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Empirical likelihood confidence intervals for the Gini measure of income inequality

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  • Qin, Yongsong
  • Rao, J.N.K.
  • Wu, Changbao

Abstract

Gini coefficient is among the most popular and widely used measures of income inequality in economic studies, with various extensions and applications in finance and other related areas. This paper studies confidence intervals on the Gini coefficient for simple random samples, using normal approximation, bootstrap percentile, bootstrap-t and the empirical likelihood method. Through both theory and simulation studies it is shown that the intervals based on normal or bootstrap approximation are less satisfactory for samples of small or moderate size than the bootstrap-calibrated empirical likelihood ratio confidence intervals which perform well for all sample sizes. Results for stratified random sampling are also presented.

Suggested Citation

  • Qin, Yongsong & Rao, J.N.K. & Wu, Changbao, 2010. "Empirical likelihood confidence intervals for the Gini measure of income inequality," Economic Modelling, Elsevier, vol. 27(6), pages 1429-1435, November.
    • Handle: RePEc:eee:ecmode:v:27:y:2010:i:6:p:1429-1435
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    1. Kakwani, Nanak C, 1977. "Applications of Lorenz Curves in Economic Analysis," Econometrica, Econometric Society, vol. 45(3), pages 719-727, April.
    2. 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.
    3. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2008. "Empirical likelihood for non-degenerate U-statistics," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 599-607, April.
    4. 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.
    5. repec:bla:obuest:v:62:y:2000:i:1:p:119-22 is not listed on IDEAS
    6. 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.
    7. Giovanni Maria Giorgi & Paola Palmitesta & Corrado Provasi, 2006. "Asymptotic and bootstrap inference for the generalized Gini indices," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 107-124.
    8. 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.
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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. Lv, Xiaofeng & Li, Rui & Fang, Zheng, 2017. "Efficient semiparametric estimation for Gini inequality treatment effects," Economics Letters, Elsevier, vol. 154(C), pages 96-100.
    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. Yang Wei & Zhouping Li & Yunqiu Dai, 2022. "Unified smoothed jackknife empirical likelihood tests for comparing income inequality indices," Statistical Papers, Springer, vol. 63(5), pages 1415-1475, October.
    5. Xiaofeng Lv & Gupeng Zhang & Guangyu Ren, 2017. "Gini index estimation for lifetime data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 275-304, April.
    6. 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.
    7. 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.
    8. 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.
    9. M. R. Narayana, 2021. "Economic inequality by age and its implications for inequity for living generations in India: evidence based on National Transfer Accounts," Asia-Pacific Journal of Regional Science, Springer, vol. 5(2), pages 373-396, June.
    10. 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.
    11. Tsao, Min & Wu, Fan, 2015. "Two-sample extended empirical likelihood for estimating equations," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 1-15.
    12. Encarnación Álvarez-Verdejo & Pablo J. Moya-Fernández & Juan F. Muñoz-Rosas, 2021. "Single Imputation Methods and Confidence Intervals for the Gini Index," Mathematics, MDPI, vol. 9(24), pages 1-20, December.
    13. Zhao, Puying & Haziza, David & Wu, Changbao, 2020. "Survey weighted estimating equation inference with nuisance functionals," Journal of Econometrics, Elsevier, vol. 216(2), pages 516-536.

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