Linear IV Model with Missing Data on the Instrumental Variable

Abstract: This paper studies the problem of identification in an IV model with missing data on the instrumental variable. I consider an agnostic stance on the distribution of the missing data and a worst-case scenario approach to confront the missing data problem. First, I characterize the identified set of the parameter of interest and make explicit that this is an extremely complex object to compute. Next, following the literature on partial identification, I propose an outer identified set—a superset of the identified set that is easier to compute. This outer identified set is based on a moment inequality model. Then, I show that, under some testable assumptions, this outer identified set is equal to the identified set.