Calvo pricing and imperfect common knowledge: a forward looking model of rational inflation inertia

In this paper we derive a Phillips curve with a role for higher order expectations of marginal cost and future inflation. We introduce a small idiosyncratic component in firms’ marginal costs and let the economywide average marginal cost be unobservable to the individual firm. The model can then replicate the backward looking component found in estimates of the ’Hybrid’ New Keynesian Phillips Curve, even though the pricing decision of the firm is entirely forward looking. The Phillips curve derived here nests the standard New Keynesian Phillips Curve as a special case. We take a structural approach to imperfect common knowledge that allow us to infer whether the assumed information imperfections necessary to replicate the data are quantitatively realistic or not. We also provide an algorithm for solving a class of models involving dynamic higher order expectations of endogenous variables.