Managing Expectations in the New Keynesian Model

We study the optimal monetary policy in a setting where the private sector is forward-looking and learning about the type of central bank in place. We consider two types of central bank, one patient type that can commit and one opportunistic type that is myopic and cannot commit. Being able to commit or not, the central bank in place chooses inflation policies optimally, taking into account the learning and rational expectation of the private sector. We show that the equilibrium can be obtained as a solution to a recursive optimization of the committed type in which the actions of the opportunistic type are subject to an incentive compatibility constraint. The numerical solution to a calibrated model reveals that the committed central bank with good initial reputation adopts policies similar to the standard solution under full commitment, whereas the committed central bank with poor initial reputation aims at building reputation with anti-inflation policies that involve real costs. If the opportunistic central bank with good initial reputation is in place, there will be lengthy real stimulations with gradually rising actual and expected inflation, followed by stagflation when the history of positive inflation surprises depletes the central bank's reputation.