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Money Demand and Seigniorage-Maximizing Inflation Author(S): William R Money Demand and Seigniorage-Maximizing Inflation Author(s): William R. Easterly, Paolo Mauro, Klaus Schmidt-Hebbel Source: Journal of Money, Credit and Banking, Vol. 27, No. 2 (May, 1995), pp. 583-603 Published by: Blackwell Publishing Stable URL: http://www.jstor.org/stable/2077885 Accessed: 18/08/2010 14:50 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=black. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Blackwell Publishing and Ohio State University Press are collaborating with JSTOR to digitize, preserve and extend access to Journal of Money, Credit and Banking. http://www.jstor.org WILLIAM R. EASTERLY PAOLO MAURO KLAUS SCHMIDT-HEBBEL Money Demand and Seigniorage-Maximizing Inflation THEREIS WIDESPREADCONSENSUS among economists that high inflationis often caused by the government'sneed to raise seignioragein order to finance high budget deficits (Sargent 1982; Dornbusch and Fischer 1986; Van Wijnbergen1989; Buiter 1990; and Easterly and Schmidt-Hebbel1994).1 Depend- ing on the shape of the money demand function, steady-stateseigniorage may fol- low a Laffercurve, where seigniorage firstrises and then falls with higher inflation. If this is the case, then there exists a rate of inflation that maximizes steady-state seigniorage, 1TmaX. Knowledge of 1TmaX may be of interestboth in orderto discrimi- nate between existing theories of inflationand for policy purposes. The literaturehas put forwardvarious hypotheses to explain high inflation. First, the economy may be experiencinghigh inflation,but still be on the left-handside of the Laffer curve. In this case, inflationmay be seen as a result of the government's need to raise seigniorage. Second, the economy may be on the "wrong"side of the Laffer curve. If inflation is above 1Tmczx and is fairly stable, then this may be inter- The authorsare indebtedto RobertBarro, Alex Cukierman,Jose De Gregorio, Fernandode Holanda Barbosa, IbrahimElbadawi, GrahamElliott, Alan Gelb, Miguel Kiguel, GregoryMankiw, Luis Serven, Raimundo Soto, Luis Suarez, SalvadorValdes-Prieto, Steve Webb, John Welch, two anonymousrefer- ees, and seminarparticipants at HarvardUniversity, the XIth LatinAmerican Meetings of the Economet- ric Society (Mexico) and the WorldBank for detailedcomments and discussions. Many thanksgo also to Jorge Canales, Mauricio Carrizosa,Janvier Kporou-Litze, Daniel Oks, Jim Stephens, and Luis Suarez for providing some of the data for this paper. 1. There is an unfortunatelack of standardlanguage in the literaturethat requiresus to define our terms precisely: by seigniorage, we mean the total revenue from money creation, which includes two components: (1) the "inflationtax" which is the inflation rate times real money balances, and (2) the growth in real money balances. This terminologyis the same as that followed by, for example, Blanchard and Fischer (1990). Some authorsuse "seigniorage"to refer to only the second component. WILLIAM R. EASTERLY and KLAUS SCHMIDT-HEBBEL are in thePolicy Research Depart- mentat the WorldBank. PAOLO MAURO is an economistat theInternational Monetary Fund. Journalof Money,Credit, and Banking, Vol. 27, No. 2 (May 1995) Copyright 1995 by The Ohio State University Press 584 : MONEY, CREDIT,AND BANKING preted as evidence in favor of the existence of a "high-inflationequilibrium." The latter may be a consequence of the absence of a nominal anchor, as in Bruno and Fischer (1990), or because of Barro-Gordon(1983) effects due to the inabilityof the monetaryauthorities to undertakecredible commitments,as in Kiguel and Liviatan (1991), or because of the authorities'high discount rate that biases policy against stabilizationswith short-termcosts and long-termbenefits. If inflationis above SmaX and is accelerating, this may be seen as the consequence of the government'sneed to raise seigniorage s' in excess of that which it can obtain by setting inflation at Smax S(XmaX) 51 in excess °f S(XmaX) can only be collected by bringingabout ever- acceleratinginflation, as emphasizedby Kiguel (1989).2 In fact, 1Thigher than SmaX has been suggested by Rodriguez(1994) as a definitionof a hyperinflation. Estimatesof the seigniorage-maximizinginflation rate may help to decide among such competing theories. Conventionalestimates