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Unit-Consistent Aggregative Multidimensional Inequality Measures: A Characterization

  • Henar Diez

    (University of the Basque Country)

  • Mª Casilda Lasso de la Vega

    ()

    (University of the Basque Country)

  • Ana Marta Urrutia

    (University of the Basque Country)

Inequality among people involves comparisons of social indicators such as income, health, education and so on. In recent years the number of studies both theoretical and empirical which take into account not only the individual’s income but also these other attributes has significantly increased. As a consequence the development of measures capable of capturing multidimensional inequality and satisfying reasonable axioms becomes a useful and important exercise.The aim of this paper is no other than this. More precisely, we consider the unit consistency axiom proposed by B. Zheng in the unidimensional framework. This axiom demands that the inequality rankings, rather than the inequality cardinal values as the traditional scale invariance principle requires, are not altered when income is measured in different monetary units. We propose a natural generalization of this axiom in the multidimensional setting and characterize the class of aggregative multidimensional inequality measures which are unit-consistent.

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File URL: http://www.ecineq.org/milano/WP/ECINEQ2007-66.pdf
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Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 66.

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Length: 23 pages
Date of creation: 2007
Date of revision:
Handle: RePEc:inq:inqwps:ecineq2007-66
Contact details of provider: Web page: http://www.ecineq.org
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  1. Kai-yuen Tsui, 2002. "Multidimensional poverty indices," Social Choice and Welfare, Springer, vol. 19(1), pages 69-93.
  2. François Bourguignon & Satya Chakravarty, 2003. "The Measurement of Multidimensional Poverty," Journal of Economic Inequality, Springer, vol. 1(1), pages 25-49, April.
  3. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  4. Thibault Gajdos & John A. Weymark, 2003. "Multidimensional Generalized Gini Indices," Vanderbilt University Department of Economics Working Papers 0311, Vanderbilt University Department of Economics, revised Jul 2003.
  5. Christian List, 1999. "Multidimensional Inequality Measurement: A Proposal," Economics Series Working Papers 1999-W27, University of Oxford, Department of Economics.
  6. Koshevoy, G. A. & Mosler, K., 1997. "Multivariate Gini Indices," Journal of Multivariate Analysis, Elsevier, vol. 60(2), pages 252-276, February.
  7. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
  8. M. Fleurbaey & A. Trannoy, 2000. "The Impossibility of a Paretian Egalitarian," THEMA Working Papers 2000-26, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  9. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
  10. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-97, July.
  11. Coral del RÎo & Javier Ruiz-Castillo, 2000. "Intermediate inequality and welfare," Social Choice and Welfare, Springer, vol. 17(2), pages 223-239.
  12. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975, March.
  13. 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.
  14. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 183-201, April.
  15. Gleb A. Koshevoy & Karl Mosler, 2007. "Multivariate Lorenz dominance based on zonoids," AStA Advances in Statistical Analysis, Springer, vol. 91(1), pages 57-76, March.
  16. Satya Chakravarty & Swami Tyagarupananda, 2009. "The subgroup decomposable intermediate indices of inequality," Spanish Economic Review, Springer, vol. 11(2), pages 83-97, June.
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