Hierarchically Regularized Entropy Balancing

We introduce hierarchically regularized entropy balancing as an extension to entropy balancing, a reweighting method that adjusts weights for control group units to achieve covariate balance in observational studies with binary treatments. Our proposed extension expands the feature space by including higher-order terms (including interactions) of covariates and then achieves approximate balance on the expanded features. This method imposes ridge penalties with a hierarchical structure on the higher-order terms. Compared with entropy balancing, this extension relaxes model dependency and improves the robustness of causal estimates while avoiding optimization failure and highly concentrated weights. It prevents specification searches by minimizing user discretion in selecting features to balance on. Our method is also computationally more efficient than kernel balancing, a kernel-based covariate balancing method. We demonstrate its performance through simulations and an empirical example. We develop an open-source package, hbal, in R to facilitate implementation