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

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Abstract

Various authors have proposed 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 OLS regression based on the data and their ranks. Accordingly, we show that obtaining an exact analytical expression for the standard error is a trivial matter. In addition, by extending the regression framework to one involving Seemingly Unrelated Regressions, several interesting hypotheses regarding the sensitivity of the Gini coefficient to changes in the data are readily tested in a formal manner.

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Bibliographic Info

Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0202.

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Length: 14 pages
Date of creation: 12 Apr 2002
Date of revision:
Handle: RePEc:vic:vicewp:0202

Note: ISSN 1485-6441
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Keywords: Gini coefficient; income inequality; standard error; SUR model;

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  1. 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 339-50, July.
  2. 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.
  3. W. Sendler, 1979. "On statistical inference in concentration measurement," Metrika, Springer, vol. 26(1), pages 109-122, December.
  4. 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.
  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 235-39, April.
  6. 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.
  7. 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.
  8. Harvey, A C, 1976. "Estimating Regression Models with Multiplicative Heteroscedasticity," Econometrica, Econometric Society, vol. 44(3), pages 461-65, May.
  9. 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.
  10. Paul Crompton, 2000. "Extending the stochastic approach to index numbers," Applied Economics Letters, Taylor & Francis Journals, vol. 7(6), pages 367-371.
  11. 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.
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Cited by:
  1. David Madden, 2012. "Methods for Studying Dominance and Inequality in Population Health," Working Papers 201205, School Of Economics, University College Dublin.
  2. Russell Davidson, 2009. "Reliable inference for the GINI Index," Working Papers halshs-00443553, HAL.
  3. 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.

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