Can Agents Learn to Rational Expectations? Some Results on Convergence and Stability of Learning in the UK Stock Market

Rational expectations are frequently justified as the point of convergence of agents' learning process. When agents' learning feeds back on the actual law of motion of the economy convergence of their learning rule to a rational expectations equilibrium (REE) is not guaranteed however. Applying new methods to analyse the convergence of learning in a model of UK stock prices we find evidence that agents could not have learned to form rational expectations if they had attempted to estimate the long-run dynamics of the model. If, however, agents have strong priors and impose a unit root on the model, thus confining their learning to the short run dynamics, there is evidence that recursive learning may eventually lead them to a REE. The learning process on the path to this equilibrium is highly volatile, suggesting that learning may help to explain excess volatility in UK stock prices.