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Copula-based Measurement of Dependence Between Dimensions of Well-being

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  • Decancq K

Abstract

Well-being consists of many dimensions such as income, health and education. A society exhibits greater dependence between its dimensions of well-being when the positions of the individuals in the different dimensions are more aligned or correlated. Differences in dependence may lead to very different societies, even when the dimension-wise distributions are identical. I propose to use a copula-based frame-work to order societies with respect to their dependence. A class of measures of dependence is derived to which the multidimensional rank correlation coefficient be- longs. I illustrate the usefulness of the approach by showing that Russian dependence between three dimensions of well-being has increased significantly between 1995 and 2003. Unfortunately, the aspect of dependence is missed by all composite well-being measures based on dimension-specific summary statistics such as the popular Human Development Index (HDI)

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Paper provided by HEDG, c/o Department of Economics, University of York in its series Health, Econometrics and Data Group (HEDG) Working Papers with number 09/32.

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Date of creation: Dec 2009
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Handle: RePEc:yor:hectdg:09/32

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  1. Koen DECANCQ, 2010. "Copula-based orderings of multivariate dependence," Center for Economic Studies - Discussion papers ces10.08, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  2. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
  3. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate conditional versions of Spearman's rho and related measures of tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1123-1140, July.
  4. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 183-201, April.
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  7. Galina Besstremyannaya, 2007. "Out-of-Pocket Health Care Expenditures by Russian Consumers with Different Health Status," Transition Studies Review, Springer, vol. 14(2), pages 331-338, November.
  8. 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.
  9. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
  10. M. Fleurbaey & A. Trannoy, 2000. "The Impossibility of a Paretian Egalitarian," THEMA Working Papers 2000-26, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  11. Inna Blam & Sergey Kovalev, 2006. "Spontaneous commercialisation, inequality and the contradictions of compulsory medical insurance in transitional Russia," Journal of International Development, John Wiley & Sons, Ltd., vol. 18(3), pages 407-423.
  12. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
  13. Michael Lokshin & Martin Ravallion, 2008. "Testing for an economic gradient in health status using subjective data," Health Economics, John Wiley & Sons, Ltd., vol. 17(11), pages 1237-1259.
  14. Indranil Dutta & Prasanta K. Pattanaik & Yongsheng Xu, 2003. "On Measuring Deprivation and the Standard of Living in a Multidimensional Framework on the Basis of Aggregate Data," Economica, London School of Economics and Political Science, vol. 70(278), pages 197-221, 05.
  15. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
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Cited by:
  1. Suman Seth, 2013. "A class of distribution and association sensitive multidimensional welfare indices," Journal of Economic Inequality, Springer, vol. 11(2), pages 133-162, June.
  2. Maria Ana Lugo & Koen Decancq, 2009. "Measuring Inequality of Well-Being with a Correlation-Sensitive Multidimensional Gini Index," Economics Series Working Papers 459, University of Oxford, Department of Economics.

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