On the Efficiency of Highly Stratified Experiments
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高度分层实验的效率
- 研究问题
- 固定大小区组内随机分配二元处理的高度分层设计，能否使朴素矩估计高效估计多类处理效应，且这种效率何时依赖快速平衡？
- 方法与思路
- 作者以已知观测数据函数构造的矩条件统一描述目标参数，比较渐近方差，利用卷积定理推导效率下界并分析快速平衡。
- 材料陈述的贡献
- 摘要称，朴素矩估计可达到其他设计经协变量调整获得的方差和效率界，并给出快速平衡成为达界必要条件的情形。
- 阅读关注点
- 应核对区组构造、区组内处理比例和渐近条件，以及效率界覆盖的估计量类别、分位数及局部平均效应所需额外条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收均未核实；摘要未列出效率与必要性条件，不能直接推断有限样本精度普遍更高。
原文摘要
This paper studies the use of highly stratified designs for the efficient estimation of a large class of treatment effect parameters that arise in the analysis of experiments. By a "highly stratified" design, we mean experiments in which units are divided into blocks of a fixed size and a proportion within each block is assigned to a binary treatment uniformly at random. The class of parameters considered are those that can be expressed as the solution to a set of moment conditions constructed using a known function of the observed data. They include, among other things, average treatment effects, quantile treatment effects, and local average treatment effects as well as the counterparts to these quantities in experiments in which the unit is itself a cluster. In this setting, we establish three results. First, we show that under a highly stratified design, the naïve method of moments estimator achieves the same asymptotic variance as what could typically be attained under alternative treatment assignment mechanisms only through ex post covariate adjustment. Second, we argue that the naïve method of moments estimator under a highly stratified design is asymptotically efficient by deriving a lower bound on the asymptotic variance of regular estimators of the parameter of interest in the form of a convolution theorem. In this sense, highly stratified experiments are attractive because they lead to efficient estimators of treatment effect parameters "by design." Finally, we strengthen this conclusion by establishing conditions under which a "fast-balancing" property of highly stratified designs is in fact necessary for the naïve method of moments estimator to attain the efficiency bound.