1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Economics
  4. Volume 12, 2020
  5. Article

Annual Review of Economics

Volume 12, 2020

Econometric Models of Network Formation

Abstract

This article provides a selective review of the recent literature on econometric models of network formation. I start with a brief exposition on basic concepts and tools for the statistical description of networks; then I offer a review of dyadic models, focusing on statistical models on pairs of nodes, and I describe several developments of interest to the econometrics literature. I also present a discussion of nondyadic models in which link formation might be influenced by the presence or absence of additional links, which themselves are subject to similar influences. This argument is related to the statistical literature on conditionally specified models and the econometrics of game theoretical models. I close with a (nonexhaustive) discussion of potential areas for further development.

Keyword(s): dyadic models, JEL C31, JEL C51, JEL D85, network econometrics, strategic network formation models
Loading

Article metrics loading...

/content/journals/10.1146/annurev-economics-093019-113859
2020-08-02
2025-04-23
Loading full text...

Full text loading...

/deliver/fulltext/economics/12/1/annurev-economics-093019-113859.html?itemId=/content/journals/10.1146/annurev-economics-093019-113859&mimeType=html&fmt=ahah

Literature Cited

  1. Anderson KA, Richards-Shubik S. 2019. Collaborative production in science: an empirical analysis of coauthorships in economics Work. Pap., Carnegie Mellon Univ Pittsburgh, PA:
     [Google Scholar]
  2. Arellano M, Honoré BE. 2001. Panel data models: some recent developments. Handbook of Econometrics 5 J Heckman, E Leamer 3229–96 Amsterdam: Elsevier
     [Google Scholar]
  3. Arnold BC, Press SJ. 1989. Compatible conditional distributions. J. Am. Stat. Assoc. 84:152–56
     [Google Scholar]
  4. Aronow P, Samii C, Assenova V 2015. Cluster-robust variance estimation for dyadic data. Political Anal 23:564–77
     [Google Scholar]
  5. Atalay E, Hortacsu A, Roberts J, Syverson C 2011. Network structure of production. PNAS 108:5199–202
     [Google Scholar]
  6. Badev A. 2018. Nash equilibria on (un)stable networks Work. Pap., Fed. Reserve Board Washington, DC:
     [Google Scholar]
  7. Ballester C, Calvó-Armengol A, Zenou Y 2006. Who's who in networks. Wanted: the key player. Econometrica 74:1403–17
     [Google Scholar]
  8. Banerjee A, Chandrasekhar A, Duflo E, Jackson M 2014. Gossip: identifying central individuals in a social network Work. Pap., Mass. Inst. Technol Cambridge:
     [Google Scholar]
  9. Barabási A, Albert R. 1999. Emergence of scaling in random networks. Science 286:509–12
     [Google Scholar]
  10. Besag J. 1975. Statistical analysis of non-lattice data. Statistician 24:179–95
     [Google Scholar]
  11. Bhamidi S, Bresler G, Sly A 2011. Mixing time of exponential random graphs. Ann. Appl. Probab. 21:2146–70
     [Google Scholar]
  12. Bhattacharya S, Bickel PJ. 2015. Subsampling bootstrap of count features of networks. Ann. Stat. 43:2384–411
     [Google Scholar]
  13. Bickel PJ, Chen A, Levina E 2011. The method of moments and degree distributions for network models. Ann. Stat. 39:2280–301
     [Google Scholar]
  14. Bloch F, Jackson MO. 2006. Definitions of equilibrium in network formation games. Int. J. Game Theory 34:305–18
     [Google Scholar]
  15. Bollobás B. 2001. Random Graphs Cambridge, UK: Cambridge Univ. Press
     [Google Scholar]
  16. Bonacich P. 1972. Factoring and weighting approaches to status scores and clique identification. J. Math. Sociol. 2:113–20
     [Google Scholar]
  17. Bonacich P. 1987. Power and centrality: a family of measures. Am. J. Sociol. 92:1170–82
     [Google Scholar]
  18. Boucher V, Mourifié I. 2017. My friend far, far away: asymptotic properties of pairwise stable networks. Econom. J. 20:S14–46
