Estimating Policy Effects using Lagged Outcome Values to Impute Counterfactuals

Causal inference requires estimation of counterfactual outcomes. Given panel data, it is customary to use unit- and time-specific information to impute counterfactuals. Additive unit and time fixed effects are often used, but a rapidly growing literature has introduced alternative methods to address some of the implicit assumptions in these models and provide better predictions. Despite the growing popularity of “vertical” methods (predictions based on outcomes in untreated units in the same time period) such as the synthetic control method, there is little recent consideration of “horizontal” estimators which predict counterfactuals using lagged, untreated outcomes. We discuss implementation of a “lagged outcome model” and its desirability in standard applied contexts. This approach should be especially useful when the number of control units is large relative to the number of pre-treatment time periods, a standard panel data structure in applied contexts. Further, this paper further highlights that such an approach has the additional advantage of leveraging cross-unit (i.e., independent) variation instead of the within-unit (i.e., serially-correlated) variation needed by vertical regression methods. We recommend a test to guide whether to exploit horizontal or vertical information, and a visualization of the variation available for each type of approach. Simulations suggest that using lagged outcomes outperforms many of the estimators frequently used in applied work. We re-analyze six applications from the literature using the lagged outcome model