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Partial multidimensional inequality orderings

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Author Info

  • Duclos, Jean-Yves
  • Sahn, David E.
  • Younger, Stephen D.

Abstract

The paper investigates how comparisons of multivariate inequality can be made robust to varying the intensity of focus on the share of the population that are more relatively deprived. It is in the spirit of Sen (1970)'s partial orderings and follows the dominance approach to making inequality comparisons. By focusing on those below a multidimensional inequality "frontier", we are able to reconcile the literature on multivariate relative poverty and multivariate inequality. Some existing approaches to multivariate inequality actually reduce the distributional analysis to a univariate problem, either by using a utility function first to aggregate an individual's multiple dimensions of well-being, or by applying a univariate inequality analysis to each dimension independently. One of our innovations is that unlike previous approaches, the distribution of relative well-being in one dimension is allowed to affect how other dimensions influence overall inequality. Our methods are also robust to choices of individual "utility" or aggregation functions. We apply our approach to data from India and Mexico to show inter alia how dependence between dimensions of well-being can influence relative poverty and inequality comparisons between two populations.

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Bibliographic Info

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

Volume (Year): 95 (2011)
Issue (Month): 3-4 (April)
Pages: 225-238

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Handle: RePEc:eee:pubeco:v:95:y:2011:i:3-4:p:225-238

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Web page: http://www.elsevier.com/locate/inca/505578

Related research

Keywords: Inequality Multidimensional comparisons Stochastic dominance;

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References

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  1. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
  2. Russell Davidson & Jean-Yves Duclos, 2009. "Testing for restricted stochastic dominance," Working Papers halshs-00443560, HAL.
  3. Kaur, Amarjot & Prakasa Rao, B.L.S. & Singh, Harshinder, 1994. "Testing for Second-Order Stochastic Dominance of Two Distributions," Econometric Theory, Cambridge University Press, vol. 10(05), pages 849-866, December.
  4. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2005. "Robust Multidimensional Spatial Poverty Comparisons in Ghana, Madagascar, and Uganda," Cahiers de recherche 0528, CIRPEE.
  5. Sen, Amartya, 1983. "Poor, Relatively Speaking," Oxford Economic Papers, Oxford University Press, vol. 35(2), pages 153-69, July.
  6. Jean-Yves Duclos & David E. Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons," Economic Journal, Royal Economic Society, vol. 116(514), pages 943-968, October.
  7. Ernesto Savaglio, 2006. "Multidimensional inequality with variable population size," Economic Theory, Springer, vol. 28(1), pages 85-94, 05.
  8. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  9. Foster, James E. & Shorrocks, Anthony F., 1988. "Inequality and poverty orderings," European Economic Review, Elsevier, vol. 32(2-3), pages 654-661, March.
  10. David Sahn & Stephen Younger, 2005. "Improvements in children’s health: Does inequality matter?," Journal of Economic Inequality, Springer, vol. 3(2), pages 125-143, August.
  11. Datt, Gaurav & Ravallion, Martin, 1992. "Growth and redistribution components of changes in poverty measures : A decomposition with applications to Brazil and India in the 1980s," Journal of Development Economics, Elsevier, vol. 38(2), pages 275-295, April.
  12. Sahn, David E. & Stifel, David C., 2000. "Poverty Comparisons Over Time and Across Countries in Africa," World Development, Elsevier, vol. 28(12), pages 2123-2155, December.
  13. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  14. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  15. Maasoumi, Esfandiar & Jeong, Jin Ho, 1985. "The trend and the measurement of world inequality over extended periods of accounting," Economics Letters, Elsevier, vol. 19(3), pages 295-301.
  16. John A. Weymark, 2003. "The Normative Approach to the Measurement of Multidimensional Inequality," Vanderbilt University Department of Economics Working Papers 0314, Vanderbilt University Department of Economics, revised Jan 2004.
  17. 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.
  18. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  19. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
  20. Horton, S. & Ross, J., 2003. "The economics of iron deficiency," Food Policy, Elsevier, vol. 28(1), pages 51-75, February.
  21. Formby, John P. & Smith, W. James & Zheng, Buhong, 1999. "The coefficient of variation, stochastic dominance and inequality: A new interpretation," Economics Letters, Elsevier, vol. 62(3), pages 319-323, March.
  22. Tsui Kai-Yuen, 1995. "Multidimensional Generalizations of the Relative and Absolute Inequality Indices: The Atkinson-Kolm-Sen Approach," Journal of Economic Theory, Elsevier, vol. 67(1), pages 251-265, October.
  23. David E. Sahn & David Stifel, 2003. "Exploring Alternative Measures of Welfare in the Absence of Expenditure Data," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 49(4), pages 463-489, December.
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Citations

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Cited by:
  1. Sonne-Schmidt, Christoffer & Tarp, Finn & Osterdal, Lars Peter, 2013. "Ordinal multidimensional inequality," Working Paper Series UNU-WIDER Research Paper , World Institute for Development Economic Research (UNU-WIDER).
  2. BOSMANS, Kristof & DECANCQ, Koen & OOGHE, Erwin, 2013. "What do normative indices of multidimensional inequality really measure?," CORE Discussion Papers 2013035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Nicholas Rohde & Ross Guest, 2013. "Multidimensional Racial Inequality in the United States," Social Indicators Research, Springer, vol. 114(2), pages 591-605, November.
  4. Esfandiar Maasoumi & Jeffrey S. Racine, 2013. "Multidimensional Poverty Frontiers: Parametric Aggregators Based on Nonparametric Distributions," Department of Economics Working Papers 2013-07, McMaster University.
  5. Echevin, Damien, 2011. "Vulnerability to asset-poverty in Sub-Saharan Africa," MPRA Paper 35660, University Library of Munich, Germany.
  6. Athanassoglou, Stergios, 2013. "Multidimensional welfare rankings," MPRA Paper 51642, University Library of Munich, Germany.
  7. Esfandiar Maasoumi & Jeffrey S. Racine, 2013. "A Solution to Aggregation and an Application to Multidimensional "Well-being" Frontiers," Emory Economics 1306, Department of Economics, Emory University (Atlanta).

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