     [Google Scholar]
  19. Bramoullé Y, Djebbari H, Fortin B 2020. Peer effects in networks: a survey. Annu. Rev. Econ. 12:603–29
     [Google Scholar]
  20. Brin S, Page L. 1998. The anatomy of a large scale hypertextual Web search engine. Comput. Netw. 30:107–17
     [Google Scholar]
  21. Cameron AC, Miller DL. 2014. Robust inference for dyadic data Work. Pap., Univ. Calif., Davis
     [Google Scholar]
  22. Candelaria LE, Ura T. 2018. Identification and inference of network formation games with misclassified links Work. Pap., Univ. Warwick Coventry, UK:
     [Google Scholar]
  23. Chandrasekhar A. 2015. Econometrics of network formation. Oxford Handbook on the Economics of Networks Y Bramoullé, A Galeotti, B Rogers 303–57 Oxford, UK: Oxford Univ. Press
     [Google Scholar]
  24. Chandrasekhar AG, Jackson M. 2016. A network formation model based on subgraphs Work. Pap., Stanford Univ Stanford, CA:
     [Google Scholar]
  25. Charbonneau KB. 2017. Multiple fixed effects in binary response panel data models. Econometrics J 20:S1–13
     [Google Scholar]
  26. Chatterjee S, Diaconis P. 2013. Estimating and understanding exponential random graph models. Ann. Stat. 41:2428–61
     [Google Scholar]
  27. Chatterjee S, Diaconis P, Sly A 2011. Random graphs with a given degree sequence. Ann. Appl. Probab. 21:1400–35
     [Google Scholar]
  28. Chiappori PA. 2019. Matching with Transfers: The Economics of Love and Marriage Princeton, NJ: Princeton Univ. Press
     [Google Scholar]
  29. Christakis NA, Fowler JH, Imbens GW, Kalyanaraman K 2020. An empirical model for strategic network formation. The Econometric Analysis of Network Data BS Graham, Á de Paula pp. 123–48 Amsterdam: Elsevier
     [Google Scholar]
  30. Chwe M. 2000. Communication and coordination in social networks. Rev. Econ. Stud. 67:1–16
     [Google Scholar]
  31. Ciliberto F, Murry C, Tamer E 2018. Market structure and competition in airline markets Work. Pap., Univ. Va: Charlottesville
     [Google Scholar]
  32. Comola M, Fafchamps M. 2014. Testing unilateral and bilateral link formation. Econ. J. 124:954–76
     [Google Scholar]
  33. Comola M, Fafchamps M. 2017. The missing transfers: estimating mis-reporting in dyadic data. Econ. Dev. Cult. Change 65:549–82
     [Google Scholar]
  34. Comola M, Prina S. 2019. Treatment effect accounting for network changes Work. Pap., Paris Sch. Econ Paris:
     [Google Scholar]
  35. Cragg JG. 1971. Some statistical models for limited dependent variables with application to the demand for durable goods. Econometrica 39:829–44
     [Google Scholar]
  36. de Paula Á 2013. Econometric analysis of games with multiple equilibria. Annu. Rev. Econ. 5:107–31
     [Google Scholar]
  37. de Paula Á 2017. Econometrics of network models. Advances in Economics and Econometrics: Theory and Applications B Honore, A Pakes, M Piazzesi, L Samuelson 268–323 Cambridge, UK: Cambridge Univ. Press
     [Google Scholar]
  38. de Paula Á, Richards-Shubik S, Tamer E 2018. Identifying preferences in networks with bounded degrees. Econometrica 86:263–88
     [Google Scholar]
  39. Dzemski A. 2019. An empirical model of dyadic link formation in a network with unobserved heterogeneity. Rev. Econ. Stat. 101:763–76
     [Google Scholar]
  40. Erdös P, Rényi A. 1959. On random graphs. Publ. Math. Debr. 6:290–97
     [Google Scholar]
  41. Erdös P, Rényi A. 1960. On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5:17–61
     [Google Scholar]
  42. Fafchamps M, Gubert F. 2007. The formation of risk sharing networks. J. Dev. Econ. 83:326–50
     [Google Scholar]
  43. Fafchamps M, Lund S. 2003. Risk-sharing networks in rural Philippines. J. Dev. Econ. 71:261–87
     [Google Scholar]
  44. Fernández-Val I, Weidner M. 2016. Individual and time effects in nonlinear panel models with large. J. Econom. 192:291–312
