This paper proposes a new method to estimate synthetic control weights. We derive the true predictor weights from a standard factor model for potential outputs and show that these can be consistently estimated by OLS or maximum likelihood methods. We focus on post-treatment data and use pre-treatment data solely as predictors. Optimal synthetic control weights are defined as minimizing the post-treatment mean squared synthetic control error. These weights can be found easily by solving a simple quadratic minimization problem. We compare this to the complex standard optimistic bilevel minimization problem and show that the latter may suffer from lack of identification and inconsistencies in the usage of pre-treatment outcomes or other endogenous variables as predictors.
This paper proposes a new method to estimate synthetic control weights. We derive the true predictor weights from a standard factor model for potential outputs and show that these can be consistently estimated by OLS or maximum likelihood methods. We focus on post-treatment data and use pre-treatment data solely as predictors. Optimal synthetic control weights are defined as minimizing the post-treatment mean squared synthetic control error. These weights can be found easily by solving a simple quadratic minimization problem. We compare this to the complex standard optimistic bilevel minimization problem and show that the latter may suffer from lack of identification and inconsistencies in the usage of pre-treatment outcomes or other endogenous variables as predictors.