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Variance Estimation for Richness Measures

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  • Michal Brzezinski

Abstract

Richness indices are distributional statistics used tomeasure incomes, earnings or wealth of the rich. This paper uses a linearization method to derive the sampling variances for recently introduced two classes of distributionally-sensitive richness measures, when estimated from survey data. The results are derived for both absolute and relative richness lines. The approach used allows easily to take into account the effects of complex sampling design. The variance formulae are illustrated with a comparison of wealth richness in Canada, Sweden, the United Kingdom and the United States.

Suggested Citation

  • Michal Brzezinski, 2011. "Variance Estimation for Richness Measures," LWS Working papers 11, LIS Cross-National Data Center in Luxembourg.
    • Handle: RePEc:lis:lwswps:11
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    1. Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
    2. Andreas Peichl & Thilo Schaefer & Christoph Scheicher, 2010. "Measuring Richness And Poverty: A Micro Data Application To Europe And Germany," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 56(3), pages 597-619, September.
    3. Buhong Zheng, 1997. "Aggregate Poverty Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 11(2), pages 123-162, June.
    4. Richard V. Burkhauser & Shuaizhang Feng & Stephen P. Jenkins & Jeff Larrimore, 2009. "Recent trends in top income shares in the USA: Reconciling estimates from March CPS and IRS tax return data," Working Papers 139, ECINEQ, Society for the Study of Economic Inequality.
    5. Antal, Erika & Tillé, Yves, 2011. "A Direct Bootstrap Method for Complex Sampling Designs From a Finite Population," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 534-543.
    6. Anthony B. Atkinson & Thomas Piketty & Emmanuel Saez, 2011. "Top Incomes in the Long Run of History," Journal of Economic Literature, American Economic Association, vol. 49(1), pages 3-71, March.
    7. Satya R. Chakravarty, 2009. "Inequality, Polarization and Poverty," Economic Studies in Inequality, Social Exclusion, and Well-Being, Springer, number 978-0-387-79253-8, July.
    8. Andreas Peichl & Nico Pestel, 2013. "Multidimensional affluence: theory and applications to Germany and the US," Applied Economics, Taylor & Francis Journals, vol. 45(32), pages 4591-4601, November.
    9. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    10. 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.
    11. 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.
    12. Frank A. Cowell, 2008. "Income Distribution and Inequality," Chapters, in: John B. Davis & Wilfred Dolfsma (ed.), The Elgar Companion to Social Economics, chapter 13, Edward Elgar Publishing.
    13. 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.
    14. Richard V. Burkhauser & Shuaizhang Feng & Stephen P. Jenkins & Jeff Larrimore, 2012. "Recent Trends in Top Income Shares in the United States: Reconciling Estimates from March CPS and IRS Tax Return Data," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 371-388, May.
    15. Marcelo Medeiros, 2006. "The Rich and the Poor: The Construction of an Affluence Line from the Poverty Line," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 78(1), pages 1-18, August.
    16. Bishop, John A & Chow, K Victor & Zheng, Buhong, 1995. "Statistical Inference and Decomposable Poverty Measures," Bulletin of Economic Research, Wiley Blackwell, vol. 47(4), pages 329-340, October.
    17. Thomas Piketty & Nancy Qian, 2009. "Income Inequality and Progressive Income Taxation in China and India, 1986-2015," American Economic Journal: Applied Economics, American Economic Association, vol. 1(2), pages 53-63, April.
    18. repec:cep:sticas:/150 is not listed on IDEAS
    19. Satya R. Chakravarty, 2019. "A New Index of Poverty," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 31-37, Springer.
    20. Leigh, Andrew & van der Eng, Pierre, 2009. "Inequality in Indonesia: What can we learn from top incomes?," Journal of Public Economics, Elsevier, vol. 93(1-2), pages 209-212, February.
    21. Zheng, Buhong, 2001. "Statistical inference for poverty measures with relative poverty lines," Journal of Econometrics, Elsevier, vol. 101(2), pages 337-356, April.
    22. Cowell, Frank, 2011. "Inequality among the wealthy," LSE Research Online Documents on Economics 43897, London School of Economics and Political Science, LSE Library.
    23. repec:bla:jecsur:v:11:y:1997:i:2:p:123-62 is not listed on IDEAS
    24. 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.
    25. 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.
    26. Frank Cowell & Maria-Pia Victoria-Feser, 2007. "Robust stochastic dominance: A semi-parametric approach," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(1), pages 21-37, April.
    27. Eisenhauer, Joseph G., 2011. "The rich, the poor, and the middle class: Thresholds and intensity indices," Research in Economics, Elsevier, vol. 65(4), pages 294-304, December.
    28. Michal Brzezinski, 2010. "Income Affluence in Poland," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 99(2), pages 285-299, November.
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    More about this item

    Keywords

    richness; affluence; distributional indices; variance estimation; statistical inference;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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