Decomposition and Interpretation of Treatment Effects in Settings with Delayed Outcome

This paper studies settings where the analyst is interested in identifying and estimating th e average causal effect of a binary treatment on an outcome. We consider a setup in whic h the outcome realization does not get immediately realized after the treatment assignme nt, a feature that is ubiquitous in empirical settings. The period between the treatment an d the realization of the outcome allows other observed actions to occur and affect the out come. In this context, we study several regression-based estimands routinely used in emp irical work to capture the average treatment effect and shed light on interpreting them in t erms of ceteris paribus effects, indirect causal effects, and selection terms. We obtain thr ee main and related takeaways. First, the three most popular estimands do not generally s atisfy what we call strong sign preservation, in the sense that these estimands may be ne gative even when the treatment positively affects the outcome conditional on any possibl e combination of other actions. Second, the most popular regression that includes the oth er actions as controls satisfies strong sign preservation if and only if these actions are mu tually exclusive binary variables. Finally, we show that a linear regression that fully stratifi es the other actions leads to estimands that satisfy strong sign preservation.