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What do normative indices of multidimensional inequality really measure?

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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?," LIDAM Discussion Papers CORE 2013035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2013035
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    3. Loïc Berger & Johannes Emmerling, 2020. "Welfare As Equity Equivalents," Journal of Economic Surveys, Wiley Blackwell, vol. 34(4), pages 727-752, September.
    4. Philipp Poppitz, 2019. "Multidimensional Inequality and Divergence: The Eurozone Crisis in Retrospect," Working Papers V-420-19, University of Oldenburg, Department of Economics, revised Feb 2019.
    5. 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.
    6. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
    7. Rohde, Kirsten I.M. & Van Ourti, Tom & Soebhag, Amar, 2023. "Reducing socioeconomic health inequalities? A questionnaire study of majorization and invariance conditions," Journal of Health Economics, Elsevier, vol. 90(C).
    8. Koen Decancq, 2020. "Measuring cumulative deprivation and affluence based on the diagonal dependence diagram," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 103-117, August.
    9. Xu, Aiting & Qiu, Keyang & Zhu, Yuhan, 2023. "The measurements and decomposition of innovation inequality: Based on Industry − University − Research perspective," Journal of Business Research, Elsevier, vol. 157(C).
    10. 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.
    11. Lidia Ceriani & Chiara Gigliarano, 2020. "Multidimensional Well-Being: A Bayesian Networks Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 152(1), pages 237-263, November.
    12. DUJARDIN, Claire & lorant, VINCENT & THOMAS, Isabelle, 2013. "Self-assessed health of elderly people in Brussels: does the built environment matter?," LIDAM Discussion Papers CORE 2013048, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Rolf Aaberge & Ugo Colombino, 2018. "Structural Labour Supply Models and Microsimulation," International Journal of Microsimulation, International Microsimulation Association, vol. 11(1), pages 162-197.
    14. 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.
    15. PAPAVASILIOU, Anthony & HE, Yi & SVOBODA, Alva, 2013. "Self-commitment of combined cycle units under electricity price uncertainty," LIDAM Discussion Papers CORE 2013051, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Suman Seth and Maria Emma Santos, 2018. "Multidimensional Inequality and Human Development," OPHI Working Papers ophiwp114_2.pdf, Queen Elizabeth House, University of Oxford.
    17. Florent Bresson & Jean-Yves Duclos & Flaviana Palmisano, 2019. "Intertemporal pro-poorness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(1), pages 65-96, January.
    18. Paolo Giovanni Piacquadio, 2017. "A Fairness Justification of Utilitarianism," Econometrica, Econometric Society, vol. 85, pages 1261-1276, July.
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    More about this item

    Keywords

    multidimensional inequality measurement; efficiency; uniform majorization; correlation increasing majorization;
    All these keywords.

    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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