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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?," 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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    as
    1. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521715348, Enero-Abr.
    2. Richard E. Kihlstrom & Leonard J. Mirman, 1981. "Constant, Increasing and Decreasing Risk Aversion with Many Commodities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(2), pages 271-280.
    3. repec:pri:rpdevs:deaton_price_indexes_inequality_and_the_measurement_of_world_poverty_aer. is not listed on IDEAS
    4. Gary S. Becker & Tomas J. Philipson & Rodrigo R. Soares, 2005. "The Quantity and Quality of Life and the Evolution of World Inequality," American Economic Review, American Economic Association, vol. 95(1), pages 277-291, March.
    5. Jeremy Lise & Shannon Seitz, 2011. "Consumption Inequality and Intra-household Allocations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 328-355.
    6. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    7. Satya R. Chakravarty, 2009. "Inequality, Polarization and Poverty," Economic Studies in Inequality, Social Exclusion, and Well-Being, Springer, number 978-0-387-79253-8, June.
    8. 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.
    9. Angus Deaton, 2010. "Price Indexes, Inequality, and the Measurement of World Poverty," American Economic Review, American Economic Association, vol. 100(1), pages 5-34, March.
    10. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 183-201.
    11. Audra J. Bowlus & Jean-Marc Robin, 2004. "Twenty Years of Rising Inequality in U.S. Lifetime Labour Income Values," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 709-742.
    12. M. Lasso de la Vega & Ana Urrutia, 2011. "Characterizing how to aggregate the individuals’ deprivations in a multidimensional framework," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(2), pages 183-194, June.
    13. Enrico Moretti, 2013. "Real Wage Inequality," American Economic Journal: Applied Economics, American Economic Association, vol. 5(1), pages 65-103, January.
    14. Kihlstrom, Richard E. & Mirman, Leonard J., 1974. "Risk aversion with many commodities," Journal of Economic Theory, Elsevier, vol. 8(3), pages 361-388, July.
    15. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931, Decembrie.
    16. Ravallion, Martin, 2012. "Troubling tradeoffs in the Human Development Index," Journal of Development Economics, Elsevier, vol. 99(2), pages 201-209.
    17. Ingvild Almas, 2012. "International Income Inequality: Measuring PPP Bias by Estimating Engel Curves for Food," American Economic Review, American Economic Association, vol. 102(2), pages 1093-1117, April.
    18. Donaldson, David & Weymark, John A., 1983. "Ethically flexible gini indices for income distributions in the continuum," Journal of Economic Theory, Elsevier, vol. 29(2), pages 353-358, April.
    19. Mark Huggett & Gustavo Ventura & Amir Yaron, 2011. "Sources of Lifetime Inequality," American Economic Review, American Economic Association, vol. 101(7), pages 2923-2954, December.
    20. Decancq, Koen & Decoster, André & Schokkaert, Erik, 2009. "The Evolution of World Inequality in Well-being," World Development, Elsevier, vol. 37(1), pages 11-25, January.
    21. Bosmans, Kristof & Lauwers, Luc & Ooghe, Erwin, 2009. "A consistent multidimensional Pigou-Dalton transfer principle," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1358-1371, May.
    22. Duclos, Jean-Yves & Sahn, David E. & Younger, Stephen D., 2011. "Partial multidimensional inequality orderings," Journal of Public Economics, Elsevier, vol. 95(3-4), pages 225-238, April.
    23. Marc Fleurbaey, 2003. "Social Welfare, Priority to the Worst-Off And the Dimensions of Individual Well-Being," IDEP Working Papers 0312, Institut d'economie publique (IDEP), Marseille, France.
    24. repec:pri:rpdevs:presidential%20address%2017january%202010%20all is not listed on IDEAS
    25. Pendakur, Krishna, 2002. "Taking prices seriously in the measurement of inequality," Journal of Public Economics, Elsevier, vol. 86(1), pages 47-69, October.
    26. Bosmans, Kristof & Decancq, Koen & Ooghe, Erwin, 2018. "Who's afraid of aggregating money metrics?," Theoretical Economics, Econometric Society, vol. 13(2), May.
    27. François Bourguignon & Christian Morrisson, 2002. "Inequality Among World Citizens: 1820-1992," American Economic Review, American Economic Association, vol. 92(4), pages 727-744, September.
    28. J De V. Graaff, 1977. "Equity and Efficiency as Components of the General Welfare," South African Journal of Economics, Economic Society of South Africa, vol. 45(4), pages 223-229, December.
    29. 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.
    30. Kannai, Yakar, 1980. "The ALEP definition of complementarity and least concave utility functions," Journal of Economic Theory, Elsevier, vol. 22(1), pages 115-117, February.
    31. Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
    32. Suman Seth, 2013. "A class of distribution and association sensitive multidimensional welfare indices," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(2), pages 133-162, June.
    33. Slesnick,Daniel T., 2001. "Consumption and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521497206, Enero-Abr.
    34. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    35. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    36. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 1-13.
    37. DECANCQ, Koen & OOGHE, Erwin, 2010. "Has the world moved forward?," LIDAM Reprints CORE 2352, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    38. A. Atkinson, 2003. "Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 51-65, April.
    39. repec:pri:rpdevs:presidential%20address%2017january%202010%20all.pdf is not listed on IDEAS
    40. Christopher J. Flinn, 2002. "Labour Market Structure and Inequality: A Comparison of Italy and the U.S," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 611-645.
    41. Decancq, Koen & Ooghe, Erwin, 2010. "Has the world moved forward? A robust multidimensional evaluation," Economics Letters, Elsevier, vol. 107(2), pages 266-269, May.
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    5. 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.
    6. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Discussion Papers 792, Statistics Norway, Research Department.
    7. 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.
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    11. Lidia Ceriani & Chiara Gigliarano & Paolo Verme, 2025. "Optimizing Data-driven Weights In Multidimensional Indexes," Papers 2504.06012, arXiv.org.
    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. 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).
    14. Paolo Giovanni Piacquadio, 2017. "A Fairness Justification of Utilitarianism," Econometrica, Econometric Society, vol. 85, pages 1261-1276, July.
    15. Rolf Aaberge & Ugo Colombino, 2018. "Structural Labour Supply Models and Microsimulation," International Journal of Microsimulation, International Microsimulation Association, vol. 11(1), pages 162-197.
    16. 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.
    17. Bosmans, Kristof & Decancq, Koen & Ooghe, Erwin, 2018. "Who's afraid of aggregating money metrics?," Theoretical Economics, Econometric Society, vol. 13(2), May.
    18. 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).
    19. 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.
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    21. Foster,James E. & Lokshin,Michael M., 2024. "Multidimensional and Specific Inequalities," Policy Research Working Paper Series 10748, The World Bank.
    22. 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.
    23. Suman Seth and Maria Emma Santos, 2018. "Multidimensional Inequality and Human Development," OPHI Working Papers ophiwp114_2.pdf, Queen Elizabeth House, University of Oxford.

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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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