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Lorenz non-consistent welfare and inequality measurement

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  • Alain Chateauneuf

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  • 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 2004

Suggested Citation

  • Alain Chateauneuf & Patrick Moyes, 2004. "Lorenz non-consistent welfare and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 2(2), pages 61-87, August.
  • Handle: RePEc:kap:jecinq:v:2:y:2004:i:2:p:61-87
    DOI: 10.1007/s10888-004-4383-7
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    References listed on IDEAS

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    Citations

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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 (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.
    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. Stephen Bazen & Patrick Moyes, 2011. "Elitism and Stochastic Dominance," Working Papers halshs-00576585, HAL.
    9. 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.
    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

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

    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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