Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 2022, Volume 90, Issue 4

The Analytic Theory of a Monetary Shock
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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Supplemental Material

Supplement to "The Analytic Theory of a Monetary Shock"

Fernando Alvarez and Francesco Lippi

This zip file contains the replication files for the manuscript.  It also contains an additional web appendix with material not contained within the manuscript.

Supplement to "The Analytic Theory of a Monetary Shock"

Fernando Alvarez and Francesco Lippi

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.