Multiple Equilibria in Heterogeneous Expectations Models

This paper fills an important gap in the literature on determinacy and existence of sunspot equilibria in stochastic linear self-referential models. The results in this paper demonstrate that heterogeneity in expectations may alter a model's regions of determinacy. We show how to associate with a heterogeneous expectations model (HE-model) a rational expectations model (ARE-model), the solutions to which are the equilibria of the HE-model. This association recasts the analysis of determinacy in the HE-model to analysis of determinacy in the ARE-model. We proceed to study a forward looking model and find that the stability properties of rational expectations models may not be robust. In particular, we present new results showing that in some models even a very small fraction of non-rational agents may preclude rational agents from coordinating on sunspots. Also, we present parameterizations of the model in which sunspots exist in the heterogeneous model when they do not exist in the rational expectations version of the model.