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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
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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. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
  2. Foster, James E, 1994. "Normative Measurement: Is Theory Relevant?," American Economic Review, American Economic Association, vol. 84(2), pages 365-70, May.
  3. Koshevoy, Gleb & Mosler, Karl, 1995. "Multivariate Gini indices," Discussion Papers in Statistics and Econometrics 7/95, University of Cologne, Department for Economic and Social Statistics.
  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 A. Weymark, 2003. "Multidimensional generalized Gini indices," ICER Working Papers - Applied Mathematics Series 16-2003, ICER - International Centre for Economic Research.
  6. 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.
  7. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  8. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
  9. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  10. Kai-yuen Tsui, 2002. "Multidimensional poverty indices," Social Choice and Welfare, Springer, vol. 19(1), pages 69-93.
  11. WEYMARK, John A., . "Generalized Gini inequality indices," CORE Discussion Papers RP -453, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. 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.
  13. Christian List, 1999. "Multidimensional Inequality Measurement: A Proposal," Economics Series Working Papers 1999-W27, University of Oxford, Department of Economics.
  14. 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.
  15. 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.
  16. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  17. 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.
  18. Pollak, Robert A, 1971. "Additive Utility Functions and Linear Engel Curves," Review of Economic Studies, Wiley Blackwell, vol. 38(116), pages 401-14, October.
  19. 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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Citations

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Cited by:
  1. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer, vol. 26(3), pages 471-496, October.
  2. 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.
  3. 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.
  4. SPRUMONT, Yves, 2007. "Resource Egalitarianism with a Dash of Efficiency," Cahiers de recherche 03-2007, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Duclos, Jean-Yves & Sahn, David E. & Younger, Stephen D., 2011. "Partial multidimensional inequality orderings," Journal of Public Economics, Elsevier, vol. 95(3), pages 225-238.
  6. 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.
  7. Kai-yuen Tsui, 2009. "Measurement of income mobility: a re-examination," Social Choice and Welfare, Springer, vol. 33(4), pages 629-645, November.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Finn Tarp & Lars Peter Østerdal, 2007. "Multivariate Discrete First Order Stochastic Dominance," Discussion Papers 07-23, University of Copenhagen. Department of Economics.

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