Uncertainty quantification is a fundamental problem in the analysis and interpretation of synthetic control (SC) methods. We develop conditional prediction intervals in the SC framework, and provide conditions under which these intervals offer finite-sample probability guarantees. Our method allows for covariate adjustment and non-stationary data. The construction begins by noting that the statistical uncertainty of the SC prediction is governed by two distinct sources of randomness: one coming from the construction of the (likely misspecified) SC weights in the pre-treatment period, and the other coming from the unobservable stochastic error in the post-treatment period when the treatment effect is analyzed. Accordingly, our proposed prediction intervals are constructed taking into account both sources of randomness. For implementation, we propose a simulation-based approach along with finite-sample-based probability bound arguments, naturally leading to principled sensitivity analysis methods. We illustrate the numerical performance of our methods using empirical applications and a small simulation study. \texttt{Python}, \texttt{R} and \texttt{Stata} software packages implementing our methodology are available.

翻译：在分析和解释合成控制(SC)方法方面,不确定性的量化是一个根本性问题。我们在SC框架内制定有条件的预测间隔,并提供这些间隔提供有限概率保障的条件。我们的方法允许共变调整和非静止数据。构建开始时指出,SC预测的统计不确定性由两种不同的随机性来源决定:一种来源是预处理期间(可能误判)SC重量的构造,另一种来源是分析处理效果时后处理期间无法观测的误差。因此,我们提议的预测间隔是在考虑到随机性两种来源的情况下构建的。为了实施,我们建议一种基于模拟的方法,加上基于有限抽样的概率约束参数,自然导致有原则的敏感度分析方法。我们用实验应用和小型模拟研究来说明我们方法的数字性表现。执行我们方法的软件包是\ texttt{Python},\textt{R}和\tutt{Stata}。