Efficient Estimation with Missing Values in Cross Section and Panel Data

I study the problem of missing values in both the outcome and the covariates in linear models with endogenous covariates. I propose an estimator that improves efficiency relative to a Two Stage Least Squares (2SLS) based only on the complete cases. My framework also unifies the literature on missing data and combining data sets, and includes the “Two-Sample 2SLS" as a special case. The method is an extension of Abrevaya and Donald (2017), who provide methods of improving efficiency over complete cases estimators in linear models with cross-section data and missing covariates. I also provide guidance on dealing with missing values in the instruments and in commonly used nonlinear functions of the endogenous covariates, likes squares and interactions, without introducing inconsistency in the estimates.