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 difference-in-differences and synthetic control as special cases. We propose a K-fold cross-fitting procedure to remove the bias induced by regularization . To avoid the  estimation of the long run variance, we construct a self-normalized t-statistic. The test statistic has an asymptotically pivotal distribution (a student t-distribution with K-1 degrees of freedom) , which makes our procedure very easy to implement . Our approach has several theoretical advantages. First, it does not rely on any sparsity assumptions. Second, it is fully robust against misspecification of the linear model. Third, it is more efficient than difference-in-means and difference-in-differences estimators. 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 .
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-test 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 many popular estimators. The proposed method is easy to implement , provably robust against misspecification , and demonstrates an excellent small sample performance .
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studies inference on treatment effects in aggregate panel data settings with a single treated unit and many control units. We propose new methods
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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
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to remove the bias induced by regularization
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long run variance, we construct
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t-statistic. The test statistic
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distribution (a student
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with K-1 degrees of freedom) , which makes our procedure very
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. Our approach has several theoretical advantages. First, it does not rely on any sparsity assumptions. Second, it is fully
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of the linear model. Third, it is more efficient than difference-in-means and difference-in-differences estimators. The proposed method
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performance in simulation experiments, and is taken to a data application, where we re-evaluate the economic consequences of terrorism
small sample performance