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Classical inequality indices, welfare functions, and the dual decomposition

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  • Oihana Aristondo
  • JosŽ Luis Garc’a-Lapresta
  • Casilda Lasso de la Vega
  • Ricardo Alberto Marques Pereira

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 , l ]^n domain, and show that it offers interesting insight on the distinct and complementary nat ure of the classical inequality indices.

Suggested Citation

  • Oihana Aristondo & JosŽ Luis Garc’a-Lapresta & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira, 2012. "Classical inequality indices, welfare functions, and the dual decomposition," DISA Working Papers 2012/06, Department of Computer and Management Sciences, University of Trento, Italy, revised Jun 2012.
    • Handle: RePEc:trt:disawp:2012/06
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    Cited by:

    1. Mariateresa Ciommi & Chiara Gigliarano & Giovanni Maria Giorgi, 2019. "Bonferroni And De Vergottini Are Back: New Subgroup Decompositions And Bipolarization Measures," Working Papers 439, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    2. 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.
    3. Elena Bárcena-Martin & Jacques Silber, 2017. "The Bonferroni index and the measurement of distributional change," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 1-16, April.

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    More about this item

    Keywords

    incarne inequality and sacial welfare; classical Gini; Banferrani; and De Vergattini inequality indices; welfare functions; aggregation functions; WA and OWA functions; dual decomposition; arness;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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