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Income distributions and decomposable divergence measures

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  • Magdalou, Brice
  • Nock, Richard

Abstract

Inequality indices evaluate the divergence between the income distribution and the hypothetical situation where all individuals receive the mean income, and are unambiguously reduced by a Pigou–Dalton progressive transfer. This paper proposes a new approach to evaluate the divergence between any two income distributions, where the latter can be a reference distribution for the former. In the case where the reference distribution is perfectly egalitarian – and uniquely in this case – we assume that any progressive transfer reduces the divergence, and that the divergence can be additively separated into inequality and efficiency loss. We characterize the unique class of decomposable divergence measures consistent with these views. We derive the associated relative and absolute subclasses, and we illustrate the applicability of our results. This approach extends the generalized entropy studied in inequality measurement.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 146 (2011)
Issue (Month): 6 ()
Pages: 2440-2454

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Handle: RePEc:eee:jetheo:v:146:y:2011:i:6:p:2440-2454

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Inequality measures; Mobility; Responsibility; Heterogeneous households; Generalized entropy; Bregman divergences;

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Cited by:
  1. Ramos, Xavi & Van de gaer, Dirk, 2012. "Empirical Approaches to Inequality of Opportunity: Principles, Measures, and Evidence," IZA Discussion Papers 6672, Institute for the Study of Labor (IZA).
  2. Nuno Crespo & Sandrina B. Moreira & Nádia Simões, 2012. "An Integrated Approach for the Measurement of Inequality, Poverty and Richness," Working Papers Series 2 12-03, ISCTE-IUL, Business Research Unit (BRU-IUL).
  3. Magali JAOUL-GRAMMARE & Brice MAGDALOU, 2013. "Opportunities in Higher Education : An Application to France," Annales d'Economie et de Statistique, ENSAE, issue 111-112, pages 12.
  4. Francesco Andreoli & Arnaud Lefranc, 2013. "Equalization of opportunity: Definitions and implementable conditions," Working Papers 310, ECINEQ, Society for the Study of Economic Inequality.
  5. Frank Cowell & Emmanuel Flachaire & Sanghamitra Bandyopadhyay, 2013. "Reference distributions and inequality measurement," Journal of Economic Inequality, Springer, Springer, vol. 11(4), pages 421-437, December.
  6. Yalonetzky, Gaston, 2011. "Measuring group disadvantage with inter-distributional inequality indices: A critical review and some amendments to existing indices," Economics Discussion Papers 2011-46, Kiel Institute for the World Economy.

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