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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 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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  • Shoya Ishimaru, 2021. "What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence," Papers 2103.12374, arXiv.org, revised Sep 2025.
    • Handle: RePEc:arx:papers:2103.12374
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