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

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  • 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)

Abstract

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.

Suggested Citation

  • Ma Casilda Lasso de la Vega & Ana Urrutia & Amaia de Sarachu, 2008. "Characterizing multidimensional inequality measures which fulfil the Pigou-Dalton bundle principle," Working Papers 99, ECINEQ, Society for the Study of Economic Inequality.
  • Handle: RePEc:inq:inqwps:ecineq2008-99
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    References listed on IDEAS

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    1. Thibault Gajdos & John Weymark, 2005. "Multidimensional generalized Gini indices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 471-496.
    2. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Oxford University Press, vol. 49(2), pages 183-201.
    3. 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.
    4. 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.
    5. List, C., 1999. "Multidimensional Inequality Measurement: a Proposal," Economics Papers 9927, Economics Group, Nuffield College, University of Oxford.
    6. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    7. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    8. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    9. Serge-Christophe Kolm, 1977. "Multidimensional Egalitarianisms," The Quarterly Journal of Economics, Oxford University Press, vol. 91(1), pages 1-13.
    10. 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, pages 1-17.
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    Cited by:

    1. Asis Kumar Banerjee, 2014. "Multidimensional Lorenz dominance: A definition and an example," Working Papers 328, ECINEQ, Society for the Study of Economic Inequality.
    2. Pablo Brañas-Garza & Juan C. Cárdenas & Máximo Rossi, 2009. "Gender, education and reciprocal generosity: Evidence from 1,500 experiment subjects," Documentos de Trabajo (working papers) 1609, Department of Economics - dECON.
    3. Asis Banerjee, 2014. "A multidimensional Lorenz dominance relation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 171-191, January.
    4. TATOUTCHOUP, Didier & GAUDET, Gérard, 2009. "The Impact of Recycling on the Long-Run Stock of Trees," Cahiers de recherche 2009-10, Universite de Montreal, Departement de sciences economiques.
    5. Walter Bossert & Satya R. Chakravarty & Conchita D'Ambrosio, 2009. "Multidimensional poverty and material deprivation," Working Papers 129, ECINEQ, Society for the Study of Economic Inequality.
    6. Ferre, Celine & Ferreira, Francisco H.G. & Lanjouw, Peter, 2010. "Is there a metropolitan bias ? the inverse relationship between poverty and city size in selected developing countries," Policy Research Working Paper Series 5508, The World Bank.

    More about this item

    Keywords

    Multidimensional inequality; Social welfare; Pigou-Dalton transfer principle;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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