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Inference for Generalized Gini Indices Using the Iterated-Bootstrap Method

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  • Xu, Kuan

Abstract

Inference using the iterated-bootstrap method proposed by Hall is appealing for cases in which the percentile method needs to be used but the nominal level of a confidence interval has to be adjusted. One natural application is for generalized Gini indices of income inequality. When applying these theoretical inequality measures directly to sample data for the purpose of statistical inference, economists must come up with some measure of sampling variation. This is particularly the case when the index estimates are compared over time to infer information on the changes of social welfare and inequality. Although there are difficulties in the existing inferential procedures, a more intuitive approach is to use the iterated-bootstrap method.

Suggested Citation

  • Xu, Kuan, 2000. "Inference for Generalized Gini Indices Using the Iterated-Bootstrap Method," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 223-227, April.
    • Handle: RePEc:bes:jnlbes:v:18:y:2000:i:2:p:223-27
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    Citations

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    Cited by:

    1. Thomas Demuynck, 2012. "An (almost) unbiased estimator for the S-Gini index," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(1), pages 109-126, March.
    2. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, J., 2017. "Maximum Tsallis entropy with generalized Gini and Gini mean difference indices constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 554-560.
    3. Stephen G. Donald & Yu‐Chin Hsu & Garry F. Barrett, 2012. "Incorporating covariates in the measurement of welfare and inequality: methods and applications," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 1-30, February.
    4. 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.
    5. Stéphane Mussard & Pi Alperin María Noel, 2006. "Measuring Significance of Inequalities with Heterogeneous Groups and Income Sources," Cahiers de recherche 06-13, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    6. Yoonseok Lee & Donggyun Shin, 2013. "Measuring Social Unrest Based on Income Distribution," Center for Policy Research Working Papers 160, Center for Policy Research, Maxwell School, Syracuse University.
    7. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, Jafar, 2018. "New functional forms of Lorenz curves by maximizing Tsallis entropy of income share function under the constraint on generalized Gini index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 280-288.
    8. 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.
    9. William Horrace & Joseph Marchand & Timothy Smeeding, 2008. "Ranking inequality: Applications of multivariate subset selection," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 5-32, March.
    10. Timothy Patrick Moran, 2006. "Statistical Inference for Measures of Inequality With a Cross-National Bootstrap Application," Sociological Methods & Research, , vol. 34(3), pages 296-333, February.
    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. 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), pages 1-17, October.
    13. Yong Tao & Xiangjun Wu & Changshuai Li, 2014. "Rawls' Fairness, Income Distribution and Alarming Level of Gini Coefficient," Papers 1409.3979, arXiv.org.
    14. Timothy Moran, 2005. "Bootstrapping the LIS: Statistical Inference and Patterns of Inequality in the Global North," LIS Working papers 378, LIS Cross-National Data Center in Luxembourg.
    15. Gangfei Luo & Shouzhen Zeng & Tomas Baležentis, 2022. "Multidimensional Measurement and Comparison of China’s Educational Inequality," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 163(2), pages 857-874, September.
    16. Mario Schlemmer, 2021. "Including the asymmetry of the Lorenz curve into measures of economic inequality," Papers 2108.03623, arXiv.org, revised Sep 2022.
    17. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, J., 2015. "Entropy maximization under the constraints on the generalized Gini index and its application in modeling income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 657-666.

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