Refinement of dynamic equilibrium using small random perturbations

Abstract

We propose a refinement process of dynamic equilibria based on small random perturbations (SRPs) of the backward perfect foresight (bpf) equilibrium map in a class of one‐step, forward‐looking dynamic models. An equilibrium is selected if its stationary measure is the limit of the stationary measures associated with the processes generated by the SRPs of the bpf maps, as the perturbation size approaches 0. We show that, for full measure sets of parameter values of a large class of one‐parameter families of unimodal bpf maps, only determinate cycles or the chaotic sunspot equilibrium defined by Araujo and Maldonado (2000) is selected. Two examples are provided illustrating such refinement process.