Practical and robust $t$-test based inference for synthetic control and related methods

Abstract

This paper proposes a practical and robust method for making inference on average treatment effects estimated by synthetic control and related methods. We develop a $K$-fold cross-fitting procedure for bias-correction. To avoid the difficult estimation of the long-run variance, inference is based on a self-normalized $t$-statistic, which has an asymptotically pivotal $t$-distribution. Our procedure only requires consistent (in $\ell_2$-norm) estimation of the parameters, which can be verified for synthetic control and many other popular estimators. The proposed method is easy to implement, provably robust against misspecification, more efficient than difference-in-differences, valid with non-stationary data, and demonstrates an excellent small sample performance.