  This paper explores the identification and estimation of social interaction
models with endogenous group formation. We characterize group formation using a
two-sided many-to-one matching model, where individuals select groups based on
their preferences, while groups rank individuals according to their
qualifications, accepting the most qualified until reaching capacities. The
selection into groups leads to a bias in standard estimates of peer effects,
which is difficult to correct for due to equilibrium effects. We employ the
limiting approximation of a market as the market size grows large to simplify
the selection bias. Assuming exchangeable unobservables, we can express the
selection bias of an individual as a group-invariant nonparametric function of
her preference and qualification indices. In addition to the selection
correction, we show that the excluded variables in group formation can serve as
instruments to tackle the reflection problem. We propose semiparametric
distribution-free estimators that are root-n consistent and asymptotically
normal.
