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The social welfare implications, decomposability, and geometry of the Sen family of poverty indices

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  • Kuan Xu
  • Lars Osberg

Abstract

In this paper, we propose a unified framework for the Sen indices of poverty intensity that shows an explicit connection between the indices and the common underlying social evaluation function. We also identify the common multiplicative decomposition of the indices that allows simple and similar geometric interpretations and easy numerical computation.

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Bibliographic Info

Article provided by Canadian Economics Association in its journal Canadian Journal of Economics.

Volume (Year): 35 (2002)
Issue (Month): 1 (February)
Pages: 138-152

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Handle: RePEc:cje:issued:v:35:y:2002:i:1:p:138-152

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References

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  1. Lars Osberg & Kuan Xu, 1999. "Poverty Intensity: How Well Do Canadian Provinces Compare?," Canadian Public Policy, University of Toronto Press, vol. 25(2), pages 179-195, June.
  2. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  3. Myles, John & Picot, Garnett, 2000. "Poverty Indices and Policy Analysis," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 46(2), pages 161-79, June.
  4. Jenkins, Stephen P & Lambert, Peter J, 1997. "Three 'I's of Poverty Curves, with an Analysis of UK Poverty Trends," Oxford Economic Papers, Oxford University Press, vol. 49(3), pages 317-27, July.
  5. Birdsall, Nancy & Londono, Juan Luis, 1997. "Asset Inequality Matters: An Assessment of the World Bank's Approach to Poverty Reduction," American Economic Review, American Economic Association, vol. 87(2), pages 32-37, May.
  6. Osberg, L & Xu, K, 1997. "International Comparisons of Poverty Intensity : Index Decomposition and Bootstrap Inference," Department of Economics at Dalhousie University working papers archive 97-03, Dalhousie, Department of Economics.
  7. Blackorby, Charles & Donaldson, David, 1978. "Measures of relative equality and their meaning in terms of social welfare," Journal of Economic Theory, Elsevier, vol. 18(1), pages 59-80, June.
  8. Clark, Stephen & Hemming, Richard & Ulph, David, 1981. "On Indices for the Measurement of Poverty," Economic Journal, Royal Economic Society, vol. 91(362), pages 515-26, June.
  9. Donaldson, David & Weymark, John A, 1986. "Properties of Fixed-Population Poverty Indices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(3), pages 667-88, October.
  10. Bourguignon, Francois & Fields, Gary, 1997. "Discontinuous losses from poverty, generalized P[alpha] measures, and optimal transfers to the poor," Journal of Public Economics, Elsevier, vol. 63(2), pages 155-175, January.
  11. Blakorby, Charles & Donaldson, David, 1980. "Ethical Indices for the Measurement of Poverty," Econometrica, Econometric Society, vol. 48(4), pages 1053-60, May.
  12. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  13. Shelley Phipps, . "Economics and Well-Being of Canadian Children," Canadian International Labour Network Working Papers 35, McMaster University.
  14. Satya R. Chakravarty, 1997. "On Shorrocks' Reinvestigation of the Sen Poverty Index," Econometrica, Econometric Society, vol. 65(5), pages 1241-1242, September.
  15. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-30, September.
  16. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
  17. Fei, John C H & Rainis, Gustav & Kuo, Shirley W Y, 1978. "Growth and the Family Distribution of Income by Factor Components," The Quarterly Journal of Economics, MIT Press, vol. 92(1), pages 17-53, February.
  18. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
  19. Bishop, John A & Formby, John P & Zheng, Buhong, 1997. "Statistical Inference and the Sen Index of Poverty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 381-87, May.
  20. Lars Osberg, 2000. "Poverty in Canada and the United States: measurement, trends, and implications," Canadian Journal of Economics, Canadian Economics Association, vol. 33(4), pages 847-877, November.
  21. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  22. Ian Rongve, 1997. "Statistical inference for poverty indices with fixed poverty lines," Applied Economics, Taylor & Francis Journals, vol. 29(3), pages 387-392.
  23. Takayama, Noriyuki, 1979. "Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered," Econometrica, Econometric Society, vol. 47(3), pages 747-59, May.
  24. Karni, Edi & Safra, Zvi, 1990. "Rank-Dependent Probabilities," Economic Journal, Royal Economic Society, vol. 100(401), pages 487-95, June.
  25. Satya Ranjan Chakravarty, 1983. "Ethically Flexible Measures of Poverty," Canadian Journal of Economics, Canadian Economics Association, vol. 16(1), pages 74-85, February.
  26. Thon, Dominique, 1979. "On Measuring Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 25(4), pages 429-39, December.
  27. Charles Blackorby & David Donaldson & Maria Auersperg, 1981. "A New Procedure for the Measurement of Inequality within and among Population Subgroups," Canadian Journal of Economics, Canadian Economics Association, vol. 14(4), pages 665-85, November.
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Citations

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Cited by:
  1. Jenkins, Stephen P. & Van Kerm, Philippe, 2003. "Trends in Income Inequality, Pro-Poor Income Growth and Income Mobility," IZA Discussion Papers 904, Institute for the Study of Labor (IZA).
  2. Mussini, Mauro, 2013. "On decomposing inequality and poverty changes over time: A multi-dimensional decomposition," Economic Modelling, Elsevier, vol. 33(C), pages 8-18.
  3. Christophe Muller, 2004. "Poverty And Inequality Under Income And Price Dispersions," Working Papers. Serie AD 2004-35, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Stéphane Mussard, 2005. "On Decomposition of the Gini Index of Equality," Cahiers de recherche 05-09, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
  5. Oihana Aristondo & José Luis García-Lapresta & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira, 2011. "The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality," Working Papers 203, ECINEQ, Society for the Study of Economic Inequality.
  6. repec:ese:iserwp:2007-11 is not listed on IDEAS
  7. Stephen P. Jenkins & John Micklewright, 2007. "New Directions in the Analysis of Inequality and Poverty," Discussion Papers of DIW Berlin 700, DIW Berlin, German Institute for Economic Research.
  8. Paolo Giordani & Giovanni Giorgi, 2010. "A fuzzy logic approach to poverty analysis based on the Gini and Bonferroni inequality indices," Statistical Methods and Applications, Springer, vol. 19(4), pages 587-607, November.
  9. Lars Osberg, 2001. "Poverty Among Senior Citizens: A Canadian Success Story," The State of Economics in Canada: Festschrift in Honour of David Slater, in: Patrick Grady & Andrew Sharpe (ed.), The State of Economics in Canada: Festschrift in Honour of David Slater, pages 151-181 Centre for the Study of Living Standards.
  10. Ian Irvine & Kuan Xu, 2002. "Crime, Punishment and Poverty in the United States," Department of Economics at Dalhousie University working papers archive uspov, Dalhousie, Department of Economics.
  11. Kuan Xu, 2003. "How Has the Literature on Gini's Index Evolved in the Past 80 Years?," Department of Economics at Dalhousie University working papers archive howgini, Dalhousie, Department of Economics.

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