Long-Term Evidence on the Tobin and Fisher Effects: A New Approach

B ofGovernorsof theFederalReosaerveSystem InternationalFinanceDiscussionPapers Number566 September199’6 Long-Term Evidenceon the Tobinand Fisher Effects: A NewApproach ShaghilAhmedandJohnH. Rogers NOTE: InternationalFinanceDiscussionPapersare preliminarymaterialscirculatedto stimulate discussionandcriticalcomment. Referencesinpublicationsto InternationalFinanceDiscussion Papers(otherthanan acknowledgmentthatthewriterhashadaccessto unpublishedmaterial)should be clearedwiththeauthoror authors.

ABSTRACT Usinga newapproach,wereexaminetheempirical evidenceonthelong-terminteractions betweeninflationandrealvariables. We find,usingover 100yearsof U.S. data,thatinthelongrzm the effectof infkationon investmentandoutputispositive(a “Tobintypeeffect”)andthe investment rate, andhencetherealinterestrate. arenotindependentof inflation. However,overthefullsample at least,thevariabilityoftheinnovationstothestochasticinflationtrendissmallrelativeto the variabilityof theinnovationsto t!leproducnvityandfiscaltrends. Weconcludethatmodels generatinga re}wse-Tobhl effect. includingstandardreal-business-cycleandendogenousgrowth modelsthatincorporatemoney.maynotbe [hebestmodelsforunderstandingthelong-termreal effectsof’inflation.

Long-TermEvidenceonthe Tobin and Fisher Effects: A NewApproach ShaghilAhmedandJohnH. Rogers* 1. Introduction Considera situationinwhich,withtheeconomyina lowinflationsteadystate,therateof inflationfallspermanently, sayby2 percentagepoints. WhatwouldbetheZong-runeffectsonreal economicvariablessuchas output,consumption,therealinterestrate, investmentandthecapital stock? Economictheoryprovidesnoclear-cutprediction. Ontheonehandthereisthefamous superneutralityresultdueto Sidruaski~1967). However,Sidruaski’sresultemergesfroma very specifictheoreticalset-up,requiring,inparticular.thestrongassumptionthatconsumptionandleisure areseparableinutility. Indeed,inseveraltheoreticalmodelsthesuperneutralityresultbreaksdown, as inflationcanhaveeitherpositiveor negativeeffectson realvariablessuchas outputand investment,dependingontheexactassumptionsconcerningpreferencesandhowmoneyis introduced intotheeconomy. Additionally,inthesemodelsthereal interestratemayor maynotbe independent oftherateof inflationinthelongrun. (seeOrphanidesandSolow[1990]for a survey.) Therefore,whetherthelong-runeffectof inflationonthecapitalstockandoutputispositive or negative,andwhethertherealinterestrateis independentof inflationor notinthelongrunare empiricalissues. Recently.therehasbeenconsiderableinterestintheexistenceof, andnatureof, the long-runrealeffectsof inflation(e.g. KingandWatson[1994]andAkerlof,Dickens,andPerry [1996]).Understandingtheseeffectsiscrucialfor evaluatingmonetarypolicy,especiallyin lightof thedebateaboutmovingfromthecurrentlowinflationrateto pricestability.l *Theauthorsare staffeconomistsintheDivisionof InternationalFinance,BoardofGovernorsof theFederalReserveSystem. For theirhelpfulcomments,wewouldliketothank,without implicating,RickBond,AllanBrunner,DavidBowman,JoeGagnon,Eric Leeper,JaimeMarquez, EnriqueMendoza,JimNason,EricRasmusen,ChrisWailerandworkshopparticipantsattheFederal ReserveBoard,IndianaUniversity,andPennStateUniversity. Thispaperrepresentstheviewsofthe authorsandshouldnotbe interpretedasreflectingtheviewsoftheBoardofGovernorsoftheFederal ReserveSystemor othermembersof itsstaff. IItmaybe arguedthatsupernon-neutralityisirrelevantinpracticebecausechangesin inflation arenotobserved tobepermanent. Butthisdoesnotappearto beverypersuasive. For example, Mishkin(1992)makesthecasethatitislikelythatinflationhasaunitroot. StudiessuchasKing- Watsonarepredicatedontheexistenceofpermanentshocksto inflation.

Withtheseconsiderationsinmind,wereexamine theempirical evidenceonthe long-term interactionsbetweeninflationandtherealeconomy.withthegoalof sortingoutwhichofthemany theoreticalchannelsofthe realeffectsof inflationary empiricallymore relevant. Weaskwhether long-termU.S. dataare consistentwitha “Tobintypeeffect”or a “reverse-Tobineffect”occurringin responseto a once-and-forallpermanentchangein inflation.We alsoexaminethe long-runvalidityof the “Fishereffect”. Tobe’precise,by a “Tobintypeeffect”wemeanthatan exogenousincreasein inflationleadsto anupwardjump inthebalanced-growthpathof thecapitalstockandtherefore investment,whereasthe “reverse-Tobinfefect” istakento indicatea downwardjump. The “Fisher effect”(Fisher[1930])holdswhentheinflationratehasa one-to-onepositiveeffecton thenominal interestrate and,consequently,doesnotaffectthereal interestrate.~ Our empiricalfindingsare organizedinthreeparts. First. theunivariatepropertiesof thedata are describedandcointegratingvectorsare estimated. Hypothesistestingon thesecointegrating vectorsrevealswhetherthedataare consistentwiththeFishereffectholdinginthelongrunor not. Our testrelieson thedirectcorrespondencebetweenthecapital-output--andhencetheinvestmentoutput--ratioandtherealrateof interestinthelongrun. Thiscorrespondenceimpliesthat, ifthereal interestrate is independentof inflation,thelattershouldhaveequaleffectson investmentandoutput overa longhorizon. Thisistestableusingcointegrationanalysis. Thus, oneimportantnovelaspect of our empiricalapproachisexaminingthelong-runvalidity of the Fisher ejiect, withoutexplicitly modelling inflationaryexpectations.3 ‘Sometimestheterms “Fisherrelation”and “Fishereffect”are usedinterchangeablyandusedto denotetherelationshipthatthenominalrate isthesumof theexun~ereal rateandexpectedinflation. We preferto callthisidentitythe “Fisherrelation”,andthroughoutthispapertakethe “Fishereffect” to mean,as seemsto bemoreprevalentin theliterature,thatthereal rate is independentofthe rate of in~ation. Aswillbecomeclear, theabsenceof a Tobinor reverse-TobineffectandtheFisher effectholdingare notnecessarilythesamethingwhenleisureisendogenous. 30urmethoddoesnot, ofcourse, shedlighton thevalidityofthe Fishereffectatshort-to-medium horizons. Theresultsof teststhatattemptto do thisare sensitiveto themodellingof inflationary expectations. -2-

Second,undercertainrestrictions,weare ableto identifyandestimateadditionalstructural parameters,whichallowusto retrievetheeffectsofchangesintheexogenouscomponentof inflation onthelevelsof consumption,investmentandoutput(asopposedto theeffectsontheconsumptionoutputandinvestment-outpurtatios,whichare obtainedfromthecointegratingvectors). The identificationschemeissimilarto King,Plosser,StockandWatson(1991).Theeffecton investment allowsusto seewhethera Tobinor reverse-Tobineffectholds. Ourestimatesindicatethepresence ofa TobintypeeffectandindicatethattheFishereffectdoesnotholdinU.S. datafrom 1889-1995. However,thevariancedecompositionsalsoshowthattheinflationtrendisnotparticularlyimportant inexplainingrealeconomicfluctuations. Third,andfinally,weexaminetherobustnessof ourfindingsoverdifferentsub-periodsofthe data,thusallowingforthepossibilitythattheremayhavebeenstructuralbreaksoverthislongperiod intheinteractionsbetweeninflationandrealvariables. Theremainderofourpape~isorganizedas follows: In section2, wesetup a general frameworkthatneststhedifferenttypesofeffectsof inflationontherealeconomythatare foundin thetheoreticalliterature. Inthisframework,thelong-runpathsofthevariablesare drivenby three stochastictrends: aproductivity(oroutput)trend, a fiscaltrend,andan inflationtrend. Section3 linksthetheoreticalmodelto ourempiricalestimation,discussestheidentifyingassumptionsand presentsourempiricalresults. Section4 concludes. 2. TheoreticalFramework Thereisnothingfundamentallynewinthetheoreticalmodelweusebelow. Ourobjectiveis to developaunifiedframeworkthatisgeneralenoughto incorporatemanyoftherelevanttheoretical resultsontherealeffectsof inflationasspecialcases. Webeginwitha briefdescriptivereviewof thetheoreticalliterature,andthenproceedto ourgeneralframework.4 4Althoughmodelswithstickypricesand/orimperfectinformation(e.g., Ball,Mankiw,andRomer -3-

Reviewofthe Literature Tobin(1965)firstestablishedtheportfoliomechanismthatgeneratesa positiveeffectof inflationon the-steady-statecapitalstock. The intuitionisthata higherinflationrate inducessaversto substitutefromholdingmoneytoholdingphysicalcapital. Thismechanismhas beendubbedthe “Tobineffect”. Becausethemarginalproductof capitalis lower, thereal interestratefalls. TheTobineffect, as originallyformulated,waswidelycriticizedon thegroundsthatit assumesan exogenoussavingsrates Thiscriticismledto a literaturethathas shownthata “Tobin typeeffect’’--bywhichwemeanonlya positiverelationshipbetweeninflationandthe capitalstock-canariseeveninoptimizingmodelswithcertainfeatures. For example,it canarise intwo-period OLGmodels,in infinitehorizonmodelswithindividualheterogeneityandfamilydisconnectednessdue to uncertainlifetimes,and inmodelswithconsumptionand moneyenteringutilityin a nonseparable wayunderparticularassumptionsabouthowthemarginalutilityof consumptionisaffectedby money.4 A positiverelationshipbetweeninflationand investmentcanalsoarise ifthereare distortions inthetax system. Specifically,BayoumiandGagnon(1996)showthatif it is nominalcapitalincome, ratherthanreal capitalincome,thatistaxed,as in Feldstein(1976),higherinflationcountrieswill tendto investmorethanlowerinflationcountries,whichisconsistentwiththedata. Thus, wedo not needto rely ontheoriginal,andperhapsimplausible,mechanismproposedin theearlypapersthat introducedtheTobineffect, to geta positiveeffectof inflationonthecapitalstockandoutput. In contrastto modelsgeneratinga “Tobintypeeffect”,thereare a lotofmodelsthatgenerate thereverse-Tobineffect. Thesimplestoneof theseisa Sidrauskitypemodel,butwithendogenous [1988])generatehighlypersistent effectsof inflation,theseeffectsdo notZastforever and, strictly speaking,long-runsuperneutralityapplies. Hencetheremainderofthediscussionfocuseson flexiblepricemodels. ‘Moreover,themechanisminTobin’soriginalformulationcannotpossiblyleadto a largeeffectof inflationonthecapitalstock(inpercentagetermsat least),givenplausiblevaluesoftheinterest elasticityof moneydemandandtheratioof non-interest-bearingmoneyto thecapitalstock. We thank Joe Gagnonfor pointingthisoutto us. bseetheOrphanidesandSOIOWpaper, andtheliteraturecitedtherein,for details. SeealsoWang . andYip [1992]for the roleof nonseparabilityinutility. -4-

