What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence

2021/03/23 by Shoya Ishimaru, Ishimaru, Shoya · 1 citation
Economics, Econometrics and Finance · Mathematics · #Advanced Causal Inference Techniques #Applied mathematics #Covariate #Discrete mathematics #Econometrics #Equivalence (formal languages) #Estimator #Generalization #Mathematical analysis #Mathematics #Panel data #Physics #Population #Regional Economics and Spatial Analysis #Regression #Sample (material) #Spatial and Panel Data Analysis #Statistics #Thermodynamics #econ.EM

paper · pdf · doi:10.48550/arxiv.2103.12374

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This paper develops numerical and causal interpretations of two-way fixed effects (TWFE) regressions in settings with nonbinary, nonstaggered treatments and time-varying covariates. Using the equivalence between TWFE and pooled first-difference (FD) regressions, I express the TWFE coefficient as a weighted average of FD coefficients across all horizons, clarifying how short- and long-run changes contribute to the estimate. Causal interpretation of the TWFE coefficient relies on common trends assumptions at all horizons simultaneously, whereas each FD coefficient relies on the assumption only at its own horizon. This structure opens the identifying assumptions to empirical scrutiny: I propose diagnostic procedures that assess common trends horizon by horizon, and illustrate them by reexamining TWFE estimates of minimum-wage effects on employment.

Citations

• Contamination Bias in Linear Regressions
• Empirical Decomposition of the IV-OLS Gap with Heterogeneous and Nonlinear Effects
• Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects
• Revisiting the Minimum Wage—Employment Debate: Throwing Out the Baby with the Bathwater?
• Semiparametric Difference-in-Differences Estimators

Related

• On the Use of Two-Way Fixed Effects Regression Models for Causal Inference with Panel Data
• Difference in Differences with Time-Varying Covariates
• When Can We Use Two-Way Fixed-Effects (TWFE): A Comparison of TWFE and Novel Dynamic Difference-in-Differences Estimators
• When can we get away with using the two-way fixed effects regression?
• Difference-in-Differences when Parallel Trends Holds Conditional on Covariates