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On the consistent measurement of attainment and shortfall inequality

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  • Lambert, Peter
  • Zheng, Buhong

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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jhecon:v:30:y:2011:i:1:p:214-219
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    1. 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.
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    Cited by:

    1. Paul Makdissi & Myra Yazbeck, 2014. "Robust Wagstaff Orderings of Distributions of Self-Reported Health Status," Discussion Papers Series 533, School of Economics, University of Queensland, Australia.
    2. 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.
    3. MUSSARD Stéphane & PI ALPERIN Maria Noel & THIREAU Véronique, 2016. "Aggregable Health Inequality Indices," LISER Working Paper Series 2016-11, LISER.
    4. Makdissi, Paul & Yazbeck, Myra, 2016. "Avoiding blindness to health status in health achievement and health inequality measurement," Social Science & Medicine, Elsevier, vol. 171(C), pages 39-47.
    5. Satya R. Chakravarty & Nachiketa Chattopadhyay & Conchita D'Ambrosio, 2016. "On a Family of Achievement and Shortfall Inequality Indices," Health Economics, John Wiley & Sons, Ltd., vol. 25(12), pages 1503-1513, December.
    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. 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.
    8. repec:bla:revinw:v:62:y:2016:i:4:p:758-774 is not listed on IDEAS
    9. 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.
    10. 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.
    11. Oihana Aristondo & Francisco J. Goerlich Gisbert & Casilda Lasso De La Vega, 2015. "A Proposal to Compare Consistently the Inequality Among the Poor," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(3), pages 561-572, September.
    12. Erreygers, Guido & Van Ourti, Tom, 2011. "Measuring socioeconomic inequality in health, health care and health financing by means of rank-dependent indices: A recipe for good practice," Journal of Health Economics, Elsevier, vol. 30(4), pages 685-694, July.
    13. Owen O'Donnell & Eddy Van Doorslaer & Tom Van Ourti, 2013. "Health and Inequality," Tinbergen Institute Discussion Papers 13-170/V, Tinbergen Institute.
    14. 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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