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A Cautionary Note on Estimating the Standard Error of the Gini Index of Inequality

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  • Reza Modarres
  • Joseph L. Gastwirth

Abstract

We will show that the regression approach to estimating the standard error of the Gini index can produce incorrect results as it does not account for the correlations introduced in the error terms once the data are ordered. To assess the effect of ignoring the correlation in the error terms we examined two distributions and show that the regression method overestimates the standard error of the Gini index. We recommend that the more mathematically complex or computationally intensive methods be used.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:obuest:v:68:y:2006:i:3:p:385-390
    DOI: 10.1111/j.1468-0084.2006.00167.x
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    Cited by:

    1. Berger Yves G. & Balay İklim Gedik, 2020. "Confidence Intervals of Gini Coefficient Under Unequal Probability Sampling," Journal of Official Statistics, Sciendo, vol. 36(2), pages 237-249, June.
    2. Gordon Anderson & Jasmin Thomas, 2019. "Measuring Multi-group Polarization, Segmentation and Ambiguity: Increasingly Unequal Yet Similar Constituent Canadian Income Distributions," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 145(3), pages 1001-1032, October.
    3. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2017. "Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 195-216, June.
    4. Dona Ghosh & Jaydeep Sengupta & Aviral Kumar Tiwari, 2020. "Revisiting the Role of Gender in Health Taxonomy: Evidence from the Elderly in India," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(2), pages 104-133, June.
    5. Lingsheng Meng & Binzhen Wu & Zhaoguo Zhan, 2016. "Linear regression with an estimated regressor: applications to aggregate indicators of economic development," Empirical Economics, Springer, vol. 50(2), pages 299-316, March.
    6. Judith A. Clarke & Ahmed A. Hoque, 2014. "On Variance Estimation for a Gini Coefficient Estimator Obtained from Complex Survey Data," Econometrics Working Papers 1401, Department of Economics, University of Victoria.
    7. Vladimir Hlasny & Paolo Verme, 2018. "Top Incomes and Inequality Measurement: A Comparative Analysis of Correction Methods Using the EU SILC Data," Econometrics, MDPI, vol. 6(2), pages 1-21, June.
    8. 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.
    9. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    10. Ogwang Tomson, 2014. "A Convenient Method of Decomposing the Gini Index by Population Subgroups," Journal of Official Statistics, Sciendo, vol. 30(1), pages 91-105, March.
    11. Joseph Gastwirth & Reza Modarres & Efstathia Bura, 2005. "The use of the Lorenz curve, Gini index and related measures of relative inequality and uniformity in securities law," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 451-469.
    12. Mazzi Gian Luigi & Mitchell James & Carausu Florabela, 2021. "Measuring and Communicating the Uncertainty in Official Economic Statistics," Journal of Official Statistics, Sciendo, vol. 37(2), pages 289-316, June.
    13. Vladimir Hlasny & Paolo Verme, 2022. "The Impact of Top Incomes Biases on the Measurement of Inequality in the United States," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(4), pages 749-788, August.
    14. Gordon Anderson & Maria Grazia Pittau & Roberto Zelli & Jasmin Thomas, 2018. "Income Inequality, Cohesiveness and Commonality in the Euro Area: A Semi-Parametric Boundary-Free Analysis," Econometrics, MDPI, vol. 6(2), pages 1-20, March.
    15. 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.
    16. Dejian Lai & Jin Huang & Jan Risser & Asha Kapadia, 2008. "Statistical Properties of Generalized Gini Coefficient with Application to Health Inequality Measurement," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 87(2), pages 249-258, June.
    17. Czarnitzki, Dirk & Ebersberger, Bernd, 2010. "Do direct R&D subsidies lead to the monopolization of R&D in the economy?," ZEW Discussion Papers 10-078, ZEW - Leibniz Centre for European Economic Research.
    18. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2017. "Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 195-216, June.

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