Causal Inference With Interference and Noncompliance in Two-Stage Randomized Experiments

In many social science experiments, subjects often interact with each other and as a result one unit’s treatment influences the outcome of another unit. Over the last decade, a significant progress has been made toward causal inference in the presence of such interference between units. Researchers have shown that the two-stage randomization of treatment assignment enables the identification of average direct and spillover effects. However, much of the literature has assumed perfect compliance with treatment assignment. In this article, we establish the nonparametric identification of the complier average direct and spillover effects in two-stage randomized experiments with interference and noncompliance. In particular, we consider the spillover effect of the treatment assignment on the treatment receipt as well as the spillover effect of the treatment receipt on the outcome. We propose consistent estimators and derive their randomization-based variances under the stratified interference assumption. We also prove the exact relationships between the proposed randomization-based estimators and the popular two-stage least squares estimators. The proposed methodology is motivated by and applied to our own randomized evaluation of India’s National Health Insurance Program (RSBY), where we find some evidence of spillover effects. The proposed methods are implemented via an open-source software package. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

在诸多社会科学实验中，研究对象往往会彼此产生互动，进而导致某一实验单元（unit）所接受的处理（treatment）会对另一实验单元的结果产生影响。近十年来，针对此类单元间存在干扰情形下的因果推断研究已取得显著进展。已有研究证实，对处理分配（treatment assignment）采用两阶段随机化方案，可实现平均直接效应与溢出效应（spillover effects）的识别。然而，现有主流文献均假设研究对象完全依从处理分配方案。本文针对存在干扰与不依从性（noncompliance）的两阶段随机实验，建立了依从者平均直接效应与溢出效应的非参数识别体系。具体而言，本文同时考量了处理分配对处理接受（treatment receipt）的溢出效应，以及处理接受对实验结果的溢出效应。本文提出了一致估计量，并在分层干扰假设（stratified interference assumption）下推导了基于随机化的方差计算公式。本文还证明了本文提出的基于随机化的估计量与主流的两阶段最小二乘（two-stage least squares）估计量之间的精确关系。本文所提出的方法论源于并应用于我们针对印度国家健康保险计划（RSBY）开展的随机评估研究，该研究中我们观测到了溢出效应的相关证据。本文提出的方法可通过一款开源软件包实现部署。本文的补充材料（包含可用于复现研究成果的标准化材料说明）可作为在线补充材料获取。