Academic journal article American Economist

An Innovative Money Multiplier

Academic journal article American Economist

An Innovative Money Multiplier

Article excerpt


Although money multiplier analysis is a basic component of all courses that deal with monetary theory and policy, empirical applications that explain actual changes in the money supply are rarely used. In virtually all cases, multiplier analysis is illustrative and conceptual, since real-world data on money supply changes cannot be used with most textbook multipliers (e.g., see Miskin, 2004, p. 377). The major reason for this is that precise empirical multiplier analysis (e.g., Friedman & Schwartz, 1963), is very complex and cumbersome both in respect to calculations and interpretation. Even though money supply targeting is no longer a policy consideration, the whole process of money creation and variations in monetary growth rates are still of interest from the standpoint of monetary theory.'

The purpose of this paper is to present an innovative money multiplier model that is more "user-friendly". This new multiplier will be compared to the standard Friedman and Schwartz model in respect to derivation, use, and interpretation of results. To illustrate the applications of this new multiplier, it will be used to analyze money supply changes in two periods: the Great Depression (1929-1933), and a recent period of unusually slow monetary growth (1991-1994).

The Friedman and Schwartz Multiplier

Humphrey (1987) credits Friedman and Schwartz (1963), and also Philip Cagan (1965), for expanding the concept of the deposit multiplier into a money multiplier. Such multipliers are derived from a defined ratio of the money supply (M) to the monetary base (R+C, or total reserves plus currency). Friedman and Schwartz (1963, p.791) utilize the following multiplier in their empirical analysis (See Appendix I of this paper for the derivation):

M = H x [D/R (1 + D/C)]/ [D/R + D/C] (1)

The money supply (M) is a function of the three "proximate determinants": the monetary base or high powered money (H), the deposit to reserve ratio (D/R), and the deposit to cash ratio (D/C). Changes in H reflect changes in the liabilities of the central bank, while D/R is heavily influenced by activities of the banking system, and D/C reflects changes in the public's demand for currency.

In order to estimate the impact of these determinants on the money supply over a specified time interval, Friedman and Schwartz transform equation (1) into log form, and then, for each proximal determinate, assume the other two determinates are unchanged in order to identify the ceteris paribus influence of each determinate (1963, p. 995). Since this technique will not account for 100 percent of the variation in M, it is then necessary to calculate a residual term which Friedman and Schwartz label the "interaction" term. This term reflects the combined, but inseparable, influences of the two ratios (D/R, D/C).

This brief explanation of the Friedman and Schwartz multiplier reveals two potential problems. Most importantly, to the extent that the interaction term is significant, the analytical specificity of the multiplier is reduced. Secondly, the log calculations that are necessary are somewhat cumbersome (see Appendix I for more details). The new money multiplier presented in the next section offers a solution to these problems.

The New Monetary Base Multiplier

Unlike the usual multipliers that are always expressed in levels, this new monetary base (MB) multiplier is defined in first difference terms:

[M.sub.t] - [M.sub.t-1] = 1/[MB.sub.t-1] /[M.sub.t-1]) x ([MB.sub.t] - [MB.sub.t-1]) (2)

The change in the money supply (M) is equal to the reciprocal of (MB/M) times the change in the monetary base. The logic here is analogous to the simple textbook money multiplier (l/legal reserve requirement times the change in total reserves), with MB/M substituted for the legal reserve requirement and the [DELTA]MB substituted for total reserves. As long as the MB/M ratio remains constant, any change in MB will have a direct and proportional impact on M. …

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