Parallel Trends

The identifying assumption of difference-in-differences: absent treatment, the treated and control groups would have followed the same trajectory over time, so the control group’s change supplies the treated group’s counterfactual change. Holds unconditionally in the canonical 2×2 design; the covariate-adjusted variant is Conditional-Parallel-Trends. It is untestable directly — pre-treatment “pre-trends” are only suggestive (see RothPretrends2022-PretestWithCaution), and it can be relaxed into bounded deviations for sensitivity analysis (RambachanRoth2023-MoreCredibleParallelTrends). Usually paired with No-Anticipation. The additive form is not invariant to rescaling the outcome, which motivates changes-in-changes (AtheyImbens2006-NonlinearDiD).

Relied on by

DiD and event-study designs (the central identifying assumption).

Referenced by

• AshenfelterCard1985-LongitudinalEarnings, Meyer1995-NaturalAndQuasiExperiments
• Abadie2005-SemiparametricDiD, AtheyImbens2006-NonlinearDiD, AtheyImbens2022-DesignBasedDiD
• GoodmanBacon2021-DiDVariationInTiming, SunAbraham2021-EventStudies, BakerLarckerWang2022-HowMuchTrustStaggeredDiD, DeChaisemartinDHaultfoeuille2023-TWFESurvey
• CallawaySantAnna2021-DiDMultiplePeriods, CallawayGoodmanBaconSantAnna-ContinuousTreatment, SantAnnaZhao2020-DoublyRobustDiD, Wooldridge2021-TWFEMundlakDiD, DeChaisemartinDHaultfoeuille2020-IntertemporalTE, DeChaisemartinDHaultfoeuille2018-FuzzyDiD
• RambachanRoth2023-MoreCredibleParallelTrends, RothPretrends2022-PretestWithCaution, RothSantAnna2023-WhatsTrendingInDiD, BakerEtAl2025-DiDPractitionerGuide
• Surveys: AngristPischke2010-CredibilityRevolution, AngristKrueger1999-EmpiricalStrategiesLaborEconomics
• Method-buildout pass (2026-06-17): contrasted with SCM’s factor model in AbadieEtAl2010-SyntheticControlMethods, AbadieEtAl2015-ComparativePoliticsSCM; DiD-matching in SmithTodd2005-ReconcilingPSMEvidence; surveys AbadieCattaneo2018-EconometricMethodsProgramEvaluation, ImbensWooldridge2009-ProgramEvaluation

New-papers pass (2026-07-04): FreyaldenhovenEtAl2019-PreEventTrendsPanelEventStudy (repairs violations via an unaffected covariate + 2SLS rather than testing or bounding); KahnLangLang2020-PromiseAndPitfallsOfDiD (functional-form dependence; parallel pre-trends neither necessary nor sufficient; explain the level difference).

New-papers pass (2026-07-13): BorusyakEtAl2024-RevisitingEventStudyDesigns (parallel trends on untreated potential outcomes; tested via OLS on untreated observations only, kept separate from dynamic-effect estimation).