**Identification and Estimation of Network Formation Games (Job Market Paper)** pdf

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 identified. We leave the equilibrium selection completely unrestricted and resort to partial identification. 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 define the identified set based on the feasible moment inequalities and discuss how to consistently estimate the identified set and construct a confidence 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.

**Program download:** graph isomorphism algorithm (bin for Matlab) Win-64bit Linux-64bit Instruction

**Nonparametric Identification of Social Interactions: Learning from Neighbors**

This paper investigates the effect of social learning from a structural perspective. Farmers learn a new agricultural technology from their neighbors' experience based on which they make the production decisions. The learning behaviors are modeled under the Bayesian framework. We present conditions under which the model can be nonparametrically identified. In the simplest i.i.d. case, the input demand function can be restricted to a nonadditive index model and identified under certain conditions according to Matzkin (2007). The production function can be identified under the same conditions, analogous to IV methods. The average learning effects on input demand and output can be identified under much weaker conditions. The results could be generalized by allowing for individual fixed effects or neighborhood fixed effects.

**A Discrete Mixture Model for Nework Formation (with Geert Ridder) (work in progress)**