This paper presents methods to study the causal effect of a binary treatment on a functional outcome with observational data. We define a Functional Average Treatment Effect and develop an outcome regression estimator. We show how to obtain valid inference on the FATE using simultaneous confidence bands, which cover the FATE with a given probability over the entire domain. Simulation experiments illustrate how the simultaneous confidence bands take the multiple comparison problem into account. Finally, we use the methods to infer the effect of early adult location on subsequent income development for one Swedish birth cohort.

翻译：本文提出了一种利用观测数据研究二元处理对功能性结果因果效应的方法。我们定义了功能性平均处理效应，并开发了结果回归估计量。我们展示了如何通过同时置信带对FATE进行有效推断，这些置信带在全域范围内以给定概率覆盖FATE。仿真实验说明了同时置信带如何考虑多重比较问题。最后，我们利用这些方法推断瑞典某出生队列中早期成年居住地对后续收入发展轨迹的影响。