Count Data Models with Social Interactions under Rational Expectations

Abstract

This paper proposes a peer effect model for counting variables using a game of incomplete information. I show that the game has a unique equilibrium under standard conditions. I also demonstrate that the identification argument in Bramoullé et al. (2009) extends to nonlinear models, particularly to the model of this paper. The model parameters are estimated using the Nested Partial Likelihood (NPL) approach, controlling for network endogeneity. I show that the linear-in-means/Tobit models with a counting outcome are particular cases of my model. However, by ignoring the counting nature of the outcome, these models can lead to inconsistent estimators. I use the model to evaluate peer effects on students' participation in extracurricular activities. I find that a one-unit increase in the expected number of activities in which a student's friends are enrolled yields an increase in the expected number of activities in which the student is enrolled by 0.08. This point estimate using the Tobit model is three times higher.

Keywords: Discrete model, Social networks, Bayesian game, Rational expectations, Network formation

JEL Classification: C25, C31, C73, D84, D85