Alexander Reisach
The Case for Time in Causal DAGs
We make the case for including time explicitly in the definition and interpretation of causal directed acyclic graphs (DAGs). Causality requires that causes precede effects in time, meaning that the causal relationships between variables in one time order may not be the same in another. Therefore, any causal model requires temporal qualification. We argue that an explicit treatment of time resolves existing ambiguity in causal DAGs and is essential to assessing the validity of the acyclicity assumption. If variables are separated in time, their causal relationship is necessarily acyclic. Otherwise, acyclicity additionally requires the absence of any cyclic effects that are permitted by the time order. We introduce a formal distinction between these two conditions and lay out their respective implications. We outline connections of our contribution with different strands of the broader causality literature and discuss the ramifications of considering time for the interpretation and applicability of DAGs as causal models.