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Comparisons of heterogeneous distributions and dominance criteria

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  • Moyes, Patrick

Abstract

We are interested in the comparisons of standard-of-living across societies when observations of both income and household structure are available. We generalise the approach of A.B. Atkinson and F. Bourguignon (1987) [3] to the case where the marginal distributions of needs can vary across the household populations under comparison. We assume that a sympathetic observer uses a utilitarian social welfare function in order to rank heterogeneous income distributions. Insofar as any individual can play the role of the observer, we take the unanimity point of view according to which the plannerʼs judgements have to comply with a certain number of basic normative principles. We impose increasingly restrictive conditions on the householdʼs utility function and we investigate their effects on the resulting rankings of the distributions. This leads us to propose four dominance criteria that can be used for providing an unambiguous ranking of income distributions for heterogeneous populations.

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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: 1351-1383

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Handle: RePEc:eee:jetheo:v:147:y:2012:i:4:p:1351-1383

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

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Keywords: Normative analysis; Utilitarianism; Welfarism; Multidimensional inequality and welfare; Bidimensional stochastic dominance; Inequality reducing transformations;

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References

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  1. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  2. Glewwe, Paul, 1991. "Household equivalence scales and the measurement of inequality : Transfers from the poor to the rich could decrease inequality," Journal of Public Economics, Elsevier, vol. 44(2), pages 211-216, March.
  3. 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.
  4. d’ASPREMONT, Claude & GEVERS, Louis, 2001. "Social welfare functionals and interpersonal comparability," CORE Discussion Papers 2001040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  6. M. Fleurbaey & C. Hagneré & A. Trannoy, 1998. "Welfare comparisons with bounded equivalence scales," THEMA Working Papers 98-23, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  7. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-97, July.
  8. 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.
  9. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  10. Patrick MOYES (GREThA, CNRS, UMR 5113) & Nicolas GRAVEL (Aix-Marseille University and AMSE (GREQAM)), 2011. "Ethically Robust Comparisons of Bidimensional Distributions with an Ordinal Attribute," Cahiers du GREThA 2011-36, Groupe de Recherche en Economie Théorique et Appliquée.
  11. 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.
  12. Udo Ebert & Patrick Moyes, 2004. "Household Decisions and Equivalence Scales," IDEP Working Papers 0404, Institut d'economie publique (IDEP), Marseille, France.
  13. Peter Lambert & Xavi Ramos, 2001. "Welfare Comparisons: Sequential Procedures for Heterogeneous Population," CESifo Working Paper Series 519, CESifo Group Munich.
  14. Buhmann, Brigitte, et al, 1988. "Equivalence Scales, Well-Being, Inequality, and Poverty: Sensitivity Estimates across Ten Countries Using the Luxembourg Income Study (LIS) Database," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 34(2), pages 115-42, June.
  15. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-72, October.
  16. Udo Ebert & Patrick Moyes, 2003. "Equivalence Scales Reconsidered," Econometrica, Econometric Society, vol. 71(1), pages 319-343, January.
  17. 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.
  18. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  19. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
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Citations

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Cited by:
  1. 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.
  2. Peter J. Lambert & Xavier Ramos, 2001. "Welfare comparisons: sequential procedures for heterogenous populations," Working Papers wp0114, Department of Applied Economics at Universitat Autonoma of Barcelona.
  3. Alain Trannoy & Christophe Muller, 2004. "A Dominance Approach To Well-Being Inequality Across Countries," Working Papers. Serie AD 2004-27, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Patrick MOYES (GREThA, CNRS, UMR 5113), 2011. "Rearrangements and Sequential Rank Order Dominance. A Result with Economic Applications," Cahiers du GREThA 2011-35, Groupe de Recherche en Economie Théorique et Appliquée.
  5. Sonne-Schmidt, Christoffer & Tarp, Finn & Osterdal, Lars Peter, 2013. "Ordinal multidimensional inequality," Working Paper Series UNU-WIDER Research Paper , World Institute for Development Economic Research (UNU-WIDER).
  6. 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.
  7. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2006. "A Good Sign for Multivariate Risk Taking," CESifo Working Paper Series 1796, CESifo Group Munich.
  8. Moyes, Patrick, 2013. "Rearrangements and sequential rank order dominance," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 278-290.
  9. N. GRAVEL & Patrick MOYES (GREThA UMR CNRS 5113), 2008. "Bidimensional Inequalities with an Ordinal Variable," Cahiers du GREThA 2008-14, Groupe de Recherche en Economie Théorique et Appliquée.
  10. Marc Fleurbaey & Cyrille Hagneré & Alain Trannoy, 2007. "Welfare Comparisons of Income Distributions and Family Size," IDEP Working Papers 0702, Institut d'economie publique (IDEP), Marseille, France, revised 16 Jan 2007.
  11. Patrick MOYES, 2013. "Rearrangements and Sequential Rank Order Dominance," Cahiers du GREThA 2013-10, Groupe de Recherche en Economie Théorique et Appliquée.
  12. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.

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