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A Class of Association Sensitive Multidimensional Welfare Indices

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  • Suman Seth

Abstract

The last few decades have seen increased theoretical and empirical interest in multidimensional measures of welfare. This paper develops a two-parameter class of welfare indices that is sensitive to two distinct forms of inter-personal inequality in the multidimensional framework. The first form of inequality pertains to the spread of each dimensional achievement across the population, as would be reflected in the multidimensional version of the usual Lorenz criterion. The second one regards association or correlation across dimensions, reflecting the key observation that inter-dimensional association may alter evaluation of individual as well as overall inequality. Most existing multi-dimensional welfare indices are, however, either completely insensitive to inter-personal inequality or are only sensitive to the first. The class of indices developed in this paper is sensitive to both forms of multidimensional inequality. An axiomatic characterization of the class is provided, and it is shown that other multidimensional indices, such as the ones developed by Bourguignon (1999) and Foster, Lopez-Calva, and Szekely (2005), are sub-classes of this new broader class. Finally, essential statistical tests are constructed to verify the reliability of the evaluations generated by the indices.

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  • Suman Seth, 2009. "A Class of Association Sensitive Multidimensional Welfare Indices," OPHI Working Papers 27, Queen Elizabeth House, University of Oxford.
    • Handle: RePEc:qeh:ophiwp:ophiwp027
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    File URL: https://ophi.org.uk/working-paper-number-27/
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    1. Ben-Porath, Elchanan & Gilboa, Itzhak & Schmeidler, David, 1997. "On the Measurement of Inequality under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 194-204, July.
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    3. François Bourguignon & Satya R. Chakravarty, 2019. "The Measurement of Multidimensional Poverty," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 83-107, Springer.
    4. Sen, Amartya, 1997. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198292975.
    5. 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.
    6. Maasoumi, Esfandiar, 1986. "The Measurement and Decomposition of Multi-dimensional Inequality," Econometrica, Econometric Society, vol. 54(4), pages 991-997, July.
    7. repec:bla:econom:v:70:y:2003:i:278:p:197-221 is not listed on IDEAS
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    1. Jeni Klugman & Francisco Rodríguez & Hyung-Jin Choi, 2011. "The HDI 2010: new controversies, old critiques," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(2), pages 249-288, June.
    2. Gaël Giraud & Cécile Renouard & Hélène L'Huillier & Raphaële de La Martinière & Camille Sutter, 2012. "Relational Capability: A Multidimensional Approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00827690, HAL.
    3. Iñaki Permanyer, 2013. "Are UNDP Indices Appropriate to Capture Gender Inequalities in Europe?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 110(3), pages 927-950, February.
    4. Gaston Yalonetzky, 2013. "Stochastic Dominance with Ordinal Variables: Conditions and a Test," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 126-163, January.
    5. Croci Angelini, Elisabetta & Michelangeli, Alessandra, 2012. "Axiomatic measurement of multidimensional well-being inequality: Some distributional questions," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 41(5), pages 548-557.

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