Advanced course on Economics of Networks by Professor Yves Zenou (Stockholm University) September, 30 – October, 02
The aim of this course is to present the relatively recent literature on social networks by exposing the economics, sociology and physics/applied mathematics approaches, showing their similarities and differences and ...
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It has been recognized for a long time that non-market interactions, i.e. interactions between agents that are not mediated by the market, are crucial to explain different economic phenomena such as stock market crashes, growth, education, religion, crime, etc. In these models, the marginal utility to one person of undertaking an action is a function of the average amount of the action taken by her peers. Peer effects are an intragroup externality, homogeneous across group members, that captures the average influence that members exert on each other. We would like to go further by explicitly providing the particular structure of this dependence on group behavior. In particular, if one considers a network of links between agents, then the peer influence varies across agents in the network, and the intra-group externality we obtain is heterogeneous across agents. This heterogeneity reflects asymmetries in network locations across group members. Networks and peer effects are in the heart of most non-market relationships.
The aim of this course is to present the relatively recent literature on social networks by exposing the economics, sociological and physics/applied mathematics approaches, showing their similarities and differences. We will expose, in particular, the two main ways of modeling network formation. While the physics/applied mathematics approach is capable of reproducing most observed networks, it does not explain why they emerge. On the contrary, the economics approach is very precise in explaining why networks emerge but does a poor job in matching real-world networks. We also analyze behaviors on networks, which take networks as given and focus on the impact of their structure on individuals’ outcomes. Using a game-theoretical framework, we then compare the results with those obtained in sociology. We will then focus on some applications of social networks: labor-market networks, R&D networks and crime networks.
The main reference for this course is:
M.O. Jackson (2008), Social and Economic Networks, Princeton: Princeton University Press.
1) Lecture 1: Motivation, Definitions and Descriptive Evidence
We will present here some key characteristics of real-world social, economic and technology networks. In terms of structure, real-world networks are characterised by:
(i) A small average shortest path length between any pairs of agents
(ii) A high clustering, which means that the neighbors of an agent are likely to be connected.
(iii) An inverse relationship between the clustering coefficient of an agent and her degree. The neighbors of a high degree agent are less likely to be connected among each other than the neighbors of an agent with low degree. This means that empirical networks are characterized by a negative clustering-degree correlation.
(iv) A highly skewed degree distribution. While some authors find power law degree distributions, others find deviations from power-laws in empirical networks, or exponential distributions.
(v) Degree-degree correlations for economic and social networks. In this case the network is said to be assortative. On the other hand, technological networks such as the internet display negative correlations. In this case the network is said to be dissortative. Others, however, find also negative correlations in social networks such as in the Ham radio network of interactions between amateur radio operators or the affiliation network in a Karate club. Networks in economic contexts may have features of both technological and social relationships and so there exist examples with positive degree correlations such as in the network between venture capitalists as well as negative degree correlations as it can be found in the world trade web, online social communities and in networks of banks.
We will also introduce some definitions and notations.
R. Albert and A. Barabási (2002), “Statistical mechanics of complex networks,” Review of Modern Physics 74, 47-97.
Goyal, S., J.L. Moraga-Gonzalez, and M. van der Leij (2006), “Economics: an emerging small world,” Journal of Political Economy114, 403-412.
Newman, M.E. (2001), “The Structure of Scientific Collaboration Networks.” Proceedings of the National Academic of Sciences of the USA98, 404-409.
2) Lecture 2: Theories of Network Formation
One of the main goals of the analysis of social networks is to shed some light on the mechanisms explaining how and why networks form. If social networks are relevant, we need to understand how networks emerge and the forces determining their shape.
There are basically two main approaches of network formation.
One possible reason why a link is formed is pure chance. Two individuals randomly meet and create a link between them, which can represent friendship or a stable working relationship. A set of different models have arisen based on this assumption. They are called random models of network formation.
Another possible reason for the formation of a link is strategic interactions. Individuals carefully decide with whom to interact and this decision entails some consent by both parts in a given relationship. Strategic network formation models are, precisely, grounded on this premise.
2.1. Random Models of Network Formation
We will expose the following models:
Erdös-Rényi (Bernoulli) Random Graphs;
Rewired Lattices and Clustering (Watts and Strogatz, 1998);
Preferential Attachment and Scale-Free Degree Distributions;
2.2. Strategic Models of Network Formation
We will define the equilibrium concept of pairwise stability (which is the most prominent equilibrium concept used in network formation games) introduced by Jackson and Wolinsky (1996) and illustrate it using two well-known examples: The “Connections Model” and the “Co-Author Model”.
We will show that there is a tension between a pairwise stablenetwork and an efficient network (from an overall society perspective). In particular, plenty of pairwise stable networks are notefficient (see, in particular, the surveys by Jackson (2007, 2008)).
