Profiling compliers and noncompliers for instrumental variable analysis with covariates: A weighting approach

Instrumental variable (IV) estimation is an essential tool to estimate the causal effect of a treatment in randomized experiments when noncompliance exists. In such studies, standard statistical approaches can be biased because compliers and noncompliers can differ in unmeasured ways that affect both the compliance behavior and outcome. Based on a few assumptions such as monotonicity, the IV estimand represents the causal effect of compliers. Profiling compliers and noncompliers has important implications because the IV estimand applies only to compliers. A method for estimating the covariate means for compliers and noncompliers has recently been proposed in political sciences literature. However, this approach requires an assumption that the instrument is randomly assigned, which confines the application of this approach to randomized experiments. In this study, we present two weighting methods for profiling compliers and noncompliers when the instrument and compliance behavior are confounded by several covariates. The proposed approach can be used for both experimental and nonexperimental studies, and hence is more broadly applicable. For the development, an instrumental propensity score is adopted to account for confounded instruments. We demonstrate the utility of the proposed methods based on simulation and real data experiments.