Learning with bounded memory in stochastic models

Learning with bounded memory in stochastic frameworks is incomplete in the sense that the learning dynamics cannot converge to a rational expectations equilibrium (REE). The properties of dynamics arising from such rules are studied for standard models with steady states. If the REE in linear models is in a certain sense expectationally stable (E-stable), then the dynamics are asymptotically stationary and forecasts are unbiased, but the economy has excess volatility. We also provide similar local results for a class of nonlinear models with small noise.