It is a standard property of neoclassical growth models involving money that in the long run, or steady state, the rate of growth of money will be equal to the rate of growth of real income and the growth of prices. 1 Expressed in terms of real money balances; this property ensures that the growth of real balances will be proportional only to the growth of real income, and that changes in the growth of nominal money will have no effect. In the short run, however, it has been observed that an increase in the rate of monetary emission results in a larger initial stock of real money balances, or, what amounts to the same thing, that velocity tends initially to move in the opposite direction of the change in monetary growth. This phenomenon has been detected empirically in the studies by Harberger (1963) on Chile, Diz (1970) on Argentina, and Pastore (1975) on Brazil. 2
In general, this short-run response of real money balances to a monetary change can be explained by the lag between the change in the supply of money and the response of inflation (or nominal income). With the existence of such a lag, an expansion in money would raise the stock of nominal money balances and, since prices would not respond to the change immediately, real money balances would increase. Empirical evidence on this lag is fairly common, and two recent examples are the studies by Vogel (1974) on a group of Latin American countries and Von Furstenberg and White (1980) on industrial countries.
Despite the empirical evidence, and the recognition by Friedman (1970) that, in the transition phase, real money balances would be expected to respond positively to changes in the growth of nominal money, standard money demand models continue to be formulated on the basis of instantaneous and equiproportional adjustment of prices and, therefore, real money balances. Equilibrium (long-run) models necessarily have this feature and therefore cannot be faulted. The criticism is directed essentially at the “dynamic” or “disequilibrium” models that purport to describe the time path between two equilibria, namely, the models that involve some type of partial-adjustment mechanism or an adaptive expectations generating scheme. 3 Neither of these two methods of introducing dynamics into the system is able to provide a satisfactory explanation as to why real money balances rise initially after a monetary change. Their basic feature is the ability to trace the time path of real money balances after a change in exogenous variables other than the growth of the nominal money supply.
Clearly, theoretical considerations alone would provide sufficient motivation for the development of money demand models that would describe this phenomenon of the initial rise in real cash balances. In addition, the importance of demand for money models in the actual formulation of monetary policy makes an examination of this issue directly relevant from a policy point of view. 4 For example, if the aim of the authorities is to affect the rate of inflation, then the use of a conventionally formulated money demand function, while perhaps yielding the correct policy in the long run, may give misleading signals during the approach to this long-run position if real money balances happen to move initially in the same direction as the change in the nominal money supply. Short-run policy, thus, may have to be designed to compensate for this effect.
It is the awareness of this issue that has led to various attempts to develop alternative theoretical models, either through the adoption of more complicated expectations formation schemes (e.g., Frenkel (1975), Auernheimer (1979)), or the introduction of the concept of temporary disequilibrium in the holding of money balances (Sjaastad (1972), Auernheimer (1974), Pastore (1975)). The purpose of this paper is to consider an alternative approach that relies on the idea of a monetary “shock,” or “surprise.” A simple adjustment model is designed in which it is hypothesized that, while prices adjust instantaneously to expected, or anticipated, changes in the growth of money, unexpected increases initially show up in increases in the public’s money holdings. Eventually, these excess money holdings are worked off and prices begin to respond. The model is in the spirit of the rational expectations literature 5 and remains consistent with the long-run monetarist proposition contained in Friedman (1970). It enables one to trace out more accurately the path that real money balances will take in reaching the new equilibrium, and consequently the dynamic behavior of inflation, after there is a change in the money supply.
Instead of dealing with the issue simply on a theoretical level, the model is estimated for a group of 11 developing countries, 7 Latin American—Argentina, Brazil, Colombia, Costa Rica, the Dominican Republic, Mexico, and Uruguay—and 4 Asian—India, Malaysia, the Philippines, and Thailand. Since the monetary and inflationary experience of these countries is fairly diverse, the general applicability of the model is put to a fair test. While there is no particular reason for concentrating exclusively on developing countries, it will be seen that certain simplifying assumptions made in the course of the analysis are somewhat easier to justify in the context of these types of economies. 6
The outline of the paper is as follows. In Section I the standard money demand models are discussed within the framework of the basic hypothesis of this paper and then compared with the model proposed here. The results from estimating the model, and dynamic simulations demonstrating both the effects of monetary shocks on inflation, and, conversely, the appropriate monetary policy to achieve a target rate of inflation, are shown in Section II. The broader policy implications of the exercise, and a summary of the findings, are contained in the concluding section.
