We study the use of exchangeable multi-task Gaussian processes (GPs) for causal inference in panel data, applying the framework to two settings: one with a single treated unit subject to a once-and-for-all treatment and another with multiple treated units and staggered treatment adoption. Our approach models the joint evolution of outcomes for treated and control units through a GP prior that ensures exchangeability across units while allowing for flexible nonlinear trends over time. The resulting posterior predictive distribution for the untreated potential outcomes of the treated unit provides a counterfactual path, from which we derive pointwise and cumulative treatment effects, along with credible intervals to quantify uncertainty. We implement several variations of the exchangeable GP model using different kernel functions. To assess prediction accuracy, we conduct a placebo-style validation within the pre-intervention window by selecting a ``fake'' intervention date. Ultimately, this study illustrates how exchangeable GPs serve as a flexible tool for policy evaluation in panel data settings and proposes a novel approach to staggered-adoption designs with a large number of treated and control units.

翻译：本研究探讨了在面板数据因果推断中应用可交换多任务高斯过程的方法，并将该框架应用于两种情境：一种是单一处理单元受到一次性永久性处理，另一种是多个处理单元存在交错的处理采用。我们的方法通过一个确保单元间可交换性、同时允许随时间灵活非线性趋势的高斯过程先验，对处理单元和控制单元结果的联合演化进行建模。由此得到的处理单元未处理潜在结果的后验预测分布提供了一个反事实路径，从中我们推导出逐点与累积处理效应，并利用可信区间量化不确定性。我们使用不同的核函数实现了可交换高斯过程模型的多种变体。为评估预测准确性，我们在干预前窗口内通过选择一个“伪”干预日期进行了安慰剂式验证。最终，本研究阐明了可交换高斯过程如何作为面板数据情境下政策评估的灵活工具，并提出了一种适用于大量处理单元与控制单元的交错采用设计的新方法。