  This paper considers a semiparametric model of dyadic network formation under
nontransferable utilities (NTU). NTU arises frequently in real-world social
interactions that require bilateral consent, but by its nature induces additive
non-separability. We show how unobserved individual heterogeneity in our model
can be canceled out without additive separability, using a novel method we call
logical differencing. The key idea is to construct events involving the
intersection of two mutually exclusive restrictions on the unobserved
heterogeneity, based on multivariate monotonicity. We provide a consistent
estimator and analyze its performance via simulation, and apply our method to
the Nyakatoke risk-sharing networks.
