Difference-in-differences Designs for Controlled Direct Effects

(2022)

(with Adam Glynn, Hanno Hilbig, and Connor Halloran Phillips)

Political scientists are increasingly interested in controlled direct effects, which are important quantities of interest for understanding why, how, and when causal effects will occur. Unfortunately, their identification has usually required strong and often unreasonable selection-on-observeables assumptions for the mediator. In this paper, we show how to identify and estimate controlled direct effects under a difference-in-differences design where we have measurements of the outcome and mediator before and after treatment assignment. This design allows us to weaken the identification assumptions to allow for linear, time-constant unmeasured confounding between the mediator and the outcome. Furthermore, we develop a semiparametrically efficient and multiply robust estimator for these quantities and apply our approach to a recent experiment evaluating the effectiveness of short conversations at reducing intergroup prejudice. An open-source software package implements the methodology with a variety of flexible, machine-learning algorithms to avoid bias from misspecification.