Measuring Social Interaction Effects When Instruments Are Weak

Studies that distinguish between exogenous and endogenous peer effects are relatively rare. To separate these effects, De Giorgi, Pellizzari, and Redaelli exploited partially overlapping peer groups where attributes of a student's peers in one group provide instrumental variables (IV) for endogenous effects in another group. We apply this identification strategy to data from a period of transition at a Chinese university: dormitory roommate assignments were changed as students moved between campuses. This transition allows us to measure the endogenous effects between test scores of current roommates, but the traditional IV method suggests the potential for weak IV. We use weak-IV robust techniques to obtain properly sized tests. The S-test, K-test, and QCLR test all reject the null of zero endogenous effects with p-values between 0.01 and 0.05, as compared with 0.003 implied by the traditional IV estimator. The largest 95% confidence interval lower bound is 0.154 from the QCLR test, in contrast to 0.244 from traditional IV. Our findings offer unique evidence that endogenous peer effects influence academic outcomes at an empirically relevant magnitude, and an example where weak-IV robust tests are essential to quantify the relationship. Our results are robust to alternative model specifications.