The finite sample variance of an inverse propensity weighted estimator is derived in the case of discrete control variables with finite support. The obtained expressions generally corroborate widely-cited asymptotic theory showing that estimated propensity scores are superior to true propensity scores in the context of inverse propensity weighting. However, similar analysis of a modified estimator demonstrates that foreknowledge of the true propensity function can confer a statistical advantage when estimating average treatment effects.

翻译：本文推导了在有限支撑的离散控制变量情形下，逆倾向得分加权估计量的有限样本方差。所得表达式总体上印证了广为引用的渐近理论，即逆倾向加权中估计倾向得分优于真实倾向得分。然而，对一种改进估计量的类似分析表明，在估计平均处理效应时，预先知晓真实倾向函数可带来统计优势。