APPENDIX: Derivation of the Coefficient Vectors (β and γ)
Recall that the value of the total elasticity of the demand for money to rb is assumed to be given. Allowing for interest arbitrage, this elasticity may be written as
By a similar process, the assumptions (a-i) in Section III can be converted from elasticities into coefficient equations as follows:
These ten equations, plus the additive constraints ((5’)-(5”‘)), generate the eleven βi, plus γ1 and γ4, for given values of
The two parameters in the reaction function (γ2, γ3) are derived from Black (1983). Black estimates a number of reaction functions for the central banks of ten industrial countries. The equations from which γ2 and γ3 are derived regress the discount rate in each country on two internal variables—inflation and unemployment—and four external variables—the ratio of reserves to imports, the ratio of exports to imports, the foreign interest rate (measured as the yield on three-month Eurodollar deposits), and the real exchange rate (measured by relative normalized unit-labor costs adjusted for changes in the nominal effective exchange rate). The coefficients on these last two variables provide the basis for estimating γ2 and γ3, respectively. This procedure implies (rather arbitrarily) that these coefficients apply to domestic interest rates generally, and not just to the discount rate.
For the United States, γ2 is equal to the weighted average of the coefficients on Eurodollar rates, the weights being taken from the multilateral exchange rate model (MERM). (See Artus and McGuirk, 1981.) For the United Kingdom, it has been assumed that each country’s reaction to a change in Eurosterling interest rates would equal its response to Eurodollar rates times the ratio of that country’s U.K. weight to its U.S. weight in the MERM. The U.S. Federal Reserve System, however, is assumed not to respond at all to changes in external variables.
As for exchange rate effects, Black’s coefficients indicate the effect on each country’s domestic interest rates of a change in its real effective exchange rate. These coefficients, times the effect of a change in the value of the U.S. dollar or the pound sterling on each other country’s effective exchange rate (i.e., the U.S. weight or the U.K. weight in the country’s MERM index), weighted in the same way as for γ2, give the required values of γ3. Note that the model used in this paper assumes that relative costs are fixed in the short run, so that changes in real and nominal exchange rates are equal.
Artus, Jacques R., and Anne Kenny McGuirk, “A Revised Version of the Multilateral Exchange Rate Model,” Staff Papers, Vol. 28 (June 1981), pp. 275–309.
Black, Stanley W., “The Use of Monetary Policy for Internal and External Balance in Ten Industrial Countries,” in Exchange Rates and International Macroeconomics, ed. by Jacob Frenkel, National Bureau of Economic Research (University of Chicago Press, 1983).
- Search Google Scholar
- Export Citation
)| false “ Black, Stanley W., The Use of Monetary Policy for Internal and External Balance in Ten Industrial Countries,” in Exchange Rates and International Macroeconomics, ed.by Jacob Frenkel, National Bureau of Economic Research( University of Chicago Press, 1983).
Boughton, James M., “Recent Instability of the Demand for Money: An International Perspective,” Southern Economic Journal, Vol. 47 (January 1981), pp. 579–97.
Frenkel, Jacob A., and Carlos A. Rodriguez, “Exchange Rate Dynamics and the Overshooting Hypothesis,” Staff Papers, Vol. 29 (March 1982), pp. 1–30.
Henderson, Dale W., “The Role of Intervention Policy in Open Economy Financial Policy: A Macroeconomic Perspective,” in Political Economy of Domestic and International Monetary Relations, ed. by Raymond E. Lombra and Willard E. Witte (Iowa State University Press, 1982).
- Search Google Scholar
- Export Citation
)| false “ Henderson, Dale W., The Role of Intervention Policy in Open Economy Financial Policy: A Macroeconomic Perspective,” in Political Economy of Domestic and International Monetary Relations, ed.by ( Raymond E. Lombraand Willard E. Witte Iowa State University Press, 1982).
Henderson, Dale W., and Kenneth Rogoff, “Negative Net Foreign Asset Positions and Stability in a World Portfolio Balance Model,” Journal of International Economics, Vol. 13 (August 1982), pp. 85–104.
Meltzer, Allan H., and others, “Is the Federal Reserve’s Monetary Control Policy Misdirected? Resolved: That the Federal Reserve’s Current Operating Procedures for Controlling Money Should Be Replaced” (debate), Journal of Money, Credit and Banking, Vol. 14 (February 1982), pp. 119–47.
