Wilson, Edgar J., Exchange rate variability: a case of non-linear rational expectations?, Department of Economics, University of Wollongong, Working Paper 90-7, 1990, 15.
A number of authors have recently shown that nominal spot exchange rates closely approximate random walks and that out-of-sample predictions of the random walk model are as good, if not better, than those of most economic models.
This paper develops an alternative economic explanation of exchange rate behaviour. We begin by modifying a simple mean-variance optimising model of Begg (1984) to incorporate rational expectations in both the first and second moments of the distribution of future exchange rates. By taking rational expectations of the conditional variance we obtain a simple nonlinear difference equation which describes the dynamic evolution of the equilibrium exchange rate.
The properties of these rational expectations paths are then considered in detail. It is observed that (similar to many linear rational expectations saddlepoint solutions) convergence and uniqueness are not necessarily guaranteed and so it is important to consider the conditions which are necessary to achieve stability. Finally, it is shown that for particular parameter values, the equilibrium exchange rate may appear to follow seemingly random paths. This phenomenon is not due to any stochastic influence, but is a result of the dynamic non-linear nature of the deterministic model.