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A Doubly Robust GMM Estimator for Sequential Non-monotone Missingness

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  • Shenshen Yang

Abstract

We study moment-based estimation with two sequentially collected variables subject to non-monotone missingness. The commonly used Missing at Random (MAR) assumption requiring all missingness mechanisms to depend on the same fully observed covariates often fails in such cases. We introduce a sequential MAR assumption that allows asymmetric missingness mechanisms across stages. Based on this assumption, we construct an Augmented Inverse-Probability-Weighted GMM (AIPW-GMM) estimator. The estimator features an asymmetric structure for the augmentation term, guarantees double robustness, and achieves the closed-form semiparametric efficiency bound. An application to two-period survey data from the Oregon Health Insurance Experiment supports the observable implications of the new assumption. The proposed approach reduces the standard errors by more than 50% for the estimated effects of the Oregon Health Plan among older adults, "driving" previously statistically insignificant estimates significant.

Suggested Citation

  • Shenshen Yang, 2022. "A Doubly Robust GMM Estimator for Sequential Non-monotone Missingness," Papers 2201.01010, arXiv.org, revised May 2026.
    • Handle: RePEc:arx:papers:2201.01010
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    File URL: https://arxiv.org/pdf/2201.01010
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