperiod.
Despitetheseuncertainties,abottom-linecomparisonoftheone-andtwo-sectormodelsisofinterest.
Supposethatthe1995-2007ratesofTFPgrowthcontinuetoholdinbothsectors(abig"if"discussedinthenextsection).
Supposealsothatthetwo-sectormodelfitswellgoingforward,asitdidinthe1948-95period.
Thenwewouldprojectthatfutureoutputperhour(likeoutputperquality-adjustedunitoflabor,showninTables1and2)willgrowonaverageabout0.
75percentagepointsperyearfasterthantheone-sectormodelwouldpredict(1.
38versus0.
63),asaresultofgreatercapitaldeepening.
Thediffer-enceisclearlysubstantial:Itisasignificantfrac-tionoftheaverage2.
15percentgrowthrateinoutputperunitoflabor(and2.
5percentgrowthrateofoutputperhour)overthe1948-2007period.
PROJECTINGTHEFUTUREForecasters,policymakers,andanumberofacademicsregularlymake"structuredguesses"aboutthelikelypathoffuturegrowth.
14Notsur-prisingly,theusualapproachistoassumethatthefuturewilllooksomethinglikethepast—butthechallengeistodecidewhichpartsofthepasttoincludeandwhichtodownplay.
Inmakingsuchpredictions,economistsoftenprojectaverageTFPgrowthfortheeconomyasawhole.
However,viewedthroughthelensofthetwo-sectormodel,oneneedstomakeseparateprojectionsforTFPgrowthinboththeinvest-mentandnon-investmentsectors.
Weconsiderthreegrowthscenarios:low,medium,andhigh(Table3).
Considerthemediumscenario,whichhasoutputperhourgrowingat2.
3(lastcolumn).
InvestmentTFPisabitslowerthanitsaverageinthepost-2000period,reflectingthatinvest-mentTFPhasgenerallyslowedsincetheburstofthelate1990s.
OtherTFPslowstoitsratein14OlinerandSichel(2002)usethephrase"structuredguesses.
"InadditiontoOlinerandSichel,recenthigh-profileexamplesofprojectionshavecomefromJorgenson,Ho,andStiroh(2008)andGordon(2006).
TheCBOandtheCouncilofEconomicAdvisersregularlyincludelonger-runprojectionsofpotentialoutput.
BasuandFernald194JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEW13Thecalculationsbelowusetheofficialpricedeflatorsfromthenationalaccounts.
Gordon(1990)arguesthatmanyequipmentdeflatorsarenotsufficientlyadjustedforqualityimprovementsovertime.
MuchofthemacroeconomicliteraturesincethenhasusedtheGordondeflators(possiblyextrapolated,asinCumminsandViolante,2002).
Ofcourse,asWhelan(2003)pointsout,muchofthediscussionofbiasesintheconsumerpriceindexinvolvesserviceprices,whichalsomissmanyqualityimprovements.
BasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST2009195Table2Two-SectorGrowthModelPredictionsfortheU.
S.
BusinessSectorRelativepriceofPredictedbusinessfixedinvestmentActualcapitaldeepeningtoothercapitaldeepeningcontributionPeriodTotalTFPgoodsandservicesInvestmentTFPOtherTFPcontributionintwo-sectormodel1948-20071.
39–0.
611.
911.
290.
760.
901948-19732.
170.
331.
892.
220.
850.
891973-19950.
52–1.
021.
390.
370.
620.
661995-20071.
34–1.
902.
941.
040.
841.
381995-20001.
29–2.
933.
780.
851.
011.
782000-20071.
37–1.
172.
361.
200.
721.
112004:Q4–2006:Q40.
210.
29–0.
040.
25——2006:Q4–2008:Q30.
98–1.
121.
940.
82——NOTE:"Othergoodsandservices"constitutesbusinessGDPlessbusinessfixedinvestment.
Capitalandlaborareadjustedforchangesincomposition.
Actualcapitaldeep-eningisα(k–l),andpredictedcapitaldeepeningis.
SOURCE:BLSmultifactorproductivitydataset,BureauofEconomicAnalysisrelative-pricedata,andauthors'calculations.
ThefinaltworowsreflectquarterlyestimatesfromFernald(2008);becauseoftheveryshortsampleperiods,wedonotshowsteady-statepredictions.
αα()tfp/1thesecondhalfofthe1990s,reflectinganassump-tionthattheexperienceoftheearly2000sisunlikelytopersist.
Productivitygrowthaveragingabout2.
25per-centisclosetoaconsensusforecast.
Forexample,inthefirstquarterof2008,themedianestimateintheSurveyofProfessionalForecasters(SPF,2008)wasfor2percentlabor-productivitygrowthoverthenext10years(and2.
75percentgrossdomesticproduct[GDP]growth).
InSeptember2008,theCongressionalBudgetOfficeestimatedthatlaborproductivity(inthenonfarmbusinesssector)wouldgrowatanaveragerateofabout2.
2percentbetween2008and2018.
15AsTable3clearlyshows,however,smallandplausiblechangesinassumptions—wellwithintherangeofrecentexperience—canmakealargedifferenceforsteady-stategrowthprojections.
Asaresult,awiderangeofplausibleoutcomesexists.
IntheSPF,thestandarddeviationacrossthe39respondentsforproductivitygrowthoverthenext10yearswasabout0.
4percent—witharangeof0.
9to3.
0percent.
Indeed,thecurrentmedianestimateof2.
0percentisdownfromanestimateof2.
5percentin2005,butremainsmuchhigherthantheone-yearestimateofonly1.
3per-centin1997.
16Thetwo-sectormodelsuggestsseveralkeyquestionsinmakinglong-runprojections.
First,whatwillbethepaceoftechnicalprogressinproducinginformationtechnology(IT)and,morebroadly,equipmentgoodsForexample,forhard-ware,Moore'slaw—thatsemiconductorcapacitydoublesapproximatelyeverytwoyears—providesplausiblebounds.
Forsoftware,however,wereallyhaveverylittlefirmgroundforspeculation.
Second,howelasticisthedemandforITThepreviousdiscussionofthetwo-sectormodelassumedthattheinvestmentsharewasconstantat0.
15.
ButanimportantpartofthepricedeclinereflectedthatIT,forwhichpriceshavebeenfallingrapidly,isbecominganincreasingshareoftotalbusinessfixedinvestment.
Atsomepoint,acon-stantshareisareasonableassumptionandcon-sistentwithabalancedgrowthpath.
Yetoverthenextfewdecades,verydifferentpathsarepossible.
