Causal Graphs for Conditional Parallel Trends
Michael C. Knaus, Henri Pfleiderer
TLDR
Δ-SWIGs, a new causal graph framework, enable reasoning about Conditional Parallel Trends in Difference-in-Differences designs with time-varying covariates.
Key contributions
- Introduces Δ-SWIGs, a novel causal graph framework for Conditional Parallel Trends (CPT) in DiD.
- Proves Δ-SWIGs allow reading CPT-implying conditional independencies via d-separation.
- Uses Δ-SWIGs to analyze DiD in complex settings with multiple periods and time-varying covariates.
- Shows post-treatment controls are required and pre-treatment trends offer limited CPT justification.
Why it matters
This paper fills a critical gap by providing a graphical framework to rigorously reason about Conditional Parallel Trends in Difference-in-Differences. It offers crucial guidance on valid conditioning strategies and clarifies the limitations of empirical pre-treatment trend checks, improving DiD application.
Original Abstract
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.
📬 Weekly AI Paper Digest
Get the top 10 AI/ML arXiv papers from the week — summarized, scored, and delivered to your inbox every Monday.