IDEAS home Printed from https://ideas.repec.org/p/inq/inqwps/ecineq2009-124.html
   My bibliography  Save this paper

Measuring inequality of well-being with a correlation-sensitive multidimensional Gini index

Author

Listed:
  • Koen Decancq

    (Katholieke Universiteit Leuven)

  • María Ana Lugo

    (University of Oxford)

Abstract

We propose to measure inequality of well-being with a multidimensional generalization of the Gini coefficient. We derive two inequality indices from their underlying social evaluation functions. These functions are conceived as a double aggregation functions: one across the dimensions of well-being, and another across the individuals. They differ only with respect to the sequencing of aggregations. We argue that the sequencing that does not exclude the Gini index to be sensitive to the correlation between the dimensions is more attractive. We illustrate both Gini indices using Russian household data on three dimensions of well-being: expenditure, health and education.

Suggested Citation

  • 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.
  • Handle: RePEc:inq:inqwps:ecineq2009-124
    as

    Download full text from publisher

    File URL: http://www.ecineq.org/milano/WP/ECINEQ2009-124.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Wagstaff, Adam & Paci, Pierella & van Doorslaer, Eddy, 1991. "On the measurement of inequalities in health," Social Science & Medicine, Elsevier, vol. 33(5), pages 545-557, January.
    2. Michael Lokshin & Martin Ravallion, 2008. "Testing for an economic gradient in health status using subjective data," Health Economics, John Wiley & Sons, Ltd., vol. 17(11), pages 1237-1259.
    3. Ebert, Udo & Welsch, Heinz, 2004. "Meaningful environmental indices: a social choice approach," Journal of Environmental Economics and Management, Elsevier, vol. 47(2), pages 270-283, March.
    4. Anonymous, 1950. "World Health Organization," International Organization, Cambridge University Press, vol. 4(3), pages 501-505, August.
    5. 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.
    6. Koen Decancq, 2014. "Copula-based measurement of dependence between dimensions of well-being," Oxford Economic Papers, Oxford University Press, vol. 66(3), pages 681-701.
    7. FrÊdÊric Gaspart, 1997. "Objective measures of well-being and the cooperative production problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 95-112.
    8. Erzo F. P. Luttmer, 2005. "Neighbors as Negatives: Relative Earnings and Well-Being," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(3), pages 963-1002.
    9. Anonymous, 1950. "World Health Organization," International Organization, Cambridge University Press, vol. 4(4), pages 683-686, November.
    10. 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.
    11. List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
    12. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975, Decembrie.
    13. Wagstaff, Adam, 2002. "Inequality aversion, health inequalities and health achievement," Journal of Health Economics, Elsevier, vol. 21(4), pages 627-641, July.
    14. Koen Decancq & María Ana Lugo, 2013. "Weights in Multidimensional Indices of Wellbeing: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 7-34, January.
    15. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
    16. 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.
    17. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, November.
    18. Inna Blam & Sergey Kovalev, 2006. "Spontaneous commercialisation, inequality and the contradictions of compulsory medical insurance in transitional Russia," Journal of International Development, John Wiley & Sons, Ltd., vol. 18(3), pages 407-423.
    19. Anonymous, 1950. "World Health Organization," International Organization, Cambridge University Press, vol. 4(1), pages 144-145, February.
    20. 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.
    21. 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.
    22. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931, Decembrie.
    23. Tsui Kai-Yuen, 1995. "Multidimensional Generalizations of the Relative and Absolute Inequality Indices: The Atkinson-Kolm-Sen Approach," Journal of Economic Theory, Elsevier, vol. 67(1), pages 251-265, October.
    24. Rietveld, Piet, 1990. "Multidimensional inequality comparisons : On aggravation and mitigation of inequalities," Economics Letters, Elsevier, vol. 32(2), pages 187-192, February.
    25. Koen Decancq & Maria Ana Lugo, 2008. "Setting Weights in Multidimensional Indices of Well-Being," OPHI Working Papers 18, Queen Elizabeth House, University of Oxford.
    26. Anonymous, 1950. "World Health Organization," International Organization, Cambridge University Press, vol. 4(2), pages 327-330, May.
    27. 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.
    28. John A. Weymark & Kai-yuen Tsui, 1997. "Social welfare orderings for ratio-scale measurable utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 241-256.
    29. Streeten, Paul, 1994. "Human Development: Means and Ends," American Economic Review, American Economic Association, vol. 84(2), pages 232-237, May.
    30. Doorslaer, Eddy van & Jones, Andrew M., 2003. "Inequalities in self-reported health: validation of a new approach to measurement," Journal of Health Economics, Elsevier, vol. 22(1), pages 61-87, January.
    31. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    32. 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.
    33. Banerjee, Asis Kumar, 2010. "A multidimensional Gini index," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 87-93, September.
    34. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    35. 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.
    36. Indranil Dutta & Prasanta K. Pattanaik & Yongsheng Xu, 2003. "On Measuring Deprivation and the Standard of Living in a Multidimensional Framework on the Basis of Aggregate Data," Economica, London School of Economics and Political Science, vol. 70(278), pages 197-221, May.
    37. Ferrer-i-Carbonell, Ada, 2005. "Income and well-being: an empirical analysis of the comparison income effect," Journal of Public Economics, Elsevier, vol. 89(5-6), pages 997-1019, June.
    38. Michael Lokshin & Martin Ravallion, 2008. "Testing for an economic gradient in health status using subjective data," Health Economics, John Wiley & Sons, Ltd., vol. 17(11), pages 1237-1259, November.
    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. Francesco Burchi & Nicole Rippin & Claudio E. Montenegro, 2018. "From income poverty to multidimensional poverty—an international comparison," One Pager Arabic 400, International Policy Centre for Inclusive Growth.
    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. 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).
    4. BOSSERT, Walter & CHAKRAVARTY, Satya R. & D’AMBROSIO, Conchita, 2009. "Multidimensional Poverty and Material Deprivation," Cahiers de recherche 2009-11, Universite de Montreal, Departement de sciences economiques.
    5. 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.
    6. E. Maasoumi & G. Yalonetzky, 2013. "Introduction to Robustness in Multidimensional Wellbeing Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 1-6, January.
    7. Ludovico Carrino, 2016. "Data Versus Survey-based Normalisation in a Multidimensional Analysis of Social Inclusion," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 2(3), pages 305-345, November.
    8. Ludovico Carrino, 2015. "The weighting role of normalisation in a multidimensional analysis of Social Inclusion," Working Papers 2015:32, Department of Economics, University of Venice "Ca' Foscari".
    9. Lauri Peterson, 2014. "The Measurement of Non-economic Inequality in Well-Being Indices," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 119(2), pages 581-598, November.

