Tractable Identification of Strategic Network Formation Models with Unobserved Heterogeneity

Abstract: We develop a tractable identification approach for strategic network formation models with both strategic link interdependence and individual unobserved heterogeneity (fixed effects). The key challenge is that endogenous network statistics (e.g. number of common friends) enter the link formation equation, while the mapping from model primitives to equilibrium network structure is generally intractable. Our approach sidesteps this difficulty using a ``bounding-by-$c$'' technique that treats endogenous covariates as random variables and exploits monotonicity restrictions to obtain identifying information. We derive a system of identifying restrictions based on subnetwork configurations: tetrad-based restrictions that completely eliminate all individual fixed effects, triad-based restrictions that partially difference out fixed effects, and general weighted cycle-based restrictions, along with point identification results. Preliminary simulations show that our approach can deliver informative bounds on the structural parameters.