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

When the goal of inference is estimating causal effects, we usually have to face problems related to the fact that treatment assignment is not under the control of the investigator; in addition some studies may be affected by different sorts of post-treatment selection of observations due to, e.g., non response, truncation or censoring “due to death”. All such complications require to somehow control for them, but the use of the standard statistical conditioning may be in general improper (Rubin, 1974; Rosembaum, 1984). In this paper we consider a specific post-treatment complication, namely the problem of nonignorable nonresponse on an outcome variable in observational studies. 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 (Frangakis and Rubin, 2002), we analyze and propose identification strategies in the presence 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.