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Bidimensional Inequalities with an Ordinal Variable

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

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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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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  1. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
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  4. Fleurbaey, Marc & Hagnere, Cyrille & Trannoy, Alain, 2003. "Welfare comparisons with bounded equivalence scales," Journal of Economic Theory, Elsevier, vol. 110(2), pages 309-336, June.
  5. 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.
  6. 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.
  7. 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.
  8. Howe, Roger, 1987. "Sections and extensions of concave functions," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 53-64, February.
  9. 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).
  10. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-16, March.
  11. 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.
  12. Hammond, Peter J, 1979. "Equity in Two Person Situations: Some Consequences," Econometrica, Econometric Society, vol. 47(5), pages 1127-35, September.
  13. Ebert, Udo, 2000. "Sequential Generalized Lorenz Dominance and Transfer Principles," Bulletin of Economic Research, Wiley Blackwell, vol. 52(2), pages 113-22, April.
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  15. James Foster & Luis Lopez-Calva & Miguel Szekely, 2005. "Measuring the Distribution of Human Development: methodology and an application to Mexico," Journal of Human Development and Capabilities, Taylor & Francis Journals, vol. 6(1), pages 5-25.
  16. 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.
  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. Allison, R. Andrew & Foster, James E., 2004. "Measuring health inequality using qualitative data," Journal of Health Economics, Elsevier, vol. 23(3), pages 505-524, May.
  19. Ebert U., 1996. "Income inequality and differences in household size," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 57-58, February.
  20. 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.
  21. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
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