EconBase
← All papers

Causal Graphs for Conditional Parallel Trends

Michael C. Knaus, Henri Pfleiderer

arXiv 14 Apr 2026 · Econometrics

arXiv:2604.12818 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

63
references
146
in-text mentions
63
distinct cited
0
self-citations
21,043
main-text words

appendix boundary found by appendix_command · 57% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Caetano, Carolina and Callaway, Brantly and Payne, Stroud and Rodrig… (2024) Difference in Differences with Time-Varying Covariates1.00093100%
2Bonhomme, Stephane (2025) Back to Feedback: Dynamics and Heterogeneity in Panel Data1.00053100%
3Callaway, Brantly and Sant’Anna, Pedro H. C (2021) Difference-in-Differences with Multiple Time Periods1.00053100%
4Caetano, Carolina and Callaway, Brantly (2024) Difference-in-Differences when Parallel Trends Holds Conditional on Covariates0.96911491%
5Ghanem, Dalia and Sant'Anna, Pedro H. C. and Wüthrich, Kaspar (2024) Selection and parallel trends0.9507586%
6Cinelli, Carlos and Forney, Andrew and Pearl, Judea (2024) A Crash Course in Good and Bad Controls0.92843100%
7Ghanem, Dalia and Sant’Anna, Pedro H C and Wüthrich, Kaspar (2026) When should pre-trends be parallel?0.87472100%
8Richardson, Thomas S and Robins, James M (2013) Single World Intervention Graphs (SWIGs): A Unification of the Counterfactual and Graphical Approaches to Causality0.86314464%
9Roth, Jonathan and Sant’Anna, Pedro H. C. and Bilinski, Alyssa and P… (2023) What’s Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature0.7373367%
10Chernozhukov, Victor and Hansen, Christian and Kallus, Nathan and Sp… (2024) Applied Causal Inference Powered by ML and AI0.73732100%

Showing the top 10 of 63 scored citations.