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

Using a new approach, we reexaminethe empirical evidenceon the long-terminteractions between inflationand real variables. We find, using over 100years of U.S. data, that in the long rzm the effect of infkationon investmentand outputis positive(a “Tobintype effect”)and the investment rate, and hence the real interest rate. are not independentof inflation. However, over the full sample at least, the variabilityof the innovationsto the stochasticinflationtrend is small relativeto the variabilityof the innovationsto t!leproducnvityand fiscal trends. We concludethat models generatinga re}wse-Tobhl effect. includingstandardreal-business-cycleand endogenousgrowth modelsthat incorporatemoney. may not be [he best modelsfor understandingthe long-termreal effectsof’inflation. 1. Long-Term Evidenceon the Tobin and Fisher Effects: A New Approach ShaghilAhmedand John H. Rogers* Introduction Considera situationin which, with the economyin a low inflationsteady state, the rate of inflationfallspermanently, say by 2 percentagepoints. What wouldbe the Zong-runeffectson real economicvariablessuch as output, consumption,the real interest rate, investmentand the capital stock? Economictheory providesno clear-cutprediction. On the one hand there is the famous superneutralityresult due to Sidruaski~1967). However, Sidruaski’sresult emerges from a very specifictheoreticalset-up, requiring, in particular. the strong assumptionthat consumptionand leisure are separablein utility. Indeed, in several theoreticalmodelsthe superneutralityresult breaks down, as inflationcan have either positiveor negativeeffectson real variablessuch as outputand investment,dependingon the exact assumptionsconcerningpreferencesand how money is introduced into the economy. Additionally,in these models the real interestrate may or may not be independent of the rate of inflationin the long run. (see Orphanidesand Solow [1990]for a survey.) Therefore, whether the long-runeffect of inflationon the capitalstock and outputis positive or negative,and whetherthe real interest rate is independentof inflationor not in the long run are empiricalissues. Recently.there has been considerableinterestin the existenceof, and nature of, the long-runreal effectsof inflation(e.g. King and Watson [1994]and Akerlof, Dickens, and Perry [1996]).Understandingthese effects is crucial for evaluatingmonetarypolicy, especiallyin light of the debate aboutmovingfrom the current low inflationrate to price stability.l *Theauthors are staff economistsin the Divisionof InternationalFinance, Board of Governorsof the Federal Reserve System. For their helpfulcomments,we would like to thank, without implicating,Rick Bond, Allan Brunner, David Bowman,Joe Gagnon,Eric Leeper, Jaime Marquez, EnriqueMendoza,Jim Nason, Eric Rasmusen,Chris Wailer and workshopparticipantsat the Federal ReserveBoard, IndianaUniversity,and Penn State University. This paper representsthe views of the authorsand shouldnot be interpretedas reflectingthe views of the Board of Governorsof the Federal Reserve Systemor other membersof its staff. IIt may be argued that super non-neutralityis irrelevantin practicebecausechanges in inflation are not observed to be permanent. But this does not appear to be very persuasive. For example, Mishkin(1992)makes the case that it is likelythat inflationhas a unit root. Studiessuch as KingWatsonare predicatedon the existenceof permanentshocks to inflation. With these considerationsin mind, wereexamine theempirical evidenceonthe long-term interactionsbetween inflationand the real economy. with the goal of sorting out which of the many theoreticalchannelsof the real effects of inflationary empiricallymore relevant. We ask whether long-termU.S. data are consistentwith a “Tobintype effect” or a “reverse-Tobineffect” occurring in response to a once-and-forall permanentchange in inflation.We also examinethe long-runvalidityof the “Fisher effect”. To be’precise, by a “Tobintype effect” we mean that an exogenousincrease in inflationleads to an upwardjump in the balanced-growthpath of the capital stock and therefore investment,whereas the “reverse-Tobine ffect” is taken to indicatea downwardjump. The “Fisher effect” (Fisher[1930])holds when the inflationrate has a one-to-onepositiveeffect on the nominal interest rate and, consequently,does not affect the real interest rate.