Technologyoptimists(suchasDeLong,2002)thinkthattheelasticityofdemandforITexceedsunity,sothatdemandwillriseevenfasterthanpricesfall.
Theythinkthatfirmsandindividualswillfindmanynewusesforcomputers,semi-conductors,and,indeed,information,asthesecommoditiesgetcheaperandcheaper.
Bycontrast,technologypessimists(suchasGordon,2000)thinkthatthegreatestcontributionoftheITrevo-lutionisinthepastratherthanthefuture.
Forexample,firmsmaydecidetheywillnotneedmuchmorecomputingpowerinthefuture,sothataspricescontinuetofall,thenominalshare15CalculatedfromdatainCBO(2008).
16TheSPFhasbeenaskingaboutlong-runprojectionsinthefirstquarterofeachyearsince1992.
Thedataareavailableatwww.
philadelphiafed.
org/research-and-data/real-time-center/survey-of-professional-forecasters/data-files/PROD10/.
BasuandFernald196JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEWTable3ARangeofEstimatesforSteady-StateLaborProductivityGrowthCapitaldeepeningLaborOutputperGrowthscenarioInvestmentTFPOtherTFPOverallTFPcontributionproductivityhourworkedLow1.
000.
700.
70.
51.
21.
5Medium2.
000.
821.
00.
92.
02.
3High2.
501.
101.
31.
22.
52.
8NOTE:Calculationsassumeaninvestmentshareofoutputof0.
15andacapitalshareinproduction,α,of0.
32.
Column3(OverallTFP)isanoutput-share-weightedaverageofcolumns1and2.
Column4iscolumn1multipliedbyα/(1–α).
Column5isoutputperunitofcomposition-adjustedlaborinputandisthesumofcolumns3and4.
Column6addsanassumedgrowthrateoflaborquality/compositionof0.
3percentperyear,andthereforeequalscolumn5plus0.
3percent.
ofexpenditureonITwillalsofall.
Forexample,newandfastercomputersmightofferfewadvan-tagesforwordprocessingrelativetoexistingcom-puters,sothereplacementcyclemightbecomelonger.
Third,whatwillhappentoTFPinthenon-IT-producingsectorsTherangeofuncertaintyhereisverylarge—larger,arguably,thanforthefirsttwoquestions.
Thegeneral-purpose-technologynatureofcomputingsuggeststhatfastercomput-ersandbetterabilitytomanageandmanipulateinformationmightwellleadtoTFPimprovementsincomputer-usingsectors.
17Forexample,manyimportantmanagementinnovations,suchastheWal-Martbusinessmodelorthewidespreaddif-fusionofwarehouseautomation,aremadepos-siblebycheapcomputingpower.
Productivityinresearchanddevelopmentmayalsorisemoredirectly;autopartsmanufacturers,forexample,candesignnewproductsonacomputerratherthanbuildingphysicalprototypemodels.
Thatis,computersmaylowerthecostandraisethereturnstoresearchanddevelopmentInaddition,arethesesortsofTFPspilloversfromITtonon-ITsectorsbestconsideredasgrowtheffectsorleveleffectsForexample,the"Wal-Martization"ofretailingraisesproductivitylevels(asmore-efficientproducersexpandandless-efficientproducerscontract)butitdoesnotnecessarilyboostlong-rungrowth.
Fourth,theeffectsnotedpreviouslymightwelldependonlabormarketskills.
Manyendoge-nousgrowthmodelsincorporateakeyroleforhumancapital,whichissurelyakeyinputintotheinnovationprocess—whetherreflectedinformalresearchanddevelopmentorinmanage-mentreorganizations.
Beaudry,Doms,andLewis(2006)findevidencethattheintensityofpersonalcomputersuseacrossU.
S.
citiesiscloselyrelatedtoeducationlevelsinthosecities.
Wehopewehaveconvincedreadersthatitisimportanttotakeatwo-sectorapproachtoesti-matingthetimepathoflong-runoutput.
Butasthis(non-exhaustive)discussiondemonstrates,knowingthecorrectframeworkforanalysisisonlyoneofmanyinputstoprojectingpotentialoutputcorrectly.
Muchstillremainsunknownaboutpotentialoutput,evenalongasteady-stategrowthpath.
Thebiggestproblemisthelackofknowl-edgeaboutthedeepsourcesofTFPgrowth.
SHORT-RUNCONSIDERATIONSGeneralIssuesinDefiningandEstimatingShort-RunPotentialOutputTraditionally,macroeconomistshavetakentheviewexpressedinSolow(1997)that,inthelong-run,agrowthmodelsuchastheonesdescribedpreviouslyexplainstheeconomy'slong-runbehavior.
Factorsuppliesandtechnologydetermineoutput,withlittlerolefor"demand"shocks.
However,theshortrunwasviewedverydifferently,whenasSolow(1997)putit,"…fluc-tuationsarepredominantlydrivenbyaggregatedemandimpulses"(p.
230).
Solow(1997)recognizesthatrealbusinesscycletheoriestakeadifferentview,providingamoreunifiedvisionoflong-rungrowthandshort-runfluctuationsthantraditionalKeynesianviewsdid.
Earlyrealbusinesscyclemodels,inparticular,emphasizedtheroleofhigh-frequencytechnologyshocks.
Thesemodelsarealsocapableofgenerat-ingfluctuationsinresponsetonontechnological"demand"shocks,suchasgovernmentspending.
Sinceearlyrealbusinesscyclemodelstypicallydonotincorporatedistortions,theyprovideexam-plesinwhichfluctuationsdrivenbygovernmentspendingorotherimpulsescouldwellbeoptimal(takingtheshocksthemselvesasgiven).
Neverthe-less,traditionalKeynesiananalysesoftenpre-sumedthatpotentialoutputwasasmoothtrend,sothatanyfluctuationswerenecessarilysubopti-mal(regardlessofwhetherpolicycoulddoany-thingaboutthem).
FullyspecifiedNewKeynesianmodelspro-videawaytothinkformallyaboutthesourcesofbusinesscyclefluctuations.
Thesemodelsaregenerallyfoundedonarealbusinesscyclemodel,albeitonewithrealdistortions,suchasfirmsBasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST200919717See,forexample,Basuetal.
(2003)foraninterpretationofthebroad-basedTFPaccelerationintermsofintangibleorganizationalcapitalassociatedwithusingcomputers.
Ofcourse,anintangible-capitalstorysuggeststhatthemeasuredshareofcapitalistoolow,andthatmeasuredcapitalisonlyasubsetofallcapital—sothemodelandcalibrationintheearliersectionareincomplete.
havingmonopolypower.
