# Prediction Intervals for Synthetic Control Methods

arXiv: https://arxiv.org/abs/1912.07120 · HTML: https://mlsanity.com/paper/1912.07120/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2019.

## Built on by (most cited first, 2 of 2)

- [Asymptotically Unbiased Synthetic Control Methods by Moment Matching](https://mlsanity.com/paper/2307.11127/) (2023)
- [Assessing the Impact: Does an Improvement to a Revenue Management System Lead to an Improved Revenue?](https://mlsanity.com/paper/2101.10249/) (2021)

## Abstract (arXiv)

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. textttPython, textttR and textttStata software packages implementing our methodology are available.