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Classical inequality indices, welfare functions, and the dual decomposition

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Author Info

  • Oihana Aristondo

    (BRIDGE Research Group, Universidad del País Vasco)

  • José Luis García-Lapres

    ()
    (PRESAD Research Group, IMUVA, Universidad Valladolid)

  • Casilda Lasso de la Vega

    ()
    (BRIDGE Research Group, Universidad del País Vasco)

  • Ricardo Alberto Marques Pereira

    ()
    (Dipartimento di Informatica e Studi Aziendali, Universitμa degli Studi di Trento)

Abstract

We consider the classical inequality measures due to Gini, Bonferroni, and De Vergottini and we present a brief review of the three inequality indices and the associated welfare functions, in the correspondence scheme introduced by Blackorby and Donaldson, and Weymark. The three classical inequality indices incorporate different value judgments in the measurement of inequality, leading to different behavior under income transfers between individuals in the population. The welfare functions associated with the Gini, Bonferroni, and (normalized) De Vergottini indices are Schur-concave OWA functions, with larger weights for lower incomes. We examine the dual decomposition and the orness degree of the three welfare functions in the standard framework of aggregation functions on the [0; 1]n domain, and show that it offers interesting insight on the distinct and complementary nature of the classical inequality indices.

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File URL: http://www.ecineq.org/milano/WP/ECINEQ2012-253.pdf
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Bibliographic Info

Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 253.

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Length: 29 pages
Date of creation: Apr 2012
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Handle: RePEc:inq:inqwps:ecineq2012-253

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Keywords: income inequality and social welfare; classical Gini; Bonferroni; and De Vergottini inequality indices; welfare functions; aggregation functions; WA and OWA functions; dual decomposition; ornessClassification-JEL: D63; I32;

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  1. Porath Elchanan Ben & Gilboa Itzhak, 1994. "Linear Measures, the Gini Index, and The Income-Equality Trade-off," Journal of Economic Theory, Elsevier, vol. 64(2), pages 443-467, December.
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  18. Oihana Aristondo & José Luis García-Lapresta & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira, 2011. "The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality," Working Papers 203, ECINEQ, Society for the Study of Economic Inequality.
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Cited by:
  1. Silvia Bortot & Ricardo Alberto Marques Pereira, 2013. "The binomial Gini inequality indices and the binomial decomposition of welfare functions," Working Papers 305, ECINEQ, Society for the Study of Economic Inequality.

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