Synthetic Control Method: Inference, Sensitivity Analysis and Confidence Sets

Abstract We extend the inference procedure for the synthetic control method in two ways. First, we propose parametric weights for the p-value that includes the equal weights benchmark of Abadie et al. [ 1 ]. By changing the value of this parameter, we can analyze the sensitivity of the test’s result to deviations from the equal weights benchmark. Second, we modify the RMSPE statistic to test any sharp null hypothesis , including, as a specific case, the null hypothesis of no effect whatsoever analyzed by Abadie et al. [ 1 ]. Based on this last extension, we invert the test statistic to estimate confidence sets that quickly show the point-estimates’ precision, and the test’s significance and robustness. We also extend these two tools to other test statistics and to problems with multiple outcome variables or multiple treated units. Furthermore, in a Monte Carlo experiment, we find that the RMSPE statistic has good properties with respect to size, power and robustness. Finally, we illustrate the usefulness of our proposed tools by reanalyzing the economic impact of ETA’s terrorism in the Basque Country, studied first by Abadie and Gardeazabal [ 2 ] and Abadie et al. [ 3 ].