Hierarchically Regularized Entropy Balancing

• In Event: Causal Inference

Abstract

Entropy balancing is a popular reweighting approach to balance pre-treatment covariates between the treated and the control units for the purpose of causal inference. However, it has two main drawbacks. First, it does not automatically balance on higher-order terms (and interactions) of the covariates. Second, there may be too many features to be balanced, especially when higher order terms are included. In this paper, we extend entropy balancing by applying a hierarchical (ridge) penalty to a series expansion of the the covariates. Compared with the original method, the new approach has several advantages: it (1) improves feasibility and stability when the covariate space is large; (2) relaxes model dependency while preventing overfitting; and (3) minimizes user discretion. It is computationally more efficient than kernel balancing, another popular covariate balance method. We demonstrate its performance through simulations and two empirical studies.

Authors

• Yiqing Xu, Stanford University

• Eddie Yang, University of California, San Diego