Phantom Counterfactuals

Researchers often seek to identify the effects of a treatment on a sequence of behaviors, such as whether citizens register to vote and whether they then cast ballots. I show that average treatment effects (ATEs) are only identified until the first behavior (registering to vote) that affects the set of possible subsequent actions (voting). When one action changes the set of possible subsequent actions, it creates ‘phantom counterfactuals,’ or undefined potential outcomes, which render ATEs unidentified. I show that applied theory allows researchers to diagnose phantom counterfactuals, which helps to recognize unidentified ATEs and focus instead on other estimands that are identified. I illustrate this approach using a stylized model of crime reporting, showing how different theories generate different sets of identified estimands while holding constant an experimental design. I thereby establish the necessity of applied theory for causal identification in empirical research with sequential behavioral outcomes.