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

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  • Shoya Ishimaru

Abstract

In any multiperiod panel, a two-way fixed effects (TWFE) regression is numerically equivalent to a first-difference (FD) regression that pools all possible between-period gaps. Building on this observation, this paper develops numerical and causal interpretations of the TWFE coefficient. At the sample level, the TWFE coefficient is a weighted average of FD coefficients with different between-period gaps. This decomposition is useful for assessing the source of identifying variation for the TWFE coefficient. At the population level, a causal interpretation of the TWFE coefficient requires a common trends assumption for any between-period gap, and the assumption has to be conditional on changes in time-varying covariates. I propose a natural generalization of the TWFE estimator that can relax these requirements.

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  • Shoya Ishimaru, 2021. "What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence," Papers 2103.12374, arXiv.org, revised Jan 2024.
    • Handle: RePEc:arx:papers:2103.12374
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    4. Luis Costa & Vivek F. Farias & Patricio Foncea & Jingyuan (Donna) Gan & Ayush Garg & Ivo Rosa Montenegro & Kumarjit Pathak & Tianyi Peng & Dusan Popovic, 2023. "Generalized Synthetic Control for TestOps at ABI: Models, Algorithms, and Infrastructure," Interfaces, INFORMS, vol. 53(5), pages 336-349, September.

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