Selection on Y(0) and Parallel Trends: Anticipating Step (4a) in Pedro's Diff-in-Diff Checklist

People select into a treatment based on any number of reasons. For instance, they could end up taking a polio vaccine because they were in a study where the polio vaccine was randomized, which is similar to saying they were assigned to the treatment because of an instrument. But sometimes it could be because of observable covariates, like their age, t…