The Case for Time in Causal DAGs
Abstract
Graphical causal models, usually in the form of directed acyclic graphs (DAGs), are a central model class for encoding and reasoning about causal relationships between different quantities. In contrast to other causal models, they do not encode the temporal relationship between variables explicitly. We demonstrate that such nontemporal causal DAGs are ambiguous and obstruct justification of the acyclicity assumption. Assuming that causes precede effects, causal relationships are relative to the time order, and causal DAGs require temporal qualification. We propose a formalization via "composite" causal variables that refer to quantities at one or multiple time points. We emphasize that the acyclicity assumption requires different justifications depending on whether the time order allows cycles. We conclude by discussing implications for the interpretation and applicability of DAGs as causal models.