|Date:||12:30 11 December 2018 - 13:30 11 December 2018|
|Speaker:||Kaspar Wüthrich UCSD|
|Venue:||Institute for Fiscal Studies|
This paper studies inference on treatment effects in aggregate panel data settings with a single treated unit and many control units. 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 classical synthetic control and difference-in-differences as special cases. We propose a K-fold cross-fitting procedure to remove the bias induced by the estimation of the counterfactuals. To avoid the estimation of the long run variance, we construct a self-normalized t-statistic, which has an asymptotically pivotal distribution (a student t-distribution). As a consequence, our procedure very easy to implement. The proposed method has several theoretical advantages. First, it does not rely on any sparsity assumptions. Second, it does not rely on the correct specification of the linear model. Third, compared to the naive difference-in-mean estimator, our method is equally efficient or more efficient in terms of asymptotic variance. The proposed method demonstrates an excellent performance in simulation experiments, and is taken to a data application, where we re-evaluate the economic consequences of terrorism.