# An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls

arXiv: https://arxiv.org/abs/1712.09089 · HTML: https://mlsanity.com/paper/1712.09089/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2017.

## Built on by (most cited first, 30 of 36)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Stable Conformal Prediction Sets](https://mlsanity.com/paper/2112.10224/) (2021)
- [Policy Analysis using Synthetic Controls in Continuous-Time](https://mlsanity.com/paper/2102.01577/) (2021)
- [Conformal Prediction via Regression-as-Classification](https://mlsanity.com/paper/2404.08168/) (2024)
- [Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders](https://mlsanity.com/paper/2303.02320/) (2023)
- [Diverse Counterfactual Explanations for Anomaly Detection in Time Series](https://mlsanity.com/paper/2203.11103/) (2022)
- [Root-finding Approaches for Computing Conformal Prediction Set](https://mlsanity.com/paper/2104.06648/) (2021)
- [Estimating Potential Outcome Distributions with Collaborating Causal Networks](https://mlsanity.com/paper/2110.01664/) (2021)
- [Synthetically Controlled Bandits](https://mlsanity.com/paper/2202.07079/) (2022)
- [Learning Treatment Effects in Panels with General Intervention Patterns](https://mlsanity.com/paper/2106.02780/) (2021)
- [Synthetic Control As Online Linear Regression](https://mlsanity.com/paper/2202.08426/) (2022)
- [Distribution-Free Matrix Prediction Under Arbitrary Missing Pattern](https://mlsanity.com/paper/2305.11640/) (2023)
- [Distribution-Free Finite-Sample Guarantees and Split Conformal Prediction](https://mlsanity.com/paper/2210.14735/) (2022)
- [Conformalization of Sparse Generalized Linear Models](https://mlsanity.com/paper/2307.05109/) (2023)
- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Spillover Detection for Donor Selection in Synthetic Control Models](https://mlsanity.com/paper/2406.11399/) (2024)
- [Deep Learning for Economists](https://mlsanity.com/paper/2407.15339/) (2024)
- [Synthetic Design: An Optimization Approach to Experimental Design with Synthetic Controls](https://mlsanity.com/paper/2112.00278/) (2021)
- [Causal Dependence Plots](https://mlsanity.com/paper/2303.04209/) (2023)
- [Forecasting Algorithms for Causal Inference with Panel Data](https://mlsanity.com/paper/2208.03489/) (2022)
- [Heterogeneous Synthetic Learner for Panel Data](https://mlsanity.com/paper/2212.14580/) (2022)
- [Asymptotically Unbiased Synthetic Control Methods by Moment Matching](https://mlsanity.com/paper/2307.11127/) (2023)
- [Structured Learning of Compositional Sequential Interventions](https://mlsanity.com/paper/2406.05745/) (2024)
- [Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces](https://mlsanity.com/paper/2507.15741/) (2025)
- [Shapes as Product Differentiation: Neural Network Embedding in the Analysis of Markets for Fonts](https://mlsanity.com/paper/2107.02739/) (2021)
- [ClusterSC: Advancing Synthetic Control with Donor Selection](https://mlsanity.com/paper/2503.21629/) (2025)
- [Time-Aware Synthetic Control](https://mlsanity.com/paper/2601.03099/) (2026)

## Abstract (arXiv)

We introduce new inference procedures for counterfactual and synthetic control methods for policy evaluation. We recast the causal inference problem as a counterfactual prediction and a structural breaks testing problem. This allows us to exploit insights from conformal prediction and structural breaks testing to develop permutation inference procedures that accommodate modern high-dimensional estimators, are valid under weak and easy-to-verify conditions, and are provably robust against misspecification. Our methods work in conjunction with many different approaches for predicting counterfactual mean outcomes in the absence of the policy intervention. Examples include synthetic controls, difference-in-differences, factor and matrix completion models, and (fused) time series panel data models. Our approach demonstrates an excellent small-sample performance in simulations and is taken to a data application where we re-evaluate the consequences of decriminalizing indoor prostitution. Open-source software for implementing our conformal inference methods is available.