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Asymptotic and bootstrap inference for inequality and poverty measures

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  • Russell Davidson

    ()
    (GREQAM et McGill University)

  • Emmanuel Flachaire

    ()
    (EUREQua)

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. Bootstrapping a poverty measure, on the other hand, gives accurate inference in small samples. We investigate the reasons for the poor performance of the bootstrap, and 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. Consequently, a bootstrap sample in which nothing is resampled from the tail can have properties very different from those of the population. 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 Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number v04100.

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Length: 26 pages
Date of creation: Mar 2004
Date of revision:
Handle: RePEc:mse:wpsorb:v04100

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Keywords: Bootstrap; statistical performance; inequality measures; poverty measures.;

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References

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  1. 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.
  2. repec:hal:cesptp:halshs-00176029 is not listed on IDEAS
  3. Cowell, Frank A. & Flachaire, Emmanuel, 2007. "Income distribution and inequality measurement: The problem of extreme values," Journal of Econometrics, Elsevier, vol. 141(2), pages 1044-1072, December.
  4. Hansen,B.E., 1998. "The grid bootstrap and the autoregressive model," Working papers 26, Wisconsin Madison - Social Systems.
  5. Davidson, Russell & Duclos, Jean-Yves, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Cahiers de recherche 9805, Université Laval - Département d'économique.
  6. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
  7. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  8. Frank Cowell & Emmanuel Flachaire, 2002. "Sensitivity of inequality measures to extreme values," LSE Research Online Documents on Economics 2213, London School of Economics and Political Science, LSE Library.
  9. 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.
  10. Davidson, R. & Mackinnon, J.G., 1996. "The Size Distorsion of Bootstrap Tests," G.R.E.Q.A.M. 96a15, Universite Aix-Marseille III.
  11. 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, vol. 66(1), pages 1-26, January.
  12. 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.
  13. Schluter, Christian & Trede, Mark, 2002. "Tails of Lorenz curves," Journal of Econometrics, Elsevier, vol. 109(1), pages 151-166, July.
  14. 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.
  15. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, vol. 108(2), pages 317-342, June.
  16. Jeffrey A. Mills & Sourushe Zandvakili, 1999. "Statistical Inference via Bootstrapping for Measures of Inequality," Macroeconomics 9902003, EconWPA.
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