An Odd Approximation Of Inflation For State-Dependent Pricing Models

We derive an aggregate state-space representation of state-dependent pricing models with random menu costs and strategic complementarities. The representation, derived from first principles, replaces the cross-sectional distribution of price gaps with a finite set of its moments (the first three), while preserving the key economic forces of state-dependent pricing–movements in the frequency of price adjustment and selection. Along the impulse response, inflation is an odd (cubic) polynomial in the average price gap. Embedded in a general equilibrium setting, the model can be solved by perturbation, filtered, and estimated with standard DSGE tools, and it matches well the global solution across shock sizes. Applied to the 2021–22 inflation surge in the United States and the euro area, it shows that much of the variation that linear models would attribute to cost-push shocks is in fact endogenous amplification through the frequency of price changes and selection.