Nonlinear inflation dynamics in menu cost economies

Existing menu cost models, when parameterized to match the micro-price data, cannot reproduce the extent to which the fraction of price changes increases with inflation. In addition, in the presence of strategic complementarities, they predict implausibly large menu costs and misallocation. We resolve these shortcomings using a multi-product menu cost model that features two key ingredients. First, the products sold by a firm are imperfect substitutes. Second, strategic complementarities are at the firm level, not the product level. In contrast to existing models, the fraction of price changes increases rapidly with the size of monetary shocks, so our model implies a nonlinear Phillips curve.