DiD

Difference-in-Differences MOC

Difference-in-differences (DiD) identifies treatment effects by comparing the change in outcomes for a treated group to the change for a control group, using the control’s trajectory as the treated group’s counterfactual. Its spine is one identifying assumption — Parallel-Trends — usually paired with No-Anticipation. This MOC tracks the literature’s arc: from the classic two-group design, through the discovery that two-way fixed effects (TWFE) breaks under staggered timing and Treatment-Effect-Heterogeneity, to the heterogeneity-robust estimators and honest parallel-trends inference that define the modern toolkit.

Papers

Classics & foundations

• AshenfelterCard1985-LongitudinalEarnings — the fixed-effects/pre-post lineage; origin of the Ashenfelter-Dip threat to Parallel-Trends.
• Meyer1995-NaturalAndQuasiExperiments — quasi-experimental design language; multiple groups/periods to test the identifying assumptions.
• Abadie2005-SemiparametricDiD — Conditional-Parallel-Trends via propensity-score reweighting.
• AtheyImbens2006-NonlinearDiD — changes-in-changes; a scale-invariant, distributional generalization of additive DiD.

Inference

• Bertrand2004-HowMuchShouldWeTrustDiD — serial correlation wrecks naive DiD standard errors; cluster or collapse.

The staggered-timing problem

• GoodmanBacon2021-DiDVariationInTiming — TWFE = weighted average of 2×2 DiDs; the Negative-Weighting “forbidden comparisons” diagnosis.
• SunAbraham2021-EventStudies — TWFE event-study leads/lags are contaminated; spurious pre-trends from heterogeneity.
• DeChaisemartinDHaultfoeuille2023-TWFESurvey — survey of the TWFE-heterogeneity problem and the robust alternatives.
• BakerLarckerWang2022-HowMuchTrustStaggeredDiD — the problem in accounting/finance, with replications.
• AtheyImbens2022-DesignBasedDiD — a design-based (randomization-inference) view of staggered adoption.

Heterogeneity-robust estimators

• CallawaySantAnna2021-DiDMultiplePeriods — group-time ATT building blocks with clean controls.
• SantAnnaZhao2020-DoublyRobustDiD — doubly robust ATT (propensity × outcome).
• Wooldridge2021-TWFEMundlakDiD — TWFE ≡ two-way Mundlak; saturated (extended) TWFE recovers heterogeneity-robust ATTs.
• ArkhangelskyImbens2024-FixedEffectsGeneralizedMundlak — Generalized Mundlak: group-level balancing scores + doubly robust estimation replace fixed effects in grouped cross-sections; FE estimands shown to be sampling-scheme-dependent.
• DeChaisemartinDHaultfoeuille2020-IntertemporalTE — non-binary, non-absorbing (switching) treatments with dynamic effects.
• DeChaisemartinDHaultfoeuille2018-FuzzyDiD — fuzzy designs; links DiD to the LATE and changes-in-changes.
• CallawayGoodmanBaconSantAnna-ContinuousTreatment — continuous/dose treatments.
• BorusyakEtAl2024-RevisitingEventStudyDesigns — the efficient robust imputation estimator; fit FEs on untreated observations, impute, then weight to the target; separates estimation from pre-trend/no-anticipation testing.

Parallel trends: testing & relaxing

• KahnLangLang2020-PromiseAndPitfallsOfDiD — explain why levels differed; parallel trends is functional-form dependent; parallel pre-trends is neither necessary nor sufficient (the 16 and Pregnant debate).
• RothPretrends2022-PretestWithCaution — pre-trend tests are underpowered and pre-testing distorts inference.
• RambachanRoth2023-MoreCredibleParallelTrends — HonestDiD: partial identification and sensitivity analysis under bounded violations.
• FreyaldenhovenEtAl2019-PreEventTrendsPanelEventStudy — repair rather than test: an unaffected covariate + 2SLS (policy leads as instruments) identifies the effect even when pre-trends are present.

Synthesis & practice

• RothSantAnna2023-WhatsTrendingInDiD — synthesis of the recent literature.
• BakerEtAl2025-DiDPractitionerGuide — an organizing framework and applied guide.

Key Concepts

Parallel-Trends · Conditional-Parallel-Trends · No-Anticipation · Treatment-Effect-Heterogeneity · Negative-Weighting · Ashenfelter-Dip · Causal-Estimand · Overlap · SUTVA

Debates & Contradictions

• Is TWFE broken? Goodman-Bacon, Sun–Abraham, and de Chaisemartin show TWFE can be badly biased under staggered timing and heterogeneity; Wooldridge replies that the problem is unsaturated TWFE — a fully interacted (extended) TWFE/Mundlak regression is fine. A disagreement about framing more than facts.
• What to do about parallel trends. Roth (2022) argues pre-trend testing can make inference worse; Rambachan–Roth replace the binary test with sensitivity analysis. The older tradition (Ashenfelter–Card, Meyer) leaned on richer designs and placebo groups.
• Conditional vs unconditional trends. Abadie, Sant’Anna–Zhao, and Callaway– Sant’Anna condition on covariates to make trends parallel; this trades the implausibility of raw parallel trends for dependence on the right covariates.
• Model-based vs design-based. Athey–Imbens (2022) justify DiD from randomized adoption timing rather than a parallel-trends model — a different epistemic footing for the same estimator.

Next

The DiD spine now connects back to Foundations (potential outcomes, estimands) and shares the LATE / changes-in-changes machinery with IV. RDD, PSM, RCT, and SCM MOCs follow as those folders are processed.