Randomization-based confidence sets for the local average treatment effect

TL;DR

This paper develops refined randomization-based confidence sets for the local average treatment effect in experiments with noncompliance, ensuring finite-sample exactness under homogeneity and asymptotic validity under heterogeneity.

Contribution

It introduces a studentized Anderson-Rubin-type statistic for improved confidence set construction in randomized experiments with noncompliance.

Findings

Finite-sample exact confidence sets under treatment effect homogeneity

Asymptotically valid confidence sets for heterogeneous effects

Efficient algorithms for constructing confidence sets

Abstract

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 and Rosenbaum (2005) has desirable properties. Namely, we show that using a studentized Anderson--Rubin-type 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 effect is heterogeneous. We provide a uniform analysis of this procedure and efficient algorithms to construct the confidence set.