GMM Estimation of Social Interaction Models with Centrality

This paper considers the speci…cation and estimation of social interaction models with network structures and the presence of endogenous, contextual, correlated, and group …xed e¤ects. When the network structure in a group is captured by a graph in which the degrees of nodes are not all equal, the di¤erent positions of group members as measured by the Bonacich (1987) centrality provide additional information for identi…cation and estimation. In this case, the Bonacich centrality measure for each group can be used as an instrument for the endogenous social e¤ect, but the number of such instruments grows with the number of groups. We consider the 2SLS and GMM estimation for the model. The proposed estimators are asymptotically e¢ cient, respectively, within the class of IV estimators and the class of GMM estimators based on linear and quadratic moments, when the sample size grows fast enough relative to the number