Inference of Causal Effects when Control Variables are Unknown

TL;DR

This paper introduces a method for estimating average causal effects in linear structural causal models without prior knowledge of control variables, ensuring valid confidence intervals even with misspecification.

Contribution

It provides a novel approach for causal inference that remains valid when control variables are unknown, specifically within acyclical linear models.

Findings

Method produces valid confidence intervals in synthetic data.

Approach is robust to control variable misspecification.

Theoretical guarantees are established for asymptotic validity.

Abstract

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.