Convergence of Least-Squares Learning in Environments with Hidden State Variables and Private Information

We study the convergence of recursive least-squares learning schemes in economic environments in which there is private information. The presence of private information leads to the presence of hidden state variables from the viewpoint of particular agents. By applying theorems of Ljung, we extend some of our earlier results to characterize conditions under which a system governed by least-squares learning will eventually converge to a rational expectations equilibrium. We apply insights from the learning results to formulate and compute the equilibrium of a version of Townsend's model.