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Statistical Inference and the Sen Index of Poverty

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  • Bishop, John A
  • Formby, John P
  • Zheng, Buhong

Abstract

Statistical inference procedures are developed for A. K. Sen's distribution-sensitive index of poverty and each of its components--the headcount ratio, income gap ratio, and the Gini index of the poor. Using results from U-statistics, the authors show that estimates of the index and its components all have a jointly asymptotically normal distribution and the variance-covariance structure can be consistently estimated. The inference tests are illustrated by applying them to the same microeconomic data set used in estimating official U.S. poverty statistics. The application reveals that the Sen index increased significantly in each of the three periods considered. Copyright 1997 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • Bishop, John A & Formby, John P & Zheng, Buhong, 1997. "Statistical Inference and the Sen Index of Poverty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 381-387, May.
    • Handle: RePEc:ier:iecrev:v:38:y:1997:i:2:p:381-87
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    Citations

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    Cited by:

    1. Zheng, Buhong & J. Cushing, Brian, 2001. "Statistical inference for testing inequality indices with dependent samples," Journal of Econometrics, Elsevier, vol. 101(2), pages 315-335, April.
    2. Yoonseok Lee & Donggyun Shin, 2013. "Measuring Social Unrest Based on Income Distribution," Center for Policy Research Working Papers 160, Center for Policy Research, Maxwell School, Syracuse University.
    3. Robert H. DeFina, 2002. "The impact of unemployment on alternative poverty measures," Working Papers 02-8, Federal Reserve Bank of Philadelphia.
    4. John A. Bishop & Jonathan M. Lee & Lester A. Zeager, 2017. "Incorporating spatial price adjustments in U.S. public policy analysis," Working Papers 438, ECINEQ, Society for the Study of Economic Inequality.
    5. Kuan Xu, 2007. "U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures," Econometric Reviews, Taylor & Francis Journals, vol. 26(5), pages 567-577.
    6. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    7. Bhargab Chattopadhyay & Shyamal Krishna De, 2016. "Estimation of Gini Index within Pre-Specified Error Bound," Econometrics, MDPI, vol. 4(3), pages 1-12, June.
    8. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    9. Christopher Johnson, 2007. "A Re-count of Poverty in US Central Cities: Just Who and Where Are the Urban Poor?," Urban Studies, Urban Studies Journal Limited, vol. 44(12), pages 2283-2303, November.
    10. Yoonseok Lee & Donggyun Shin, 2016. "Measuring Social Tension from Income Class Segregation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 457-471, July.
    11. Zheng, Buhong, 2001. "Statistical inference for poverty measures with relative poverty lines," Journal of Econometrics, Elsevier, vol. 101(2), pages 337-356, April.
    12. Kuan Xu & Ian Irvine, 2002. "Crime, Punishment and the Measurement of Poverty in the United States, 1979-1997," LIS Working papers 333, LIS Cross-National Data Center in Luxembourg.
    13. Brennan S. Thompson, 2013. "Empirical Likelihood-Based Inference for Poverty Measures with Relative Poverty Lines," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 513-523, December.
    14. Bishop John A. & Lee Jonathan M. & Zeager Lester A., 2018. "U.S. Income Comparisons with Regional Price Parity Adjustments," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 18(4), pages 1-17, October.
    15. Buhong Zheng, 1997. "Statistical Inferences for Poverty Measures with Relative Poverty Rates," LIS Working papers 167, LIS Cross-National Data Center in Luxembourg.
    16. Giuseppe Pignataro & Michele Costa, 2023. "The Foster-Greer-Thorbecke index and the inequality factors: an analysis through the Gini index decomposition," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 21(2), pages 483-497, June.

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