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Generalized Pareto Curves: Theory and Applications

Author

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  • Thomas Blanchet

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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)

  • Juliette Fournier

    (MIT - Massachusetts Institute of Technology)

  • Thomas Piketty

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - 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)

Abstract

We define generalized Pareto curves as the curve of inverted Pareto coefficients b(p), where b(p) is the ratio between average income 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 income distributions. We develop a method to flexibly recover a continuous distribution based on tabulated income 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 show the precision of our method. It gives better results than the most commonly used interpolation techniques for the top half of the distribution.

Suggested Citation

  • Thomas Blanchet & Juliette Fournier & Thomas Piketty, 2022. "Generalized Pareto Curves: Theory and Applications," Post-Print halshs-03760338, HAL.
  • Handle: RePEc:hal:journl:halshs-03760338
    DOI: 10.1111/roiw.12510
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-03760338
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