Received: 7 August 2015 Revised: 1 June 2017
Multivariate choices and identification of social interactions
Econ One Research, Berkeley, CA, USA
Department of Economics, University of
Colorado, Boulder, CO, USA
Department of Economics, Monash
University, Melbourne, Victoria, Australia
IFN, Stockholm, Sweden
Xiaodong Liu, Department of Economics,
University of Colorado, Boulder, CO
This paper considers the identification of social interaction effects in the context of
multivariate choices. First, we generalize the theoretical social interaction model to
allow individuals to make interdependent choices in different activities. Based on the
theoretical model, we propose a simultaneous equation network model and discuss
the identification of social interaction effects in the econometric model. We also
provide an empirical example to show the empirical salience of this model. Using the
Add Health data, we find that a student's academic performance is not only affected
by academic performance of his peers but also affected by screen-related activities
of his peers.
Peer choices and/or peer characteristics have been shown to be important in predicting individual outcomes, ranging from edu-
cation and crime to participation in the labor market (see, e.g., Ioannides & Loury, 2004; Patacchini & Zenou, 2012; Sacerdote,
2011). Most of this literature has, however, focused on peer effects on choices regarding one specific activity.
In reality, individuals make a multitude of choices in different activities, many of which may depend on each other. As a
result, an individual may have different and sometimes opposite influences on his friend. For example, if a student is very active
in extracurricular activities but also studies very hard, how would these choices affect the study effort of his friends? The peer
effects of interdependent choices is what we study in this paper. Our purpose is to help understand the decision making process
involving multiple activities in the context of peer influences and social networks.
The contribution of this paper is threefold. First, we provide a microfoundation that helps characterize the decision-making
process in multiple activities in a social interaction setting. The theoretical model we consider has two important features. First,
as is common in this literature (see, e.g., Ballester, Calvó-Armengol, & Zenou, 2006; Bramoullé and Kranton, 2007; Bramoullé,
Kranton, & D'Amours, 2014; Jackson & Zenou, 2015), our model has the feature that individuals enjoy utility as a function
of peers' choices. Second, our model allows individuals to make choices in multiple activities that have an arbitrary degree
of complementarity or substitutability.
The model is general enough to encompass arbitrary combinations of choices without
making assumptions regarding the orderings of choice bundles. This generality is essential because combining sets of choices
into bundles in a social interaction context dramatically restricts the set of possible actions available to individuals. It is easy to
construct examples of preference reversals in the bundled goods setting that comply with standard choice axioms in the general
setting considered here.
Second, we investigate the identification of peer effects in the context of multivariate choices. The econometric model implied
by the best response function of the theoretical model extends the simultaneous equation spatial autoregressive model intro-
duced by Kelejian and Prucha (2004) to allow for network fixed effects. As single-activity social interaction models (e.g.,
Bramoullé, Djebbari, & Fortin, 2009; Lee, Liu, & Lin, 2010), our model includes the within-activity peer effect (also known
Belhaj and Deroïan (2014) and Chen, Zenou, and Zhou (2017) develop a network model where two activities are considered. Both papers only analyze the
theoretical implications of their respective models without addressing econometric issues.
J Appl Econ. 2018;33:165–178. wileyonlinelibrary.com/journal/jae Copyright © 2017 John Wiley & Sons, Ltd. 165