Weak Identification and Network Measurement Error in Peer Effects Estimation

Abstract

The growing availability of social network data has enabled a surge of research on social interactions. In particular, peer effects, once considered unidentifiable, have now been shown to be identified given knowledge of the network structure. Despite this positive result, questions remain about the existence and nature of peer effects, due to concerns about identification strength and the reliability of network data. This work investigates two key threats to the estimation of peer effects: weak identification and network measurement error. We show that weak instrument problems arise in moderately dense networks due to rapid averaging, leading to slow convergence rates even when estimators remain consistent. On the measurement error side, we show that additive edge weight errors can be mitigated in such networks due to the same averaging phenomena, but the error remains a relevant threat to consistency in sparser networks. We further demonstrate that when both issues are present, the resulting estimators exhibit non-vanishing bias, suggesting that the combined effect of weak instruments and measurement error can be more severe than either problem in isolation. Overall, our results aim to clarify how these non-standard estimation challenges impact our ability to study peer effects using network data.