The synthetic control method: Small T, small N Monte Carlo evidence and an application to the effects of privatizing probation services on revoke rates

Relying on synthetic controls to estimate treatment effects recently gained popularity in applied econometrics. The small sample properties of the synthetic control estimator are however not suffciently investigated and even the proofs of consistency impose a factor model and require either the pre-treatment period or the pre-treatment period and the size of the donor pool going to infinity. Since applications often ignore the lack of statistical foundation in small samples, a small T small N Monte Carlo study covering standard econometric models like the ones from Differences-in-Differences setups, heterogeneous ADLX models with and without unit roots and random coeffcient models is conducted. The results suggest that the estimator is frequently unbiased, that unit roots are problematic and that a main placebo test has good size and mediocre power properties. Furthermore, the synthetic control method is used to estimate the causal effect of outsourcing probation and parole services on revoke rates by exploiting a natural experiment in Germany. Results provide evidence against increases in revoke rates due to outsourcing.