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Multidimensional inequality comparisons: A compensation perspective

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  • Muller, Christophe
  • Trannoy, Alain

Abstract

We provide a unified treatment of the two approaches pioneered by Atkinson and Bourguignon (1982, 1987) [3,4] by resorting to compensation principles in the bivariate case. We treat the attributes of individual utility asymmetrically by assuming that one attribute can be used to compensate another. Our main result consists of two sufficient second-order stochastic dominance conditions. In the case where the compensated variable has a discrete distribution, the distribution of the compensating variable must satisfy a condition which degenerates to the Sequential Generalized Lorenz test for identical marginal distributions of the compensated variable. Furthermore, the distributions of the compensated variable must satisfy the Generalized Lorenz test.

Suggested Citation

  • Muller, Christophe & Trannoy, Alain, 2012. "Multidimensional inequality comparisons: A compensation perspective," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1427-1449.
    • Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1427-1449
    DOI: 10.1016/j.jet.2011.09.002
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    1. Banks, James & Johnson, Paul, 1994. "Equivalence Scale Relativities Revisited," Economic Journal, Royal Economic Society, vol. 104(425), pages 883-890, July.
    2. A.B. Atkinson & F. Bourguignon (ed.), 2000. "Handbook of Income Distribution," Handbook of Income Distribution, Elsevier, edition 1, volume 1, number 1.
    3. repec:bla:revinw:v:39:y:1993:i:4:p:337-56 is not listed on IDEAS
    4. Erik Schokkaert & Kurt Devooght, 2003. "Responsibility-sensitive fair compensation in different cultures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 207-242, October.
    5. 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.
    6. Peter C. Fishburn & Irving H. Lavalle, 1995. "Stochastic Dominance on Unidimensional Grids," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 513-525, August.
    7. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    8. Anthony F. Shorrocks, 2004. "Inequality and Welfare Evaluation of Heterogeneous Income Distributions," WIDER Working Paper Series RP2004-01, World Institute for Development Economic Research (UNU-WIDER).
    9. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    10. Muller, Christophe & Trannoy, Alain, 2011. "A dominance approach to the appraisal of the distribution of well-being across countries," Journal of Public Economics, Elsevier, vol. 95(3), pages 239-246.
    11. Fleurbaey, Marc, 2012. "Fairness, Responsibility, and Welfare," OUP Catalogue, Oxford University Press, number 9780199653591.
    12. repec:bla:econom:v:69:y:2002:i:276:p:549-62 is not listed on IDEAS
    13. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
    14. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 485-497.
    15. Christine Chambaz & Eric Maurin, 1998. "Atkinson And Bourguignon'S Dominance Criteria: Extended And Applied To The Measurement Of Poverty In France," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 44(4), pages 497-513, December.
    16. Stephen P. Jenkins & Peter J. Lambert, 1993. "Ranking Income Distributions When Needs Differ," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 39(4), pages 337-356, December.
    17. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
    18. Denuit, Michel & Mesfioui, Mhamed, 2010. "Generalized increasing convex and directionally convex orders," LIDAM Discussion Papers ISBA 2010012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    20. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(1), pages 1-13.
    21. Anthony B. Atkinson & François Bourguignon, 1987. "Income Distribution and Differences in Needs," Palgrave Macmillan Books, in: George R. Feiwel (ed.), Arrow and the Foundations of the Theory of Economic Policy, chapter 12, pages 350-370, Palgrave Macmillan.
    22. Udo Ebert, 1999. "Using equivalent income of equivalent adults to rank income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 233-258.
    23. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
    24. Anthony Shorrocks, 2004. "Inequality and welfare evaluation of heterogeneous income distributions," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 2(3), pages 193-218, July.
    25. Denuit, Michel & Mesfioui, Mhamed, 2010. "Generalized increasing convex and directionally convex orders," LIDAM Reprints ISBA 2010029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

    1. Moyes, Patrick, 2013. "Rearrangements and sequential rank order dominance," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 278-290.
    2. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART 14-01, INRAE UMR SMART.
    3. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
    4. Christophe Muller & Asha Kannan & Roland Alcindor, 2016. "Multidimensional Poverty in Seychelles," AMSE Working Papers 1601, Aix-Marseille School of Economics, France, revised Jan 2016.
    5. 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).
    6. Christophe Muller, 2019. "Social Shock Sharing and Stochastic Dominance," AMSE Working Papers 1903, Aix-Marseille School of Economics, France.
    7. 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.
    8. Christophe Muller & Alain Trannoy, 2003. "A Dominance Approach to Well-Being Inequality across Countries," IDEP Working Papers 0313, Institut d'economie publique (IDEP), Marseille, France.
    9. Nicoleta Anca Matei & Claudio Zoli, 2012. "Restricted Finite Time Dominance," Working Papers 30/2012, University of Verona, Department of Economics.
    10. Thi Kim Thanh Bui & Guido Erreygers, 2020. "Multidimensional Inequality in Vietnam, 2002–2012," Economies, MDPI, vol. 8(2), pages 1-31, April.
    11. Therese Nilsson, 2010. "Health, Wealth and Wisdom: Exploring Multidimensional Inequality in a Developing Country," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 95(2), pages 299-323, January.
    12. 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.
    13. Mohamad A. Khaled & Paul Makdissi & D.S. Prasada Rao & Myra Yazbeck, 2023. "A unidimensional representation of multidimensional inequality, with an application to the Arab region," Discussion Papers Series 659, School of Economics, University of Queensland, Australia.
    14. Mathews, Timothy & Schwartz, Jesse A., 2019. "Comparisons of utility inequality and income inequality," Economics Letters, Elsevier, vol. 178(C), pages 18-20.
    15. Nicholas Rohde & Ross Guest, 2013. "Multidimensional Racial Inequality in the United States," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 114(2), pages 591-605, November.

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    More about this item

    Keywords

    Multidimensional welfare; Compensation; Dominance; Lorenz criterion;
    All these keywords.

    JEL classification:

    • D3 - Microeconomics - - 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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