Abstract We extend the inference procedure for the synthetic control method in two ways. First, we propose parametric weights for the p-value that includes the equal weights benchmark of Abadie et al. [1]. By changing the value of this parameter, we can analyze the sensitivity of the test’s result to deviations from the equal weights benchmark. Second, we modify the RMSPE statistic to test any sharp null hypothesis, including, as a specific case, the null hypothesis of no effect whatsoever analyzed by Abadie et al. [1]. Based on this last extension, we invert the test statistic to estimate confidence sets that quickly show the point-estimates’ precision, and the test’s significance and robustness. We also extend these two tools to other test statistics and to problems with multiple outcome variables or multiple treated units. Furthermore, in a Monte Carlo experiment, we find that the RMSPE statistic has good properties with respect to size, power and robustness. Finally, we illustrate the usefulness of our proposed tools by reanalyzing the economic impact of ETA’s terrorism in the Basque Country, studied first by Abadie and Gardeazabal [2] and Abadie et al. [3].

中文翻译：

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综合控制方法：推理、灵敏度分析和置信集

摘要 我们以两种方式扩展了合成控制方法的推理过程。首先，我们为 p 值提出参数权重，其中包括 Abadie 等人的等权重基准。[1]。通过改变这个参数的值，我们可以分析测试结果对等权重基准偏差的敏感性。其次，我们修改 RMSPE 统计量以测试任何尖锐的零假设，包括作为特定案例，Abadie 等人分析的无影响的零假设。[1]。基于最后一个扩展，我们反转检验统计量以估计置信集，这些置信集可以快速显示点估计的精度以及检验的显着性和稳健性。我们还将这两个工具扩展到其他测试统计数据以及具有多个结果变量或多个处理单元的问题。此外，在蒙特卡罗实验中，我们发现 RMSPE 统计量在大小、功效和稳健性方面具有良好的特性。最后，我们通过重新分析 ETA 恐怖主义在巴斯克地区的经济影响来说明我们提出的工具的有用性，该影响首先由 Abadie 和 Gardeazabal [2] 以及 Abadie 等人进行了研究。[3]。