Social capital I: measurement and associations with economic mobility

Many theoretical studies have shown how the structure of social networks can shape a variety of outcomes, from the formation of human capital to the degree of adherence to social norms. These studies of social capital conceptualize the cohesiveness of networks in two ways: (1) the cohesiveness of a given individual’s personal network (measured, for example, by the extent to which their friends are in turn friends with each other), and (2) the cohesiveness of the whole community (measured by the degree of fragmentation into subcommunities). Empirical studies have shown that these measures are associated with a range of outcomes, including the dynamics of various types of contagion. Motivated by this literature, we construct three measures of social capital that characterize the structure of friendship links in a community.

The first measure is clustering, which is the rate at which two friends of a given person are in turn friends with each other. The logic underlying clustering as a measure of social capital is that if a person’s friends are friends with each other, they can act together to pressure or sanction that person, which enforces norms and induces pro-social behaviour and investment. Clustering ranges from 0 to 1, with a value of 0 meaning that all of a person’s friends are isolated from each other and 1 meaning that all of a person’s friends are friends with each other. We measure the degree of clustering in a community as the average rate of clustering in friendships for people living in that community (Methods: ‘Measuring cohesiveness’).

A related, but distinct, measure of cohesiveness is the support ratio, which captures the rate at which pairs of friends in a community have other friends in common. The potential role of this measure of social capital can be microfounded in game theoretic models of the extent to which cooperative behaviour between two individuals can be sustained. Specifically, when two people have friends in common, their mutual friends can witness their behaviour and react to it by enforcing norms. We say that a friendship between two people is supported if they have at least one other friend in common. We measure the support ratio in a given community as the share of friendships among its members that are supported (Methods: ‘Measuring cohesiveness’). The support ratio of a community varies from 0 to 1, with 0 implying that none of the friendships between members of a community are supported, and 1 implying that all such friendships are supported.

The third measure of network cohesiveness we consider is spectral homophily, which captures the extent to which a network is fragmented into separate groups (a formal definition is provided in the Methods: ‘Measuring cohesiveness’). Spectral homophily also ranges from 0 to 1. A value of 0 implies that there is no homophily, such that individuals are equally likely to be friends with any other member of the community. By contrast, a value of 1 implies that the network fragments into two or more distinct groups across which no one interacts.

All three of these measures of network cohesiveness exhibit broadly similar spatial patterns, with absolute pairwise correlations of 0.51–0.64 with each other across counties (Table 1). In general, clustering and support ratios are highest in the South, Appalachia and rural Midwest (Fig. 2c and Extended Data Fig. 1c). Spectral homophily tends to be lowest in these areas and highest in the Southwest (Extended Data Fig. 1d). Dense urban centres often exhibit high levels of spectral homophily and low levels of clustering, consistent with Coleman's prediction that areas with greater levels of geographical mobility will have less clustered networks.

The network cohesiveness measures exhibit different geographical patterns from economic connectedness, with correlations ranging from –0.25 to 0.01 with EC across counties (Table 1 and Fig. 2a,c). These differences emerge not just across counties but across neighbourhoods within counties, as illustrated by the ZIP-code-level maps of the Los Angeles metro area (Fig. 2b,d).