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Measuring Inequality Using Censored Data: A Multiple Imputation Approach

  • Stephen P. Jenkins
  • Richard V. Burkhauser
  • Shuaizhang Feng
  • Jeff Larrimore

To measure income inequality with right censored (topcoded) data, we propose multiple imputation for censored observations using draws from Generalized Beta of the Second Kind distributions to provide partially synthetic datasets analyzed using complete data methods. Estimation and inference uses Reiter's (Survey Methodology 2003) formulae. Using Current Population Survey (CPS) internal data, we find few statistically significant differences in income inequality for pairs of years between 1995 and 2004. We also show that using CPS public use data with cell mean imputations may lead to incorrect inferences about inequality differences. Multiply-imputed public use data provide an intermediate solution.

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File URL: http://www.diw.de/documents/publikationen/73/diw_01.c.95918.de/dp866.pdf
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Paper provided by DIW Berlin, German Institute for Economic Research in its series Discussion Papers of DIW Berlin with number 866.

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Length: II, 29 p.
Date of creation: 2009
Date of revision:
Handle: RePEc:diw:diwwpp:dp866
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  1. Martin Biewen & Stephen P. Jenkins, 2006. "Variance Estimation for Generalized Entropy and Atkinson Inequality Indices: the Complex Survey Data Case," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(3), pages 371-383, 06.
  2. Schluter, Christian & Trede, Mark, 2002. "Tails of Lorenz curves," Journal of Econometrics, Elsevier, vol. 109(1), pages 151-166, July.
  3. Richard Burkhauser & Shuaizhang Feng & Stephen Jenkins & Jeff Larrimore, 2011. "Estimating trends in US income inequality using the Current Population Survey: the importance of controlling for censoring," Journal of Economic Inequality, Springer, vol. 9(3), pages 393-415, September.
  4. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  5. Di An & Roderick J. A. Little, 2007. "Multiple imputation: an alternative to top coding for statistical disclosure control," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 923-940.
  6. Cowell, F.A., 2000. "Measurement of inequality," Handbook of Income Distribution, in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 2, pages 87-166 Elsevier.
  7. Thomas Piketty & Emmanuel Saez, 2003. "Income Inequality In The United States, 1913-1998," The Quarterly Journal of Economics, MIT Press, vol. 118(1), pages 1-39, February.
  8. Jeff Larrimore & Richard Burkhauser & Shuaizhang Feng & Laura Zayatz, 2008. "Consistent Cell Means for Topcoded Incomes in the Public Use March CPS (1976-2007)," Working Papers 08-06, Center for Economic Studies, U.S. Census Bureau.
  9. Beach, Charles M & Richmond, James, 1985. "Joint Confidence Intervals for Income Shares and Lorenz Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 439-50, June.
  10. Thomas Lemieux, 2006. "Increasing Residual Wage Inequality: Composition Effects, Noisy Data, or Rising Demand for Skill?," American Economic Review, American Economic Association, vol. 96(3), pages 461-498, June.
  11. Bishop, John A & Chiou, Jong-Rong & Formby, John P, 1994. "Truncation Bias and the Ordinal Evaluation of Income Inequality," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 123-27, January.
  12. Stephen P. Jenkins & Martin Biewen, 2005. "SVYGEI_SVYATK: Stata module to derive the sampling variances of Generalized Entropy and Atkinson inequality indices when estimated from complex survey data," Statistical Software Components S453601, Boston College Department of Economics.
  13. Richard Burkhauser & Shuaizhang Feng & Jeff Larrimore, 2008. "Measuring Labor Earnings Inequality Using Public-Use March Current Population Survey Data: The Value of Including Variances and Cell Means When Imputing Topcoded Values," Working Papers 08-38, Center for Economic Studies, U.S. Census Bureau.
  14. Bishop, John A & Formby, John P & Smith, W James, 1991. "International Comparisons of Income Inequality: Tests for Lorenz Dominance across Nine Countries," Economica, London School of Economics and Political Science, vol. 58(232), pages 461-77, November.
  15. Gartner, Hermann & Rässler, Susanne, 2005. "Analyzing the changing gender wage gap based on multiply imputed right censored wages," IAB Discussion Paper 200505, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].
  16. Stephen P. Jenkins, 2006. "SVYLORENZ: Stata module to derive distribution-free variance estimates from complex survey data, of quantile group shares of a total, cumulative quantile group shares," Statistical Software Components S456602, Boston College Department of Economics, revised 19 Sep 2006.
  17. Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
  18. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
  19. David H. Autor & Lawrence F. Katz & Melissa S. Kearney, 2008. "Trends in U.S. Wage Inequality: Revising the Revisionists," The Review of Economics and Statistics, MIT Press, vol. 90(2), pages 300-323, May.
  20. Feng, Shuaizhang & Burkhauser, Richard V. & Butler, J.S., 2006. "Levels and Long-Term Trends in Earnings Inequality: Overcoming Current Population Survey Censoring Problems Using the GB2 Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 57-62, January.
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