The Problem: Misspecifying the Lag Structure
In event-study and carryover models, the lag structure (how long past treatments affect outcomes) is crucial. If you estimate effects with the wrong lag (m), your estimand is not the true causal effect, but a misspecified version. This can bias results and mislead inference.
Simulation Study: What Goes Wrong?
Section 5.5 explores this with simulations:
- Setup: Simulate outcomes under a known lag structure, then estimate effects using the correct lag, a too-short lag, and a too-long lag.
- Inference: Compare exact and asymptotic inference methods for hypothesis testing.
Key Findings
- Exact vs. Asymptotic Inference: Exact inference yields smaller p-values (stronger evidence against the null) than asymptotic inference, especially as the degree of misspecification increases.
- Misspecified Estimands: When the lag is misspecified, the estimated effect is not the true causal effect, but a “misspecified” version. This can be misleading if interpreted causally.
- Variance Estimation: Asymptotic inference uses a conservative upper bound for variance, leading to larger p-values and less power.
Practical Implications
- Always check your lag structure. If you’re unsure, use diagnostic tools or model selection procedures to test different lag lengths.
- Interpret with caution: If the lag is misspecified, your estimates may not reflect the true effect dynamics.
- Prefer exact inference when possible, especially in small samples or when model assumptions are in doubt.
Summary
Misspecifying the lag structure in event-study or carryover models can lead to biased estimands and misleading inference. Use simulation, diagnostics, and robust inference methods to guard against these pitfalls.