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Lorenz Non-Consistent Welfare and Inequality Measurement

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  • Alain Chateauneuf

    (CERMSEM, Université Paris 1 Panthéon-Sorbonne)

  • Patrick Moyes

    ()
    (CNRS, IDEP and GRAPE, Université Montesquieu Bordeaux IV)

Abstract

inequality decreases and welfare increases as a result of a progressive transfer. We explore the implications for welfare and inequality measurement of substituting the weaker absolute differentials and deprivation quasi-orderings for the Lorenz quasi-ordering. Restricting attention to distributions of equal means, we show that the utilitarian model {the so-called expected utility model in the theory of risk {does not permit one to make a distinction between the views embedded in the differentials, deprivation and Lorenz quasi-orderings. In contrast it is possible within the dual model of M. Yaari (Econometrica 55 (1987), 99{115) to derive the restrictions to be placed on the weighting function which guarantee that the corresponding welfare orderings are consistent with the differentials and deprivation quasi-orderings respectively. Finally we drop the equal mean condition and indicate the implications of our approach for the absolute ethical inequality indices.

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Bibliographic Info

Paper provided by Institut d'economie publique (IDEP), Marseille, France in its series IDEP Working Papers with number 0406.

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Length: 28 pages
Date of creation: May 2004
Date of revision: May 2004
Handle: RePEc:iep:wpidep:0406

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Keywords: Income Differentials; Deprivation; Lorenz Dominance; Expected Utility; Dual model of choice under risk; Generalized. Gini social welfare functions.;

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References

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  1. Kakwani, Nanak, 1984. "The Relative Deprivation Curve and Its Applications," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 384-94, October.
  2. Hey, John D & Lambert, Peter J, 1980. "Relative Deprivation and the Gini Coefficient: Comment," The Quarterly Journal of Economics, MIT Press, vol. 95(3), pages 567-73, November.
  3. Weiss, Y. & Fershtman, C., 1997. "Social Status and Economic Performance: A Survey," Papers 19-97, Tel Aviv.
  4. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
  5. Rosen, Sherwin, 1984. "The Relative Deprivation Curve and Its Applications," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 395-97, October.
  6. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
  7. Yitzhaki, Shlomo, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, MIT Press, vol. 93(2), pages 321-24, May.
  8. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  9. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
  10. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
  11. Amiel, Yoram & Cowell, Frank A., 1992. "Measurement of income inequality : Experimental test by questionnaire," Journal of Public Economics, Elsevier, vol. 47(1), pages 3-26, February.
  12. Harrison, Elizabeth & Seidl, Christian, 1994. " Perceptional Inequality and Preferential Judgements: An Empirical Examination of Distributional Axioms," Public Choice, Springer, vol. 79(1-2), pages 61-81, April.
  13. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  14. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
  15. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-92, July.
  16. Kakwani, Nanak, 1984. "The Relative Deprivation Curve and Its Applications: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 400-405, October.
  17. Thon, Dominique, 1987. "Redistributive properties of progressive taxation," Mathematical Social Sciences, Elsevier, vol. 14(2), pages 185-191, October.
  18. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
  19. Udo Ebert & Patrick Moyes, 2002. "Welfare, inequality and the transformation of incomes the case of weighted income distributions," Journal of Economics, Springer, vol. 9(1), pages 9-50, December.
  20. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
  21. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-16, March.
  22. Gaertner, Wulf & Namazie, Ceema, 2003. "Income inequality, risk, and the transfer principle: A questionnaire-experimental investigation," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 229-245, April.
  23. Satya R. Chakravarty & Patrick Moyes, 2003. "Individual welfare, social deprivation and income taxation," Economic Theory, Springer, vol. 21(4), pages 843-869, 06.
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Citations

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Cited by:
  1. Kristof Bosmans, 2007. "Comparing degrees of inequality aversion," Social Choice and Welfare, Springer, vol. 29(3), pages 405-428, October.
  2. William C. Horrace & Joseph T. Marchand & Timothy M. Smeeding, 2005. "Ranking Inequality: Applications of Multivariate Subset Selection," Center for Policy Research Working Papers 70, Center for Policy Research, Maxwell School, Syracuse University.
  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. Stephen Bazen & Patrick Moyes, 2011. "Elitism and Stochastic Dominance," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00576585, HAL.
  5. repec:hal:wpaper:halshs-00576585 is not listed on IDEAS
  6. Ronny Aboudi & Dominique Thon, 2010. "Characterizations of egalitarian binary relations as transitive closures with a special reference to Lorenz dominance and to single-crossing conditions," Social Choice and Welfare, Springer, vol. 35(4), pages 575-593, October.
  7. Udo Ebert, 2009. "Taking empirical studies seriously: the principle of concentration and the measurement of welfare and inequality," Social Choice and Welfare, Springer, vol. 32(4), pages 555-574, May.
  8. Brice Magdalou & Patrick Moyes, 2009. "Deprivation, welfare and inequality," Social Choice and Welfare, Springer, vol. 32(2), pages 253-273, February.
  9. Brice MAGDALOU (CEREGMIA) & Patrick MOYES (GREThA UMR CNRS 5113), 2008. "Social Welfare, Inequality and Deprivation," Cahiers du GREThA 2008-23, Groupe de Recherche en Economie Théorique et Appliquée.

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