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Variance estimation for a low income proportion

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  • Yves G. Berger
  • Chris J. Skinner

Abstract

Proportions below a given fraction of a quantile of an income distribution are often estimated from survey data in comparisons of poverty. We consider the estimation of the variance of such a proportion, estimated from Family Expenditure Survey data. We show how a linearization method of variance estimation may be applied to this proportion, allowing for the effects of both a complex sampling design and weighting by a raking method to population controls. We show that, for data for 1998-1999, the estimated variances are always increased when allowance is made for the design and raking weights, the principal effect arising from the design. We also study the properties of a simplified variance estimator and discuss extensions to a wider class of poverty measures. Copyright 2003 Royal Statistical Society.

Suggested Citation

  • Yves G. Berger & Chris J. Skinner, 2003. "Variance estimation for a low income proportion," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 457-468.
  • Handle: RePEc:bla:jorssc:v:52:y:2003:i:4:p:457-468
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    References listed on IDEAS

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    1. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    2. Alissa Goodman & Steven Webb, 1994. "For richer, for poorer: the changing distribution of income in the United Kingdom, 1961-91," Fiscal Studies, Institute for Fiscal Studies, vol. 15(4), pages 29-62, November.
    3. Zheng, Buhong, 2001. "Statistical inference for poverty measures with relative poverty lines," Journal of Econometrics, Elsevier, vol. 101(2), pages 337-356, April.
    4. Howes, Stephen & Lanjouw, Jean Olson, 1998. "Does Sample Design Matter for Poverty Rate Comparisons?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 44(1), pages 99-109, March.
    5. Richard Blundell & Ian Preston, 1998. "Consumption Inequality and Income Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 113(2), pages 603-640.
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    Cited by:

    1. Tim Goedemé & Diego Collado, 2016. "The EU Convergence Machine at Work. To the Benefit of the EU's Poorest Citizens?," Journal of Common Market Studies, Wiley Blackwell, vol. 54(5), pages 1142-1158, September.
    2. Tim Goedemé & Lorena Zardo Trindade & Frank Vandenbroucke, 2017. "A Pan-European Perspective on Low-Income Dynamics in the EU," Working Papers 1703, Herman Deleeck Centre for Social Policy, University of Antwerp.
    3. Mike Brewer & Liam Wren-Lewis, 2016. "Accounting for Changes in Income Inequality: Decomposition Analyses for the UK, 1978–2008," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(3), pages 289-322, June.
    4. Muñoz Rosas, Juan Francisco & Alvarez Verdejo, Encarnación, 2009. "Métodos de imputación para el tratamiento de datos faltantes: aplicación mediante R/Splus = Imputation methods to handle the problem of missing data: an application using R/Splus," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 7(1), pages 3-30, June.
    5. Michal Brzezinski, 2011. "Variance Estimation for Richness Measures," LWS Working papers 11, LIS Cross-National Data Center in Luxembourg.
    6. Tim Goedemé & Karel Van den Bosch & Lina Salanauskaite & Gerlinde Verbist, 2013. "Testing the Statistical Significance of Microsimulation Results: A Plea," International Journal of Microsimulation, International Microsimulation Association, vol. 6(3), pages 50-77.
    7. 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.
    8. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    9. J. Muñoz & E. Álvarez-Verdejo & R. García-Fernández & L. Barroso, 2015. "Efficient Estimation of the Headcount Index," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 123(3), pages 713-732, September.
    10. Tim Goedemé & Karel Van den Bosch & Lina Salanauskaite & Gerlinde Verbist, 2013. "Testing the Statistical Significance of Microsimulation Results: Often Easier than You Think. A Technical Note," ImPRovE Working Papers 13/10, Herman Deleeck Centre for Social Policy, University of Antwerp.

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