Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects

Abstract: Many causal estimands are only partially identifiable since they depend on the unobservable joint distribution between potential outcomes. Stratification on pretreatment covariates can yield sharper bounds; however, unless the covariates are discrete with relatively small support, this approach typically requires binning covariates or estimating the conditional distributions of the potential outcomes given the covariates. Binning can result in substantial efficiency loss and become challenging to implement, even with a moderate number of covariates. Estimating conditional distributions, on the other hand, may yield invalid inference if the distributions are inaccurately estimated, such as when a misspecified model is used or when the covariates are high-dimensional. In this paper, we propose a unified and model-agnostic inferential approach for a wide class of partially identified estimands. Our method, based on duality theory for optimal transport problems, has four key properties. First, in randomized experiments, our approach can wrap around any estimates of the conditional distributions and provide uniformly valid inference, even if the initial estimates are arbitrarily inaccurate. A simple extension of our method to observational studies is doubly robust in the usual sense. Second, if nuisance parameters are estimated at semiparametric rates, our estimator is asymptotically unbiased for the sharp partial identification bound. Third, we can apply the multiplier bootstrap to select covariates and models without sacrificing validity, even if the true model is not selected. Finally, our method is computationally efficient. Overall, in three empirical applications, our method consistently reduces the width of estimated identified sets and confidence intervals without making additional structural assumptions.