Becauseofstickywagesand/orprices,purelynominalshocks,suchasmonetarypolicyshocks,canaffectrealoutcomes.
Thenominalrigiditiesalsoaffecthowtheecon-omyrespondstorealshocks,whethertotechnol-ogy,preferences,orgovernmentspending.
Short-runpotentialoutputisnaturallydefinedastherateofoutputtheeconomywouldhaveiftherewerenonominalrigidities,thatis,bytheresponsesintherealbusinesscyclemodelunderlyingthestickypricemodel.
18Thisisourapproachtoproducingatimeseriesofpotentialoutputfluctuationsintheshortrun.
InNewKeynesianmodels,wherepricesand/orwagesmightadjustslowlytowardtheirlong-runequilibriumvalues,actualoutputmightwelldeviatefromthisshort-termmeasureofpoten-tialoutput.
Inmanyofthesemodels,the"outputgap"—thedifferencebetweenactualandpotentialoutput—isthekeyvariableindeterminingtheevolutionofinflation.
Kuttner(1994)andLaubachandWilliams(2003)usethisintuitiontoestimatetheoutputgapasanunobservedcomponentinaPhillipscurverelationship.
Theyfindfairlysub-stantialtimevariationinpotentialoutput.
InthecontextofNewKeynesianDSGEmodels,isthereanyreasontothinkthatpotentialoutputisasmoothseriesAtaminimum,alowvarianceofaggregatetechnologyshocksaswellasinelasticlaborsupplyisneeded.
Rotemberg(2002),forexample,suggeststhatbecauseofslowdiffusionoftechnologyacrossproducers,stochastictech-nologicalimprovementsmightdrivelong-rungrowthwithoutbeinganimportantfactoratbusi-nesscyclefrequencies.
19Nevertheless,althoughapriorionemightbelievethattechnologychangesonlysmoothlyovertime,thereisscantevidencetosupportthisposition.
Basu,Fernald,andKimball(2006)con-troleconometricallyfornontechnologicalfactorsaffectingtheSolowresidual—nonconstantreturnstoscale,variationsinlaboreffortandcapital'sworkweek,andvariousreallocationeffects—andstillfinda"purifiedtechnology"residualthatishighlyvariable.
Alexopoulos(2006)usespublica-tionsoftechnicalbooksasaproxyforunobservedtechnicalchangeandfindsthatthisseriesisnotonlyhighlyvolatile,butexplainsasubstantialfractionofGDPandTFP.
Finally,variancedecom-positionsoftensuggestthatinnovationstotech-nologyexplainasubstantialshareofthevarianceofoutputandinputsatbusinesscyclefrequencies;seeBasu,Fernald,andKimball(2006)andFisher(2006).
Whenproducingatimeseriesofshort-runpotentialoutput,itisnecessarynotonlytoknow"the"correctmodeloftheeconomy,butalsotheseriesofhistoricalshocksthathaveaffectedtheeconomy.
Oneapproachistospecifyamodel,whichisoftencomplex,andthenuseBayesianmethodstoestimatethemodelparametersonthedata.
Asaby-product,themodelestimatesthetimeseriesofalltheshocksthatthemodelallows.
20BecauseDSGEmodelsare"structural"inthesenseofLucas's(1976)critique,onecanperformcounterfactualsimulations—forexam-ple,byturningoffnominalrigiditiesandusingtheestimatedmodelandshockstocreateatimeseriesofflexiblepricepotentialoutput.
WedonotusethisapproachbecausewearenotsurethatBayesianestimationofDSGEmodelsalwaysusesreliableschemestoidentifytherele-vantshocks.
Thefull-informationapproachofthesemodelsis,ofcourse,preferableinaneffi-ciencysense—ifoneissurethatonehasspecified18SeeWoodford(2003).
Thereisasubtleissueindefiningflexiblepricepotentialoutputwhenthetimepathofactualoutputmaybeinfluencedbynominalrigidities.
Intheory,theflexiblepriceout-putseriesshouldbeapurelyforward-lookingconstruct,whichisgeneratedby"turningoff"allnominalrigiditiesinthemodel,butstartingfromcurrentvaluesofallstatevariables,includingthecapitalstock.
Ofcourse,thecurrentvalueofthecapitalstockmightbedifferentfromwhatitwouldhavebeeninaflexiblepricemodelwiththesamehistoryofshocksbecausenominalrigiditiesoperatedinthepast.
Thus,inprinciple,thepotential-outputseriesshouldbegeneratedbyinitializingaflexiblepricemodeleveryperiod,ratherthantakinganalternativetime-serieshistoryfromtheflexiblepricemodelhitbythesamesequenceofrealshocks.
Wedothelatterratherthantheformerbecausewebelievethatnominalrigidi-tiescauseonlysmalldeviationsinthecapitalstock,butitispos-siblethattheresultingerrorinourpotential-outputseriesmightactuallybeimportant.
BasuandFernald198JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEW19ArecentpaperbyJustinianoandPrimiceri(2008)estimatesbothsimpleandcomplexNewKeynesianmodelsandfindsthatmostofthevolatilityintheflexible-wage/priceeconomyreflectsextremevolatilityinmarkupshocks.
Theystillestimatethatthereiscon-siderablequarter-to-quartervolatilityintechnology,sothateveniftheonlyshocksweretechnologyshocks,theirflexiblepricemeasureofoutputwouldalsohaveconsiderablevolatilityfromonequartertothenext.
20SeeSmetsandWouters(2007).
thecorrectstructuralmodeloftheeconomywithallitsfrictions.
Weprefertouselimited-informationmethodstoestimatethekeyshocks—technologyshocks,inourcase—andthenfeedthemintosmall,plausiblycalibratedmodelsoffluctuations.
Atworst,ourmethodshouldprovidearobust,albeitinefficient,methodofassessingsomeofthekeyfindingsofDSGEmodelsesti-matedusingBayesianmethods.
Webelievethatourmethodofestimatingthekeyshocksisbothmoretransparentinitsidenti-ficationandrobustinitsmethodbecauseitdoesnotrelyonspecifyingcorrectlythefullmodeloftheeconomy,butonlysmallpiecesofsuchamodel.
AsinthecaseoftheBasu,Fernald,andKimball(2006)procedureunderlyingourshockseries,wespecifyonlyproductionfunctionsandcostsofvaryingfactorutilizationandassumethatfirmsminimizecosts—allstandardelementsofcurrent"medium-scale"DSGEmodels.
