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Fast Methods for Jackknifing Inequality Indices

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  • Lynn A. Karoly
  • Carsten Schröder

Abstract

The jackknife is a resampling method that uses subsets of the original database by leaving out one observation at a time from the sample. The paper develops fast algorithms for jackknifing inequality indices with only a few passes through the data. The number of passes is independent of the number of observations. Hence, the method provides an efficient way to obtain standard errors of the estimators even if sample size is large. We apply our method using micro data on individual incomes for Germany and the US.

Suggested Citation

  • Lynn A. Karoly & Carsten Schröder, 2014. "Fast Methods for Jackknifing Inequality Indices," SOEPpapers on Multidisciplinary Panel Data Research 643, DIW Berlin, The German Socio-Economic Panel (SOEP).
    • Handle: RePEc:diw:diwsop:diw_sp643
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    File URL: https://www.diw.de/documents/publikationen/73/diw_01.c.461509.de/diw_sp0643.pdf
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    References listed on IDEAS

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    1. Heshmati, Almas, 2004. "A Review of Decomposition of Income Inequality," IZA Discussion Papers 1221, Institute of Labor Economics (IZA).
    2. Schröder, Carsten & Bönke, Timm, 2012. "Country inequality rankings and conversion schemes," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 6, pages 1-43.
    3. Karoly, Lynn & Schröder, Carsten, 2015. "Fast methods for jackknifing inequality indices," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 37(1), pages 125-138.
    4. Yitzhaki, Shlomo, 1991. "Calculating Jackknife Variance Estimators for Parameters of the Gini Method," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(2), pages 235-239, April.
    5. David E. A. Giles, 2004. "Calculating a Standard Error for the Gini Coefficient: Some Further Results," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 425-433, July.
    6. Cowell, Frank A., 1989. "Sampling variance and decomposable inequality measures," Journal of Econometrics, Elsevier, vol. 42(1), pages 27-41, September.
    7. repec:bla:revinw:v:46:y:2000:i:2:p:139-59 is not listed on IDEAS
    8. Karoly, Lynn A, 1992. "Changes in the Distribution of Individual Earnings in the United States: 1967-1986," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 107-115, February.
    9. Reza Modarres & Joseph L. Gastwirth, 2006. "A Cautionary Note on Estimating the Standard Error of the Gini Index of Inequality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(3), pages 385-390, June.
    10. Jonathan Morduch & Terry Sicular, 2002. "Rethinking Inequality Decomposition, With Evidence from Rural China," Economic Journal, Royal Economic Society, vol. 112(476), pages 93-106, January.
    11. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    12. Tomson Ogwang, 2000. "A Convenient Method of Computing the Gini Index and its Standard Error," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(1), pages 123-129, February.
    13. Elias Karagiannis & Milorad Kovacevic', 2000. "A Method to Calculate the Jackknife Variance Estimator For the Gini Coefficient," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(1), pages 119-122, February.
    14. repec:bla:obuest:v:62:y:2000:i:1:p:123-29 is not listed on IDEAS
    15. repec:bla:obuest:v:62:y:2000:i:1:p:119-22 is not listed on IDEAS
    16. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, vol. 137(2), pages 674-707, April.
    17. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, vol. 108(2), pages 317-342, June.
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    Cited by:

    1. Karoly, Lynn & Schröder, Carsten, 2015. "Fast methods for jackknifing inequality indices," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 37(1), pages 125-138.

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    More about this item

    Keywords

    Jackknife; Resampling; Sampling Variability; Inequality;
    All these keywords.

    JEL classification:

    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
    • D3 - Microeconomics - - Distribution

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