IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00175929.html
   My bibliography  Save this paper

Asymptotic and bootstrap inference for inequality and poverty measures

Author

Listed:
  • Russell Davidson

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Emmanuel Flachaire

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Russell Davidson & Emmanuel Flachaire, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Post-Print halshs-00175929, HAL.
  • Handle: RePEc:hal:journl:halshs-00175929
    DOI: 10.1016/j.jeconom.2007.01.009
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00175929
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00175929/document
    Download Restriction: no

    File URL: https://libkey.io/10.1016/j.jeconom.2007.01.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    3. 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.
    4. 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.
    5. 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.
    6. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    7. Kakwani, Nanak, 1993. "Statistical Inference in the Measurement of Poverty," The Review of Economics and Statistics, MIT Press, vol. 75(4), pages 632-639, November.
    8. 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 133-150, March-Apr.
    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.
    10. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    11. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, December.
    12. 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.
    13. Schluter, Christian & Trede, Mark, 2002. "Tails of Lorenz curves," Journal of Econometrics, Elsevier, vol. 109(1), pages 151-166, July.
    14. 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.
    15. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, vol. 108(2), pages 317-342, June.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Timothy Patrick Moran, 2006. "Statistical Inference for Measures of Inequality With a Cross-National Bootstrap Application," Sociological Methods & Research, , vol. 34(3), pages 296-333, February.
    2. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    3. Tim Goedemé, 2013. "How much Confidence can we have in EU-SILC? Complex Sample Designs and the Standard Error of the Europe 2020 Poverty Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 110(1), pages 89-110, January.
    4. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    5. James E. Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster-Greer-Thorbecke (FGT) Poverty Measures: Twenty-Five Years Later," Working Papers 2010-14, The George Washington University, Institute for International Economic Policy.
    6. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, vol. 108(2), pages 317-342, June.
    7. Cosme Vodounou, 2004. "Pauvreté, croissance et ciblage : propriétés asymptotiques des estimateurs des élasticités avec application au Bénin," Revue d’économie du développement, De Boeck Université, vol. 12(2), pages 65-84.
    8. Ilaria Benedetti & Gianni Betti & Federico Crescenzi, 2020. "Measuring Child Poverty and Its Uncertainty: A Case Study of 33 European Countries," Sustainability, MDPI, vol. 12(19), pages 1-12, October.
    9. Ilaria Benedetti & Federico Crescenzi & Tiziana Laureti, 2020. "Measuring Uncertainty for Poverty Indicators at Regional Level: The Case of Mediterranean Countries," Sustainability, MDPI, vol. 12(19), pages 1-19, October.
    10. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 491-524, December.
    11. Flachaire, Emmanuel & Nunez, Olivier, 2007. "Estimation of the income distribution and detection of subpopulations: An explanatory model," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3368-3380, April.
    12. Christian Peretti, 2007. "Long Memory and Hysteresis," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 363-389, Springer.
    13. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    14. Schluter, Christian & van Garderen, Kees Jan, 2009. "Edgeworth expansions and normalizing transforms for inequality measures," Journal of Econometrics, Elsevier, vol. 150(1), pages 16-29, May.
    15. Simons, Andrew M., 2022. "What is the optimal locus of control for social assistance programs? Evidence from the Productive Safety Net Program in Ethiopia," Journal of Development Economics, Elsevier, vol. 158(C).
    16. Higgins, Sean & Lustig, Nora, 2016. "Can a poverty-reducing and progressive tax and transfer system hurt the poor?," Journal of Development Economics, Elsevier, vol. 122(C), pages 63-75.
    17. Hagos, Fitsum & Erkossa, Teklu & Lefore, Nicole & Langan, Simon, 2014. "Spate irrigation and poverty in Ethiopia," Conference Papers h046926, International Water Management Institute.
    18. Bönke Timm & Schröder Carsten, 2011. "Poverty in Germany – Statistical Inference and Decomposition," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(2), pages 178-209, April.
    19. 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.
    20. Mark Trede, 2002. "Bootstrapping inequality measures under the null hypothesis: Is it worth the effort?," Journal of Economics, Springer, vol. 9(1), pages 261-282, December.

    More about this item

    Keywords

    Income distribution; Poverty; Bootstrap inference;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:halshs-00175929. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.