Further-more,weassumethattruetechnologyshocksareorthogonaltootherstructuralshocks,suchasmonetarypolicyshocks,whichcanthereforebeusedasinstrumentsforestimation.
Finally,becausewedonothavetheoverheadofspecify-ingandestimatingacompletestructuralgeneralequilibriummodel,weareabletomodeltheproductionsideoftheeconomyingreaterdetail.
Ratherthanassumingthatanaggregateproduc-tionfunctionexists,weestimateindustry-levelproductionfunctionsandaggregatetechnologyshocksfromthesemoredisaggregatedestimates.
BasuandFernald(1997)arguethatthisapproachispreferableinprincipleandsolvesanumberofpuzzlesinrecentproduction-functionestimationinpractice.
Weusetimeseriesof"purified"technologyshocks,similartothosepresentedinBasu,Fernald,andKimball(2006)andBasuetal.
(2008).
However,theseseriesareatanannualfrequency.
Fernald(2008)appliesthemethodsinthesearticlestoquarterlydataandproduceshigher-frequencyestimatesoftechnologyshocks.
Fernaldestimatesutilization-adjustedmeasuresofTFPfortheaggregateeconomy,aswellasfortheinvest-mentandconsumptionsector.
Inbrief,aggregateTFPismeasuredusingdatafromtheBLSquarterlylaborproductivitydata,combinedwithcapital-servicedataestimatedfromdetailedquarterlyinvestmentdata.
LaborqualityandfactorsharesareinterpolatedfromtheBLSmultifactor-productivitydataset.
Therelativepriceofinvest-mentgoodsisusedtodecomposeaggregateTFPintoinvestmentandconsumptioncomponents,usingthe(often-used)assumptionthatrelativepricesreflectrelativeTFPs.
Theutilizationadjust-mentfollowsBasu,Fernald,andKimball(2006),whousehoursperworkerasaproxyforutiliza-tionchange(withaneconometricallyestimatedcoefficient)atanindustrylevel.
Theinput-outputmatrixwasusedtoaggregateindustryutilizationchangeintoinvestmentandconsumptionutiliza-tionchange,followingBasuetal.
(2008).
21Toproduceourestimatedpotentialoutputseries,wefeedthetechnologyshocksestimatedbyFernald(2008)intosimpleone-andtwo-sectormodelsoffluctuations(seetheappendix).
Tech-nologyshocksshifttheproductionfunctiondirectly,eveniftheyarenotamplifiedbychangesinlaborsupplyinresponsetovariationsinwagesandinterestrates.
Iflaborsupplyiselastic,thenafortiorithechangesinpotentialoutputwillbemorevariableforanygivenseriesoftechnologyshocks.
Elasticlaborsupplyalsoallowsnontechnologyshockstomoveshort-run,flexiblepriceoutputdiscontinuously.
Shockstogovernmentspending,eveniffinancedbylump-sumtaxes,causechangesinlaborsupplyviaawealtheffect.
Shockstodis-tortionarytaxratesonlaborincomeshiftlabordemandandgenerallycauselaborinput,andhenceoutput,tochange.
Shockstothepreferenceforconsumptionrelativetoleisurecanalsocausechangesinoutputanditscomponents.
TheimportanceofalloftheseshocksformovementsinflexiblepricepotentialoutputdependscruciallyonthesizeoftheFrisch(wealth-constant)elasticityoflaborsupply.
Unfortunately,thisisoneoftheparametersineconomicswhosevalueismostcontroversial,atleastatanaggregatelevel.
Mostmacroeconomistsassumevaluesbetween1and4forthiscrucialBasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST200919921Becauseofalackofdataataquarterlyfrequency,Fernald(2008)doesnotcorrectfordeviationsfromconstantreturnsorforhetero-geneityacrossindustriesinreturnstoscale—issuesthatBasu,Fernald,andKimball(2006)argueareimportant.
parameter,butnotforparticularlystrongrea-sons.
22Ontheotherhand,Card(1994)reviewsbothmicroeconomicandaggregativeevidenceandconcludesthereislittleevidenceinfavorofanonzeroFrischelasticityoflaborsupply.
ThecanonicalmodelsofHansen(1985)andRogerson(1988)attempttobridgethemacro-microdivide.
However,Mulligan(2001)arguesthatthestrongimplicationofthesemodels,aninfiniteaggregatelaborsupplyelasticity,dependscruciallyontheassumptionthatworkersarehomogeneousandcaneasilydisappearwhenoneallowsforhetero-geneityinworkerpreferences.
Wedonotmodelreal,nontechnologicalshockstotheeconomyincreatingourseriesonpotentialoutput.
OurdecisionispartlyduetouncertaintyoverthecorrectvalueoftheaggregateFrischlaborsupplyelasticity,whichasdiscussedpreviouslyiscrucialforcalibratingtheimpor-tanceofsuchshocks.
Wealsomakethisdecisionbecauseinourjudgmentthereisevenlesscon-sensusintheliteratureoveridentifyingtrueinno-vationstofiscalpolicyortopreferencesthanthereisonidentifyingtechnologyshocks.
Ourdecisiontoignorenontechnologicalrealshocksclearlyhasthepotentialtobiasourseriesonpotentialoutput,anddependingonthevaluesofkeyparam-eters,thisbiascouldbesignificant.
One-SectorversusTwo-SectorModelsInthecanonicalNewKeynesianPhillipscurve,derivedwithCalvopricesettingandflexi-blewages,inflationtodaydependsonexpectedinflationtomorrow,aswellasonthegapbetweenactualoutputandthelevelofoutputthatwouldoccurwithflexibleprices.
Toassesshowpotentialandactualoutputrespondintheshortruninaone-versustwo-sectormodel,weusedaverysimpletwo-sectorNewKeynesianmodel(seetheappendix).
Asinthelong-runmodel,weassumethatinvestmentandconsumptionproductionusesaCobb-Douglastechnologywiththesamefactorsharesbutwitha(potentially)differentmultiplicativetechnologyparameter.
Tokeepthingssimple,factorsarecompletelymobile,sothataone-sectormodelisthespecialcasewhenthesametechnologyshockhitsbothsectors.
Wesimulatedtheone-andtwo-sectormodelsusingtheutilization-adjustedtechnologyshocksestimatedinFernald(2008).
Table4showsstan-darddeviationsofselectedvariablesinflexibleandstickypriceversionsoftheone-andtwo-sectormodels,alongwithactualdatafortheU.
S.
economy.