leisurethatisnotseparablefromconsumption,andwithmoneyintroducedthrougha cash-in-advance (CIA)constrainton consumption(e.g. CooleyandHansen[1989]).Inthisset-up,a higherinflation ratetaxesconsumptionmore, leadingpeopleto switchintononmarketactivity(leisure). Thisshiftsin themarginalproductof capitalschedule,so thatthesteady-statecapitalstockfalls. TheFishereffect stillapplies,though,sincethecapital-laborratioisconstantinthesteady-state.’ To simultaneouslygeneratea reverse-Tobineffectandatthesametimethe Fishereffectnot holding,onecanconsidera CIAmodeloftheStockman(1981)typewiththeCIAconstraintapplying to bothconsumptionandinvestment. In thiscase, inflationrepresentsan additionalcostto investment and,therefore,a higherinflationrateleadsto lessinvestmentandan increaseintherealinterestrate. Abel(1985)derivestheaboveresultsandcompares(abstractingfromthelabor/leisurechoice)the dynamicaccumulationofcapitalinmodelswheretheCIAconstraintappliesonlyto conusmptionand modelsinwhichwhichitappliestobothconsumptionandinvestment. Finally,thereisthemoremoderngenreofendogenous growthmodelswithmoney. These modelsalsogeneratelong-runrealeffectsof inflationandthecrucialfactoristhedependenceof the .. leisure-laborchoiceon inflation. Theseendogenousgrowthmodelsgeneratea reverse-Tobineffectof thetype describedabove.buttheyalsodisplaysomeimportantadditionalfeatures. Typically,inthese modelsa once-and-forallrisein inflationhasa negativeeffecton thesteady-state growth rate ofthe economyas well. (For example,seeGomme[1993]andDe Gregorio[1993]). However,ifoutput growthisstationary,shocksto therandomwalkcomponentof inflationcouldnotempiricallyhaveany significantpermanenteffectongrowth. Thisraisesthequestionofwhetheritimpossiblein optimizingmodelsto haveinflationaffectingtherealinterestratebutnotthegrowthrateof the economyinthelongrun. Wewillreturntothisissuelater. ‘Therearealsomodelsin whichinflationhasanambiguouseffectonthesteady-statecapital stock. Twoexamplesare Fischer(1983),inwhich moneyenterstheproductionfunction,andBrock (1974),inwhichmoneyentersutilityandleisureisendogenous. -5-

A General TheoreticalFramework Preferences and Production The representativeagent’sutilityfunctionat timet is: (1) whereC = consumption,N = thefractionoftimespentworking,W = desiredholdingsof money, P is thepricelevel,and$~,$~ > 0 are preferenceparameters. Thetechnologyis: (2) Y, =exp{$g,}A~ F(N,,K,) = exp{$g,}A~N~K,’* where Yisoutput,K isthecapitalstock,A isa technologyshiftvariable,g = G/Yrepresentsthesize of governmentwithGbeingaggregategovernmentpurchasesofgoodsandservicesand& e are fixed . parameterswithO c 0 < 1. TheabovespecificationisstandardCobb-Douglas,exceptthatitallows thesizeof governmentto affectprivateproductionpossibilities.8In ourtheoreticalset-upno stanceis takenon whethergovernmentsizeshiftstheproductionfbnctionup ($ > O),down($ < O),or hasno effect($ = O). Eq. (2) impliesthatoutputavailableto theprivatesector, Y-G,isgivenby: (3) whereZ = [exp{$g}(1-g)]’”Arepresentstliescalefactorfor privateoutput. TheGovernment Thegovernmentissubjectto thefollowingbudgetconstraint: AA’q Q, “ +* =“ + (4) P,q whereQ isthe lump-sumtransferfromthegovernmentandA4isthebeginningof periodmoney supply. Multiplyingthroughby PY,(4)just equatestheusesandsourcesofgovernmentfunds. Note 8BarroandSala-i-Martin(1995)arguethatputtinggovernmentsize, ratherthanthelevelof governmentspending,intheproductionfunctionisappropriateifgovernmentalactivitiesare subjectto congestion. -6-

thatwehaveabstractedfromgovernmentdebt. WithRicardianequivalence,ouranalysiswould essentiallybeunchangedwiththeintroductionofdebt. Eventhoughhouseholdstakethelump-sumtransfers,Q, asgiven,monetarypolicymakesthe transfersproportionalto existingmoneyholdings,sothat: Q =AMtq =pp, (5) Eqs. (4)and(5)implythatg, = 7,. We assumethatagentsinternalizethegovernment’sbudget constraintandknowthattaxrateswillbesetaccordingtothispolicy. Cons~raintsFacingHouseholds For simplicity,householdsaretreatedas integratedworker-firmunits. Sincebeginningof periodt moneyholdingshavealreadybeendeterminedbydecisionsmadeatt-1, J#,, whichequalsM, inequilibrium,isa statevariable. Transferpayments.beinglump-sum,Q,isalsoa statevariablefor households. Thehousehold’sbudgetconstraint.equatingthesourcesandusesof finds is: :~,”+Q, Z,°F(N,,K,) + - [K,+- (l+)K/l -C, - + =O (6) P: t where6 isthedepreciationrateandwehavealreadysubstituted1,= Ki+l- (1-5)K~forinvestment.9 HouseholdsalsofacethefollowingCIAconstraintw. ithafractionac ofconsumptionanda fractionaKof investmentbeingfinancedby cashholdings: (7) It seemsratherawkwardto havemoneyintheutilityfimctionas wellasa CIAconstraint. Thisisfor convenience,inorderto haveonegeneralset-upfromwhichdifferentmodelscanemergeasspecial cases. In thecasesreconsider below,eithermoneyprovidesutilityorthe CIAconstraintis relevant, butneverboth. 9Strictlyspeaking,(6)shouldbean inequalityconstraint. However,we imposestandard conditionsonpreferencesandtechnologythatleadto freedisposalneverbeingexercised. -7-

OptimizationProblem ~ ~ Therepresentativehousehold’soptimizationproblemisto (8) subjectto thesequenceof constraints(6)and(7). Bellman’srecursiverepresentationof theabove problemandthefirstorder conditionsthatemergeare standardand are relegatedto AppendixA. The implicationsoftheseconditionsfor steady-statepathsare alsostandard,butsincetheyare importantin tightlyrelatingour empiricalworkto thetheoreticalliterature,wedescribethembelow. Steadj-State Paths Itcanbe shownthatif, inthe longrun,g, isexpectedto be constantatg and ifA,isexpected togrowata constantgrowthrateP~--thegrowthrateoftheeconomy--thenthesteady-statepathsof theeconomyare characterizedby: (9) (10) (11’! (12) (13) I 7 J’q~*J _a~ (14) Y, p aK(p+A6)K, =0 cl - I 4 wherek, y,representthe Lagrangemultipliersassociatedwith(6) and(7) respectively,andn representsthesteady-stategrowthrateofprices, whichis easilyshownto bePM- PA. -8-

Interpretationof theseequationsisstraightforward. Eq. (9)equatesthemarginalutilityloss fromforegoingconsumptiontodayto themarginalutilitygainfromhavingextraincometo saveplus themarginalutilitygainfromhavingtheCIAconstraintrelaxeda littlebit. Eq. (10)equatesthe marginalutilitylossfromforegoingleisureto themarginalproductof laborinutilityunits. Eq. (11)resultsfromthetradeoffbetweencurrentincomeandendofperiodmoneyholdings. The1efthandsideisthemarginalbenefitofhavingan additionalunitof realbalancesnextperiod, whichconsistsofthediscountedvalueofthreeterms--thedirectutilityobtainedfromthereal balances,themarginalutilityfromspendingrealbalancesnextperiod,andthemarginalgainfromthe relaxationoftheCIAconstraintnextperiod. Therighthandsideisthelossfromnothavingthe currentincomeavailablefor alternativeuses. whichconsistsofthemarginalutilityof income(L,) timestheamountoftoday’sreal incomeittakesto augmentfuturerealbalancesby oneunit(1+K). Eq. (12)equatesthernarginalbenefitof investmenttothemarginal costof investment. The marginalcost(therighthandside)istheutilitylossfromnothavingtheincomeavailablefor alternativeusesplustheutilitylossduetoCIArequirement. Themarginalbenefit(lefthandside) consistsofthediscountedvalueoftwoterms--thegaininutilityfromthegross marginalproductof capitalandthegaininutilitythatcomesaboutbecausecapitalalreadyinplaceisnotsubjectto CIA. Eq. (13)isthesteady-stateversionoftheresourceconstraint,equatingprivateoutputtothe sumofconsumptionandsteady-stateinvestment. Finally,(14)statesthateithertheCIAconstraint mustbind,or themarginalutilityofhavingitrelaxeda littlebit(YJmustbezero. Pro@tMaximizingFirms-andAn Implication of the Fisher Efiect Althoughhouseholdsandfirmshereare integrated,thereisan analogueeconomyinwhich explicitcompetitivemarketsfor laborandcapitalexist. Inthateconomy,thetypicalfirm’sprofit maximizingconditionis: H K, + Y (15) r, =(~@ ~pl -6 =(la)# -3 1 Thisequationisveryimportantinjustifyingourtestofthelong-runFisherrelationbecausethe -9- —.-

constancyof Y/K alsoimpliesconstancyof Y/I. Hence, wecantestfor the independenceofthereal interestratefrom inflationinthelongrun by examiningwhetherchangesin inflationhavea zero long-termeffecton theinvestment-outputratio.‘“ Theequationalsoclearlyshowsthatwhenwork effortdependson inflation.theFishereffectholdingis notthesamepropertyas K7Zbeing independentof n; iftheeffectsof n on 2/NandJUZare offsetting(as, for example,inCooleyand Hansen),thereal ratecanbe independentof n eventhoughK7Zisnot. Four Models as Spcciai Case>” Threespecialcasesofthegeneralmodeiemergein a straightforwardmanner: (i) no CIAconstraint(a, = ~ =L:~j,~abe]le~Sidnwski .%iode~: (ii)CIA for consumptiononly~ac= 1,a~= 0, moneyprovidesno directutility(~~ = 0), which closelyresemblesCooleyandHansen,and islabelledThe Inj.7ation-Tbx-on-ConsumptionModel; (iii)CIA for consumptionandinvestment(a~= 1 = aJ, butwithmoneyprovidingnodirectutility (4M= 0), whichcloselyresemblesthemodelof Stockman.andis labelledIniation-Tax-on- Consunl&ption-a)ld-Illvesljlle~Mltodel. ThefourthmodelweconsidermotivatestheTobineffect. Although,thereare severalwaysto generatea Tobin-typeeffectwithinanoptimizationmodel,weproceedinthespiritoftheoriginal formulationby makingthesavingsrateexogenous. For simplicity,we fixleisureanddroptheCIA constraint. Thus. N isfixed.w = O= av, andsavingsisa fixedproportion,s, ofdisposableincome, whichisthesumof realprivateoutputandthechangein realbalances. Conjecturingthatin steadystateN andiWPZN will be constant (which means n = A1.I-P4)t,his implies: ( M, (16) C, =(1S) Z,tiNeK,’++p~— [ P, 1 Eqs. (13)and(16)imply: 1~e abstractfromincome[axes. For theeffectsof changesintax rateson investmentand growthseeMedozae~.ai. (1995)andfor the interactionsbetweeninflation,taxes,andinvestmentsee theBayoumiandGagnonpapercitedearlier. -10-

