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Robustness to Parametric Assumptions in Missing Data Models

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  • Bryan S. Graham
  • Keisuke Hirano

Abstract

We consider estimation of population averages when data are missing at random. If some cells contain few observations, there can be substantial gains from imposing parametric restrictions on the cell means, but there is also a danger of misspecification. We develop a simple empirical Bayes estimator, which combines parametric and unadjusted estimates of cell means in a data-driven way. We also consider ways to use knowledge of the form of the propensity score to increase robustness. We develop an empirical Bayes extension of a double robust estimator. In a small simulation study, the empirical Bayes estimators perform well. They are similar to fully nonparametric methods and robust to misspecification when cells are moderate to large in size, and when cells are small they maintain the benefits of parametric methods and can have lower sampling variance.

Suggested Citation

  • Bryan S. Graham & Keisuke Hirano, 2011. "Robustness to Parametric Assumptions in Missing Data Models," American Economic Review, American Economic Association, vol. 101(3), pages 538-543, May.
  • Handle: RePEc:aea:aecrev:v:101:y:2011:i:3:p:538-43
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    File URL: http://www.aeaweb.org/articles.php?doi=10.1257/aer.101.3.538
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    References listed on IDEAS

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    1. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    2. Weihua Cao & Anastasios A. Tsiatis & Marie Davidian, 2009. "Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data," Biometrika, Biometrika Trust, vol. 96(3), pages 723-734.
    3. Chen, Xiaohong & Hong, Han & Tarozzi, Alessandro, 2008. "Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects," Working Papers 42, Yale University, Department of Economics.
    4. Lee, David S. & Card, David, 2008. "Regression discontinuity inference with specification error," Journal of Econometrics, Elsevier, vol. 142(2), pages 655-674, February.
    5. Joshua Angrist & Jinyong Hahn, 2004. "When to Control for Covariates? Panel Asymptotics for Estimates of Treatment Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 58-72, February.
    6. Bryan S. Graham & Cristine Campos De Xavier Pinto & Daniel Egel, 2012. "Inverse Probability Tilting for Moment Condition Models with Missing Data," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 1053-1079.
    7. Wooldridge, Jeffrey M., 2007. "Inverse probability weighted estimation for general missing data problems," Journal of Econometrics, Elsevier, vol. 141(2), pages 1281-1301, December.
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    Cited by:

    1. Keisuke Hirano & Jack R. Porter, 2016. "Panel Asymptotics and Statistical Decision Theory," The Japanese Economic Review, Japanese Economic Association, vol. 67(1), pages 33-49, March.

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