Central bank reputation with noise

This paper presents a model of central bank reputation where inflation is a noisy function of central bank actions. In the model, a central bank can be “hawkish”, with a relatively high penalty for taking inflationary actions, or “dovish”, with a relatively low penalty. The central bank's type varies according to a Markov process, and its reputation is the Bayesian posterior of households that it is a hawkish type. We show analytically that no Markov pooling equilibria exist: hawkish and dovish central banks must act differently. We then argue that without sufficient noise, it is difficult for Markov separating equilibria to exist either. But with sufficient noise, we show computationally that pure strategy separating equilibria exist and have appealing characteristics: both hawkish and dovish banks choose lower inflationary actions than they would in the absence of reputation considerations, and both types are most aggressive in attempting to gain a hawkish reputation when their current reputation is middling.