Learning in a misspecified multivariate self-referential linear stochastic model

This paper introduces a general method to study learnability of equilibria resulting from agents using misspecified forecasting models. One can represent the actual and perceived laws of motion (PLM) as seemingly unrelated regressions and then linearly project the actual law of motion into the same class as the PLM. I present an application using the New Keynesian IS-AS model with inertia under several simple Taylor policy rules. It turns out that the results presented in Bullard and Mitra [2002. Learning about monetary policy rules. Journal of Monetary Economics 49, 1105-1129; 2005. Determinacy, Learnability, and Monetary Policy Inertia. Journal of Money, Credit, and Banking, forthcoming] are robust when agents do not include all the state variables in their forecasting models.