The Development of a Model for Estimating a Velocity Function for the Money Supply: A Tool for Policymakers

This paper develops a model for the velocity of the money stock that simultaneously estimates the functional form and the parameters of the velocity equation. The study is based on the data since 1991, a period characterized by an abrupt shift in the velocity level. The results show that a Box-Cox model may be more appropriate than a logarithmic model for specifying a velocity function. The accepted model and the estimated coefficients should have useful implications for the policymakers. I. Introduction A stable and predictable velocity of money has important implications for macroeconomic policy because the velocity is a link between the monetary aggregate and nominal GDP. From 1970 through the mid-1980s the Federal Reserve Board found Ml (currency plus demand deposits, traveler's checks and other checkable deposits) to be a useful gauge of economic and financial conditions and employed it as an intermediate target for achieving macroeconomic objectives. In recent years, however, M1 has been found to be less useful since its velocity could not be explained or estimated with reliability. The Fed is now considering (M I plus saving deposits and money market mutual fund balances) as a potential tool for attaining desirable levels of GDP, controlling inflation and pursuing other macroeconomic objectives. Consequently, the behavior of the velocity is becoming the subject of much research (see for example Carlson et al (2000), Duca (200O)). Feldstein and Stock ( 1994) investigated the relationship between and nominal GDP and found it to be stable. Since the mid-1990s, however, most models predicted the quantity of to be less than actual amount and correspondingly the velocity to be higher than its actual value. Some authors have labeled this as the case of money since for the given levels of GDP the level of should have been higher. Duca (2000) believes that the missing M2 problem may be resolved when the effect of the shift in bond mutual fund costs on the quantity of money is taken into account. Carlson, et al (2000) argued that the recent instability in the magnitude of the velocity was characterized by a permanent upward shift, which began around 1990 and was largely over 1994. They hypothesized that during this period, households permanently reallocated a part of their assets from time deposits to mutual funds and argued that this substitution could be explained by an appropriately measured opportunity cost. A number of other papers have analyzed the characteristics of velocity in recent years (e.g. Feinman and Porter (1992), Estrella and Mishkin (1997), Orphanides and Porter ( 1998)), but no consensus has been reached regarding the appropriate method of specifying the relationship between the velocity and its explanatory variables. It should therefore be useful to further explore this relationship before a monetary aggregate such as M2, could be used as a policy alternative by the Fed. This paper reconsiders the velocity function derived from a standard money demand equation. A Box-Cox transformation of variables is used to specify the functional form of the income velocity of money. In a time-series regression, seemingly autoregressive residuals may be due to an incorrect functional specification or autocorrelation or both. The Box-Cox model of Savin and White ( 1978) will, therefore, be used to simultaneously estimate the functional form of the equation and test for autocorrelation. A likelihood ratio test is employed to compare alternative specifications of the velocity function. The equation specifying the velocity function is described in section 2. The data and empirical results are presented and analyzed in section 3. Concluding remarks are made in section 4. II. The Model Celeris pari bu s, the velocity of money varies directly with the level of real income. The coefficient of real income in a money demand function is usually less than 1, which also suggests that the coefficient of income (β^sub 1^) in equation (4) should be positive. …