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We expand upon the simulation study of Setodji et al. (2017) which comparedthree promising balancing methods when assessing the average treatment effecton the treated for binary treatments: generalized boosted models (GBM),covariate-balancing propensity scores (CBPS), and entropy balance (EB). Thestudy showed that GBM can outperform CBPS and EB when there are likely to benon-linear associations in both the treatment assignment and outcome models andCBPS and EB are fine-tuned to obtain balance only on first order moments. Weexplore the potential benefit of using higher-order moments in the balancingconditions for CBPS and EB. Our findings showcase that CBPS and EB should, bydefault, include higher order moments and that focusing only on first momentscan result in substantial bias in both CBPS and EB estimated treatment effectestimates that could be avoided by the use of higher moments.

Balancing Higher Moments Matters for Causal Estimation: Further Context for the Results of Setodji et al. (2017)