A Structural Model of Segregation in Social Networks

Abstract

In this paper, I develop and estimate a dynamic model of strategic network formation with heterogeneous agents. The main theoretical result is the existence of a unique stationary equilibrium, which characterizes the probability of observing a specific network in the data. As a consequence, the structural parameters can be estimated using only one observation of the network at a single point in time. The estimation is challenging, since the exact evaluation of the likelihood function is computationally infeasible even for very small networks. To overcome this problem, I propose a Bayesian Markov Chain Monte Carlo algorithm that avoids the direct evaluation of the likelihood. This method drastically reduces the computational burden of estimating the posterior distribution and allows inference in high dimensional models. I present an application to the study of segregation in school friendship networks, using data from Add Health. The latter contains the actual social network of each student in a representative sample of US schools. My results suggest that for White students, the value of a same-race friend decreases with the fraction of whites in the school. This relationship is of opposite sign for African American students. The model is used to study how different desegregation policies may affect the structure of the network in equilibrium. I find an inverted U-shape relationship between the fraction of students belonging to a racial group and the expected equilibrium segregation levels. These results suggests that these policies should be carefully designed in order to be effective.