Disinflations in a model of imperfectly anchored expectations

We study disinflations under imperfect credibility of the central bank. We propose a framework to model imperfectly credible announcements and use it to study the distribution of the output cost for a given disinflation. Imperfect credibility is modeled as the extent to which agents rely on adaptive learning to form expectations. Lower credibility increases the mean, variance, and skewness of the distribution of the sacrifice ratio. When credibility is low, disinflations become very costly for adverse realizations of the shocks. But, an opportunistic disinflation, a disinflation implemented after a period of below trend inflation, can significantly lower the sacrifice ratio. With simulated data, we reinterpret the reduced form evidence in sacrifice ratio regressions. Coefficient estimates from these regressions can be misleading for policymakers considering the cost of disinflation.