Identification of Social Effects with Endogenous Networks and Covariates: Theory and Simulations

The estimation of spillover and peer effects presents challenges that are still unsolved. In fact, even if separate algebraic identification of the endogenous and exogenous effects is possible, these might be contaminated by the simultaneous dependence of outcomes, covariates and the network structure upon spatially correlated unobservables. In this paper we characterize the identification conditions for consistently estimating all the parameters of a spatially autoregressive or linear-in-means model in presence of linear forms of endogeneity. We show that identification is possible if the spatial correlation of individual covariates and that of unobservables do not overlap, and we relate this idea to a schooling context in which the factors that determine friendships and socioeconomic characteristics are different. We propose a GMM estimator to estimate the relevant parameters and we evaluate its performance through Monte Carlo simulations