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 (such as squared and cubic terms and interactions) of covariates and then achieves approximate balance on the expanded features using ridge penalties with a hierarchical structure. Compared with entropy balancing, this extension relaxes model dependency and improves the robustness of causal estimates while avoiding optimization failure or highly concentrated weights. It prevents specification searches by minimizing user discretion in selecting features to balance on and 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 R package, hbal, to facilitate implementation.