    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. 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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Thi Kim Thanh Bui & Guido Erreygers, 2020. "Multidimensional Inequality in Vietnam, 2002–2012," Economies, MDPI, vol. 8(2), pages 1-31, April.
    7. 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.
    8. 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.
    9. Bosmans, Kristof & Decancq, Koen & Ooghe, Erwin, 2015. "What do normative indices of multidimensional inequality really measure?," Journal of Public Economics, Elsevier, vol. 130(C), pages 94-104.
    10. Koen Decancq, 2014. "Copula-based measurement of dependence between dimensions of well-being," Oxford Economic Papers, Oxford University Press, vol. 66(3), pages 681-701.
    11. Casilda Lasso de la Vega & Ana Urrutia & Amaia Sarachu, 2010. "Characterizing multidimensional inequality measures which fulfil the Pigou–Dalton bundle principle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 319-329, July.
    12. Bleichrodt, Han & van Doorslaer, Eddy, 2006. "A welfare economics foundation for health inequality measurement," Journal of Health Economics, Elsevier, vol. 25(5), pages 945-957, September.
    13. FLEURBAEY, Marc & SCHOKKAERT, Erik, 2011. "Equity in health and health care," LIDAM Discussion Papers CORE 2011026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. 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.
    15. Koen Decancq & Marc Fleurbaey & François Maniquet, 2019. "Multidimensional poverty measurement with individual preferences," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 17(1), pages 29-49, March.
    16. 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.
    17. Bleichrodt, Han & Rohde, Kirsten I.M. & Van Ourti, Tom, 2012. "An experimental test of the concentration index," Journal of Health Economics, Elsevier, vol. 31(1), pages 86-98.
    18. Sonne-Schmidt, Christoffer & Tarp, Finn & Peter, Lars, 2011. "Ordinal multidimensional inequality: theory and application to the 2x2 case," MPRA Paper 72838, University Library of Munich, Germany.
    19. I. Josa & A. Aguado, 2020. "Measuring Unidimensional Inequality: Practical Framework for the Choice of an Appropriate Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 541-570, June.
    20. 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.

    More about this item

    Keywords

    multidimensional inequality; single parameter Gini index; correlation increasing majorization; Russia.;
    All these keywords.

    JEL classification:

    • 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
    • O52 - Economic Development, Innovation, Technological Change, and Growth - - Economywide Country Studies - - - Europe

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:inq:inqwps:ecineq2009-124. 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: Maria Ana Lugo (email available below). General contact details of provider: https://edirc.repec.org/data/ecineea.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.