GMM identification and estimation of peer effects in a system of simultaneous equations

Abstract

This paper considers the identification and estimation of network models with agents interacting in multiple activities. We establish the model identification using both linear and quadratic moment conditions. The quadratic moment conditions exploit the correlation of individual decisions within and across different activities, and provide an additional channel to identify peer effects. Combining linear and quadratic moment conditions, we propose a general GMM framework for the estimation of simultaneous equations network models. The GMM estimator improves the asymptotic efficiency of the existing IV-based linear estimators in the literature. Simulation experiments show that the GMM estimator performs well in finite samples.

Simultaneous Equations Models With Higher-Order Spatial or Social Network Interactions

“…However, we also want discussed in more detail below, they do not provide a full asymptotic theory for all considered estimators and their setup only covers first-order spatial lags. Liu (2014Liu ( , 2019Liu ( , 2020; Cohen-Cole, Liu, and Zenou (2018), and Liu and Saraiva (2019) build and extend the methodology of Kelejian and Prucha (2004) within the context of social interaction models with first-order spatial lags, and cross-sectionally independent disturbances. Their contributions include one-step GMM estimation methods that utilize both linear and quadratic moment conditions, identification conditions, bias correction procedures for many instruments, heteroskedasticity, and an estimation methodology for a simultaneous system of equations with binary outcomes generated from an incomplete information network game.…”