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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. 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.
  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. 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.
  4. d'Aspremont, Claude & Gevers, Louis, 2002. "Social welfare functionals and interpersonal comparability," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 10, pages 459-541 Elsevier.
  5. Fleurbaey, M. & Hagnere, C. & Trannoy, A., 1998. "Welfare Comparisons with Bounded Equivalence Scales," Papers 9823, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  6. 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.
  7. Udo Ebert & Patrick Moyes, 2009. "Household decisions and equivalence scales," Journal of Population Economics, Springer, vol. 22(4), pages 1039-1062, October.
  8. 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.
  9. Lambert, Peter J & Ramos, Xavier, 2002. "Welfare Comparisons: Sequential Procedures for Heterogeneous Populations," Economica, London School of Economics and Political Science, vol. 69(276), pages 549-62, November.
  10. 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.
  11. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  12. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-72, October.
  13. Udo Ebert & Patrick Moyes, 2003. "Equivalence Scales Reconsidered," Econometrica, Econometric Society, vol. 71(1), pages 319-343, January.
  14. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  15. 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.
  16. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  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. Shorrocks, Anthony F & Foster, James E, 1987. "Transfer Sensitive Inequality Measures," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 485-97, July.
  19. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-97, July.
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Citations

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Cited by:
  1. 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.
  2. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
  3. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2006. "A Good Sign for Multivariate Risk Taking," CESifo Working Paper Series 1796, CESifo Group Munich.
  4. 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.
  5. Moyes, Patrick, 2013. "Rearrangements and sequential rank order dominance," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 278-290.
  6. 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).
  7. Patrick MOYES, 2013. "Rearrangements and Sequential Rank Order Dominance," Cahiers du GREThA 2013-10, Groupe de Recherche en Economie Théorique et Appliquée.
  8. 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.
  9. Peter Lambert & Xavi Ramos, 2001. "Welfare Comparisons: Sequential Procedures for Heterogeneous Population," CESifo Working Paper Series 519, CESifo Group Munich.
  10. 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.
  11. 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.
  12. 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.

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