Dynamic Macroeconomic Stability with or without Equilibrium in Money and Labour Markets

A familiar proposition in the descriptive monetary growth literature is that perfect foresight in predicting the rate of inflation will typically cause saddlepoint-type instability in the movement of prices.' In an important and influential paper, Sargent and Wallace (1973) have shown that in a simple one-dimensional model stability can be restored by dropping the conventional assumption of continuous prices and instead allowing discontinuous price jumps to equilibrate the money market. In this paper we examine a two-dimensional system that, unlike the simple Sargent-Wallace formulation, is capable of generating dynamic equilibria which are legitimate saddlepoints, and thus we are able to analyse the behaviour along stable paths.2 These stable paths are of particular economic interest because they are implied by the familiar hypothesis that economic agents form convergent rational expectations.3 Our interest in a two-dimensional macroeconomic model is more than a trivial mathematical generalization. For example, in the one-dimensional SargentWallace model, the assumption of convergent rational expectations necessitates that prices adjust instantaneously, so that the economy is always at the dynamic equilibrium point. If in actuality prices in an economy adjust only sluggishly, then this procedure is illegitimate. We introduce a labour market and we allow for the possibility that the money market and the labour market will adjust at finite rates rather than being in continuous equilibrium. As relative speeds of adjustment vary in the two markets, this extended model is capable of generating a variety of dynamic time paths, including the familiar saddlepoint behaviour, convergence to a stable node, or divergence from an unstable node. The type of dynamic equilibrium that will prevail depends upon the values of parameters and hence is an empirical issue. The methods for stabilizing the system in the various cases, determined by the pattern of adjustment speeds, are described in Section I, with the more technical details being relegated to the Appendix. In particular, if the price level is not free to adjust, we show that stability can be obtained through the labour market. And, conversely, if labour market adjustment is not possible at an instant of time, we show how stability can be obtained through the money market. In Section II we analyse the effects of expansionary monetary policy for the