s(k‘)1*-(g,,+3)k” - (1a)pxm *=O (17) wherelowercaseletterswithasterisksdenotesteady-stale values of variables deflated by ZN (i.e. k* is thesteady-statevalueof WZN-.etc). WeassumethatJWPandK arestilloptimallychosen. In this newset-up. (Al), (A2),(A6)intheAppendixdropout. (A4)and(A5)are stillvalid,butthe indirectmarginalutilitiesof A47PandA“aredifferem. ThisfourthmodelislabelledTobinModel. Thesemodelsdifferas to thesignsof thederivativesof steady-statevalueswithrespectto inflation(denotedby thesubscriptx), asdescribedbelow: Long-Tern~Effectsof Inflation MODEL EFFECTSOF SUPERNEU- TOBIN REVERSE FISHER INFLATION TRALITY? EFFECT? TOBIN? EFFECT? I. !Xdrauski c*m=Ok,*K=O, i*T=o,y*r=o. Yes ,No No Yes ;%T*X=/(’)~,-izj*:=0 III. CIAfor C*=CO.k*K-=O. Consumption i*Z<Oy,*X<O, No iNo Yes No & Investment N*Z<O,@~l*K<O IV. Tobin’J C*=(?)k,*zXl, i*=>O,y*=>~, No Yes No No N* =0, c1j2~*z4 x Thesuperneutralitypropertyof theSidrauskimodeliswell-known.12Thenegativeeffectof “Withexogenousworkeffort,N, = Oholdsby assumption. In general,ina Tobintypemodel, thenegativeeffectof inflationon workeffort,tendingto counterthepositivedirecteffecton investmentoutput,couldbepresent. Weassumethestabilityconditionsfl-e)k- oc PA+5 holds. 12Notethatsuperneutralityisgenerallytakento meanthatallrealvariablesexcept reaZbalances aredeterminedindependentlyfrominflation,whichishowweusetheterminthispaper. ——

inflationon workeffortin theCIA-on-consumptionmodelisintuitive:inflationactsas a taxon consumption,inducinghouseholdsto substituteintoleisure. However,inthe longrun therealinterest rateisstillindependentof inflationinthismodel. Thereal rate, fromconstantreturnsto scale, dependsonlyonthecapital-outputratio. whichinthelongrun isindependentof inflation,sincethe CIAconstraintdoesnotapplyto investment. Sinceinflationdoesdecreasework effort, k* = (K7ZN)* beingindependentof inflation,impliesa downwardshiftinthebalanced-growthpathofK (i.e. a fall inKZZ)W WhentheCIA constrain(appliesto iwestme?zt also(ModelIII)thecapital-outputratiofalls inresponseto inflationandthe realraterises. Thisisbecauseinflationactsas a tax on investment alsointhiscase. Theessentialintuitionbehindtheresultsin theTobinmodelcanbe seenby considering(17). . As longasthestabilityconditions(I-8) k-6< U4+6holds,anything(includinginflation)that decreasessteady-stateeffectiveper capitarealbaiances,m“, mustincreasetheeffectiveper capita capitalstock.k*. If k* rises. thereal interestrate. of course.falls. 3. TheEmpiricalFramework and Results The Data Ourdataconsistsof annualobservationsfromtheU.S.from 1889to 1995. Output, consumption.investment,and governmentspendingon goodsandservicesare per capitabillionsof 1987dollars. Inflationisthe logfirst-differenceoftheGDPdeflator. Totalresidentpopulationis usedto oi.xamper capita-values. Thenotationusedin reportingtheempiricalresultsisas follows: y, c, andi are theper capitalogsof realoutput,realconsumption,andreal investment,respectively, G/Y istheratioof real governmentspendingto output,andn isinflation. Thedataappendixcontains additionaldetailsandliststhesources. .. Table 1reportssummarystatistics. Overthefullsample1889-1995,inflationaverages 3.05%. whiletheshare in totalGDp ofgover~ent spending,consumption,and investmentis 19.4%, -12-

63.8%, and 16.6%, respectively. As iswell-known,andas canbe seenfromtheplotsin figure1, therehavebeendramaticshiftsin inflationandtherealvariablesduringsub-periodsofour sample. TheGreatDepressionera, for example,iswell-knownas a timeofdeflationandvery lowinvestment. Thepre-WorldWar Iperiod, ontheotherhand.ischaracterizedby lowinflation(anannualaverage rateof0.81%)andhighinvestment(22.9%ofGDP), as indicatedby coh.mm2 oftable1. Ourpost- WWIIperiodreflectstheopposite.witha4.30% averageinflationrateand 15.8%investmentshare. Theshareofconsumptionintotaloutputhasremainedfairlysteadyoverthedifferentsub-periods. UnivariateProperties Theuse ofper capitadatafor output,consumption,andinvestmentamountsto deflatingthe aggregatequantitiesofthesevariablesbythedeterministiccomponentofthetrend inworkeffort.13 Therepresentativeagenttheoreticalframeworklaidoutearlierpresumesthatthevariablesy, c, i, G/Yandn havestochastictrendsembeddedinthem(i.e. haveunitroots). Weconductthreetypesof univariateanalysisto evaluatethisprior: lookingatplotsofthedata,examiningtheautocorrelations, andconductingmoreformalunitroottests. Figure 1plotsthedeterministicallydetrendedlogsofper capitaoutput,consumption, investmentandalsoplotsgovernmentsize, inflationandthenominalinterestrate. Thenominal interestratedataisprovidedfor thepurposeofcomparisonwithinflation. Detrendedper capita output,consumptionandinvestmentappeartobe nonstationary. Thequestionofthestationarity,or otherwise,of governmentsizeandinflationisnotsoclear-cutfromtheplotsofthedata. Plotsofthe firstdifferences(notreported)givea strongindicationthatthedifferencesare stationary. Theautocorrelationsof thevariablesdisplayedinfigure1areplottedinfigure2. The autocorrelationsofthedetrendedper capitalevelsofconsumption,investment,output,and governmentsizedo notdieawayquickly,againindicatingnonstationarity.Theautocorrelationsof 13Analternativeprocedurewouldbe to insteaduseaggregatelevels,butincludea timetrend separatelyinthecointegrating(CI)vectors. ResultsfromestimatingCIvectorswiththisalternative procedureare notreported,butbrieflydiscussedinthetextlater. -13-

I inflationtakeabout4 yearsto dieaway,whichisquickerthanthe rateat whichthedetrendedoutput, consumption,andinvestmentautocorrelationsdieaway,butslowerthantherateatwhichthe autocorrelationsof thefirstdifferences(notshown)dieaway.14 Table2 reportstheresultsof twoformaltestsfor unitroots:theaugmentedDickeyFuller (ADF)test, whichhastheunitrootas thenullhypothesis(Dickeyand Fuller[1979]),andtheKPSS test, for whichthenullis stationarityor trend-stationarity(Kwiatowski,Phillips,SchmidtandShin [1992]). Thetrend isnotincludedinthecaseofthegovernmentsizevariable,sincethisratiois boundedbetweenOand 1. The resultsare containedinthefirstfourcolumns. Thereissubstantial evidenceforunitrootsinper capitavaluesof output,consumption,investment,andgovernmentsize, buttheresultson inflationare very borderlineandsensitiveto theexactsampleperiodused. Because someof theseriesdisplayunusualdynamicsduringthewars, wealsoconductedADFtestsallowing interactionofthelaggedfirstdifferenceswitha wartimedummyinthe Dickey-Fullerregressions. Thisessentiallyallowsthewartimedynamicsto bedifferentfromtherest ofthesampleperiod. The results, reportedinthefinalcolumn,indicateunitrootsin allthevariables. Wethusproceedwiththemaintainedhypothesisofunitrootsiny, c, i, andn. In thecaseof G/Y, we alternativelyreportresultsbothundertheassumptionofa unitrootandstationarity. There are two factorsthataffectedour decisioninthisrespect. First, manyof themodelsthatconsiderthe effectsof fiscalpolicyin a general-equilibriumsetting,assumethatGIYismean-reverting,although deviationsfromthemeanvaluemaybe verypersistent. (See, for example,BaxterandKing[1993].) Second,althoughourunivariatetestsdo supporttheunitrootin G/Y, thetestsarebasedonan assumptionof a linearprocess, whereasthisvariable--beinga ratioboundedbetweenOand l--camot be a restriction-freelinearunitrootprocess. Wealsorealizethatthequestionof a unitrootin inflationiscontroversial. However,thereis a vasttheoreticalliteratureanalyzingthereal effectsof once-and-for-allunanticipatedchangesin 1~he firstdifferenceplotsare omittedto conservespace, sincewhattheyindicate--thatthe variablesplottedin figure 1are notintegratedof orderhigherthanone--isunlikelyto be controversial. -14-

inflationandwhethera long-runinflation-unemploymenttradeoffcanexistor not. Thisliteratureputs a very strongprior ona unitrootin inflation. Moreover,thereareempiricalresultsthatare sympathetictounitrootsin inflation(See,for example,Mishkin[1992]andKingandWatson[1994]). Barsky(1987)hasalsoarguedthatsince1914,shocksto inflationhavebecomemorepersistent, particularlyin thepost-warperiod. Giventheseconsiderationsandtheborderlinenatureof ourown tests, weproceedwiththeassumptionofa unitrootinn. The General Modelin a StochasticEnvironment Theunivariateanalysissuggeststhepresenceof stochastictrends. Therefore,forempirical implementation,wenowdiscusstheextensionofour analysisaboveto allowonce-and-for-all permanentshocksto theproductivitytrend, thegovernmentsizetrend,andtheinflationtrend. It is convenientto separateoutthetrendandcyclicalcomponentsof ourvariables. For thevariablesA, g andn--withabar overthevariableindicatingthetrendcomponentanda tildedenotingthecyclical component(thedeviationfromthesteady-statepath)-- wehave: (18) Invokingcertaintyequivalence,wecanstillcharacterizethesteady-statepathoftheeconomyby (9)- (14)(withtheimplicationsfor thedifferentmodelssummarizedinthepanelonp.11), providedwe replacethe(previouslyconstant)steady-stateinflationrateby itsexpectedvalue. Thelatter,fromthe randomwalkpropertyof stochastictrends, isthecurrentpermanentcomponent,n,withabar over head. Withthischange,whichimpliesthatthelong-runpathsc*,k*, etc. nowhavetimesubscripts, wecanwrite: C’=H“==C[$(El“=’=;k[(-E4’1;=i(E1 * (19) II Y,(l@ ~,” ~ =y(ii); N,”=N(E);m,”=m(%). -w, Notethaty* is long-runeffectiveper capitap-ivate, ratherthantotal,output. -15-

For estimation,wepostulatelinearrelationshipsbetweenthelogsofthevariablesontheleft handsideof sideof (19)andthepermanentcomponentof inflation. Giventhis, (18), (19), andthe definitionofZ (whichimpliesInZ = ($1O)g + (lm) in {~-g)+ InA = in~ - [(1-$)~] g), yield: (20) (21) (22) wherea tildeover a variablerepresentsitsdeviationfromthesteady-statepath, so thatthetermsin curlybracketsin (20)-(22)representstationarycomponentsthatare constantalongsteady-statepaths. In our long-termdataset,N is anunobservedvariable,andso wehavesubstitutedoutfor it. Also,we do notreportthe analogousequationfor K, sincethecapitalstockisalsounobservableinourdata. Eqs. (20)-(22)implythetwo independentcointegrating(CI)relationshipsgivenbelow: ( \ -(ppc,)- g, “a,.- (1WY) -1 1 01“ a’X, = ln~ -I(O) (23) a,- (1-aY) - (P,- P,) -1 0 1 ~nc 1 u lnr, Theselong-termrelationshipscanbe estimatedandwecantestwhetheror nottheFishereffectholds by testingthe nullhypothesisl?,: ~1- ~Y= O. It isalsoclearfrom(23)thatthe restrictionsctY= ar = al are overidentificationrestrictions;theysetthecoefficientong inthetwoCI vectorsto unity, whichcanbe tested,giventhattheserestrictionsare notneededfor identification.ls Thus, we estimatethe followingCI relationshipsusingthemaximum-likelihoodJohansen method(seeJohansenandJuselius[1992]),as implementedinthePCGIVEstatisticalpackage: 150urparticulartheoreticalset-upimpliesthatac = a, = ctY= (1-+)~, but,withmoregenerality, e.g. whengovernmentspendingentersutilityina nonseparableway, theserestrictionswillnot necessarilyhold. -16-

