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Measuring inequality using Censored data: A multiple imputation approach

Author

Listed:
  • Stephen P. Jenkins

    () (University of Essex)

  • Richard V. Burkhauser

    (Cornell University)

  • Shuaizhang Feng

    (Shanghai University of Finance and Economics and Princeton University)

  • Jeff Larrimore

    (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.

Suggested Citation

  • Stephen P. Jenkins & Richard V. Burkhauser & Shuaizhang Feng & Jeff Larrimore, 2009. "Measuring inequality using Censored data: A multiple imputation approach," Working Papers 108, ECINEQ, Society for the Study of Economic Inequality.
  • Handle: RePEc:inq:inqwps:ecineq2009-108
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    References listed on IDEAS

    as
    1. 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," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, pages 393-415.
    2. 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, pages 300-323.
    3. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    4. Schluter, Christian & Trede, Mark, 2002. "Tails of Lorenz curves," Journal of Econometrics, Elsevier, pages 151-166.
    5. Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
    6. Jeff Larrimore & Richard V. Burkhauser & Shuaizhang Feng & Laura Zayatz, 2008. "Consistent Cell Means for Topcoded Incomes in the Public Use March CPS (1976-2007)," NBER Working Papers 13941, National Bureau of Economic Research, Inc.
    7. 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.
    8. Michael Lechner & Conny Wunsch, 2009. "Are Training Programs More Effective When Unemployment Is High?," Journal of Labor Economics, University of Chicago Press, vol. 27(4), pages 653-692, October.
    9. 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 15 Sep 2015.
    10. 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.
    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, revised 31 Aug 2017.
    12. 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, June.
    13. 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 123-127, January.
    14. 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.
    15. 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 461-477, November.
    16. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    17. 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 439-450, June.
    18. Charles E. Scott & John J. Siegfried, 2017. "American Economic Association Universal Academic Questionnaire Summary Statistics," American Economic Review, American Economic Association, pages 678-680.
    19. 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.
    20. 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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    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," Working Papers 139, ECINEQ, Society for the Study of Economic Inequality.
    2. 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," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, pages 393-415.
    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).
    4. Nora Lustig, 2016. "Commitment to Equity Handbook. A Guide to Estimating the Impact of Fiscal Policy on Inequality and Poverty," Commitment to Equity (CEQ) Working Paper Series 1301, Tulane University, Department of Economics.
    5. 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, pages 184-188.
    6. Kitov, Ivan & Kitov, Oleg, 2015. "Gender income disparity in the USA: analysis and dynamic modelling," MPRA Paper 67146, University Library of Munich, Germany.
    7. SOLOGON Denisa & VAN KERM Philippe, 2014. "Earnings dynamics, foreign workers and the stability of inequality trends in Luxembourg 1988-2009," LISER Working Paper Series 2014-03, LISER.

    More about this item

    Keywords

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

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access

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