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Abstract:
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Imbalance in covariate distributions leads to biased estimates of causal effects. Weighting methods attempt to correct this imbalance but rely on specifying models for the treatment assignment mechanism, which is unknown in observational studies. This leaves researchers to choose the proper weighting method and the appropriate covariate functions for these models without knowing the correct combination to achieve distributional balance. In response to these difficulties, we propose a nonparametric generalization of several other weighting schemes found in the literature: Causal Optimal Transport. This new method directly targets distributional balance by minimizing optimal transport distances between any source and target population. Our approach is semiparametrically efficient and model-free but can also incorporate any important functions of covariates that a researcher desires to balance. Moreover, we show how this method can provide nonparametric imputations of the missing potential outcomes and give rates of convergence for this estimator. We find that Causal Optimal Transport outperforms competitor methods when both the propensity score and outcome models are misspecified.
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