Michael C. Knaus, Henri Pfleiderer
arXiv 14 Apr 2026 · Econometrics
arXiv:2604.12818 · PDF · DOI · OpenAlex · Extracted main text
Difference-in-Differences (DiD) is a widely used research design that often relies on a conditional parallel trends (CPT) assumption. In contrast to settings with unconfoundedness, where causal graphs provide powerful frameworks for reasoning about valid conditioning variables, general-purpose graphical tools for CPT are missing. We introduce transformed Single World Intervention Graphs (SWIGs), the $Δ$-SWIGs, and prove that they enable us to read off conditional independencies via $d$-separation that imply CPT. Using $Δ$-SWIGs, we study valid conditioning strategies for DiD in complex settings with multiple periods and time-varying covariates. We show that when time-varying covariates affect the outcome, controlling for post-treatment variables is required for identification. However, even when such controls are included, pre-treatment parallel trends are only informative about a subset of the assumptions required for unbiased post-treatment effects, highlighting the limitations of purely empirical justifications of CPT.
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