A Weak Law for Moments of Pairwise Stable Networks

This paper studies the dependence structure of sparse networks realized according to a strategic model of network formation with homophilous agents. We argue that equilibrium selection and chains of indirect dependence generated by strategic interactions are the main drivers of network dependence. Drawing on results in random-graph theory, we derive weak-dependence conditions under which a law of large numbers holds for a general class of network moments. A key condition restricts the strength of strategic interactions, which constitutes the network analog of conventional weak-dependence assumptions in time series and spatial econometrics that bound the magnitude of autoregressive parameters. We apply our result to estimating models of strategic network formation and treatment effects under network interference.

[1]  P. Bickel,et al.  The method of moments and degree distributions for network models , 2011, 1202.5101.

[2]  D. Owen.  A table of normal integrals , 1980 .

[3]  B. Fortin,et al.  social networks: econometrics , 2010 .

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

[5]  Bruce A. Desmarais,et al.  Inferential Network Analysis with Exponential Random Graph Models , 2011, Political Analysis.

[6]  W. Powell,et al.  Network Dynamics and Field Evolution: The Growth of Interorganizational Collaboration in the Life Sciences1 , 2005, American Journal of Sociology.

[7]  Peter D. Hoff,et al.  Modeling Dependencies in International Relations Networks , 2004, Political Analysis.

[8]  Matthew O. Jackson,et al.  The Evolution of Social and Economic Networks , 2002, J. Econ. Theory.

[9]  NeÅŸe Yildiz.  CONSISTENCY OF PLUG-IN ESTIMATORS OF UPPER CONTOUR AND LEVEL SETS , 2011, Econometric Theory.

[10]  Shuyang Sheng,et al.  Identi…cation and Estimation of Network Formation Games , 2012 .

[11]  V. Chernozhukov,et al.  Estimation and Confidence Regions for Parameter Sets in Econometric Models , 2007 .

[12]  S. Goodreau,et al.  Birds of a feather, or friend of a friend? using exponential random graph models to investigate adolescent social networks* , 2009, Demography.

[13]  Vincent Boucher,et al.  My Friend Far Far Away: Asymptotic Properties of Pairwise Stable Networks , 2015 .

[14]  Angelo Mele,et al.  A Structural Model of Dense Network Formation , 2017 .

[15]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[16]  Elie Tamer,et al.  Identification of Preferences in Network Formation Games , 2014 .

[17]  I. Prucha,et al.  On Spatial Processes and Asymptotic Inference under Near-Epoch Dependence. , 2012, Journal of econometrics.

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

[19]  Cosma Rohilla Shalizi,et al.  Homophily and Contagion Are Generically Confounded in Observational Social Network Studies , 2010, Sociological methods & research.

[20]  Xiaoxia Shi,et al.  Inference Based on Conditional Moment Inequalities , 2010 .

[21]  Tyler H. McCormick,et al.  Using Aggregated Relational Data to Feasibly Identify Network Structure Without Network Data , 2017, The American economic review.

[22]  Bryan S. Graham,et al.  Homophily and Transitivity in Dynamic Network Formation , 2016 .

[23]  Aureo de Paula,et al.  Econometric Analysis of Games with Multiple Equilibria , 2012 .

[24]  M. McPherson,et al.  BIRDS OF A FEATHER: Homophily , 2001 .

[25]  Yuhei Miyauchi.  Structural Estimation of Pairwise Stable Networks with Nonnegative Externality , 2016 .

[26]  J. Dall,et al.  Random geometric graphs. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  M. McPherson,et al.  Birds of a Feather: Homophily in Social Networks , 2001 .

[28]  Andreas Dzemski,et al.  An Empirical Model of Dyadic Link Formation in a Network with Unobserved Heterogeneity , 2018, Review of Economics and Statistics.

[29]  Matthew O. Jackson,et al.  A Network Formation Model Based on Subgraphs , 2016, ArXiv.

[30]  Arun G. Chandrasekhar,et al.  Econometrics of Network Formation , 2016 .

[31]  Ismael Mourifié,et al.  My Friend Far, Far Away: A Random Field Approach to Exponential Random Graph Models , 2017, The econometrics journal.

