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The Normative Approach to the Measurement of Multidimensional Inequality

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Author Info
John A. Weymark () (Department of Economics, Vanderbilt University)

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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.vanderbilt.edu/Econ/wparchive/workpaper/vu03-w14R.pdf
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File Function: Revised, 2004
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Publisher Info
Paper provided by Department of Economics, Vanderbilt University in its series 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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Related research
Keywords: Multidimensional inequality; inequality indices; multivariate inequality measurement; multivariate majorization;

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Find related papers by JEL classification:
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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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.:
  1. Thibault Gajdos & Eric Maurin, 2004. "Unequal Uncertainties and Uncertain Inequalities: An Axiomatic Approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085940_v1, HAL. [Downloadable!]
    Other versions:
  2. Thibault Gajdos & John A. Weymark, 2003. "Multidimensional generalized Gini indices," ICER Working Papers - Applied Mathematics Series 16-2003, ICER - International Centre for Economic Research. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Marc Fleurbaey & Alain Trannoy, 2003. "The impossibility of a Paretian egalitarian," Social Choice and Welfare, Springer, vol. 21(2), pages 243-263, October. [Downloadable!] (restricted)
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  6. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Blackwell Publishing, vol. 49(2), pages 183-201, April. [Downloadable!] (restricted)
  7. Kai-yuen Tsui, 2002. "Multidimensional poverty indices," Social Choice and Welfare, Springer, vol. 19(1), pages 69-93. [Downloadable!] (restricted)
  8. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August. [Downloadable!] (restricted)
  9. Koshevoy, G.A. & Mosler, K., 1995. "Multivariate Gini Indices," Statistics and Econometrics 7/95, Universitaet zu Koeln. [Downloadable!]
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  10. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February. [Downloadable!] (restricted)
  11. List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
  12. Ebert, Udo, 1995. "Income inequality and differences in household size," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 37-55, August. [Downloadable!] (restricted)
  13. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June. [Downloadable!] (restricted)
  14. Blackorby, C. & Bossert, W. & Donaldson, D., 1995. "Income Inequality Measurement: The Normative Approach," UBC Departmental Archives 95-23, UBC Department of Economics.
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  15. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Blackwell Publishing, vol. 54(3), pages 485-97, July. [Downloadable!] (restricted)
  16. 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. [Downloadable!] (restricted)
  17. Foster, James E, 1994. "Normative Measurement: Is Theory Relevant?," American Economic Review, American Economic Association, vol. 84(2), pages 365-70, May. [Downloadable!] (restricted)
  18. Pollak, Robert A, 1971. "Additive Utility Functions and Linear Engel Curves," Review of Economic Studies, Blackwell Publishing, vol. 38(116), pages 401-14, October. [Downloadable!] (restricted)
  19. Bourguignon, F. & Chakravarty, S.R., 1998. "The Measurement of Multidimensional Poverty," DELTA Working Papers 98-12, DELTA (Ecole normale supérieure).
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  20. 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. [Downloadable!] (restricted)
  21. Walter Bossert & John A. Weymark, . "Utility in Social Choice," Old UBC Departmental Papers 9623, UBC Department of Economics. [Downloadable!]
  22. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February. [Downloadable!] (restricted)
Full references

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. 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!]
  2. Benoit Tarroux, 2006. "Are Equalization Payments Making Canadians Better Off? A Two-Dimensional Dominance Answer," IDEP Working Papers 0608, Institut d'economie publique (IDEP), Marseille, France, revised 15 Nov 2006. [Downloadable!]
  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. [Downloadable!]
  4. 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. [Downloadable!]
  5. Thibault Gajdos & John A. Weymark, 2003. "Multidimensional Generalized Gini Indices," Working Papers 0311, Department of Economics, Vanderbilt University, revised Jul 2003. [Downloadable!]
    Other versions:
  6. Finn Tarp & Lars Peter Østerdal, 2007. "Multivariate Discrete First Order Stochastic Dominance," Discussion Papers 07-23, University of Copenhagen. Department of Economics. [Downloadable!]
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