JOHN F.O. BILSON *
This paper examines the empirical validity of a simple monetary model of exchange rate determination. The model is characterized as “monetary” because it assumes the existence of a stable money demand function and integrated world markets. The monetary model provides a useful tool for exchange rate analysis because it (a) clearly defines the role of speculation among the determinants of the exchange rate, (b) provides a simple definition of the equilibrium exchange rate, and (c) directly relates the equilibrium rate to the underlying instruments of monetary policy.
Professor Friedman, in his classic defense of flexible exchange rate regimes, stressed that flexible exchange rates need not be unstable. He wrote,
The ultimate objective is a world in which exchange rates, while free to vary, are in fact highly stable. Instability of exchange rates is a symptom of instability in the underlying economic structure. 2
These words offer little consolation to those who have experienced the volatile exchange rates of the current floating rate period. Many market participants appear to have regressed from Friedman’s logic toward the belief that the exchange rate is determined by speculation and “market psychology” rather than by underlying economic conditions. This belief has been encouraged by the lack of a generally accepted economic theory of the determination of the exchange rate, since, without such a theory, it is difficult to define the elements of the “underlying economic structure” that have been responsible for the erratic movements in the rates. This theoretical vacuum, induced primarily by the inability of economic models based upon trade flows to explain exchange rate movements in the inflationary environment of the 1970s, has been rapidly filled by a number of papers stressing the role of asset markets in the determination of the exchange rate.3 The asset market models concentrate on the mechanisms through which the exchange rate eliminates incipient capital flows, including adjustment in real money balances through exchange rate-induced price level variation and adjustments in nominal interest rates through changes in the expected rate of exchange rate depreciation.
The primary object of this paper is to examine the empirical validity of a simple asset market model of exchange rate determination. The model is characterized as “monetary” because it is based upon two assumptions associated with the “monetary approach to the balance of payments” and is carried over, in the manner suggested by Johnson, 4 into the study of flexible rates. These assumptions are that the demand for money is a stable function of a limited number of aggregate economic variables and that, in the absence of transportation costs and restrictions upon trade, the law of one price will hold in international markets. In the monetary model, the law of one price appears in the form of the purchasing-power-parity and interest rate parity conditions that link international price and interest rate movements to developments in the foreign exchange market. In the simple model, these arbitrage conditions are assumed to hold at each point in time, although some dynamic aspects will be introduced into the money market analysis.
The model is tested using monthly data for the Federal Republic of Germany and the United Kingdom over the period from April 1970 to May 1977. The sample period includes the last years of the fixed rate system in order to increase the number of observations and because the fundamental assumptions of the monetary approach, as stated above, are not dependent upon the particular money supply rule followed by the central bank. This does not mean, of course, that the endogeneity of the money supply under fixed exchange rates can be ignored econometrically, but it does imply that the parameters of the money demand function should be invariant with respect to the exchange rate regime. The deutsche mark/pound (DM/pound) rate provides an interesting and difficult test of the monetary approach. The interest lies in the fact that there has been a great deal of variation in the economic factors stressed by the theory, so that the influence of these factors on the exchange rate should be clearly discernible. The difficulty associated with the DM/pound rate is obvious—not only has this rate appreciated more rapidly than most other exchange rates but it has also exhibited sharp short-term fluctuations around the trend. The empirical analysis examines whether this history is consistent with the predictions of the monetary model.
The primary object of the paper is, therefore, to test a particular hypothesis concerning the determinants of the exchange rate, rather than to provide a detailed description of the behavior of the DM/pound rate. Consequently, the specific institutional factors that influence exchange rates and interest rates in the two countries are ignored, and no attempt is made to account for the endogeneity of the money supply, as is done, for example, by Artus (1976). Despite these limitations, the results may be useful as a foundation for individual country studies and as an indication of the relationship between monetary policy and the exchange rate.
In this Appendix, the test of the compatibility between the sample and prior information is explained. The sample information may be compactly stated in the relation,
y = the dependent variable
X = the matrix of independent variables
β = the vector of regression coefficients
u = the vector of residuals.
