Econometrica: Jul 2022, Volume 90, Issue 4

The Analytic Theory of a Monetary Shock

https://doi.org/10.3982/ECTA17348
p. 1655-1680

Fernando Alvarez, Francesco Lippi

We propose an analytical method to analyze the propagation of an aggregate shock in a broad class of sticky‐price models. The method is based on the eigenvalue‐eigenfunction representation of the dynamics of the cross‐sectional distribution of firms' desired adjustments. A key novelty is that we can approximate the whole profile of the impulse response for any moment of interest in response to an aggregate shock (any displacement of the invariant distribution). We present several applications for an economy with low inflation and idiosyncratic shocks. We show that the shape of the impulse response of the canonical menu cost model is fully encoded by a single parameter, just like the Calvo model, although the shapes are very different. A model with a quadratic hazard function, arguably a good fit to the micro data on price setting, yields an impulse response that is close to the canonical menu cost model.



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Supplement to "The Analytic Theory of a Monetary Shock"

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Supplement to "The Analytic Theory of a Monetary Shock"

This document contains all the proofs of the paper “The Analytic Theory of a Monetary Shock”. The document also contains two applications of the method developed in the paper for Multiproduct firms and for a general random fixed cost problem.

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