Existence of Adaptively Stable Sunspot Equilibria Near an Indeterminate Steady State

Abstract

We examine the nonlinear model x(t)=E(t)F(x(t+1)). Markov SSEs (stationary sunspot equilibria) exist near an indeterminate steady state, x=F(x), provided |F'(x)| >1. Despite the importance of indeterminacy in macroeconomics, earlier results have not provided conditions for the existence of adaptively stable SSEs near an indeterminate steady state. We show that there exist Markov SSEs near x that are E-stable, and therefore locally stable under adaptive learning, if F'(x)<-1.

Keywords: Indeterminacy, Learnability, Expectational Stability, Endogenous Fluctuations

JEL Classification: C62, D83, D84, E31, E32