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Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality

  • Davidson, Russell
  • Duclos, Jean-Yves

    ()

We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality or social welfare is greater in one distribution than in another for general classes of indices. We also derive the sampling distribution of the maximal poverty lines (or income censoring thresholds) up to which we may confidently assert that poverty or social welfare is greater in one distribution than in another. The sampling distribution of convenient estimators for dual approaches to the measurement of poverty is also established. The statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes. Our results are briefly illustrated using data for 6 countries drawn from the Luxembourg Income Study data bases. On étudie les propriétés asymptotiques de plusieurs estimateurs fréquemment utilisés pour ordonner les répartitions de revenus en termes de pauvreté, bien-être social, et inégalité. Ces estimateurs incluent les estimateurs de la plupart des indices de pauvreté couramment en usage ainsi que les estimateurs des courbes utiles pour l'inférence de la dominance stochastique de n'importe quel ordre. Ces courbes nous permettent de déterminer si la pauvreté, l'inégalité ou le bien-être social sont plus élevés dans une répartition que dans une autre pour des classes générales d'indices. On étudie aussi la distribution échantillonnale des seuils maximum de pauvreté ou de censure des revenus jusqu'auxquels on peut affirmer sans ambiguïté que la pauvreté ou le bien-être social sont plus élevés dans une répartition de revenus que dans une autre. La distribution échantillonnale d'estimateurs pour l'approche duale à la mesure de la pauvreté est aussi dérivée. Les résultats statistiques s'appliquent à des seuils déterministes ou stochastiques et à des échantillons dépendants ou indépendants. On illustre brièvement nos résultats à l'aide de données sur 6 pays tirées des banques de données du Luxembourg Income Study.

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Paper provided by Université Laval - Département d'économique in its series Cahiers de recherche with number 9805.

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Date of creation: 1998
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Handle: RePEc:lvl:laeccr:9805
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  1. Blakorby, Charles & Donaldson, David, 1980. "Ethical Indices for the Measurement of Poverty," Econometrica, Econometric Society, vol. 48(4), pages 1053-60, May.
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  4. 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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  6. 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.
  7. Davidson, R. & Duclos, J.Y., 1995. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Papers 9521, Laval - Recherche en Politique Economique.
  8. Kakwani, Nanak, 1993. "Statistical Inference in the Measurement of Poverty," The Review of Economics and Statistics, MIT Press, vol. 75(4), pages 632-39, November.
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  11. Muffels, R.J.A. & van den Bosch, K. & Callan, T., 1993. "A comparison of poverty in seven European countries and regions using subjective and relative measures," WORC Paper 2, Tilburg University, Work and Organization Research Centre.
  12. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
  13. 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.
  14. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
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  16. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-64, July.
  17. Van den Bosch, Karel & Callan, Tim & Estivill, Jordi & Hausman, Piette & Jeandidier, Bruno & Muffels, Ruud & Yfantopoulos, John, 1993. "A Comparison of Poverty in Seven European Countries and Regions Using Subjective and Relative Measures," Journal of Population Economics, Springer;European Society for Population Economics, vol. 6(3), pages 235-59.
  18. Chakravarty, Satya R., 1983. "A new index of poverty," Mathematical Social Sciences, Elsevier, vol. 6(3), pages 307-313, December.
  19. Ian Rongve, 1997. "Statistical inference for poverty indices with fixed poverty lines," Applied Economics, Taylor & Francis Journals, vol. 29(3), pages 387-392.
  20. Peter Gottschalk & Timothy M. Smeeding, 1997. "Cross-National Comparisons of Earnings and Income Inequality," Journal of Economic Literature, American Economic Association, vol. 35(2), pages 633-687, June.
  21. Satya R. Chakravarty, 1997. "On Shorrocks' Reinvestigation of the Sen Poverty Index," Econometrica, Econometric Society, vol. 65(5), pages 1241-1242, September.
  22. Greer, Joel & Thorbecke, Erik, 1986. "A methodology for measuring food poverty applied to Kenya," Journal of Development Economics, Elsevier, vol. 24(1), pages 59-74, November.
  23. 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.
  24. Gustafsson, Bjorn & Nivorozhkina, Ludmila, 1996. "Relative Poverty in Two Egalitarian Societies: A Comparison between Taganrog, Russia during the Soviet Era and Sweden," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 42(3), pages 321-34, September.
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