     [Google Scholar]
  45. Fernández-Val I, Weidner M. 2018. Fixed effects estimation of large-t panel data models. Annu. Rev. Econ. 10:109–38
     [Google Scholar]
  46. Frank O, Strauss D. 1986. Markov graphs. J. Am. Stat. Assoc. 81:832–42
     [Google Scholar]
  47. Gao WY 2020. Nonparametric identification in index models of link formation. J. Econom. 215:399–413
     [Google Scholar]
  48. Ghili S. 2018. Network formation and bargaining in vertical markets: the case of narrow networks in health insurance Work. Pap., Yale Univ New Haven, CT:
     [Google Scholar]
  49. Gilbert E. 1959. Random graphs. Ann. Math. Stat. 30:1141–44
     [Google Scholar]
  50. Gilleskie D, Zhang YS. 2009. Friendship formation and smoking initiation among teens Work. Pap., Univ. N.C Chapel Hill:
     [Google Scholar]
  51. Gilmore M. 2016. The curse of the Ramones. Rolling Stone May 19. https://www.rollingstone.com/culture/culture-news/the-curse-of-the-ramones-165741/
    [Google Scholar]
  52. Goldsmith-Pinkham P, Imbens G. 2013. Social networks and the identification of peer effects. J. Bus. Econ. Stat. 31:253–64
     [Google Scholar]
  53. Gould P. 1967. On the geographical interpretation of eigenvalues. Trans. Inst. Br. Geogr. 42:53–86
     [Google Scholar]
  54. Graham BS. 2015. Methods of identification in social networks. Annu. Rev. Econ. 7:465–85
     [Google Scholar]
  55. Graham BS. 2016. Homophily and transitivity in dynamic network formation Work. Pap., Univ. Calif Berkeley:
     [Google Scholar]
  56. Graham BS. 2017. An econometric model of network formation with degree heterogeneity. Econometrica 85:1033–63
     [Google Scholar]
  57. Graham BS. 2020. The econometrics of networks. Handbook of Econometrics 7A S Durlauf, L Hansen, JJ Heckman, R Matzkin Amsterdam: Elsevier. In press
     [Google Scholar]
  58. Graham BS, de Paula Á 2020. The Econometric Analysis of Network Data Amsterdam: Elsevier
     [Google Scholar]
  59. Gualdani C. 2019. An econometric model of network formation with an application to board interlocks between firms Work. Pap., Toulouse Sch. Econ Toulouse, Fr.:
     [Google Scholar]
  60. Han A. 1987. Non-parametric analysis of a generalized regression model: the maximum rank correlation estimator. J. Econom. 35:303–16
     [Google Scholar]
  61. Han X, Hsieh CS, Ko S 2019. Spatial modeling approach for dynamic network formation and interactions Work. Pap., Natl. Taiwan Univ Taipei:
     [Google Scholar]
  62. Ho K, Lee R. 2019. Equilibrium provider networks: bargaining and exclusion in health care markets. Am. Econ. Rev. 109:473–522
     [Google Scholar]
  63. Hoff P. 2005. Bilinear mixed-effects models for dyadic data. J. Am. Stat. Assoc. 100:286–95
     [Google Scholar]
  64. Holland PW, Leinhardt S. 1976. Local structure in social networks. Sociol. Methodol. 7:1–45
     [Google Scholar]
  65. Holland PW, Leinhardt S. 1981. An exponential family of probability distributions for directed graphs. J. Am. Stat. Assoc. 76:33–65
     [Google Scholar]
  66. Horn H, Wolinsky A. 1988. Bilateral monopolies and incentives for merger. RAND J. Econ. 19:408–19
     [Google Scholar]
  67. Hsieh CS, Lee LF. 2016. A social interactions model with endogenous friendship formation and selectivity. J. Appl. Econom. 31:301–19
     [Google Scholar]
  68. Hsieh CS, Lee LF, Boucher V 2019. Specification and estimation of network formation and network interaction models with the exponential probability distribution Work. Pap., Ohio State Univ Columbus:
     [Google Scholar]
  69. Jackson M. 2009. Social and Economic Networks Princeton, NJ: Princeton Univ. Press
     [Google Scholar]
  70. Jackson MO, Watts A. 2002. The evolution of social and economic networks. J. Econ. Theory 106:265–95
     [Google Scholar]
  71. Jackson MO, Wolinsky A. 1996. A strategic model of social and economic networks. J. Econ. Theory 71:44–74
