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Asymptotic And Bootstrap Inference For Inequality And Poverty Measures

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Russell Davidson ()
Emmanuel Flachaire ()

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Abstract

A random sample drawn from a population would appear to offer an ideal opportunity to use the bootstrap in order to perform accurate inference, since the observations of the sample are IID. In this paper, Monte Carlo results suggest that bootstrapping a commonly used index of inequality leads to inference that is not accurate even in very large samples,although inference with poverty indices is satisfactory. We find that the major cause is the extreme sensitivity of many inequality indices to the exact nature of the upper tail of the income distribution. This leads us to study two non-standard bootstraps, the m out of n bootstrap, which is valid in some situations where the standard bootstrap fails, and a bootstrap in which the upper tail is modelled parametrically. Monte Carlo results suggest that accurate inference can be achieved with this last method in moderately large samples.

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Paper provided by McGill University, Department of Economics in its series Departmental Working Papers with number 2005-06.

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Length: 32 pages
Date of creation: Sep 2006
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Handle: RePEc:mcl:mclwop:2005-06

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C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, vol. 108(2), pages 317-342, June. [Downloadable!] (restricted)
  2. Cowell, Frank A. & Victoria-Feser, Maria-Pia, 1996. "Poverty measurement with contaminated data: A robust approach," European Economic Review, Elsevier, vol. 40(9), pages 1761-1771, December. [Downloadable!] (restricted)
  3. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, Blackwell Publishing, vol. 66(1), pages 1-26, January.
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  4. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January. [Downloadable!] (restricted)
  5. Russell Davidson & Jean-Yves Duclos, 1997. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Econometrica, Econometric Society, vol. 65(6), pages 1453-1466, November.
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  6. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November. [Downloadable!] (restricted)
  7. Mills, Jeffrey A & Zandvakili, Sourushe, 1997. "Statistical Inference via Bootstrapping for Measures of Inequality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 133-50, March-Apr. [Downloadable!]
  8. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June. [Downloadable!]
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  9. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
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  10. Kakwani, Nanak, 1993. "Statistical Inference in the Measurement of Poverty," The Review of Economics and Statistics, MIT Press, vol. 75(4), pages 632-39, November. [Downloadable!] (restricted)
  11. Schluter, Christian & Trede, Mark, 2002. "Tails of Lorenz curves," Journal of Econometrics, Elsevier, vol. 109(1), pages 151-166, July. [Downloadable!] (restricted)
  12. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May. [Downloadable!] (restricted)
  13. Frank A Cowell & Emmanuel Flachaire, 2002. "Sensitivity of Inequality Measures to Extreme Values," STICERD - Distributional Analysis Research Programme Papers 60, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Stéphane Mussard & Patrick Richard, 2008. "Linking Yitzhaki’s and Dagum’s Gini Decompositions," Working Papers 08-13, LAMETA, Universtiy of Montpellier, revised Jul 2008. [Downloadable!]
    Other versions:
  2. William C. Horrace & Joseph T. Marchand & Timothy M. Smeeding, 2005. "Ranking Inequality: Applications of Multivariate Subset Selection," Center for Policy Research Working Papers 70, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
    Other versions:
  3. Judith A. Clarke & Nilanjana Roy, 2009. "On Statistical Inference for Inequality Measures Calculated from Complex Survey Data," Econometrics Working Papers 0904, Department of Economics, University of Victoria. [Downloadable!]
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