Before revision:  We propose new methods for making inference on average treatment effects in settings where both the number of pre-treatment and the number of post-treatment periods are large. We use linear models to approximate the counterfactual mean outcomes in the absence of the treatment. The counterfactuals are estimated using constrained Lasso, an essentially tuning free regression approach that nests difference-in-differences and synthetic control as special cases. We propose a K-fold cross-fitting procedure to remove the bias induced by regularization .
After revision:  We propose new methods for making inference on average treatment effects estimated by synthetic control and related methods. We develop a K-fold cross-fitting procedure to remove the bias induced by regularization .