Collaborative Research: Multiplexing: Theories and Tests of Interactions Between Types of Relationships

Project Outcomes Statement

We wanted to understand different theoretical and policy-based implications of the phenomenon of multiplexing -- the formation of multi-layered social and economic networks. In order to achieve this, we develop a theoretical model and used the network data collected across 143 villages in the state of Karnataka, India (Banerjee et al., 2013, 2019), where we have detailed information on 13 types of social and economic relationships, ranging from borrowing and lending to giving and receiving advice. We also used randomized controlled trials conducted in these villages. Our broad findings are listed below.

First, we develop a taxonomy of multiplexing based on four determinants of why multiplexing may occur. One is that there are cost-savings in establishing and maintaining relationships. For instance, it is easier to share information with coworkers than to form new relationships specifically for sharing information. Second, there can be synergies across layers. For instance, combining informal borrowing of money with exchanges of favors can allow people to reciprocate on different dimensions, thereby enhancing cooperation. Third, people's compatibility may correlate their relationships: for instance, new parents may wish to exchange favors (e.g., childcare) with other new parents, as well as exchange information they learn about parenting with the same people. Finally, and relatedly, people tend to form relationships with others whose behavior they are better able to predict and with whom they can best coordinate -- those who are similar to themselves -- thus, a reason for multiplexing that relates to homophily.

Second, to understand how much relationships overlap in practice, and the structure of the overlap, we apply a statistical method called principal component analysis. We show that across both of our empirical samples, a single "link summary" has strong predictive power for informational, social, and financial layers, explaining more than 50-70% of the variation. Using this we can construct a "backbone" of the social network. Strikingly, the standard measures of social capital and peer influence usually used in the literature such as geographic distance or co-ethnicity are essentially uncorrelated with the backbone, showing that social network structure cannot be proxied for with other, readily available measures.

Third, we show that this distinction can be crucial for researchers attempting to study economic outcomes. To do this, we use data from a randomized control trial where peer monitors were assigned to observe a saver's progress in attaining the saver's savings goal over a period of six months (Breza and Chandrasekhar 2019). The question is how the properties of the monitor affect the effectiveness of monitoring for incentivizing a desired behavior. If the researchers had used conventional measures of social linkage such as co-ethnicity, co-worker relationships, and geographical proximity, network properties of the monitor would not seem to matter for savings outcomes. On the other hand, if the backbone network is used, we can identify a very strong network effect when monitor and saver are in proximity to each other or when the monitor is central in the network.

Fourth, we use the results from a different randomized controlled trial, involving information diffusion, to assess which "layer" of the network -- which type of social relationship -- best predicts how well information diffuses. For this we use a very recent machine learning technique (post-LASSO with a Puffer transformation) to select which layer is associated with diffusion. Despite there being a strong underlying backbone structure, only the advice network is selected. This demonstrates that the "marginal" informational link is important in predicting diffusion.

Using the same data, we also explore whether multiplexing is associated with reduced diffusion. Villages with high levels of multiplexing in general exhibit less diffusion and lower returns to increasing the centrality of the random seeds. We show that networks with high multiplexing levels have longer path lengths and lower degrees (once we control for the network structure across other layers, as well as wealth).

Further, using individual-level wealth indicators, we show that poorer households are associated with higher levels of multiplexing. This could be a consequence of higher reliance on networks for risk-sharing and favor exchange among people with lower wealth levels. Prior work, as well as our own modeling, establishes that stronger relationships are a natural mechanism for "reinforcing" favor-trading relationships such as borrowing and lending. Finally, we develop a model that shows how such "reinforcing" behavior tends to yield worse informational networks, with slower diffusion. This highlights a potentially important and new force in social networks: how disparities in multiplexing incentives can result in persistent inequalities in network structures.