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Correcting the Bias in the Concentration Index when Income is Grouped

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  • Philip Clarke
  • Tom Van Ourti

Abstract

The problem introduced by grouping income data when measuring socioeconomic inequalities in health (and health care) has been highlighted in a recent study. We reexamine this issue and show there is a tendency to underestimate the concentration index at an increasing rate when lowering the number of income categories. This bias results from a form of measurement error and we propose two correction methods. Firstly, the use of instrumental variables (IV) can reduce the error within income categories. Secondly, through a simple formula for correction that is based only on the number of groups. We compare the performance of these methods using data from 15 European countries and the United States. We find that the simple correction formula reduces the impact of grouping and always outperforms the IV approach. Use of this correction can substantially improve comparisons of the concentration index both across countries and across time.

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Bibliographic Info

Paper provided by Centre for Economic Policy Research, Research School of Economics, Australian National University in its series CEPR Discussion Papers with number 599.

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Date of creation: Jan 2009
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Handle: RePEc:auu:dpaper:599

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Keywords: concentration index; errors-in-variables; instrumental variables; categorical data; first-order correction;

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References

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  1. Villasenor, JoseA. & Arnold, Barry C., 1989. "Elliptical Lorenz curves," Journal of Econometrics, Elsevier, vol. 40(2), pages 327-338, February.
  2. Tomson Ogwang, 2003. "Bounds of the Gini Index Using Sparse Information on Mean Incomes," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 49(3), pages 415-423, 09.
  3. Teresa Bago d’Uva & Eddy Van Doorslaer & Maarten Lindeboom & Owen O’Donnell & Somnath Chatterji, 2006. "Does reporting heterogeneity bias the measurement of health disparities?," Health, Econometrics and Data Group (HEDG) Working Papers 06/03, HEDG, c/o Department of Economics, University of York.
  4. Tom Van Ourti, 2004. "Measuring horizontal inequity in Belgian health care using a Gaussian random effects two part count data model," Health Economics, John Wiley & Sons, Ltd., vol. 13(7), pages 705-724.
  5. Doorslaer, Eddy van & Jones, Andrew M., 2003. "Inequalities in self-reported health: validation of a new approach to measurement," Journal of Health Economics, Elsevier, vol. 22(1), pages 61-87, January.
  6. Kakwani, Nanak & Wagstaff, Adam & van Doorslaer, Eddy, 1997. "Socioeconomic inequalities in health: Measurement, computation, and statistical inference," Journal of Econometrics, Elsevier, vol. 77(1), pages 87-103, March.
  7. Teresa Bago d'Uva & Andrew M. Jones & Eddy van Doorslaer, 2007. "Measurement of Horizontal Inequity in Health Care Utilisation using European Panel Data," Tinbergen Institute Discussion Papers 07-059/3, Tinbergen Institute.
  8. Tom Van Ourti & Philip Clarke, 2008. "The Bias of the Gini Coefficient due to Grouping," Tinbergen Institute Discussion Papers 08-095/3, Tinbergen Institute.
  9. Wagstaff, Adam & van Doorslaer, Eddy, 2000. "Chapter 34 Equity in health care finance and delivery," Handbook of Health Economics, in: A. J. Culyer & J. P. Newhouse (ed.), Handbook of Health Economics, edition 1, volume 1, chapter 34, pages 1803-1862 Elsevier.
  10. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.
  11. Wagstaff, Adam, 2002. "Inequality aversion, health inequalities, and health achievement," Policy Research Working Paper Series 2765, The World Bank.
  12. Wagstaff, Adam & Van Doorslaer, Eddy & Watanabe, Naoko, 2001. "On decomposing the causes of health sector inequalities with an application to malnutrition inequalities in Vietnam," Policy Research Working Paper Series 2714, The World Bank.
  13. Jens Gundgaard & Jørgen Lauridsen, 2006. "A decomposition of income-related health inequality applied to EQ-5D," The European Journal of Health Economics, Springer, vol. 7(4), pages 231-237, December.
  14. Adam Wagstaff, 2005. "The bounds of the concentration index when the variable of interest is binary, with an application to immunization inequality," Health Economics, John Wiley & Sons, Ltd., vol. 14(4), pages 429-432.
  15. Chen, Zhuo & Roy, Kakoli, 2009. "Calculating concentration index with repetitive values of indicators of economic welfare," Journal of Health Economics, Elsevier, vol. 28(1), pages 169-175, January.
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Cited by:
  1. David Madden, 2013. "The Socio-Economic Gradient Of Obesity In Ireland," The Economic and Social Review, Economic and Social Studies, vol. 44(2), pages 181-196.
  2. Clarke, Philip & Van Ourti, Tom, 2010. "Calculating the concentration index when income is grouped," Journal of Health Economics, Elsevier, vol. 29(1), pages 151-157, January.

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