Identifying and Estimating Causal Moderation for Treated and Targeted Subgroups

Extant literature on moderation effects narrowly focuses on the average moderated treatment effect across the entire sample (AMTE). Missing is the average moderated treatment effect on the treated (AMTT) and other targeted subgroups (AMTS). Much like the average treatment effect on the treated (ATT) for main effects, the AMTS changes the target of inferences from the entire sample to targeted subgroups. Relative to the AMTE, the AMTS is identified under weaker assumptions and often captures more policy-relevant effects. We present a theoretical framework that introduces the AMTS under the potential outcomes framework and delineates the assumptions for causal identification. We then propose a generalized propensity score method as a tool to estimate the AMTS using weights derived with Bayes Theorem. We illustrate the results and differences among the estimands using data from the Early Childhood Longitudinal Study. We conclude with suggestions for future research.