Estimating spillovers using panel data, with an application to the classroom

Obtaining consistent estimates of spillovers in an educational context is hampered by at least two issues: selection into peer groups and peer effects emanating from unobservable characteristics. We develop an algorithm for estimating spillovers using panel data that addresses both of these problems. The key innovation is to allow the spillover to operate through the fixed effects of a student's peers. The only data requirements are multiple outcomes per student and heterogeneity in the peer group over time. We first show that the nonlinear least squares estimate of the spillover parameter is consistent and asymptotically normal for a fixed T. We then provide an iterative estimation algorithm that is easy to implement and converges to the nonlinear least squares solution. Using University of Maryland transcript data, we find statistically significant peer effects on course grades, particularly in courses of a collaborative nature. We compare our method with traditional approaches to the estimation of peer effects, and quantify separately the biases associated with selection and spillovers through peer unobservables.