Covariate balance aims to eliminate the correlation between covariates and treatment variables.The estimation methods for causal inference which incorporate covariate balance are less prone to introduce extreme weights and tend to be more robust and accurate in estimation.There are lots of studies on the covariate balance under binary treatment variables,while the covariate balance under continuous treatment variables still needs further studies.Moreover,the existing research realizes covariate balance based on the perspective of balance weight directly.The corresponding optimizations are nonlinear programming with equality and inequality constraints,which leads to complex optimization solutions and limitations for large samples especially for microdata.To avoid the above deficiencies,this paper proposes a covariate balance method under continuous treatment variables based on generalized propensity score,which makes the weighted sample means of approximation sieves of covariates equal to the sample means of approximation sieves of covariates,and the corresponding estimator of average dose response function is unbiased asymptotically and consistent.In particular,the optimization function is strictly convex without any constraint,and accordingly the optimization function has a unique solution and the optimization solution is simple.Hence our method is suitable for large samples,especially for microdata.This paper also proposes a special J-fold cross validation to select the order of the approximation sieves which could make our method data-driven.The numerical simulations show that the proposed method obtains high estimation accuracy.By applying the method to the data of China Family Panel Studies,this paper demonstrates that the puzzle of U-shaped age saving profile exists in China,and the age at inflection point is 42.
关键词
因果推断/协变量平衡/连续处理变量/年龄-储蓄率之谜
Key words
Causal Inference/Covariate Balance/Continuous Treatment Variables/Puzzle of Age Saving Rate
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