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

Shoya Ishimaru

arXiv 23 Mar 2021 · Econometrics · 1 citations (OpenAlex)

arXiv:2103.12374 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper develops numerical and causal interpretations of two-way fixed effects (TWFE) regressions, allowing for general scalar treatments with non-staggered designs and time-varying covariates. Building on the numerical equivalence between TWFE and pooled first-difference regressions, I decompose the TWFE coefficient into a weighted average of first-difference coefficients across varying horizons, clarifying contributions of short-run versus long-run changes. Causal interpretation of the TWFE coefficient requires common trends assumptions for all time horizons, conditional on changes, not levels, of time-varying covariates. I develop diagnostic procedures to assess this assumption's plausibility across different horizons, extending beyond recent literature's focus on binary, staggered treatments.

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33
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1de Chaisemartin and D'Haultfuille (2020) Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects0.92810480%
2Borusyak, Jaravel and Spiess (2024) Revisiting Event-Study Designs: Robust and Efficient Estimation0.92843100%
3Callaway and Sant'Anna (2021) Difference-in-differences with multiple time periods0.92843100%
4Wooldridge (2025) Two-way fixed effects, the two-way mundlak regression, and difference-in-differences estimators: JM Wooldridre0.81142100%
5Goodman-Bacon (2021) Difference-in-differences with variation in treatment timing0.77313446%
6Li and Strezhnev (2024) A Guide to Dynamic Difference-in-Differences Regressions for Political Scientists0.7374350%
7Callaway, Goodman-Bacon and Sant'Anna (2024) Difference-in-differences with a continuous treatment0.73732100%
8Han and Lee (2017) Efficient Estimation of Linear Panel Data Models with Sample Selection and Fixed Effects0.64422100%
9de Chaisemartin and D'Haultfuille (2024) Difference-in-differences estimators of intertemporal treatment effects0.64422100%
10de Chaisemartin, d'Haultfuille, Pasquier and Vazquez-Bare (2022) Difference-in-differences estimators for treatments continuously distributed at every period0.64422100%

Showing the top 10 of 33 scored citations.