Exogeneity within the M2 Demand Function: Evidence from a Large Macroeconomic System

A large body of literature investigates whether a stable and predictable long-run association between money and its arguments exists. One point of variation between models is whether to include an interest rate measure directly within the long-run relationship. Several recent studies indicate that empirical findings are sensitive to the choice. Therefore, the present article reexamines the empirical significance of the interest rate within a four-equation macroeconomic system. The results suggest that the interest rate (1) may be excluded from the M2 demand function, (2) is strongly exogenous to most of the system's remaining variables, and (3) may represent a common trend. (JEL E41, E52, C32) I. INTRODUCTION Much of recent macroeconomic literature has been dedicated to investigating whether long-run relationships exist between macroeconomic variables. (1) Such preoccupation is understandable given the myriad models in which these relationships play a dominant role. A significant portion of this literature has focused on whether a long-run relationship exists between money demand and its arguments. (2) Of course, the close association between the variables is an integral part of theories that suggest that the monetary authority may qualitatively influence the direction of the aggregate economy. The estimation of long-run money demand models have differed in their methodological approach and in countless other ways. One specific way in which they may differ in whether the investigator(s) incorporates an interest rate measure directly within the long-run relationship. For example, although Fischer and Nicholetti (1993) and Baba et al. (1992) incorporate various interest rate measures to identify the long-run money demand function, Hendry and Mizon (1998) and Hendry and Ericsson (1991) estimate the long-run money demand function without an interest rate measure. Although the theoretical importance of the interest rate within the money demand function predates Pigou's (1917) classic treatment and has been discussed at length elsewhere, the importance empirically has recently been high-lighted by Sims (1980). In examining whether money Granger causes output, Sims's results suggest that the tests are sensitive to whether a short-term interest rate measure is included. Campbell and Perron (1991) further argue that Sims's findings are an outgrowth of whether the trivariate model of money, prices and output are cointegrated, that is, I(0), or whether reduction to stationarity requires the introduction of a fourth variable, the interest rate. Reduction to stationarity is important because estimating Granger causality with nonstationary residuals may yield biased estimates due to nonstandard residual distributions. The present article reexamines the significance of the interest rate within the long-run money demand function. Specifically, I examine two aspects of interest rate-money behavior. The initial examination is to test whether the interest rate measure (three-month Treasury bill rate) can be directly excluded from the long-run M2 demand function. Following the methodology advanced by Hendry and Mizon (1993), Johansen and Juselius (1992, 1994), and Ericsson et al. (1990), the test involves estimating the long-run relationship with the interest rate measure and then impose the overidentifying zero restriction. The associated log-likelihood ratio statistics are distributed [chi square] (n) where (n) represents the number of overidentifying restrictions. This approach, however, only examines whether the interest rate may be removed from the long-run money demand vector. A second area of interest is concerned with the short-run responses of the interest rate. More specifically, the short-run responses provide a test for Granger causality within the cointegrated variables. Following Ericsson et al. (1998), Granger causality is estimated where one or more cointegrated variables reject strong exogeneity. …