雙重差分法 (Difference-in-Differences)
Overview
Difference-in-Differences (DID) estimates causal effects by comparing the change in outcomes over time between a treatment group (affected by an intervention) and a control group (unaffected). By differencing out both time-invariant group differences and common time trends, DID isolates the treatment effect under the parallel trends assumption.
When to Use
- Evaluating the impact of a policy, regulation, or intervention
- A natural experiment assigns treatment at a group level (state, industry, firm)
- Panel or repeated cross-section data with pre- and post-treatment periods
- Randomized experiment is infeasible but a plausible control group exists
When NOT to Use
- Parallel trends assumption is violated and cannot be remedied
- Treatment and control groups differ in ways that change over time
- Treatment is self-selected based on anticipated outcomes (anticipation effects)
- Only post-treatment data are available (no pre-treatment baseline)
Assumptions
IRON LAW: DID is valid ONLY if the parallel trends assumption holds —
without it, the estimated treatment effect is biased by differential
pre-existing trends.Key assumptions:
- Parallel trends: absent treatment, treated and control groups would have followed the same trajectory
- No spillover effects from treated to control units (SUTVA)
- Treatment timing is sharp and exogenous
- Composition of groups is stable over time (no differential attrition)
Methodology
Step 1 — Establish Treatment and Control Groups
Define who is treated and when. Verify groups are comparable on pre-treatment observables. Document the treatment event and its timing.
Step 2 — Test Parallel Trends
Plot outcome trends for treatment vs control groups in pre-treatment periods. Run an event-study specification with leads and lags. Pre-treatment coefficients should be statistically insignificant.
Step 3 — Estimate the DID Model
Y = β₀ + β₁×Treat + β₂×Post + β₃×(Treat×Post) + Controls + ε. The coefficient β₃ is the DID estimator. Cluster standard errors at the treatment assignment level. See references/ for staggered adoption extensions.
Step 4 — Robustness Checks
Run placebo tests (fake treatment dates, fake treatment groups). Test sensitivity to control group choice. For staggered DID, use Callaway-Sant'Anna or Sun-Abraham estimators.
Output Format
## DID Analysis: [Policy / Intervention]
### Research Design
| Element | Description |
|---------|-------------|
| Treatment group | [who] |
| Control group | [who] |
| Treatment date | [when] |
| Pre-treatment periods | [range] |
### Parallel Trends Test
| Pre-period lead | Coefficient | S.E. | p-value |
|-----------------|-------------|------|---------|
| t-3 | x.xx | x.xx | x.xx |
| t-2 | x.xx | x.xx | x.xx |
| t-1 | x.xx | x.xx | x.xx |
### DID Estimate
| Specification | β (Treat×Post) | S.E. | p-value | N |
|---------------|----------------|------|---------|---|
| Baseline | x.xx | x.xx | x.xx | xxx |
| With controls | x.xx | x.xx | x.xx | xxx |
### Robustness
- Placebo test result: [pass/fail]
- Alternative control group: [result]
### Limitations
- [Note any assumption violations]Gotchas
- Visual parallel trends are necessary but not sufficient — the assumption is about counterfactual trends
- Too few clusters for clustering standard errors inflates Type I error (use wild bootstrap if clusters < 50)
- Staggered adoption makes the standard two-way FE DID estimator biased (use recent robust estimators)
- Anticipation effects violate the sharp treatment timing assumption
- Differential pre-trends are often "fixed" by adding group-specific trends, but this is fragile
- DID estimates a local average treatment effect on the treated (ATT), not ATE
References
- Angrist, J. D., & Pischke, J.-S. (2009). *Mostly Harmless Econometrics*. Princeton University Press.
- Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-differences with multiple time periods. *Journal of Econometrics*, 225(2), 200-230.
- Goodman-Bacon, A. (2021). Difference-in-differences with variation in treatment timing. *Journal of Econometrics*, 225(2), 254-277.