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Measuring Inequality Using Censored Data: A Multiple Imputation Approach

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Author Info

  • Stephen Jenkins
  • Richard Burkhauser
  • Shuaizhang Feng
  • Jeff Larrimore

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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File URL: ftp://ftp2.census.gov/ces/wp/2009/CES-WP-09-05.pdf
File Function: First version, 2009
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Bibliographic Info

Paper provided by Center for Economic Studies, U.S. Census Bureau in its series Working Papers with number 09-05.

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Length: 35 pages
Date of creation: Apr 2009
Date of revision:
Handle: RePEc:cen:wpaper:09-05

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Keywords: Income Inequality; Topcoding; Partially Synthetic Data; CPS; Current Population Survey; Generalized Beta of the Second Kind distribution;

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References

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  1. 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.
  2. 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.
  3. Richard V. Burkhauser & Shuaizhang Feng & Stephen P. Jenkins & Jeff Larrimore, 2008. "Estimating Trends in US Income Inequality Using the Current Population Survey: The Importance of Controlling for Censoring," NBER Working Papers 14247, National Bureau of Economic Research, Inc.
  4. Richard V. 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," NBER Working Papers 14458, National Bureau of Economic Research, Inc.
  5. 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.
  6. 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.
  7. 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.
  8. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
  9. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  10. Schluter, Christian & Trede, Mark, 2002. "Tails of Lorenz curves," Journal of Econometrics, Elsevier, vol. 109(1), pages 151-166, July.
  11. 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.
  12. Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
  13. 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.
  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. 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.
  16. 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.
  17. 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.
  18. 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].
  19. 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.
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Citations

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Cited by:
  1. 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," NBER Working Papers 15320, National Bureau of Economic Research, Inc.
  2. Burkhauser, Richard V. & Feng, Shuaizhang & Jenkins, Stephen P. & Larrimore, Jeff, 2008. "Estimating Trends in US Income Inequality Using the Current Population Survey: The Importance of Controlling for Censoring," IZA Discussion Papers 3690, Institute for the Study of Labor (IZA).
  3. Doerrenberg, Philipp & Duncan, Denvil & Fuest, Clemens & Peichl, Andreas, 2012. "Nice Guys Finish Last: Are People with Higher Tax Morale Taxed More Heavily?," IZA Discussion Papers 6275, Institute for the Study of Labor (IZA).

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