My Friend Far Far Away: Asymptotic Properties of Pairwise Stable Networks

We explore the asymptotic properties of pairwise stables networks (Jackson and Wolinsky, 1996). Speci fically, we want to recover a set of parameters from the individuals' utility functions using the observation of a single pairwise stable network. We develop Pseudo Maximum Likelihood estimator and show that it is consistent and asymptotically normally distributed under a very weak version of homophily. The approach is compelling as it provides explicit, easy-to-check conditions on the admissible set of preferences. Moreover, the method is easily implementable using pre-programmed estimators available in most statistical packages. We provide an application of our method using the Add Health database.

[1]  Bernard Fortin,et al.  Identification of Peer Effects through Social Networks , 2007, SSRN Electronic Journal.

[2]  Jiue-An Yang,et al.  Spatial Social Networks , 2017 .

[3]  Michael P. Leung,et al.  Two-Step Estimation of Network-Formation Models with Incomplete Information , 2015 .

[4]  Federico Echenique,et al.  A Measure of Segregation Based on Social Interactions , 2007 .

[5]  M. Jackson,et al.  A Strategic Model of Social and Economic Networks , 1996 .

[6]  I. Prucha,et al.  Central Limit Theorems and Uniform Laws of Large Numbers for Arrays of Random Fields. , 2009, Journal of econometrics.

[7]  Matthew O. Jackson,et al.  The Existence of Pairwise Stable Networks , 2002 .

[8]  D. McFadden.  Econometric Models of Probabilistic Choice , 1981 .

[9]  D. McFadden.  Econometric Models for Probabilistic Choice Among Products , 1980 .

[10]  Joris Pinkse,et al.  Contracting in space: An application of spatial statistics to discrete-choice models , 1998 .

[11]  Matthew O. Jackson,et al.  Homophily and Long-Run Integration in Social Networks , 2012, J. Econ. Theory.

[12]  Matthew O. Jackson,et al.  Tractable and Consistent Random Graph Models , 2012, ArXiv.

[13]  Dale J. Poirier,et al.  Partial observability in bivariate probit models , 1980 .

[14]  G. Imbens,et al.  Social Networks and the Identification of Peer Effects , 2013 .

[15]  Lung-fei Lee,et al.  A Social Interactions Model with Endogenous Friendship Formation and , 2016 .

[16]  Alison C. Watts.  Formation of Segregated and Integrated Groups , 2006 .

[17]  On the relationship between unexplained wage gap and social network connections for ethnical groups , 2013 .

[18]  Y. Zenou,et al.  Ethnic Networks and Employment Outcomes , 2012, SSRN Electronic Journal.

[19]  Jeffrey M. Wooldridge,et al.  Partial maximum likelihood estimation of spatial probit models , 2013 .

[20]  H. White.  Asymptotic theory for econometricians , 1985 .

[21]  Alain Monfort,et al.  General concepts, estimation, prediction, and algorithms , 1995 .

[22]  M. Jackson,et al.  An Economic Model of Friendship: Homophily, Minorities and Segregation , 2007 .

[23]  Angelo Mele,et al.  A Structural Model of Segregation in Social Networks , 2010 .

[24]  Paolo Pin,et al.  Identifying the roles of race-based choice and chance in high school friendship network formation , 2010, Proceedings of the National Academy of Sciences.

[25]  Pradeep Ravikumar,et al.  Conditional Random Fields via Univariate Exponential Families , 2013, NIPS.

[26]  Yuichiro Kamada,et al.  Social distance and network structures , 2017 .

[27]  H. White,et al.  A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models , 1988 .

[28]  Timothy G. Conley.  GMM estimation with cross sectional dependence , 1999 .

[29]  Robert P. Gilles,et al.  Network potentials , 2007 .

[30]  Bernard Fortin,et al.  Série Scientifique Scientific Series 2011 s20 Peer Effects , Fast Food Consumption and Adolescent Weight Gain , 2011 .

[31]  Yann Bramoullé,et al.  Diversity and Popularity in Social Networks , 2009 .

[32]  Timothy G. Conley,et al.  Inference with dependent data using cluster covariance estimators , 2011 .

[33]  Sanjeev Goyal,et al.  Unequal connections , 2006, Int. J. Game Theory.

[34]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[35]  Marc Henry,et al.  Euclidean Revealed Preferences: Testing the Spatial Voting Model , 2010 .

[36]  David Marmaros,et al.  How Do Friendships Form? , 2005 .

[37]  J. Kadane.  Structural Analysis of Discrete Data with Econometric Applications , 1984 .

[38]  C. Gouriéroux,et al.  PSEUDO MAXIMUM LIKELIHOOD METHODS: THEORY , 1984 .

[39]  Vincent Boucher.  Conformism and Self-Selection in Social Networks , 2014 .

[40]  E. Tamer.  Incomplete Simultaneous Discrete Response Model with Multiple Equilibria , 2003 .

[41]  Konrad Menzel.  Large Matching Markets as Two‐Sided Demand Systems , 2015 .

[42]  Anton I Badev,et al.  Discrete Games in Endogenous Networks: Theory and Policy , 2014 .

[43]  Marc Henry,et al.  Set Identification in Models with Multiple Equilibria , 2011, 2102.12249.

[44]  R. Kranton,et al.  A Theory of Buyer-Seller Networks , 2001 .