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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 - INSEE - École Nationale de la Statistique et de l'Administration Économique, EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - CNRS : UMR8594 - Université Paris I - Panthéon-Sorbonne)

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.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00086028.

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Date of creation: 2004
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Publication status: Published, Mathematical Social Sciences, 2004, 47, 1, 21-36
Handle: RePEc:hal:cesptp:halshs-00086028

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00086028
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Keywords: Inequality measures; Intersecting Lorenz Curves; Spreads;

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References

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  1. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  2. Alain Chateauneuf & Michèle Cohen & Isaac Meilijson, 2005. "More pessimism than greediness: a characterization of monotone risk aversion in the Rank-Dependent Expected Utility model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00211906, HAL.
  3. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
  4. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  5. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer, vol. 16(2), pages 183-196.
  6. Hoy, M. & Davies, J., 1991. "The Normative Significance of Using Third-Degree Stochastic Dominance in Comparing Income Distributions," Working Papers 1991-8, University of Guelph, Department of Economics and Finance.
  7. Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, vol. 49(2), pages 314-323, December.
  8. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  9. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  10. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
  11. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
  12. Bossert, Walter, 1990. "An axiomatization of the single-series Ginis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 82-92, February.
  13. Foster, James E. & Shorrocks, Anthony F., 1988. "Inequality and poverty orderings," European Economic Review, Elsevier, vol. 32(2-3), pages 654-661, March.
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Cited by:
  1. 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.
  2. Mussard, Stéphane, 2007. "Between-Group Pigou-Dalton Transfers," IRISS Working Paper Series 2007-02, IRISS at CEPS/INSTEAD.
  3. Paul Makdissi & Stéphane Mussard, 2008. "Decomposition of s-concentration curves," Canadian Journal of Economics, Canadian Economics Association, vol. 41(4), pages 1312-1328, November.
  4. Michel Le Breton & Eugenio Peluso, 2009. "Third-degree stochastic dominance and inequality measurement," Journal of Economic Inequality, Springer, vol. 7(3), pages 249-268, September.

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