Inflation Expectations and Central Bank Communication with Unknown Prior

We construct a noisy information model of central bank communication on future inflation rates and highlight an informational friction that plays a key role in explaining several empirical properties of firms' inflation expectations. Using a survey of Japanese firms' inflation expectations, we document new empirical facts related to the size of firms and their inflation expectations. We observe a persistent deviation of expectations from the central bank's inflation target and find that the deviation is monotonically increasing in firm size, while the degree of the forecasting imprecision, responsiveness to actual inflation, and the heterogeneity in firms' expectations are monotonically decreasing in firm size. To reconcile these empirical regularities, we construct a dynamic model of inflation expectation formation by Bayesian firms where the central bank's inflation forecast serves as a noisy public signal of future inflation rates and propose an informational friction in the communication about future inflation: the central bank's prior about the future inflation rate, which is unknown to firms. In this setup, the sluggishness of the adjustment of inflation expectations is amplified by the central bank's communication. Moreover, this friction drastically changes the role and the effect of central bank communication on firms' expectations formation. Firms utilize the inflation forecast as a signal not of the level but of changes in future inflation rates.