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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. Ian Preston, 1995. "Sampling Distributions of Relative Poverty Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(1), pages 91-99, March.
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    5. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    6. 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.
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    Cited by:

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    2. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    3. 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.
    4. 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.
    5. 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.
    6. Michal Brzezinski, 2011. "Variance Estimation for Richness Measures," LWS Working papers 11, LIS Cross-National Data Center in Luxembourg.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    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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