Generalized Rotemberg price-setting

We propose a generalized Rotemberg pricing scheme which is able to explain important aspects of the observed nonlinear behavior of price adjustment at the macroeconomic level, such as higher pass-through in response to larger shocks, a positive impact of trend inflation on price flexibility, and the relationship between announcement and implementation effects. This is achieved by replacing the linear marginal adjustment cost in Rotemberg pricing by a monotonically increasing, but bounded marginal cost function, specifically some version of a sigmoid function. Conditional on computing a nonlinear model solution, the generalized pricing function is equally tractable as Rotemberg pricing, and equivalent to it for small shocks around a zero-inflation steady state. We show that a suitable calibration of the model has similar effects on macroeconomic variables as standard versions of the menu cost model. It replicates the effect of trend inflation on the impulse response to money supply shocks that has been established in the literature in a model of logit-price dynamics.