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

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  • Patrick Kline
  • Andres Santos

Abstract

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.

Suggested Citation

  • Patrick Kline & Andres Santos, 2010. "Sensitivity to Missing Data Assumptions: Theory and An Evaluation of the U.S. Wage Structure," NBER Working Papers 15716, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:15716 Note: LS TWP
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    Cited by:

    1. Breunig, Christoph, 2017. "Testing Missing At Random Using Instrumental Variables," Rationality and Competition Discussion Paper Series 59, CRC TRR 190 Rationality and Competition.
    2. Manski, Charles F., 2016. "Credible interval estimates for official statistics with survey nonresponse," Journal of Econometrics, Elsevier, vol. 191(2), pages 293-301.
    3. David Card & Jörg Heining & Patrick Kline, 2013. "Workplace Heterogeneity and the Rise of West German Wage Inequality," The Quarterly Journal of Economics, Oxford University Press, vol. 128(3), pages 967-1015.
    4. Melvin Stephens, Jr. & Takashi Unayama, 2015. "Estimating the Impacts of Program Benefits: Using Instrumental Variables with Underreported and Imputed Data," NBER Working Papers 21248, National Bureau of Economic Research, Inc.
    5. Arun Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2012. "Inference for best linear approximations to set identified functions," CeMMAP working papers CWP43/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Raj Chetty & Nathaniel Hendren & Patrick Kline & Emmanuel Saez, 2014. "Where is the land of Opportunity? The Geography of Intergenerational Mobility in the United States," The Quarterly Journal of Economics, Oxford University Press, vol. 129(4), pages 1553-1623.
    7. Bryan S. Graham & Jinyong Hahn & Alexandre Poirier & James L. Powell, 2015. "Quantile Regression with Panel Data," NBER Working Papers 21034, National Bureau of Economic Research, Inc.
    8. Battistin, Erich & Chesher, Andrew, 2014. "Treatment effect estimation with covariate measurement error," Journal of Econometrics, Elsevier, vol. 178(2), pages 707-715.
    9. Christoph Breunig, 2015. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2015-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Breunig, Christoph & Kummer, Michael & Ohnemus, Jörg & Viete, Steffen, 2016. "IT outsourcing and firm productivity: Eliminating bias from selective missingness in the dependent variable," ZEW Discussion Papers 16-092, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    11. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. repec:hrv:faseco:30750027 is not listed on IDEAS
    13. Ilić, Ivana, 2012. "On tail index estimation using a sample with missing observations," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 949-958.
    14. Christoph Breunig, 2017. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2017-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • J3 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs

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