APPENDIX: Data Sources and Definitions
All the data used in this paper were taken from International Monetary Fund, International Financial Statistics (IFS). The basic series, covering the period 1962 to 1976, are centered at the middle of the quarter. The rate of inflation (Δlog Pt) and the growth of money (Δlog Mt) are thus centered at the beginning of the quarter. The definitions of the variables are as follows:
M = money plus quasi-money; IFS, lines 34 and 35
P = consumer price index; IFS, line 64
y = real income
For Argentina, India, Mexico, the Philippines, and Uruguay, gross domestic product at 1975 prices (IFS, line 99b. p) was used; for the remaining countries, nominal gross domestic product (IFS, line 99b) deflated by the consumer price index had to be used. Since these series on income are not available on a quarterly basis, the annual data (in real terms) was interpolated by a linear interpolation method.
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Aghevli, Bijan B., Mohsin S. Khan, P. R. Narvekar, and Brock K. Short, “Monetary Policy in Selected Asian Countries,” Staff Papers, Vol. 26 (December 1979), pp. 775–824.
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Auernheimer, Leonardo,, “Adaptive-Regressive Expectations and the Price Level: A Reformulation,” Journal of Monetary Economics, Vol. 5 (January 1979), pp. 123–32.
Barro, Robert J., “Rational Expectations and the Role of Monetary Policy,” Journal of Monetary Economics, Vol. 2 (January 1976), pp. 1–32.
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Barro, Robert J.,, “Unanticipated Money, Output, and the Price Level in the United States,” Journal of Political Economy, Vol. 86 (August 1978), pp. 549–80.
Brillembourg, Arturo, “The Role of Savings in Flow Demand for Money: Alternative Partial Adjustment Models,” Staff Papers, Vol. 25 (June 1978), pp. 278–92.
Brillembourg, Arturo,, “The Dynamics of Inflation: Forward Contracts and Money,” Staff Papers, Vol. 26 (December 1979), pp. 755–74
Buiter, Willem H., “The Macroeconomics of Dr. Pangloss: A Critical Survey of the New Classical Macroeconomics,” Economic Journal, Vol. 90 (March 1980), pp. 34–50.
Cagan, Phillip, “The Monetary Dynamics of Hyperinflation,” in Studies in the Quantity Theory of Money, ed. by Milton Friedman (University of Chicago Press, 1956), pp. 25–117.
Carr, Jack, and Michael R. Darby, “The Role of Money Supply Shocks in the Short-Run Demand for Money” (unpublished, University of Toronto, and University of California, Los Angeles, and National Bureau of Economic Research, September 27, 1978).
Chow, Gregory C., “On the Long-Run and Short-Run Demand for Money,” Journal of Political Economy, Vol. 74 (April 1966), pp. 111–31.
Coats, Warren L., Jr., “Modelling the Short-Run Demand for Money with Exogenous Supply” (unpublished, International Monetary Fund, December 20, 1978).
Diz, Adolfo C., “Money and Prices in Argentina, 1935–1962,” in Varieties of Monetary Experience, ed. by David Meiselman (University of Chicago Press, 1970), pp. 71–162.
Fernandez, Roque B., “An Empirical Inquiry on the Short-Run Dynamics of Output and Prices,” American Economic Review, Vol. 67 (September 1977), pp. 595–609.
Frenkel, Jacob A., “Inflation and the Formation of Expectations,” Journal of Monetary Economics, Vol. 1 (October 1975), pp. 403–21.
Frenkel, Jacob A., and Harry G. Johnson, eds., The Monetary Approach to the Balance of Payments (University of Toronto Press, 1976).
Frenkel, Jacob A., and Carlos A. Rodriguez, “Notes on Output and Expectations in the Process of Inflation,” Weltwirtschaftliches Archiv, Vol. 113 (No. 3, 1977), pp. 423–34.
