🔍 What This Paper Proposes

Political scientists increasingly focus on causal mediation and, in particular, the controlled direct effect (CDE) — the causal effect of a treatment on an outcome when a mediator is fixed at a specific value. This paper introduces an alternative estimation approach called regression-with-residuals (RWR) for estimating the CDE.

🔬 How the new method fits with existing tools

• Sequential g-estimation was developed for this task by Joffe and Greene (2009) and Vansteelandt (2009) and was introduced to political science audiences by Acharya, Blackwell, and Sen (2016).
• In special cases, RWR is algebraically equivalent to sequential g-estimation, showing that RWR nests familiar solutions under certain assumptions.

📌 What RWR does differently

• RWR easily accommodates several types of effect moderation, including situations where the mediator's effect on the outcome is moderated by a posttreatment confounder.
• Such moderation is common in the social sciences but is typically assumed away in applications of sequential g-estimation; ignoring it can produce biased CDE estimates.

📊 Evidence and illustration

• Mathematical comparisons demonstrate algebraic equivalence between RWR and sequential g-estimation in special cases.
• Analytical arguments show RWR’s flexibility for modeling effect moderation that sequential g-estimation usually cannot handle without additional assumptions.
• An applied example estimates the CDE of negative media framing on public support for immigration while controlling for respondent anxiety to illustrate RWR in practice.

🔑 Why it matters

• Accurate CDE estimation matters for causal claims about policy and communication effects. RWR offers a practical, accessible alternative that preserves correct inference when effect moderation by posttreatment confounders is present.