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Consistent comparisons of attainment and shortfall inequality: A critical examination

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  • Bosmans, K.G.M.

    (General Economics 1 (Micro))

Abstract

An inequality measure is ‘consistent’ if it ranks distributions the same irrespective of whether health quantities are represented in terms of attainment or shortfalls. This consistency property severely restricts the set of admissible inequality measures. We show that, within a more general setting of separate measures for attainments and shortfalls, the consistency property is a combination of two conditions. The first is a compelling rationality condition that says that the attainment measure should rank attainment distributions as the shortfall measure ranks shortfall distributions. The second is an overly demanding condition that says that the attainment measure and the shortfall measure should be identical. By dropping the latter condition, the restrictions on the admissible inequality measures disappear.

Suggested Citation

  • Bosmans, K.G.M., 2013. "Consistent comparisons of attainment and shortfall inequality: A critical examination," Research Memorandum 064, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2013064
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    1. 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.
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    3. Thierry Marchant, 2008. "Scale invariance and similar invariance conditions for bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 709-710, December.
    4. Kjellsson, Gustav & Gerdtham, Ulf-G., 2013. "Lost in Translation: Rethinking the Inequality-Equivalence Criteria for Bounded Health Variables," Working Papers 2013:18, Lund University, Department of Economics, revised 02 Jan 2014.
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    6. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    7. Clarke, Philip M. & Gerdtham, Ulf-G. & Johannesson, Magnus & Bingefors, Kerstin & Smith, Len, 2002. "On the measurement of relative and absolute income-related health inequality," Social Science & Medicine, Elsevier, vol. 55(11), pages 1923-1928, December.
    8. Buhong Zheng, 2007. "Unit-Consistent Decomposable Inequality Measures," Economica, London School of Economics and Political Science, vol. 74(293), pages 97-111, February.
    9. Paul Allanson & Dennis Petrie, 2014. "Understanding The Vertical Equity Judgements Underpinning Health Inequality Measures," Health Economics, John Wiley & Sons, Ltd., vol. 23(11), pages 1390-1396, November.
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    Cited by:

    1. Nanak Kakwani & Hyun H. Son, 2015. "Income inequality and social well-being," Working Papers 380, ECINEQ, Society for the Study of Economic Inequality.
    2. Calara, Paul Samuel & Gerdtham, Ulf-G & Petrie, Dennis, 2016. "The Dynamics of Income-Related Health Inequalities in Australia versus Great Britain," Working Papers 2016:20, Lund University, Department of Economics.

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