Exploiting instrumental variables in causal inference with nonignorable outcome nonresponse using principal stratification

In this paper we consider a specific post-treatment complication that may arise in both randomized and observational studies, namely the problem of nonignorable nonresponse on an outcome variable. This is a typical topic usually known in the econometric literature as endogenous selection; here we tackle this problem specifically within a causal inference framework. By exploiting Principal Stratification, we analyze and propose identification strategies with and without the availability of an instrumental variable for nonresponse. We focus on the different role and meaning of the instrumental variable, also by comparing our framework with a general nonseparable selection model setting. As a motivating example we consider a simplified evaluation study in the field of financial aids to firms, where typically missingness on the outcome variables, such as variables related to firms’performances, can rarely be assumed missing at random.