Two Margins in Difference-in-Differences with a Continuous Treatment
连续处理双重差分中的水平与响应两种边际
This paper studies difference-in-differences with staggered adoption and a continuous, time-invariant dose. Each cohort-time comparison contains two margins. The level margin is the average treatment effect at realized doses. Under level parallel trends it equals the level contrast between the treated cohort and not-yet-treated controls. The response margin is the within-cohort slope of the outcome change on dose. It uses no controls, and its causal interpretation requires a…