Tractable Identification of Strategic Network Formation Models with Unobserved Heterogeneity

TL;DR

This paper introduces a new, tractable method for identifying strategic network formation models that include unobserved heterogeneity, using bounding techniques and fixed-effects strategies to overcome intractability.

Contribution

It develops a novel bounding-by-c technique and fixed-effects handling strategies for network models with endogenous covariates and unobserved heterogeneity.

Findings

The approach provides informative bounds on structural parameters.

Simulation results demonstrate the method's effectiveness.

The method handles complex fixed-effects configurations.

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. A central contribution is to develop a spectrum of fixed-effects handling strategies based on subnetwork configurations: tetrad-based restrictions that difference out all individual fixed effects, triad-based and weighted restrictions that combine ``difference-out'' and ``integrate-out'' steps by differencing out some fixed effects and profiling over the remainder conditional on observed characteristics, and general weighted cycle-based restrictions that unify these cases. We also provide point identification results. Preliminary simulations show that the approach can deliver informative bounds on the structural parameters.