Causal inference in staggered adoption panels: The correct comparison set depends on your intervention

A powerful data structure for causal inference is staggered adoption: many units are observed over many time periods, during which some units adopt an irreversible treatment at various time points while others remain untreated. Popular methods that apply in this setting include difference in difference, fixed effects, matching, and synthetic control. All of these methods compare the future outcomes of treatment adopters and non-adopters to answer the question: for units who adopt treatment, what outcomes would have been realized if they had remained untreated? We show that this question actually hides two very different causal questions of interest. The first is what would have happened under a momentary intervention to prevent treatment at its factual adoption time. The second is what would have happened to a treated unit under a longitudinal ban preventing treatment at all periods until outcome measurement. We show how to answer each question under conditionally ignorable treatment adoption or under parallel trends. We highlight that common methods cannot answer the second question because this question requires a time-varying comparison set with time-varying weights.