  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. These may be used to circumvent
cross-validation when selecting either the weighting matrix in the SCM with
covariates, or the tuning parameter in model averaging or penalized variants of
SCM. We assess the impact of car license rationing in Tianjin and make a novel
use of SCM; while a natural match is available, 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 model averaging or penalized
variants of SCM and, with short pre-treatment series, model selection per
information criteria outperforms that per cross-validation.