P,lg,+IW, +131lr3%+W =el, ; P2g,+P22~+,132ln3~ +1~, = (24) e2, whereei,i= 1,2, isthestationarydeviationfromtheithcointegrating(long-term)relationship. If the cointegratingrankistwo, theestimatedcointegratingvectorscanbethoughtof astwolinear combinationsofthevectorsgivenin(23). If wenormalizethecoefficienton lnCinthefirstestimated vectorandthecoefficientonlti inthesecondestimatedvectortobeunity,thencomparingtwolinear combinationsof (23)withtheestimatedvectorswillprovideeightequationsineightunknowns. Hence,thestructuralcointegratingrelationshipsarejust identified. Anyfurtherrestrictionsplacedon the~coefficientsare potentiallytestable. Ourmodelimpliesthefollowingrestrictionsonthe P coefficients: ~]]= I = ~Z~, theFishereffect F/3 = ‘1 = p23., p]2 = f& - h’> ~22 = p, - p,,. When holds,wealsohavef122= 0 = ~,z. CointegrationTestResultsandEvidenceontheFisherEffect Wefirstexaminethecointegratingrankforboththethree-trendspecification(inwhichG/Yis treatedasnonstationary)andthetwotrendspecification(stationaryG/Y). Theresultsare intable3. ThelaglengthintheVARwasselectedstartingwitha laglengthof fiveandsequentiallyeliminating lagswithF-testsusedto checkthevalidityof eachreduction. Thenullhypothesisofp cointegrating vectors(CIrank = p) istestedagainstthealternativeof p+ 1cointegratingvectorsusingthe maximumeigenvalueteststatistic.andthemoregeneralalternativeof at least p+ 1cointegrating vectorsusingthetracestatistic. Thevaluesofthemaximumeigenvalueandtracestatisticsare reportedbothwithandwithouta smallsamplecorrectiondueto Reimers(1992). For thethree-tre~dspecification,a cointegratingrankof2, whichis impliedby thetheoretical model,isconsistentwiththeresultsreportedintheupperhalfoftable3. (Theexceptionisa borderlinerejectionifthetracestatisticisusedwithoutthedegreesof freedom(df)correction.lb)The resultsforthetwotrendspecificationinthelowerpartoftable3are evenstronger. Thenullof one 1bTheredoesnotappearto beanyconsensusyeton whetherReimer’sdegrees-of-freedom correctionisthepreferredcorrection. -17-

(or fewer)CI vectorisstronglyrejectedwithor withoutthedf correction,whilethenullof twoCI vectorscannotbe rejected. Wetaketheseresultsto indicatethattheassumptionthattheCI rankistwo, implicitinour theoreticalmodel,isnotat oddswiththedata. Table4 displaysour estimatesof thecointegratingvectors: onefor the5-variablesystemof thetheoreticalmodelandanotherfor the4-variablesystem,inwhichG/Y istreatedas a stationary variable.17Recallthatour theoreticalmodelputs someoveridenti~ingrestrictionson theCI relationshipsgivenin (24). Specifically,thecoefficienton outputshouldbe -1 andthecoefficienton governmentsizeshouldbe 1. Webeganby testingtheseoveridenti~ingrestrictions. Therestriction on thegovernmentsizevariableis rejectedmostof thetime. Therestrictionon theoutputvariableis also rejectedoften. However,thisisbecause,despitethefactthatthecoefficientsare closeto the predictedvalue(-1.07and-0.99 inthetwovectorsof the5-variablesystem),theyhavesmallstandard errors (.02 and .09). Thisisseenin thelastrow oftable4. Thejoint restrictionofa unitcoefficient on outputinbothvectorsisrejectedat anylevelof significance. Basedoneconomicsignificance, however,theserestrictionscouldbe claimedto be satisfied. Oneshouldbear inmindthatit is possiblefor a more generalspecificationof our theoreticalmodelin whichthecoefficienton G/Y is notunity(e.g. if governmentspendingentersutilityina nonseparablemanner). Bycontrast, economictheoryconsiderationsputa very strongprior onthe-1 coefficienton output;itarisesfrom productivitychangesleadingtobalancedgrowth. In lightofthe above,weproceedto estimatethe cointegratingvectorswiththeoutputvariablerestrictedand G/Yunrestricted. The estimatedstructuralcointegratingvectorsare reportedintable4. Forthefive-variable model,keepingfixedtheeffectsof governmentsize, a permanentincreasein inflationisassociated withadrop intheconsumption-outpurtatio and a rise intheinvestment-outputratio. The coeff~cient ..- “We reporttheresultsfor theper capitaspecificationonly. However,we alsoconductedour analysisfor thelevelspecification,witha timetrend includedinthecointegratingvectors,for thefull samplemodelat least,withquitesimilarresults. -18-

estimatesare statisticallysignificantatcustomarylevels. Theyindicatethatapermanentone percemagepointincrease in inflationisassociatedwithalong-run drop intheconsumption-output ratioof aboutfourpercentandrise intheinvestment-outpurtatioofaboutfiveandone-halfpercent. Thistranslatesintoa dropintheshareofconsumptionintotalGDPofabout2.5 percentagepoints andriseintheinvestmentshareof about1.0percentagepoint,usingas initialsharesthefull-sample meansreportedintable1. Theseestimatesare large,astheyimplythata permanent,onestandard deviationchangeintherateof inflation(5.54%accordingtotable1)isassociatedwithapproximately a onestandarddeviationchangeinI/Y andconsiderablymorethana onestandarddeviationchangein C/Y(whichare 5.40 and5.41, respectively). Table4 alsoreportstheresultsfromthefour-variable specificationinwhichgovernmentsizeisstationary. Heretootheestimatedvectorsimplya positive (negative)relationshipbetweeninflationandinvestment(consumption).Thepointestimatesinthe4variablespecificationare ofthesamesignas inthe5-variablesystemandare alsosignificant. The coefficientonconsumptionisnoticeablylargerinthe4-variablesystem. Theresultsoftable4 are consistentwiththeFishereflec~not holding:inthelongrun, the capital-outputratiorises, andthereforetherealinterestratefalls,as inflationrises.18Since,typically, modeisinwhichthereal interestratefallswithhigherinflation,are onesinwhichtheTobineffect holds,thiswouldalsoseemto providesomeindirectevidenceontheexistenceofa Tobin-typeeffect. However,as emphasizedearlier.themechanismwhichgeneratesthisTobin-typeeffectcan, in principle,bedifferentfromthatemphasizedinTobin’soriginalspecification,sinceendogenous savingsratemodelscanalsogeneratethistypeofeffectundercertainconditions. ‘*Ifwechoosevaluesfortheparameters9, 5,PA,thenwecanuseour estimatedeffectof ~ on I/Y, eq. (15),andthesteady-staterelationshipI/Y= (p~+5)lVYto determinetheeffectof inflationon thesteady-staterealrateof interest. Whenwedo suchcalculationsforplausibleparametervaluesand overthefullsampleperiod,theeffectontherealrateis implausiblylarge. However,introducing quadraticadjustmentcoststochangingthecapitalstockmodifies(15)andyieldsmoreplausibleeffects ofinflation ontherealrate. Wedo notreportthesenumbersbecausetherangevarieswidely dependingonthesize oftheadjustmentcosts,whichisdifficuk topindown. Also,ourestimatesfor thepost-WWIIsub-periodshownbelowwouldprovidemoreplausibleeffects. -19-

TestingtheTobinEffect: ModellingtheStochasticTrends Theanalysisso far, basedon estimatedcointegrationvectors, doesnottellus aboutthe directionofcausation betweeninflationandtherealvariables. In order to interpretresultsmore cleaniyinlightof ourtheoreticalframework,weneedto identifyexogenousshocksto inflation,which requiresadditionalidenti~ing assumptions. Thisalsoallowsus to testfor theTobinor reverse-Tobin effectdirectly. Webeginbymodellingtherelationshipamongour stochastictrends: it, ‘~,, +PGE,; i, =(PM-P,)+~,,,,+e=, (27) wherethe c’s are zero-mean,seriallyuncorrelateddisturbanceterms. Eqs. (25)and(26), respectively,implythattheproductivitytrendandthelong-runsizeof governmentare exogenously given,tothe inflationtrend at least. Additionally,thestochasticpart of theproductivitytrendis constrainedno~to affectinflationinthelongrun. We allowfor thefiscaltrendto affectsteady-state inflation(~G#@. The interpretationofthesignof ~~isthatit representswhethertheinflationtax is complementaryto (~~> O)or substitutablewith(~~< O)generalincometaxation. A keyissuebeforeweproceediswhethertherestrictionsembeddedin (25)-(27)are consistent withreasonabletheoreticalmodelsor not. Thereare twoconsiderations. First, doesitmakesense thatthestochasticpart of theproductivitytrenddoesnotaffectinflationin thelongrun? Second,is it possiblethata permanentchangein inflationcanhavea long-runeffecton the investmentrate--and . hencetherealinterestrate--butno long-runeffecton thegrowthrateof theeconomy? Wediscuss eachofthesequestionsin turn. Onthefirstpoint,economictheoryprovidesa clear-cutanswer:once-and-for-allpermanent shockstothesupplyof outputaffectthelong-runpricelevelbutnotitslong-runrate of change. of course,economictheoryconsiderationsalsodictatethatthedrift in output,PA,influencessteady-state inflation,butweallowfor thisin(27). Thissuggeststhatthefirst restrictionis sensible. -20-

