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The Analytic Theory of a Monetary Shock

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  • Fernando Alvarez
  • Francesco Lippi

Abstract

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.

Suggested Citation

  • Fernando Alvarez & Francesco Lippi, 2022. "The Analytic Theory of a Monetary Shock," Econometrica, Econometric Society, vol. 90(4), pages 1655-1680, July.
    • Handle: RePEc:wly:emetrp:v:90:y:2022:i:4:p:1655-1680
    DOI: 10.3982/ECTA17348
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    References listed on IDEAS

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    Cited by:

    1. Yuki SHIGETA, 2022. "A Continuous-Time Utility Maximization Problem with Borrowing Constraints in Macroeconomic Heterogeneous Agent Models:A Case of Regular Controls under Markov Chain Uncertainty," Discussion papers e-22-009, Graduate School of Economics , Kyoto University.
    2. Dirk Krueger & Harald Uhlig, 2022. "Neoclassical Growth with Long-Term One-Sided Commitment Contracts," NBER Working Papers 30518, National Bureau of Economic Research, Inc.
    3. Fernando Alvarez & Francesco Lippi & Panagiotis Souganidis, 2023. "Price Setting With Strategic Complementarities as a Mean Field Game," Econometrica, Econometric Society, vol. 91(6), pages 2005-2039, November.
    4. Dirk Krueger & Harald Uhlig, 2024. "Neoclassical Growth with Limited Commitment," PIER Working Paper Archive 22-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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