Benjamin Golub

Financial Networks and Contagion

We model contagions and cascades of failures among organizations linked through a network of financial interdependencies. We identify how the network propagates discontinuous changes in asset values triggered by failures (e.g., bankruptcies, defaults, and other insolvencies) and use that to study the consequences of integration (each organization becoming more dependent on its counterparties) and diversification (each organization interacting with a larger number of counterparties). Integration and diversification have different, nonmonotonic effects on the extent of cascades. Initial increases in diversification connect the network which permits cascades to propagate further, but eventually, more diversification makes contagion between any pair of organizations less likely as they become less dependent on each other. Integration also faces tradeoffs: increased dependence on other organizations versus less sensitivity to own investments. Finally, we illustrate some aspects of the model with data on European debt cross-holdings.

Using selection bias to explain the observed structure of Internet diffusions

Recently, large datasets stored on the Internet have enabled the analysis of processes, such as large-scale diffusions of information, at new levels of detail. In a recent study, Liben-Nowell and Kleinberg [(2008) Proc Natl Acad Sci USA 105:4633–4638] observed that the flow of information on the Internet exhibits surprising patterns whereby a chain letter reaches its typical recipient through long paths of hundreds of intermediaries. We show that a basic Galton–Watson epidemic model combined with the selection bias of observing only large diffusions suffices to explain these patterns. Thus, selection biases of which data we observe can radically change the estimation of classical diffusion processes.

Network Structure and the Speed of Learning: Measuring Homophily Based on its Consequences

Homophily is the tendency of people to associate relatively more with those who are similar to them than with those who are not. In Golub and Jackson (2010a), we introduced degree-weighted homophily (DWH), a new measure of this phenomenon, and showed that it gives a lower bound on the time it takes for a certain natural best-reply or learning process operating in a social network to converge. Here we show that, in important settings, the DWH convergence bound does substantially better than previous bounds based on the Cheeger inequality. We also develop a new complementary upper bound on convergence time, tightening the relationship between DWH and updating processes on networks. In doing so, we suggest that DWH is a natural homophily measure because it tightly tracks a key consequence of homophily - namely, slowdowns in updating processes.

Stabilizing brokerage

A variety of social and economic arrangements exist to facilitate the exchange of goods, services, and information over gaps in social structure. Each of these arrangements bears some relationship to the idea of brokerage, but this brokerage is rarely like the pure and formal economic intermediation seen in some modern markets. Indeed, for reasons illuminated by existing sociological and economic models, brokerage is a fragile relationship. In this paper, we review the causes of instability in brokerage and identify three social mechanisms that can stabilize fragile brokerage relationships: social isolation, broker capture, and organizational grafting. Each of these mechanisms rests on the emergence or existence of supporting institutions. We suggest that organizational grafting may be the most stable and effective resolution to the tensions inherent in brokerage, but it is also the most institutionally demanding.

Does Homophily Predict Consensus Times? Testing a Model of Network Structure via a Dynamic Process

Abstract We test theoretical results from Golub and Jackson (2012a), which are based on a random network model, regarding time to convergence of a learning/behavior-updating process. In particular, we see how well those theoretical results match the process when it is simulated on empirically observed high school friendship networks. This tests whether a parsimonious random network model mimics real-world networks with regard to predicting properties of a class of behavioral processes. It also tests whether our theoretical predictions for asymptotically large societies are accurate when applied to populations ranging from thirty to three thousand individuals. We find that the theoretical results account for more than half of the variation in convergence times on the real networks. We conclude that a simple multi-type random network model with types defined by simple observable attributes (age, sex, race) captures aspects of real networks that are relevant for a class of iterated updating processes.

Learning in Social Networks

This survey covers models of how agents update behaviors and beliefs using information conveyed through social connections. We begin with sequential social learning models, in which each agent makes a decision once and for all after observing a subset of prior decisions; the discussion is organized around the concepts of diffusion and aggregation of information. Next, we present the DeGroot framework of average-based repeated updating, whose long- and medium-run dynamics can be completely characterized in terms of measures of network centrality and segregation. Finally, we turn to various models of repeated updating that feature richer optimizing behavior, and conclude by urging the development of network learning theories that can deal adequately with the observed phenomenon of persistent disagreement.

