Error learning behaviour and stability revisited

We study the implications of error learning behaviour on the global dynamic properties of stationary equilibria in discrete time deterministic models under bounded rationality. We assume agents' ability to learn from the past performance of their expectations formation mechanism, so that such mechanism itself is made endogenous. We determine sufficient conditions under which this type of error learning behaviour enhances the stability properties of the economy. Also, we show that the set of error learning rules compatible with these conditions is not small in a topological sense and that this set can be used to approximate, with arbitrary precision, alternative learning rules that have been considered in the literature. We focus on the consequences of these results on a class of models in which agents possess fading memory, along the lines of a thread of recent literature. In particular, in this framework we treat adaptive expectations as a special case. We propose a generalisation of this expectation mechanism with fading memory which tries to capture the attitude of agents in the presence of exogenous shocks or structural breaks.