Friedman, Benjamin M., “Stability and Rationality in Models of Hyperinflation,” International Economic Review, Vol. 19 (February 1978), pp. 45–64.
Friedman, Milton, “A Theoretical Framework for Monetary Analysis,” Journal of Political Economy, Vol. 78 (March/April 1970), pp. 193–238.
Galbis, Vicente, “Inflation and Interest Rate Policies in Latin America, 1967–76,” Staff Papers, Vol. 26 (June 1979), pp. 334–66.
Harberger, Arnold C., “The Dynamics of Inflation in Chile,” in Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld (Stanford University Press, 1963), pp. 219–50.
Heller, H. Robert, and Mohsin S. Khan, “The Demand for Money and the Term Structure of Interest Rates,” Journal of Political Economy, Vol. 87 (February 1979), pp. 109–29.
Khan, Mohsin S. (1977 a), “The Variability of Expectations in Hyperinflations,” Journal of Political Economy, Vol. 85 (August 1977), pp. 817–27.
Khan, Mohsin S. (1977 b), “Variable Expectations and the Demand for Money in High-Inflation Countries,” Manchester School, Vol. 45 (September 1977), pp. 270–293.
Laidler, David E. W., “The Demand and Supply of Money Yet Again,” paper presented at the Carnegie-Rochester Conference, April 1979.
Mundell, Robert A., “The Problem of Stopping Inflation,” Ch. 7 in Monetary Theory: Inflation, Interest and Growth in the World Economy (Pacific Palisades, California, 1971), pp. 64–73.
Mussa, Michael, “Adaptive and Regressive Expectations in a Rational Model of the Inflationary Process,” Journal of Monetary Economics, Vol. 1 (October 1975), pp. 423–42.
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Mr. Khan, Assistant Chief of the Financial Studies Division of the Research Department, is a graduate of Columbia University and the London School of Economics.
The author is grateful to Tomas Balitño, Willem Buiter, Rudiger Dornbusch, Jacob Frenkel, David Laidler, and John Williamson for helpful comments on this paper.
See, for example, Friedman (1969, Ch. I) and also (1970). This result requires that the income elasticity of money demand be unity. If not, trend changes in velocity would also have to be taken into account.
For a discussion of the role of the demand for money function in the operation of monetary policy, see Organization for Economic Cooperation and Development (1979) and, in relation to Fund stabilization programs, Robichek (1967).
In the interests of theoretical consistency, the scale variable should also be expected, or “permanent,” real income. As in practice it does not appear to matter greatly which particular scale variable is used, for simplicity current real income is utilized.
To the extent that interest rates paid on time and savings deposits are indexed to the rate of inflation, the elimination of Rde from the specification could result in some bias in the coefficient of expected inflation, a2. In the particular sample here, only Brazil has consistently had a system of indexation of interest rates, with Colombia and Costa Rica having only short-lived experiments with such schemes. The cases of these countries, and also those where the rates are somewhat flexible, are discussed in Section II.
It is generally necessary, as pointed out earlier, in the steady state to assume that the income elasticity of demand for money, al, is unity.
The focus here is only on discrete time adjustment models, including those that are approximated from continuous time models for estimation purposes. In theoretical continuous time models, one has to be more careful in distinguishing between the effects of a stepwise increase in the growth of money, and an increase in the stock of money, on the rate of inflation. The adjustment to the former is instantaneous, but may be delayed with respect to the latter.
See White (1978, p. 570). In order to derive this, it is assumed that Md is deflated by the actual, rather than the expected, price level.
The nominal-adjustment model, equation (8), continues to indicate an initial decline in real money balances even when the adaptive expectations formulation for inflation is introduced into the model.
In a rational expectations framework, Mussa (1975) has shown that a money supply process that contains regressive and extrapolative elements will also yield the path for real money balances shown in Figure 1.
Assuming that real income is constant. If real income is increasing, the two will differ by the growth in real income times the income elasticity of the demand for money.
If there was two-way causality between inflation and the growth of money, a model along the lines proposed by Aghevli and Khan (1978) could be employed. Models such as the ones developed by Barro (1977) and (1978), Fernandez (1977), and Frenkel and Rodriguez (1977) could be considered if one was interested in the response of real income to monetary changes.
