Bayesian learning behaviour and the stability of equilibrium forecasts

Abstract

The issue of learning in an intertemporal, stochastic, rational expectations, setting is studied here. We study a sequence of games in which the stochastic kernel that links the state variable is unknown. Successive stage games are played by successive generations of identical players. Each generation makes a rational expectations forecast of the state, given their belief about the true kernel and the equilibrium implemented by the players. Beliefs are updated by Bayes rule after observing the actual state. The results concern the dynamic behaviour of the forecasts, beliefs, and the state variable. We show that while full learning in the sense of ultimately learning the true transition structure of the economy may not occur, partial learning in the sense of being able to better predict the future of the state variable does occur. We also characterize the limiting behaviour of the processes of beliefs, forecasts, and the state variable.