Two-way Fixed Effects Estimators with Heterogeneous Treatment Effects
Abstract
Linear regressions with period and group fixed effects are widely used to estimate treatment effects.We show that they identify weighted sums of the average treatment effects (ATE) in each group and period, with weights that may be negative.Due to the negative weights, the linear regression estimand may for instance be negative while all the ATEs are positive.In two articles that have used those regressions, half of the weights are negative.We propose another estimator that solves this issue.In one of the articles we revisit, it is of a different sign than the linear regression estimator.
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Results of Gardner (2022), Borusyak, Jaravel, and Spiess (2021), and Chaisemartin and D'Haultfoeuille (2019) all characterize the weights w_gt from the static TWFE regression.
“Results of Gardner (2022), Borusyak, Jaravel, and Spiess (2021), and Chaisemartin and D'Haultfoeuille (2019) all characterize the weights wgt from this regression.”
From did2s: Two-Stage Difference-in-Differences (2022) · cites this paper as Chaisemartin and D'Haultfoeuille (2019)
Cites
Semiparametric Difference-in-Differences Estimators
Abadie, A. (2005) · The Review of Economic Studies · doi:10.1111/0034-6527.00321 · Cited by 2,286 · see citing works
Duflo, E. (2001) · American Economic Review · doi:10.1257/aer.91.4.795 · Cited by 1,940 · see citing works
Bustos, P. (2011) · American Economic Review · doi:10.1257/aer.101.1.304 · Cited by 1,552 · see citing works
Design-based analysis in Difference-In-Differences settings with staggered adoption
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The gender wage gap and domestic violence
Aizer, A. (2010) · American Economic Review · doi:10.1257/aer.100.4.1847 · Cited by 828 · see citing works
Inference with “Difference in Differences” with a Small Number of Policy Changes
Conley, T. G., & Taber, C. R. (2011) · Review of Economics and Statistics · doi:10.1162/rest_a_00049 · Cited by 633 · see citing works
On the Use of Two-Way Fixed Effects Regression Models for Causal Inference with Panel Data
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The Effect of Newspaper Entry and Exit on Electoral Politics
Gentzkow, M., Shapiro, J. M., & Sinkinson, M. (2011) · American Economic Review · doi:10.1257/aer.101.7.2980 · Cited by 497 · see citing works
Revisiting Event Study Designs
Borusyak, K., & Jaravel, X. (2016) · SSRN Electronic Journal · doi:10.2139/ssrn.2826228 · Cited by 463 · see citing works
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Callaway, B., & Sant’Anna, P. H. C. (2021) · Journal of Econometrics · doi:10.1016/j.jeconom.2020.12.001 · Cited by 9,126 · see citing works
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Schmidheiny, K., & Siegloch, S. (2023) · Journal of Applied Econometrics · doi:10.1002/jae.2971 · Cited by 293 · see citing works
Two-way fixed effects, the two-way Mundlak regression, and difference-in-differences estimators
Wooldridge, J. M. (2025) · Empirical Economics · doi:10.1007/s00181-025-02807-z · Cited by 139 · see citing works
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Butts, K., & Gardner, J. (2022) · The R Journal · doi:10.32614/rj-2022-048 · Cited by 89 · see citing works
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- Authors
- de Chaisemartin, C., & D'Haultfoeuille, X.
- Venue
- National Bureau of Economic Research
- Publisher
- National Bureau of Economic Research
- Published
- 2019-05
- OpenAlex
- W2795047867
- Cited by
- 350
- References
- 9
- Citations by year
- 2026: 6 · 2025: 16 · 2024: 45 · 2023: 77 · 2022: 79 · 2021: 56 · 2020: 43 · 2019: 13 · 2018: 13 · 2017: 1 · 2016: 1
- Type
- report
- Language
- en
- Open access
- closed
- Locations
- National Bureau of Economic Research (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- two-way fixed effects, treatment effect heterogeneity, average treatment effect, estimation bias, negative weights, treatment effect identification, causal inference
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