Summary We consider the problem of generating confidence sets in randomized experiments with noncompliance. We show that a refinement of a randomization-based procedure proposed by Imbens & Rosenbaum (2005) has desirable properties. Specifically, we show that using a studentized Anderson–Rubin statistic as a test statistic yields confidence sets that are finite-sample exact under treatment effect homogeneity and remain asymptotically valid for the local average treatment effect when the treatment effects are heterogeneous. We provide a uniform analysis of this procedure and efficient algorithms to construct the confidence sets.
Aronow et al. (Tue,) studied this question.