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Statistical Inference and the Sen Index of Poverty

Author

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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, 2001. "Statistical inference for poverty measures with relative poverty lines," Journal of Econometrics, Elsevier, vol. 101(2), pages 337-356, April.
    2. 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.
    3. 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.
    4. Gabriela Flores & Jaya Krishnakumar & Sudip Ranjan Basu, 2004. "Demand System Estimations and Welfare Comparisons: Application to Indian Household Data," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 2004.13, Institut d'Economie et Econométrie, Université de Genève.
    5. Kuan Xu & Lars Osberg, 2002. "The social welfare implications, decomposability, and geometry of the Sen family of poverty indices," Canadian Journal of Economics, Canadian Economics Association, vol. 35(1), pages 138-152, February.
    6. 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.
    7. 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.
    8. Robert H. DeFina, 2002. "The impact of unemployment on alternative poverty measures," Working Papers 02-8, Federal Reserve Bank of Philadelphia.
    9. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    10. 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.
    11. Kuan Xu & Lars Osberg, 2002. "On Sen's Approach to Poverty Measures and Recent Developments," Department of Economics at Dalhousie University working papers archive sensw, Dalhousie, Department of Economics.
    12. Sudip Ranjan Basu & Jaya Krishnakumar & Gabriela Flores, 2004. "Spatial Distribution of Welfare Across States and Different Socio-Economic Groups in Rural and Urban India," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 2004.14, Institut d'Economie et Econométrie, Université de Genève.
    13. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    14. Bhargab Chattopadhyay & Shyamal Krishna De, 2016. "Estimation of Gini Index within Pre-Specified Error Bound," Econometrics, MDPI, Open Access Journal, vol. 4(3), pages 1-12, June.
    15. Ian Irvine & Kuan Xu, 2002. "Crime, Punishment and Poverty in the United States," Department of Economics at Dalhousie University working papers archive uspov, Dalhousie, Department of Economics.

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