What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence
Shoya Ishimaru
Papers from arXiv.org
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 improves transparency by revealing the sources of variation that the TWFE coefficient captures. At the population level, causal interpretation of the TWFE coefficient relies on a common trends assumption for any between-period gap, conditional on changes, not levels, of time-varying covariates. I propose a simple modification to the TWFE approach that naturally eases this assumption.
Date: 2021-03, Revised 2025-04
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2103.12374
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