基于倾向性得分匹配法的平均处理效应的自助法推断

Bootstrap Inference of Propensity Score Matching Estimators for Average Treatment Effects

倾向性得分匹配法是估计平均处理效应的常见方法,但是经典的自助法不能直接用于固定匹配个数时平均处理效应的匹配法估计量的统计推断。把每个个体的被匹配次数视为观测值,这解决了重抽样样本中个体被匹配数不是原样本的一致估计问题,基于此提出了两种解决倾向性得分匹配估计的自助法推断方法,一是将基于欧氏距离匹配法的加权自助法推广至倾向性得分匹配法,二是进一步提出了比前者更简单的直接应用经典自助法的方法。由此提出的两种自助法可以正确估计倾向性得分匹配法的平均处理效应的方差及置信区间,同时更容易实现倾向性得分匹配法估计结果的渐正方差公式。数值模拟部分显示两种自助法随着样本量的增加而与样本误差平方和及Abadie和Imbens的渐近结果越来越接近。最后,将此方法用于2016年中国综合社会调查数据,分别得到了性别、婚姻状况、健康状况等对居民收入影响的平均处理效应。

Propensity score matching method is widely used in the estimation of average treatment effects.However,the classical bootstrap cannot be used directly in the inference of matching estimators for average treatment effects when the number of matches is fixed.We treat the matched times of individuals as samples,which solves the problem of that the matched times from resamples cannot reproduce the distribution of the matched times from original samples.Two methods are proposed to solve how to do bootstrap inference in the estimation of propensity score matching method.First,generalize the method of weighted bootstrap under Euclidean distance matching to propensity score matching.Second,propose a procedure that how to do bootstrap inference directly.Two proposed methods can correctly estimate the variance and confidence intervals of average treatment effects obtained by propensity score matching.The part of simulation indicates that proposed methods have closed results compared with the sum of squares due to error and asymptotic results of propensity scove matching.At last,apply the proposed methods to Chinese general social survey data,which we treat gender,marriage status,health condition and so on as treatment variable respectively,and analyze their average treatment effects on income.