Double machine learning (DML) is becoming an increasingly popular tool for automated model selection in high-dimensional settings. At its core, DML assumes unconfoundedness, or exogeneity of all considered controls, which might likely be violated if the covariate space is large. In this paper, we lay out a theory of bad controls building on the graph-theoretic approach to causality. We then demonstrate, based on simulation studies and an application to real-world data, that DML is very sensitive to the inclusion of bad controls and exhibits considerable bias even with only a few endogenous variables present in the conditioning set. The extent of this bias depends on the precise nature of the assumed causal model, which calls into question the ability of selecting appropriate controls for regressions in a purely data-driven way.
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