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Characterizing multidimensional inequality measures which fulfil the Pigou-Dalton bundle principle

  • Ma Casilda Lasso de la Vega


    (Department of Applied Economics, University of the Basque Country, Dep. Economía Aplicada)

  • Ana Urrutia


    (Department of Applied Economics, University of the Basque Country, Dep. Economía Aplicada)

  • Amaia de Sarachu


    (Department of Applied Economics, University of the Basque Country, Dep. Economía Aplicada)

In the unidimensional setting, the well known Pigou-Dalton transfer principle is the basic axiom to order distribution in terms of inequality. This axiom has a number of generalizations to the multidimensional approach which have been used to derive multidimensional inequality measures. However, up to now, none of them has assumed the Pigou-Dalton bundle dominance criterion, introduced by Fleurbaey and Trannoy (2003) although this principle captures the basic idea of the original Pigou-Dalton transfer principle, demanding that also in the multidimensional context “a transfer from a richer person to a poorer one decreases inequality”. Assuming this criterion the aim of this paper is to characterize multidimensional inequality measures. For doing so, firstly we derive the canonical forms of multidimensional aggregative inequality measures, both relative and absolute, which fulfil this property. Then following the Atkinson and Kolm-Pollak approaches we identify sub-families whose underlying social evaluation functions are separable. The inequality measures we derive share their functional forms with other parameter families already characterized in the literature, the major difference being the restrictions upon the parameters. Nevertheless, we show that it is not necessary to give up any of the usual requirements to assume the Pigou-Dalton bundle criterion. Thus, in empirical applications it makes sense to choose measures that also fulfil this principle.

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Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 99.

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Length: 31 pages
Date of creation: 2008
Date of revision:
Handle: RePEc:inq:inqwps:ecineq2008-99
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  1. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-97, July.
  2. List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
  3. Thibault Gajdos & John Weymark, 2005. "Multidimensional Generalized Gini Indices," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085881, HAL.
  4. 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.
  5. Kolm, Serge-Christophe, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, MIT Press, vol. 91(1), pages 1-13, February.
  6. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-85, November.
  7. Tsui Kai-Yuen, 1995. "Multidimensional Generalizations of the Relative and Absolute Inequality Indices: The Atkinson-Kolm-Sen Approach," Journal of Economic Theory, Elsevier, vol. 67(1), pages 251-265, October.
  8. John A. Weymark, 2003. "The Normative Approach to the Measurement of Multidimensional Inequality," Vanderbilt University Department of Economics Working Papers 0314, Vanderbilt University Department of Economics, revised Jan 2004.
  9. Diez Henar & Lasso de la Vega M. Casilda & de Sarachu Amaia & Urrutia Ana M., 2007. "A Consistent Multidimensional Generalization of the Pigou-Dalton Transfer Principle: An Analysis," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-17, December.
  10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  11. Chipman, John S., 1977. "An empirical implication of Auspitz-Lieben-Edgeworth-Pareto complementarity," Journal of Economic Theory, Elsevier, vol. 14(1), pages 228-231, February.
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