Individuals’ behaviors, attitudes or efforts are often influenced by peers through social interactions. Spatial econometrics is one of the most popular statistical tools used to evaluate the effect of social network on socioeconomic outcomes. However, real-world networks often violate the exogeneity assumption of the adjacency matrix representing network relationships. My dissertation relaxes this assumption and focuses on the mechanism behind social network formation. Whereas the first two essays relies on undirected networks, the third essay develops new network statistics for directed networks. The first essay extents the Double Metropolis Hastings algorithm to include latent unobserved nodal heterogeneity in order to estimate the impact of network formation on individual outcomes. The second essay applies this method using the Add Health dataset to estimate the impact of peer effects on students' academic performance. The third essay tests for network misspecification by introducing new higher-order configurations that combine individual attributes with purely structural network effects.
Essay 1:
We extend the dyadic-dependent Exponential Random Graph Model (ERGM) to include observed agent characteristics and unobserved agent-level heterogeneity in order to properly model the mechanism behind link formation. Monte Carlo simulations are designed to compare our proposed Double Metropolis Hastings estimation procedure with the traditional logistic regression. Results show that omitting higher-order dependence statistics or unobserved individual heterogeneity might lead to biased estimates.
Essay 2:
An empirical illustration using friendship networks across 12 US high schools is discussed in the second essay. A higher-order spatial Durbin model (SDM) is implemented in order to capture within and across grade-level peer effects on students’ academic performance on four subjects. The estimation results reveal that peer effects are strongly significant across and within grades in Science. They are even stronger across grades than within grades. In History, peer effects seem to have an impact only across grades whereas there is no evidence of peer effect in English and Mathematics. The individual unobserved heterogeneity has a strong impact on network formation and a negative effect on academic performance.
Essay 3:
We focus on a generalized formation model of directed networks. A comprehensive set of network statistics with categorical and continuous nodal attributes are presented to allow for any type of structural configurations and attributes to be accounted for. We investigate the importance of triadic configurations with continuous attributes in shaping cohesive group structures. Monte Carlo simulations compare our estimation procedure with the state-of-the-art R suite of packages Statnet.