📝 SummarXiv

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 difference lengths. 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 varying horizons, which helps clarify the relative contributions of short-run and long-run changes to the overall estimate. At the population level, causal interpretation of the TWFE coefficient relies on a common trends assumption for any time horizons, conditional on changes, not levels, of time-varying covariates. I develop diagnostic procedures to assess plausibility of this assumption across different time horizons.