Learning in linear models with expectational leads

This paper provides an adaptive learning algorithm for linear stochastic models with expectational leads in which forecasts for an arbitrary period ahead of the current state feed back into the economic system. The concept of an unbiased forecasting rule with generates rational expectations equilibria is introduced. It is shown that the learning scheme provides an arbitrary precise approximation of an unbiased forecasting rule such that all trajectories generated by the scheme converge to rational expectations equilibria globally for all initial conditions. We strengthen convergence results in relaxing standard assumptions and in providing conditions ensuring algorithm convergence which are much easier to verify and to interprete as compared to those known previously in the literature.