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A GMM Approach for Dealing with Missing Data on Regressors

Author

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  • Jason Abrevaya

    (University of Texas)

  • Stephen G. Donald

    (University of Texas)

Abstract

Missing data are a common challenge facing empirical researchers. This paper presents a general GMM framework and estimator for dealing with missing values of an explanatory variable in linear regression analysis. The GMM estimator is efficient under assumptions needed for consistency of linear-imputation methods. The estimator, which also allows for a specification test of the missingness assumptions, is compared to existing linear imputation, complete data, and dummy variable methods commonly used in empirical research. The dummy variable method is generally inconsistent even when data are missing completely at random, and the dummy variable method, when consistent, can be less efficient than the complete data method.

Suggested Citation

  • Jason Abrevaya & Stephen G. Donald, 2017. "A GMM Approach for Dealing with Missing Data on Regressors," The Review of Economics and Statistics, MIT Press, vol. 99(4), pages 657-662, July.
    • Handle: RePEc:tpr:restat:v:99:y:2017:i:4:p:657-662
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    Citations

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    Cited by:

    1. Hongyu Chen & David Simchi-Levi & Ruoxuan Xiong, 2026. "Partial Identification under Missing Data Using Weak Shadow Variables from Pretrained Models," Papers 2602.16061, arXiv.org.
    2. Abrevaya, Jason, 2019. "Missing dependent variables in fixed-effects models," Journal of Econometrics, Elsevier, vol. 211(1), pages 151-165.
    3. Bang, Minji & Gao, Wayne Yuan & Postlewaite, Andrew & Sieg, Holger, 2023. "Using monotonicity restrictions to identify models with partially latent covariates," Journal of Econometrics, Elsevier, vol. 235(2), pages 892-921.
    4. Figueiredo, Erik & Lima, Luiz Renato & Orefice, Gianluca, 2020. "Migration, trade and spillover effects," Journal of Comparative Economics, Elsevier, vol. 48(2), pages 405-421.
    5. Akanksha Negi & Didier Nibbering, 2025. "Identification of dynamic treatment effects when treatment histories are partially observed," Papers 2501.04853, arXiv.org, revised Jun 2025.
    6. Beckmeyer, Heiner & Wiedemann, Timo, 2022. "Recovering Missing Firm Characteristics with Attention-Based Machine Learning," VfS Annual Conference 2022 (Basel): Big Data in Economics 264135, Verein für Socialpolitik / German Economic Association.
    7. Chris Muris, 2020. "Efficient GMM Estimation with Incomplete Data," The Review of Economics and Statistics, MIT Press, vol. 102(3), pages 518-530, July.
    8. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2019. "Consequences of Model Misspecification for Maximum Likelihood Estimation with Missing Data," Econometrics, MDPI, vol. 7(3), pages 1-27, September.
    9. Gobillon, Laurent & Magnac, Thierry & Roux, Sébastien, 2022. "Lifecycle Wages and Human Capital Investments: Selection and Missing Data," TSE Working Papers 22-1299, Toulouse School of Economics (TSE).

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