Adaptive learning in an expectational difference equation with several lags : selecting among learnable REE

Abstract

It is demonstrated in this paper that adaptive learning in least squares sense may be incapable to reduce, in a satisfactory way, the number of attainable equilibria in a rational expectations model.The model investigated, as an illustration, is the monetary approach to exchange rate determination that is augmented with technical trading in the currency market in the form of moving averages since it is the most commonly used technique according to questionnaire surveys.Because of technical trading in foreign exchange, the current exchange rate is dependent on jmax lags of the exchange rate, and the model has, therefore jmax + 1 nonbubble rational expectations equilibria (REE), where most of them are adaptively learnable.However, by assuming that a solution to the model should have a solution to a nested model as its limit, it is possible to single out a unique equilibrium among the adaptively learnable equilibria that is economically meaningful.Key words: asset pricing, heterogenous agents, least squares learnability, rational expectations equilibria and technical trading JEL classification numbers: C62, F31, G12