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Social Choice and Welfare

, Volume 39, Issue 2–3, pp 649–673 | Cite as

Sequential procedures for poverty gap dominance

  • Claudio Zoli
  • Peter J. LambertEmail author
Original Paper

Abstract

Poverty evaluations differ from welfare evaluations in one significant aspect, the existence of a threshold or reference point, the poverty line. We build up normative evaluation models in which comparisons are made taking distances from this reference point rather than from the origin to be ethically relevant, by focussing upon poverty gaps and not incomes. When poverty lines differ for different groups in a socially heterogeneous population, choosing poverty gaps instead of incomes as the relevant indicator brings in normatively appealing classes of poverty indices not previously accommodated, for which poverty comparisons are implemented through sequential poverty gap curves (or poverty gap distributions) dominance. These conditions are logically related to those suggested by Atkinson and Bourguignon (Arrow and the foundations of the theory of economic policy, Macmillan, London, 1987) and Bourguignon (J Econom 42:67–80, 1989) for welfare comparisons. However, the proportion of poor individuals in the society and their average poverty gap play a role in our comparisons, though they do not in the existing poverty dominance criteria for heterogeneous populations.

Keywords

Poverty Line Stochastic Dominance Dominance Condition Poverty Index Headcount Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Atkinson AB (1970) On the measurement of inequality. J Econ Theory 2: 244–263CrossRefGoogle Scholar
  2. Atkinson AB (1987) On the measurement of poverty. Econometrica 55: 749–764CrossRefGoogle Scholar
  3. Atkinson AB (1992) Measuring poverty and differences in family composition. Economica 59: 1–16CrossRefGoogle Scholar
  4. Atkinson AB, Bourguignon F (1987) Income distribution and differences in needs. In: Feiwel (ed) Arrow and the foundations of the theory of economic policy. Macmillan, London, pp 350–370Google Scholar
  5. Bazen S, Moyes P (2003) International comparisons of income distributions when population structures differ. Res Econ Inequal 9: 85–104CrossRefGoogle Scholar
  6. Bosmans K, Lauwers L, Ooghe E (2009) A consistent multidimensional Pigou-Dalton transfer principle. J Econ Theory 144: 1351–1358CrossRefGoogle Scholar
  7. Bourguignon F (1989) Family size and social utility: income distribution dominance criteria. J Econom 42: 67–80CrossRefGoogle Scholar
  8. Bourguignon F, Fields G (1997) Discontinuous losses from poverty, generalized P measures and optimal transfers to the poor. J Public Econ 63: 155–175CrossRefGoogle Scholar
  9. Chakravarty SR (1983) Ethically flexible measures of poverty. Can J Econ 16: 74–85CrossRefGoogle Scholar
  10. Chakravarty SR (1983) Measures of poverty based on the representative income gap. Sankya 45B: 69–74Google Scholar
  11. Chambaz C, Maurin E (1998) Atkinson and Bourguignon’s dominance criteria: extended and applied to the measurement of poverty in France. Rev Income Wealth 44: 497–515CrossRefGoogle Scholar
  12. Davidson R, Duclos JY (2000) Statistical inference for stochastic dominance and for the measurement of poverty and inequality. Econometrica 68: 1435–1465CrossRefGoogle Scholar
  13. Donaldson D, Pendakur K (2004) Equivalent-expenditure functions and expenditure-dependent equivalence scales. J Public Econ 88: 175–208CrossRefGoogle Scholar
  14. Duclos JY, Makdissi P (2005) Sequential stochastic dominance and the robustness of poverty orderings. Rev Income Wealth 51: 63–88CrossRefGoogle Scholar
  15. Duclos JY, Sahn D, Younger SD (2006) Robust multidimensional poverty comparisons. Econ J 116: 943–968CrossRefGoogle Scholar
  16. Ebert U, Moyes P (2003) Equivalence scales reexamined. Econometrica 71: 319–343CrossRefGoogle Scholar
  17. Fishburn PC, Vickson RG (1978) Theoretical foundations of stochastic dominance. In: Whitmore GA, Findlay MC (eds) Stochastic dominance. Lexington Books, Lexington, MA, pp 39–113Google Scholar
  18. Fleurbaey M, Hagneré C, Trannoy A (2003) Welfare comparisons with bounded equivalence scales. J Econ Theory 110: 309–336CrossRefGoogle Scholar
  19. Foster J, Shorrocks AF (1988a) Poverty orderings. Econometrica 56: 173–177CrossRefGoogle Scholar
  20. Foster J, Shorrocks AF (1988b) Poverty orderings and welfare dominance. Soc Choice Welf 5: 179–198CrossRefGoogle Scholar
  21. Foster J, Greer J, Thorbecke D (1984) A class of decomposable poverty measures. Econometrica 52: 761–766CrossRefGoogle Scholar
  22. Gravel N, Moyes P (2006) Ethically robust comparisons of distributions with two individual attributes. WP 0605 IDEPGoogle Scholar
  23. Jenkins S, Lambert PJ (1993) Ranking income distributions when needs differ. Rev Income Wealth 39: 337–356CrossRefGoogle Scholar
  24. Jenkins S, Lambert PJ (1997) Three I’s of poverty curves, with an analysis of UK poverty trends. Oxf Econ Pap 49: 317–327CrossRefGoogle Scholar
  25. Lambert P, Ramos X (2002) Welfare comparisons: sequential procedures for heterogeneous populations. Economica 69: 549–562CrossRefGoogle Scholar
  26. Ooghe E, Lambert PJ (2006) Bounded sequential dominance criteria. Math Soc Sci 52: 15–30CrossRefGoogle Scholar
  27. Saposnik R (1981) Rank-dominance in income distributions. Public Choice 36: 51–147CrossRefGoogle Scholar
  28. Shorrocks AF (1995) Revisiting the Sen poverty index. Econometrica 63: 1225–1230CrossRefGoogle Scholar
  29. Shorrocks AF (1998) Deprivation profiles and deprivation indices. In: Jenkins SA, Kaptein SA, Praag B (eds) The distribution of welfare and household production: international perspectives. Cambridge University Press, London, pp 250–267Google Scholar
  30. Spencer BD, Fisher S (1992) On comparing distributions of poverty gaps. Sankya 54B: 114–126Google Scholar
  31. Thistle P (1989) Ranking distributions with generalized Lorenz curves. South Econ J 56: 1–12CrossRefGoogle Scholar
  32. Weir AJ (1991) Lebesgue integration and measure. Cambridge University Press, CambridgeGoogle Scholar
  33. Zheng B (1999) On the power of poverty orderings. Soc Choice Welf 16: 349–371CrossRefGoogle Scholar
  34. Zoli C (2000) Inverse sequential stochastic dominance: rank-dependent welfare, deprivation and poverty measurement. University of Nottingham, Discussion Paper in Economics 00/11Google Scholar
  35. Zoli C, Lambert PJ (2005) Sequential procedures for poverty gap dominance. University of Oregon Economics Discussion Paper No. 2005/1Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Dipartimento di Scienze EconomicheUniversità di VeronaVeronaItaly
  2. 2.Department of EconomicsUniversity of OregonEugeneUSA

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