We propose a generalization of the synthetic control and interventions methods to the setting with dynamic treatment effects. We consider the estimation of unit-specific treatment effects from panel data collected under a general treatment sequence. Here, each unit receives multiple treatments sequentially, according to an adaptive policy that depends on a latent, endogenously time-varying confounding state. Under a low-rank latent factor model assumption, we develop an identification strategy for any unit-specific mean outcome under any sequence of interventions. The latent factor model we propose admits linear time-varying and time-invariant dynamical systems as special cases. Our approach can be viewed as an identification strategy for structural nested mean models -- a widely used framework for dynamic treatment effects -- under a low-rank latent factor assumption on the blip effects. Unlike these models, however, it is more permissive in observational settings, thereby broadening its applicability. Our method, which we term synthetic blip effects, is a backwards induction process in which the blip effect of a treatment at each period and for a target unit is recursively expressed as a linear combination of the blip effects of a group of other units that received the designated treatment. This strategy avoids the combinatorial explosion in the number of units that would otherwise be required by a naive application of prior synthetic control and intervention methods in dynamic treatment settings. We provide estimation algorithms that are easy to implement in practice and yield estimators with desirable properties. Using unique Korean firm-level panel data, we demonstrate how the proposed framework can be used to estimate individualized dynamic treatment effects and to derive optimal treatment allocation rules in the context of financial support for exporting firms.

翻译：本文提出了一种针对动态处理效应场景的合成控制与干预方法的推广框架。我们研究在一般处理序列下收集的面板数据中，针对特定单元的处理效应估计问题。在此设定下，每个单元根据依赖于潜在内生时变混杂状态的自适应策略，依次接受多重处理。基于低秩潜在因子模型假设，我们建立了任意干预序列下单元特异性平均结果的识别策略。所提出的潜在因子模型将线性时变与时不变动力系统作为特例包含其中。该方法可视为在脉冲效应满足低秩潜在因子假设下，对结构嵌套均值模型——一种广泛使用的动态处理效应框架——的识别策略。然而与传统模型不同，该方法在观测性研究中具有更强的容许性，从而拓宽了其适用边界。我们提出的"合成脉冲效应"方法是一种逆向归纳过程：通过递归地将目标单元在每个时期的处理脉冲效应，表示为接受指定处理的其他单元组脉冲效应的线性组合。该策略避免了在动态处理场景中直接应用现有合成控制与干预方法可能导致的单元数量组合爆炸问题。我们提供了易于实践实现的估计算法，所得估计量具有良好的统计特性。基于独特的韩国企业级面板数据，我们演示了如何运用该框架估计出口企业金融支持情境下的个性化动态处理效应，并推导最优处理分配规则。