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Asymptotic and bootstrap inference for inequality and poverty measures

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  • Russell Davidson

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - École des Hautes Études en Sciences Sociales (EHESS) - CNRS : UMR6579)

  • Emmanuel Flachaire

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

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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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00175929.

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Date of creation: Nov 2007
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Publication status: Published, Journal of Econometrics, 2007, 141, 1, 141-166
Handle: RePEc:hal:cesptp:halshs-00175929

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Keywords: Income distribution; Poverty; Bootstrap inference;

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  1. 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.
  2. Frank A. Cowell & Emmanuel Flachaire, 2007. "Income distribution and inequality measurement: The problem of extreme values," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00176029, HAL.
  3. Davidson, R. & Mackinnon, J.G., 1996. "The Size Distorsion of Bootstrap Tests," G.R.E.Q.A.M., Universite Aix-Marseille III 96a15, Universite Aix-Marseille III.
  4. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, Econometric Society, vol. 52(3), pages 761-66, May.
  5. Davidson, Russell & Duclos, Jean-Yves, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Cahiers de recherche, Université Laval - Département d'économique 9805, Université Laval - Département d'économique.
  6. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, University of Manchester, vol. 66(1), pages 1-26, January.
  7. Russell Davidson & Jean-Yves Duclos, 1997. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Econometrica, Econometric Society, Econometric Society, vol. 65(6), pages 1453-1466, November.
  8. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, Econometric Society, vol. 71(1), pages 285-317, January.
  9. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, Elsevier, vol. 108(2), pages 317-342, June.
  10. Hansen,B.E., 1998. "The grid bootstrap and the autoregressive model," Working papers, Wisconsin Madison - Social Systems 26, Wisconsin Madison - Social Systems.
  11. Frank A Cowell & Emmanuel Flachaire, 2002. "Sensitivity of Inequality Measures to Extreme Values," STICERD - Distributional Analysis Research Programme Papers, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE 60, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  12. Schluter, Christian & Trede, Mark, 2002. "Tails of Lorenz curves," Journal of Econometrics, Elsevier, Elsevier, vol. 109(1), pages 151-166, July.
  13. Cowell, Frank A. & Victoria-Feser, Maria-Pia, 1996. "Poverty measurement with contaminated data: A robust approach," European Economic Review, Elsevier, Elsevier, vol. 40(9), pages 1761-1771, December.
  14. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195060119, October.
  15. Mills, Jeffrey A & Zandvakili, Sourushe, 1997. "Statistical Inference via Bootstrapping for Measures of Inequality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 12(2), pages 133-50, March-Apr.
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