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Variance estimation for a low income proportion

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  • Yves G. Berger
  • Chris J. Skinner

Abstract

Summary. 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.

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, October.
    • Handle: RePEc:bla:jorssc:v:52:y:2003:i:4:p:457-468
    DOI: 10.1111/1467-9876.00417
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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.
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    6. Richard Blundell & Ian Preston, 1998. "Consumption Inequality and Income Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 113(2), pages 603-640.
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    Cited by:

    1. 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.
    2. Michal Brzezinski, 2011. "Variance Estimation for Richness Measures," LWS Working papers 11, LIS Cross-National Data Center in Luxembourg.
    3. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    4. Verbist, Gerlinde & Goedemé, Tim & Van den Bosch, Karel & Salanauskaite, Lina, 2013. "Testing the statistical significance of microsimulation results: often easier than you think. A technical note," EUROMOD Working Papers EM18/13, EUROMOD at the Institute for Social and Economic Research.
    5. 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.
    6. 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.
    7. Vijay Verma & Gianni Betti, 2011. "Taylor linearization sampling errors and design effects for poverty measures and other complex statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1549-1576, August.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Gianni Betti & Francesca Gagliardi, 2018. "Extension of JRR Method for Variance Estimation of Net Changes in Inequality Measures," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 137(1), pages 45-60, May.
    13. Yuyin Shi & Bing Liu & Gengsheng Qin, 2020. "Influence function-based empirical likelihood and generalized confidence intervals for the Lorenz curve," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 427-446, September.
    14. Goedemé, Tim & Decerf, Benoit & Van den Bosch, Karel, 2020. "A new poverty indicator for Europe: the extended headcount ratio," INET Oxford Working Papers 2020-26, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.

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