We propose a difference-in-differences (DiD) framework designed for time-varying continuous treatments across multiple periods. Specifically, we estimate the average treatment effect on the treated (ATET) by comparing distinct non-zero treatment intensities. Identification rests on a conditional parallel trends assumption that accounts for observed covariates and past treatment histories. Our approach allows for lagged treatment effects and, in repeated cross-sectional settings, accommodates compositional changes in covariates. We develop kernel-based ATET estimators for both repeated cross-sections and panel data, leveraging the double/debiased machine learning framework to handle potentially high-dimensional covariates and histories. We establish the asymptotic properties of our estimators under mild regularity conditions and demonstrate via simulations that their undersmoothed versions perform well in finite samples. As an empirical illustration, we apply our estimator to assess the effect of the second-dose COVID-19 vaccination rate in Brazil and find that higher vaccination rates reduce COVID-19-related mortality after a lag of several weeks.

翻译：本文提出了一种适用于多时期时变连续处理的双重差分（DiD）框架。具体而言，我们通过比较不同的非零处理强度来估计处理组的平均处理效应（ATET）。识别基于条件平行趋势假设，该假设考虑了观测协变量和既往处理历史。我们的方法允许存在滞后处理效应，并且在重复横截面设定中能够适应协变量的结构变化。我们针对重复横截面数据和面板数据开发了基于核函数的ATET估计量，利用双重/去偏机器学习框架处理潜在的高维协变量和历史信息。我们在温和的正则性条件下建立了估计量的渐近性质，并通过模拟证明其欠平滑版本在有限样本中表现良好。作为实证示例，我们将该估计量应用于评估巴西第二剂COVID-19疫苗接种率的影响，发现较高的疫苗接种率在滞后数周后能够降低COVID-19相关死亡率。