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Generalized Pareto Curves : Theory and Applications

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  • Thomas Blanchet

    (Paris School of Economics)

  • Juliette Fournier

    (MIT)

  • Thomas Piketty

    (Paris School of Economics)

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," Working Papers 201703, World Inequality Lab.
  • Handle: RePEc:wel:wpaper:201703
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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. 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.
    4. 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.
    5. Piketty, Thomas & Zucman, Gabriel, 2014. "Wealth and Inheritance in the Long Run," CEPR Discussion Papers 10072, C.E.P.R. Discussion Papers.
    6. Kacperczyk, Marcin & Nosal, Jaromir & Stevens, Luminita, 2019. "Investor sophistication and capital income inequality," Journal of Monetary Economics, Elsevier, vol. 107(C), pages 18-31.
    7. 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.
    8. Thomas Blanchet & Juliette Fournier & Thomas Piketty, 2017. "Generalized Pareto Curves : Theory and Applications," Working Papers 201703, World Inequality Lab.
    9. Bertrand Garbinti & Jonathan Goupille-Lebret & Thomas Piketty, 2017. "Income Inequality in France, 1900-2014: Evidence from Distributional National Accounts," Working Papers 201704, World Inequality Lab.
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