| 2024.04.25 (THU) 16:20-17:50 |
| Title: | What Do We Get from Two-Way Fixed Effects Regressions? Implications from Numerical Equivalence |
 | 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. I illustrate the practical importance of these insights by examining the TWFE estimates of the minimum wage effect on employment outcomes in the U.S. state–year panel. |
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