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Sequential procedures for poverty gap dominance

  • Claudio Zoli

    ()

  • Peter Lambert

    ()

Poverty evaluations differ from welfare evaluations in one significant aspect, the existence of a threshold or reference point, the poverty line. It is therefore possible to build up normative evaluation models in which comparisons are made taking distances from this reference point and not only from the origin to be ethically relevant. This is the case in our model of poverty comparisons over heterogeneous populations, which focuses upon poverty gaps and not incomes. When poverty lines differ for the different groups in the population we show that choosing poverty gaps instead of incomes as the relevant indicator brings in normatively appealing classes of poverty indices not previously accommodated. For these indices poverty comparisons over heterogeneous populations are implemented through sequential poverty gap curves (or poverty gap distributions) dominance. These novel conditions are logically related to those suggested in Atkinson and Bourguignon (1987) for welfare comparisons, and can also be grounded firmly upon those of Bourguignon (1989). The proportion of poor individuals in the society or their average poverty gap play a role in our comparisons that was neglected in the existing poverty dominance criteria for heterogeneous populations. Various intermediate poverty dominance conditions and a generalization of the poverty gap approach are also investigated.

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File URL: http://hdl.handle.net/10.1007/s00355-011-0601-y
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Article provided by Springer & The Society for Social Choice and Welfare in its journal Social Choice and Welfare.

Volume (Year): 39 (2012)
Issue (Month): 2 (July)
Pages: 649-673

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Handle: RePEc:spr:sochwe:v:39:y:2012:i:2:p:649-673
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  1. Davidson, R. & Duclos, J.-Y., 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," G.R.E.Q.A.M. 98a14, Universite Aix-Marseille III.
  2. Patrick Moyes & Nicolas Gravel, 2007. "Ethically robust comprisons of distributions of two individual attributes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00389601, HAL.
  3. Atkinson, A B, 1992. "Measuring Poverty and Differences in Family Composition," Economica, London School of Economics and Political Science, vol. 59(233), pages 1-16, February.
  4. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-30, September.
  5. Chambaz, Christine & Maurin, Eric, 1998. "Atkinson and Bourguignon's Dominance Criteria: Extended and Applied to the Measurement of Poverty in France," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 44(4), pages 497-513, December.
  6. Jean-Yves Duclos & Paul Makdissi, 2005. "Sequential Stochastic Dominance And The Robustness Of Poverty Orderings," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 51(1), pages 63-87, 03.
  7. Stephen Bazen & Patrick Moyes, 2003. "International comparisons of income distributions when population structures differ," Post-Print hal-00156458, HAL.
  8. Erwin Ooghe, 2004. "Bounded Sequential Dominance Criteria," Working Papers Department of Economics ces0405, KU Leuven, Faculty of Economics and Business, Department of Economics.
  9. Duclos, Jean-Yves & Sahn, David & Younger, Stephen D., 2001. "Robust Multidimensional Poverty Comparisons," Cahiers de recherche 0115, Université Laval - Département d'économique.
  10. Lambert, Peter J & Ramos, Xavier, 2002. "Welfare Comparisons: Sequential Procedures for Heterogeneous Populations," Economica, London School of Economics and Political Science, vol. 69(276), pages 549-62, November.
  11. Bourguignon, Francois, 1989. "Family size and social utility : Income distribution dominance criteria," Journal of Econometrics, Elsevier, vol. 42(1), pages 67-80, September.
  12. Bosmans, Kristof & Lauwers, Luc & Ooghe, Erwin, 2009. "A consistent multidimensional Pigou-Dalton transfer principle," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1358-1371, May.
  13. Jenkins, Stephen P & Lambert, Peter J, 1993. "Ranking Income Distributions When Needs Differ," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 39(4), pages 337-56, December.
  14. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  15. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  16. Satya Ranjan Chakravarty, 1983. "Ethically Flexible Measures of Poverty," Canadian Journal of Economics, Canadian Economics Association, vol. 16(1), pages 74-85, February.
  17. Donaldson, David & Pendakur, Krishna, 2004. "Equivalent-expenditure functions and expenditure-dependent equivalence scales," Journal of Public Economics, Elsevier, vol. 88(1-2), pages 175-208, January.
  18. Buhong Zheng, 1999. "On the power of poverty orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(3), pages 349-371.
  19. 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.
  20. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-64, July.
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