A New Estimator for Encouragement Design in Randomized Controlled Trials When the Exclusion Restriction Is Violated

Abstract

Encouragement design is widely used in randomized controlled trials when noncompliance in the treatment group, control group, or both is non-negligible. The standard identification strategy is to use the randomized group assignment as an instrumental variable to estimate the local average treatment effect (LATE). In many experiments, however, this instrument may violate the exclusion restriction condition, because the encouragement can directly impact the interested outcome variable. We develop a new root-n-consistent estimator using the randomized group assignment to construct an instrument that relies on the heteroskedasticity of treatment intensities between groups. Our identification strategy can recover not only LATE but also the direct impact of the encouragement on outcomes. We further propose a min-max estimator for consistent nonparametric estimation of heterogeneous treatment effects. Finally, we conducted a large-scale field experiment with a social media platform to study how expanding users' social networks influences their platform usage. While ordinary least squares and standard two-stage least squares estimators report a positive effect, our estimator suggests that the effect comes solely from the encouragement. We find evidence supporting the null effect of network expansion, indicating that firms may waste resources on false positives when the exclusion restriction is violated in their field experiments.

Keywords: Randomized Controlled Trials, Noncompliance, Encouragement Design, Instrumental Variable, Exclusion Restriction, Heteroskedasticity