🤖 AI Summary
This paper addresses the identification and estimation of the direct causal effect of a binary treatment on a final outcome under delayed-outcome settings, where post-treatment, pre-outcome mediating behaviors confound causal inference. To address sign bias—where conventional regression estimators may yield incorrect effect directions—we introduce the concept of “strong sign preservation” and rigorously characterize its necessary and sufficient conditions. We prove that fully stratified linear regression guarantees sign consistency, whereas standard control regression achieves it only under mutual exclusivity of mediators. Within the potential outcomes framework, we combine linear regression decomposition with ceteris paribus effect analysis to clarify the causal interpretations of three widely used estimators, explicitly disentangling indirect effects from selection-bias artifacts. Our results provide a theoretically grounded, interpretable, and robust estimation pathway for delayed causal effects.
📝 Abstract
This paper studies settings where the analyst is interested in identifying and estimating the average causal effect of a binary treatment on an outcome. We consider a setup in which the outcome realization does not get immediately realized after the treatment assignment, a feature that is ubiquitous in empirical settings. The period between the treatment and the realization of the outcome allows other observed actions to occur and affect the outcome. In this context, we study several regression-based estimands routinely used in empirical work to capture the average treatment effect and shed light on interpreting them in terms of ceteris paribus effects, indirect causal effects, and selection terms. We obtain three main and related takeaways. First, the three most popular estimands do not generally satisfy what we call emph{strong sign preservation}, in the sense that these estimands may be negative even when the treatment positively affects the outcome conditional on any possible combination of other actions. Second, the most popular regression that includes the other actions as controls satisfies strong sign preservation emph{if and only if} these actions are mutually exclusive binary variables. Finally, we show that a linear regression that fully stratifies the other actions leads to estimands that satisfy strong sign preservation.
