Stability properties for learning with heterogeneous expectations and multiple equilibria

This paper examines learning with heterogeneous expectations in a simple macroeconomic model with multiple equilibria where expectations are formed from heterogeneous forecast functions. Stability properties of the equilibria are determined by the distribution of heterogeneity. These results differ greatly from those which impose homogeneous expectations a priori. When the distribution of heterogeneity is allowed to vary, the stability conditions obtained guarantee that each equilibrium is stationary when it is stable under learning. The central result is that the two equilibria exchange stability when the mean squared error of using the simpler updating rule is minimized.