Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models

Abstract

Linear models involving expectations of future endogenous variables generally have multiple rational expectations equilibria. This paper investigates the stability of solutions in the disequilibrium sense of whether, given a small deviation of expectations functions from some rational expectations equilibrium, the system returns to that solution under a natural revision rule. Weak and strong local stability are distinguished. Stability conditions are calculated for a simple general linear model and applied to two macroeconomic examples. In some cases there is a unique stable equilibrium. In other cases a continuum of equilibria forms a weakly but not strongly stable class.