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Controlling a distribution of heterogeneous agents

Author

Listed:
  • Galo Nuño

    (Banco de España)

  • Benjamin Moll

    (Princeton university)

Abstract

This paper analyzes the problem of a benevolent planner wishing to control a population of heterogeneous agents subject to idiosyncratic shocks. This is equivalent to a deterministic control problem in which the state variable is the cross-sectional distribution. We show how, in continuous time, this problem can be broken down into a dynamic programming equation plus the law of motion of the distribution, and we introduce a new numerical algorithm to solve it. As an application, we analyze the constrained-efficient allocation of an Aiyagari economy with a fat-tailed wealth distribution. We fi nd that the constrained-efficient allocation features more wealth inequality than the competitive equilibrium.

Suggested Citation

  • Galo Nuño & Benjamin Moll, 2015. "Controlling a distribution of heterogeneous agents," Working Papers 1533, Banco de España.
    • Handle: RePEc:bde:wpaper:1533
    as

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    File URL: http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/15/Fich/dt1533e.pdf
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    References listed on IDEAS

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    1. Daron Acemoglu & James A. Robinson, 2015. "The Rise and Decline of General Laws of Capitalism," Journal of Economic Perspectives, American Economic Association, vol. 29(1), pages 3-28, Winter.
    2. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    3. Julio Dávila & Jay H. Hong & Per Krusell & José‐Víctor Ríos‐Rull, 2012. "Constrained Efficiency in the Neoclassical Growth Model With Uninsurable Idiosyncratic Shocks," Econometrica, Econometric Society, vol. 80(6), pages 2431-2467, November.
    4. Robert E. Lucas Jr. & Benjamin Moll, 2014. "Knowledge Growth and the Allocation of Time," Journal of Political Economy, University of Chicago Press, vol. 122(1), pages 1-51.
    5. Jovanovic, Boyan, 1979. "Job Matching and the Theory of Turnover," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 972-990, October.
    6. Rocheteau, Guillaume & Weill, Pierre-Olivier & Wong, Russell, 2018. "A tractable model of monetary exchange with ex-post heterogeneity," Theoretical Economics, Econometric Society, vol. 13(3), September.
    7. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1103-1144.
    8. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-247, April.
    9. Thomas Piketty & Emmanuel Saez, 2003. "Income Inequality in the United States, 1913–1998," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(1), pages 1-41.
    10. Piketty, Thomas & Zucman, Gabriel, 2014. "Wealth and Inheritance in the Long Run," CEPR Discussion Papers 10072, C.E.P.R. Discussion Papers.
    11. Charles I. Jones, 2015. "Pareto and Piketty: The Macroeconomics of Top Income and Wealth Inequality," Journal of Economic Perspectives, American Economic Association, vol. 29(1), pages 29-46, Winter.
    12. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
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    More about this item

    Keywords

    Kolmogorov forward equation; 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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