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Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes

Author

Listed:
  • Xiaofeng Lv

    (Southwestern University of Finance and Economics)

  • Gupeng Zhang

    (University of Chinese Academy of Science)

  • Xinkuo Xu

    (Capital University of Economics and Business)

  • Qinghai Li

    (Nanjing University of Finance and Economics)

Abstract

Measuring the difference between two Gini indexes is important in comparing the inequality between two groups. This paper systematically provides confidence intervals for this difference. First, normal approximation- and bootstrap-based confidence intervals are provided for the difference. Second, empirical likelihood (EL)-based confidence intervals are proposed according to a ratio statistic that is proven to have a weighted Chi-squared distribution with one degree of freedom. Third, two calibration approaches are established to improve the undercoverage issue of the EL method; these two approaches are augmented EL and bootstrap-calibrated EL. Monte Carlo simulations show that bootstrap-calibrated EL generally outperforms other methods in constructing confidence intervals. In the simulations, these methods are compared with the permutation method to test the equality of two Gini indexes. Lastly, these methods are applied to real data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecin:v:15:y:2017:i:2:d:10.1007_s10888-017-9348-8
    DOI: 10.1007/s10888-017-9348-8
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