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Statistical Inference with Generalized Gini Indices of Inequality, Poverty, and Welfare

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  • Barrett, Garry F.
  • Donald, Stephen G.

Abstract

This article considers statistical inference for consistent estimators of generalized Gini indices of inequality, poverty, and welfare. Our method does not require grouping the population into a fixed number of quantiles. The empirical indices are shown to be asymptotically normally distributed using functional limit theory. Easily computed asymptotic variance expressions are obtained using influence functions. Inference based on first-order asymptotics is then compared with the grouped method and various bootstrap methods in simulations and with U.S. income data. The bootstrap-t method based on our asymptotic theory is found to have superior size and power properties in small samples.

Suggested Citation

  • Barrett, Garry F. & Donald, Stephen G., 2009. "Statistical Inference with Generalized Gini Indices of Inequality, Poverty, and Welfare," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 1-17.
    • Handle: RePEc:bes:jnlbes:v:27:y:2009:p:1-17
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    Citations

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    Cited by:

    1. Stephen P. Jenkins & Philippe Van Kerm, 2016. "Assessing Individual Income Growth," Economica, London School of Economics and Political Science, vol. 83(332), pages 679-703, October.
    2. 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.
    3. Ricardas Zitikis, 2002. "Analysis Of Indices Of Economic Inequality From A Mathematical Point Of View," RePAd Working Paper Series lrsp-TRS366, Département des sciences administratives, UQO.
    4. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    5. Elsayed Elamir, 2013. "On estimation of some abbreviated social welfare measures," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(3), pages 1561-1576, April.
    6. Brantly Callaway & Weige Huang, 2020. "Distributional Effects of a Continuous Treatment with an Application on Intergenerational Mobility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(4), pages 808-842, August.
    7. Francesco Andreoli, 2013. "Inference for Inverse Stochastic Dominance," Working Papers 295, ECINEQ, Society for the Study of Economic Inequality.
    8. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    9. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
    10. Yoonseok Lee & Donggyun Shin, 2016. "Measuring Social Tension from Income Class Segregation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 457-471, July.
    11. Yong Tao & Xiangjun Wu & Changshuai Li, 2014. "Rawls' Fairness, Income Distribution and Alarming Level of Gini Coefficient," Papers 1409.3979, arXiv.org.
    12. Sudheesh K. Kattumannil & N. Sreelakshmi & N. Balakrishnan, 2022. "Non-Parametric Inference for Gini Covariance and its Variants," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 790-807, August.
    13. Russell Davidson, 2010. "Innis Lecture: Inference on income distributions," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 43(4), pages 1122-1148, November.
    14. Andrew Leigh, 2005. "Can Redistributive State Taxes Reduce Inequality?," CEPR Discussion Papers 490, Centre for Economic Policy Research, Research School of Economics, Australian National University.
    15. Barrett, Garry F. & Donald, Stephen G. & Hsu, Yu-Chin, 2016. "Consistent tests for poverty dominance relations," Journal of Econometrics, Elsevier, vol. 191(2), pages 360-373.
    16. Garry F. Barrett & Stephen G. Donald & Debopam Bhattacharya, 2014. "Consistent Nonparametric Tests for Lorenz Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 1-13, January.
    17. Kock, Anders Bredahl & Preinerstorfer, David & Veliyev, Bezirgen, 2023. "Treatment recommendation with distributional targets," Journal of Econometrics, Elsevier, vol. 234(2), pages 624-646.
    18. Duangkamon Chotikapanich & William E. Griffiths, 2006. "Bayesian Assessment of Lorenz and Stochastic Dominance in Income Distributions," Department of Economics - Working Papers Series 960, The University of Melbourne.
    19. Francesco Andreoli, 2018. "Robust Inference for Inverse Stochastic Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 146-159, January.
    20. Daniel Dugger & Peter Lambert, 2014. "The 1913 paper of René Gâteaux, upon which the modern-day influence function is based," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(1), pages 149-152, March.

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