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The Social Welfare Implications, Decomposability, and Geometry of the Sen Family of Poverty Indices

Author

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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.

Suggested Citation

  • Kuan Xu & Lars Osberg, 2000. "The Social Welfare Implications, Decomposability, and Geometry of the Sen Family of Poverty Indices," Department of Economics at Dalhousie University working papers archive sendeco, Dalhousie, Department of Economics.
  • Handle: RePEc:dal:wparch:sendeco
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    References listed on IDEAS

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    1. Satya R. Chakravarty, 1997. "On Shorrocks' Reinvestigation of the Sen Poverty Index," Econometrica, Econometric Society, vol. 65(5), pages 1241-1242, September.
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    5. 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.
    6. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    7. 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.
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    Citations

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    Cited by:

    1. 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.
    2. Stéphane Mussard, 2005. "On Decomposition of the Gini Index of Equality," Cahiers de recherche 05-09, Departement d'Economique de l'École de gestion à l'Université de Sherbrooke.
    3. 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.
    4. Kuan Xu & Ian Irvine, 2002. "Crime, Punishment and the Measurement of Poverty in the United States, 1979-1997," LIS Working papers 333, LIS Cross-National Data Center in Luxembourg.
    5. Paolo Giordani & Giovanni Giorgi, 2010. "A fuzzy logic approach to poverty analysis based on the Gini and Bonferroni inequality indices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 587-607, November.
    6. 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.
    7. Stephen P. Jenkins & Philippe Van Kerm, 2006. "Trends in income inequality, pro-poor income growth, and income mobility," Oxford Economic Papers, Oxford University Press, vol. 58(3), pages 531-548, July.
    8. Christophe Muller, 2005. "Poverty and inequality under income and price dispersions," Canadian Journal of Economics, Canadian Economics Association, vol. 38(3), pages 979-998, August.
    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. Oihana Aristondo & Francisco J. Goerlich Gisbert & Casilda Lasso De La Vega, 2015. "A Proposal to Compare Consistently the Inequality Among the Poor," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(3), pages 561-572, September.
    11. Mussini, Mauro, 2013. "On decomposing inequality and poverty changes over time: A multi-dimensional decomposition," Economic Modelling, Elsevier, vol. 33(C), pages 8-18.
    12. Mussa, Richard, 2015. "A joint analysis of correlates of poverty intensity, incidence, and gap with application to Malawi," MPRA Paper 65205, University Library of Munich, Germany.
    13. 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.

    More about this item

    Keywords

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

    JEL classification:

    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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