The PCDID Approach to Treatment Effects Estimation: A Further Investigation

In the present paper, we study the so‐called “PCDID” approach to treatment effects estimation in panels with interactive effects where the factors represent trends whose effect need not be parallel across the cross‐sectional units. Our interest in this step‐wise approach originates with the observation that the interactive effects are ignored in the first step, which should not be possible without affecting subsequent steps. We confirm that the estimated second‐step factors are inconsistent in the empirically relevant scenario where the included covariates are correlated with the true factors. Interestingly enough, though, fixed effects demeaning, which is in theory unnecessary since fixed effects are special interactive effects, is shown to restore consistency of the final‐step average treatment effects estimate; however, only under special circumstances. As a general solution to the inconsistency of the estimated factors, we propose an iterated PCDID version.