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On the consistent measurement of attainment and shortfall inequality

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  • Lambert, Peter
  • Zheng, Buhong
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    Abstract

    In measuring inequality of a bounded variable such as health status, one can focus on attainments or shortfalls. However, rankings of social states by attainment and shortfall inequality do not necessarily mirror one another. We propose a requirement, that attainment inequality and shortfall inequality be measured consistently, and we examine the performance of partial orderings and indices of inequality in this respect. For relative inequality and all currently documented intermediate inequality concepts, the orderings fail our consistency requirement, as do all indices which respect these orderings. However, the absolute inequality partial ordering satisfies consistency. We identify two classes of indices of absolute inequality, one containing rank-independent and the other rank-dependent indices, which measure attainment and shortfall inequality consistently (in fact identically). The only subgroup decomposable inequality index, of any type, which measures attainment and shortfall inequality consistently is the variance. We discuss implications for the study of pure health inequality.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Health Economics.

    Volume (Year): 30 (2011)
    Issue (Month): 1 (January)
    Pages: 214-219

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    Handle: RePEc:eee:jhecon:v:30:y:2011:i:1:p:214-219

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    Web page: http://www.elsevier.com/locate/inca/505560

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    Keywords: Achievement inequality Shortfall inequality Consistency;

    References

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    1. Erreygers, Guido, 2009. "Can a single indicator measure both attainment and shortfall inequality?," Journal of Health Economics, Elsevier, vol. 28(4), pages 885-893, July.
    2. Buhong Zheng, 2007. "Unit-Consistent Decomposable Inequality Measures," Economica, London School of Economics and Political Science, vol. 74(293), pages 97-111, 02.
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    5. ERREYGERS, Guido, 2006. "Correcting the Concentration Index," Working Papers 2006027, University of Antwerp, Faculty of Applied Economics.
    6. ERREYGERS, Guido & CLARKE, Philip & VAN OURTI, Tom, 2010. "Mirror, mirror, on the wall, who in this land is fairest of all? Revisiting the extended concentration index," Working Papers 2010015, University of Antwerp, Faculty of Applied Economics.
    7. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
    8. Erreygers, Guido, 2009. "Correcting the Concentration Index: A reply to Wagstaff," Journal of Health Economics, Elsevier, vol. 28(2), pages 521-524, March.
    9. Pfingsten, Andreas, 1986. "Distributionally-neutral tax changes for different inequality concepts," Journal of Public Economics, Elsevier, vol. 30(3), pages 385-393, August.
    10. Tateo Yoshida, 2005. "Social welfare rankings of income distributions A new parametric concept of intermediate inequality," Social Choice and Welfare, Springer, vol. 24(3), pages 557-574, 06.
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    13. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    14. 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.
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    Citations

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    Cited by:
    1. Guido Erreygers & Tom Van Ourti, 2010. "Measuring Socioeconomic Inequality in Health, Health Care and Health Financing by Means of Rank-Dependent Indices: A Recipe for Good Practice," Tinbergen Institute Discussion Papers 10-076/3, Tinbergen Institute.
    2. Allanson, Paul & Petrie, Dennis, 2012. "Understanding the vertical equity judgements underpinning health inequality measures," SIRE Discussion Papers 2012-06, Scottish Institute for Research in Economics (SIRE).
    3. Owen O'Donnell & Eddy Van Doorslaer & Tom Van Ourti, 2013. "Health and Inequality," Tinbergen Institute Discussion Papers 13-170/V, Tinbergen Institute.
    4. Casilda Lasso de la Vega & Oihana Aristondo, 2010. "Proposing indicators to measure achievement and shortfall inequality consistently," Brooks World Poverty Institute Working Paper Series 12010, BWPI, The University of Manchester.
    5. Paul Makdissi & Myra Yazbeck, 2012. "Avoiding Blinding to Health Status: A New Class of Health Achievement and Inequality Indices," Working Papers 1207E, University of Ottawa, Department of Economics.
    6. Makdissi, Paul & Yazbeck, Myra, 2014. "Measuring socioeconomic health inequalities in presence of multiple categorical information," Journal of Health Economics, Elsevier, vol. 34(C), pages 84-95.
    7. Satya R. Chakravarty & Nachiketa Chattopadhyay & Conchita D’Ambrosio, 2013. "On a family of achievement and shortfall inequality indices," Working Papers 300, ECINEQ, Society for the Study of Economic Inequality.
    8. Baeten, Steef & Van Ourti, Tom & van Doorslaer, Eddy, 2013. "Rising inequalities in income and health in China: Who is left behind?," Journal of Health Economics, Elsevier, vol. 32(6), pages 1214-1229.
    9. 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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