# Uncertainty Quantification in Synthetic Controls with Staggered Treatment Adoption

arXiv: https://arxiv.org/abs/2210.05026 · HTML: https://mlsanity.com/paper/2210.05026/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2022.

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

- [Asymptotically Unbiased Synthetic Control Methods by Moment Matching](https://mlsanity.com/paper/2307.11127/) (2023)
- [Risk-Set Transported Synthetic Control with Difference-in-Differences Adjustment under Staggered Treatment Adoption](https://mlsanity.com/paper/2609.20264/) (2026)

## Abstract (arXiv)

We propose principled prediction intervals to quantify the uncertainty of a large class of synthetic control predictions (or estimators) in settings with staggered treatment adoption, offering precise non-asymptotic coverage probability guarantees. From a methodological perspective, we provide a detailed discussion of different causal quantities to be predicted, which we call causal predictands, allowing for multiple treated units with treatment adoption at possibly different points in time. From a theoretical perspective, our uncertainty quantification methods improve on prior literature by (i) covering a large class of causal predictands in staggered adoption settings, (ii) allowing for synthetic control methods with possibly nonlinear constraints, (iii) proposing scalable robust conic optimization methods and principled data-driven tuning parameter selection, and (iv) offering valid uniform inference across post-treatment periods. We illustrate our methodology with an empirical application studying the effects of economic liberalization on real GDP per capita for Sub-Saharan African countries. Companion software packages are provided in Python, R, and Stata.