Risk aversion and networks Microfoundations for network formation Jaromir Kovarik University of the Basque Country Marco van der Leij University of Alicante August 2009

Introduction Many studies argue that individual economic outcomes are for a part determined by the position an individual occupies in the social network This raises important questions on the formation of social networks: How are social networks formed? Why do some agents get into a good position and others not? Two approaches: Economic: Jackson & Wolinsky (1996) Statistical Mechanics: Barabasi & Albert (1999) Jackson (2006, 2008): Synergies possible!

Introduction In this project, we first present a statistical mechanics model of network formation, in which: Agents enter sequentially, and search for partners Random search and Local search (among friends of friends) Vázquez (2003) and Jackson & Rogers (2007) Decision to search randomly or locally is endogenized and follows from utility-maximization Agents learn about the friends of friends Search randomly if the friends of friends are all unattractive

Introduction Our model allows us to make predictions on the role of risk aversion in the formation of social networks Risk aversion is not related to degree Risk aversion is positively related to clustering We empirically test and confirm these predictions Our model allows us to relate individual payoffs to individual network position Risk aversion is negatively related to payoff Clustering is positively related to payoff

The Model The model is specified as follows: Each period one agent i enters the network network growth model Agent i’s objective: to create m links maximizing utility Benefit bij of i linking to j is initially unknown bij is drawn from a i.i.d. distribution F with mean We assume that agents have a CARA utility function

Link Formation

Link Formation new node: i

Link Formation m l j k new node: i

Link Formation m l j k new node: i

Link Formation m n l j k new node: i

Link Formation m n l j k new node: i

Link Formation m n l j k new node: i

Link Formation m n l j k new node: i

Link Formation new node

The Model Our network formation model has the same network properties of Vázquez (2003) and Jackson & Rogers (2007) Fat tail degree distribution High clustering coefficient Small network distances Negative correlation Degree-Clustering Positive correlation Degree-neighbor’s degree

Risk and network position Let the risk premium ri be i.i.d. from distribution G What is the relation of an agent’s risk aversion to its network position? Relation to in-degree, out-degree, degree Relation to clustering

Risk and network position Proposition: The agent’s risk premium ri is uncorrelated with the agent’s number of links, di. Number of links depends on the linking decisions of other agents j entering after i Proposition: The risk premium ri is positively correlated with the clustering coefficient Ci The probability that an entering node i, after linking to j, decides to link to a neighbor of j is increasing in ri Everytime that agent i decides to link a friend of a friend, at least 1 edge between the neighbors of i is created Everytime that agent i decides to link randomly, the probability of a new edge between the neighbors of i is very small

Empirical Analysis We test our predictions on a dataset of 256 undergraduate students at the University of Granada Dataset obtained through a series of lab experiments on the same set of students in Spring 2005, see Brañas et al. (2006, 2008) We use data on two experiments: Network elicitation experiment Risk elicitation experiment We test that risk aversion is not related to degree and that it is positively related to clustering. Both our predictions are empirically confirmed.

Network positions and payoffs Our model allows us to analyze the relation between payoffs and network position Proposition: The expected payoff of an agent with risk premium r, is decreasing with r Risk averse agents accept a sure relative low payoff from second-order neighbors in order to avoid risky decisions Proposition: The expected payoff of an agent conditional on her clustering coefficient, C, is increasing in C. Agents only link in network if benefit of neighbor is high enough

Summary We have presented a model of network formation statistic model, which can be tested microfoundations for decision to form a link Risk aversion! We relate risk aversion to network position No relation risk aversion and degree Positive relation risk aversion and clustering These predictions are empirically confirmed

Conclusion We obtain a negative relation between clustering and payoffs. People with more clustered networks earn more. This gives an alternative view to the standard sociological discussion on network position and payoff