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Bidimensional Inequalities with an Ordinal Variable

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  • N. GRAVEL
  • Patrick MOYES (GREThA UMR CNRS 5113)

Abstract

We investigate the normative foundations of two empirically implementable dominance criteria for comparing distributions of two attributes, where the first one is cardinal while the second is ordinal. The criteria we consider are Atkinson and Bourguignon\'s (1982) first quasi-ordering and a generalization of Bourguignon\'s (1989) ordered poverty gap criterion. In each case we specify the restrictions to be placed on the individual utility functions, which guarantee that all utility-inequality averse welfarist ethical observers will rank the distributions under comparison in the same way as the dominance criterion. We also identify the elementary inequality reducing transformations successive applications of which permit to derive the dominating distribution from the dominated one.

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Bibliographic Info

Paper provided by Groupe de Recherche en Economie Théorique et Appliquée in its series Cahiers du GREThA with number 2008-14.

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Date of creation: 2008
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Handle: RePEc:grt:wpegrt:2008-14

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Keywords: Normative Analysis; Utilitarianism; Welfarism; Bidimensional Stochastic Dominance; Inequality Reducing Transformations;

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References

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  1. 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.
  2. Udo Ebert, 2008. "Living Standard, Social Welfare, and the Redistribution of Income in a Heterogeneous Population," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(5), pages 873-889, October.
  3. Patrick MOYES (GREThA et IDEP Marseille), 2011. "Comparisons of Heterogeneous Distributions and Dominance Criteria," Cahiers du GREThA 2011-23, Groupe de Recherche en Economie Théorique et Appliquée.
  4. Nicolas Gravel & Patrick Moyes & Beno�T Tarroux, 2009. "Robust International Comparisons of Distributions of Disposable Income and Regional Public Goods," Economica, London School of Economics and Political Science, vol. 76(303), pages 432-461, 07.
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  8. 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).
  9. 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.
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  11. Ebert, Udo, 2000. "Sequential Generalized Lorenz Dominance and Transfer Principles," Bulletin of Economic Research, Wiley Blackwell, vol. 52(2), pages 113-22, April.
  12. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
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  14. 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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  17. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-16, March.
  18. Nicolas Gravel & Patrick Moyes, 2006. "Ethically Robust Comparisons of Distributions of Two Individual Attributes," IDEP Working Papers 0605, Institut d'economie publique (IDEP), Marseille, France, revised Aug 2006.
  19. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
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Citations

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Cited by:
  1. 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).
  2. C. Schluter & D. Van De Gaer, 2008. "Structural Mobility, Exchange Mobility and Subgroup Consistent Mobility Measurement – US–German Mobility Measurements Revisited," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 08/543, Ghent University, Faculty of Economics and Business Administration.
  3. Nicolas Gravel & Patrick Moyes, 2011. "Utilitarianism or Welfarism: Does it Make a Difference?," Working Papers halshs-00634010, HAL.
  4. repec:hal:wpaper:halshs-00576585 is not listed on IDEAS
  5. 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).

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