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

Abstract

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.

Cited by in corpus (5)

• Estimation and Inference for Synthetic Control Methods with Spillover Effects
• Synthetic Interventions
• How well can we learn large factor models without assuming strong factors?
• Matching Estimators with Few Treated and Many Control Observations
• Efficient and minimal length parametric conformal prediction regions