  This paper deals with the estimation of exogeneous peer effects for partially
observed networks under the new inferential paradigm of design identification,
which characterizes the missing data challenge arising with sampled networks
with the central idea that two full data versions which are topologically
compatible with the observed data may give rise to two different probability
distributions. We show that peer effects cannot be identified by design when
network links between sampled and unsampled units are not observed. Under
realistic modeling conditions, and under the assumption that sampled units
report on the size of their network of contacts, the asymptotic bias arising
from estimating peer effects with incomplete network data is characterized, and
a bias-corrected estimator is proposed. The finite sample performance of our
methodology is investigated via simulations.
