On the use of synthetic difference-in-differences approach with (-out) covariates: The case study of Brexit referendum
通过英国脱欧公投数据和蒙特卡洛模拟，比较了合成双重差分（SDID）与其他合成控制方法的优劣，发现SDID能同时最小化外推和插值偏差，且估计的脱欧对英国GDP影响高于以往文献。
.The synthetic control (SC) method has been a popular and dominant method for evaluating treatment and intervention effects in the last two decades. The method is powerful yet very intuitive to use for both empirical researchers and policy experts, but it is not without shortcomings. As a response to this, the new demeaned SC (DSC) and synthetic difference-in-differences (SDID) approaches were introduced in the literature. Focusing on these two estimators, we evaluate the relative benefits of using DSC and SDID using in-sample placebo analysis on the real data on the Brexit referendum and an extensive Monte Carlo study. We also compare these estimators with the augmented SC (ASCM) and the matching and SC (MASC) estimators and show that while the conventional SC and matching estimators only minimize the extrapolation and the interpolation biases, respectively, the SDID estimator minimizes both biases. In our empirical study, we find that the estimated effect of the Brexit referendum on UK GDP at the end of 2018 and 2019 is higher than previously documented in the literature.