Combining Matching and Synthetic Controls to Trade off Biases from Extrapolation and Interpolation

The synthetic control method is widely used in comparative case studies to adjust for differences in pre-treatment characteristics. A major attraction of the method is that it limits extrapolation bias that can occur when untreated units with different pre-treatment characteristics are combined using a traditional adjustment, such as a linear regression. Instead, the SC estimator is susceptible to interpolation bias because it uses a convex weighted average of the untreated units to create a synthetic untreated unit with pre-treatment characteristics similar to those of the treated unit. More traditional matching estimators exhibit the opposite behavior: They limit interpolation bias at the potential expense of extrapolation bias. We propose combining the matching and synthetic control estimators through model averaging. We show how to use a rolling-origin cross-validation procedure to train the model averaging estimator to resolve trade-offs between interpolation and extrapolation bias. We evaluate the estimator through Monte Carlo simulations and placebo studies before using it to re-examine the economic costs of conflicts. Not only does the model averaging estimator perform far better than synthetic controls and other alternatives in the simulations and placebo exercises. It also yields treatment effect estimates that are substantially different from the other estimators