On the use of synthetic difference-in-differences approach with (-out) covariates: The case study of Brexit referendum

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.