- Search Google Scholar
- Export Citation
)| false “ Meltzer, Allan H., and others, Is the Federal Reserve’s Monetary Control Policy Misdirected?” (debate), Resolved: That the Federal Reserve’s Current Operating Procedures for Controlling Money Should Be Replaced Journal of Money, Credit and Banking, Vol. 14( February 1982), pp. 119– 47.
Poole, William, “Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model,” Quarterly Journal of Economics, Vol. 84 (May 1970), pp. 197–216.
Radecki, Lawrence, “Short-Run Monetary Control: An Analysis of Some Possible Dangers,” Federal Reserve Bank of New York, Quarterly Review, Vol. 7 (Spring 1982), pp. 1–10.
Scadding, John L., “An Annual Money Demand and Supply Model for the U.S.: 1924-1940/1949-1966,” Journal of Monetary Economics, Vol. 3 (January 1977), pp. 41–58.
Tobin, James, “A General Equilibrium Approach to Monetary Theory,” Journal of Money, Credit and Banking, Vol. 1 (February 1969), pp. 15–29.
Tobin, James, and William Buiter, “Fiscal and Monetary Policies, Capital Formation, and Economic Activity,” in The Government and Capital Formation, ed. by George M. von Furstenberg (Cambridge, Massachusetts, 1978), pp. 73–151.
Mr. Boughton, Senior Economist in the External Adjustment Division of the Research Department, is currently on leave of absence from Indiana University, where he is Professor of Economics. He holds advanced degrees from the University of Michigan and Duke University and has published two books on monetary economics, as well as a number of articles in economic journals.
The author is indebted to Michael Dooley and Willard Witte, in addition to Fund colleagues, for their clarifying suggestions.
This argument is made, for example, by Meltzer in Meltzer and others (1982), pp. 138–39. The counterargument, that excessive attention by the central bank to short-run control may destabilize economic activity, has been made by Ra-decki (1982).
The problem of determining optimal policies when the authorities do have sufficient information about the distribution of disturbances to the economy has been the subject of extensive study, following the seminal paper by Poole (1970). For a recent example of an application to an open economy, see Henderson (1982).
In a more general model of the demand for money, inflationary expectations would also enter the equation as a component of the relative return on real assets. They are omitted from the demand functions of the present model on the grounds that inflationary expectations are unlikely to respond systematically to short-run financial shocks or to generate systematic shifts between financial assets at given interest rates.
In this paper, shift parameters are denoted by αi, structural coefficients by βi, and expectational and reaction coefficients by γi. All the βi, and γi are hypothesized to be nonnegative.
This expectations function is similar to that of Frenkel and Rodriguez (1982), where it is shown that under rational expectations, γ1 (θ in their notation) may be derived as a function of the model’s parameters.
B includes only government bonds, since private domestic bonds are not net wealth to domestic asset holders. Neither the decision to exclude private bonds nor the decision to include government bonds is without controversy, but the issues are primarily relevant to long-run analysis. See, for example, Tobin and Buiter (1978). Foreign bonds held by the domestic public—net of domestic bonds (government and private) held abroad—are included in F rather than in B.
For example, under perfect mobility of capital the exchange rate might over-shoot or move perversely in response to monetary control; see Frenkel and Rodriguez (1982).
A negative value for γ3 would imply a destabilizing policy.
See Tobin (1969). This point does not deny that the economically relevant distinction of money is its negotiability, but in a macromodel the quality of negotiability does not enter directly and is captured only in interest rate fixity.
The restriction γ4 < 1 ensures that a given change in market interest rates results in a smaller change in rm, and α8> 0 ensures that the elasticity of rm to rb is less than unity.
To simplify the notation, E and W have been normalized on unity; M, B, and F thus are measured as portions of W.
These estimates are from Boughton (1981). Since the present model includes a broader range of interest rates, these estimates are applied to the total elasticities to rb, not the partials. In the notation of this paper, η indicates a total elasticity, and ε indicates a partial elasticity.
For example, ε(Fd, r) ≡ Σjε(Fd, rj).
The figure for the United States is based on Scadding (1977). The higher value for the United Kingdom is assigned on the basis of the relative variation in the money-to-base ratio described earlier.
The derivation of the vectors β and γ is explained further in the Appendix.
The parameter λ4 is determined primarily by k4 and hence does not play an independent role.
With the U.S. parameters, k4>0.782 generates negative values for β7 and β8; the permitted range has been truncated accordingly.
Recall that the initial values of E, Ē, and W are set equal to unity. Interest rates are expressed as ratios (e.g., 10 per cent = 0.1).