30.12 Robustness Checks

A well-executed Difference-in-Differences analysis requires robustness checks to verify the validity of estimated treatment effects and best practices to ensure methodological rigor.

---

30.12.1 Robustness Checks to Strengthen Causal Interpretation

Once the parallel trends assumption is assessed, additional robustness tests ensure that treatment effects are not driven by confounding factors or modeling choices.

1. Varying the Time Window

• Shorter time windows reduce exposure to long-term confounders but risk losing statistical power.
• Longer time windows capture persistent effects but may introduce unrelated policy changes.
• Solution: Estimate the DiD model across different time horizons and check if results are stable.

2. Higher-Order Polynomial Time Trends

• Standard DiD models assume a linear time trend.
• If trends are nonlinear, this assumption may be too restrictive.
• Solution: Introduce quadratic or cubic time trends and verify whether results hold.

3. Testing Alternative Dependent Variables

• The treatment should only affect the expected dependent variable.
• A robustness check involves running the DiD on unrelated dependent variables.
• If treatment effects appear where they should not, this signals a possible identification problem.

4. Triple-Difference (DDD) Strategy

A Triple-Difference (DDD) model adds an additional comparison group to address remaining biases:

$$\begin{aligned} Y_{ijt} &= \alpha + \gamma Treat_{i} + \lambda Post_t + \theta Group_j + \delta_1 (Treat_i \times Post_t) \\ &+ \delta_2 (Treat_i \times Group_j) + \delta_3 (Post_t \times Group_j) \\ &+ \delta_4 (Treat_i \times Post_t \times Group_j) + \epsilon_{ijt} \end{aligned}$$

where:

• $Group_j$ represents a subgroup within treatment/control (e.g., high- vs. low-intensity exposure).

• $\delta_4$ captures the DDD effect, which removes residual biases present in the standard DiD model.

---

30.12.2 Best Practices for Reliable DiD Implementation

To improve the credibility and transparency of DiD estimates, researchers should adhere to the following best practices:

1. Documenting Treatment Cohorts

• Clearly report the number of treated and control units over time.
• If treatment is staggered, adjust for different exposure durations.

2. Checking Covariate Balance & Overlap

• Verify whether the distribution of covariates is similar across treatment and control groups.
• If treatment and control groups differ significantly, consider using matching methods.

3. Conducting Sensitivity Analyses for Parallel Trends

• Apply alternative weighting schemes (e.g., entropy balancing) to reduce dependence on model assumptions.
• Use honestDiD to test robustness under different parallel trends violations.