~ Our empiricalfindingsare organizedin three parts. First. the univariatepropertiesof the data are described and cointegratingvectors are estimated. Hypothesistesting on these cointegrating vectors reveals whether the data are consistentwith the Fisher effect holding in the long run or not. Our test relies on the direct correspondencebetweenthe capital-output--andhence the investmentoutput--ratioand the real rate of interest in interest rate is independentof inflation,the over a long horizon. This is testableusing of our empiricalapproach is examiningthe modelling inflationary expectations.3 the long run. This correspondenceimpliesthat, if the real latter should have equal effects on investmentand output cointegrationanalysis. Thus, one importantnovel aspect long-run validity of the Fisher ejiect, without explicitly ‘Sometimesthe terms “Fisher relation”and “Fishereffect” are used interchangeablyand used to denote the relationshipthat the nominalrate is the sum of the ex un~ereal rate and expectedinflation. We prefer to call this identitythe “Fisher relation”, and throughoutthis paper take the “Fishereffect” to mean, as seems to be more prevalent in the literature, that the real rate is independent of the rate of in~ation. As will become clear, the absenceof a Tobin or reverse-Tobineffect and the Fisher effect holdingare not necessarilythe same thing when leisure is endogenous. 30ur methoddoes not, of course, shed light on the validity of the Fisher effect at short-to-medium horizons. The results of tests that attemptto do this are sensitiveto the modellingof inflationary expectations. -2Second,under certain restrictions,we are able to identifyand estimateadditionalstructural parameters,which allowus to retrieve the effectsof changes in the exogenouscomponentof inflation on the levelsof consumption,investmentand output (as opposedto the effectson the consumptionoutputand investment-output ratios, whichare obtainedfrom the cointegratingvectors). The identificationschemeis similar to King, Plosser, Stockand Watson (1991). The effect on investment allowsus to see whether a Tobin or reverse-Tobineffect holds. Our estimatesindicatethe presence of a Tobin type effect and indicatethat the Fisher effect does not hold in U.S. data from 1889-1995. However, the variancedecompositionsalso show that the inflationtrend is not particularly important in explainingreal economicfluctuations. Third, and finally, we examinethe robustnessof our findingsover different sub-periodsof the data, thus allowingfor the possibilitythat there may have been structuralbreaks over this long period in the interactionsbetweeninflation The remainderof our pape~ and real variables. is organizedas follows: In section2, we set up a general frameworkthat nests the differenttypes of effectsof inflationon the real economythat are found in the theoreticalliterature. In this framework, the long-runpaths of the variablesare driven by three stochastictrends: a productivity(or output)trend, a fiscal trend, and an inflationtrend. Section3 links the theoreticalmodel to our empiricalestimation, presentsour empiricalresults. Section4 concludes. discussesthe identifyingassumptionsand 2. Theoretical Framework There is nothingfundamentallynew in the theoreticalmodel we use below. Our objectiveis to developa unifiedframeworkthat is generalenoughto incorporatemany of the relevanttheoretical results on the real effectsof inflationas specialcases. We begin with a brief descriptivereview of the theoreticalliterature, and then proceedto our general framework.4 4Althoughmodelswith stickyprices and/or imperfectinformation(e.g., Ball, Mankiw, and Romer -3Review of the Literature Tobin (1965) first establishedthe portfolio mechanismthat generates a positiveeffect of inflationon the-steady-statecapital stock. The intuitionis that a higher inflationrate inducessavers to substitutefrom holdingmoney to holdingphysicalcapital. This mechanismhas been dubbed the “Tobineffect”. Because the marginal product of capital is lower, the real interest rate falls. The Tobin effect, as originallyformulated,was widely criticized on the grounds that it assumes an exogenoussavings rates This criticismled to a literature that has shown that a “Tobin type effect’’--bywhich