关键词: 因果推断, 倾向得分, 能源距离, 协变量平衡

Abstract: In this paper, we construct some weights based on propensity score, and utilize energy distance to respectively measure the differences between the weighted distributions of the covariates with respect to the treatment group and the control group and the distribution of the covariates with respect to the population. By minimizing the energy distance, optimal distribution balance has been reached, and the propensity score and the average treatment effect are estimated consequently. Our optimization is without only constraint, and exists unique solution. Moreover, the average treatment effect estimator is root n consistent and obtains good performance in accuracy. This paper applies the method to investigate the effect of pension insurance on fertility intention, the result is more reliable compared with regression analysis.

Key words: Causal Inference, Propensity Score, Energy Distance, Covariate Balance