Lagged Outcomes, Lagged Predictors, and Lagged Errors: A Clarification on Common Factors

Debate on the use of lagged dependent variables has a long history in political science. The latest contribution to this discussion is Wilkins (2018, Political Science Research and Methods, 6, 393–411), which advocates the use of an ADL(2,1) model when there is serial dependence in the outcome and disturbance. While this specification does offer some insurance against serially correlated disturbances, this is never the best (linear unbiased estimator) approach and should not be pursued as a general strategy. First, this strategy is only appropriate when the data-generating process (DGP) actually implies a more parsimonious model. Second, when this is not the DGP—e.g., lags of the predictors have independent effects—this strategy mischaracterizes the dynamic process. We clarify this issue and detail a Wald test that can be used to evaluate the appropriateness of the Wilkins approach. In general, we argue that researchers need to always: (i) ensure models are dynamically complete and (ii) test whether more restrictive models are appropriate.