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Estimation of average treatment effects based on parametric propensity score model
Authors:Lili Yao  Zhihua Sun  Qihua Wang
Institution:1. Academy of Mathematics and System Science, Chinese Academy of Science, China;2. Department of Statistics and Actuary Sciences, University of Hong Kong, Hong Kong;3. Department of Statistics, Northwestern University, USA;4. Department of Mathematics, Graduate University of Chinese Academy of Sciences, China
Abstract:In this paper, the estimation of average treatment effects is examined given that the propensity score is of a parametric form with some unknown parameters. Under the assumption that the treatment is ignorable given some observed characteristics, the MLEs for those unknown parameters in the probability assignment model have been achieved firstly and then three estimators have been defined by the inverse probability weighted, regression and imputation methods, respectively. All the estimators are shown asymptotically normal and more importantly, the substantial efficiency gains of the first two estimates have been obtained theoretically compared with the existing estimators in Hahn (1998) and Hirano et al. (2003), i.e., the inverse weighted probability estimator and the regression estimator have smaller asymptotic variances. Our simulation analysis verifies the theoretical results in terms of biases, SEs and MSEs.
Keywords:Average treatment effects  Propensity score  MLE  Inverse probability weighted  Regression and imputation method
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