Themodeldoesareasonablejobofapproxi-matingthevariationinactualdata,consideringhowsimpleitisandthatonlytechnologyshocksareincluded.
Investmentinthedataisslightlylessvolatilethaneitherinthestickypricemodelorthetwo-sectorflexiblepricemodel.
Thisisnotsurprising,giventhatthemodeldoesnothaveanyadjustmentcostsorothermechanismstosmoothoutinvestment.
Consumption,labor,andoutputinthedataaremorevolatilethaninthemodels.
23Additionalshocks(e.
g.
,togovernmentspending,monetarypolicy,orpreferences)wouldpresum-ablyaddvolatilitytomodelsimulations.
AnimportantobservationfromTable4isthatpotentialoutput—theflexiblepricesimulations,ineithertheone-ortwo-sectorvariants—ishighlyvariable,roughlyasvariableasstickypriceout-put.
Theshort-runvariabilityofpotentialoutputinNewKeynesianmodelshasbeenemphasizedbyNeissandNelson(2005)andEdge,Kiley,andLaforte(2007).
Thesemodels,withtheshockswehaveadded,showaveryhighcorrelationofflexibleandstickypriceoutput.
Inthetwo-sectorcase,thecorrela-tionis0.
91.
Nevertheless,theimpliedoutputgap(showninthepenultimatelineofTable4asthedifferencebetweenoutputintheflexibleandstickypricecases)ismorevolatilethanwouldbeimpliedifpotentialoutputwereestimatedwiththeone-sectormodel(thefinalline).
BasuandFernald200JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEW22Inmanycases,itissimplybecausemacromodelsdonot"work"—thatis,displaysufficientamplificationofshocks—forsmallervaluesoftheFrischlaborsupplyelasticity.
Inothercases,valueslike4arerationalizedbyassuming,withoutindependentevidence,thattherepresentativeconsumer'sutilityfromleisuretakesthelogarithmicform.
However,thisrestrictionisnotimposedbytheKing-Plosser-Rebelo(1988)utilityfunction,whichguaranteesbalancedgrowthforanyvalueoftheFrischelasticity.
23Therelativevolatilityofconsumptionisnotthatsurprising,becausethemodelsdonothaveconsumerdurablesandwehavenotyetanalyzedconsumptionofnondurablesandservicesintheactualdata.
Figure3showsthattheassumptionthatpoten-tialoutputhasnobusinesscyclevariation—whichistantamounttousing(Hodrick-Prescott–filtered)stickypriceoutputitselfasaproxyfortheoutputgap—wouldoverestimatethevariationintheoutputgap.
Thiswouldnotmattertoomuchiftheoutputgapwereperfectlycorrelatedwithstickypriceoutputitself—then,atleast,thesign,ifnotthemagnitude,wouldbecorrect.
However,asthefigureshows,the"true"two-sectoroutputgapinthemodel(two-sectorstickypriceoutputlesstwo-sectorflexiblepriceoutput)isimperfectlycorrelatedwithstickypriceoutput—indeed,thecorrelationisonly0.
25.
Sointhismodel,policy-makerscouldeasilybemisledbyfocusingsolelyonoutputfluctuationsratherthantheoutputgap.
ImplicationsforStabilizationPolicyIfpotentialoutputfluctuatessubstantiallyovertime,thenthishaspotentialimplicationsforthedesirabilityofstabilizationpolicy.
Inpar-ticular,policymakersshouldbefocusedonlyonstabilizingundesirablefluctuations.
Ofcourse,thewelfarebenefitsofsuchpoliciesremaincontroversial.
Lucas(1987,2003)famouslyarguedthat,giventhefluctuationsweobserve,thewelfaregainsfromadditionalstabilizationoftheeconomyarelikelytobesmall.
Inparticular,givenstandardpreferencesandtheobservedvarianceofconsumption(aroundalineartrend),arepresentativeconsumerwouldbewillingtoreducehisorheraverageconsumptionbyonlyaboutof1/10thof1percentinexchangeforeliminatingallremainingvariabilityinconsump-tion.
Notethatthiscalculationdoesnotneces-sarilyimplythatstabilizationpolicydoesnotmatter,becausethecalculationtakesasgiventhestabilizationpoliciesimplementedinthepast.
Stabilizationpoliciesmightwellhavebeenvalu-able—forexample,ineliminatingrecurrencesoftheGreatDepressionorbyminimizingthefre-quencyofsevererecessions—butadditionalsta-bilizationmightnotofferlargebenefits.
Thiscalculationamountstosome$5billionperyearintheUnitedStates,orabout$16perperson.
Comparedwiththepremiumswepayforverypartialinsurance(e.
g.
,forcollisioncoverageonourcars),thisisalmostimplausiblylow.
Anypoliticianwouldsurelyvotetopay$5billionforapolicythatwouldeliminaterecessions.
Hence,asizableliteratureconsiderswaystoobtainlargercostsofbusinesscyclefluctuations,withmixedresults.
Argumentsinfavorofstabi-lizationincludeGalí,Gertler,andLópez-Salido(2007),whoarguethatthewelfareeffectsofboomsBasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST2009201Table4StandardDeviations,ModelSimulations,andDataVariableInvestmentConsumptionLaborOutputOne-sector,flexibleprice4.
400.
810.
471.
52Two-sector,flexibleprice6.
280.
890.
731.
66One-sector,stickyprice4.
820.
840.
641.
60Two-sector,stickyprice5.
520.
870.
851.
68Data4.
541.
121.
141.
95Outputgap(two-sectorstickyprice5.
780.
590.
960.
72lesstwo-sectorflexibleprice)"One-sector"estimatedgap(two-sectorstickyprice2.
550.
180.
590.
41lessone-sectorflexibleprice)NOTE:Modelsimulationsuseutilization-adjustedTFPshocksfromFernald(2008).
Two-sectorsimulationsuseestimatedquarterlyconsumptionandinvestmenttechnology;one-sectorsimulationsusethesameaggregateshock(ashare-weightedaverageofthetwosectoralshocks)inbothsectors.
AllvariablesarefilteredwiththeChristiano-Fitzgeraldbandpassfiltertoextractvariationbetween6and32quarters.
andrecessionsmaybeasymmetric.
Inparticular,becauseofwageandpricemarkups,steady-stateemploymentandoutputareinefficientlylowintheirmodel,sothatthecostsoffluctuationsdependonhowfartheeconomyisfromfullemployment.
Recessionsareparticularlycostly—welfarefallsbymoreduringabusinesscycledownturnthanitrisesduringasymmetricexpan-sion.
