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Partial Multidimensional Inequality Orderings

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

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 follows the dominance approach to making inequality comparisons, as developed for instance by Atkinson (1970), Foster and Shorrocks (1988) and Formby, Smith, and Zheng (1999) in the unidimensional context, and Atkinson and Bourguignon (1982) in the multidimensional context. 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. We apply our approach to data from India and Mexico using monetary and non-monetary indicators of well-being.

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Bibliographic Info

Paper provided by CIRPEE in its series Cahiers de recherche with number 1003.

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Date of creation: 2010
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Handle: RePEc:lvl:lacicr:1003

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Keywords: Inequality; multidimensional comparisons; stochastic dominance;

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References

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  1. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
  2. 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.
  3. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931, October.
  4. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Spatial Poverty Comparisons in Ghana, Madagascar, and Uganda," World Bank Economic Review, World Bank Group, vol. 20(1), pages 91-113.
  5. Davidson, Russell & Duclos, Jean-Yves, 2006. "Testing for Restricted Stochastic Dominance," IZA Discussion Papers 2047, Institute for the Study of Labor (IZA).
  6. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  7. Horton, S. & Ross, J., 2003. "The economics of iron deficiency," Food Policy, Elsevier, vol. 28(1), pages 51-75, February.
  8. 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.
  9. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  16. Duclos, Jean-Yves & Sahn, David & Younger, Stephen D., 2001. "Robust Multidimensional Poverty Comparisons," Cahiers de recherche 0115, Université Laval - Département d'économique.
  17. Foster, James E. & Shorrocks, Anthony F., 1988. "Inequality and poverty orderings," European Economic Review, Elsevier, vol. 32(2-3), pages 654-661, March.
  18. 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.
  19. 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.
  20. Ernesto Savaglio, 2006. "Multidimensional inequality with variable population size," Economic Theory, Springer, vol. 28(1), pages 85-94, 05.
  21. Maasoumi, Esfandiar & Nickelsburg, Gerald, 1988. "Multivariate Measures of Well-Being and an Analysis of Inequality in the Michigan Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 326-34, July.
  22. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  23. 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.
  24. Sen, Amartya, 1983. "Poor, Relatively Speaking," Oxford Economic Papers, Oxford University Press, vol. 35(2), pages 153-69, July.
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Citations

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Cited by:
  1. Athanassoglou, Stergios, 2013. "Multidimensional welfare rankings," MPRA Paper 51642, University Library of Munich, Germany.
  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. Martyna Kobus, 2014. "Multidimensional polarization for ordinal data," Working Papers 326, ECINEQ, Society for the Study of Economic Inequality.
  4. Hussain, M. Azhar & Jørgensen, Mette Møller & Østerdal, Lars Peter, 2014. "Refining Population Health Comparisons: A Multidimensional First Order Dominance Approach," COHERE Working Paper 2014:5, COHERE - Centre of Health Economics Research, University of Southern Denmark.
  5. Nicholas Rohde & Ross Guest, 2013. "Multidimensional Racial Inequality in the United States," Social Indicators Research, Springer, vol. 114(2), pages 591-605, November.
  6. Esfandiar Maasoumi & Jeffrey S. Racine, 2013. "Multidimensional Poverty Frontiers: Parametric Aggregators Based on Nonparametric Distributions," Department of Economics Working Papers 2013-07, McMaster University.
  7. Echevin, Damien, 2011. "Vulnerability to asset-poverty in Sub-Saharan Africa," MPRA Paper 35660, University Library of Munich, Germany.
  8. 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).
  9. 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).

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