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A Structural Model of Segregation in Social Networks

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Abstract

In this paper, I develop and estimate a dynamic model of strategic network formation with heterogeneous agents. The main theoretical result is the existence of a unique stationary equilibrium, which characterizes the probability of observing a specific network in the data. As a consequence, the structural parameters can be estimated using only one observation of the network at a single point in time. The estimation is challenging, since the exact evaluation of the likelihood function is computationally infeasible even for very small networks. To overcome this problem, I propose a Bayesian Markov Chain Monte Carlo algorithm that avoids the direct evaluation of the likelihood. This method drastically reduces the computational burden of estimating the posterior distribution and allows inference in high dimensional models. I present an application to the study of segregation in school friendship networks, using data from Add Health. The latter contains the actual social network of each student in a representative sample of US schools. My results suggest that for White students, the value of a same-race friend decreases with the fraction of whites in the school. This relationship is of opposite sign for African American students. The model is used to study how different desegregation policies may affect the structure of the network in equilibrium. I find an inverted U-shape relationship between the fraction of students belonging to a racial group and the expected equilibrium segregation levels. These results suggests that these policies should be carefully designed in order to be effective.

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Bibliographic Info

Paper provided by NET Institute in its series Working Papers with number 10-16.

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Length: 56 pages
Date of creation: Sep 2010
Date of revision:
Handle: RePEc:net:wpaper:1016

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Web page: http://www.NETinst.org/

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Keywords: Social Networks; Bayesian Estimation; Markov Chain Monte Carlo;

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References

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  1. Nicholas A. Christakis & James H. Fowler & Guido W. Imbens & Karthik Kalyanaraman, 2010. "An Empirical Model for Strategic Network Formation," NBER Working Papers 16039, National Bureau of Economic Research, Inc.
  2. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  3. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
  4. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
  5. Sergio Currarini & Matthew O. Jackson & Paolo Pin, 2009. "An Economic Model of Friendship: Homophily, Minorities, and Segregation," Econometrica, Econometric Society, vol. 77(4), pages 1003-1045, 07.
  6. De Martí, Joan & Zenou, Yves, 2009. "Ethnic Identity and Social Distance in Friendship Formation," CEPR Discussion Papers 7566, C.E.P.R. Discussion Papers.
  7. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  8. Oriana Bandiera & Imran Rasul, 2006. "Social Networks and Technology Adoption in Northern Mozambique," Economic Journal, Royal Economic Society, vol. 116(514), pages 869-902, October.
  9. Andrea Galeotti, 2006. "One-way flow networks: the role of heterogeneity," Economic Theory, Springer, vol. 29(1), pages 163-179, September.
  10. Topa, Giorgio, 1997. "Social Interactions, Local Spillovers and Unemployment," Working Papers 97-17, C.V. Starr Center for Applied Economics, New York University.
  11. Giacomo De Giorgi & Michele Pellizzari & Silvia Redaelli, 2010. "Identification of Social Interactions through Partially Overlapping Peer Groups," American Economic Journal: Applied Economics, American Economic Association, vol. 2(2), pages 241-75, April.
  12. Ryo Nakajima, 2007. "Measuring Peer Effects on Youth Smoking Behaviour," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 897-935.
  13. Gilles, R.P. & Sarangi, S., 2004. "Social Network Formation with Consent," Discussion Paper 2004-70, Tilburg University, Center for Economic Research.
  14. Mayer, Adalbert & Puller, Steven L., 2008. "The old boy (and girl) network: Social network formation on university campuses," Journal of Public Economics, Elsevier, vol. 92(1-2), pages 329-347, February.
  15. Topa, Giorgio, 2001. "Social Interactions, Local Spillovers and Unemployment," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 261-95, April.
  16. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 70(1), pages 147-165, January.
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Cited by:
  1. Angelo Mele, 2013. "Approximate variational inference for a model of social interactions," Working Papers 13-16, NET Institute.
  2. Vincent BOUCHER & Ismael MOURIFIÉ, 2013. "My Friend Far Far Away: Asymptotic Properties of Pairwise Stable Networks," Working Papers tecipa-499, University of Toronto, Department of Economics.

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