On “Imputation of Counterfactual Outcomes When the Errors Are Predictable”: Viewing the PUP as the DID and the LDV

I discuss the practical unbiased predictor (PUP; Gonçalves and Ng) from the viewpoint of the literature on identification in event studies. The PUP can be seen as the prediction based on a generalized estimand that encompasses both the difference-in-differences (DID) and the lagged dependent variable (LDV). This feature of the PUP allows for a doubly robust property that the identification is achieved when either the parallel trend assumption or the LDV assumption holds at the expense of richer data. Furthermore, in this case, the bracketing property implies that the PUP identifying the true causal effect is bounded below by the LDV and above by the DID.