Convergence of least squares learning mechanisms in self-referential linear stochastic models

Abstract

We study a class of models in which the law of motion perceived by agents influences the law of motion that they actually face. We assume that agents update their perceived law of motion by least squares. We show how the perceived law of motion and the actual one may converge to one another, depending on the behavior of a particular ordinary differential equation. The differential equation involves the operator that maps the perceived law of motion into the actual one.