A More Credible Approach to Parallel Trends
Causal Question / Estimand
The dynamic treatment effect in DiD/event-study designs (Causal-Estimand) when Parallel-Trends may not hold exactly. Rather than point-identify under exact parallel trends, the paper partially identifies the effect under transparent restrictions on how far trends can deviate.
Identification Strategy
The HonestDiD framework. Impose restrictions relating post-treatment violations of parallel trends to the observed pre-treatment differences in trends — e.g. the post-period violation is no larger than the pre-period one (“relative magnitudes”), or trends deviate smoothly (“smoothness”). The causal parameter is then partially identified; the paper delivers uniformly valid confidence sets and a sensitivity analysis showing which conclusions survive which assumed degree of violation.
Key Assumptions
Replaces exact Parallel-Trends with bounded deviations from it, disciplined by economic knowledge and observed pre-trends. No-Anticipation for the pre-period benchmark; SUTVA throughout. The output is a set, not a point.
Threats to Validity
n/a — the paper’s purpose is to handle the central threat (parallel-trends violations) honestly. Its caveat: the credibility of the conclusions depends on the credibility of the imposed restriction on trend deviations, which must be argued substantively.
Setting / Data
n/a — econometric methodology (the HonestDiD R/Stata package). Illustrated with two
economic applications where domain knowledge informs the restriction set.
Key Claims
- Exact parallel trends is often incredible; partial identification under bounded violations is more honest.
- Provides uniformly valid inference and formal sensitivity analysis (“breakdown” values) for DiD conclusions.
- Connects pre-trend evidence to post-treatment inference rigorously, instead of the binary “passed/failed” pre-test.
Connections
- Directly addresses the pitfalls flagged by: RothPretrends2022-PretestWithCaution
- Synthesized in: RothSantAnna2023-WhatsTrendingInDiD
- Complements robust point estimators: CallawaySantAnna2021-DiDMultiplePeriods, SunAbraham2021-EventStudies
- Alternative repair when an unaffected covariate exists: FreyaldenhovenEtAl2019-PreEventTrendsPanelEventStudy
- See also: DiD
Citation
Rambachan, A., & Roth, J. (2023). A More Credible Approach to Parallel Trends. The Review of Economic Studies, 90(5), 2555–2591. https://doi.org/10.1093/restud/rdad018