This paper describes two models of an agency that is collecting and reporting observations on a dynamical linear stochastic economy. The first is a "classical" model, with the agency reporting data that are the sum of a vector of "true" variables and a vector of measurement errors that are orthogonal to the true variables. The second is a model of an agency that uses an optimal filtering method to construct least-squares estimates of the true variables. These two models of the reporting agency imply different likelihood functions. A model of the investment accelerator is used as an example to illustrate the differing implications of the models.

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.