Difference-in-Differences (Diff-in-Diff)
Also known as: diff-in-diff, DiD, Farkların Farkı (Diff-in-Diff)
Difference-in-Differences is a causal-inference method that estimates the effect of an intervention by comparing how a treatment group and a control group change over time. Made famous by Card and Krueger's 1994 minimum-wage study and developed in Angrist and Pischke's Mostly Harmless Econometrics, it isolates the treatment effect as the difference between the two groups' before-after changes.
Key highlights
- Identifies a causal effect from observational data without randomisation, by differencing out fixed group differences and common time shocks.
- Simple to estimate and interpret: the treatment effect is a single interaction coefficient.
- Robust to any time-invariant confounders that differ between the groups, since they cancel in the differencing.
Intuition
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How it works
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When to use it
Use DiD when you have an intervention or policy that affects one group but not another, and you observe outcomes for both groups in at least two periods (before and after). The data should be panel or repeated cross-sections with a continuous or binary outcome, and a reasonable sample of at least about 40 observations. The central requirement is the parallel-trends assumption: in the absence of treatment, the two groups would have moved in parallel. It is not appropriate with only a single period, or when the groups were already on diverging paths.
Strengths & limitations
- Identifies a causal effect from observational data without randomisation, by differencing out fixed group differences and common time shocks.
- Simple to estimate and interpret: the treatment effect is a single interaction coefficient.
- Robust to any time-invariant confounders that differ between the groups, since they cancel in the differencing.
- The whole approach rests on the parallel-trends assumption; if the groups were already diverging, the estimate is biased and the causal interpretation fails.
- Requires at least two time periods — a single cross-section cannot support the difference of differences.
- Small treatment or control groups (n < 40) make standard errors unreliable.
Common pitfalls
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Applications
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Frequently asked
What is the parallel-trends assumption?
It states that, absent the intervention, the treatment and control groups would have followed the same trend over time. DiD relies on this so that the control group's change validly stands in for what the treatment group would have experienced without treatment. You support it by checking that pre-treatment trends were parallel.
Which coefficient is the treatment effect?
The interaction term between the treatment indicator and the post-period indicator. Its coefficient β₃ is the difference-in-differences estimate of the average treatment effect on the treated (ATT).
How many periods and observations do I need?
At least two periods (before and after) are essential, since the method differences over time. A single period cannot identify the effect. A reasonable sample of around 40 or more observations is advised so the standard errors are trustworthy.
What if parallel trends do not hold?
Then the DiD estimate is biased and the causal reading is invalid. A propensity-score matching design that balances the groups on observed characteristics is a common alternative.
Sources
- 1.Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.ISBN 978-0691120355
- 2.Card, D., & Krueger, A. B. (1994). Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania. American Economic Review, 84(4), 772-793.
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Cite this page
ScholarGate. (2026, June 1). Difference-in-Differences. ScholarGate. https://scholargate.app/econometrics/difference-in-differences