we mean only a positiverelationshipbetween inflationand the capital stock-can arise even in optimizingmodels with certain features. For example, it can arise in two-period OLG models, in infinitehorizon models with individualheterogeneityand family disconnectednessdue to uncertain lifetimes, and in models with consumptionand money entering utility in a nonseparable way under particular assumptionsabout how the marginalutility of consumptionis affectedby money.4 A positiverelationshipbetween inflationand investmentcan also arise if there are distortions in the tax system. Specifically,Bayoumiand Gagnon(1996) show that if it is nominalcapital income, rather than real capital income, that is taxed, as in Feldstein(1976), higher inflationcountries will tend to invest more than lower inflationcountries, which is consistentwith the data. Thus, we do not need to rely on the original, and perhaps implausible,mechanismproposed in the early papers that introducedthe Tobin effect, to get a positiveeffect of inflationon the capital stock and output. In contrast to models generatinga “Tobintype effect”, there are a lot of models that generate the reverse-Tobineffect. The simplestone of these is a Sidrauskitype model, but with endogenous [1988])generate highlypersistent effects of inflation,these effects do notZastforever and, strictly speaking, long-runsuperneutralityapplies. Hence the remainder of the discussionfocuses on flexibleprice models. ‘Moreover, the mechanismin Tobin’s original formulationcannotpossibly lead to a large effect of inflationon the capital stock (in percentageterms at least), given plausiblevalues of the interest elasticityof money demand and the ratio of non-interest-bearingmoney to the capital stock. We thank Joe Gagnon for pointing this out to us. bsee the Orphanidesand SOIOWpaper, and the literaturecited therein, for details. See also Wang . and Yip [1992]for the role of nonseparabilityin utility. -4leisure that is not separablefrom consumption,and with money introducedthrough a cash-in-advance (CIA) constrainton consumption(e.g. Cooley and Hansen[1989]). In this set-up, a higher inflation rate taxes consumptionmore, leadingpeople to switch into nonmarketactivity(leisure). This shifts in the marginalproductof capital schedule,so that the steady-statecapitalstock falls. still applies, though, since the capital-laborratio is constantin the steady-state.’ To simultaneouslygeneratea reverse-Tobineffect and at the same time the The Fisher effect Fisher effect not holding,one can considera CIA modelof the Stockman(1981)type with the CIA constraintapplying to both consumptionand investment. In this case, inflationrepresentsan additionalcost to investment and, therefore, a higher inflationrate leads to less investmentand an increase in the real interest rate. Abel (1985)derives the above results and compares(abstractingfrom the labor/leisurechoice)the dynamicaccumulationof capital in modelswhere the CIA constraintappliesonly to conusmptionand models models in which which it appliesto both consumptionand investment. Finally, there is the more moderngenre ofendogenous growthmodels with money. These also generate long-runreal effectsof inflationand the crucial factor is the dependenceof the .. leisure-laborchoiceon inflation. These endogenousgrowthmodelsgeneratea reverse-Tobineffect of thetype describedabove. but they also displaysome importantadditionalfeatures. Typically,in these modelsa once-and-forall rise in inflationhas a negativeeffect on the steady-state growth rate of the economyas well. (For example,see Gomme[1993]and De Gregorio [1993]). However, if output growth is stationary,shocks to the randomwalk componentof inflationcould not empiricallyhave any significantpermanenteffect on growth. This raises the questionof whether it impossiblein optimizingmodelsto have inflationaffectingthe real interest rate but not the growth rate of the economyin the long run. We will return to this issue later. ‘There are also models in which inflationhas an ambiguous effect on the steady-statecapital stock. Two examplesare Fischer (1983), inwhich money enters the productionfunction,and Brock (1974), in whichmoney enters utilityand leisure is endogenous. -5A General Theoretical Framework Preferences and Production The representativeagent’sutility functionat time t is: