Instrumental variables estimation with partially missing instruments

We examine instrumental variables estimation in situations where the instrument is only observed for a sub-sample, which is fairly common in empirical research. Typically, researchers simply limit the analysis to the sub-sample where the instrument is non-missing. We show that when the instrument is non-randomly missing, standard IV estimators require strong, auxiliary assumptions to be consistent. In many (quasi)natural experiments, the auxiliary assumptions are unlikely to hold. We therefore introduce alternative IV estimators that are robust to non-randomly missing instruments without auxiliary assumptions. A Monte-Carlo study illustrates our results.