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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

This paper develops general numerical and causal interpretations of the two-way fixed effects (TWFE) estimator in any multiperiod panel. At the sample level, the TWFE coefficient is a weighted average of first difference regression coefficients using all possible between-period gaps. This decomposition improves transparency by revealing the sources of variation that the TWFE coefficient captures. At the population level, a causal interpretation of the TWFE coefficient requires 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 relaxes 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 Oct 2024.
    • Handle: RePEc:arx:papers:2103.12374
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    2. Siverskog, Jonathan & Henriksson, Martin, 2022. "The health cost of reducing hospital bed capacity," Social Science & Medicine, Elsevier, vol. 313(C).
    3. Carolina Caetano & Brantly Callaway & Stroud Payne & Hugo Sant'Anna Rodrigues, 2022. "Difference in Differences with Time-Varying Covariates," Papers 2202.02903, arXiv.org, revised Jun 2024.
    4. Brantly Callaway, 2022. "Difference-in-Differences for Policy Evaluation," Papers 2203.15646, arXiv.org.

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