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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 147 (2012)
Issue (Month): 4 ()
Pages: 1427-1449

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1427-1449

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Multidimensional welfare; Compensation; Dominance; Lorenz criterion;

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References

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  1. Shorrocks, Anthony, 2004. "Inequality and Welfare Evaluation of Heterogeneous Income Distributions," Working Paper Series UNU-WIDER Research Paper , World Institute for Development Economic Research (UNU-WIDER).
  2. 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.
  3. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  4. Banks, James & Johnson, Paul, 1994. "Equivalence Scale Relativities Revisited," Economic Journal, Royal Economic Society, vol. 104(425), pages 883-90, July.
  5. Chambaz, Christine & Maurin, Eric, 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.
  6. 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.
  7. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
  8. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2006. "A Good Sign for Multivariate Risk Taking," CESifo Working Paper Series 1796, CESifo Group Munich.
  9. Erik Schokkaert & Kurt Devooght, 2003. "Responsibility-sensitive fair compensation in different cultures," Social Choice and Welfare, Springer, vol. 21(2), pages 207-242, October.
  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(3-4), pages 239-246, April.
  11. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  12. Fleurbaey, Marc, 2012. "Fairness, Responsibility, and Welfare," OUP Catalogue, Oxford University Press, number 9780199653591.
  13. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 183-201, April.
  14. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  15. Anthony Shorrocks, 2004. "Inequality and welfare evaluation of heterogeneous income distributions," Journal of Economic Inequality, Springer, vol. 2(3), pages 193-218, July.
  16. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  17. Jenkins, Stephen P & Lambert, Peter J, 1993. "Ranking Income Distributions When Needs Differ," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 39(4), pages 337-56, December.
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Citations

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Cited by:
  1. FLEURBAEY, Marc & SCHOKKAERT, Erik, 2011. "Equity in health and health care," CORE Discussion Papers 2011026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. 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.
  3. Therese Nilsson, 2010. "Health, Wealth and Wisdom: Exploring Multidimensional Inequality in a Developing Country," Social Indicators Research, Springer, vol. 95(2), pages 299-323, January.
  4. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
  5. Patrick MOYES, 2013. "Rearrangements and Sequential Rank Order Dominance," Cahiers du GREThA 2013-10, Groupe de Recherche en Economie Théorique et Appliquée.
  6. Christoph Heinzel, 2014. "Term structure of discount rates under multivariate s-ordered consumption growth," Working Papers SMART - LERECO 14-01, INRA UMR SMART.
  7. Moyes, Patrick, 2013. "Rearrangements and sequential rank order dominance," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 278-290.
  8. Nicholas Rohde & Ross Guest, 2013. "Multidimensional Racial Inequality in the United States," Social Indicators Research, Springer, vol. 114(2), pages 591-605, November.

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