Agents interact in markets as well as socially, that is, in the various socio economic groups they belong to. Models of social interactions are designed to capture in a simple abstract way socio economic environments inwhich markets do not mediate all of agents’ choices. In such environments agents’ choices are determined by their preferences as well as by their ability to interact with others, on their position in a predetermined network of relationships, e.g., a family, a peer group, or more generally any socio economic group.
Social interactions arguably provide a rationale for several important phenomena, Peer effects, in particular, have been indicated as one of the main empirical determinants of risky behavior in adolescents. Relatedly, peer effects have been studied in connection with education outcomes, obesity, friendship and sex, labor market referrals, neighborhood and employment segregation, criminal activity, and several other socioeconomic phenomena.
The large majority of the existing models of social interactions are static; or, when dynamic models of social interactions are studied, it is typically assumed that agents are myopic and their choices are subject to particular behavioral assumptions. In this paper, we contribute to this literature by studying social interactions in dynamic economies. We focus our attention on linear economies, in which each agent’s preferences are quadratic. Dynamic linear models of course have appealing analytical properties. Hansen and Sargent (2004) study this class of models systematically, exploiting the tractability of linear control methods and matrix Riccati equations.
While the class of economies we study in this paper allows however for a countable number of heterogeneous agents and an infinite horizon, giving rise to infinite dimensional systems, some tractability is maintained. Furthermore, in the class of economies we study agents display preferences for conformity, that is, preferences which incorporate the desire to conform to the choices of agents in a reference group.
