Degrees of Freedom and Information Criteria for the Synthetic Control Method
We provide an analytical characterization of the model flexibility of the synthetic control method (SCM) in the familiar form of degrees of freedom. We obtain estimable information criteria, which may be used to circumvent cross-validation when selecting either the tuning parameter in penalized variants of SCM or the weighting matrix in the SCM with covariates. We assess the impact of car license rationing in Tianjin; while a natural match is available, both it and other donors are noisy, inviting the use of SCM to average over approximately matching donors. The very large number of candidate donors calls for penalized variants of SCM and we observe that model selection using information criteria outperforms that based on cross-validation.
econ.EM↗