The Connections Model: We will expose the results in both of equilibrium (pairwise stability) and efficiency.
Extensions of the “Connections Model”:
The spatialconnection models explaining small world phenomena.
Johnson and Gilles (2000), Carayol and Roux (2004), Carayol, Roux, and Yildizoglu (2008), Jackson and Rogers (2005).
The Co-Author Model. We will expose the results in both of equilibrium (pairwise stability) and efficiency.
Another approach to network formation is the non-cooperative game introduced by Myerson (1977) and analyzed, for instance, by Bala and Goyal (2000) for the case of directed networks. We will expose and discuss this game for the case of un-directed networks, where link formation required mutual consent, using the paper by Calvó-Armengol and Ilkiliç (2009). This paper has also a very nice example for which the empty network, which happens to be a trembling-hand equilibrium network for the Myerson game, is not pairwise stable. This paper shows than one needs to resort to equilibrium notion of properness to reconcile the non-cooperative and cooperative approaches.
2.3. Hybrid models: mixing random networks and strategic network formation
We will mainly expose the paper by Jackson and Rogers (2007).
R. Albert and A. Barabási (2002), “Statistical mechanics of complex networks,” Review of Modern Physics 74, 47-97.
V. Bala and S. Goyal (2000), “A Non-Cooperative Model of Network Formation,” Econometrica 68, 1181-1230.
F. Bloch and M.O. Jackson (2006), “Definitions of equilibrium in network formation games,” International Journal of Game Theory 34, 305–318.
A. Calvó-Armengol and R. Ilkiliç (2009), “Pairwise Stability and Nash Equilibria in Network Formation,” International Journal of Game Theory.
Carayol and Roux (2004), “Behavioral foundations and equilibrium notions for social network formation processes,” Advances in Complex Systems.
Carayol, Roux, and Yildizoglu (2008), “Inefficiencies in a model of spatial networks formation with positive externalities,” Journal of Economic Behavior and Organization 67, 495-511.
M.O. Jackson and A. Wolinsky (1996), “A Strategic Model of Social and Economic Networks,” Journal of Economic Theory 71, 44-74.
M.O. Jackson (2005), “A Survey of Models of Network Formation: Stability and Efficiency,” in Group Formation in Economics: Networks, Clubs and Coalitions, G. Demange and M. Wooders (Eds.), Cambridge: Cambridge University Press, pp. 11-88.
M.O. Jackson (2007), “The Economics of Social Networks,” in Proceedings of the Ninth World Congress of the Econometric Society, R. Blundell, W. Newey and T. Persson (Eds.), Cambridge: Cambridge University Press, pp 1-56.
M.O. Jackson (2008), Social and Economic Networks, Princeton: Princeton University Press.
M.O. Jackson and B.W. Rogers (2005), “The economics of small worlds,” Journal of the European Economic Association 3, 617-627.
M.O. Jackson and B.W. Rogers (2007), “Meeting strangers and friends of friends: How random are social networks?” American Economic Review 97, 890-915.
C. Johnson and R.P. Gilles (2000), “Spatial social networks,” Review of Economic Design 5, 273-299.
F. Vega-Redondo (2007), Complex Social Networks, Econometric Society Monograph Series, Cambridge: Cambridge University Press.
3) Lecture 3: Games on Networks
The network structure of social interactions influences a variety of behaviors and economic outcomes, including the formation of opinions, decisions on which products to buy, investment in education, access to jobs, and social mobility, just to name a few.
In this lecture, we take networks as given (thus we leave aside the issue of network formation) and analyze the consequence of network structures on economic outcomes. The starting point of this analysis will be the paper by Ballester, Calvó-Armengol and Zenou (2006). They use a linear-quadratic utility function that exhibits both strategic substituabilities and complementarities between agents and each agent chooses the optimal amount of an action by maximizing this utility function. They show that, if the largest eigenvalue of the adjency matrix (the matrix that represents the graph of the network) is bounded above, then there is a unique Nash equilibrium and each action is proportional to the Bonacich centrality (in the network) of each agent.
We develop further this approach by using the paper of Ballester and Calvó-Armengol (2010), who show the robustness of the first paper by reformulating the model as a linear-complementarity problem, a well-known issue in applied mathematics. One interesting result is to show that, using a suitable linear transformation of the interaction matrix (the one that gives the cross-derivatives), a linear-quadratic utility function that does not initially exhibit strategic complementarities can have complementarities in the induced game. This is referred to as hidden complementarities.
One example of a model that exhibits hidden complementarities is that of Bramoullé and Kranton (2007), which a model of public goods in networks. We will expose the model, and analyze the case with hidden complementarities as well as that with pure susbtitutabilities. A recent work on games on networks with incomplete information about the network structure is Galeotti et al. (2010).