The residuals are assumed to be independently and identically distributed with variance
Similarly, the prior information may be stated as
where r′ = [1, -1, 1.5, -1, 1, 0.76]
The compatibility test is a test of whether the regression coefficients
where r is the point estimate of the regression coefficients from the prior information, while R
The covariance matrix of the difference between the point estimates is,
where ν is the variance/covariance matrix of the prior information. The quadratic form,
is consequently the sum of q squared standardized normal variables, which are distributed X2(g), where q is the number of prior restrictions, under the compatibility hypothesis. Ninety per cent of the observations drawn from their distribution, with six degrees of freedom, will lie within the range from 1.635 to 12.592. If the actual value of the statistic lies outside of this range, then the hypothesis that the sample and prior information are compatible is rejected by the test at this level of significance. Since the actual value of the statistic was 10.570, which lies within the confidence interval, it was not possible to reject the hypothesis that the two information sets are compatible.
The two information sets were then combined into one equation, as specified in
Since the two errors have differing variances, it is not possible to obtain efficient estimates by simply applying ordinary least squares to equation (32). Multiplying the prior information by συ/σνi standardized the variance of the prior errors, so that they had the same variance as the sample errors. Application of ordinary least squares to the transformed equation yields the appropriate generalized least-squares estimate of the regression coefficients. This technique is discussed in detail in Theil (1971, pp. 350–51).
Artus, Jacques R., “Exchange Rate Stability and Managed Floating: The Experience of the Federal Republic of Germany,” Staff Papers, Vol.23 (July 1976), pp. 312–33.
Bilson, John F.O. (1977), “A Simple Long-Run Model of Exchange Rate Determination” (unpublished, International Monetary Fund, April 1977).
Bilson, John F.O. (1978), “Rational Expectations and the Exchange Rate,” in Studies in the Economics of Exchange Rates, ed. by Jacob A. Frenkel and Harry G. Johnson (forthcoming, Reading, Massachusetts, 1978).
Bilson, John F.O. and Richard M. Levich, “A Test of the Forecasting Efficiency of the Forward Exchange Rate” (mimeographed, New York University, Graduate School of Business Administration, 1977).
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.
Calvo, Guillermo A., and Carlos Alfredo Rodriguez; “A Model of Exchange Rate Determination under Currency Substitution and Rational Expectations,” Journal of Political Economy, Vol. 85 (June 1977), pp. 617–25.
Dornbusch, Rudiger (1976 a), “The Theory of Flexible Exchange Rate Regimes and Macroeconomic Policy,” Scandinavian Journal of Economics, Vol. 78, No. 2(1976), pp. 255–76.
Dornbusch, Rudiger (1976 b), “Expectations and Exchange Rate Dynamics,” Journal of Political Economy, Vol. 84 (December 1976), pp. 1161–76.
Frenkel, Jacob A., “A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence,” Scandinavian Journal of Economics, Vol. 78, No. 2 (1976), pp. 200–224.
Frenkel, Jacob A., and Harry G. Johnson (1978), eds., Studies in the Economics of Exchange Rates (forthcoming, Reading, Massachusetts, 1978).
Friedman, Milton, “The Case for Flexible Exchange Rates,” in his book, Essays in Positive Economics (University of Chicago Press, 1953), pp. 157–203.
Girton, Lance, and Don Roper, “Theory and Implications of Currency Substitution,” International Finance Discussion Paper No. 56, Board of Governors of the Federal Reserve System (August 1976).
Goldfeld, Stephen M., “The Demand for Money Revisited,” Brookings Papers on Economic Activity: 3 (1973), pp. 577–638.
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Johnson, Harry G., “The Monetary Approach to Balance-of-Payments Theory,” in his book, Further Essays in Monetary Economics (Harvard University Press, 1973), pp. 229–49.
Knight, Malcolm, “Output, Prices and the Floating Exchange Rate in Canada: A Monetary Approach” (unpublished, International Monetary Fund, December 30, 1976).
Laidler, David, “Some Evidence on the Demand for Money,” Journal of Political Economy, Vol. 74 (February 1966), pp. 55–68.
Magee, Stephen P. (1974), “U.S. Import Prices in the Currency-Contract Period,” Brookings Papers on Economic Activity: 1 (1974), pp. 117–64.
Magee, Stephen P. (1978), “Contracting and Spurious Deviations from Purchasing Power Parity,” in Studies in the Economics of Exchange Rates, ed. by Jacob A. Frenkel and Harry G. Johnson (forthcoming, Reading, Massachusetts, 1978).
McKinnon, Ronald I., “Floating Foreign Exchange Rates 1973–74: The Emperor’s New Clothes,” in Institutional Arrangements and the Inflation Problem, ed. by Karl Brunner and Allan H. Meltzer, Carnegie-Rochester Conference on Public Policy, Vol. 3 (Amsterdam, 1976), pp. 79–114.