Strategic Random Networks: Why Social Networking Technology Matters

This paper develops strategic foundations for an important statistical model of random networks with heterogeneous expected degrees. Based on this, we show how social networking services that subtly alter the costs and indirect benefits of relationships can cause large changes in behavior and welfare. In the model, agents who value friends and friends of friends choose how much to socialize, which increases the probabilities of links but is costly. There is a sharp transition from fragmented, sparse equilibrium networks to connected, dense ones when the value of friends of friends crosses a cost-dependent threshold. This transition mitigates an extreme inefficiency.

Strategic Random Networks

To study how economic fundamentals affect the formation of social networks, a model is needed that (i) has agents responding rationally to incentives (ii) can be taken to the data. This paper combines game-theoretic and statistical approaches to network formation in order to develop such a model. Agents spend costly resources to socialize. Their effort levels determine the probabilities of relationships, which are valuable for their direct benefits and also because they lead to other relationships in a second stage of “meeting friends of friends”. The model predicts random graphs with tunable degree distributions and clustering, and characterizes how those statistics depend on the economic fundamentals. When the value of friends-of-friends is low, equilibrium networks can be either sparse or thick. But as soon as this value crosses a key threshold, the sparse equilibrium disappears completely and only densely connected networks are possible. This transition mitigates an extreme inefficiency.

A Network Approach to Public Goods

Suppose that agents can exert costly effort that creates nonrival, heterogeneous benefits for each other. At each possible outcome, a weighted, directed network describing marginal externalities is defined. We show that Pareto efficient outcomes are those at which the largest eigenvalue of the network is 1. An important set of efficient solutions—Lindahl outcomes—are characterized by contributions being proportional to agents’ eigenvector centralities in the network. The outcomes we focus on are motivated by negotiations. We apply the results to identify who is essential for Pareto improvements, how to efficiently subdivide negotiations, and whom to optimally add to a team.

Social Learning in a Dynamic Environment

Agents learn about a state using private signals and the past actions of their neighbors. In contrast to most models of social learning in a network, the target being learned about is moving around. We ask: when can a group aggregate information quickly, keeping up with the changing state? First, if each agent has access to neighbors with sufficiently diverse kinds of signals, then Bayesian learning achieves good information aggregation. Second, without such diversity, there are cases in which Bayesian information aggregation necessarily falls far short of efficient benchmarks. Third, good aggregation can be achieved only if agents “anti-imitate” some neighbors: otherwise, equilibrium estimates are inefficiently confounded by “echoes.” Agents’ stationary equilibrium learning rules incorporate past information by taking linear combinations of other agents’ past estimates (as in the simple DeGroot heuristic), and we characterize the coefficients in these linear combinations. We discuss how the resulting tractability is useful for structural estimation of equilibrium learning models and testing against behavioral alternatives. Department of Economics, Harvard University, Cambridge, U.S.A., dasarath@g.harvard.edu, bgolub@fas.harvard.edu, nirhak@g.harvard.edu. We are grateful to (in random order) Alireza TahbazSalehi, Evan Sadler, Muhamet Yildiz, Philipp Strack, Drew Fudenberg, Nageeb Ali, Tomasz Strzalecki, Jeroen Swinkels, Margaret Meyer, Michael Powell, Michael Ostrovsky, Leeat Yariv, Eric Maskin, Elliot Lipnowski, Kevin He, Eddie Dekel, Annie Liang, Iosif Pinelis, Ozan Candogan, Bob Wilson, Omer Tamuz, Jeff Zwiebel, Matthew O. Jackson, Xavier Vives, Matthew Rabin, and Andrzej Skrzypacz for valuable conversations, and especially to David Hirshleifer for detailed comments on a draft. We also thank numerous seminar participants for helpful questions and comments. ar X iv :1 80 1. 02 04 2v 3 [ ec on .T H ] 2 2 A ug 2 01 8 SOCIAL LEARNING IN A DYNAMIC ENVIRONMENT 1