  We consider Bayes and Empirical Bayes (EB) approaches for dealing with
violations of parallel trends. In the Bayes approach, the researcher specifies
a prior over both the pre-treatment violations of parallel trends
$\delta_{pre}$ and the post-treatment violations $\delta_{post}$. The
researcher then updates their posterior about the post-treatment bias
$\delta_{post}$ given an estimate of the pre-trends $\delta_{pre}$. This allows
them to form posterior means and credible sets for the treatment effect of
interest, $\tau_{post}$. In the EB approach, the prior on the violations of
parallel trends is learned from the pre-treatment observations. We illustrate
these approaches in two empirical applications.
