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Measuring Inequality Using Censored Data: A Multiple Imputation Approach

Author

Listed:
  • Jenkins, Stephen P.

    (London School of Economics)

  • Burkhauser, Richard V.

    (University of Texas at Austin)

  • Feng, Shuaizhang

    (Shanghai University of Finance and Economics)

  • Larrimore, Jeff

    (Federal Reserve Board)

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

  • Jenkins, Stephen P. & Burkhauser, Richard V. & Feng, Shuaizhang & Larrimore, Jeff, 2009. "Measuring Inequality Using Censored Data: A Multiple Imputation Approach," IZA Discussion Papers 4011, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp4011
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    References listed on IDEAS

    as
    1. Richard Burkhauser & Jeff Larrimore, 2008. "Using Internal Current Population Survey Data to Reevaluate Trends in Labor Earnings Gaps by Gender, Race, and Education Level," Working Papers 08-18, Center for Economic Studies, U.S. Census Bureau.
    2. 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.
    3. 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].
    4. 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.
    5. Angle, John & Tolbert, Charles M., 1999. "Topcodes and the Great U-Turn in Nonmetro/Metro Wage and Salary Inequality," Staff Reports 278835, United States Department of Agriculture, Economic Research Service.
    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. 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.
    8. 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.
    9. Richard Burkhauser & Jeff Larrimore, 2008. "Trends in the Relative Household Income of Working-Age Men with Work Limitations: Correcting the Record Using Internal Current Population Survey Data," Working Papers 08-05, Center for Economic Studies, U.S. Census Bureau.
    10. 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, vol. 9(3), pages 393-415, September.
    11. Peter Gottschalk & Sheldon Danziger, 2005. "Inequality Of Wage Rates, Earnings And Family Income In The United States, 1975–2002," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 51(2), pages 231-254, June.
    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 123-127, January.
    13. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    14. 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.
    15. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    16. Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
    17. 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.
    18. 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.
    19. A.B. Atkinson & F. Bourguignon (ed.), 2000. "Handbook of Income Distribution," Handbook of Income Distribution, Elsevier, edition 1, volume 1, number 1.
    20. 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.
    21. Schluter, Christian & Trede, Mark, 2002. "Tails of Lorenz curves," Journal of Econometrics, Elsevier, vol. 109(1), pages 151-166, July.
    22. 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.
    23. repec:bla:econom:v:58:y:1991:i:232:p:461-77 is not listed on IDEAS
    24. 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, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    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. 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, vol. 9(3), pages 393-415, September.
    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 of Labor Economics (IZA).
    4. Kitov, Ivan & Kitov, Oleg, 2015. "Gender income disparity in the USA: analysis and dynamic modelling," MPRA Paper 67146, University Library of Munich, Germany.
    5. 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, Luxembourg Institute of Socio-Economic Research (LISER).
    6. Weber, Jan David & Scharfenaker, Ellis, 2024. "Measures of firm performance and concentration: Stylized facts and a dilemma of data reproduction," Economics Letters, Elsevier, vol. 234(C).
    7. 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.
    8. 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 184-188, May.

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    More about this item

    Keywords

    topcoding; income inequality; CPS; Current Population Survey; partially synthetic data; Generalized Beta of the Second Kind distribution;
    All these keywords.

    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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