Multivariate Choice and Identification of Social Interactions

In this paper, we investigate the impact of peers on own outcomes where all agents embedded in a network choose more than one activity. We develop a simple network model that illustrates these issues. We differentiate between the ‘seemingly unrelated’ simultaneous equations model where people are influenced only by others within the same activity, the ‘triangular’ simultaneous equations model, where there is some asymmetry in the peers’ cross effects, and the ‘square’ simultaneous equations model, where all possible cross-choice effects are taken into account. We develop the conditions under which each model is identified, showing that the general ‘square’ simultaneous equations model with both simultaneity effect and cross-choice peer effect cannot be identified without any exclusion restrictions. We then study the impact of peer effects on education and screen activities and show that the estimated within- and cross-choice peer effects both have non-trivial impacts on adolescent behavior. We find, in particular, that, keeping peers’ grades and screen activities fixed, watching more TV could be beneficial to a student’s grade.