Combining Matching and Synthetic Control to Trade Off Biases from Extrapolation and Interpolation

Abstract

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 to create an estimator called MASC. We show how to use a rolling-origin cross-validation procedure to train the MASC to resolve trade-offs between interpolation and extrapolation bias. We use a series of empirically-based placebo and Monte Carlo simulations to shed light on when the SC, matching, MASC and penalized SC estimators do (and do not) perform well. Then, we use the MASC re-examine the economic costs of conflicts and find evidence of larger effects than with SC.