Policy design with private sector skepticism in the textbook New Keynesian model

How should policy be optimally designed when a monetary authority faces a private sector that is somewhat skeptical about policy announcements and which interprets economic data as providing evidence about the monetary authority's preferences or its ability to carry through on policy plans? To provide an answer to this question, we extend the standard New Keynesian macroeconomic model to include imperfect inflation control (implementation error relative to an inflation action) and Bayesian learning by private agents about whether the monetary authority is the committed type (capable of following through on announced plans) or an alternative type (producing higher and more volatile inflation). In a benchmark case, we find that optimal policy involves dramatic anti-inflation actions which include an interval of deflation during the early stages of a plan, motivated by investing in a reputation for strength. Such policies resemble recommendations during the 1980s for a "cold turkey" approach to disinflation. However, we also find that such policy is not robustly optimal. A more "gradualist" policy arises if the initial level of credibility is very low. We also investigate a setting where the alternative monetary authority follows a simple behavioral rule that mimics variations in the committed authority's policy action but with a bias toward higher and more volatile inflation. In this case, which we call a "tag along" alternative policymaker, a form of gradualism is always optimal.