An Alternative to Synthetic Control for Models with Many Covariates Under Sparsity

The synthetic control method is a an econometric tool to evaluate causal effects when only one unit is treated. While initially aimed at evaluating the effect of large-scale macroeconomic changes with very few available control units, it has increasingly been used in place of more well-known microeconometric tools in a broad range of applications, but its properties in this context are unknown. This paper introduces an alternative to the synthetic control method, which is developed both in the usual asymptotic framework and in the high-dimensional scenario. We propose an estimator of average treatment effect that is doubly robust, consistent and asymptotically normal. It is also immunized against first-step selection mistakes. We illustrate these properties using Monte Carlo simulations and applications to both standard and potentially high-dimensional settings, and offer a comparison with the synthetic control method.