Stability Analysis of Heterogeneous Learning in Self-Referential Linear Stochastic Models

There is by now a large literature characterizing conditions under which learning schemes converge to rational expectations equilibria (REEs). A number of authors have claimed that these results are dependent on the assumption of homogeneous agents and homogeneous learning. We study the local stability of REEs under heterogeneous adaptive learning, for the broad class of self-referential linear stochastic models. We introduce three types of heterogeneity related to the way agents learn: different expectations, different degrees of inertia in updating, and different learning algorithms. We provide general conditions for local stability of an REE. Even though in general, hetereogeneity may lead to different stability conditions, we provide applications to various economic models where the stability conditions are identical to the conditions required under aggregation. This suggests that heterogeneity may affect the local stability of the learning scheme but that in most models aggregation works locally.