Ballester, C., A. Calvó-Armengol and Y. Zenou (2006), « Who’s Who in Networks. Wanted: the Key Player », Econometrica 74, 1403-1417.
Ballester, C. and A. Calvó-Armengol (2010), « Interaction Patterns with Hidden Complementarities », Regional Science and Urban Economics.
Bramoullé, Y. and R. Kranton (2007), “Strategic Experimentation in Networks,” Journal of Economic Theory.
Galeotti, A., S. Goyal, M.O. Jackson, F. Vega-Redondo and L. Yariv (2010), “Network Games,” Review of Economic Studies.
M.O. Jackson and Y. Zenou (2014), “Games on networks”, In: P. Young and S. Zamir (Eds.), Handbook of Game Theory Vol. 4, Amsterdam: Elsevier Publisher, forthcoming.
4) Lecture 4: Games on Networks and Network Formation
We will endogeneize the network formation in the previous network games. In particular, we will expose the recent paper by Galeotti and Goyal (2010) who introduce network formation in the strategic experimentation game of Bramoullé and Kranton (2007).
We will also expose the model of König, Tessone and Zenou (2010) which extends the model of Ballester, Calvo-Armengol and Zenou (2006) by introducing network formation in a dynamic framework.
Galeotti, A. and S. Goyal (2010), “The law of the few,” American Economic Review, forthcoming.
M. König, C. Tessone and Y. Zenou (2010), “A dynamic model of network formation with strategic interactions,” Unpusblished manuscript, Stockholm University.
5) Lecture 6: Applications to Labor Economics
The exchange and diffusion of information is critical to the functioning of most labor markets, where individuals seeking jobs mobilize their local networks of friends and relatives. Networks of personal contacts mediate employment opportunities that flow through word-of-mouth and, in many cases, constitute a valid alternative source of employment information to more formal methods. The empirical evidences indeed suggest that about half of all jobs are filled through contacts (Holzer, 1988).
We will use the tools learned in Lectures 2 and 3 to deal with these labor network issues. Direct applications are made in the papers by Calvó-Armengol (2004) and Calvó-Armengol and Zenou (2005). We will expose these papers and show how they explain the role of networks in the labor market, in particular how people transmit job information to their friends.
Another approach, which is dynamic and has a more explicit structure (though there is no network formation) is that of Calvó-Armengol and Jackson (2004). This is a beautiful model that has very strong implications. In particular, it explains unemployment duration dependence.
A nice survey of this literature can be found in Ioannides and Loury (2004).
Calvó-Armengol, A. (2004), “Job Contact Networks,” Journal of Economic Theory, 115, 191-206.
Calvó-Armengol, A. and M.O. Jackson (2004), “The Effects of Social Networks on Employment and Inequality,” American Economic Review, 94, 426-454.
Calvó-Armengol, A. and Y. Zenou (2005), “Job matching, social network and word-of-mouth communication”, Journal of Urban Economics, 57, 500-522.
H. Holzer (1988), “Search Method Used by Unemployed Youth”, Journal of Labor Economics, 6, 1-20.
Ioannides M. and L. Loury (2004), “Job Information Networks, Neighborhood Effects, and Inequality,” Journal of Economic Literature 42, 1056-1093.
6) Lecture 7: Applications Crime
Crime is a “social” activity. Peers and friends have an important impact on crime decisions and crime activities. Indeed, most offenders belong to a network of friends that help them in their deeds. In their seminal study, Shaw and McKay (1942) show that delinquent boys in certain areas of US cities have contact not only with other delinquents who are their contemporaries but also with older offenders, who in turn had contact with delinquents preceding them, and so on ... This contact means that the traditions of delinquency can be and are transmitted down through successive generations of boys and across members of the same generation, in much the same way that language and other social forms are transmitted. In economics, the empirical evidence collected so far suggests that peer effects are, indeed, very strong in criminal decisions (Ludwig et al. 2001).
However, few theoretical models have investigated this issue. The first paper on this issue is the one by Glaeser, Sacerdote and Scheinkman (1996), where agents are located on the circumference of a circle and decide criminal activities by looking at their neighbors. They show that there are multiplier effects in the sense that the variance of crime is much higher when there are social interactions.
Calvó-Armengol and Zenou (2004) develop another explicit network model where any network structure (and not only the circle) is studied. They also analyze the network formation of criminals (using the pairwise-stability equilibrium concept) and show how social interactions affect crime decisions.
Another interesting approach is to differentiate between weak and strong ties in crime and to see how they affect both crime and labor activities. For that, we will expose the paper by Calvó-Armengol, Verdier and Zenou (2007).
