A Doubly Robust GMM Estimator for Sequential Non-monotone Missingness

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.