Causal inference with a functional outcome

This article 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 (FATE) 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.