Covariate balancing using the integral probability metric for causal inference
This addresses the issue of model misspecification and high variance in weighting methods for causal inference, offering a more robust approach for researchers and practitioners.
The paper tackles the problem of covariate balancing in causal inference by using the integral probability metric (IPM) to determine optimal weights, proving that the estimator is consistent without requiring correct model specification and showing it outperforms existing methods with large margins in finite samples.
Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.