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Lorenz non-consistent welfare and inequality measurement

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  • Alain Chateauneuf

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Patrick Moyes

    (GREThA - Groupe de Recherche en Economie Théorique et Appliquée - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique)

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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Suggested Citation

  • Alain Chateauneuf & Patrick Moyes, 2004. "Lorenz non-consistent welfare and inequality measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00156441, HAL.
    • Handle: RePEc:hal:cesptp:hal-00156441
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    Cited by:

    1. 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.
    2. 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.
    3. Brice MAGDALOU & Patrick MOYES, 2008. "Social Welfare, Inequality and Deprivation," Cahiers du GREThA (2007-2019) 2008-23, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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. 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.

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    More about this item

    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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