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

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  • Davidson, Russell
  • Duclos, Jean-Yves

Abstract

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.

Suggested Citation

  • Davidson, Russell & Duclos, Jean-Yves, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Cahiers de recherche 9805, Université Laval - Département d'économique.
  • Handle: RePEc:lvl:laeccr:9805
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    1. Satya R. Chakravarty, 2019. "On Shorrocks’ Reinvestigation of the Sen Poverty Index," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 27-29, Springer.
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    5. Satya R. Chakravarty, 2019. "A New Index of Poverty," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 31-37, Springer.
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    12. Buhong Zheng, 1997. "Statistical Inferences for Poverty Measures with Relative Poverty Rates," LIS Working papers 167, LIS Cross-National Data Center in Luxembourg.
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    15. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    16. 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.
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    18. Thon, Dominique, 1979. "On Measuring Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 25(4), pages 429-439, December.
    19. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
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    More about this item

    Keywords

    Stochastic Dominance; Poverty; Inequality; Relative and Critical Poverty Lines; Distribution-free statistical inference; Dominance stochastique; Pauvreté; Inégalité; Seuils de pauvreté relatifs et critiques; Inférence statistique robuste;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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