The Parallel Trends Assumption
By the end of this lesson, you should be able to: state the parallel trends assumption, check it with an event study, explain why a passing pre-trend test is weak evidence, and decide what to do when the assumption is in doubt.
The one thing difference-in-differences needs
Difference-in-differences (lesson 10) subtracts the comparison group's change from the treated group's change. That only gives the treatment effect if, without the treatment, both groups would have changed by the same amount. This is the parallel trends assumption.
The groups don't need to be at the same level, or even be very similar. Their changes need to match. If the treated group was already growing faster before the treatment, DiD will count that faster growth as part of the effect.
The trouble is that after the treatment starts, you can't see what the treated group would have done without it. The assumption is about a counterfactual, so it can never be checked directly. What you can do is look for evidence for and against it.
Looking at it: the event study
The most common check is an event study. Instead of one before-and-after comparison, estimate the difference between treated and comparison groups separately for each period, before and after the treatment, relative to the period just before it.
- Periods after the treatment show the effect over time.
- Periods before the treatment should show roughly zero. Nothing had happened yet, so if the groups were moving in parallel, the gap shouldn't have been changing.
If the pre-treatment estimates trend up or down, the groups weren't moving together even before the treatment, and the DiD estimate is suspect.