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Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

Author

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  • Yves Achdou
  • Jiequn Han
  • Jean-Michel Lasry
  • Pierre-Louis Lions
  • Benjamin Moll

Abstract

We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one; (iv) characterization of “soft” borrowing constraints. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including – but not limited to – the Aiyagari-Bewley-Huggett model.

Suggested Citation

  • Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:23732
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    References listed on IDEAS

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    Cited by:

    1. Perets, Gadi & Yashiv, Eran, 2018. "Lie Symmetries and Essential Restrictions in Economic Optimization," CEPR Discussion Papers 12611, C.E.P.R. Discussion Papers.
    2. Greg Kaplan & Benjamin Moll & Giovanni L. Violante, 2018. "Monetary Policy According to HANK," American Economic Review, American Economic Association, vol. 108(3), pages 697-743, March.
    3. Hoang Khieu & Klaus Wälde, 2018. "Capital Income Risk and the Dynamics of the Wealth Distribution," Working Papers 1814, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    4. Erosa, Andrés & González, Beatriz, 2019. "Taxation and the life cycle of firms," Journal of Monetary Economics, Elsevier, vol. 105(C), pages 114-130.
    5. Łukasz Rachel & Lawrence H. Summers, 2019. "On Secular Stagnation in the Industrialized World," NBER Working Papers 26198, National Bureau of Economic Research, Inc.
    6. Jesus Fernandez-Villaverde & Samuel Hurtado & Galo Nuno, 2019. "Financial Frictions and the Wealth Distribution," PIER Working Paper Archive 19-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. Gouin-Bonenfant, Emilien & Toda, Alexis Akira, 2018. "Pareto Extrapolation: Bridging Theoretical and Quantitative Models of Wealth Inequality," University of California at San Diego, Economics Working Paper Series qt90n2h2bb, Department of Economics, UC San Diego.
    8. Toda, Alexis Akira, 2019. "Wealth distribution with random discount factors," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 101-113.
    9. Hoang Khieu & Klaus Wälde, 2019. "Capital Income Risk and the Dynamics of the Wealth Distribution," CESifo Working Paper Series 7970, CESifo Group Munich.
    10. Pietro Dindo & Andrea Modena & Loriana Pelizzon, 2019. "Risk Pooling, Leverage, and the Business Cycle," Working Papers 2019: 21, Department of Economics, University of Venice "Ca' Foscari".
    11. Matteo Escud'e & Ludvig Sinander, 2019. "Strategic research funding," Papers 1903.09055, arXiv.org.
    12. Toda, Alexis Akira, 2017. "Huggett economies with multiple stationary equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 77-90.
    13. Holm, Martin Blomhoff, 2018. "Consumption with liquidity constraints: An analytical characterization," Economics Letters, Elsevier, vol. 167(C), pages 40-42.
    14. Karun Adusumilli & Friedrich Geiecke & Claudio Schilter, 2019. "Dynamically optimal treatment allocation using Reinforcement Learning," Papers 1904.01047, arXiv.org, revised Jul 2019.
    15. Siddhartha Sanghi, 2019. "Health Inequality: Role of Insurance and Technological Progress," 2019 Meeting Papers 703, Society for Economic Dynamics.
    16. Lehrer, Ehud & Light, Bar, 2018. "The effect of interest rates on consumption in an income fluctuation problem," Journal of Economic Dynamics and Control, Elsevier, vol. 94(C), pages 63-71.
    17. Alisdair McKay & Johannes F. Wieland, 2019. "Lumpy Durable Consumption Demand and the Limited Ammunition of Monetary Policy," NBER Working Papers 26175, National Bureau of Economic Research, Inc.
    18. Christian Bayer & Alan Rendall & Klaus Wälde, 2018. "The Invariant Distribution of Wealth and Employment Status in a Small Open Economy with Precautionary Savings," Working Papers 1822, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.

    More about this item

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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