Sharing a very interesting new paper on DiD methods when used with heterogeneous treatment effects:
Andrew Goodman-Bacon, 2018. Differences-in-Differences with Variation in Treatment Timing, Working Paper.
The paper shows how (and when) a DiD estimator can be decomposed as a weighted average of 4 simple and intuitive “2×2” average causal effects. Some of these effects may have negative “weights” which arise because already-treated units sometimes act as controls, leading to a biased DiD estimator. Hence, DiD estimates can be too small (or even wrong-signed!). The author notes that “this does not imply a failure of the underlying design, but it does caution against the use of a single-coefficient two-way fixed effects specification to summarize time-varying effects”. Several implications for the intuition, theory and practice of this well-known econometric method are discussed.