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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.

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File URL: http://pubs.amstat.org/doi/abs/10.1198/jbes.2009.0001
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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 27 (2009)
Issue (Month): ()
Pages: 1-17

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Handle: RePEc:bes:jnlbes:v:27:y:2009:p:1-17

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Cited by:
  1. Thomas Demuynck, 2012. "An (almost) unbiased estimator for the S-Gini index," Journal of Economic Inequality, Springer, vol. 10(1), pages 109-126, March.
  2. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
  3. 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.
  4. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
  5. Stephen G. Donald & Garry F. Barrett, 2004. "Consistent Nonparametric Tests for Lorenz Dominance," Econometric Society 2004 Australasian Meetings 321, Econometric Society.
  6. Francesco Andreoli, 2013. "Inference for Inverse Stochastic Dominance," Working Papers 295, ECINEQ, Society for the Study of Economic Inequality.
  7. Daniel Dugger & Peter Lambert, 2014. "The 1913 paper of René Gâteaux, upon which the modern-day influence function is based," Journal of Economic Inequality, Springer, vol. 12(1), pages 149-152, March.
  8. 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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