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Social Optima in Economies with Heterogeneous Agents

Author

Listed:
  • Galo Nuno

    (Banco de Espana)

  • Benjamin Moll

    (Princeton University)

Abstract

This paper analyzes the problem of computing the social optimum in models with heterogeneous agents subject to idiosyncratic shocks. This is equivalent to a deterministic optimal control problem in which the state variable is the infinite-dimensional cross-sectional distribution. We show how, in continuous time, the problem can be broken down into two finite-dimensional partial differential equations: a dynamic programming equation and the law of motion of the distribution, and we introduce a new numerical algorithm to solve it. We illustrate this methodology with two examples: social optima in an Aiyagari economy with stochastic lifetimes and in a model of on-the-job search with learning. (Copyright: Elsevier)

Suggested Citation

  • Galo Nuno & Benjamin Moll, 2018. "Social Optima in Economies with Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 28, pages 150-180, April.
    • Handle: RePEc:red:issued:15-330
    DOI: 10.1016/j.red.2017.08.003
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    2. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    3. Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2023. "The dynamics of Pareto distributed wealth in a small open economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 607-644, August.
    4. Schünemann, Johannes & Trimborn, Timo, 2023. "Boosting taxes for boasting about houses? Status concerns in the housing market," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 120-143.
    5. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    6. Christian Loenser & Joost Röttger & Andreas Schabert, 2022. "Financial Regulation, Interest Rate Responses, and Distributive Effects," ECONtribute Discussion Papers Series 143, University of Bonn and University of Cologne, Germany.
    7. Bayer, Christian & Rendall, Alan D. & Wälde, Klaus, 2019. "The invariant distribution of wealth and employment status in a small open economy with precautionary savings," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 17-37.
    8. Rendahl, Pontus, 2022. "Continuous vs. discrete time: Some computational insights," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    9. Andrea Modena & Luca Regis, 2024. "Capital risk, fiscal policy, and the distribution of wealth," Mathematics and Financial Economics, Springer, volume 18, number 8, February.
    10. Gatt, William, 2024. "Wealth inequality and the distributional effects of maximum loan-to-value ratio policy," Journal of Economic Dynamics and Control, Elsevier, vol. 164(C).
    11. Jiequn Han & Yucheng Yang & Weinan E, 2021. "DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks," Papers 2112.14377, arXiv.org, revised Feb 2022.
    12. Schesch, Constantin, 2024. "Pseudospectral methods for continuous-time heterogeneous-agent models," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
    13. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    14. Fischer, Thomas, 2019. "Determinants of Wealth Inequality and Mobility in General Equilibrium," Working Papers 2019:22, Lund University, Department of Economics.

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    More about this item

    Keywords

    Kolmogorov forward equation; Gateaux derivative; wealth distribution; social welfare function; mean field control;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D3 - Microeconomics - - Distribution
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment

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