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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. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    2. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    3. 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.
    4. 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.
    5. Francesco Andreoli, 2013. "Inference for Inverse Stochastic Dominance," Working Papers 295, ECINEQ, Society for the Study of Economic Inequality.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Yong Tao & Xiangjun Wu & Changshuai Li, 2014. "Rawls' Fairness, Income Distribution and Alarming Level of Gini Coefficient," Papers 1409.3979, arXiv.org.
    13. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
    14. 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.

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