Adaptive Experimental Design Using the Propensity Score
针对多波次或重复的社会实验，提出利用第一阶段数据选择第二阶段的条件处理分配规则（即倾向得分），以最小化平均处理效应估计的渐近方差，提高因果效应估计效率。
Many social experiments are run in multiple waves or replicate earlier social experiments. In principle, the sampling design can be modified in later stages or replications to allow for more efficient estimation of causal effects. We consider the design of a two-stage experiment for estimating an average treatment effect when covariate information is available for experimental subjects. We use data from the first stage to choose a conditional treatment assignment rule for units in the second stage of the experiment. This amounts to choosing the propensity score , the conditional probability of treatment given covariates. We propose to select the propensity score to minimize the asymptotic variance bound for estimating the average treatment effect. Our procedure can be implemented simply using standard statistical software and has attractive large-sample properties.