[32]  B. Graham.  An Econometric Model of Network Formation With Degree Heterogeneity , 2017 .

[33]  Lung-fei Lee,et al.  A Structural Modeling Approach for Network Formation and Social Interactions – with Applications to Students ’ Friendship Choices and Selectivity on Activities , 2012 .

[34]  M. R. Leadbetter.  Poisson Processes , 2011, International Encyclopedia of Statistical Science.

[35]  J. Yukich,et al.  Weak laws of large numbers in geometric probability , 2003 .

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

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

[38]  Elie Tamer,et al.  Identifying preferences in networks with bounded degree , 2016 .

[39]  Bryan S. Graham,et al.  An empirical model of network formation : detecting homophily when agents are heterogeneous , 2014 .

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

[41]  Mathew D. Penrose,et al.  Gaussian Limts for Random Geometric Measures , 2007 .

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

[43]  Kosuke Uetake.  Strategic Network Formation and Performance in the Venture Capital Industry , 2012 .

[44]  Albert-Lszl Barabsi,et al.  Network Science , 2016, Encyclopedia of Big Data.

[45]  James E. West,et al.  From Natural Variation to Optimal Policy? the Importance of Endogenous Peer Group Formation * 1 Data 1.1 the Dataset 2 Experimental Design and Sorting Methodology , 2022 .

[46]  J. Yukich,et al.  Central limit theorems for some graphs in computational geometry , 2001 .

[47]  Béla Bollobás,et al.  The phase transition in inhomogeneous random graphs , 2007, Random Struct. Algorithms.

[48]  Simon Jackman,et al.  Democracy as a Latent Variable , 2008 .

[49]  Robert M. de Jong,et al.  DYNAMIC TIME SERIES BINARY CHOICE , 2011, Econometric Theory.

[50]  Lung-fei Lee,et al.  Best Spatial Two‐Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances , 2003 .

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

[52]  Jonathan Newton,et al.  Coalitional stochastic stability , 2012, Games Econ. Behav..

[53]  Karyne B. Charbonneau,et al.  Multiple Fixed Effects in Binary Response Panel Data Models , 2017 .

[54]  Lung-fei Lee.  Estimation of a Binary Choice Game Model with Network Links , 2015 .

[55]  Ida Johnsson,et al.  Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach , 2017, Review of Economics and Statistics.

[56]  Peter D. Hoff,et al.  Latent Space Approaches to Social Network Analysis , 2002 .

[57]  P. Bearman,et al.  The Estimation of Network Formation Games with Positive Spillovers , 2017 .

[58]  R. Ambartzumian.  Stochastic and integral geometry , 1987 .

[59]  Geert Ridder,et al.  Estimation of Large Network Formation Games , 2020 .

[60]  Tim Hellmann,et al.  On the existence and uniqueness of pairwise stable networks , 2013, Int. J. Game Theory.

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

[62]  E. Michael.  Continuous Selections. I , 1956 .

[63]  Haiqing Xu,et al.  Social Interactions in Large Networks: A Game Theoretic Approach , 2016, ArXiv.

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

[65]  Margherita Comola.  Estimating Local Network Externalities , 2016 .

[66]  Tom A. B. Snijders,et al.  Introduction to stochastic actor-based models for network dynamics , 2010, Soc. Networks.

[67]  Larry G. Epstein,et al.  Robust Confidence Regions for Incomplete Models , 2015 .

[68]  M. Mobius,et al.  How Much is a Friend Worth? Directed Altruism and Enforced Reciprocity in Social Networks , 2007 .

[69]  P. Bickel,et al.  A nonparametric view of network models and Newman–Girvan and other modularities , 2009, Proceedings of the National Academy of Sciences.

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

[71]  Peter M. Aronow,et al.  Estimating Average Causal Effects Under Interference Between Units , 2013, 1305.6156.

[72]  Marcel Fafchamps,et al.  The formation of risk sharing networks , 2007 .

[73]  Toby E. Stuart,et al.  Syndication Networks and the Spatial Distribution of Venture Capital Investments1 , 1999, American Journal of Sociology.