Incomplete information, higher-order beliefs and price inertia

The question that motivates this paper is how incomplete information impacts the response of prices to nominal shocks. Our baseline model is a variant of the Calvo model in which firms observe the underlying nominal shocks with noise. In this model, the response of prices is pinned down by three parameters: the precision of available information about the nominal shock, the frequency of price adjustment, and the degree of strategic complementarity in pricing decisions. This result synthesizes the broader lessons of the pertinent literature. However, this synthesis provides only a partial view of the role of incomplete information. Once one allows for more general information structures than those used in previous work, one cannot quantify the degree of price inertia without data on the dynamics of higher-order beliefs, or of the agents' forecasts of inflation. We highlight this with three extensions of our baseline model, all of which break the tight connection between the precision of information and higher-order beliefs featured in previous work.