Higher Moments for Optimal Balance Weighting in Causal Estimation.

Area of Science:

• Causal inference
• Statistical modeling
• Health econometrics

Background:

• Estimating the average treatment effect on the treated (ATT) is crucial for policy and research.
• Generalized boosted models (GBM), covariate-balancing propensity scores (CBPS), and entropy balance (EB) are advanced methods for ATT estimation.
• Previous research indicated GBM's superiority under specific nonlinear conditions when CBPS and EB used only first-order moments.

Purpose of the Study:

• To investigate the impact of higher-order moments on the performance of CBPS and EB methods for ATT estimation.
• To compare the bias reduction achieved by incorporating higher-order moments versus relying solely on first-order moments in CBPS and EB.

Main Methods:

• Simulation study expanding on a previous comparison of GBM, CBPS, and EB.
• Systematic evaluation of CBPS and EB with balancing conditions including first-order and higher-order moments.
• Assessment of treatment effect estimate bias under varying model specifications.

Main Results:

• Covariate-balancing propensity scores and entropy balance methods benefit substantially from including higher-order moments in balancing conditions.
• Focusing exclusively on first-order moments in CBPS and EB can lead to significant bias in estimated treatment effects.
• The inclusion of higher-order moments in CBPS and EB mitigates bias, improving the accuracy of average treatment effect on the treated estimates.

Conclusions:

• Covariate-balancing propensity scores and entropy balance methods should incorporate higher-order moments by default for robust ATT estimation.
• Researchers should prioritize using higher-order moments in balancing conditions to avoid potential bias in treatment effect estimates.
• The findings offer practical guidance for improving the reliability of causal inference methods in observational studies.