A Closer Look at Long-Run U.S. Money Demand: Linear or Nonlinear Error-Correction with M0, M1, or M2?

By Haug, Alfred A.; Tam, Julie | Economic Inquiry, April 2007 | Go to article overview

A Closer Look at Long-Run U.S. Money Demand: Linear or Nonlinear Error-Correction with M0, M1, or M2?


Haug, Alfred A., Tam, Julie, Economic Inquiry


I. INTRODUCTION

The stability of money demand has been a long-standing issue. (1) Lucas (1988) informally analyzes the stability of a log-linear M1 money demand function and concludes that real money demand is a stable function, and he supports earlier findings of Meltzer (1963) with an income (or wealth) elasticity of around unity. (2) With the development of cointegration methods (Engle and Granger 1987), numerous empirical studies have applied these techniques to long-run U.S. money demand. Examples are Baba, Hendry, and Starr (1992), Haferand Jansen (1991), Hoffman and Rasche (1991), and Miller (1991), who find support for a cointegrated money demand model with either M1 or M2. (3) King et al. (1991) also find support for cointegration with M2 and a short-term interest rate.

In contrast to these studies, others have argued against a stable U.S. money demand function in the postwar period. For example, Friedman and Kuttner (1992) do not find support for cointegration, particularly when the period March 1970 to April 1990 is considered. Similarly, Miyao (1996) studies the behavior of the M2 money demand function over the period from 1959 to 1993 with quarterly data and various interest rates, in levels and in logs. Miyao concludes that M2 is not a useful intermediate target for monetary policy in the 1990s. (4) However, Carlson et al. (2000) reach the conclusion that M2 does have predictive content for nominal economic activity and that the real M2 money demand function is stable but only after accounting for financial innovation in the first half of the 1990s.

Two recent papers, Ball (2001) and Stock and Watson (1993), focus on especially long data sets for the United States and M1. Stock and Watson (1993) analyze various estimation methods for cointegrating relationships and illustrate their performance for money demand functions with annual data from 1900 to 1987. They pay particular attention to the postwar period and use monthly data in addition to annual data for this period. They employ a semi-log-linear real M1 money demand model with real net national product and the level of the 6-mo commercial paper rate. For the postwar period, they also consider the 90-day Treasury bill rate and the 10-yr Treasury bond rate. They compare and contrast their results to those of various others. They also carry out recursive estimations to check their results for stability.

Stock and Watson (1993) conclude that a long span of data is needed to estimate long-run money demand functions precisely. Their overall evidence is in favor of a stable long-run money demand function with an income elasticity near one and an interest rate semielasticity near -0.10. However, the postwar data are found to be not very informative. A lack of low frequency variation in the postwar data, as suggested by Lucas (1988), does not allow a disentangling of the effects of output and interest rates on money demand for this time period. Estimates are imprecise and sensitive to subsample specifications due to substantial colinearity.

Ball (2001) revisits the M1 money demand model of Stock and Watson (1993), using the same data set but extended through 1996. He applies the same array of estimation techniques as Stock and Watson did. Ball obtains precise estimates over the postwar period for his extended data set: an income elasticity of approximately 0.5 and a semielasticity of -0.05 for the interest rate. He does not find support for a velocity specification. The M1 model is not stable over the period 1900-1996.

Lutkepohl, Terasvirta, and Wolters (1999) apply a nonlinear error-correction model with smooth transition adjustment to capture instabilities in the linear cointegration model. The long-run equilibrium is described by a linear cointegrating relation, and the adjustment to this long-run equilibrium is nonlinear. They analyze German M1 money demand. Granger and Terisvirta (1993), Terasvirta (1998), and Van Dijk, Terasvirta, and Franses (2002) provide details on the econometric theory for estimating and testing such nonlinear models. …

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