Binary Outcomes and Linear Interactions

We consider general models of linear interactions in binary outcomes. We first characterize the conditions under which these models are coherent and complete. Next, we show that models of linear interactions admit sound microfoundations under assumptions of incomplete information and independence. To help guide practitioners, we discuss key modeling choices and testable restrictions. We then consider a specification that is linear in parameters, and propose a simple Two-Stage Least Squares estimator. We revisit the empirical analysis of teenage smoking and peer effects of Lee, Li, and Lin. Our reanalysis highlights the main advantages of the linear framework, including minimal computational and data requirements and ability to handle fixed effects. Supplementary materials for this article are available online.