Restricted perception equilibria and rational expectation equilibrium

This paper studies a cobweb economy in which agents make decisions using a misspecified model of their stochastic environment. Specifically, the agents' model of the price process is restricted to be a moving average of order q (MA(q)), minimizing the mean square of their forecast error. We prove existence and uniqueness of this MA(q)-optimal equilibrium and we show that, as q goes to infinity, the MA(q)-optimal equilibrium converges in mean square towards the rational expectations equilibrium. The speed of convergence is dictated by the persistence of the underlying exogenous process. Lastly, we show that when all other agents use the correctly specified model, the misspecified MA(q) model can provide accurate forecasts. This suggests that, if agents have to pay for their forecasting model and if the correctly specified model is more costly, a situation in which all agents use the correctly specified model might not be an equilibrium.