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Measuring Inequality Using Censored Data: A Multiple Imputation Approach

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Author Info

  • Jenkins, Stephen P.

    ()
    (London School of Economics)

  • Burkhauser, Richard V.

    ()
    (Cornell University)

  • Feng, Shuaizhang

    ()
    (Shanghai University of Finance and Economics)

  • Larrimore, Jeff

    ()
    (Cornell University)

Abstract

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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Bibliographic Info

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 4011.

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Length: 32 pages
Date of creation: Feb 2009
Date of revision:
Handle: RePEc:iza:izadps:dp4011

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Keywords: topcoding; income inequality; CPS; Current Population Survey; partially synthetic data; Generalized Beta of the Second Kind distribution;

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References

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  1. 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.
  2. Frank Cowell, 1998. "Measurement of inequality," LSE Research Online Documents on Economics 2084, London School of Economics and Political Science, LSE Library.
  3. 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.
  4. 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.
  5. 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.
  6. Martin Biewen, 2006. "Variance estimation for generalized entropy and Atkinson inequality indices: The complex survey data case," German Stata Users' Group Meetings 2006 04, Stata Users Group.
  7. 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.
  8. 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.
  9. Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
  10. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Schluter, Christian & Trede, Mark, 2002. "Tails of Lorenz curves," Journal of Econometrics, Elsevier, vol. 109(1), pages 151-166, July.
  17. repec:ese:iserwp:2008-25 is not listed on IDEAS
  18. 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.
  19. 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.
  20. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
  21. 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].
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Citations

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Cited by:
  1. Richard Burkhauser & Shuaizhang Feng & Stephen Jenkins & Jeff Larrimore, 2008. "Estimating Trends in U.S. Income Inequality Using the Current Population Survey: The Importance of Controlling for Censoring," Working Papers 08-25, Center for Economic Studies, U.S. Census Bureau.
  2. Jonathan D. Fisher & David S. Johnson & Timothy M. Smeeding, 2013. "Measuring the Trends in Inequality of Individuals and Families: Income and Consumption," American Economic Review, American Economic Association, vol. 103(3), pages 184-88, May.
  3. SOLOGON Denisa & VAN KERM Philippe, 2014. "Earnings dynamics, foreign workers and the stability of inequality trends in Luxembourg 1988-2009," CEPS/INSTEAD Working Paper Series 2014-03, CEPS/INSTEAD.
  4. Burkhauser, Richard V. & Feng, Shuaizhang & Jenkins, Stephen P. & Larrimore, Jeff, 2009. "Recent Trends in Top Income Shares in the USA: Reconciling Estimates from March CPS and IRS Tax Return Data," IZA Discussion Papers 4426, Institute for the Study of Labor (IZA).
  5. repec:ese:iserwp:2008-25 is not listed on IDEAS
  6. Philipp Doerrenberg & Denvil Duncan & Clemens Fuest & Andreas Peichl, 2012. "Nice guys finish last: are people with higher tax morale taxed more heavily?," Cologne Graduate School Working Paper Series 03-02, Cologne Graduate School in Management, Economics and Social Sciences.

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