IDEAS home Printed from https://ideas.repec.org/p/cor/louvrp/2838.html
   My bibliography  Save this paper

What do normative indices of multidimensional inequality really measure?

Author

Listed:
  • Kristof BOSMANS
  • Koen DECANCQ
  • Erwin OOGHE

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 us to quantify these two parts of inequality. Strikingly, the inequity component turns out to be a two-stage measure, that is, a measure that applies a unidimensional inequality measure to the vector of individual well-being levels. The decomposition also clarifies existing controversies surrounding two prominent transfer axioms, viz., uniform majorization and correlation increasing majorization. An application to inequality in human development illustrates the analysis.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Kristof BOSMANS & Koen DECANCQ & Erwin OOGHE, 2015. "What do normative indices of multidimensional inequality really measure?," LIDAM Reprints CORE 2838, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvrp:2838
    Note: In : Journal of Public Economics, 130, 94-104, 2015
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521715348, September.
    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, July.
    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.
    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, September.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Förster, Manuel & Mauleon, Ana & Vannetelbosch, Vincent J., 2016. "Trust and manipulation in social networks," Network Science, Cambridge University Press, vol. 4(2), pages 216-243, June.
    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. Da Costa, Shaun & O’Donnell, Owen & Van Gestel, Raf, 2024. "Distributionally sensitive measurement and valuation of population health," Journal of Health Economics, Elsevier, vol. 93(C).
    9. 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.
    10. 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).
    11. 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.
    12. 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.
    13. 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).
    14. Rolf Aaberge & Ugo Colombino, 2018. "Structural Labour Supply Models and Microsimulation," International Journal of Microsimulation, International Microsimulation Association, vol. 11(1), pages 162-197.
    15. 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.
    16. 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).
    17. Suman Seth and Maria Emma Santos, 2018. "Multidimensional Inequality and Human Development," OPHI Working Papers ophiwp114_2.pdf, Queen Elizabeth House, University of Oxford.
    18. 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.
    19. Paolo Giovanni Piacquadio, 2017. "A Fairness Justification of Utilitarianism," Econometrica, Econometric Society, vol. 85, pages 1261-1276, July.
    20. Bosmans, Kristof & Decancq, Koen & Ooghe, Erwin, 2018. "Who's afraid of aggregating money metrics?," Theoretical Economics, Econometric Society, vol. 13(2), May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. DECANCQ, Koen & FLEURBAEY, Marc & SCHOKKAERT, Erik, 2014. "Inequality, income, and well-being," LIDAM Discussion Papers CORE 2014018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Croci Angelini, Elisabetta & Michelangeli, Alessandra, 2012. "Axiomatic measurement of multidimensional well-being inequality: Some distributional questions," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 41(5), pages 548-557.
    3. Koen Decancq & María Ana Lugo, 2009. "Measuring inequality of well-being with a correlation-sensitive multidimensional Gini index," Working Papers 124, ECINEQ, Society for the Study of Economic Inequality.
    4. 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.
    5. Rolf Aaberge & Andrea Brandolini, 2014. "Multidimensional poverty and inequality," Temi di discussione (Economic working papers) 976, Bank of Italy, Economic Research and International Relations Area.
    6. Nicholas Rohde & Ross Guest, 2018. "Multidimensional Inequality Across Three Developed Countries," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 64(3), pages 576-591, September.
    7. 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.
    8. Marcello Basili & Paulo Casaca & Alain Chateauneuf & Maurizio Franzini, 2017. "Multidimensional Pigou–Dalton transfers and social evaluation functions," Theory and Decision, Springer, vol. 83(4), pages 573-590, December.
    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. Elisa Pagani, 2015. "Certainty Equivalent: Many Meanings of a Mean," Working Papers 24/2015, University of Verona, Department of Economics.
    11. Maasoumi, Esfandiar & Racine, Jeffrey S., 2016. "A solution to aggregation and an application to multidimensional ‘well-being’ frontiers," Journal of Econometrics, Elsevier, vol. 191(2), pages 374-383.
    12. 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.
    13. 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.
    14. 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.
    15. Jaya Krishnakumar, 2018. "Trade-Offs in a Multidimensional Human Development Index," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(3), pages 991-1022, August.
    16. Thi Kim Thanh Bui & Guido Erreygers, 2020. "Multidimensional Inequality in Vietnam, 2002–2012," Economies, MDPI, vol. 8(2), pages 1-31, April.
    17. Christophe Muller & Asha Kannan & Roland Alcindor, 2016. "Multidimensional Poverty in Seychelles," Working Papers halshs-01264444, HAL.
    18. Paolo Giovanni Piacquadio, 2017. "A Fairness Justification of Utilitarianism," Econometrica, Econometric Society, vol. 85, pages 1261-1276, July.
    19. Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.
    20. Iñaki Permanyer, 2019. "Measuring poverty in multidimensional contexts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 677-708, December.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cor:louvrp:2838. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.