Statistics and Its Interface

Volume 15 (2022)

Number 3

Estimation of conditional average treatment effect by covariates balance methods

Pages: 312 – 322



Jun Wang (Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming, China)

Changbiao Liu (ollege of Mathematical Sciences, Inner Mongolia Normal University, Hohhot, China)


Conditional average treatment effects estimation is one of the crucial mainstays in observational studies. The conditional average treatment effect is defined as a functional parameter which is used to describe the variation of average treatment effect condition on some covariates. Based on the unconfoundedness assumption, we propose the covariates balance method to estimate the propensity score, and the estimated propensity score is applied to the non-parametric method to estimate the conditional average treatment effect. The proposed method is robust and superior to the parametric approach. The proposed method has a smaller RMSE than the true method when the propensity score model is correct specified. Meanwhile, compared with the kernel method, the proposed method is much more computationally efficient. The proposed estimator is consistent and asymptotic under some regularity conditions. Finally, we apply the proposed method to estimate the effect of maternal smoking on low birth weight infants given the age of mothers.


conditional average treatment effects, covariates balance, heterogeneity, propensity score, unconfoundedness

The authors’ work was supported by the National Natural Science Foundation of China (no. 12101545), the scientific research project of colleges and universities in Inner Mongolia Autonomous Region (no. NJSY21569) and the startup fund project of Introducing High-level Talents in Inner Mongolia Normal University (no. 2020YJRC055).

Received 16 October 2020

Accepted 29 June 2021

Published 14 February 2022