🔎 Central Issue:
Debate over the use of lagged dependent variables in political science continues. Wilkins (2018) recommends an ADL(2,1) specification when both the outcome and the disturbance show serial dependence. That specification can reduce bias from serially correlated disturbances, but it is not a universally optimal choice.
🔍 What Wilkins (2018) Proposes:
- ADL(2,1) is suggested when the outcome and the error term exhibit serial dependence.
- This specification can offer some protection against serially correlated disturbances.
⚠️ When ADL(2,1) Misleads:
- ADL(2,1) is only appropriate if the data-generating process (DGP) actually implies the more parsimonious model that ADL(2,1) imposes.
- If the true DGP includes independent effects from lags of the predictors, ADL(2,1) mischaracterizes the dynamic process and therefore is not the correct linear model.
- Importantly, ADL(2,1) is never the best linear unbiased estimator (i.e., it should not be treated as a default, universally optimal solution).
🧪 How to Check Whether ADL(2,1) Is Appropriate:
- A Wald test is detailed that evaluates whether the restrictions implied by the Wilkins approach hold in the data.
- The test helps determine whether the more restrictive ADL(2,1) is consistent with the underlying DGP or whether a fuller dynamic specification is required.
✅ Practical Takeaways for Researchers:
- Always ensure models are dynamically complete: include the lag structure that the DGP plausibly implies.
- Test whether more restrictive models (like ADL(2,1)) are appropriate rather than adopting them as a general strategy.
- Use the provided Wald test as a diagnostic before favoring the ADL(2,1) specification.
