ARTURO BRILLEMBOURG *
Economic theory is usually better suited to describing the long-run values of variables than their short-run or dynamic properties, although the latter may be of equal, if not greater, interest. In lieu of a strong theoretical foundation, economists have often resorted to ad hoc mechanisms that transform an otherwise static theory into a dynamic one. Nowhere has this been more prevalent than in studies of asset demand functions, particularly those concerned with the demand for money.
In studies that treat the flow demand for an asset, it is common practice to postulate a static or long-run stock demand function for the asset and then to transform this function into a dynamic function by invoking the partial stock adjustment model. This model states that the change in the demand for an asset (the flow demand) is proportional to the difference between the desired and the actual levels of the stock of that asset. While this model has been found to lack a strong theoretical foundation, its simplicity in application has given it a predominant role in empirical studies.1
In many cases, the dynamic properties of the flow demand functions have been augmented by postulating more complex formulations of the partial adjustment model and/or by assuming autocorrelation of the estimated residual errors. In general, this practice too has had no theoretical foundation and can be justified only on grounds of empirical validity.
The purpose of this paper is to reformulate the theoretical underpinnings of the partial adjustment model in such a way as to make this last step more theoretically defensible. In particular, this paper reformulates a simple but common version of the partial adjustment model under conditions of uncertainty. In doing so, it highlights the role of savings in the adjustment toward asset equilibrium. Indeed, perhaps the main contribution of this paper is that, by giving some theoretical foundation for a prevailing practice, it brings together two strands of the literature on the dynamic specification of asset demand functions: one that emphasizes the role of savings and the other that grows out of empirical pragmatism. It is hoped that, rather than providing some theoretical justification for a proliferation of variations on the partial adjustment model, this paper will induce a research effort to provide a more consistent and stronger theoretical underpinning for the alternative modifications of the partial adjustment model.
The paper is divided into five sections. Section I introduces the issues raised by the paper by discussing the role of savings in the adjustment to asset demand disequilibria. Section II derives, in the context of uncertainty, a general partial adjustment that takes into account the role of savings. Nowhere is the application of the partial adjustment mechanism more prevalent than in the empirical literature of the flow demand for money. It is, therefore, useful to illustrate, in Section III, the application of the general partial adjustment model to the demand for money by formulating various models of flow demand. Section IV estimates these various models using quarterly data for the United States during the period extending from the first quarter of 1960 to the first quarter of 1977. Finally, the conclusions of the paper are given in Section V.
Brainard, William C., and James Tobin, “Pitfalls in Financial Model Building,” American Economic Review, Vol. 58 (May 1968), pp. 99-122.
Brillembourg, Arturo, “Pitfalls in Financial Model Building: Accounting for Capital Gains and Losses” (unpublished, International Monetary Fund, 1976).
Foley, Duncan K., “On Two Specifications of Asset Equilibrium in Macroeconomic Models,” Journal of Political Economy, Vol. 83 (April 1975), pp. 303-24.
Friedman, Benjamin M., “Financial Flow Variables and the Short-Run Determination of Long-Term Interest Rates,” Journal of Political Economy, Vol. 85 (August 1977), pp. 661-90.
Modigliani, Franco, “The Dynamics of Portfolio Adjustment and the Flow of Savings Through Financial Intermediaries,” in Savings Deposits, Mortgages and Housing, ed. by E. M. Gramlich and D. M. Jaffee (Lexington, Massachusetts, 1972), pp. 63-102.
Mukherjee, Robin, and Edward Zabel, “Consumption and Portfolio Choices with Transaction Costs,” in Essays on Economic Behavior Under Uncertainty, ed. by M. S. Balch, D. L. McFadden, and S. Y. Wu (New York, 1974).
Purvis, Douglas D., “Dynamic Models of Portfolio Behavior: More on Pitfalls in Financial Model Building,” forthcoming in the June 1978 issue of the American Economic Review.
Turnovsky, Stephen J., and Edwin Burmeister, “Perfect Foresight, Expectational Consistency, and Macroeconomic Equilibrium,” Journal of Political Economy, Vol. 85 (April 1977), pp. 379-93.
White, William H., “Improving the Demand-for-Money Function in Moderate Inflation,” (unpublished, International Monetary Fund, October 31, 1977).
Mr. Brillembourg, economist in the Special Studies Division of the Research Department, is a graduate of Harvard University and of the University of Chicago.
See Mukherjee and Zabel (1974) for a theoretical model of dynamic asset allocation under uncertainty.
If, for example, there are more offers to buy than to sell at a given price, all the assets will be sold, but there will still be an excess demand for that asset. The type of arrangement to distribute assets among demanders will depend on the market.
See Griliches (1967). For simplicity, the reallocation of savings is assumed to be costless.
In other words, in a world of transaction costs, there may be a premium paid for equity rather than debt control.
It is assumed here that the variances of the disequilibrium and transactions costs are constant. In a less restrictive context, they could be responsive to the horizon period. For example, in periods of turbulence, the costs may be decreased by making rebalancing decisions more often than in tranquil periods, since the variance of these costs depends positively on the number of time units ahead that the forecast of the costs is made. This generalization is left for future research.
The careful reader will note that the term [(l–θ)α–γ]et-1 has been dropped from the equation in order to simplify the estimating equation.
It may seem more natural to postulate a reaction to the divergence between the desired and the expected passive money stocks. Unfortunately, this leads to a complex nonlinear estimating equation.
All variables are centered in the middle of the period. The interest rate is a period average. Both the actual current and the adjusted lagged money stocks are averages of data at the end of the period. Data source is the Fund’s International Financial Statistics. It is noted that the interest rate is not in logarithms. A test of Model C using interest rates in logarithms showed slightly worse fits. The theoretical advantage of this formulation is that it treats the inflation rate and the interest rate in a parallel manner. In order to simplify the estimation procedures, equation (7) uses actual variables, rather than the expected variables required by the general partial adjustment model. Similarly, the lagged money stock is adjusted by the actual, rather than the expected, inflation rate.