Measuring Social Interaction Effects when Instruments are Weak

Studies that can distinguish between exogenous and endogenous peer effects of social interactions are relatively rare. One recent identification strategy exploits partial overlapping groups of peers. If a student has two groups of separated peers, the peer choices are correlated through that specific student's choice, but one group's attributes are assumed to directly influence neither the other peer group's attributes nor the choices. In the context of academic performance in higher education, however, the evidence of peer effects on academic outcomes has been mixed, creating a potential for weak instruments. We utilize a period of transition when students were being reassigned to dormitories from a new campus to an old campus. Many groups of roommates were broken up at the end of freshman year, and then combined with other groups of students from the same school in the sophomore year. We find reduced-form evidence that information about a student's previous year roommates can explain the current test scores of their new roommates. However, due to weak instruments, the estimated endogenous effects appear unreasonably large. We draw on weak-IV robust tests, namely the Anderson-Rubin-type S-test (Stock and Wright, 2000) and Kleibergen's Lagrangian multiplier test (Kleibergen, 2005), to provide properly-sized tests for the endogenous effects between the test scores of current roommates and to calculate lower bounds of such effects. These tests strongly reject the null hypothesis of no endogenous effects.