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.