This paper studies the estimation and inference of treatment histories in panel data settings when treatments change dynamically over time. We propose a 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 treatment trajectories; (iii) heterogeneity of treatment effects. Our approach recursively projects potential outcomes' expectations on past histories. It then controls the bias by balancing dynamically observable characteristics. We study the asymptotic and 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变量随时间动态变化时处理历史的估计与推断问题。我们提出了一种方法，允许：(i) 基于高维协变量、历史结果及处理变量，处理变量随时间动态分配；(ii) 结果变量及随时间变化的协变量依赖于处理轨迹；(iii) 处理效应存在异质性。我们的方法通过递归投影潜在结果期望至历史轨迹，进而通过平衡动态可观测特征来控制偏差。我们研究了该估计量的渐近性质与数值性质，并通过实证应用展示了该方法的优势。