Barlevy(2004)arguesinanendogenous-growthframeworkthatstabilizationmightincreasetheeconomy'slong-rungrowthrate;thisallowedhimtoobtainverylargewelfareeffectsfrombusi-nesscyclevolatility.
Thisdiscussionofwelfareeffectshighlightsthatmuchworkremainstounderstandthedesir-abilityofobservedfluctuations,theabilityofpolicytosmooththeundesirablefluctuationsintheoutputgap,andthewelfarebenefitsofsuchpolicies.
WHATISCURRENTPOTENTIALOUTPUTGROWTHConsiderthecurrentsituation,asoflate2008:Ispotentialoutputgrowthrelativelyhigh,rela-tivelylow,orclosetoitssteady-statevalue24Theanswerisimportantforpolicymakers,wherestatementsbytheFederalOpenMarketCommittee(FOMC)participantshaveemphasizedtheimpor-BasuandFernald202JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEW–6–4–20246Percent1947:Q31952:Q31957:Q31962:Q31967:Q31972:Q31977:Q31982:Q31987:Q31992:Q31997:Q32002:Q32007:Q3Two-SectorStickyPriceModelTwo-SectorOutputFigure3OutputGapandStickyPriceOutputNOTE:Bandpass-filtered(6to32quarters)outputfromtwo-sectorstickypricemodelandthecorrespondingoutputgap(definedasstickypriceoutputlessflexiblepriceoutput).
24Wecould,equivalently,discussthemagnitudeorevensignoftheoutputgap,whichisnaturallydefinedinlevels.
Thelevelistheintegralofthegrowthrates,ofcourse,andgrowthratesmakeitalittleeasiertofocus,atleastimplicitly,onhowtheoutputgapislikelytochangeovertime.
tanceofeconomicweaknessinreducinginflation-arypressures.
25Moreover,adiscussionoftheissuehighlightssomeofwhatweknow,anddonotknow,aboutpotentialoutput.
Someoftheconsiderationsarecloselylinkedtoearlierpointswehavemade,buttheseconsiderationsalsoallowadiscussionofotherissuesthatarenotincludedinthesimplemodelsdiscussedhere.
Severalargumentssuggestthatpotentialoutputgrowthmightcurrentlyberunningatarelativelyrapidpace.
First,andperhapsmostimportantly,TFPgrowthhasbeenrelativelyrapidfromtheendof2006throughthethirdquarterof2008(seeTable2).
Duringthisperiodoutputgrowthitselfwasrelativelyweak,andhoursperworkerweregenerallyfalling;hence,followingthelogicinBasu,Fernald,andKimball(2006),factorutilizationappearstohavebeenfallingaswell.
Asaresult,inboththeconsumptionandtheinvestmentsectors,utilization-adjustedTFP(fromFernald,2008)hasgrownatamorerapidpacethanitspost-1995average.
Thisfastpacehasoccurreddespitethereallocationsofresourcesawayfromhousingandfinanceandthehighleveloffinancialstress.
Second,substantialdeclinesinwealtharelikelytoincreasedesiredlaborsupply.
Mostobviously,housingwealthhasfallenandstockmarketvalueshaveplunged;buttaxandexpen-diturepoliciesaimedatstabilizingtheeconomycouldalsosuggestahigherpresentvalueoftaxes.
Decliningwealthhasadirect,positiveeffectonlaborsupply.
Inaddition,asthelogicofCampbellandHercowitz(2006)wouldimply,risingfinan-cialstresscouldleadtoincreasesinlaborsupplyasworkersneedtoacquirelargerdownpaymentsforpurchasesofconsumerdurables.
Andifthereishabitpersistenceinconsumption,workersmightalsoseek,atleasttemporarily,toworkmorehourstosmooththeeffectsofshockstogasolineandfoodprices.
Nevertheless,therearealsoreasonstobecon-cernedthatpotentialoutputgrowthiscurrentlylowerthanitspaceoverthepastdecadeorso.
First,Phelps(2008)raisesthepossibilitythatbecauseofasectoralshiftawayfromhousing-relatedactivitiesandfinance,potentialoutputgrowthistemporarilylowandthenaturalrateofunemploymentistemporarilyhigh.
Althoughqualitativelysuggestive,itisunclearthatthesec-toralshiftsargumentisquantitativelyimportant.
Forexample,VallettaandCleary(2008)lookatthe(weighted)dispersionofemploymentgrowthacrossindustries,ameasureusedbyLilien(1982).
Theyfindthatasofthethirdquarterof2008,"thedegreeofsectoralreallocation…remainslowrela-tivetopasteconomicdownturns.
"VallettaandCleary(2008)alsoconsiderjobvacancydata,whichAbrahamandKatz(1986)suggestcouldhelpdistinguishbetweensectoralshiftsandpurecyclicalincreasesinunemploymentandemploy-mentdispersion.
Thebasiclogicisthatinasec-toralshiftsstory,expandingfirmsshouldhavehighvacanciesthatpartiallyorcompletelyoffsetthelowvacanciesincontractingfirms.
VallettaandClearyfindthatthevacancyratehasbeensteadilyfallingsincelate2006.
26Third,Bloom(2008)arguesthatuncertaintyshocksarelikelytoleadtoasharpdeclineinout-put.
Asheputsit,therehasbeen"ahugesurgeinuncertaintythatisgeneratingarapidslow-downinactivity,acollapseofbankingpreventingmanyofthefewremainingfirmsandconsumersthatwanttoinvestfromdoingso,andashiftinthepoliticallandscapelockinginthedamagethroughprotectionismandanti-competitivepolicies"(p.
4).
Hisargumentisbasedonthemodelsimu-lationsinBloom(2007),inwhichanincreaseinmacrouncertaintycausesfirmstotemporarilypauseinvestmentandhiring.
Inhismodel,pro-ductivitygrowthalsofallstemporarilybecauseofreducedreallocationfromlower-tohigher-productivityestablishments.
Fourth,thecreditfreezecoulddirectlyreduceproductivity-improvingreallocations,alongthelinessuggestedbyBloom(2007),aswellasEisfeldtandRampini(2006).
EisfeldtandRampiniarguethat,empirically,capitalreallocationisprocycli-BasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST200920325Forexample,intheminutesfromtheSeptember2008FOMCmeeting,participantsforecastthatovertime"increasedeconomicslackwouldtendtodampinflation"(BoardofGovernors,2008).
26VallettaandClearydofindsomeevidencethattheU.
