The Stability of Exchange Rate Dynamics under Perfect Myopic Foresight

Abstract

The stability of financial markets under conditions of perfect foresight has recently been a subject discussed extensively by monetary economists; see e.g. Sidrauski [1967], Burmeister and Dobell [1970], Nagatani [1970], Olivera [1971], Sargent and Wallace [1973], Black [1974]. One of the main findings to come out of this literature is that the dynamics of such markets under perfect foresight will typically be associated with saddle-point instability. That is, unless the initial conditions happen to place the system somewhere on the stable arm of the saddle point, the system will tend to arch around the equilibrium and ultimately to diverge from it. One financial market of particular importance is the foreign exchange market. In a recent article, Dornbusch [1976] has developed an interesting model analyzing the role of exchange rate expectations in the dynamic adjustment of the exchange rate following an exogenous change in monetary policy. While most of his analysis is based on an arbitrary regressive expectations hypothesis, he also considers what he calls expectations, when the hypothesis he introduces is consistent with a form of perfect myopic foresight.2 This is obviously desirable, since as he argues, perfect myopic foresight is the only assumption which is not arbitrary and does not in general involve systematic forecasting errors. At first sight, the stability of the Dornbusch model under consistent expectations may appear to contradict the above monetary literature. The purpose of this paper is therefore to investigate more fully the relationship of the Dornbusch analysis to the perfect foresight model. It is shown how the introduction of perfect myopic foresight into his model does indeed generate saddle point type behavior. Stability of the system can then be achieved by following a procedure originally outlined by Sargent and Wallace [1973].3 Essentially this involves