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Single Crossing Lorenz Curves and Inequality Comparisons

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  • Thibault Gajdos

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Since the order generated by the Lorenz criterion is partial, it is a natural question to wonder how to extend this order. Most of the literature that is concerned with that question focuses on local changes in the income distribution. We follow a different approach, and define uniform $\alpha$-spreads, which are global changes in the income distribution. We give necessary and sufficient conditions for an Expected Utility or Rank-Dependent Expected Utility maximizer to respect the principle of transfers and to be favorable to uniform $\alpha$-spreads. Finally, we apply these results to inequality indices.

Suggested Citation

  • Thibault Gajdos, 2004. "Single Crossing Lorenz Curves and Inequality Comparisons," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00086028, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00086028
    DOI: 10.1016/S0165-4896(03)00078-7
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00086028
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    References listed on IDEAS

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    Cited by:

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    2. Uberti, Pierpaolo & Figini, Silvia, 2010. "How to measure single-name credit risk concentrations," European Journal of Operational Research, Elsevier, vol. 202(1), pages 232-238, April.
    3. Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559.
    4. Bertoli-Barsotti, Lucio & Gagolewski, Marek & Siudem, Grzegorz & Żogała-Siudem, Barbara, 2024. "Gini-stable Lorenz curves and their relation to the generalised Pareto distribution," Journal of Informetrics, Elsevier, vol. 18(2).
    5. Stéphane Mussard, 2007. "Between-Group Pigou Dalton Transfers," Cahiers de recherche 07-06, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    6. Michel Le Breton & Eugenio Peluso, 2009. "Third-degree stochastic dominance and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(3), pages 249-268, September.

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