We finally study the policy implications of crime networks using the paper by Ballester, Calvó-Armengol and Zenou (2010). Instead of punishing randomly criminals, they study the key-player policy, which consists in getting rid of the criminal whose removal results in the maximal decrease in overall activity.
Ballester, C., A. Calvó-Armengol and Y. Zenou (2010), “Delinquent networks,” Journal of the European Economic Association 8, 34-61.
Calvó-Armengol, A., T. Verdier and Y. Zenou (2007), “Strong Ties and Weak Ties in Employment and Crime,” Journal of Public Economics 91, 203-233.
Calvó-Armengol, A. and Y. Zenou (2004), “Social Networks and Crime Decisions: The Role of Social Structure in Facilitating Delinquent Behavior,” International Economic Review, 45, 935-954.
Glaeser, E.L., B. Sacerdote and J. Scheinkman (1996), “Crime and Social Interactions,” Quarterly Journal of Economics, 111, 508-548.
Ludwig, J., G.J. Duncan and P. Hirschfield (2001), “Urban Poverty and Juvenile Crime: Evidence from a Randomized Housing-Mobility Experiment,” Quarterly Journal of Economics, 116, 655-679.
Shaw, C. and H. McKay (1942), Juvenile Delinquency and Urban Areas, Chicago: University of Chicago Press.
Lecture 9: Empirical Aspects of Social Networks
In this last lecture, we will explore the empirical studies of some of the theoretical papers mentioned above. In particular, we will study how peer effects and social networks affect labor and crime activities.
We will start by the econometric problems that plague this literature. Indeed, empirical tests of models of social interactions are quite problematic because of well-known issues that render the identification and measurement of peer effects quite difficult: (i) reflection, which is a particular case of simultaneity (Manski, 1993) and (ii) endogeneity, which may arise for both peer self-selection and unobserved common (group) correlated effects.
We will first expose the paper by Bramoulle, Djebbari and Fortin (2009) who give some answers to these problems by exploiting the architecture of social networks to overcome this set of problems and to achieve the identification of endogenous peer effects.
We will also expose the paper by Calvó-Armengol, Patacchini and Zenou (2009) who apply the methodology of Bramoulle, Djebbari and Fortin (2009) to test peer effects in educations.
Other important papers that have test social network effects will be also exposed. Among others, we will expose Topa (2001) for unemployment rates in the US, Conley and Udry (2005), who investigate the role of social learning in the diffusion of a new agricultural technology in Ghana, Fafchamps and Lund (2003) who study risk-sharing networks in rural Philippines, Munshi (2003) who studies the social networks of Mexican Migrants in the U.S, and Wahba and Zenou (2005) who test labor-market networks in Egypt.
Bramoullé, Y., H. Djebbari, and B. Fortin (2009), “Identification of Peer Effects through Social Networks,” Journal of Econometrics 150, 41-55.
Calvó-Armengol, A., E. Patacchini and Y. Zenou (2009), “Peer Effects and Social Networks in Education,” Review of Economic Studies 76, 1239-1267.
Conley, T.G. and C.R. Udry (2010), “Learning About a New Technology: Pineapple in Ghana,”.
Fafchamps, M. and S. Lund (2003), “Risk Sharing Networks in Rural Philippines,” Journal of Development Economics 71, 261-87.
Manski, C.F. (1993), “Identification of Endogenous Effects: The Reflection Problem,” Review of Economic Studies 60, 531-542.
Munshi K. (2003), “Networks in the Modern Economy: Mexican Migrants in the U.S. Labor Market,” Quarterly Journal of Economics 118, 549-597.
Patacchini, E. and Y. Zenou (2010), “Juvenile Delinquency and Conformism,” Journal of Law, Economics, and Organization, forthcoming.
Topa, G. (2001), “Social interactions, local spillovers and unemployment,” Review of Economic Studies 68, 261-295.
Wahba, J. and Y. Zenou (2005), “Density, Social Networks and Job Search Methods: Theory and Applications to Egypt,” Journal of Development Economics 78, 443-473.
The course takes place at St. Petersburg, Souza Pechatnikov str., 16, room 410
10-00 - 11-30 Motivation, Definitions and Descriptive Evidence
11-45 - 13-15 Theories of Network Formation I
14-15 - 15-45 Theories of Network Formation II
16-00 - 17-30 Games on Networks I
10-00 - 11-30 Games on Networks and Network Formation
11-45 - 13-15 Applications to Labor Economics I
14-15 - 15-45 Applications to Labor Economics II
16-00 - 17-30 Applications Crime
10-00 - 11-30 Empirical Aspects of Social Networks I
11-45 - 13-15 Empirical Aspects of Social Networks II