IS THE PRICE ELASTICITY OF MONEY DEMAND ALWAYS UNITY

I. INTRODUCTION For much of history, money largely consisted of monetary metals. In particular, during late nineteenth and early twentieth centuries, many countries adopted gold standards and gold served as money--either directly as coins held by the public or as claims on bullion held by commercial and central banks. At the same time that large stocks of gold were being held for monetary uses, even larger stocks were being held for nonmonetary uses owing to gold's superior luster, reflectivity, malleability, conductivity, ductility, and resistance to corrosion. (1) In its monetary uses, it was valued only in terms of its ability to purchase consumption goods. As a result, asset holders demanded real gold balances, that is, the nominal stock deflated by an appropriate index of prices for goods. By contrast, in its nonmonetary uses, it was valued in terms of its physical units, that is, its undeflated nominal stock. These dual uses of gold imply that the demand for monetary gold should not be expected to be unit-elastic with respect to the price level, a result that we demonstrate formally in the next section. (2) Empirical researchers have not noticed that money demand behaves differently under commodity standards from how it behaves under fiat standards. Since the available historical data are dominated by observations from fiat standards, the characteristics of money demand under commodity standards are largely concealed when the researchers use data that span both commodity and fiat standards. More specifically, the hypothesis of long-run price homogeneity is usually not rejected. For example, Meltzer (1963) used U.S. data from 1900 to 1958 to estimate money demand functions formulated in both nominal and real terms and found little evidence against price homogeneity. Laidler (1971) carried out a similar test using both U.K. and U.S. data over the period of 1900-1965 and obtained a similar result notwithstanding a different specification. Friedman and Schwartz (1982) also found support for price homogeneity for both United Kingdom and United States over the period of 1867-1975 using the method of phase averaging to extract the long-run correlation between nominal money demand and the price level. Hendry and Ericsson (1991) applied cointegration methods to the annual U.K. data from Friedman and Schwartz (1982) to confirm price homogeneity. Applying the same approach to annual U.S. data from 1874 to 1975, MacDonald and Taylor (1992) found that price homogeneity cannot be rejected at the .05 statistical significance level but can be rejected at the .10 level. [FIGURE 1 OMITTED] The United Kingdom and United States were on fiat standards for the bulk of the sample periods that these researchers employed. (3) For this reason, their findings do not serve as evidence for price homogeneity under commodity standards. In Section II, we present a simple theoretical model that employs the money-in-utility framework augmented by also giving utility to holdings of nonmonetary gold. We demonstrate that under fairly general conditions, the price elasticity of money demand should be less than 1 under commodity standards. Section III uses three data sets to provide empirical evidence supporting this theoretical prediction. Section IV draws some final conclusions. II. THEORETICAL MODEL Consider a representative household that chooses the paths for its consumption C, stock of monetary gold M, stock of nonmonetary gold N, and real stock of assets A taking as given the paths for non-asset income Y, the price level P, and the nominal and real interest rates i and r that it earns on A. In making its choices, it seeks to maximize the objective function: (1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] subject to a sequence of budget and portfolio constraints of the form: (4) (2) [C.sub.t] + [i.sub.t][([M.sub.t] + [N.sub.t])/[P.sub.t]] + [A.sub.t] [less than or equal to] [Y. …