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What do normative indices of multidimensional inequality really measure?

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  • BOSMANS, Kristof

    ()
    (Department of Economics, Maastricht University, NL-6211 LM Maastricht, The Netherlands)

  • DECANCQ, Koen

    ()
    (Herman Deleeck Centre for Social Policy, University of Antwerp, B-2000 Antwerp, Belgium; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • OOGHE, Erwin

    ()
    (Center for Economic Studies, KU Leuven, B-3000 Leuve, Belgium)

Abstract

We argue that normative indices of multidimensional inequality do not only measure a distribution’s extent of inequity (i.e., the gaps between the better-off and the worse-off), but also its extent of inefficiency (i.e., the non-realized mutually beneficial exchanges of goods). We provide a decomposition that allows quantifying these two parts of inequality. Exact formulas of the inequity and inefficiency components are provided for a generic class of social welfare functions. The inequity component turns out to be a two-stage measure, which applies a unidimensional inequality measure to the vector of well-being levels. We critically discuss two prominent transfer principles, viz., uniform majorization and correlation increasing majorization, in the light of the decomposition. A decomposition of inequality in human development illustrates the analysis.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2013035.

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Date of creation: 09 Jul 2013
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Handle: RePEc:cor:louvco:2013035

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Keywords: multidimensional inequality measurement; efficiency; uniform majorization; correlation increasing majorization;

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  1. Kristof Bismans & Luc Lauwers & Erwin Ooghe, 2006. "A consistent multidimensional Pigou-Dalton transfer principle," Center for Economic Studies - Discussion papers ces0620, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  2. Koen Decancq & André Decoster & Erik Schokkaert, 2007. "The evolution of World inequality in Well-being," Center for Economic Studies - Discussion papers ces0704, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  3. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
  4. A. Atkinson, 2003. "Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches," Journal of Economic Inequality, Springer, vol. 1(1), pages 51-65, April.
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  6. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  7. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer, vol. 26(3), pages 471-496, October.
  8. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  9. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
  10. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
  11. François Bourguignon & Satya Chakravarty, 2003. "The Measurement of Multidimensional Poverty," Journal of Economic Inequality, Springer, vol. 1(1), pages 25-49, April.
  12. Duclos, Jean-Yves & Sahn, David E. & Younger, Stephen D., 2011. "Partial multidimensional inequality orderings," Journal of Public Economics, Elsevier, vol. 95(3-4), pages 225-238, April.
  13. Decancq, Koen & Ooghe, Erwin, 2010. "Has the world moved forward? A robust multidimensional evaluation," Economics Letters, Elsevier, vol. 107(2), pages 266-269, May.
  14. M. Lasso de la Vega & Ana Urrutia, 2011. "Characterizing how to aggregate the individuals’ deprivations in a multidimensional framework," Journal of Economic Inequality, Springer, vol. 9(2), pages 183-194, June.
  15. Kihlstrom, Richard E & Mirman, Leonard J, 1981. "Constant, Increasing and Decreasing Risk Aversion with Many Commodities," Review of Economic Studies, Wiley Blackwell, vol. 48(2), pages 271-80, April.
  16. 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.
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