关键词: 合成控制法, 安慰剂检验, 自抽样, 置信区间

Abstract: The inference of the synthetic control method mainly relies on the “placebo test”, which is based on the permutation test. However, because of the poor fitting in the pre-intervention period which results in ineffective inference, previous studies choose to subjectively delete the control units with poor pre-intervention fitting. This article introduces a process of quasi-standardized transformation to eliminate the noise component in the placebo test in order to improve the comparability of treatment effects in the post-intervention period and to ensure that we can implement placebo tests without subjectively deleting any units. We find that our method has several advantages: Firstly, it can effectively improve the comparability of control units and treated unit during the pre-intervention period, reducing the influence of noise components on the test result. Our Monte Carlo simulation results further proves the robustness of this conclusion. Secondly, it avoids the manual deletion of the poor fitting control units so that the inference can be more objective. Finally, we can use the data, transformed by the quasi-standardized processing, and the bootstrap method to construct the confidence interval of the treatment effects, thereby ensuring that our statistical inference framework for the synthetic control method can be consistent with traditional inference methods.

Key words: Synthetic Control Method, Placebo Test, Bootstrap, Confidence Interval