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Multidimensional generalized Gini indices

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Author Info
Thibault Gajdos ()
John Weymark ()

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Abstract

The axioms that characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a two-stage aggregation representation if these axioms and a separability assumption are satisfied. In the first stage, the distributions of each attribute are aggregated using generalized Gini social evaluation functions. The functional form of the second-stage aggregator depends on the number of attributes and on which version of a comonotonic additivity axiom is used. The implications of these results for the corresponding multidimensional indices of relative and absolute inequality are also considered. Copyright Springer-Verlag Berlin/Heidelberg 2005

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File URL: http://hdl.handle.net/10.1007/s00199-004-0529-x
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Publisher Info
Article provided by Springer in its journal Economic Theory.

Volume (Year): 26 (2005)
Issue (Month): 3 (October)
Pages: 471-496
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Handle: RePEc:spr:joecth:v:26:y:2005:i:3:p:471-496

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Keywords: Generalized Gini; multidimensional inequality.;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    Other versions:
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  7. François Bourguignon & Satya Chakravarty, 2003. "The Measurement of Multidimensional Poverty," Journal of Economic Inequality, Springer, vol. 1(1), pages 25-49, April. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Rebeca Echávarri & Iñaki Permanyer, 2008. "Ranking profiles of capability sets," Social Choice and Welfare, Springer, vol. 31(3), pages 521-535, October. [Downloadable!] (restricted)
  2. Alfred Müller & Marco Scarsini, 2003. "Archimedean Copulae and Positive Dependence," ICER Working Papers - Applied Mathematics Series 25-2003, ICER - International Centre for Economic Research. [Downloadable!]
    Other versions:
  3. Marat Ibragimov & Rustam Ibragimov, 2007. "Market Demand Elasticity and Income Inequality," Economic Theory, Springer, vol. 32(3), pages 579-587, September. [Downloadable!] (restricted)
  4. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research. [Downloadable!]
  5. Elisabetta Croci Angelini & Alessandra Michelangeli, 2008. "Measuring Well-Being differences across EU Countries. A Multidimensional Analysis of Income, Housing, Health, and Education," Working Papers 15-2008, Macerata University, Department of Studies on Economic Development (DiSSE), revised Nov 2008. [Downloadable!]
  6. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research. [Downloadable!]
  7. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003. [Downloadable!]
    Other versions:
  8. Thibault Gajdos & Eric Maurin, 2002. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," ICER Working Papers - Applied Mathematics Series 15-2003, ICER - International Centre for Economic Research, revised Mar 2003. [Downloadable!]
    Other versions:
  9. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003. [Downloadable!]
  10. John A. Weymark, 2003. "The Normative Approach to the Measurement of Multidimensional Inequality," Working Papers 0314, Department of Economics, Vanderbilt University, revised Jan 2004. [Downloadable!]
  11. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research. [Downloadable!]
  12. Masato Okamoto, 2009. "Decomposition of gini and multivariate gini indices," Journal of Economic Inequality, Springer, vol. 7(2), pages 153-177, June. [Downloadable!] (restricted)
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