,“ Onthesecondpoint,itwouldappearthatiftheinflationrateaffectstherealinterestxate,then itmustalsoaffectthelong-termgrowthratefromthestandardconsumptionintertemporalefficiency condition. Butthisisnottrue ingeneral. Conjecturingthatinthesteady-state thegrowthrateofthe economyisequalto PA,thegrowthrateofZ, (10), (13),and(15)canbeusedto showthat: (28) Eq. (28) reducestothefamiliar~(l+r) = (l+p~ withlog-utility,ONLY whentheCIAconstraintdoes NOT applyto investment(a~= 0). Butthoseare alsothecases(ModelsI or II) whentherealrateof interestis independentof inflation. WhenCIAappliesto investmentalso, it isfeasibleto havea steady-stateinwhichtherealrateof returndependson inflation,yetPAdoesnot, sincetheratioofthe LagrangemultipliersyL4alsodependson inflationandenterstheintertemporalefficiencycondition. Thus,our empiricalwork, thattreatsthegrowthrateoftheeconomyas stationary,admitsof allthefourmodelswediscussedearlier. It isalsoconsistentwiththeunivariatepropertiesofoutput growthas wellas cross-sectionalevidencethathasfoundonlysmallgrowthrateeffectsof inflation-suchas Barro(1991).19It alsoadmitsoftheendogenousgrowthclassofmodelswithmoney, providedtheparameterizationissuchthatwecanhavesignificanteffectsof inflationonthe investmentrate, yetthegrowthrateeffectsare negligible.20 Followingmuchof theinflationandgrowthliterature,wehavenotmodelledmonetarypolicy explicitlyhere. However,implicitly,onenaturalinterpretationofthepermanentshockto inflation (cJ ischangesinthemonetaryauthority’stargetinflationrate. In keepingwiththespiritof relating ourempiricalmodelto thetheoreticalliteratureontherealeffectsof inflation,wewill,for themost 19Thereissomeempiricalevidence,though,ofa moresignificantnegativerelationshipbetween inflationandgrowthfor high inflationcountries. For example,DeGregorio(1993)documentssucha relationshipfortheLatinAmericancountries. *“Therecertainlyareendogenousgrowthmodelswheretheinvestmentratehasaunitroot, yetthe . growthrateeffectsofthisunitrootcanbe smallwithsuitableparameterization.(See,for example, theMendozaet. al. papermentionedearlier,althoughthesourceoftheunitrootintheinvestmentrate inthatworkistax rates, ratherthaninflation). -21- ----- ——

part, refer to c. as an inflationshock,ratherthanexplicitlyas a moneysupplygrowthshock. l%eEstimated VECA4 Thevectorofour fiveobservedvariables,X, cannowbethoughtof asbeingdeterminedby thethreepermanentimovationsto thestochastictrends, c~, CXPCAa,nd twotransitorydisturbances, whichwe labelC,,T,C2,TI.n movingaverageform, thestructuralempiricalmodelnowbecomes: AX,=e(L)c, (29) where c = (c~ene. CITel~ Thetheoreticalframeworkwiththe impliedCI relationshipsgiven by (23)meansthatthematrixof long-runmultipliers,0(1)--obtainedby settingL= 1in(l(_L)--is: (30) e(l) = (31) Thus, in(30),thematrixe istheproductof a matrixconsistingof knowncoefficients(since E&-L PI -PY)%-c% and%-% CaII be obtaiIEd fromtheestimatesOfthecointegratingVeCtOrSa)nda lowertriangularmatrix. In addition,assume,thatthepermanentimovations, e~pCXPc~,are orthogonalto eachother. Undertheseproperties,itcanbe shownthattheparameters~., ~.+~r), (p~+p~, fi~+p~, ay, ctc,al are identified,andcanbe retrievedfromthereduced-formvectorerrorcorrectionmodel(VECM). The formalproofof identificationis very similarto thatinKinget al. (1991)andisgivenin AppendixB. Theintuitionofwhytheseparametersare identified’liesin therecursivenatureofthe -22-

long-runmodel. Specifically,sincethegovernmentsizetrendiscausallypriorto inflationand independentoftheproductivitytrend,thelong-termbehaviorofg willidentifythistrend. Accounting for theeffectofthistrendon inflation,thelong-termbehaviorof inflationthenidentifiestheinflation trend. Similarly,accountingfor thelong-runeffectsof inflationandgovernmentsizeonconsumption, investment,andoutput,thelong-runbehaviorof anyoneof thesethreevariablesidentifiesthe productivitytrend. The reasonthatanyofthethreevariablescanbeusedto identifitheproductivity trendisthatthelong-runresponsesofthesethreevariablestotheproductivitytrendare constrainedto . be equalfromthecointegratingvectorsimposed. Thus,undertheassumptionsthat(i)theproductivitytrendis independentofthefiscaland inflationtrendsand(ii)thefiscaltrendiscausallypriorto theinflationtrend,wecan identi~ the long-runeffectsof exogenousshocksto inflationonthelog-levelsofconsumption,investmentand output(p~+pc,fl~+~,,13~+~Yre,spectively). Moreover,for thespecificationsinwhichG/Y is nonstationary,~~is alsoidentified. However,sincewehaverejectedtheunitaryrestrictiononG/Y, (1-$)/8isnotidentified. CoefficientEstimates: Evidence on the TobinE#ect Thepointestimatesandstandarderrors ofthe~parametersarereportedintable5. Estimates fromboththefive-variableandfour-variablemodelsindicatethata Tobintypeeffectispresent:a permanentlyhigherinflationrateincreasesoutput,investment,andconsumption(~Y,PC,PI> 0). Withtheexceptionof PC,whichisborderline,theseare allstatisticallysignificant. Ourtime-series evidenceon investmentthuscomplementsthecross-sectionalresultsofBayoumiandGagnon,who findthathigherinflationcountriestendto investmore. Wealsofindthat P,> ~Y> &-,sothata rise in inflationleadsto a rise intheinvestmentoutputratioanddropintheconsumption-outpurtatio,just as inthecaseoftheestimatesof table4. Becausetheestimatedcointegrationvectorsare imposedinestimatingtheVECM,themagnitudesof theratiochangesarethe sameas intable4: apermanentonepercentagepointincreasein inflationis -23-

associatedwitha-long-rundrop intheshareof consumptionintotalGDP of about2.5 percentage pointsand risein the investmentshareofabout l.Opercentagepoint. Thiswouldagainsuggestthat theFisher effectdoesnothold inthe longrun. Finally,wefindthat~~ > 0, indicatingthatthe revenuecreationfunctionof inflationisused ina complementaryfashionto othertaxes. Thisis consistentwiththeideaof spreadinga tax increaseoverdifferenttypesof taxes, includinginflation. VarianceDecompositions: Evidence on the Importance of lqjlation Shocks Table6 displaysthefractionof theforecasterror varianceof eachvariablethatisattributable to thethreepermanentshocks:fiscal, intlation,andoutputshocks. Theeffectsof the inflationshock inthefive-variablemodelare reportedinpart Boftable6A. The inflationshockaccountsfor no morethantwentypercentof theforecasterror varianceof eitheroutputor investment,andno more thansix percentof theerror varianceof consumption,atanyhorizon. Mostofthesepointestimates are insignificantlydifferentfrom zero. Fiscalshocksaccountfor mostof thevarianceof G/Y, anda sizableamountofthe.varianceof inflationandoutput,accordingto part A. Theerror varianceof consumptionisalmostentirelyaccountedfor by thepermanentoutputshock(partC), while investmentisexplainedby a combinationof thepermanentandtransitoryshocks.Thelackof importanceoftransitoryshocksinexplainingconsumptionisconsistentwithpredictionsofthe lifecyclepermanent-incomehypothesesof consumptionbehavior. Table6Breportsthevariancedecompositionsofthe four-variablemodel. Onceagain, inflationshocksexplaina very smallpercentage-- lessthan 10percent-- of theforecasterror varianceof eitherconsumptionor investment. Thecontributionof inflationshocksto output variability-- abovethirtypercent-- ishigherthaninthefive-variablemodelbutwithlargestandard errors. Consumptionisonceagain explainednearlyentirelyby outputshocks,whileinvestmentis explainedby a combinationof thepermanentoutputshocksandthetransitoryshocks. Thevariancedecompositionresultsare instructivefor understandingthelong-runreal effects of inflation. From our cointegrationanalysisweestimatethatpermanentchangesin inflationhave -24-

fairlylargeeffectson output,investment,andconsumptioninthelongrun. However,thevariance decompositionsrevealthatinflationshocksaccountfor verylittleoftheforecasterror variancesof thesesamevariables. Thissuggeststhat,overthislongspanofdata,theexogenouspart ofthe permanentcomponentof inflationhasbeenrelativelysmall. Analysisof Sub-Periods Accordingto theresultsdiscussedabove,long-termdatafromtheU.S. do notappeartobe consistentwithmodelsin whicheithersuperneutralityholdsor inwhichtheonlymechanismthrough whichinflationinfluencesrealactivityinthelongrun isactingas a taxon consumptionand investment. However,itcouldbe arguedthattheseresultsaredrivenby specialsub-periodsofthe datasuchaswarsor theGreatDepression,whichwasaperiodofdeflationandlowinvestment. Table1andfigure1givean indicationofhowdifferenttheinflationandothervariables’processes havebeeninthepre-WWI,interwar,andpost-1949periods. To examinetherobustnessofour results,weestimatethemodelsovertwosubsamples:thepost-warperiod(1950-1995)andtheinterwarperiod(1918-1941).21 Theresultsfromthesub-samplesare containedintable7. Accordingto thefirstrowofthe table,bothsub-periodsare characterizedby a positiverelationshipbetweeninflationandthe investment-outpurtatioanda negativerelationshipbetweeninflationandtheconsumption-outpurtatio. Therelationshipof inflationwiththeinvestmentratioismuchstrongerfortheinter-warperiodthan thefullsample. Theestimateimpliesthata permanent1percentagepointdropin inflationis associatedwitha long-rundrop intheshareof investmentintotalGDPof4 percentagepoints(e.g., startingfroma 14%shareto a 10%share). Thislargeeffectnodoubtreflectsthedramatic movementsininflationandinvestmentduringtheGreatDepression. Eichengreen(1992)argues persuasivelythatthedirectionofcausationinthisinterwarrelationshiplikelygoesfrommonetary 21Theresultsfromthesub-periodsmustbe interpretedwithsomecaution,however,since cointegrationandVECMestimationtechniquesaremoreappropriatefor longerspansofdata. -25-

contraction(andhencea fallin inflation)to investmentandoutputratherthanviceversa. This is consistentwiththe importanceattachedto inflationshocksinour interwarperiodvariance decompositionresultsfromtheestimationof the~idlyidentzjledstructuralmodel(discussedshortly). In thepost-WWIIperiod, thelong-runrelationshipbetweeninflationandinvestment,although stillpositiveandsignificant,isconsiderablysmallerthanin thefullsample:theestimateimpliesthata permanent1percentagepointdrop in inflationisassociatedwitha drop intheshareof investmentin totalGDP of2/10 of a percentagepoint(e.g., startingfrom a 14%shareto a 13.8%share). Thevariancedecompositionresultsare reportedinthe finalrow ofthetable. In bothsubperiods,theinflationshockaccountsfor a largepercentageof theforecasterror variancesof output, consumption,andinvestment. In thepost-WWIIperiod, for example,the inflationshockaccountsfor over60percentofthevarianceof output(atthetwo-yearhorizon),whichisapproximately30to40 percentmorethanin thefull-sampleresultsof table6. For investment,theincreasedimportanceof inflationshocksduringthepost-WWIIperiodis ofthesameorder of magnitude. Clearly,the inflationtrendbecameincreasinglyimportantrelativeto theotherpermanenttrendsinthelatterpart of thesample,a resultwhichprobablyreflectstheincreasedpersistenceof inflationitself,as notedby Bars~ (1987)and others. Thecombinedanalysisofthecointegrationvectorsandvariancedecompositions,for thefull sampleandsub-periods,suggeststhefollowing. Overtheentire 1889-1995period,permanentshocks to inflation,whentheydooccur, havelargelong-runeffectson real variables. However,significant shocksto inflationappearnot to occurvery frequentlyduringmuchof thesample. However,the post-WWIIperiodisnoticeablydifferent. Althoughsignificant“permanent”shocksto inflationare a moreregularfeatureof thedata,thelong-runeffectsof agiven size shockare muchsmaller. For instance,thedecadeaverageinflationratefellby about5 percentagepointsfromthe 1970sto the 1980s. Despitethislargepermanentdrop inthe inflationrate, neitherinvestmentnortheinvestment rate fellby as muchas wouldbe impliedby the fullsampleestimates. Onemightconcludefromthis -26-

