Stable sunspot solutions in models with predetermined variables

We consider a linear stochastic univariate rational expectations model, with a predetermined variable, and provide alternative representations of stationary sunspot equilibria (SSEs). For a strict subset of the parameter space there exist SSEs that are locally stable under least-squares learning provided agents use a common factor representation for their estimated law of motion. These results indicate that for some parameter regions SSEs are more likely to arise under private agent learning than previously recognized.