Difference in Differences, explained.
Difference in differences subtracts a comparison group's change from a treated group's change to estimate an intervention effect under a parallel untreated-trends assumption.
Why it happens
Four periods have comparison outcomes 40 + 5t and treated outcomes 50 + 5t + extraTrend × t. Treatment adds eight from period two. The displayed estimate compares period one with period two, recovering eight plus the differential trend.
Difference in differences subtracts a comparison group's change from a treated group's change to estimate an intervention effect under a parallel untreated-trends assumption.
Read the result
Compare period-one to period-two changes, not just final levels. Revealing the synthetic no-policy line shows exactly which untreated trend the comparison must recover.
A worked example
Two cities after a new programme
With extra trend zero, the treated group gains thirteen while the comparison group gains five across the policy boundary.
Subtract the comparison change to recover the authored eight-unit intervention effect despite different starting levels.
Raise the extra treated trend to three. The estimate becomes eleven, attributing three untreated trend units to policy.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Four periods have comparison outcomes 40 + 5t and treated outcomes 50 + 5t + extraTrend × t. Treatment adds eight from period two. The displayed estimate compares period one with period two, recovering eight plus the differential trend.
Where this idea is useful
A practical use
Two cities with different baseline employment levels can still inform a policy comparison if their untreated changes would have been parallel.
A common misconception
“Different starting levels invalidate difference in differences.”
Levels may differ while untreated changes remain parallel. Conversely, similar starting levels do not establish the required counterfactual trend.
What this explanation leaves out
- The no-policy line is known only because the data are synthetic. Pre-period agreement does not prove future parallel trends. No staggered treatment timing, spillovers, uncertainty, or compositional changes are modelled.
Does a matching pretrend prove the assumption?
No. Pre-period evidence can challenge an assumption, but cannot establish an unobserved post-policy counterfactual by itself.
Why should your chosen comparison group reproduce the treated group's change without intervention?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.