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Solving discrete time heterogeneous agent models with aggregate risk and many idiosyncratic states by perturbation

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  • Christian Bayer
  • Ralph Luetticke
Abstract
This paper describes a method for solving heterogeneous agent models with aggregate risk and many idiosyncratic states formulated in discrete time. It extends the method proposed by Reiter (2009) and complements recent work by Ahn, Kaplan, Moll, Winberry, and Wolf (2017) on how to solve such models in continuous time. We suggest first solving for the stationary equilibrium of the model without aggregate risk. We then write the functionals that describe the dynamic equilibrium as sparse expansions around their stationary equilibrium counterparts. Finally, we use the perturbation method of Schmitt‐Grohé and Uribe (2004) to approximate the aggregate dynamics of the model.

Suggested Citation

  • Christian Bayer & Ralph Luetticke, 2020. "Solving discrete time heterogeneous agent models with aggregate risk and many idiosyncratic states by perturbation," Quantitative Economics, Econometric Society, vol. 11(4), pages 1253-1288, November.
    • Handle: RePEc:wly:quante:v:11:y:2020:i:4:p:1253-1288
    DOI: 10.3982/QE1243
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    References listed on IDEAS

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    11. Greg Kaplan & Giovanni L. Violante, 2014. "A Model of the Consumption Response to Fiscal Stimulus Payments," Econometrica, Econometric Society, vol. 82(4), pages 1199-1239, July.
    12. Christian Bayer & Ralph Luetticke & Lien Pham‐Dao & Volker Tjaden, 2019. "Precautionary Savings, Illiquid Assets, and the Aggregate Consequences of Shocks to Household Income Risk," Econometrica, Econometric Society, vol. 87(1), pages 255-290, January.
    13. Ralph Luetticke, 2021. "Transmission of Monetary Policy with Heterogeneity in Household Portfolios," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(2), pages 1-25, April.
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    2. Christian Bayer & Benjamin Born & Ralph Luetticke & Gernot J Müller, 2023. "The Coronavirus Stimulus Package: How Large is the Transfer Multiplier," The Economic Journal, Royal Economic Society, vol. 133(652), pages 1318-1347.
    3. Christian Bayer & Ralph Luetticke & Maximilian Weiss & Yannik Winkelmann, 2024. "An Endogenous Gridpoint Method for Distributional Dynamics," ECONtribute Discussion Papers Series 311, University of Bonn and University of Cologne, Germany.
    4. Dobrew, Michael & Gerke, Rafael & Giesen, Sebastian & Röttger, Joost, 2023. "Make-Up Strategies with Incomplete Markets and Bounded Rationality," VfS Annual Conference 2023 (Regensburg): Growth and the "sociale Frage" 277697, Verein für Socialpolitik / German Economic Association.
    5. Dobrew, Michael & Gerke, Rafael & Giesen, Sebastian & Röttger, Joost, 2023. "Make-up strategies with incomplete markets and bounded rationality," Discussion Papers 01/2023, Deutsche Bundesbank.
    6. Juan Carlos Parra‐Alvarez & Olaf Posch & Mu‐Chun Wang, 2023. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(2), pages 304-330, April.
    7. Donggyu Lee, 2024. "Quantitative Easing and Inequality," Staff Reports 1108, Federal Reserve Bank of New York.
    8. Dengler, Thomas & Gerke, Rafael & Giesen, Sebastian & Kienzler, Daniel & Röttger, Joost & Scheer, Alexander & Wacks, Johannes, 2024. "A primer on optimal policy projections," Technical Papers 01/2024, Deutsche Bundesbank.
    9. Consolo, Agostino & Hänsel, Matthias, 2024. "HANK faces unemployment," Working Paper Series 2953, European Central Bank.
    10. Langot, François & Malmberg, Selma & Tripier, Fabien & Hairault, Jean-Olivier, 2023. "The Macroeconomic and Redistributive Effects of Shielding Consumers from Rising Energy Prices: the French Experiment," CEPREMAP Working Papers (Docweb) 2305, CEPREMAP.

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