Two-Way Fixed Effects and DiD with Heterogeneous Treatment Effects: A Survey
Causal Question / Estimand
A survey of what two-way fixed-effects (TWFE) regressions estimate when treatment effects are heterogeneous, and what alternative estimands and estimators recover interpretable averages of unit-time effects (Causal-Estimand).
Identification Strategy
Reviews the now-standard result that TWFE coefficients are weighted sums of unit-time treatment effects with weights that can be negative, so a single TWFE number need not equal any sensible average effect. Catalogues the heterogeneity-robust alternatives (Callaway–Sant’Anna, Sun–Abraham, de Chaisemartin–D’Haultfœuille, Borusyak et al., Wooldridge) and the assumptions each requires. Re-examines Wolfers (2006) on divorce laws to show the differences in practice.
Key Assumptions
Parallel-Trends (and often strong/conditional versions), No-Anticipation, and an honest account of Treatment-Effect-Heterogeneity. The survey’s organizing theme is that TWFE silently assumes effect homogeneity; dropping that assumption exposes Negative-Weighting.
Threats to Validity
n/a — survey. Its cautionary message: TWFE estimates can be misleading (even sign-reversed) under heterogeneous effects; robust estimators differ in their comparison groups, weighting, and treatment of covariates, so the choice matters.
Setting / Data
n/a — methodological survey. Empirical illustration: revisiting Wolfers (2006a) on unilateral divorce laws and divorce rates.
Key Claims
- TWFE regressions are extremely common (26 of the 100 most-cited 2015–2019 AER papers) yet vulnerable to heterogeneity bias.
- A fast-growing literature provides estimators robust to heterogeneous effects; the survey maps their assumptions and trade-offs.
- Practitioners should report weights/diagnostics and prefer robust estimators when effects plausibly vary across groups or time.
Connections
- Surveys/organizes: GoodmanBacon2021-DiDVariationInTiming, SunAbraham2021-EventStudies, CallawaySantAnna2021-DiDMultiplePeriods, Wooldridge2021-TWFEMundlakDiD, DeChaisemartinDHaultfoeuille2020-IntertemporalTE
- By the same authors: DeChaisemartinDHaultfoeuille2018-FuzzyDiD, DeChaisemartinDHaultfoeuille2020-IntertemporalTE
- See also: Negative-Weighting, RothSantAnna2023-WhatsTrendingInDiD, DiD
Citation
de Chaisemartin, C., & D’Haultfœuille, X. (2023). Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey. The Econometrics Journal, 26(3), C1–C30. https://doi.org/10.1093/ectj/utac017