Inference of Causal Effects when Control Variables are Unknown
This work provides a method for researchers and practitioners to infer causal effects more reliably in situations where the precise set of control variables is not known, reducing the risk of erroneous inferences.
This paper addresses the problem of inferring average causal effects when all potential confounders are observed but the specific control variables are unknown. The proposed method is proven to yield asymptotically valid confidence intervals for acyclical linear structural causal models, and its effectiveness is verified using synthetic data.
Conventional methods in causal effect inferencetypically rely on specifying a valid set of control variables. When this set is unknown or misspecified, inferences will be erroneous. We propose a method for inferring average causal effects when all potential confounders are observed, but thecontrol variables are unknown. When the data-generating process belongs to the class of acyclical linear structural causal models, we prove that themethod yields asymptotically valid confidence intervals. Our results build upon a smooth characterization of linear directed acyclic graphs. We verify the capability of the method to produce valid confidence intervals for average causal effects using synthetic data, even when the appropriate specification of control variables is unknown.