  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.
