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The Normative Approach to the Measurement of Multidimensional Inequality

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  • John A. Weymark

    ()
    (Department of Economics, Vanderbilt University)

Abstract

This article provides an introduction to the normative approach to multidimensional inequality measurement. Multivariate generalizations of the procedures used to construct univariate inequality indices from social evaluation orderings are described. Axiomatizations of multivariate Atkinson, Kolm-Pollak, and generalized Gini indices are discussed. Maasoumi's Econometrica (1986) two-stage procedure for constructing a multivariate inequality index is critically examined. A dominance criterion proposed by Tsui Social Choice and Welfare (1999) that takes account of the dependence between the individual distributions of the attributes is also considered.

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File URL: http://www.accessecon.com/pubs/VUECON/vu03-w14R.pdf
File Function: Revised, 2004
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Bibliographic Info

Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0314.

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Date of creation: Jul 2003
Date of revision: Jan 2004
Handle: RePEc:van:wpaper:0314

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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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Keywords: Multidimensional inequality; inequality indices; multivariate inequality measurement; multivariate majorization;

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References

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  1. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  2. Foster, James E, 1994. "Normative Measurement: Is Theory Relevant?," American Economic Review, American Economic Association, vol. 84(2), pages 365-70, May.
  3. Marc Fleurbaey & Alain Trannoy, 2003. "The impossibility of a Paretian egalitarian," Social Choice and Welfare, Springer, vol. 21(2), pages 243-263, October.
  4. Ebert U., 1996. "Income inequality and differences in household size," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 57-58, February.
  5. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer, vol. 26(3), pages 471-496, October.
  6. 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.
  7. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  8. WEYMARK, John A., . "Generalized Gini inequality indices," CORE Discussion Papers RP -453, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Kai-yuen Tsui, 1999. "Multidimensional inequality and multidimensional generalized entropy measures: An axiomatic derivation," Social Choice and Welfare, Springer, vol. 16(1), pages 145-157.
  10. Thibault Gadjos & Eric Maurin, 2002. "Unequal Uncertainties and Uncertain Inequalities : An Axiomatic Approach," Working Papers 2002-32, Centre de Recherche en Economie et Statistique.
  11. List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
  12. Koshevoy, G. A. & Mosler, K., 1997. "Multivariate Gini Indices," Journal of Multivariate Analysis, Elsevier, vol. 60(2), pages 252-276, February.
  13. Pollak, Robert A, 1971. "Additive Utility Functions and Linear Engel Curves," Review of Economic Studies, Wiley Blackwell, vol. 38(116), pages 401-14, October.
  14. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
  15. Tsui Kai-Yuen, 1995. "Multidimensional Generalizations of the Relative and Absolute Inequality Indices: The Atkinson-Kolm-Sen Approach," Journal of Economic Theory, Elsevier, vol. 67(1), pages 251-265, October.
  16. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-85, November.
  17. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
  18. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  19. Kai-yuen Tsui, 2002. "Multidimensional poverty indices," Social Choice and Welfare, Springer, vol. 19(1), pages 69-93.
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Citations

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Cited by:
  1. 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.
  2. Jean-Yves Duclos & David E. Sahn & Stephen D. Younger, 2010. "Partial Multidimensional Inequality Orderings," Cahiers de recherche 1003, CIRPEE.
  3. 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.
  4. Finn Tarp & Lars Peter Østerdal, 2007. "Multivariate Discrete First Order Stochastic Dominance," Discussion Papers 07-23, University of Copenhagen. Department of Economics.
  5. Maria Ana Lugo & Koen Decancq, 2009. "Measuring Inequality of Well-Being with a Correlation-Sensitive Multidimensional Gini Index," Economics Series Working Papers 459, University of Oxford, Department of Economics.
  6. Benoît Tarroux, 2012. "Are equalization payments making Canadians better off? A two-dimensional dominance answer," Journal of Economic Inequality, Springer, vol. 10(1), pages 19-44, March.
  7. Thibault Gadjos & John A, Weymark, 2003. "Multidimensional Generalized Gini Indices," Working Papers 2003-16, Centre de Recherche en Economie et Statistique.
  8. 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.
  9. SPRUMONT, Yves, 2007. "Resource Egalitarianism with a Dash of Efficiency," Cahiers de recherche 2007-03, Universite de Montreal, Departement de sciences economiques.
  10. 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.
  11. 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.
  12. Kai-yuen Tsui, 2009. "Measurement of income mobility: a re-examination," Social Choice and Welfare, Springer, vol. 33(4), pages 629-645, November.
  13. Nicolas Gravel & Patrick Moyes, 2006. "Ethically Robust Comparisons of Distributions of Two Individual Attributes," IDEP Working Papers 0605, Institut d'economie publique (IDEP), Marseille, France, revised Aug 2006.

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