Parallel trends
Also known as: Common trends assumption
The key bet behind difference-in-differences: absent treatment, the groups would have moved together.
What it means
Parallel trends is the central identifying assumption of difference-in-differences estimation: in the absence of the treatment, the average outcome for the treated group would have followed the same trajectory over time as the comparison group. It is what licenses using the untreated group's change as the counterfactual for what would have happened to the treated group, so that subtracting one trend from the other isolates the causal effect. The assumption is about an unobservable counterfactual and so can never be proven, but it is made credible by showing that the groups moved in parallel during pre-treatment periods, by event-study plots, and by placebo tests on outcomes that should be unaffected. It can be violated by differential shocks, by groups on different growth paths, or by anticipation of the treatment, any of which biases the estimate. It matters because the entire validity of a difference-in-differences study — common in policy evaluation — stands or falls on this single, untestable premise.
Examples
To study a state's new law, researchers first show its outcome moved in lockstep with a neighboring control state for years beforehand, lending credibility that the post-law divergence reflects the law.
A hospital gives new scheduling software to its night shift only. Night and day shifts had tracked each other on overtime for two years, so the later divergence is credited to the software.
The assumption breaks when a company announces a bonus scheme months early: staff ease off while they wait, so the comparison group no longer describes what the treated group would have done.