Figure 1From “What are parallel trends? The assumption behind difference-in-differences”
The synthetic parallel-trends screen
A similar pre-period path can motivate a design review, but it does not reveal the treated group's post-period counterfactual.
Figure 1The synthetic parallel-trends screen
Source: Author's synthetic trend illustration grounded in Callaway and Sant'Anna (2021) and Roth, Sant'Anna, Bilinski and Poe (2023). The indexed paths illustrate a review question, not an observed treatment effect or benchmark.
Source and evidence
Each line names a claim related to this exhibit, its source, and how it was checked.
- A CS21-C1 The parameter, named: "the disaggregated causal parameter that we call the group time average treatment effect i e the average treatment effect for group g at time t where a group is defined by the time period when units are first treated"Callaway & Sant'Anna. (2021)
- A CS21-C2 Parallel trends is the identifying assumption: comparison groups "would have followed parallel paths over time which is the so called parallel trends assumption"Callaway & Sant'Anna. (2021)
- A RSP23-C1 A synthesis with advice attached: "this paper synthesizes recent advances in the econometrics of difference in differences did and provides concrete recommendations for practitioners"Roth, Sant'Anna, Bilinski & Poe. (2023)
- A RSP23-C2 TWFE is the baseline it complicates: the ATT "can be consistently estimated using a two way fixed effects twfe regression specification" under the canonical assumptions, and recent advances are classified as relaxing thoseRoth, Sant'Anna, Bilinski & Poe. (2023)
- B R10-OWN-C1 Parallel trends is a design assumption that treated and comparison units would have followed comparable outcome paths absent treatmentAuthor framework grounded in CS21-C1 and RSP23-C1
- B R10-OWN-C2 Pre-treatment visual similarity is evidence about the assumption, not proof that post-treatment counterfactual trends are parallelAuthor boundary
- B R10-OWN-C3 A parallel-trends review should declare treatment timing, comparison set, outcome, pre-period, post-period, aggregation, and event maturityAuthor operating framework
- B R10-OWN-C4 Anticipation, composition change, differential shocks, staggered timing, and outcome redefinition can threaten a parallel-trends argumentAuthor diagnostic framework
Grades: A, verified against the printed page of the primary source · B, primary source, text layer only · C, authoritative secondary · D, reported.
From the essay
From the research bench
What are parallel trends? The assumption behind difference-in-differences
Parallel trends is a counterfactual assumption, not a pre-trend badge. Declare the estimand, timing, overlap, and sensitivity before interpreting DiD.
Read the essayThis exhibit belongs to an essay: the numbers live here, the argument lives there.
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