Title: Asymptotic properties of synthetic control method Authors:  Xiaomeng Zhang - Academy of Mathematics and Systems Science, Chinese Academy of Sciences (China) [presenting]
Wendun Wang - Erasmus University Rotterdam (Netherlands)
Xinyu Zhang - Academy of Mathematics and Systems Science, Chinese Academy of Sciences (China)
Abstract: The aim is to provide new insights into the asymptotic properties of the synthetic control method (SCM). It is shown that the synthetic control (SC) weight converges to a limiting weight that minimizes the mean squared prediction risk of the treatment-effect estimator when the number of pretreatment periods goes to infinity, and it is also quantified the rate of convergence. Observing the link between the SCM and model averaging, further the asymptotic optimality of the SC estimator is established under imperfect pre-treatment fit, in the sense that it achieves the lowest possible squared prediction error among all possible treatment effect estimators that are based on an average of control units, such as matching, inverse probability weighting and difference-in-differences. The asymptotic optimality holds regardless of whether the number of control units is fixed or divergent. Thus, the results provide justifications for the SCM in a wide range of applications. The theoretical results are verified via simulations.