A note on sunspot equilibrium in sequential economies

Abstract

In this paper, we consider the occurrence of sunspot equilibria in the proximity of the steady state of a nonlinear aggregative dynamic economy with possibly predetermined variables. By means of [J. Econ. Theory 80 (1998) 59] geometric method, sunspot equilibria can be studied through the invariance properties, in the deterministic equilibrium dynamics, of their supports. We show that such suitable invariant sets exist, around a steady state, if the steady state is locally indeterminate. Furthermore, when the steady state is locally determinate, no suitable invariant sets exist in a neighborhood of that steady state, independently of the properties of underlying sunspot equilibria, thus clarifying an open issue in the literature on sunspot equilibria in sequential economies.