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Lorenz non-consistent welfare and inequality measurement

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Author Info
Alain Chateauneuf ()
Patrick Moyes ()

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Abstract

Typical welfare and inequality measures are required to be Lorenz consistent which guarantees that 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. Copyright Kluwer Academic Publishers 2005

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Publisher Info
Article provided by Springer in its journal The Journal of Economic Inequality.

Volume (Year): 2 (2005)
Issue (Month): 2 (January)
Pages: 61-87
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Handle: RePEc:kap:jecinq:v:2:y:2005:i:2:p:61-87

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Web page: http://springerlink.metapress.com/link.asp?id=111137

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Related research
Keywords: deprivation; dual model of choice under risk; expected utility; generalized Gini social welfare functions; income differentials; Lorenz dominance;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207. [Downloadable!] (restricted)
  4. 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.
  5. 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. [Downloadable!] (restricted)
  6. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August. [Downloadable!] (restricted)
  7. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-16, March. [Downloadable!] (restricted)
  8. Yitzhaki, Shlomo, 1979. "Relative Deprivation and the Gini Coefficient," The Quarterly Journal of Economics, MIT Press, vol. 93(2), pages 321-24, May. [Downloadable!] (restricted)
  9. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June. [Downloadable!] (restricted)
  10. 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.
  11. Blackorby, C. & Bossert, W. & Donaldson, D., 1995. "Income Inequality Measurement: The Normative Approach," UBC Departmental Archives 95-23, UBC Department of Economics.
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  12. Weiss, Yoram & Fershtman, Chaim, 1998. "Social status and economic performance:: A survey," European Economic Review, Elsevier, vol. 42(3-5), pages 801-820, May. [Downloadable!] (restricted)
    Other versions:
  13. 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.
  14. 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. [Downloadable!] (restricted)
  15. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April. [Downloadable!] (restricted)
  16. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January. [Downloadable!] (restricted)
  17. 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.
  18. Alain Chateauneuf & Michèle Cohen & Isaac Meilijson, 2004. "Four notions of mean preserving increase in risk, risk attitudes and applications to the Rank-Dependent Expected Utility model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00212281_v1, HAL. [Downloadable!]
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  19. Satya R. Chakravarty & Patrick Moyes, 2003. "Individual welfare, social deprivation and income taxation," Economic Theory, Springer, vol. 21(4), pages 843-869, 06. [Downloadable!] (restricted)
  20. 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. [Downloadable!] (restricted)
  21. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September. [Downloadable!] (restricted)
  22. Thon, Dominique, 1987. "Redistributive properties of progressive taxation," Mathematical Social Sciences, Elsevier, vol. 14(2), pages 185-191, October. [Downloadable!] (restricted)
  23. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April. [Downloadable!] (restricted)
  24. 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.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Brice Magdalou & Patrick Moyes, 2009. "Deprivation, welfare and inequality," Social Choice and Welfare, Springer, vol. 32(2), pages 253-273, February. [Downloadable!] (restricted)
  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. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!] (restricted)
  4. Kristof Bosmans, 2007. "Comparing degrees of inequality aversion," Social Choice and Welfare, Springer, vol. 29(3), pages 405-428, October. [Downloadable!] (restricted)
    Other versions:
  5. 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. [Downloadable!]
  6. 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. [Downloadable!]
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