The Dynamics of Learning in Optimal Monetary Policy

This paper analyzes the dynamic properties of a standard New Keynesian monetary policy model when private agents expectations are assumed to be formed under a learning mechanism. As pointed out in the literature, learning with decreasing gain estimators tends to lead to convergence to the rational expectations equilibrium; however, under constant gain, persistent learning dynamics prevail and nonlinear dynamics of the state variables may subsist over the long term. By assuming a gain sequence that is asymptotically constant, explicit local and global stability results are presented for two specifications of an optimal monetary policy model. In the first setting, the central bank believes that private agents possess rational expectations; while inthe second, the bank incorporates the learning rule in its optimal decisions. In such a framework we find out interesting long term results, in particular, the presence of endogenous business cycles should bestressed as an expected outcome.