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Bidimensional Inequalities with an Ordinal Variable

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Author Info
N. GRAVEL
Patrick MOYES (GREThA UMR CNRS 5113)

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

Find related papers by JEL classification:
D30 - Microeconomics - - Distribution - - - General
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
I32 - Health, Education, and Welfare - - Welfare and Poverty - - - Measurement and Analysis of Poverty

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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). [Downloadable!]
    Other versions:
  2. 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
    Other versions:
  4. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Blackwell Publishing, vol. 49(2), pages 183-201, April. [Downloadable!] (restricted)
  5. 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. [Downloadable!]
  6. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-16, March. [Downloadable!] (restricted)
  7. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February. [Downloadable!] (restricted)
  8. Ebert, Udo, 1995. "Income inequality and differences in household size," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 37-55, August. [Downloadable!] (restricted)
  9. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  12. NICOLAS GRAVEL & PATRICK MOYES & BENOÎT 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. [Downloadable!] (restricted)
  13. Jenkins, Stephen P & Lambert, Peter J, 1993. "Ranking Income Distributions When Needs Differ," Review of Income and Wealth, Blackwell Publishing, vol. 39(4), pages 337-56, December.
  14. Howe, Roger, 1987. "Sections and extensions of concave functions," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 53-64, February. [Downloadable!] (restricted)
  15. Hammond, Peter J, 1979. "Equity in Two Person Situations: Some Consequences," Econometrica, Econometric Society, vol. 47(5), pages 1127-35, September. [Downloadable!] (restricted)
  16. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February. [Downloadable!] (restricted)
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  1. 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. [Downloadable!]
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