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A Monetarist Money Demand Function

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A Monetarist Money Demand Function A MONETARIST MONEY DEMAND: FUNCTION Robert L. Hetzel Introduction The public cares about the real quantity of money it holds, while the actions of the central bank deter- In the first part of this article, inflation as a mone- mine the nominal quantity of money available for the tary phenomenon is discussed. The discussion is public to hold. The price level translates the real from the perspective of the modern formulation of quantity of’ money demanded, by the, public into the the quantity theory. (See, in particular, Chapter 2 corresponding nominal quantity demanded. The price in Friedman and Schwartz, Monetary Trends in the level varies in order to equate this nominal quantity United States and the United Kingdom [2]). In demanded to the given nominal quantity supplied. the second part of the article, empirical estimation of the relationship between money growth and infla- The quantity equation serves as a useful summary tion is discussed. The article that accompanies this of the supply and demand relationship that deter- one; “The Behavior of the M1 Demand Function in mines the price level. In expression (1), the nominal the Early 1980s” contains the results of estimating money stock, M, equals the product of a factor k this relationship for the post-Korean War period in and nominal expenditure, where nominal expenditure the United States. is expressed as the product of the price level, P; and real expenditure, Y. By definition, k is the fraction The Quantity Theory Framework of nominal expenditure held as nominal money balances. The modern formulation of the quantity theory places the determination of the price level within the (1) M=k[P*Y] analytical framework of supply and demand. The price level, or more appropriately its inverse, is the The definitional relationship shown in (1) can be goods price of money. The price level is determined transformed into a substantive economic hypothesis “by the interaction of the supply and demand for by interpreting it within the framework of a supply money. and demand relationship. A discussion of the determination of the price level must begin with the distinction between real and nominal variables. Nominal variables are either measured directly in current dollars or in a way that For this purpose, (1) is rewritten as (2). Now, M depends upon the use of dollars as a measure of value: is interpreted as the nominal quantity of, money Examples of nominal variables are the number of supplied. The product in brackets, k * Y, is inter- dollars in circulation and the dollar expenditure of preted as the real quantity of money demanded. the public on final goods and services. Because mar- Finally, the price level, P, adjusts to equate money ket, rates of interest, at least in principle, vary directly demanded to money supplied. Below, expression (2) in response to changes in the future price level antici- is given substance as a theory of the determination of pated by the public, they are also examples of nominal the price level through specific hypotheses about the variables. Real variables, in contrast, are measured behavior of its components and their interaction. in ways that do not make use of current dollars as Interpretation of (2) within the framework of supply the unit of account. Examples of real variables are and demand, however, already entails the substantive the exchange rate between two commodities and final economic hypothesis that the determinants of the physical output. The quantity of money expressed in supply of money can generally be considered as con terms of its purchasing power over goods and services ceptually distinct from the determinants of the de- is a real variable. mand for money. FEDERAL RESERVE BANK OF RICHMOND 15 The Money Supply Adjustment of the Price Level to Money From the perspective of the quantity theory, the The price level is the rate of exchange between real nominal quantity of money is assumed to be deter- output and dollars. It translates the real quantity of mined largely independently of the public’s demand money desired by the public into a corresponding for money. The public adjusts to the nominal money desired nominal quantity. As discussed below, the stock by varying the rate of its nominal expenditure. quantity theory assumes that ultimately the price level adjusts when, at the pre-existing price level, Conversely, the nominal money stock does not adjust changes in the nominal quantity of money supplied to the rate of expenditure of the public: Each indi- produce excess supply or demand for money. vidual economic entity can proportion its money Changes in nominal money are not offset, except holdings to its expenditure by varying its money over short periods, by changes in k, the factor ex- holdings, but collectively this behavior is not possible. pressing the way in which the public’s demand for Collectively, the public proportions its money hold- real money balances depends upon variables such as ings to its expenditures through a change in expendi- real income and the market rate of interest. On the tures. From the quantity theory perspective, major contrary, changes in k may reinforce the effect of changes in the nominal expenditure of the public prior changes in money growth. For example, an reflect the public’s adjustment to changes in the increase in the rate of growth of the money supply money stock. will at some point result in a higher anticipated infla- tion rate, which will increase market rates of interest. As money becomes more expensive to hold, the public Money Demand will reduce its real money holdings. This reduction, a Holders of money care about the real quantity of reduction in k, will drive the price level up beyond money they hold, that is, what they can purchase in what was implied by the increased money growth. terms of goods and services with their money hold- Historically, changes in money growth have affected ings. The real quantity of money demanded is ex- real expenditure before affecting the inflation rate. pressed in (2) by the terms k * Y. Y is considered The effect of money on real expenditure and output here to be real annual expenditure on final output. is referred to as the nonneutrality of money and is The demand for real money holdings is, then, ex- not well understood theoretically. According to the pressed as a fraction k of the annual real expenditure quantity theory tradition, however, this effect causes of the public. The term k * Y expresses the fraction movements in the money supply to be the major of a year’s real expenditures that the desired real source of the business cycle. As explained below, the money stock would finance. The inverse of k is the quantity theory assumes that the ultimate impact of expenditure velocity of money, that is, the number changes in money is on changes in the price level, of times that a dollar on average is used in a year to not on real economic activity. effect transactions involving the sale of final goods Nothing about the number of dollars in circulation and services. The term k is considered to be a pre- affects in any fundamental way the real resource dictable function of a small number of variables, for endowments of an economy, the technological ca- example, the nominal rate of interest and real income pacity of an economy to transform endowments into or wealth. output, or the preferences of individuals with respect The statement that inflation is a monetary phe- to consumption of this output. For these reasons, a nomenon is true in a trivial sense in that the price change in the nominal quantity of money cannot level is determined by the interaction of the demand exert a permanent effect on real economic activity. for and the supply of money. This statement, how- The hypotheses of this section can be summarized ever, refers to the empirical generalization that by reference to expression (2). A change in M will changes in the demand for money proceed in a fairly not be absorbed by an offsetting change in k, nor will predictable, moderate fashion, while changes in the a change in M affect Y in a lasting way. A change in supply of money frequently occur that are large rela- M must ultimately affect P. The sections that follow tive to changes in the demand for money. constitute a discussion of one way of quantifying the 16 ECONOMIC REVIEW, NOVEMBER/DECEMBER 1984 empirical relationship existing between money and spirit is (4), where ln is the natural logarithm. (A price level. difference in the logarithms of variables, multiplied by 100, can be interpreted as the percentage differ- Empirical Association of Money Growth ence in the variables.) and Inflation A functional form is suggested in this section for examining the empirical evidence on the ability of The percentage change in the price level is assumed the, growth rate of the money supply to predict infla- tion. (See Hetzel [3].) The following section dis- ancy between the nominal money stock determined plays the associated algebra. by the central bank and the nominal money stock Initially, a functional form is posited to explain the desired by the public at the inherited price level. public’s demand for real money holdings. This form (The desired nominal money stock is the product of is assumed to depend upon time, a nominal interest the desired real money stock and the price level.) rate, and real expenditure. In order to estimate this Combining (3) and (4) yields functional form, dependent and independent variables must be chosen and a lag structure imposed on the latter.
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