Identification of Peer Effects with Miss-specified Peer Groups: Missing Data and Group Uncertainty

Abstract

We consider identification of peer effects under peer group miss-specification. Two leading cases are missing data and peer group uncertainty. Missing data can take the form of some individuals being entirely absent from the data. The researcher need not have any information on missing individuals and need not even know that they are missing. We show that peer effects are nevertheless identifiable under mild restrictions on the probabilities of observing individuals, and propose a GMM estimator to estimate the peer effects. In practice this means that the researcher need only have access to an individual level sample with group identifiers. Group uncertainty arises when the relevant peer group for the outcome under study is unknown. We show that peer effects are nevertheless identifiable if the candidate groups are nested within one another and propose a non-linear least squares estimator. We conduct a Monte-Carlo experiment to demonstrate our identification results and the performance of the proposed estimators, and apply our method to study peer effects in the career decisions of junior lawyers.