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Lorenz Non-Consistent Welfare and Inequality Measurement

Author

Listed:
  • 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.

Suggested Citation

  • Alain Chateauneuf & Patrick Moyes, 2004. "Lorenz Non-Consistent Welfare and Inequality Measurement," IDEP Working Papers 0406, Institut d'economie publique (IDEP), Marseille, France, revised May 2004.
  • Handle: RePEc:iep:wpidep:0406
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    References listed on IDEAS

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    1. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
    2. 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.
    3. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
    4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    5. 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 1065-1092, July.
    6. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    7. Satya R. Chakravarty & Patrick Moyes, 2003. "Individual welfare, social deprivation and income taxation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 843-869, June.
    8. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-316, March.
    9. 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.
    10. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    11. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    12. Kakwani, Nanak, 1984. "The Relative Deprivation Curve and Its Applications," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 384-394, October.
    13. Weiss, Yoram & Fershtman, Chaim, 1998. "Social status and economic performance:: A survey," European Economic Review, Elsevier, vol. 42(3-5), pages 801-820, May.
    14. 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.
    15. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
    16. 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.
    17. 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.
    18. C. Seidl & Patrick Moyes & A. F. Shorrocks, 2002. "Inequalities: Theory, experiments and applications," Post-Print hal-00157353, HAL.
    19. Thon, Dominique, 1987. "Redistributive properties of progressive taxation," Mathematical Social Sciences, Elsevier, vol. 14(2), pages 185-191, October.
    20. 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.
    21. Rosen, Sherwin, 1984. "The Relative Deprivation Curve and Its Applications," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 395-397, October.
    22. Shlomo Yitzhaki, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, Oxford University Press, vol. 93(2), pages 321-324.
    23. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    24. John D. Hey & Peter J. Lambert, 1980. "Relative Deprivation and the Gini Coefficient: Comment," The Quarterly Journal of Economics, Oxford University Press, vol. 95(3), pages 567-573.
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    Citations

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    Cited by:

    1. Brice Magdalou & Patrick Moyes, 2009. "Deprivation, welfare and inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 253-273, February.
    2. Kristof Bosmans, 2007. "Comparing degrees of inequality aversion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(3), pages 405-428, October.
    3. William Horrace & Joseph Marchand & Timothy Smeeding, 2008. "Ranking inequality: Applications of multivariate subset selection," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 5-32, March.
    4. 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.
    5. Patrick Moyes & Brice Magdalou, 2008. "Social Welfare, Inequality and Deprivation," LIS Working papers 502, LIS Cross-National Data Center in Luxembourg.
    6. Stephen Bazen & Patrick Moyes, 2012. "Elitism and stochastic dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 207-251, June.
    7. Stephen Bazen & Patrick Moyes, 2011. "Elitism and Stochastic Dominance," Working Papers halshs-00576585, HAL.
    8. Udo Ebert, 2009. "Taking empirical studies seriously: the principle of concentration and the measurement of welfare and inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(4), pages 555-574, May.
    9. 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;The Society for Social Choice and Welfare, vol. 35(4), pages 575-593, October.
    10. Giovagnoli, Alessandra & Wynn, Henry P., 2012. "(U,V) ordering and a duality theorem for risk aversion and Lorenz type orderings," LSE Research Online Documents on Economics 55856, London School of Economics and Political Science, LSE Library.

    More about this item

    Keywords

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

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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