Expectational Stability of Stationary Sunspot Equilibria in a Forward-Looking Linear Model

We consider the stability under adaptive learning of the complete set of solutions to the model x(t)= b*Ex{t+1} when |b| > 1. In addition to the fundamentals solution, the literature describes both finite-state Markov sunspot solutions and autoregressive solutions depending on an arbitrary martingale difference sequence. We clarify the relationships between these solutions and show that the stability properties of equilibria may depend crucially on the representation used by agents in the learning process. Autoregressive forms of solutions are not learnable, but finite-state Markov sunspot solutions are stable under learning if b < -1