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

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  • Russell Davidson
  • Jean-Yves Duclos

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.

Suggested Citation

  • Russell Davidson & Jean-Yves Duclos, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," LIS Working papers 181, LIS Cross-National Data Center in Luxembourg.
    • Handle: RePEc:lis:liswps:181
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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.
    2. Russell Davidson & Jean-Yves Duclos, 1997. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Econometrica, Econometric Society, vol. 65(6), pages 1453-1466, November.
    3. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    4. 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 235-259.
    5. Hagenaars, Aldi J M, 1987. "A Class of Poverty Indices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 583-607, October.
    6. Bishop, John A & Chow, K Victor & Zheng, Buhong, 1995. "Statistical Inference and Decomposable Poverty Measures," Bulletin of Economic Research, Wiley Blackwell, vol. 47(4), pages 329-340, October.
    7. 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.
    8. Ravallion, Martin & Bidani, Benu, 1994. "How Robust Is a Poverty Profile?," The World Bank Economic Review, World Bank, vol. 8(1), pages 75-102, January.
    9. Ian Preston, 1995. "Sampling Distributions of Relative Poverty Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(1), pages 91-99, March.
    10. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    11. 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.
    12. Kakwani, Nanak, 1993. "Statistical Inference in the Measurement of Poverty," The Review of Economics and Statistics, MIT Press, vol. 75(4), pages 632-639, November.
    13. 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.
    14. Beach, Charles M & Richmond, James, 1985. "Joint Confidence Intervals for Income Shares and Lorenz Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 439-450, June.
    15. Dominique Thon, 1979. "On Measuring Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 25(4), pages 429-439, December.
    16. Bishop, John A & Chakraborti, S & Thistle, Paul D, 1989. "Asymptotically Distribution-Free Statistical Inference for Generalized Lorenz Curves," The Review of Economics and Statistics, MIT Press, vol. 71(4), pages 725-727, November.
    17. Buhong Zheng, 1997. "Statistical Inferences for Poverty Measures with Relative Poverty Rates," LIS Working papers 167, LIS Cross-National Data Center in Luxembourg.
    18. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    19. 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 321-334, September.
    20. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    21. 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.
    22. Clark, Stephen & Hemming, Richard & Ulph, David, 1981. "On Indices for the Measurement of Poverty," Economic Journal, Royal Economic Society, vol. 91(362), pages 515-526, June.
    23. Björn Gustafsson & Ludmila Nivorozhkina, 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 321-334, September.
    24. 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.
    25. Robert Summers & Alan Heston, 1991. "The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950–1988," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(2), pages 327-368.
    26. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    27. Blackorby, Charles & Donaldson, David, 1978. "Measures of relative equality and their meaning in terms of social welfare," Journal of Economic Theory, Elsevier, vol. 18(1), pages 59-80, June.
    28. Ian Rongve, 1997. "Statistical inference for poverty indices with fixed poverty lines," Applied Economics, Taylor & Francis Journals, vol. 29(3), pages 387-392.
    29. Takayama, Noriyuki, 1979. "Poverty, Income Inequality, and Their Measures: Professor Sen's Axiomatic Approach Reconsidered," Econometrica, Econometric Society, vol. 47(3), pages 747-759, May.
    30. 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 317-327, July.
    31. Blakorby, Charles & Donaldson, David, 1980. "Ethical Indices for the Measurement of Poverty," Econometrica, Econometric Society, vol. 48(4), pages 1053-1060, May.
    32. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 723-735.
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    More about this item

    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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