of the seigniorage-maximizingin- flation rate generally make use of the Cagan (1956) function, where the log of real money is a linear function of inflation. The Cagan function is appealingbecause of its simplicity and its attractivealgebraic property:SmaX is given by one over the coefficient on inflation. However, this simplicity is achieved at the expense of a re- strictivefunctional form, which assumes a constantsemielasticity of money demand with respect to inflation. The estimates of SmaX using the Cagan form also usually define the inflationrate affecting money demandas the percentchange in prices (or sometimes the log change in prices), when theory implies that the correct oppor- tunity cost of holding money per period is the inflationrate divided by one plus the inflationrate. Our aim is to test the sensitivity of estimates°f SmaX to the assumption of constant semielasticity in the Cagan form and to the definitionof the opportunity cost of money. Section 1 develops a model of money demand, inflation, and seigniorage based on an optimizingconsumer-investor-portfolio allocator, who faces a cash-in-advance constraint,forcing this agent to hold a combinationof money and bonds before in- curring consumption expenditure. It will be shown that the existence of a Laffer curve depends critically on how good substitutesmoney and bonds are in aggregate financial assets held as "cash"-in-advance. Section 2 presents both individual-countryand combined cross-country time- series evidence that supports the notion that the semielasticity of money demand with respect to inflationvaries with inflation. The empiricalevidence, collected for all high-inflation countries during the 1960-1990 period, is also used to provide estimates of the seigniorage-maximizinginflation rate. It will be shown that both these estimates and those for the semielasticity differ substantiallyfrom those ob- tained underthe conventionalCagan approach.The results also have strikingimpli- cations for the substitutabilityof bonds and money. The results will also show that the semielasticity and the seigniorage-maximizinginflation rate, when based on the correct measure of the opportunitycost of holding money, difter markedly from 2. Bruno and Fischer (1990) also mention this possibility. With referenceto the hyperinflationof the 1920s, Barro (1972) notices that inflation tends to accelerate when the revenue-maximizingrate is exceeded. WILLIAMR. EASTERLY,PAOLO MAURO, AND KLAUS SCHMIDT-HEBBEL : 585 those obtainedwhen using conventionalbut incorrectmeasures of inflation. Section 3 concludes. 1. THE MODEL This section develops a simple model of money demand, inflation, and seignior- age. It shows that both the semielasticityof money demandwith respect to the op- portunitycost of holding money and the inflationrate that maximizes seignioragein the steady state depend on the degree of substitutabilitybetween money and bonds. In addition, the inflation semielasticity of money demand is shown to vary with inflation. An infinitely lived optimizing representativeagent takes consumption, invest- ment, and portfolio decisions in a closed economy. This agent holds money and bonds for transaction purposes and maximizes a standard intertemporalutility function: rX cl-J - 1 max J e-Pt dt (1) where p is the discount rate, c is consumption,and 1/cris the intertemporalelastici- ty of substitution. Production(y) in the one-good economy is assumed to depend only on a broad concept of capital (k), as in Barro(1990) and Rebelo (1991):3 y = A k . (2) There are three assets available to the consumer capital k, nonindexedmoney (real value m), and indexed money (real value b, referredto as "bonds"for short). Bonds pay no interest, but are fully indexed to the price level.4 We assume that inflationcannot fall below-A. There is no uncertainty.Since capitalhas real return A (net of depreciation),it always dominatesbonds and money. However, a cash-in- advance constraintrequires that some combination of money and bonds must be held in orderto purchaseconsumption goods: f(m, b)-c-O (3) 3. Populationis assumed fixed and normalizedat one, so all variablescan be interpretedin per capita terms. 4. The classic example of this kind of asset in developing countriesis foreign currency,which main- tains its value as the nominal exchange
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