thatlong-runsuperneutrality,althougha goodstartingpointinexplainingrealeconomicfluctuations, isnotstrictly-speakinga correctdescriptionofthedatagenerationprocess. Recallthatthepost-WWIIperiodischaracterizedby a largervarianceof inflationshocks,as wellas smallerlong-runeffectsof inflationonrealvariablesfor agiven size shock. Thismaywellbe theconsequenceof monetarypolicyhavingmovedincreasinglyawayfrom “rules”andtoward “discretion”. Clearly,movingto amorediscretionarymonetarypolicyis likelyto makemonetary policyshocks,andtherebyinflationshocks,morevolatile. Andto theextentthatthediscretionary stabilizationpolicyis successful,itwillalsomeanthattheobserved responseofrealvariablesto a given size monetarypolicyshockwouldbe smaller. Thislatterpointhasbeenmadeby Mankiw (1986),for instance. 5. ConcludingRemarks Understandingthelong-runrealeffectsofpermanentchangesininflationisessentialto debatesinacademiccirclesconcerningthechannelsofmonetarypolicytransmission,as wellas to debatesinpolicymakingcirclesrelatedtothegoalofpricestability.Usinga newapproach,thispaper empiricallyanalyzessucheffectsfroma muchdifferentanalyticalperspectivethanexistingstudies. Theevidencefromlong-termU.S. dataindicatesthattheinvestmentrate, andhenceimplicitly therealrateof interest,is notindependentofinflationinthelongrun. Specifically,a permanent unanticipatedrise in inflationisassociatedwitha riseintheinvestment-outpurtatiointhelongrun. Thisisconsistentwiththerealinterestratefallinganda Tobin-typeeffect. Directevidenceonthe Tobin/reverse-Tobineffectconfirmsthis. Our empiricalapproachdoesnottellustheexact mechanismthatgeneratesa Tobintypeeffect. Weleaveasopenthequestionofwhethera Tobintype effectholdsdueto factorssuchas finitelifetimes,individualheterogeneity,anduncertainlifetimes highlightedintheliteraturecitedinOrphanidesandSolow’ssurveypaper, or dueto taxdistortionsof thetypehighlightedby Feldsteinandby BayoumiandGagnon,for instance,or possiblydueto -27-

downwardrigidtyof nominalwageswithindividualfirmsexperiencingstochasticshocksto the demandfor theiroutput,as emphasizedrecentlyby Akerlofefal. Our results,however,do appearto be inconsistentwithmodelsthatemphasizeeither superneutralityor only theroleof inflationas a taxon consumptionor investment,or endogenous growthmodelswithmoney,whichalsogeneratea reverse-Tobineffect. Onemustbear inmind, though,thatour variancedecompositionsfromthefullsample,suggestthat, whilea significantTobin typeeffectisfound,therole of inflationinexplainingthefluctuationsin thelevelsof real variablesis very limited,comparedto theroleplayedby productivityandfiscaltrends. Weconcludethatrealbusiness-cyclemodelsand endogenousgrowthmodelsappearto beusefidapproximationsin explainingrealeconomicfluctuations. Buttheyareperhapsnotthebestmodels,evenwhenextended to incorporatemoney,for understandingthelong-termreal effectsof inflation,atleastin theform in whichtheyare currentlypopular. The resuitsfromthepost-war(1950-1995)and inter-war(1918-1941)subsamplesconfirmthe existenceof a Tobintypeeffect,butdifferfromthefull-sampleestimatesintwoways. First, the estimatedlong-runeffectsonoutput,investment,andconsumptionare muchlarger(smaller)inthe inter-war(post-war)periodthanin thefullsample. Second,as measuredby thevariance decompositions,theinflationtrend isquiteimportantinthesub-periods. Comparingthefull-sample andpost-WWIIresultssuggeststhat, in thoseperiodswhenpermanentchangesin inflationare estimatedto havelargelong-runrealeffects(pre-WWII),suchshocksdid notoccuroften. However, when “permanent”shocksto inflationare a moreregularpart of thedata, as inthepost-WWIIperiod, suchshockshavesmallerlong-runeffects. A convincingexplanationofbothoftheseresultscould centeron themoreactiviststanceof monetarypolicyinthepost-WWIIperiod. Two fhrtheravenuesof researchare worthyofpursuit. First, itwouldbe ausefulextension to incorporatenetexportsintoboththetheoreticalandempiricalanalysisandalsoprovideevidenceon thelong-runeffectsof inflationonthisvariable. Second,it wouldbe interestingto undertakea crosscountryanalysisalongsimilarlines. -28-

REFERENCES Abel,AndrewB. (1985) “DynamicBehaviorofCapitalAccumulationina Cash-In-Advance Model,”Journal ofiktbnetary Economics, July, 16,55-71. Akerlof,George,WilliamDickens,andGeorgePerry (1996) “TheMacroeconomicsof Low Inflation,”Brookings Papers on Economic Activi@, forthcoming. Ball,Laurence,N. GregoryMankiw,andDavidRomer(1988) “TheNewKeynesianEconomicsand theOutputInflationTradeoff.”Brookings Papers on Economic Activity, 1, 1-65. Barro, RobertJ. (1991) “EconomicGrowthina Cross-Sectionof Countries,”Quarterly Journal of Economics, May, 106,407-443. Barro, RobertJ. andXavierSala-i-Martin. (1995) Economic Growth (New York:Mc-GrawHill). Bayoumi,TamimandJosephGagnon. (1996) “TaxationandInflation:A NewExplanationfor InternationalCapitalFlows,”Journal ofikfonetary Economics, forthcoming. Barsky,RobertB. (1987) “TheFisherHypothesisandtheForecastabilityandPersistenceof Inflation,”Journal ofMonetary Economics, January, 19,3-24. Brock,WilliamA. (1974) “MoneyandGrowth:TheCaseofLongRunPerfectForesight,” International Economic Review, 15, 750-777. Cooled,”ThomasF. andGaryD. Hansen. (1989) “TheInflationTaxina RealBusinessCycle Model,”American Economic Review, September,79:4, 733-748. Dickey,DavidA. andWayneA. Fuller. (1979) “DistributionoftheEstimatorsfor Autoregressive TimeSeriesWitha UnitRoot,”Journal of theAmerican Statistical Association, June,74, ‘ 427-431. DeGregorio,Jose. (1993) “Inflation,Taxation,andLong-RunGrowth,”Journal ofMonetary Economics, June, 31, 271-298. -29-

Eichengreen,Barry. (1992) Golden Fetters: TheGold Standard and the Great Depression, 1919- 1939 (New York:OxfordUniversityPress). Feldstein,MartinS. (1976) “Inflation,IncomeTaxes, andtheRateofInterest:A Theoretical Analysis,American EconomicReview, 66, 809-820. Fischer,Stanley. (1983) “InflationandGrowth,” NBERworkingpaper, Number1235. Fisher, Irving. (1930) TheTheoryoflnterest (New York:Macmillan). Friedman,Milton,andAma Schwartz. (1963) A Monetary History of the United States (Princeton: PrincetonUniversityPress). Gomme,Paul. (1993) “Moneyand GrowthRevisited:MeasuringtheCostsofInflationinan EndogenousGrowthModel,”Journal ofMonetary Economics, August,32, 51-77. Johansen,SorenandKatarinaJuselius. (1990) “MaximumLikelihoodEstimationandInferenceon CointegrationWithApplicationto theDemandfor Money,”OxfordBulletinof Economics and Statistics, 52, 169-210. King,RobertG., CharlesI. Plosser, JamesH. Stock,andMarkW. Watson. (1991)American Economic Review, September,81, 819-840. King,RobertG. andMarkW. Watson. (1994) “ThePost-WarU.S. PhillipsCurve:A Revisionist EconometricHistory,”Carnegie-Rochester ConferenceSeries onPublic Policy, December, 41, 157-219. Kwiatowski,Phillips,Schmidt,andShin.(1992) “TestingtheNullHypothesisof StationarityAgainst theAlternativeofa UnitRoot:HowSureAreWe rhat EconomicTimeSeriesHaveUnit Roots?”JournalofEconometrics, 54, 159-178. Mankiw,GregoryN. (1986) “Commenton ‘DoEquilibriumRealBusinessCycleTheoriesExplain PostwarU.S. BusinessCycles’,”A?BERMacroeconomics Annual, 1, 139-145. Mendoza,EnriqueG., MariaMilesi-Ferretti,andPatrickAsea. (1995) “DoTaxesMatterFor Long- RunGrowth?:Harberger’sSuperneutralityConjecture,”InternationalFinanceDiscussion Paper, Boardof GovernorsoftheFederalReserveSystem,Number511,June. -30-

Mishkin,FredericS. (1992) “IstheFisher Effectfor Real? A Rexaminationof theRelationship BetweenInflationandInterestRates,”Journalof MonetaryEconomics, November,30:2, 195- 215. Orphanides,AthanasiosandRobertM. Solow. (1990) “Money,InflationandGrowth,”inHandbook ofMonetaryEconomics (editedby B.M. FriedmanandF.H. Hahn),(Amsterdam:North- Holland. Reimers,H.-E. (1992) “ComparisonsofTestsforMultivariateCointegration”, Statistical Papers, 33, 335-359. Sidrauski,Miguel. (1967) “InflationandEconomicGrowth,”JournalofPolitical Economy, 75, 796- 810. Stockman,AlanC. (1981) “AnticipatedInflationandtheCapitalStockina Cash-In-Advance Economy,”JournalofMonetaryEconomics, 8, 387-393. Tobin,James. (1965) “MoneyandEconomicGrowth,”Econometric, 33, 671-684. Wang,PingandChongK. Yip. (1992) “AlternativeApproachesto MoneyandGrowth,”Journalof Money, Credit, and Banking,November,24:4, 553-562. * -31-

I I AppendixA: RecursiveRepresentationof theOptimizationProblem From Bellman,if Visthevaluefunction,themaximizationproblemdescribedinthetexthasthe . followingrecursiverepresentation: .fK1.lwl[u[c’+:l+~ (Al) V(M,J,K,,P,) = max ’Kp.)t LettheLagrangemultipliersassociatedwith(6)and(7)be k,andy,,respectively. Thenusing Bellman’sequationand imposingi@,= M,, thefirst-ordernecessaryconditionsof themaximization problemare (6)andthefollowingequations: - UC(.J=L,+acY, (A2) (A3) U,(.,) =&@N(.) fw,(.lq) =# (A4) t flV2(.,+2)=A, +aKy, (A5) (lWQ, ) (A6) - a,ci - a~[K,4- (1~)K~ =O ‘Y, P, J AppendixB:IdentificationandEstimationStrategy ThestructuralmodelinW formis (29)inthetextandreproducedbelowfor convenience: [1 s,, S,2 [e, 1o (Bl) Ax, =e(L)&,; var(e~ =S z e(1) = [e o] = ~ 0, S,2S22,’ 2 whererecall e = (&gc= &A&,7’cz~)consistsof thethreepermanentandtwotransitoryshocksand X = (g,n, lnY,lnC. lnZ,,.Sii (3x3),Szz(2x2)are thediagnol covariancematricesofthestructural -32-

permanentandtransitorydisturbancesrespectivelyandSpz= Sj, = O,implyingtheindependenceof thepermanentandtransitorydisturbances.Thematrix O(5x3)istheproductofthetwomatrices givenin(31) inthe textandfor conveniencewehavepartitionede furtherinto8,(3x3) and6Z(2X3), where0, islowertriangular. Thereduced-from?L5Ci14cabneused to obtainthefollowingreduced-formMMrepresentation: II c, (B2) AX, =C(L)e~ var(e~ =V, C(1) = C2 wherefor convenienceC(l) hasbeenpartitionedintoitsfirstthreerows, Cl (3x5),anditslastOAK, rows, Cz(2x5). Nextweexpressthestructuraldisturbancesas a linearcombinationofthereduced-form disturbances: (B3) whereP’ hasbeenpartitionedfor convenienceintoitsfirstthreerows,P, (3x5), anditslasttwo rows,PI (2x5). To showthatourmodelidentifiesthepermanentstructuraldisturbances,wehaveto demonstratethatundertheassumptionsgivenabovethatS,l, Szzarediagnolmatrices,S,z,Sz,are null matrices,and6, islowertriangular,P, is determineduniquely. ObtainingtheFirst ThreeRows ofP-’(PJ From(Bl), (B2),and(B3), e(l)E, =C(l)el = e(l)se(l)’ =C(l)vc(l)’ =W (B4) = 0,s,16; =w,,, . where W,, istheupperleft-hand(3x3)submatrixof W. It followsdirectlyfromthelastlineof (B4) thattheCholeskifactorof W,, willgivetheuniquee, suchthatS,, istheidentitymatrix. Thenfrom thefirstlineof (B4) (B3),andthepartitionsfor e(l) andC(l) givenin (Bl), (B2)respectively,itin turnsfollowsthatP, = e;]c,. -33-

Obtaining the Last Two ROWSofP_’(Pj We needtodo thisto completeour identification.This isto ensurethatthetransitory disturbancesare independentof thepermanentdisturbances,so thatthe impulseresponsesand variancedecompositionswithrespectto thepermanentdisturbancesare reallyidentifiedand not gettingmixedup withtheeffectsof thetransitorydisturbances. From (B3),itfollowsthat: s =P4VP4 3 S,2 =PIVP; (B5) s = .P2VP2’ 22 WemustchoosePzsuchthatS,j = OandSzzis invertible. Thiscanbe donebypickinganytwo linear{y independentsolutionsto P,Kr = O,wherex is a (5x1)vectorofunknownsbeingsolvedfor. Onewayto do thisisto pickthetwo independenteigenvectorsassociatedwiththenon-zero eigenvaluesofthematrixM, whereikl= I-A‘@4‘)-’A,withA s P,V. SinceJ& = &x,wheretheLis are theeigenvaluesofAl,AM = O(whichistrueby construction)impliesAx = O. Notethatthisis just one way to obtainP2andthatiswhythetransito~ disturbances are not individually identl~ed. Rightnow,S{,isthe identitymatrixand0 is notintheexactformgivenby (30), in thesense of having1‘sontheleadingdiagnol. To put0 intherequiredform, wecan renorrnalizethesizeof the shockssuchthatthelong-runresponseof a variableto itsownshockisnormalizedto be unity. Thiswillput9 intheformof (30)andmakeS,, diagnolonly, ratherthanthe identitymatrix. DATAAPPENDIX (1)Y = realgrossdomesticproductin billionsof 1987dollars. Thesourcesare Kendrick(1961) tableA-IIafrom 1889-1928,andthe NationalIncomeandProductAccounts(NIPA)from 1929-1995 . (U.S. Departmentof Commerce(1993)andvariousissuesofthesurvey of C~ent BWIIl@. (2) c = realcons~ption expendi~res inbillionsof 1987dollars. Sourcesarethesameas for Y. -34-

(3) x= realgrossprivatedomesticinvestmentinbillionsof 1987dollars. Sourcesarethesameasfor Y. (4) G = realfederalgovernmentexpendituresongoodsandservicesinbillionsof 1987dollars. SourcesarethesameasforY. (5)P= GDPdeflator,takenastheratioofnominal GDPtoreal GDP(1987 = 1.00). NominalGDP dataare takenfromKendrick(1961)tableA-Hbfrom 1889-1928,andNIPA from 1929-1995. (6)POl?=total residentpopulationoftheUnitedStates,takenfromU.S. Bureauof theCensus(1976 and 1992)andupdates. REFERENCES Hendrick,JohnW. (1961)ProductivityTrendsintheUnitedStates. GeneralSeries,no.71. Princeton,NJ: PrincetonUniversityPress(for NBER). UnitedStatesDepartmentofCommerce,Bureauof EconomicAnalysis(1993)JfIaitonalIncomeand ProductAccounts.VolumeI. 1929-58andVolumeII. 1959-8&(Washington,DC). --------------------------------------------------------------S--u-rveyoccurrent Business(Washington,DC). UnitedStatesBureauoftheCensus(1976)StatisticalHistorvoftheUnitedStates(Washington,DC). ---------------------------------(-1992)StatisticalAbstractoftheU nitedStates(Washington,DC). -35-

Table1:SummaryStatistics- Means.andStandardDeviations Full Sample Pre-WWI Inter-War Post-war Post-OPEC (1889-1995) (1889-1914) (1918-41) (1950-95) (1973-95) GN 19.4 11.6 18.3 21.7 19.0 (8.56) (0.92) (5.66) (3.19) (0.69) z 3.05 0.81 0.36 4.30 5.56 (5.54) (2.72) (7.03) (2.42) (2.48) CN 63.8 64.1 67.8 63.3 66.1 (5.40) (2.10) (4.52) (3.27) (1.52) IN 16.6 22.9 13.7 15.8 16.1 (5.41) (3.13) (4.98) (1.25) (1.32) Ay 3.13 3.49 2.92 3.08 2.39 (5.92) (5.82) (7.29) (2.40) (2.15) Notes: GN,C/Y, and IN denote, respectively, the ratios ofreal government purchases, real consumption, and real investmentto real GDP; xdenotes the annual percentage change inthe GDP deflato~and Ay denotes real GDP growth. Reported above isthe mean and standard deviation (in parenthesis) ofeach series, in percent. Table2: Unit RootsTests Variabie ADF ADF KPSS KPSS ADF-level (level) (lst cliff.) (level) (1901-92) [wardynam] c -2.14 -4.24* 0.24** 2.12** -2.05 i -2.24 -4.80** 0.28** 0.47** -2.24 Y -2.95 -4.57** 0.08 2.02** -2.82 n -3.51* -6.00** 0.05 0.25** -2.62 GN -2.28 -5.98** 0.65* 0.65** -0.49 Notes: c, i, and y denote, respectively, the logs of real per capita consumption, investment, and GDP; n denotes the annual percentage change in the CPI, and GN is the ratio of government purchases to GDP. ADFdenotes the Augmented Dickey-Fuller test statistic fortheunit root null hypothesis. KPSS denotes the Kwiatkowski, Phillips, Schmidt, and Shin test of the null of stationarity. ADF [war dynam] refers to the ADF tests that allow the short-run dynamics for the world war years to be different. The sample period is 1889-1995except in the final column, which displays results for the 1901-95 sample period. A #, *, and ** indicates rejectionof thenullat 10%,5Y0,ad IVO, respectively. A timetrend is includedinalltests forallvariablesexcept. A laglengjh of 5 is used in all tests. -36-

Table 3: Tests of Cointegrating rank Resultsfor 5 Variable Model Trace Trace 95Y0 statistic statistic critical (df) value ~ 44.84** I 38.31* I 33.5 106.1** 90.69** ~ 68.5 61.3** 52.38* 47.2 I p<2 I 19.85 I 16.96 I 21.0 33.23* 28.39 I 29.7 p<3 I 13.26 I 11.33 I 14.1 13.38 11.43 I 15.4 p<4 I 0.12 I 0.10 I 3.8 0.12 0.11 I 3.8 System: G/Y,n. y, c. i; Sample = 1893-1995; Lag length = 3. Constant included in the deterministic component. Resultsfor 4 Variable Model I-lo:CI Max Max 95% Trace Trace 95% rank=p eigenvalue eigenvalue critical statistic statistic critical statistic statistic value (df) value (dfl I p=() [ 42.3** I 374** I 27.1 82.6** 73.0** 47.2 I I p<l 27.4** -74.2** I 21.0 40.3** I 35.6** 29.7 I ps2 12.7 I 11.2 1 14.1 12.8 I 11.4 15.4 I I I p<3 0.22 0.20 3.8 0.22 I 0.20 3.8 System: n, y, c, i; Sample = 1893-1995; Lag length = 3. Constant,GW and3 lagsof G/Yare includedinthedeterministiccomponent. NOTES: (1) * (**) indicates significance at the 5% (1’XO).(2) The maximum eigenvalue static (df) and trace statistic (df) apply a simplesmall-samplecorrectionto Johansen’sstatistics(replacingT by T-rim,where T = number observations, n=number of variables, m = number of lags) as recommended by Reimers (1992). -37-

Table4: Estimates of Structural Cointcgrating Vectors Coefficient Variable Five-Variable System Four-Variable System’ Vector 1 Vector 2 Vector 1 Vector 2 c 1.Oor O.oor 1.00’ 0.00’ i 0.00’ 1.00’ 0.00’ 1.Oor Y -1.00’ -1.00’ -1.00’ -1.00’ n 4.02 -5.58 11.0 -6.52 (0.72) (1.17) (1.95) (1.26) GN -0.63 3.84 --- (0.39) (0.63) ‘-- Lag length 3 3 ~2(2)[p-value]* 16.5 [.00] 17.7 [.00] Coefficient on y -1.075 -0.99 -1.08 -0.97 (unrestricted)3 (0.024) (0.09) (0.03) (0.10) Notes: Standard errors are in parentheses. A “ r“ indicates that the coefficient was constrained to the value shown. (1)In the four-variablesystem,GY istreatedas stationaryandexogenous;its contemporaneousvalueandthree laggedvaluesare includedas deterministiccomponentsof the VAR equations. (2) This is the Chi-squared statistic associated with the likelihood ratio test of the null hypothesis that the restrictions imposed on the output variable in the two vectors arejointly satisfied. “P-value” refers to the marginal significance level of the X2statistic. (3) The coefficient on y from a separate estimate in which the unit coefficient restriction is relaxed. Table 5: Estimates of Structural Parameters Model Coefficient 5-Variable System 7.47 3.45 13.1 0.48 (2.14) (1.77) (2.44) (0.18) 4-Variable System 20.7 9.74 27.3 --- (5.84) (5.09) (5.98) Notes: Standard errors, shown in parenthesis, were computed by Monte Carlo simulation using 1,000 replications. -38-

Table6A: VarianceDecompositions:Five-VariableModel A. Fractionoftheforecasterrorvarianceattributedto thefiscalshock Horizon: GN n Y e’ i 42.9 49.7 0.17 0.18 (14.9) (16.3) (7.35) (8.43) 37.9 53.2 1.86 1.45 (13.5) (14.6) (6.96) (8.05) 5’ 62.3 32.8 51.1 1.82 1.94 (15.4) (11.4) (13.3) (6.52) (7.23) 20 60.8 32.4 51.0 1.92 2.87 (14.9) (11,1) (13,2) (6.47) (6.97) B.Fractionoftheforecasterrorvarianceattributedto the inflationshock ~ Horizon: G/Y” n c i 1 ~,57 2.68 17.5 5.13 1.94 (4.33’) (6.64) (12.0) (8.31) (7.01) 2 9.37 8.89 18.5 5.35 3.31 (6.30) (6.56) (10.6) (7.58) (6.48) 5 18.3 14.8 17.8 5.63 14.1 (6.95) (7.01) (9.54) (6.64) (6.27) 20 19.0 15.3 1759 5.77 15.7 (7.03) (7.04) (9.43) (6.66) (6.68) C. Fraction of the forecast error variance attributed to the output shock y Horizon: GN n c i 1 1.93 4.06 28.8 90.9 25.1 (6.54) (6.83) (15.8) (14.1) (13.0) 2 3.71 7.27 24.2 83.9 28.6 (7.08) (7.79) (12.4) (12.7) (11.8) 5 3.61 6.81 23.9 81.4 24.7 (6.26) (6.87) (11.2) (11.7) (9.95) 20 3.90 6.74 23.9 81.0 24.3 (6.16) (6.75) (11.1) (11.6) (9.46) Notes: Standarderrors,showninparenthesis,werecomputedbyMonteCarlosimulationusing1,000 replications. -39-

Table6B: Variance Decompositions:Four-Variable Model A. Fractionofthe forecasterrorvarianceattributedto the inflationshock Horizon: n Y c i 1 2.80 34.1 5.23 1.89 (7.70) (18.6) (8.98) (7.63) 2 8.04 34.7 7.80 1.86 (7.22) (18.1) (8.44) (7.12) 5 10.8 38.8 7.92 4.78 (7.91) (14.5) (7.44) (6.74) ~’) 11.0 39.6 8.16 6.31 (8.01) (14.2) (7.44) (6.65) B. Fraction of the forecast error variance attributed to the output shock Horizon: n Y c i 1 0.11 56.6 94.4 37.1 (3.89) (19.1) (12.0) (15.8) 2 2.89 55.5 86.2 39.0 (5.24) (18.0) (11.0) (14.7) 5 3.24 50.0 83.5 36.6 (5.13) (14.6) (10.2) (13.3) 49.0 83.2 36.5 (14.4) (10.3) (13.0) Notes: Standard errors, shown in parenthesis, were computed by Monte Carlo simulation using 1,000 replications. -40-

Table7: Analysisof Sub-periods Mock] Estimates 5-Var..Post-war 5-Var.,Inter-war 4-Var.,Post-war 4-Var.,Inter-war (1950-95) (1918-41) (1950-95) (1918-41) Cointegratingvectors: ~ G/Y z GIY z E (1) ILOr(c-y),n, G/Y] 0.71, 1.87 6.38,-3.27 1.01,--- 2.24,--- (~) [l.Or(i-y).n, G/Y] -1.00,0.67 -29.2,22.6 -0.95,--- -11.3---- Structuralparameters: 2.69, 1.98, 11.7,5.35, 1.51,0.50, 4.90,2.66, (PN+PY, P/v+Pc, BN+P~IP(;) 3.69,-1.49 40.9,0.78 2.46,--- 16.2,--- ForecastErrorVDCS’: (1)Pet.due to fiscalshock 65.6,20.6,6.55, 64.4,38.1,17.5, --- --- [G/Y,n, y. c, i;2-year] 22.8, 16.7 5.94,35.3 (2)Pet. due to inflation shock 15.6,3.62, 62.4, 15.9,6.49, 50.2, ---, 10.7,64.1, ---, 45.9, 89.9, [G/Y, n, y, c, i; 2-year] 43.8, 31.2 50.7, 51.8 24.8, 48.4 58.0, 84.9 (3) Pet. due to output shock 13.6, 70.9,28.6, 7.80, 9.12, 27.9, ---, 24.4, 25.0, ---, 22.9, 6.28, [G/Y, n, y, c, i; z-year] 32.2, 35.8 41.7, 7.76 65.2, 23.7 39.0, 6.18 Notes: A “‘“ indicates that the coefficient was constrained to the value shown. (1) The fraction of the forecast error variance of each variable attributed to the fiscal, inflation, and output shocks, at the 2-year horizon. -41- .——

Figure1. Data in Levels Output(detrended) Government Size 0.4 0.6 A 0.3 0.5 0.2 0.1 0.4 a -0.0 v -0.1 0.3 -0.2 -0.3 0.2 1 -0.4 0.1 I 1111 Iwo leo4 1916 1932 1946 1960 1974 1968 1890 1904 1918 1932 1946 Ieao 1974 1988 Consumption(detrended) Inflation 0.20 I 0.25 I II 0.20 0.10 0.15 0.05 0.10 -0.00 0.05 -0.05 I 0.00 /“ I 1 -0.10 1 -0.05 -0.15 I -0.20 -0.25 I I 1890 1904 1918 1932 1946 1960 1974 1988 1691 leo5 1919 1933 1947 1961 1975 1989 Investment (detrended) Short-Term Interest Rate 0.60 , 1 I 15.0 0.30 12.5 0.00 10.0 -0.30 -0.60 7.5 -0.eo 5.0 -1.20 2.5 -1.50 -1.8I0 llm~r ) 0.0 1890 1904 1918 1932 1946 1960 1974 1988 1668 1885 leo2 1919 1936 1953 1970 1987

Figure 2. AutocorrekNions- Levels @vemment Size (Mput (detrendec!) .—-—— —..— IOQ I 100 ‘— “-”–~ I 075 ~4 : ,75 T I I $ 050 1 052 L I I ~ \ I J :5 - ~25 I I ( “’=4> ~ —–—–4 OOG j —-— — --+-” I , ! I ‘~ 1 -025 -0.25 ; j ~ -050 i -0.50 4 \ II -075 4 -c75 4 I I I -100 ‘ IiIf1I11,r~ -1,00 $\ [ 1I ,, I 11I ! I ! I 1i I ! , ! 1! I 11111 111[ ! o 5 10 15 20 25 30 0 5 IO 15 20 25 30 35 40 Inflation Consumption(detrended) — 100 100 I 0.75 0.75 ~ 050 0.50 +, 1 0.25 i 0.25 ; O.(MI 000 -025 J -025 1, I -0.50 -050 j I I -0.75 1 -075 -1 -1.0I 0 I I I I 11I r I t 1I 1I I 11I I I 111111I I I t I I I I I 1I t t 1I -1.00 1 0 III1I 5 11I1I 1 r 0 I1If 1 I 5 IIII 2 I 0 r1rI 2 1 5 11f1 3 I 0 II11 3 1 5 11I1 4 1 0 o 5 10 15 20 25 30 35 40 Short-Term InterestRate Investment(detrended) 1.00 la) 1 I 0.75 J 0.75 4 0.50 ] 050 - 1 0.25 025 { { 0.00 0.00 -0,25 - -0.25 - -0.501 -0.50 I i -0.75 + I -0.75 4 , I ! I -1.00 II II11I1iI1II Br,I1II 1I#1F1III11!111#1111v11 J -lJM o 11u11 5 11v18 1 I 0 I 8v: 1 1 5 I r I I 2 I 0 1t #r 2 I 5 1K s t o #I I 1 3 1 5 t I 1! 4 I 0 0 5 10 15 20 25 30 = 40 43

International Finance Discussion Papers IFDP Number Titles Author@ 1996 566 Long-Term Evidence on the Tobin and Fisher Shaghil Ahmed Effects: A New Approach John H. Rogers 565 Some Evidence on the Efllcacy of the UK Inflation Chan Huh Targeting Regime: An Out-of-Sample Forecast Approach 564 The Use of the Parallel Market Rate as a Guide NitaGhei to Setting the Official Exchange Rate StevenB.Kamin 563 Country Fund Discounts and the Mexican Crisis of Jefliey A. Frankel December 1994: Did Local Residents Turn SergioL. Schmukler Pessimistic Before International Investors? 562 Eastern European Export Petiormance during Nathan Sheets the Transition Simona Boata 561 Inflation-Adjusted Potential Output Jane T. Haltmaier 560 The Management of Financial Risks at German Allen B. Frankel Nonfinancial Firms: The Case of Metallgesellschail David E. Palmer 559 Broad Money Demand and Financial Liberalization Neil R. Ericsson in Greece Sunil Sharma 558 Stockholding Behavior of U.S. Households: Evidence Carol C. Bertaut from the 1983-89 Survey of Consumer Finances 557 Firm Size and the Impact of Profit-Margin Uncertainty VivekGhosal on Investment: Do Financing Constraints Play a Role? PrakashLoungani 556 Regulation and the Cost of Capital in Japan: A Case JohnAmmer Study MichaelS.Gibson 555 The Sovereignty Option: The Quebec Referendum and MichaelP. Leahy Market Views on the Canadian Dollar CharlesP.Thomas 554 Real Exchange Rates and Inflation in Exchange-Rate StevenB.Kamin” Based Stabilizations: An Empirical Examination Please address requests for copies to International Finance Discussion Papers, Division of International Finance, Stop 24, Board of Governors of the Federal Reserve System, Washington, DC 20551. 44

International Finance Discussion J?apers IFDP Number Titles 1996 553 Macroeconomic State Variables as Determinants JohnAmmer of Asset Price Covariances 552 The Tequila Effect: Theory and Evidence from MartinUribe Argentina 551 The Accumulation of Human Capital: Alternative MuratF. Iyigun Methods and Why They Matter AnnL. Owen 550 Alternatives in Human Capital Accumulation: MuratF. Iyigun Implications for Economic Growth AnnL. Owen 549 More Evidence on the Link between Bank MichaelS.Gibson Health and Investment in Japan 548 The Syndrome of Exchange-Rate-Based Enrique G. Mendoza Stabilization and the Uncertain Duration of Martin Uribe Currency Pegs 547 German Unification: What Have We Learned Joseph E. Gagnon from Multi-Country Models? Paul R. Masson Warwick J. McKibbin 546 Returns to Scale in U.S. Production: Estimates Susanto Basu and Implications John G. Femald 545 Mexico’s Balance-of-Payments Crisis: A Chronicle Guillermo A. Calvo of Death Foretold Enrique G. Mendoza 544 The Twin Crises: The Causesof Banking and Graciela L. Kaminsky Balance-of-Payments Problems Carmen M. Reinhart 543 High Real Interest Rates in the Aftermath of Graciela L. Kaminsky Disinflation: Is it a Lack of Credibility? Leonardo Leiderman 542 Precautionary Portfolio Behavior from a Life-Cycle Carol C. Bertaut Perspective Michael Haliassos 541 Using Options Prices to Infer PDF’s for Asset Prices: William R. Melick An Application to Oil Prices During the Gulf Crisis Charles P. Thomas 540 Monetary Policy inthe End-Game to Exchange-Rate Steven B. Kamin Based Stabilizations: The Case of Mexico John H. Rogers 45

International Finance Discussion Papers IFDP Number Titles Author(s) 1996 539 Comparing the Welfare Costs and the Initial Dynamics Martin Uribe of Alternative Temporary Stabilization Policies 538 Long Memory in Inflation Expectations: Evidence Joseph E. Gagnon from International Financial Markets 537 UsingMeasuresof Expectationsto Identi&the AlIanD. Brunner Effectsof a MonetaryPolicyShock 536 Regime Switching in the Dynamic Relationship Chan Huh between the Federal Funds Rate and Innovations in Nonborrowed Reserves 535 The Risksand Implications of External Financial Edwin M. Truman Shocks: Lessons from Mexico 534 Currency Crashes in Emerging Markets: An Jeffrey A. Frankel Empirical Treatment Andrew K. Rose 533 Regional Patterns in the Law of One Price: The Charles Engel Roles of Geography Vs. Currencies John H. Rogers 46