Randomization Tests for Peer Effects in Group Formation Experiments



Measuring the effect of peers on an individual’s outcome is a challenging problem, in part because individuals often select peers who are similar in both observable and unobservable ways. Group formation experiments avoid this problem by randomly assigning individuals to groups and observing their responses; for example, do first-year students have better grades when they are randomly assigned roommates who have stronger academic backgrounds? In this paper, we develop randomization tests in group formation experiments, extending classical Fisherian randomization tests to this setting. The proposed tests are justified by the randomization itself, require relatively few assumptions, and are exact in finite samples. Our second main contribution is to derive sufficient conditions under which our randomization tests can be implemented easily via permutations. We identify equivariance as the key algebraic property, which, roughly speaking, ensures that an invariance on the experiment design translates into an invariance on peer exposure. Our paper thus provides one of the first, general theoretical results on efficient implementation of randomization tests for peer effects via permutations. We also apply the proposed tests to two recent group formation experiments in education and interfirm relationships.