Primary Submission Category: Synthetic Control Method
Estimating Policy Effects using Lagged Outcome Values to Impute Counterfactuals
Authors: Beth Ann Griffin, David Powell, Tal Wolfson,
Presenting Author: Beth Ann Griffin*
Causal inference requires estimation of counterfactuals. With panel data, it is common to use information from the pre-treatment period of the treated units combined with information from untreated units to impute these counterfactual outcomes. Difference-in-differences methods, such as two-way fixed effects models, have frequently been used to predict counterfactual outcomes assuming additive fixed unit and time effects. Despite the growth of panel data estimators which impute counterfactuals, little research considers using lagged outcomes to directly predict post-treatment counterfactual outcomes. We discuss implementation of a “lagged outcome model (LOM)”. The LOM estimator involves regressing the outcome variable on pre-treatment period lags using untreated units only, penalizing the inclusion of additional lags. Given the resulting estimates, it is then possible to impute the counterfactual for the treated observations. We compare the LOM approach to commonly used methods in applied work including the synthetic control method, synthetic difference-in-differences, synthetic control estimation with bias-correction, de-meaned synthetic control estimation, the matrix completion method, and a penalized vertical regression. The LOM performs well relative to these estimators in simulations regardless of pre-period length. These results suggest that LOM should become a more standard part of the panel data imputation toolkit for empirical researchers.