GMM with Multiple Missing Variables

Summary We consider efficient estimation in moment conditions models with non‐monotonically missing‐at‐random (MAR) variables. A version of MAR point‐identifies the parameters of interest and gives a closed‐form efficient influence function that can be used directly to obtain efficient semi‐parametric generalized method of moments (GMM) estimators under standard regularity conditions. A small‐scale Monte Carlo experiment with MAR instrumental variables demonstrates that the asymptotic superiority of these estimators over the standard methods carries over to finite samples. An illustrative empirical study of the relationship between a child's years of schooling and number of siblings indicates that these GMM estimators can generate results with substantive differences from standard methods. Copyright © 2015 John Wiley & Sons, Ltd.