Rational Learning and Rational Expectations

A general formulation of a rational (Bayesian) learning model with rational expectations is given. The martingale convergence theorem is used to prove that in any rational learning model, each agents posterior assessments converge as time passes. An example is developed to show that, with sufficient smoothness, this implies convergence of beliefs to accurate beliefs. The usefulness of rational learning models in investigating how agents learn about the relation between prices and states in a rational expectations equilibrium is discussed.