Why Estimate the Lag Order?
In event-study and carryover models, the lag order $m$ (how many past periods treatment can affect outcomes) is critical. Misspecifying $m$ can bias your results and invalidate inference. Section 5.6 explores how to estimate $m$ using simulation-based procedures.
Simulation-Based Estimation Procedure
- Stepwise Testing: Start with a plausible upper bound for $m$. Sequentially test hypotheses $m \leq k$ for decreasing $k$ (e.g., $m \leq 2$, then $m \leq 1$).
- Inference: For each test, calculate p-values using both exact and asymptotic inference. If the p-value is large, do not reject the null; if small, reject and move to a lower $k$.
- Sample Size Matters: Larger time horizons (T) improve the power of these tests. The authors recommend $T/p > 100$ for reliable inference.
Example: Simulation Results
- With $T = 210$, the p-value for $m \leq 2$ is 0.956 (do not reject); for $m \leq 1$ it is 0.182 (still do not reject).
- With $T = 2010$, the p-value for $m \leq 2$ is 0.760 (do not reject); for $m \leq 1$ it is 0.037 (reject, so $m = 2$ is supported).
- Takeaway: More data (larger $T$) makes it easier to distinguish the correct lag order.
Practical Guidance
- Start with a reasonable upper bound for $m$ based on domain knowledge.
- Use stepwise hypothesis testing to narrow down $m$.
- Ensure your time horizon is long enough for reliable inference.
- Report both exact and asymptotic p-values for transparency.
Summary
Estimating the correct lag order is essential for valid causal inference in event-study and carryover models. Use stepwise testing, sufficient data, and robust inference methods to identify $m$ and avoid misspecification pitfalls.