A0179
Title: What do we get from two-way fixed effects regressions? Implications from numerical equivalence
Authors: Shoya Ishimaru - Hitotsubashi University (Japan) [presenting]
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, numerical and causal interpretations of the TWFE coefficient are developed. 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. A causal interpretation of the TWFE coefficient at the population level requires a common trend assumption for any between-period gap. The assumption has to be conditional on changes in time-varying covariates. It is shown that these requirements can be naturally relaxed by modifying the estimator using a pooled FD regression.
