Identication and Estimation of Network Formation Games

Social and economic networks play an important role in shaping individual behaviors. In this paper, we aim to identify and estimate network formation games using observed data on network structure, i.e., who is linked with whom. We use pairwise stability, introduced by Jackson and Wolinsky (1996), as the equilibrium condition to map observed networks to model primitives. Because the fraction of unique equilibria is close to zero, the model is generally not identi…ed. We leave the equilibrium selection completely unrestricted and resort to partial identi…cation. Following Ciliberto and Tamer (2009), we derive from the pairwise stability condition bounds on the probability of observing a network. The moment inequalities obtained from these bounds, however, are computationally infeasible if networks are large. To proceed, we propose a novel approach based on subnetworks. A subnetwork is the restriction of a network to a subset of the individuals. We derive bounds on the probability of observing a subnetwork, considering only the pairwise stability of the subnetwork. Under a local externality assumption about the utility function, these new bounds yield moment inequalities that are computationally feasible provided that we only use small subnetworks. We de…ne the identi…ed set based on the feasible moment inequalities and discuss how to consistently estimate the identi…ed set and construct a con…dence region. When estimating the distribution of subnetworks, we use graph isomorphism to group the subnetworks into equivalence classes to avoid the labeling problem and to resolve the indeterminacy in picking the subnetworks from a network. The bounds are computed by simulation if they do not have closed forms. KEYWORDS: Network formation games, pairwise stability, multiple equilibria, partial identi…cation, computation, subnetworks, graph isomorphism, simulation. JEL Classi…cations: C31, C62, D85 Email: [email protected], address: Department of Economics, University of Southern California, 3620 S. Vermont Ave., KAP 300, Los Angeles, CA 90089. I am very grateful to my advisor Geert Ridder for his enormously valuable advice and comments. I also thank Aureo de Paula, Bryan Graham, Cheng Hsiao, Matthew Jackson, Max Kasy, Roger Moon, Je¤rey Nugent, Hashem Pesaran, Matthew Shum, John Strauss, Martin Weidner, Simon Wilkie and participants in Econometrics Seminar at USC, California Econometrics Conference, North American Summer Meeting of the Econometric Society, European Meeting of the Econometric Society for useful discussions and comments. All the errors are mine.