Abstract
We propose a practical and robust method for making inferences on average treatment effects estimated by synthetic controls. We develop a -fold cross-fitting procedure for bias correction. To avoid the difficult estimation of the long-run variance, inference is based on a self-normalized -statistic, which has an asymptotically pivotal -distribution. Our -test is easy to implement, provably robust against misspecification, and valid with stationary and non-stationary data. It demonstrates an excellent small sample performance in application-based simulations and performs well relative to other methods. We illustrate the usefulness of the -test by revisiting the effect of carbon taxes on emissions.