Existence of adaptively stable sunspot equilibria near an indeterminate steady state

We examine the nonlinear model x(l) = ElF(x(l+1)). Markov stationary sunspot equilibria (SSEs) exist near an indeterminate steady state, (x) over cap = F((x) over cap), provided \F'(x) over cap \ > 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) over cap that are E-stable, and therefore locally stable under adaptive learning, if F'((x) over cap) < -1.