In this paper, we model network formation and network interactions under a unified framework. The key feature of our model is to allow individuals to respond to incentives that stem from interaction benefits of certain activities when they choose friends (network links), while capturing homophily in terms of unobserved characteristic variables in network formation and activities. There are two advantages of this modeling approach: first, one can evaluate whether incentives from certain interactions are important factors for friendship formation or not. Second, in addition to homophily effects in terms of unobserved characteristics, inclusion of incentive effects in the network formulation also corrects possible friendship selection bias on activity outcomes under network interactions. A theoretical foundation of this unified model is based on a sub-game perfect equilibrium of a two-stage game. A tractable Bayesian MCMC approach is proposed for the estimation of the model, and we demonstrate its finite sample performance in a simulation study. We apply the model to study empirically American high school students’ friendship networks from the Add Health dataset. We consider two activity variables, GPA and smoking frequency, and find a significant incentive effect from GPA, but not from smoking, on friendship formation. These results suggest that the benefit of interactions in academic learning is an important factor for friendship formation, whereas the interaction benefit of smoking is not. On the other hand, from the perspective of network interactions, both GPA and smoking frequency are subject to significant positive interaction (peer) effects.
Chih-Sheng Hsieh : Department of Economics, The Chinese University of Hong Kong.
Lung-Fei Lee : Department of Economics, The Ohio State University.
Vincent Boucher : Department of Economics, Université Laval.
A previous version of this paper was circulated under the title, “A structural modeling approach for network formation and social interactions with applications to students’ friendship choices and selectivity on activities.” The authors are grateful to the editor, Christopher Taber, two anonymous referees, Matthew Jackson, as well as conference participants at 2013 AMES in Singapore and seminar participants at Academia Sinica, Chicago Booth, Chinese University of Hong Kong, Lingnan University, National Taiwan University, Ohio State University, Shanghai University of Finance and Economics, and Xiamen University for helpful comments. Thanks also to Murray Hay for proofreading the manuscript. Vincent Boucher gratefully acknowledge financial support from SSHRC (430-2016-00777). This research uses data from Add Health, a program project directed by Kathleen Mullan Harris and designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris at the University of North Carolina at Chapel Hill, and funded by grant P01- HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 23 other federal agencies and foundations. Special acknowledgment is due Ronald R. Rindfuss and Barbara Entwisle for assistance in the original design. Information on how to obtain the Add Health data files is available on the Add Health website (http://www.cpc.unc.edu/addhealth). No direct support was received from grant P01-HD31921 for this analysis.