A Social Interactions Model with Endogenous Friendship Formation and

This paper considers the problem caused by endogenous association of members within a network when the spatial autoregressive (SAR) model is used to study outcomes with social interactions. When the spatial weights matrix (sociomatrix; adjacency matrix) in the SAR model represents a network structure, it might correlate with the disturbance term of the outcome equations which in consequence causes an endogenous selection problem in outcomes. We take into account this problem of selection bias with a modeling approach for a friendship network. In this approach, a statistical network model which has an economic foundation is adopted to explain the endogenous network formation process. By specifying unobserved components in both the network model and the SAR outcome equation, we can capture the correlation between the network formation process and the outcome process and then restore a proper estimation procedure for the SAR outcome equations. The estimation of this model is demonstrated to be computationally tractable via Bayesian simulation methods. We provide a Monte Carlo experiment and empirical applications using the Add Health data to demonstrate the usefulness of this modeling approach.

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