Social capital I: measurement and associations with economic mobility

We represent a set of friendships by the matrix A ∈ {0, 1}n×n, where Aij = 1 denotes the existence of a friendship (edge) between individuals i and j, and Aij = 0 denotes the absence of a friendship. We focus on three measures of the structure of A: clustering and support ratio, which are measures of local correlation in friendships, and spectral homophily, a measure of overall network fragmentation. Other measures of cohesiveness, such as algebraic connectivity, are also informative, but are difficult to compute or even approximate for networks of the scale we analyse. The three measures of cohesiveness we focus on here have the advantage of being computationally tractable in large samples.

Clustering

Previous work has argued that if person i is friends with both persons j and k, then having j and k be friends with each other can help them collectively pressure and sanction person i, thereby helping to enforce norms. Motivated by this logic, many studies have measured the extent of such ‘network closure’ by the degree of clustering within a person’s network: the frequency with which two friends of that person are in turn friends with each other. Letting Ni(A) denote the set of i’s friends and di(A) its cardinality (the number of friends i has), the clustering of i’s network is defined asWe measure clustering in a community c as the average of equation (4) across people living in that community as follows:

Support ratio

Letting Ac denote the subset of friendships between individuals who are both members of community c, we measure a community c’s support ratio as the overall frequency with which pairs of friends have at least one friend in common, focusing only on the people and friendships within that community:

Spectral homophily

Spectral homophily measures the extent to which a network is fragmented into separate groups, and relates to the speed of information aggregation in a network. A wide variety of algorithms can detect subcommunities, and spectral homophily provides a simple measure of how strongly a network splits into such subcommunities. Formally, spectral homophily is the second largest eigenvalue of the degree-normalized (row-stochasticized) adjacency matrix Acs∈[0,1]n×n. We measure spectral homophily in each county on the basis of the set of friendships among individuals in our primary sample living in that county. Friendship matrices are too sparse to estimate spectral homophily reliably at the ZIP code level. In the rare instances when there are fully isolated nodes within a county, we calculate spectral homophily on the largest connected component, which usually makes up the majority of users living in a county.

Measuring civic engagement

Volunteering rate

We start with the set of all Facebook Groups in the United States that are predicted to be about volunteering or activism based on their titles and do not have the privacy setting ‘secret’ enabled. To further improve this classification, we manually review the 50 largest such groups in the United States and the largest such group in each state, and remove the very small number of groups that are clearly misclassified. We then define the volunteering rate as the share of Facebook users in an area who are a member of at least one volunteering or activism group.

Civic organizations

We start with the set of all Facebook Pages in the United States that are categorized as ‘public good’ pages on the basis of the page title and page category. We then remove pages that do not have a website linked, do not have a description on their Facebook page or do not have an address listed. We then assign the page to a ZIP code and county on the basis of its listed address, and calculate the density of civic organizations as the number of such pages per 1,000 Facebook users in the area.

Correlations

We weight all correlations and regressions by the number of individuals with below-national-median parental income as calculated using Census data, unless otherwise noted. We cluster standard errors in all county-level regressions by commuting zone and ZIP-code-level regressions by county to adjust for potential spatial autocorrelation in errors, unless otherwise noted.

The causal effect estimates used in the ‘Causal effects of place versus selection’ section are identified solely from individuals who move across areas and are therefore much less precise than the baseline observational estimates of economic mobility used in the rest of the paper, making it necessary to adjust for attenuation bias in those correlation estimates due to sampling error. We adjust for attenuation bias by dividing the raw correlation between the causal estimates of mobility and EC by the square root of the reliability of the causal estimates of mobility, as estimated by Chetty and Hendren. The causal effect estimates are also unavailable at the ZIP-code level owing to small sample sizes for ZIP-code-level moves. This is why we focus on the observational estimates of upward income mobility in our baseline analysis.

Privacy and ethics

This project focuses on drawing high-level insights about communities and groups of people, rather than individuals. We used a server-side analysis script that was designed to automatically process the raw data, strip the data of personal identifiers, and generate aggregated results, which we analyzed to produce the conclusions in this paper. The script then promptly deleted the raw data generated for this project. While we used various publicly available sources of aggregate statistics to supplement our analysis, we do not link any external individual-level information to the Facebook data. All inferences made as part of this research were created and used solely for the purpose of this research and were not used by Meta for any other purpose.

A publicly available dataset, which only includes aggregate statistics on social capital, is available at https://www.socialcapital.org. We use methods from the differential privacy literature to add noise to these aggregate statistics to protect privacy while maintaining a high level of statistical reliability; see https://www.socialcapital.org for further details on these procedures. The project was approved under Harvard University IRB 17-1692.