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An Endogenous Gridpoint Method for Distributional Dynamics

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  • Christian Bayer
  • Ralph Luetticke
  • Maximilian Weiss
  • Yannik Winkelmann

Abstract

The “histogram method” (Young, 2010), while the standard approach for analyzing distributional dynamics in heterogeneous agent models, is linear in optimal policies. We introduce a novel method that captures nonlinearities of distributional dynamics. This method solves the distributional dynamics by interpolation instead of integration, which is made possible by making the grid endogenous. It retains the tractability and speed of the histogram method, while increasing numerical efficiency even in the steady state and producing significant economic differences in scenarios with aggregate risk. We document this by studying aggregate investment risk with a third-order solution using perturbation techniques.

Suggested Citation

  • Christian Bayer & Ralph Luetticke & Maximilian Weiss & Yannik Winkelmann, 2024. "An Endogenous Gridpoint Method for Distributional Dynamics," CRC TR 224 Discussion Paper Series crctr224_2024_548, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2024_548
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    File URL: https://www.crctr224.de/research/discussion-papers/archive/dp548
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    References listed on IDEAS

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    1. Christian Bayer & Benjamin Born & Ralph Luetticke, 2024. "Shocks, Frictions, and Inequality in US Business Cycles," American Economic Review, American Economic Association, vol. 114(5), pages 1211-1247, May.
    2. Robert J. Barro, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(3), pages 823-866.
    3. Adrien Auclert & Bence Bardóczy & Matthew Rognlie & Ludwig Straub, 2021. "Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models," Econometrica, Econometric Society, vol. 89(5), pages 2375-2408, September.
    4. Reiter, Michael, 2009. "Solving heterogeneous-agent models by projection and perturbation," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 649-665, March.
    5. S. Rao Aiyagari, 1994. "Uninsured Idiosyncratic Risk and Aggregate Saving," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(3), pages 659-684.
    6. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
    7. Den Haan, Wouter J. & Judd, Kenneth L. & Juillard, Michel, 2010. "Computational suite of models with heterogeneous agents: Incomplete markets and aggregate uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 1-3, January.
    8. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    9. Levintal, Oren, 2017. "Fifth-order perturbation solution to DSGE models," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 1-16.
    10. 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.
    11. George-Marios Angeletos, 2007. "Uninsured Idiosyncratic Investment Risk and Aggregate Saving," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(1), pages 1-30, January.
    12. Anmol Bhandari & Thomas Bourany & David Evans & Mikhail Golosov, 2023. "A Perturbational Approach for Approximating Heterogeneous Agent Models," NBER Working Papers 31744, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Kase, Hanno & Melosi, Leonardo & Rottner, Matthias, 2024. "Estimating Nonlinear Heterogeneous Agent Models with Neural Networks," The Warwick Economics Research Paper Series (TWERPS) 1499, University of Warwick, Department of Economics.

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    More about this item

    Keywords

    Numerical Methods; Distributions; Heterogeneous Agent Models; Linearization;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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