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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

    ()
    (Department of Economics, Dalhousie University)

Abstract

This paper proposes a unified framework for the Sen indices of poverty intensity, which shows an explicit connection between the indices and the common underlying social evaluation function. This paper also identifies the common multiplicative decomposition of the indices that allows simple and similar geometric interpretations, easy numerical computation, and common subgroup decompositions. These results are useful to policy analysis.

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File URL: http://www.economics.dal.ca/RePEc/dal/wparch/sendeco.pdf
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Bibliographic Info

Paper provided by Dalhousie, Department of Economics in its series Department of Economics at Dalhousie University working papers archive with number sendeco.

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Length: 27 pages
Date of creation: 27 Oct 2000
Date of revision:
Handle: RePEc:dal:wparch:sendeco

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Related research

Keywords: Poverty Intensity; Poverty Rate; Poverty Gap; Sugroup Decomposition; Equally-Distributed-Equivalent-Income; Social Evaluation Function; Gini Index;

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References

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  1. Lars Osberg & Kuan Xu, 2000. "International Comparisons of Poverty Intensity: Index Decomposition and Bootstrap Inference," Journal of Human Resources, University of Wisconsin Press, vol. 35(1), pages 51-81.
  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. 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.
  4. 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.
  5. Shelley Phipps, . "Economics and Well-Being of Canadian Children," Canadian International Labour Network Working Papers 35, McMaster University.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Satya Ranjan Chakravarty, 1983. "Ethically Flexible Measures of Poverty," Canadian Journal of Economics, Canadian Economics Association, vol. 16(1), pages 74-85, February.
  11. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
  12. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  13. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  14. Satya R. Chakravarty, 1997. "On Shorrocks' Reinvestigation of the Sen Poverty Index," Econometrica, Econometric Society, vol. 65(5), pages 1241-1242, September.
  15. 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.
  16. Ian Rongve, 1997. "Statistical inference for poverty indices with fixed poverty lines," Applied Economics, Taylor & Francis Journals, vol. 29(3), pages 387-392.
  17. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-30, September.
  18. 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.
  19. 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.
  20. 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.
  21. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
  22. Karni, E. & Safra, Z., 1988. "Rank-Dependent Probabilities," Papers 11-88, Tel Aviv.
  23. 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.
  24. 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.
  25. 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.
  26. Blakorby, Charles & Donaldson, David, 1980. "Ethical Indices for the Measurement of Poverty," Econometrica, Econometric Society, vol. 48(4), pages 1053-60, May.
  27. 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.
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Citations

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Cited by:
  1. Stephen P. Jenkins & Philippe VanKerm, 2003. "Trends in Income Inequality, Pro-Poor Income Growth and Income Mobility," Discussion Papers of DIW Berlin 377, DIW Berlin, German Institute for Economic Research.
  2. 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.
  3. Stephen P. Jenkins & John Micklewright, 2007. "New Directions in the Analysis of Inequality and Poverty," Working Papers 71, ECINEQ, Society for the Study of Economic Inequality.
  4. 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.
  5. Mussini, Mauro, 2013. "On decomposing inequality and poverty changes over time: A multi-dimensional decomposition," Economic Modelling, Elsevier, vol. 33(C), pages 8-18.
  6. 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.
  7. 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).
  8. 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.
  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. 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.

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