Estimating Policy Effects using Lagged Outcome Values to Impute Counterfactuals 

Abstract: Causal inference requires estimation of counterfactuals.  Despite the recent popularity of “vertical” methods (predictions based on outcomes in untreated units in the same period) such as the synthetic control method, there is little consideration of “horizontal” estimators which predict counterfactuals using lagged outcomes.  We discuss implementation of “lagged outcome models,” highlighting that this approach has the advantage of leveraging cross-unit (independent) variation instead of within-unit (serially-correlated) variation. We recommend a test to guide whether to exploit horizontal or vertical information and apply this test to six applications from the literature.  Simulations suggest that using lagged outcomes outperforms many popular estimators.