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Calculating a Standard Error for the Gini Coefficient: Some Further Results

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  • David E. A. Giles

Abstract

Several authors have suggested using the jackknife technique to approximate a standard error for the Gini coefficient. It has also been shown that the Gini measure can be obtained simply from an artificial ordinary least square (OLS) regression based on the data and their ranks. We show that obtaining an exact analytical expression for the standard error is actually a trivial matter. Further, by extending the regression framework to one involving seemingly unrelated regressions (SUR), several interesting hypotheses regarding the sensitivity of the Gini coefficient to changes in the data are readily tested in a formal manner. Copyright 2004 Blackwell Publishing Ltd.

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  • 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.
  • Handle: RePEc:bla:obuest:v:66:y:2004:i:3:p:425-433
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    References listed on IDEAS

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    1. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-465, May.
    2. Karagiannis, Elias & Kovacevic', Milorad, 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.
    3. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    4. Paul Crompton, 2000. "Extending the stochastic approach to index numbers," Applied Economics Letters, Taylor & Francis Journals, vol. 7(6), pages 367-371.
    5. 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.
    6. W. Sendler, 1979. "On statistical inference in concentration measurement," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 26(1), pages 109-122, December.
    7. Sandstrom, Arne & Wretman, Jan H & Walden, Bertil, 1988. "Variance Estimators of the Gini Coefficient--Probability Sampling," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 113-119, January.
    8. Lerman, Robert I. & Yitzhaki, Shlomo, 1984. "A note on the calculation and interpretation of the Gini index," Economics Letters, Elsevier, vol. 15(3-4), pages 363-368.
    9. Clements, Kenneth W & Izan, H Y, 1987. "The Measurement of Inflation: A Stochastic Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(3), pages 339-350, July.
    10. Ogwang, Tomson, 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.
    11. Shalit, Haim, 1985. "Calculating the Gini Index of Inequality for Individual Data," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 47(2), pages 185-189, May.
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    Cited by:

    1. Karoly, Lynn & Schröder, Carsten, 2015. "Fast methods for jackknifing inequality indices," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 37(1), pages 125-138.
    2. Wang, Dongliang & Zhao, Yichuan & Gilmore, Dirk W., 2016. "Jackknife empirical likelihood confidence interval for the Gini index," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 289-295.
    3. David (David Patrick) Madden, 2012. "Methods for studying dominance and inequality in population health," Working Papers 201205, School of Economics, University College Dublin.
    4. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, pages 30-40.
    5. Lubrano, Michel & Ndoye, Abdoul Aziz Junior, 2016. "Income inequality decomposition using a finite mixture of log-normal distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 830-846.
    6. Bowden, Roger J., 2016. "Giving Gini direction: An asymmetry metric for economic disadvantage," Economics Letters, Elsevier, vol. 138(C), pages 96-99.
    7. Shirmohammadli, Abdolmatin & Louen, Conny & Vallée, Dirk, 2016. "Exploring mobility equity in a society undergoing changes in travel behavior: A case study of Aachen, Germany," Transport Policy, Elsevier, vol. 46(C), pages 32-39.
    8. El-Osta, Hisham S. & Morehart, Mitchell J., 2009. "Welfare Decomposition in the Context of the Life Cycle of Farm Operators: What Does a National Survey Reveal?," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 38(2), October.

    More about this item

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

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