Some economists continue to insist that linearity is a good assumption for all economic time series, despite the fact that economic theory provides virtually no support for the assumption of linearity; see, e.g., Barnett and Chen (1986, 1988). The controversy is partly due to the fact that the currently available tests do not test for the existence of chaos or nonlinearity produced from within the structure of the economy. As recently pointed out by Day (1992), the tests have no way of determining the sources of the chaos or nonlinearity. In other words, even if the economy is totally linear and stable, the current tests, such as the Brock–Dechert–Scheinkman (Brock 1986), could still catch evidence of nonlinearity or even chaos in economic data if the economy is affected by a chaotic and unstable surrounding weather system. Therefore it is interesting if we can identify some sources of potential nonlinearity and instability within the economic system.

In this chapter we theoretically show that money velocity is nonlinear within a monetary general-equilibrium model and that a traditional money velocity function may be unstable within the economic system. We use the comparison between model simulation and estimation to examine the relevance of our theoretical results. Traditionally money velocity is viewed as a constant or at least a stable function of its few determinants. The unusual behavior of money velocity and the instability of the traditional money demand function since the late 1970s in the United States has called for a reexamination of the traditional views; see, e.g., Stone and Thornton (1987).

Several lines of research have been pursued in recent monetary economicliterature.