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Multidimensional Inequality Measurement: A Proposal

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  • Christian List

Abstract

Two essential intuitions about the concept of multidimensional inequality have been highlighted in the emerging body of literature on this subject: first, multidimensional inequality should be a function of the uniform inequality of a multivariate distribution of goods or attributes across people (Kolm, 1977); and second, it should also be a function of the cross-correlation between distributions of goods or attributes in different dimensions (Atkinson and Bourguignon, 1982; Walzer, 1983). While the first intuition has played a major role in the design of fully-fledged multidimensional inequality indices, the second one has only recently received attention (Tsui, 1999); and, so far, multidimensional generalized entropy measures are the only inequality measures known to respect both intuitions. The present paper proposes a general method of designing a wider range of multidimensional inequality indices that also respect both intuitions and illustrates this method by defining two classes of such indices: a generalization of the Gini coefficient, and a generalization of Atkinsons one-dimensional measure of inequality.

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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 1999-W27.

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Date of creation: 01 Nov 1999
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Handle: RePEc:oxf:wpaper:1999-w27

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Keywords: multidimensional inequality; multivariate majorization;

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Cited by:
  1. Kai-yuen Tsui, 2009. "Measurement of income mobility: a re-examination," Social Choice and Welfare, Springer, vol. 33(4), pages 629-645, November.
  2. Casilda Lasso de la Vega & Ana Urrutia & Amaia Sarachu, 2010. "Characterizing multidimensional inequality measures which fulfil the Pigou–Dalton bundle principle," Social Choice and Welfare, Springer, vol. 35(2), pages 319-329, July.
  3. Barry C. Arnold, 2005. "Inequality measures for multivariate distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 317-327.
  4. Andrea Brandolini, 2008. "On applying synthetic indices of multidimensional well-being: health and income inequalities in selected EU countries," Temi di discussione (Economic working papers) 668, Bank of Italy, Economic Research and International Relations Area.
  5. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer, vol. 26(3), pages 471-496, October.
  6. Koen Decancq & María Ana Lugo, 2009. "Measuring inequality of well-being with a correlation-sensitive multidimensional Gini index," Working Papers 124, ECINEQ, Society for the Study of Economic Inequality.
  7. Henar Diez & Mª Casilda Lasso de la Vega & Ana Marta Urrutia, 2007. "Unit-Consistent Aggregative Multidimensional Inequality Measures: A Characterization," Working Papers 66, ECINEQ, Society for the Study of Economic Inequality.
  8. John A. Weymark, 2003. "The Normative Approach to the Measurement of Multidimensional Inequality," Vanderbilt University Department of Economics Working Papers 0314, Vanderbilt University Department of Economics, revised Jan 2004.
  9. Banerjee, Asis Kumar, 2010. "A multidimensional Gini index," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 87-93, September.

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