Causal interaction and effect modification: same model, different concepts

Social scientists use the concept of interactions to study effect dependency. In the causal inference literature, interaction terms may be used in two distinct type of analysis. The first type of analysis focuses on causal interactions, where the analyst is interested in whether two treatments have differing effects when both are administered. The second type of analysis focuses on effect modification, where the analyst investigates whether the effect of a single treatment varies across levels of a baseline covariate. While both forms of interaction analysis are typically conducted using the same type of statistical model, the identification assumptions for these two types of analysis are very different. In this paper, we clarify the difference between these two types of interaction analysis. We demonstrate that this distinction is mostly ignored in the political science literature. We conclude with a review of several applications where we show that the form of the interaction is critical to proper interpretation of empirical results.