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

  • David E. A. Giles

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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Article provided by Department of Economics, University of Oxford in its journal Oxford Bulletin of Economics & Statistics.

Volume (Year): 66 (2004)
Issue (Month): 3 (07)
Pages: 425-433

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Handle: RePEc:bla:obuest:v:66:y:2004:i:3:p:425-433
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  1. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  2. 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 235-39, April.
  3. 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 123-29, February.
  4. 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 119-22, February.
  5. W. Sendler, 1979. "On statistical inference in concentration measurement," Metrika, Springer, vol. 26(1), pages 109-122, December.
  6. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-65, May.
  7. K.W. Clements & H.Y. Izan, 1984. "The Measurement of Inflation: a Stochastic Approach," Economics Discussion / Working Papers 84-10, The University of Western Australia, Department of Economics.
  8. 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 185-89, May.
  9. Paul Crompton, 2000. "Extending the stochastic approach to index numbers," Applied Economics Letters, Taylor & Francis Journals, vol. 7(6), pages 367-371.
  10. 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 113-19, January.
  11. 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.
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