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Inverse stochastic dominance, inequality measurement and Gini indices

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  • Claudio Zoli

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Abstract

We investigate the relationship between the third degree inverse stochastic dominance criterion introduced in Muliere and Scarsini (1989) and inequality dominance when Lorenz curves intersect. We propose a new definition of transfer sensitivity aimed at strengthening the Pigou-Dalton Principle of Transfers. Our definition is dual to that suggested by Shorrocks and Foster (1987). It involves a regressive transfer and a progressive transfer both from the same donor, leaving the Gini index unchanged. We prove that finite sequences of these transfers and/or progressive transfers characterize the third degree inverse stochastic dominance criterion. This criterion allows us to make unanimous inequality judgements even when Lorenz curves intersect. The Gini coefficient becomes relevant in these cases in order to conclusively rank the distributions. Copyright Springer-Verlag 2002

Suggested Citation

  • Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 77(1), pages 119-161, December.
  • Handle: RePEc:kap:jeczfn:v:77:y:2002:i:1:p:119-161
    DOI: 10.1007/BF03052502
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    Citations

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    Cited by:

    1. Francesco Andreoli & Arnaud Lefranc, 2013. "Equalization of opportunity: Definitions and implementable conditions," Working Papers 310, ECINEQ, Society for the Study of Economic Inequality.
    2. Mornet, Pauline & Zoli, Claudio & Mussard, Stéphane & Sadefo-Kamdem, Jules & Seyte, Françoise & Terraza, Michel, 2013. "The (α, β)-multi-level α-Gini decomposition with an illustration to income inequality in France in 2005," Economic Modelling, Elsevier, vol. 35(C), pages 944-963.
    3. 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.
    4. repec:eee:infome:v:11:y:2017:i:3:p:689-703 is not listed on IDEAS
    5. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    6. Francesco Andreoli, 2013. "Inference for Inverse Stochastic Dominance," Working Papers 295, ECINEQ, Society for the Study of Economic Inequality.
    7. Andreoli, Francesco & Havnes, Tarjei & Lefranc, Arnaud, 2014. "Equalization of Opportunity: Definitions, Implementable Conditions and Application to Early-Childhood Policy Evaluation," IZA Discussion Papers 8503, Institute for the Study of Labor (IZA).
    8. Patrick Moyes & Brice Magdalou, 2008. "Social Welfare, Inequality and Deprivation," LIS Working papers 502, LIS Cross-National Data Center in Luxembourg.
    9. repec:spr:sochwe:v:51:y:2018:i:1:d:10.1007_s00355-017-1106-0 is not listed on IDEAS
    10. Manfred Krtscha, 2017. "Some axiomatics of inequality measurement, with specific reference to intermediate indices," Working Papers 445, ECINEQ, Society for the Study of Economic Inequality.
    11. repec:eee:ecolet:v:159:y:2017:i:c:p:100-103 is not listed on IDEAS
    12. Buhong Zheng, 2011. "A new approach to measure socioeconomic inequality in health," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 555-577, December.
    13. Patrick Moyes, 2007. "An extended Gini approach to inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 279-303, December.
    14. Tommaso Lando & Lucio Bertoli-Barsotti, 2016. "Weak orderings for intersecting Lorenz curves," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 177-192, August.
    15. Peter Lambert & Giuseppe Lanza, 2006. "The effect on inequality of changing one or two incomes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 4(3), pages 253-277, December.
    16. Michel Le Breton & Eugenio Peluso, 2009. "Third-degree stochastic dominance and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(3), pages 249-268, September.
    17. Sreenivasan Subramanian, 2015. "More tricks with the lorenz curve," Economics Bulletin, AccessEcon, vol. 35(1), pages 580-589.

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