This paper studies the estimation and inference of treatment effects in panel data settings when treatments change dynamically over time. We propose a balancing method that allows for (i) treatments to be assigned dynamically over time based on high-dimensional covariates, past outcomes, and treatments; (ii) outcomes and time-varying covariates to depend on the trajectory of all past treatments; (iii) heterogeneity of treatment effects. Our approach recursively projects potential outcomes' expectations on past histories. It then controls the bias arising from the non-experimental and sequential nature of this setting by balancing dynamically observable characteristics over time. We establish inferential guarantees of the proposed method even when the number of observable characteristics significantly exceeds the sample size. We study numerical properties of the estimator and illustrate the benefits of the procedure in an empirical application.

翻译：本文研究面板数据中处理随时间动态变化时处理效应的估计与推断问题。我们提出一种平衡方法，允许：(i) 处理基于高维协变量、历史结果和处理随时间动态分配；(ii) 结果变量与时变协变量依赖于所有历史处理的轨迹；(iii) 处理效应存在异质性。我们的方法通过递归地将潜在结果期望投影到历史信息上，进而通过动态平衡可观测特征随时间的变化，控制由非实验性和序列性设定产生的偏差。即使当可观测特征数量显著超过样本量时，我们仍为所提方法建立了推断保证。我们研究了估计量的数值性质，并通过实证应用展示了该方法的优势。