Endogenous Social Networks and Inequality in an Intergenerational Setting

In a world where individuals interact in myriads of ways, one wonders how the benefits of one's connections with others compare with those conferred by individual characteristics when it comes to acquisition of human capital. It is particularly interesting to be able to distinguish between connections that are the outcome of deliberate decisions by individuals and connections being given exogenously and beyond an individual's control. The paper explores the consequences of the joint evolution of social connections and human capital investments. It thus allows one to study a broad range of possibilities in which social connections may influence inequality in consumption, human capital investment and welfare across the members of the economy, cross-sectionally and intertemporally. It embeds inequality analysis in models of endogenous social network formation. The novelty of the model lies in its joint treatment of human capital investment and social network formation in intergenerational settings, while distinguishing between the case of impact on human capital from endogenous as opposed to exogenous social networking. Among several results in the case of exogenous connections, we demonstrate conditions under which the limit distribution of human capital has a Pareto upper tail. One of the dynamic models we develop allow for intergenerational transfers in a dynastic version of the infinite horizon Ramsey-Cass-Koopmans model. The models share the property that human capital accumulation, transfers and social connections, when all are optimized, are, along steady states, proportional to cognitive skills. Thus, intergenerational transfers of both human capital endowments and social networking endowments are jointly determined. Interestingly, the consequences for inequality of the endogeneity of social connections are underscored by examining the models when they are assumed to be exogenous. When social connections are not optimized, individuals' human capital reflects a much more general dependence on social connections. The dependence does not reduce to aggregate statistics of social connections. We show that the dynamics of demographically increasingly complex models, as expressed by a sequence of models with increasing number of overlapping generations, depend on the product of the adjacency matrices associated with each of the overlapping generations.