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On a family of achievement and shortfall inequality indices

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  • Satya R. Chakravarty

    ()
    (Indian Statistical Institute, Kolkata , India)

  • Nachiketa Chattopadhyay

    ()
    (Indian Statistical Institute, Kolkata , India)

  • Conchita D’Ambrosio

    ()
    (Université du Luxembourg)

Abstract

This paper identifies a family of absolute consistent inequality indices using a weakly decomposable postulate suggested by Ebert (2010). Since one member employs an Atkinson (1970) type aggregation we refer to it as the Atkinson index of consistent inequality. A second member of this family parallels the Kolm (1976) index of inequality while a third member of the family can be regarded as the normalized Theil (1972) consistent mean logarithmic deviation index. Two innovative features of these indices are that no specific structure is imposed on the form of the index at the outset and no transformation of any existing index is considered to ensure consistency. Each of them regards an achievement distribution as equally unequal as the corresponding shortfall distribution. We apply these indices to study inequality in mental health in Britain between 1991 and 2008.

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File URL: http://www.ecineq.org/milano/WP/ECINEQ2013-300.pdf
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Bibliographic Info

Paper provided by ECINEQ, Society for the Study of Economic Inequality in its series Working Papers with number 300.

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Length: 21 pages
Date of creation: Aug 2013
Date of revision:
Handle: RePEc:inq:inqwps:ecineq2013-300

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Keywords: Achievement inequality; shortfall inequality; consistency; BHPS.;

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  1. Lambert, Peter & Zheng, Buhong, 2011. "On the consistent measurement of attainment and shortfall inequality," Journal of Health Economics, Elsevier, vol. 30(1), pages 214-219, January.
  2. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-28, October.
  3. 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.
  4. Ebert, Udo, 1988. "A Family of Aggregative Compromise Inequality Measures," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(2), pages 363-76, May.
  5. Udo Ebert, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Working Papers V-325-10, University of Oldenburg, Department of Economics, revised May 2010.
  6. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-25, April.
  7. Ebert, Udo, 2010. "The decomposition of inequality reconsidered: Weakly decomposable measures," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 94-103, September.
  8. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
  9. Chakravarty, Satya R, 1988. "Extended Gini Indices of Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(1), pages 147-56, February.
  10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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  12. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  13. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer, vol. 16(2), pages 183-196.
  14. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-20, July.
  15. Lasso de la Vega, Casilda & Aristondo, Oihana, 2012. "Proposing indicators to measure achievement and shortfall inequality consistently," Journal of Health Economics, Elsevier, vol. 31(4), pages 578-583.
  16. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
  17. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
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