S.
Beveridgecurvemighthaveshiftedoutinrecentquartersrelativetoitsposi-tionfrom2000to2006.
cal,whereasthebenefits(reflectingcross-sectionaldispersionofmarginalproducts)arecounter-cyclical.
Theseobservationssuggestthattheinformationalandcontractualfrictions,includingfinancingconstraints,arehigherinrecessions.
Thesituationasoflate2008isoneinwhichfinancingconstraintsareparticularlysevere,whichislikelytoreduceefficientreallocationsofbothcapitalandlabor.
Fifth,therecouldbeothereffectsfromtheseize-upoffinancialmarketsin2008.
Financialintermediationisanimportantintermediateinputintoproductioninallsectors.
Ifitiscomplemen-tarywithotherinputs(asinJones,2008),forexample,youneedaccesstothecommercialpapermarkettofinanceworkingcapitalneeds—thenitcouldleadtosubstantialdisruptionsofrealoperations.
Finally,thesubstantialvolatilityincommod-ityprices,especiallyoil,inrecentyearscouldaffectpotentialoutput.
Thatsaid,althoughoilisacrucialintermediateinputintoproduction,changesinoilpricesdonothaveaclear-cuteffectonTFP,measuredasdomesticvalueaddedrela-tivetoprimaryinputsofcapitalandlabor.
Theymight,nevertheless,influenceequilibriumoutputbyaffectingequilibriumlaborsupply.
BlanchardandGalí(2007)andBodenstein,Erceg,andGuerrieri(2008),however,aretworecentanalysesinwhich,becauseof(standard)separableprefer-ences,thereisnoeffectonflexiblepriceGDPoremploymentfromchangesinoilprices.
Sothereisnoapriorireasontoexpectfluctuationsinoilpricestohaveasubstantialeffectonthelevelorgrowthrateofpotentialoutput.
Adifficultyforalltheseargumentsthatpoten-tialoutputgrowthmightbetemporarilylowistheobservationalreadymade,thatproductivitygrowth(especiallyafteradjustingforutilization)has,infact,beenrelativelyrapidoverthepastsevenquarters.
Itispossibletheproductivitydatahavebeenmismeasuredinrecentquarters.
27Basu,Fernald,andShapiro(2001)highlightvariationsindisrup-tioncostsassociatedwithtangibleinvestment.
Comparing2004:Q4–2006:Q4(whenproductivitygrowthwasweak)with2006:Q4–2008:Q3(whenproductivitywasstrong),growthinbusinessfixedinvestmentwasverysimilar,suggestingthattime-varyingdisruptioncostsprobablyexplainlittleoftherecentvariationinproductivitygrowthrates.
Basuetal.
(2004)andOliner,Sichel,andStiroh(2007)discusstheroleofmismeasurementassociatedwithintangibleinvestments,suchasorganizationalchangesassociatedwithIT.
Withgreaterconcernsaboutcreditandcashflow,firmsmighthavedeferredorganizationalinvestmentsandreallocations;intheshortrun,suchdeferralwouldimplyfastermeasuredproductivitygrowth,eveniftrueproductivitygrowth(intermsoftotaloutput,thesumofmeasuredoutputplusunob-servedintangibleinvestment)wereconstant.
Basuetal.
(2004)argueforalinkbetweenobservedinvestmentsincomputerequipmentandunob-servedintangibleinvestmentsinorganizationalchange.
Growthincomputerandsoftwareinvest-mentdoesnotshowanotabledifferencebetweenthe2004:Q4–2006:Q4and2006:Q4–2008:Q3periods.
Ifanything,theinvestmentratewashigherinthelatterperiod—sothatthisproxyagaindoesnotimplymismeasurement.
Givenwealtheffectsonlaborsupplyandstrongrecentproductivityperformance—alongwiththefailureoftypicalproxiesformismeasure-menttoexplaintheproductivityperformance—therearereasonsforoptimismabouttheshort-runpaceofpotentialoutputgrowth.
Nevertheless,themajoreffectsoftheadverseshocksonpotentialoutputseemlikelytobeaheadofus.
Forexample,thewidespreadseize-upoffinancialmarketshasbeenespeciallypronouncedonlyinthesecondhalfof2008.
Weexpectthatastheeffectsofthecollapseinfinancialintermediation,thesurgeinuncertainty,andtheresultingdeclinesinfactorreallocationplayoutoverthenextseveralyears,short-runpotentialoutputgrowthwillbecon-strainedrelativetowhereitotherwisewouldhavebeen.
27Notealsothatthedataareallsubjecttorevision.
Forexample,theannualrevisionin2009willrevisedatafrom2006forward.
Inaddi-tion,labor-productivitydataforthenonfinancialcorporatesector,whichisbasedonincome-sideratherthanexpenditure-sidedata,showlessofaslowdownin2005and2006andlessofapickupsincethen.
Thatsaid,eventhenonfinancialcorporateproductivitynumbershaveremainedrelativelystronginthepastfewyears.
BasuandFernald204JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEWCONCLUSIONThisarticlehashighlightedafewthingswethinkweknowaboutpotentialoutput—namely,theimportanceinboththeshortrunandthelongrunofrapidtechnologicalchangeinproducingequipmentinvestmentgoodsandthelikelytimevariationintheshort-rungrowthrateofpotential.
Ourdiscussionofthesepointshas,ofcourse,pointedtowardsomeofthemanythingswedonotknow.
Takingastepback,wehaveadvocatedthink-ingaboutpolicyinthecontextofexplicitmodelsthatsuggestwaystothinkabouttheworldecon-omy,includingpotentialoutput.
Butthereisanimportantinterplaybetweentheoryandmeasure-ment,asthediscussionsuggests.
Everyday,pol-icymakersgrapplewithchallengesthatarenotpresentinthestandardmodels.
Notonlydotheynotknowthetruemodeloftheeconomy,theyalsodonotknowthecurrentstatevariablesortheshockswithanyprecision;andtheenvironmentispotentiallynonstationary,withthecontinuingquestionofwhetherstructuralchange(e.
g.
,param-eterdrift)hasoccurred.
Theory(andpracticalexperience)tellsusthatourmeasurementsareimperfect,particularlyinrealtime.
Notsurpris-ingly,centralbankerslookatmanyofthereal-timeindicatorsandfilterthemanalytically—relyingontheoryandexperience.
Estimatingpotentialoutputgrowthisonemodestandrelativelytrans-parentexampleofthisinterplaybetweentheoryandmeasurement.
