Randomization tests for peer effects in group formation experiments

Measuring the effect of peers on individual outcomes 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? Standard approaches for analyzing these experiments, however, are heavily model-dependent and generally fail to exploit the randomized design. In this paper, we extend methods from randomization-based testing under interference to group formation experiments. The proposed tests are justified by the randomization itself, require relatively few assumptions, and are exact in finite samples. First, we develop procedures that yield valid tests for arbitrary group formation designs. Second, we derive sufficient conditions on the design such that the randomization test can be implemented via simple random permutations. We apply this approach to two recent group formation experiments and implement the proposed method in the new RGroupFormation R package.