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)| false McKinnon, Ronald I., “Floating Foreign Exchange Rates 1973–74: The Emperor’s New Clothes,”in Institutional Arrangements and the Inflation Problem, ed. by Carnegie-Rochester Conference on Public Policy, Karl Brunnerand Allan H. Meltzer, Vol. 3( Amsterdam, 1976), pp. 79– 114.
Mussa, Michael, “The Exchange Rate, the Balance of Payments, and Monetary and Fiscal Policy Under a Regime of Controlled Floating,” Scandinavian Journal of Economics, Vol. 78, No. 2 (1976), pp. 229–48.
Muth, John F., “Rational Expectations and the Theory of Price Movements,” Econometrica, Vol. 29 (July 1961), pp. 315–35.
Sargent, Thomas J., and Neil Wallace, “Rational Expectations and the Dynamics of Hyperinflation,” International Economic Review, Vol. 14 (June 1973), pp. 328–50.
Schadler, Susan, “Sources of Exchange Rate Variability: Theory and Empirical Evidence, Staff Papers, Vol. 24 (July 1977), pp. 253–96.
Mr. Bilson, economist in the External Adjustment Division of the Research Department, is a graduate of Monash University, Melbourne, and the University of Chicago. During 1977–78 he is on leave from Northwestern University, where he is a member of the faculty.
The author gratefully acknowledges the advice and suggestions of Professors Robert Z. Aliber, Rudiger Dornbusch, Stephen P. Magee, and the late Harry G. Johnson. A special debt is due to Jacob A. Frenkel, whose detailed comments on an earlier draft substantially improved the quality of the paper.
See the Scandinavian Journal of Economics, Vol. 78, No. 2 (1976) and Frenkel and Johnson, eds. (1978) for collections of papers on the asset market approach. Schadler (1977) provides a useful survey of the theoretical and empirical literature on the sources of exchange rate variability.
“These assumptions are relaxed in structural asset market models, for example, Artus (1976) and Knight (1976). This paper should be considered as an investigation of one component of a wider structural model.
See Sargent and Wallace (1973). This issue is examined in greater depth in the last section of the present paper.
An M2 definition of the money supply is not available for the United Kingdom over this period. Both series are taken from the Fund’s International Financial Statistics data tape, as are the industrial production indices.
Treasury bill rate differentials were also considered, but were found to be less successful in explaining variation in the exchange rate. The forward premium is a better empirical proxy for the type of interest rate stressed by monetary theorists, since it is predominantly influenced by speculative factors.
The exchange rate and forward exchange premium were taken from the Harris Bank data tape, which was provided by Professor Robert Z. Aliber of the Graduate School of Business, University of Chicago.
Expressed in terms of the lagged dependent variable coefficient, the mean lag is equal to β7/(1–β7). Allowing the mean lag to take values between 0 and 12, each having probability 1/13, the associated distribution of β7 may be derived. This distribution has mean 0.76 and standard deviation 0.26.
In the test, the estimated value of the coefficient on the lagged dependent variable in the unrestricted regression was used to transform the covariance matrix of the prior information. The unrestricted equation was also estimated subject to the assumption that the residual was generated by a first-order autoregressive process.
The numbers in parentheses are t-statistics.
For these estimates, the t-statistics are derived from the mixed estimation results. However, the summary statistics beneath the equation only refer to the sample information.
The t-statistics beneath the coefficients in this equation are approximations derived from a first-order Taylor’s series expansion of the long-run elasticities.
It is extremely difficult to specify, within the single-equation framework, whether equation (14) is an equation determining prices, exchange rates, or interest rate differentials. It is, therefore, put forward as a simple empirical regularity without any strong presumption concerning causality.
A nested model contains only a subset of the variables in a larger model. In contrast, a non-nested model includes at least one variable that is not present in the larger model.
The concept of “rational expectations” was introduced into economics by Muth (1961). Some tests of the forecasting efficiency of the forward exchange rate are presented in Bilson and Levich (1977); these authors find that the predictions of the forward rate are comparable, in terms of bias and standard error, to the predictions of simple time-series models.
The interest rate differential employed in the regression analysis is expressed as an annual percentage rate. It is therefore necessary to multiply the regression coefficient by 12 in order to arrive at the true monthly value of ε.
Two-stage least-squares estimates of the equations, using the 12-month forward premium as an instrument for the 1-month premium, did indicate a small but significant bias in the estimates of the interest elasticity of the demand for money. Estimates of the rational expectations model are not possible because not all of the parameters are identified.