发表机构
School of Economics, University of Sydney（悉尼大学经济学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出连续剂量双重差分中区分水平边际与响应边际的框架，证明OLS系数为二者凸组合，并给出估计与推断方法，应用于水力压裂研究。
AI 中文摘要
本文研究了在交错采用和连续、时不变剂量条件下的双重差分方法。每个队列-时间比较包含两个边际。水平边际是在实现剂量下的平均处理效应。在水平平行趋势假设下，它等于处理队列与尚未处理对照组之间的水平对比。响应边际是结果变化对剂量的队列内斜率。它不使用对照组，其因果解释需要响应平行趋势假设和对收益选择性的限制。我们证明，在每个队列-时间比较中，连续剂量OLS系数是响应指数和每单位平均剂量的水平对比的凸组合，其混合权重取决于尚未处理队列的份额。我们提供了两个边际的估计量、跨队列-时间比较和事件时间聚合的联合推断，以及协变量调整的扩展。在一个关于水力压裂的应用中，水平边际的估计结果拒绝了联合零限制，而响应指数的估计结果则没有。连续剂量OLS系数主要来源于水平边际。我们分别报告水平边际和响应边际。
英文摘要
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 response parallel trends assumption and a restriction on selection on gains. We show that the continuous-dose OLS coefficient in each cohort-time comparison is a convex combination of the response index and the level contrast per unit of mean dose, with a mixing weight that depends on the not-yet-treated share. We provide estimators of both margins, joint inference across cohort-time comparisons and event-time aggregates, and a covariate-adjusted extension. In an application to hydraulic fracturing, the level leads reject a joint zero restriction, whereas the response-index leads do not. The continuous-dose OLS coefficient draws primarily on the level margin. We report the level and response margin separately.
