Synthetic difference-in-differences estimation with staggered treatment timing

This note formalizes the synthetic difference-in-differences estimator for staggered treatment adoption settings, as briefly described in Arkhangelsky et al. (2021). To illustrate the importance of this estimator, I use replication data from Abrams (2012). I compare the estimators obtained using SynthDiD, TWFE, the group time average treatment effect estimator of Callaway and Sant'Anna (2021), and the partially pooled synthetic control method estimator of Ben-Michael et al. (2021) in a staggered treatment adoption setting. I find that in this staggered treatment setting, SynthDiD provides a numerically different estimate of the average treatment effect. Simulation results show that these differences may be attributable to the underlying data generating process more closely mirroring that of the latent factor model assumed for SynthDiD than that of additive fixed effects assumed under traditional difference-in-differences frameworks.