Two-Step Estimation of Incomplete Information Social Interaction Models with Missing Outcome Data

In this study, we consider linear social interaction models under incomplete information that allow for missing outcome data due to sample selection. For model estimation, assuming that each individual forms his/her belief about the other members' outcomes based on heterogeneous rational expectations, we propose a two-step series nonlinear least squares estimator. Both consistency and asymptotic normality of the estimator are established. As an empirical illustration, we apply the proposed model and method to National Longitudinal Study of Adolescent Health (Add Health) data in order to examine the impacts of friendship interactions on adolescents' academic achievements. We provide empirical evidence that the interaction effects are important determinants of grade point average, and that controlling for sample selection bias has certain impacts on the estimation results, particularly on the endogenous interaction effects