Uncertainty quantification is a fundamental problem in the analysis and interpretation of synthetic control (SC) methods. We develop  prediction intervals in the canonical SC framework, and provide conditions under which these intervals offer finite-sample probability guarantees. Our  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 multiplier bootstrap approach along with finite-sample-based probability bound arguments  . We illustrate the  performance of our proposed prediction intervals in the context of three empirical applications from the SC literature .
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, among other practically relevant features. 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 .
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conditional
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canonical
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method allows for covariate adjustment and non-stationary data, among other practically relevant features. The
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multiplier bootstrap
simulation-based
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, naturally leading to principled sensitivity analysis methods
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numerical
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proposed prediction intervals in the context of three empirical applications from the SC literature
methods using empirical applications and a small simulation study