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Lost in Translation: Rethinking the Inequality-Equivalence Criteria for Bounded Health Variables

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  • Kjellsson, Gustav

    ()
    (Department of Economics, Lund University)

  • Gerdtham, Ulf-G.

    ()
    (Department of Economics, Lund University)

Abstract

What change in the distribution of a population’s health preserves the level of inequality? The answer to this analogous question in the context of income inequality lies somewhere between a uniform and a proportional change. These polar positions represent the absolute and relative inequality equivalence criterion (IEC), respectively. A bounded health variable may be presented in terms of both health attainments and shortfalls. As a distributional change cannot simultaneously be proportional to attainments and to shortfalls, relative inequality measures may rank populations differently from the two perspectives. In contrast to the literature that stresses the importance of measuring inequality in attainments and shortfalls consistently using an absolute IEC, this chapter formalizes a new compromise concept for a bounded variable by explicitly considering the two relative IECs, defined with respect to attainments and shortfalls, to represent the polar cases of defensible positions. We use a surplus-sharing approach to provide new insights on commonly used inequality indices by evaluating the underpinning IECs in terms of how infinitesimal surpluses of health must be successively distributed to preserve the level of inequality. We derive a one-parameter IEC that, unlike those implicit in commonly used indices, assigns constant weights to the polar cases independent of the health distribution.

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Bibliographic Info

Paper provided by Lund University, Department of Economics in its series Working Papers with number 2013:18.

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Length: 23 pages
Date of creation: 29 May 2013
Date of revision: 02 Jan 2014
Publication status: Published as Kjellsson, Gustav and Ulf-G. Gerdtham, 'Lost in Translation: Rethinking the Inequality-Equivalence Criteria for Bounded Health Variables' in Research on Economic Inequality, 2013, pages 3-32.
Handle: RePEc:hhs:lunewp:2013_018

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Postal: Department of Economics, School of Economics and Management, Lund University, Box 7082, S-220 07 Lund,Sweden
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Fax: +46 +46 2224613
Web page: http://www.nek.lu.se/en
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Keywords: health inequality; bounded variable; inequality equivalence criteria;

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  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. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
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  5. Erreygers, Guido, 2009. "Correcting the Concentration Index: A reply to Wagstaff," Journal of Health Economics, Elsevier, vol. 28(2), pages 521-524, March.
  6. Bossert, Walter & Pfingsten, Andreas, 1990. "Intermediate inequality: concepts, indices, and welfare implications," Mathematical Social Sciences, Elsevier, vol. 19(2), pages 117-134, April.
  7. 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.
  8. Paul Allanson & Dennis Petrie, 2013. "On The Choice Of Health Inequality Measure For The Longitudinal Analysis Of Income‐Related Health Inequalities," Health Economics, John Wiley & Sons, Ltd., vol. 22(3), pages 353-365, 03.
  9. Paul Allanson & Dennis Petrie, 2012. "Understanding the vertical equity judgements underpinning health inequality measures," Dundee Discussion Papers in Economics 264, Economic Studies, University of Dundee.
  10. Buhong Zheng, 2007. "Unit-Consistent Decomposable Inequality Measures," Economica, London School of Economics and Political Science, vol. 74(293), pages 97-111, 02.
  11. 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.
  12. Kjellsson, Gustav & Gerdtham, Ulf-G., 2013. "On correcting the concentration index for binary variables," Journal of Health Economics, Elsevier, vol. 32(3), pages 659-670.
  13. Guido Erreygers & Tom Van Ourti, 2011. "Putting the cart before the horse. A comment on Wagstaff on inequality measurement in the presence of binary variables," Health Economics, John Wiley & Sons, Ltd., vol. 20(10), pages 1161-1165, October.
  14. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
  15. ERREYGERS, Guido, 2006. "Correcting the Concentration Index," Working Papers 2006027, University of Antwerp, Faculty of Applied Economics.
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