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Variance estimation for richness measures

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  • Michał Brzeziński

    (Faculty of Economic Sciences, University of Warsaw)

Abstract

Richness indices are distributional statistics used to measure the incomes, earnings, or wealth of the rich. This paper uses a linearization method to derive the sampling variances for recently introduced distributionally-sensitive richness measures when estimated from survey data. The results are derived for two cases: (1) when the richness line is known, and (2) when it has to be estimated from the sample. The proposed approach enables easy consideration of the effects of a complex sampling design. Monte Carlo results suggest that the proposed approach allows for reliable inference in case of “concave” richness indices, but that it is not satisfactory in case of “convex” richness measures.

Suggested Citation

  • Michał Brzeziński, 2013. "Variance estimation for richness measures," Working Papers 2013-03, Faculty of Economic Sciences, University of Warsaw.
    • Handle: RePEc:war:wpaper:2013-03
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    File URL: http://www.wne.uw.edu.pl/inf/wyd/WP/WNE_WP88.pdf
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    References listed on IDEAS

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    1. Richard Burkhauser & Shuaizhang Feng & Stephen 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 09-26, Center for Economic Studies, U.S. Census Bureau.
    2. 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.
    3. 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.
    4. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Zheng, Buhong, 2001. "Statistical inference for poverty measures with relative poverty lines," Journal of Econometrics, Elsevier, vol. 101(2), pages 337-356, April.
    12. 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.
    13. Cowell, Frank, 2011. "Inequality among the wealthy," LSE Research Online Documents on Economics 43897, London School of Economics and Political Science, LSE Library.
    14. 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.
    15. 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.
    16. 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.
    17. Satya R. Chakravarty, 2009. "Inequality, Polarization and Poverty," Economic Studies in Inequality, Social Exclusion, and Well-Being, Springer, number 978-0-387-79253-8, Fall.
    18. 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.
    19. 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.
    20. 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.
    21. repec:cep:sticas:/150 is not listed on IDEAS
    22. 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.
    23. 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.
    24. 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.
    25. Zheng, Buhong, 1997. "Aggregate Poverty Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 11(2), pages 123-162, June.
    26. 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.
    27. Buhong Zheng, 1997. "Aggregate Poverty Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 11(2), pages 123-162, June.
    28. 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.
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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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