This paper studies a two-stage model of experimentation, where the researcher first samples representative units from an eligible pool, then assigns each sampled unit to treatment or control. To implement balanced sampling and assignment, we introduce a new family of finely stratified designs that generalize matched pairs randomization to propensities p(x) not equal to 1/2. We show that two-stage stratification nonparametrically dampens the variance of treatment effect estimation. We formulate and solve the optimal stratification problem with heterogeneous costs and fixed budget, providing simple heuristics for the optimal design. In settings with pilot data, we show that implementing a consistent estimate of this design is also efficient, minimizing asymptotic variance subject to the budget constraint. We also provide new asymptotically exact inference methods, allowing experimenters to fully exploit the efficiency gains from both stratified sampling and assignment. An application to nine papers recently published in top economics journals demonstrates the value of our methods.

翻译：本文研究了一个两阶段的实验模型，研究者首先从合格样本池中抽取代表性单位，然后将每个抽取的单位分配到处理组或对照组。为了实现均衡的抽样与分配，我们引入了一类新的精细分层设计，将配对随机化方法推广到倾向性p(x)不等于1/2的情形。我们证明两阶段分层可以在非参数意义上抑制处理效应估计的方差。针对存在异质性成本与固定预算的情况，我们构建并求解了最优分层问题，为最优设计提供了简单的启发式方法。在存在试点数据的情形下，我们证明实施该设计的一致性估计也是有效的，能够在预算约束下最小化渐近方差。我们还提供了新的渐近精确推断方法，使实验者能够充分利用分层抽样与分配带来的效率提升。对近期发表于顶级经济学期刊的九篇论文的应用分析，证明了我们方法的实用价值。