Randomization Inference for Peer Effects

Abstract

Many previous causal inference studies require no interference, that is, the potential outcomes of a unit do not depend on the treatments of other units. However, this no-interference assumption becomes unreasonable when a unit interacts with other units in the same group or cluster. In a motivating application, a top Chinese university admits students through two channels: the college entrance exam (also known as Gaokao) and recommendation (often based on Olympiads in various subjects). The university randomly assigns students to dorms, each of which hosts four students. Students within the same dorm live together and have extensive interactions. Therefore, it is likely that peer effects exist and the no-interference assumption does not hold. It is important to understand peer effects, because they give useful guidance for future roommate assignment to improve the performance of students. We define peer effects using potential outcomes. We then propose a randomization-based inference framework to study peer effects with arbitrary numbers of peers and peer types. Our inferential procedure does not assume any parametric model on the outcome distribution. Our analysis gives useful practical guidance for policy makers of the university. Supplementary materials for this article are available online.

Keywords:

• Causal inference
• Design-based inference
• Grade point average (GPA)
• Interference
• Optimal treatment assignment
• Spillover effect

Supplementary Material

Appendix A1 gives supporting materials for Section 7. Appendix A2 gives more technical details for general treatment assignment mechanisms. Appendix A3 gives more technical details for complete randomization. Appendix A4 gives more technical details for random partitioning.

Acknowledgments

The authors thank Don Rubin, Luke Miratrix, Zach Branson and Kristen Hunter at Harvard University, the associate editor, and two reviewers for insightful comments. Dr. Avi Feller at UC Berkeley kindly edited their final version.

Additional information

Funding

The authors gratefully acknowledge financial support from the National Science Foundation (Peng Ding: DMS grant no. 1713152; Jun Liu: DMS no. 1712714).