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Sensitivity to Missing Data Assumptions: Theory and An Evaluation of the U.S. Wage Structure

  • Patrick Kline
  • Andres Santos

This paper develops methods for assessing the sensitivity of empirical conclusions regarding conditional distributions to departures from the missing at random (MAR) assumption. We index the degree of non-ignorable selection governing the missingness process by the maximal Kolmogorov-Smirnov (KS) distance between the distributions of missing and observed outcomes across all values of the covariates. Sharp bounds on minimum mean square approximations to conditional quantiles are derived as a function of the nominal level of selection considered in the sensitivity analysis and a weighted bootstrap procedure is developed for conducting inference. Using these techniques, we conduct an empirical assessment of the sensitivity of observed earnings patterns in U.S. Census data to deviations from the MAR assumption. We find that the well-documented increase in the returns to schooling between 1980 and 1990 is relatively robust to deviations from the missing at random assumption except at the lowest quantiles of the distribution, but that conclusions regarding heterogeneity in returns and changes in the returns function between 1990 and 2000 are very sensitive to departures from ignorability.

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File URL: http://www.nber.org/papers/w15716.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15716.

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Date of creation: Feb 2010
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Publication status: published as Patrick Kline & Andres Santos, 2013. "Sensitivity to missing data assumptions: Theory and an evaluation of the U.S. wage structure," Quantitative Economics, Econometric Society, vol. 4(2), pages 231-267, 07.
Handle: RePEc:nbr:nberwo:15716
Note: LS TWP
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  1. Thomas Lemieux, 2006. "Postsecondary Education and Increasing Wage Inequality," American Economic Review, American Economic Association, vol. 96(2), pages 195-199, May.
  2. David Card & Thomas Lemieux, 1993. "Wage Dispersion, Returns to Skill, and Black-White Wage Differentials," NBER Working Papers 4365, National Bureau of Economic Research, Inc.
  3. Hirsch, Barry & Schumacher, Edward J., 2003. "Match Bias in Wage Gap Estimates Due to Earnings Imputation," IZA Discussion Papers 783, Institute for the Study of Labor (IZA).
  4. Lee Lillard & James P. Smith & Finis Welch, 2004. "What Do We Really Know About Wages: The Importance of Nonreporting and Census Imputation," Labor and Demography 0404005, EconWPA.
  5. Horowitz, Joel L. & Manski, Charles F., 2006. "Identification and estimation of statistical functionals using incomplete data," Journal of Econometrics, Elsevier, vol. 132(2), pages 445-459, June.
  6. Juhn, Chinhui & Murphy, Kevin M & Pierce, Brooks, 1993. "Wage Inequality and the Rise in Returns to Skill," Journal of Political Economy, University of Chicago Press, vol. 101(3), pages 410-42, June.
  7. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2006. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," CIRJE F-Series CIRJE-F-420, CIRJE, Faculty of Economics, University of Tokyo.
  8. Joshua Angrist & Victor Chernozhukov & Ivan Fernandez-Val, 2004. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," NBER Working Papers 10428, National Bureau of Economic Research, Inc.
  9. Joseph G. Altonji & Todd E. Elder & Christopher R. Taber, 2000. "Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools," NBER Working Papers 7831, National Bureau of Economic Research, Inc.
  10. Azeem Shaikh & Edward Vytlacil, 2005. "Threshold Crossing Models and Bounds on Treatment Effects: A Nonparametric Analysis," NBER Technical Working Papers 0307, National Bureau of Economic Research, Inc.
  11. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, vol. 93(2), pages 126-132, May.
  12. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 1071-1102.
  13. Derek Neal, 2004. "The Measured Black-White Wage Gap among Women Is Too Small," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages S1-S28, February.
  14. Maria Ponomareva & Elie Tamer, 2011. "Misspecification in moment inequality models: back to moment equalities?," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 186-203, 07.
  15. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-94, July.
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