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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.

Suggested Citation

  • 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.
    • Handle: RePEc:van:wpaper:0314
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    References listed on IDEAS

    as
    1. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 471-496, October.
    2. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    3. Ben-Porath, Elchanan & Gilboa, Itzhak & Schmeidler, David, 1997. "On the Measurement of Inequality under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 194-204, July.
    4. 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.
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    6. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    7. List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
    8. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    9. 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 665-685, November.
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    13. François Bourguignon & Satya R. Chakravarty, 2019. "The Measurement of Multidimensional Poverty," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 83-107, Springer.
    14. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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    16. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    17. Robert A. Pollak, 1971. "Additive Utility Functions and Linear Engel Curves," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(4), pages 401-414.
    18. Marc Fleurbaey & Alain Trannoy, 2003. "The impossibility of a Paretian egalitarian," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 243-263, October.
    19. Kai-yuen Tsui, 2002. "Multidimensional poverty indices," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(1), pages 69-93.
    20. 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.
    21. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    22. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 1-13.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Kai-yuen Tsui, 2009. "Measurement of income mobility: a re-examination," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(4), pages 629-645, November.
    2. Benoît Tarroux, 2015. "Comparing two-dimensional distributions: a questionnaire-experimental approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 87-108, January.
    3. Sebastian Leitner & Robert Stehrer, 2011. "Subgroup and Shapely Value Decompositions of Multidimensional Inequality: An Application to South East European Countries," wiiw Balkan Observatory Working Papers 96, The Vienna Institute for International Economic Studies, wiiw.
    4. 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.
    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. Patricia Justino, 2012. "Multidimensional welfare distributions: empirical application to household panel data from Vietnam," Applied Economics, Taylor & Francis Journals, vol. 44(26), pages 3391-3405, September.
    7. Benoît Tarroux, 2012. "Are equalization payments making Canadians better off? A two-dimensional dominance answer," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(1), pages 19-44, March.
    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. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    10. Benoît Tarroux, 2012. "Appraising two-Dimensional Inequality: A Questionnaire-Experimental Approach," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201216, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.

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    More about this item

    Keywords

    Multidimensional inequality; inequality indices; multivariate inequality measurement; multivariate majorization;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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