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Generalized Pareto Curves : Theory and Applications

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  • Thomas Blanchet

    (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, WIL - World Inequality Lab)

  • Juliette Fournier

    (MIT - Massachusetts Institute of Technology)

  • Thomas Piketty

    (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, WIL - World Inequality Lab)

Abstract

We define generalized Pareto curves as the curve of inverted Pareto coefficients b(p), where b(p) is the ratio between average income or wealth above rank p and the p-th quantile Q(p) (i.e. b(p) = E[X|X > Q(p)]/Q(p)). We use them to characterize entire distributions, including places like the top where power laws are a good description, and places further down where they are not. We develop a method to nonparametrically recover the entire distribution based on tabulated income or wealth data as is generally available from tax authorities, which produces smooth and realistic shapes of generalized Pareto curves. Using detailed tabulations from quasi-exhaustive tax data, we demonstrate the precision of our method both empirically and analytically. It gives better results than the most commonly used interpolation techniques. Finally, we use Pareto curves to identify recurring distributional patterns, and connect those findings to the existing literature that explains observed distributions by random growth models.

Suggested Citation

  • Thomas Blanchet & Juliette Fournier & Thomas Piketty, 2017. "Generalized Pareto Curves : Theory and Applications," World Inequality Lab Working Papers halshs-02658851, HAL.
  • Handle: RePEc:hal:wilwps:halshs-02658851
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-02658851
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    References listed on IDEAS

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    1. Taleb, Nassim Nicholas & Douady, Raphael, 2015. "On the super-additivity and estimation biases of quantile contributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 252-260.
    2. Neil Bania & Laura Leete, 2009. "Monthly household income volatility in the U.S., 1991/92 vs. 2002/03," Economics Bulletin, AccessEcon, vol. 29(3), pages 2100-2112.
    3. Thomas Piketty & Emmanuel Saez & Gabriel Zucman, 2016. "Appendix to "Distributional National Accounts: Methods and Estimates for the United States"," Working Papers 201604, World Inequality Lab.
    4. Garbinti, Bertrand & Goupille-Lebret, Jonathan & Piketty, Thomas, 2018. "Income inequality in France, 1900–2014: Evidence from Distributional National Accounts (DINA)," Journal of Public Economics, Elsevier, vol. 162(C), pages 63-77.
    5. Thomas Piketty & Emmanuel Saez & Gabriel Zucman, 2018. "Distributional National Accounts: Methods and Estimates for the United States," The Quarterly Journal of Economics, Oxford University Press, vol. 133(2), pages 553-609.
    6. Simon Kuznets & Elizabeth Jenks, 1953. "Shares of Upper Income Groups in Income and Savings (1953)," NBER Books, National Bureau of Economic Research, Inc, number kuzn53-1, September.
    7. Piketty, Thomas & Zucman, Gabriel, 2014. "Wealth and Inheritance in the Long Run," CEPR Discussion Papers 10072, C.E.P.R. Discussion Papers.
    8. Thomas Blanchet & Juliette Fournier & Thomas Piketty, 2017. "Generalized Pareto Curves : Theory and Applications," Working Papers halshs-02658851, HAL.
    9. Kacperczyk, Marcin & Nosal, Jaromir & Stevens, Luminita, 2019. "Investor sophistication and capital income inequality," Journal of Monetary Economics, Elsevier, vol. 107(C), pages 18-31.
    10. Charles I. Jones & Jihee Kim, 2018. "A Schumpeterian Model of Top Income Inequality," Journal of Political Economy, University of Chicago Press, vol. 126(5), pages 1785-1826.
    11. Bertrand Garbinti & Jonathan Goupille-Lebret & Thomas Piketty, 2017. "Income Inequality in France, 1900-2014: Evidence from Distributional National Accounts," Working Papers halshs-02658875, HAL.
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