In the absence of direct observations on expectations, it is necessary to generate these on the basis of the past behavior of the series in question.
In the context of the Cagan model of hyperinflation, the process for the growth of the money supply has the form
This implicitly assumes that people do not learn to change their way of forming expectations even in the face of unexpected monetary changes. They continue to believe that the authorities will conduct monetary policy in a manner that would validate their expectations.
Ignoring the effects of Δlog y and ΔΠ may certainly involve some mis-specification, but it does turn out that for the countries in the sample these variables generally displayed very little variation over time.
In a completely rational model, the expected rate of inflation would be equal to the actual rate, lit = Δlog Pt. For a discussion of some of the properties of the adaptive expectations scheme for inflation, see Khan (1977 a) and (1977 b).
Adjusted for the growth in real income times the income elasticity of money demand.
The constant a0 can be assumed to include the arguments that were contained in the variable k, defined earlier.
The equation is now written without imposing a negative sign on the coefficient of Δlog Pt, since this is to be freely estimated.
Actually, it is likely that this variable would have an inverted U-shape. As monetization occurs, this ratio would rise, and, as the economy became more sophisticated financially and alternative assets were available, the ratio of money to income would tend to fall.
Recalling the previous comments on the difficulty in simply comparing this ratio across countries. Two countries with exactly the same ratio of money to income may well be substantially different in terms of financial development.
Interest rates were freed in Brazil only in 1975, Argentina in mid-1977, Uruguay in 1977, and Malaysia in 1978. Rates in Brazil have been indexed to the rate of inflation since 1964, but even so real rates have been consistently negative. Interest rates were partially indexed in Colombia during 1972–74, and in Costa Rica in 1974.
Assuming that foreign assets are zero. If not, an adjustment would have to be made, but broad money would still be the relevant variable. The equation was also estimated with money narrowly defined, and the results of this exercise are available upon request from the author, whose address is Research Department, International Monetary Fund, Washington, D.C. 20431.
Were this parameter to turn out to be equal to unity, the model would reduce to the standard partial-adjustment equation (6).
Since 1 – γ is significantly different from zero at the 5 per cent level. For Malaysia, the use of the current value of the rate of growth of money in the equation yielded an estimate of the coefficient of adjustment, λ, that was negative. Therefore, the results reported for this country in Table 2 were obtained by using the one-quarter lagged value of the growth in money.
Even though the point estimates are greater than zero.
Examining the time-series properties of the errors in the model through the methods of Box and Jenkins (1970), and then imposing a similar time-series structure on the model, may be the appropriate strategy to follow.
In fact, if there were significant economies of scale in the holding of money because of the existence of financial alternatives, the elasticity could easily be less than unity. See Laidler (1977).
It should be noted that this elasticity is not independent of the unit of observation. The elasticity shown in Table 2 is evaluated at the sample mean of the quarterly rates of inflation.
Higher-order autocorrelation may still, of course, be present.
Whether the approach is oscillatory or not depends on
Except in the Dominican Republic and Thailand, the movement to equilibrium displayed (damped) oscillations. The parameters in these two countries yielded two real roots, rather than a pair of complex conjugates.
Needless to say, since the interest here is in the dynamic path of inflation, the lagged values of the endogenous variables were themselves generated by the system.
The average for the parameter a2 was calculated excluding the abnormally large estimates obtained for India and Malaysia.
The stock of real money balances would grow at a constant rate, while the rate of inflation would be lowered by a constant factor.
Given the growth rates of nominal money and prices, the behavior of real money balances is readily calculated.
The oscillations observed were to be expected from the formal stability analysis.
A reduction in the growth of money supply is probably the more realistic type of policy.
It is not exact because the coefficients of the lagged endogenous variables in the reduced form differ between the two cases. Only in the initial period are the simulations an exact transposition. The reduced form for nominal money growth has the form Δlog Mt = −(A3(L)/ A4(L)) log yt + (Det / A4(L)) Δlog Pt.
It is assumed that the authorities wish to reduce the rate of inflation by 0.25 per cent in each period.
And, if necessary, the trend change in velocity.