🤖 AI Summary
This study addresses the identification and estimation of social effects in linear-in-means models with endogenous network structures. By leveraging randomized assignment combined with observed network data, and invoking the assumption that initially randomized peers exert no direct social influence, the authors construct local heterogeneity–robust moment conditions applicable to the full sample. Building on ψ-dependent network structures, they develop a generalized method of moments (GMM) estimator that admits a closed-form solution, ensuring both theoretical rigor and computational tractability. Monte Carlo simulations demonstrate strong finite-sample performance. Empirically, the analysis reveals a significant positive spillover effect: among Hong Kong high school students, being assigned by teachers to sit next to a randomly allocated peer positively influences the mathematics achievement of that peer’s study partners.
📝 Abstract
This paper introduces an innovative approach to identifying and estimating the parameters of interest in the widely recognized linear-in-means regression model under conditions where the initial randomization of peers determines the observed network. We assert that peers who are initially randomized do not produce social effects. However, after randomization, agents can endogenously develop significant connections that potentially generate peer influences. We present a moment condition that compiles local heterogeneous identifying information for all agents within the population. Under the assumption of $ψ$-dependence in the endogenous network space, we propose a Generalized Method of Moments (GMM) estimator, which is proven to be consistent, asymptotically normally distributed, and straightforward to implement using commonly available statistical software due to its closed-form expression. Monte Carlo simulations demonstrate the GMM estimator's strong small-sample performance. An empirical analysis utilizing data from Hong Kong high school students reveals substantial positive spillover effects on math test scores among study partners in our sample, provided that their seatmates were exogenously assigned by their teachers.