Learning, convergence, and stability with multiple rational expectations equilibria

Abstract

For a linear model with multiple rational expectations equilibria (REE) we discuss the set of possible REE. Solutions include (i) locally unique minimal state variable solutions, taking an AR(1) form and (ii) continua of solutions which may depend on sunspots. We analyze the convergence of econometric learning to the different REE. There exist cases with more than one stable AR(1) solution. It is also possible for a continuum of solutions to be stable, but this property is not robust to overparametrization. An application is developed, and it is suggested that the exhibited phenomena may arise in applied macroeconomic models.