Stage-based identification of policy effects

We develop a method that identifies the effects of nationwide policy, i.e., policy implemented across all regions at the same time. The core idea is to track outcome paths in terms of stages rather than time, where a stage of a regional outcome at time t is its location on the support of a reference path. The method proceeds in two steps. First, a normalization maps the time paths of regional outcomes onto the reference path-using only pre-policy data. This uncovers cross-regional heterogeneity of the stage at which policy is implemented. Second, this stage variation identifies policy effects inside a window of stages where a stage-leading region provides the no-policy counterfactual path for non-leading regions that are subject to policy inside that window. We assess our method's performance with Monte-Carlo experiments, illustrate it with empirical applications, and show that it captures heterogeneous policy effects across stages.