Efficient GMM Estimation with Incomplete Data

Abstract

In the standard missing data model, data are either complete or completely missing. However, applied researchers face situations with an arbitrary number of strata of incompleteness. Examples include unbalanced panels and instrumental variables settings where some observations are missing some instruments. I propose a model for settings where observations may be incomplete, with an arbitrary number of strata of incompleteness. I derive a set of moment conditions that generalizes those in Graham's ( 2011 ) standard missing data setup. I derive the associated efficiency bound and propose efficient estimators. Identification can be achieved even if it fails in each stratum of incompleteness.