Inference under Covariate-Adaptive Randomization with Imperfect Compliance
协变量自适应随机化与不完全依从下的推断AI 解读 ↓
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协变量自适应随机化与不完全依从下的推断
- 研究问题
- 当随机试验按基线协变量分层平衡分配，但参与者可内生决定是否接受二元处理时，如何估计和推断局部平均处理效应？
- 方法与思路
- 作者研究完全饱和的工具变量回归型 LATE 估计量，推导渐近方差及一致标准误，并在特定分配比例条件下比较其他估计量。
- 材料陈述的贡献
- 摘要称该估计量渐近正态，配套检验渐近精确；方差刻画还用于依据试点数据设计降低假想试验估计方差的策略。
- 阅读关注点
- 应核对 LATE 的识别条件、分层随机化对方差的影响、不同工具变量估计量的适用范围，以及试验优化策略所需信息。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未展开识别条件与方差公式，也未给出模拟或应用的具体数值。
原文摘要
This paper studies inference in a randomized controlled trial (RCT) with covariate-adaptive randomization (CAR) and imperfect compliance of a binary treatment. In this context, we study inference on the LATE. As in Bugni et al. (2018,2019), CAR refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve "balance" within each stratum. In contrast to these papers, however, we allow participants of the RCT to endogenously decide to comply or not with the assigned treatment status. We study the properties of an estimator of the LATE derived from a "fully saturated" IV linear regression, i.e., a linear regression of the outcome on all indicators for all strata and their interaction with the treatment decision, with the latter instrumented with the treatment assignment. We show that the proposed LATE estimator is asymptotically normal, and we characterize its asymptotic variance in terms of primitives of the problem. We provide consistent estimators of the standard errors and asymptotically exact hypothesis tests. In the special case when the target proportion of units assigned to each treatment does not vary across strata, we can also consider two other estimators of the LATE, including the one based on the "strata fixed effects" IV linear regression, i.e., a linear regression of the outcome on indicators for all strata and the treatment decision, with the latter instrumented with the treatment assignment. Our characterization of the asymptotic variance of the LATE estimators allows us to understand the influence of the parameters of the RCT. We use this to propose strategies to minimize their asymptotic variance in a hypothetical RCT based on data from a pilot study. We illustrate the practical relevance of these results using a simulation study and an empirical application based on Dupas et al. (2018).