  This paper illustrates the use of entropy balancing in
difference-in-differences analyses when pre-intervention outcome trends suggest
a possible violation of the parallel trends assumption. We describe a set of
assumptions under which weighting to balance intervention and comparison groups
on pre-intervention outcome trends leads to consistent
difference-in-differences estimates even when pre-intervention outcome trends
are not parallel. Simulated results verify that entropy balancing of
pre-intervention outcomes trends can remove bias when the parallel trends
assumption is not directly satisfied, and thus may enable researchers to use
difference-in-differences designs in a wider range of observational settings
than previously acknowledged.