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LOUISREVIEWAPPENDIXASIMPLETWO-SECTORSTICKYPRICEMODEL28HouseholdsTheeconomyispopulatedbyarepresentativehouseholdwhichmaximizesitslifetimeutility,denotedaswhereCtisconsumptionofaconstantelasticityofsubstitutionbasketofdifferentiatedvarietiesandLtislaboreffort.
u,theperiodfelicityfunction,takesthefollowingform:whereηistheinverseoftheFrischelasticityoflaborsupply.
Themaximizationproblemissubjecttoseveralconstraints.
Theflowbudgetconstraint,innominalterms,isthefollowing:whereThepriceindicesaredefinedasfollows:Moreover,(A1)(A2)(A3)max,,EuCLttt0=0∞∑()CCzdzt=0111∫()ξξξξuCLttt=11ln,++ηηBPIPCWLRKiBttIttCttttttt()+=1111,IIzdz=0111∫()ξξξξ.
PPzdzPPzdztCtCtItI==01111011∫∫()()()(ξξξ))11ξ.
KIKttt=11+()δLLLttCtI=+KKKttCtI+1=.
BasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST200920928TheappendixwaswrittenprimarilybyAlessandroBarattieri.
Noticethattotalcapitalispredetermined,whilesector-specificcapitalisfreetomoveineachperiod.
Tosolvetheproblem,wewritetheLagrangianasThefirst-orderconditionsofthemaximizationproblemforconsumption,nominalbond,labor,andcapitalareasfollows:(A4)(A5)(A6)(A7)TableA1providesbaselinecalibrationsforallparameters.
LCLBPIPCWLRtttttIttCttt=1.
.
.
1ln++ηηΛttttttttttIKiBEBPI++++()()+1111111ΛβtttCttttttttPCWLRKiB()111111111.
.
.
()1=CPttCtΛΛΛttttEi=11β+()+Lwttη=ΛΛΛttIttttIPERP=1111βδ++++()().
210JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEWTableA1BaselineCalibrationParameterValueParameterValueβ0.
99η0.
25αC0.
3αI0.
3δ0.
025ΓC1.
1ΓI1.
1θC0.
75θI0.
75ζCζI11()()θβθθCCC11()()θβθθIIIINV_SHARE0.
2C_SHARE0.
8LI/L0.
2LC/L0.
8KI/K0.
2KC/K0.
8ρi0.
8φπ1.
5φ0.
5ρC0.
99ρI0.
99σεtC1σεtI1σvt1BasuandFernaldFirmsBothsectorsarecharacterizedbyaunitarymassofatomisticmonopolisticallycompetitivefirms.
ProductionfunctionsareCobb-Douglas(possiblywithdifferentfactorintensities).
ProductivityinthetwosectorsisrepresentedbytwoAR(1)processes.
Thecostminimizationproblemforthefirmszoperatingintheconsumptionandinvestmentsectorscanbeexpressed,innominalterms,asandanalogouslyasCallingiwithi=C,Ithemultiplierattachedtotheminimizationproblem,reflectingnominalmarginalcost,wecanexpressthefactordemandasfollows,whereweomitzassumingasymmetricequilibrium:Takingtheratioforeachsector,weget(A8)(A9)Inflationratesarenaturallydefinedas(A10)Finally,giventheCobb-Douglasassumption,itispossibletoexpressthenominalmarginalcostasfollows:(A11)withj=C,I.
Mins.
t.
WLzRKzYzAKzttCttCtCtCtC()+()()()(=))()()ααCtCCCLz1ΦMins.
t.
WLzRKzIAKzttIttIttItII()+()()()=αLLztIII()()1αΦ.
WAKLRAKttCtCtCCtCCttCtCtCαααα=1=())()αααααCtCCttItItIItILWAKL11=1IIttItItIItIIRAKLααα=11()().
KLWRtCtCtt=1ααKLWRtItItt=1αα.
ΠtjtjtjPP=1.
MCAfRWYjjjj=111ααα()+()Φ,BasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST2009211WeintroducenominalrigiditiesthroughstandardCalvo(1983)pricing.
InsteadofwritingtherathercomplexequationsforthepricelevelsintheCandIsectors,wejumpdirectlytothelog-linearizedCalvoequationsfortheevolutionofinflationrates,equations(25)and(26)below.
MonetaryPolicyMonetarypolicyisconductedthroughaTaylor-typerulewithasmoothingparameterandreactiontoinflationandmarginalcost.
Again,wewritetheTaylorruledirectlyinlog-linearizedform,asequation(A32)below.
EquilibriumBeyondthefactormarket–clearingconditionsalreadyexpressed,equilibriumalsorequiresabondmarket–clearingcondition(B=0),aconsumptiongoodsmarket–clearingcondition(YC=C),andanaggregateadding-upcondition(C+I=Y).
(ByWalras'slaw,wedroptheinvestmentmarket–clearingcondition.
)TheLinearizedModelTheequationsofthemodellinearizedarounditsnonstochasticsteadystatearerepresentedbyequations(A12)through(A36),whichare25equationsforthe25unknownendogenousvariables,c,lI,lC,l,kC,kI,k,λ,w,wC,r,i,yC,I,y,pI,pC,π,πC,πI,,I,C,aC,aI,asfollows:(A12)(A13)(A14)(A15)(A16)(A17)(A18)(A19)(A20)(A21)(A22)kIkttt=11δδ+()LLlLLllItICtCt+=KKkKKkkItICtCt+=1+cptttC=λλλttti=1++ηλlwtt=+λλβδβδttItttIprp++()+()+++=111111yakltCCtCCtCCtC=1Γ++()()ααIakltItIItIItI=1Γ++()()ααkrwltCtttC++=krwltItttI++=BasuandFernald212JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEW(A23)(A24)(A25)(A26)(A27)(A28)(A29)(A30)(A31)(A32)(A33)(A34)(A35)(A36).
πβπζtCtCtCCp=1++()πβπζtItItIIp=1++()πtCtCtCpp=1πtItCtIpp=1ttCtICshareINVshare=__+πππttCtICshareINVshare=__+wwptCttC=iitititt=11ρρφπφπ+()+()yCsharecINVshareIttt=__+yctCt=aatCCtCtC=1ρε+aatIItItI=1ρε+ααtCtttCrwa=1+()ααtItttIrwa=1+()BasuandFernaldFEDERALRESERVEBANKOFST.
LOUISREVIEWJULY/AUGUST2009213214JULY/AUGUST2009FEDERALRESERVEBANKOFST.
LOUISREVIEW