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What do normative indices of multidimensional inequality really measure?

Author

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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.

Suggested Citation

  • BOSMANS, Kristof & DECANCQ, Koen & OOGHE, Erwin, 2013. "What do normative indices of multidimensional inequality really measure?," CORE Discussion Papers 2013035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2013035
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Shatakshee Dhongde & Yi Li & Prasanta K. Pattanaik & Yongsheng Xu, 2016. "Binary data, hierarchy of attributes, and multidimensional deprivation," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 14(4), pages 363-378, December.
    2. repec:bla:econom:v:84:y:2017:i:334:p:210-238 is not listed on IDEAS
    3. Koen Decancq & Marc Fleurbaey & Erik Schokkaert, 2017. "Wellbeing Inequality and Preference Heterogeneity," Economica, London School of Economics and Political Science, vol. 84(334), pages 210-238, April.
    4. Kristof Bosmans & Z. Emel Öztürk, 2018. "An axiomatic approach to the measurement of envy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 247-264, February.
    5. Bosmans, Kristof & Decancq, Koen & Ooghe, Erwin, 0. "Who's afraid of aggregating money metrics?," Theoretical Economics, Econometric Society.
    6. Koen Decancq, 2017. "Measuring Multidimensional Inequality in the OECD Member Countries with a Distribution-Sensitive Better Life Index," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 131(3), pages 1057-1086, April.
    7. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
    8. repec:wly:emetrp:v:85:y:2017:i::p:1261-1276 is not listed on IDEAS
    9. Paolo Giovanni Piacquadio, 2017. "A Fairness Justification of Utilitarianism," Econometrica, Econometric Society, vol. 85, pages 1261-1276, July.
    10. Lidia Ceriani & Chiara Gigliarano, 2016. "Multidimensional well-being: A Bayesian Networks approach," Working Papers 399, ECINEQ, Society for the Study of Economic Inequality.

    More about this item

    Keywords

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

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

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