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
