Prediction Error Learning and Rational Expectations in Autoregressive Models with Forecast Feedback

The rational expectations hypothesis is supported if rational expectations are stable with respect to reasonable learning procedures. We consider the Stochastic Gradient-Algorithm as a boundedly rational learning procedure in an univariate ARX-Model with forecast feedback. We prove that whenever there exists a stable rational expectations equilibrium and the influence of the forecast feedback is limited the learning agents cannot destabilize the model and learn to form rational expectations with probability one.