     [Google Scholar]
  72. Jochmans K. 2018. Semiparametric analysis of network formation. J. Bus. Econ. Stat. 36:705–13
     [Google Scholar]
  73. Jordan MI, Wainwright MJ. 2008. Graphical Models, Exponential Families, and Variational Inference Delft, Neth: Now Publ.
     [Google Scholar]
  74. Katz L. 1953. A new status index derived from sociometric analysis. Psychometrica 18:39–43
     [Google Scholar]
  75. Kolaczyk E. 2009. Statistical Analysis of Network Data Berlin: Springer-Verlag
     [Google Scholar]
  76. Leung M. 2015a. A random-field approach to inference in large models of network formation Work. Pap., Stanford Univ Stanford, CA:
     [Google Scholar]
  77. Leung M. 2015b. Two-step estimation of network formation models with incomplete information. J. Econom. 188:182–95
     [Google Scholar]
  78. Liebman E. 2018. Bargaining in markets with exclusion: an analysis of health insurance networks Work. Pap., Univ. Ga Athens:
     [Google Scholar]
  79. Manski CF. 1993. Identification of endogenous social effects: the reflection problem. Rev. Econ. Stud. 60:531–42
     [Google Scholar]
  80. Mele A. 2017. A structural model of dense network formation. Econometrica 85:825–50
     [Google Scholar]
  81. Mele A. 2020. Does school desegregation promote diverse interactions? An equilibrium model of segregation within schools. Am. Econ. J. Econ. Policy 12:228–57
     [Google Scholar]
  82. Mele A, Zhu L. 2019. Approximate variational estimation for a model of network formation Work. Pap., Johns Hopkins Univ Baltimore, MD:
     [Google Scholar]
  83. Menzel K. 2016. Strategic network formation with many agents Work. Pap., New York Univ New York:
     [Google Scholar]
  84. Miyauchi Y. 2016. Structural estimation of a pairwise stable network with nonnegative externality. J. Econom. 195:224–35
     [Google Scholar]
  85. Murray I, Ghahramani Z, MacKay D 2006. MCMC for doubly-intractable distributions. Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence R Dechter, T Richardson 359–66 Arlington, VA: AUAI Press
     [Google Scholar]
  86. Orbanz P, Roy DM. 2015. Bayesian models of graphs, arrays and other exchangeable randoms structures. IEEE Trans. Pattern Anal. Mach. Intell. 37:437–61
     [Google Scholar]
  87. Pelican A, Graham B. 2019. Testing for strategic interaction in social and economic network formation Work. Pap., Univ. Calif. Berkeley:
     [Google Scholar]
  88. Poirier D. 1980. Partial observability in bivariate probit models. J. Econom. 12:209–17
     [Google Scholar]
  89. Rasch G. 1960. Probabilistic Models for Some Intelligence and Attainment Tests Chicago: Univ. Chicago Press
     [Google Scholar]
  90. Ridder G, Sheng S. 2015. Estimation of large network formation games Work. Pap., Univ. South. Calif Los Angeles:
     [Google Scholar]
  91. Robins G, Pattison P, Kalish Y, Lusher D 2007. An introduction to exponential random graph (p*) models for social networks. Soc. Netw. 29:173–91
     [Google Scholar]
  92. Sheng S. 2018. A structural econometric analysis of network formation games through subnetworks Work. Pap., Univ. Calif Los Angeles:
     [Google Scholar]
  93. Shi Z, Chen X. 2016. A structural network pairwise regression model with individual heterogeneity Work. Pap., Chin. Univ. Hong Kong Hong Kong:
     [Google Scholar]
  94. Snijders T. 2002. Markov chain Monte Carlo estimation of exponential random graph models. J. Soc. Struct. 3:1–40
     [Google Scholar]
  95. Strauss D, Ikeda M. 1990. Pseudolikelihood estimation for social networks. J. Am. Stat. Assoc. 85:204–12
     [Google Scholar]
  96. Tabord-Meehan M. 2019. Inference with dyadic data: asymptotic behavior of the dyadic-robust t-statistic. J. Bus. Econ. Stat. 37:671–80
     [Google Scholar]
  97. Tamer E. 2010. Partial identification in econometrics. Annu. Rev. Econ. 2:167–95
     [Google Scholar]
  98. Toth P. 2018. Semiparametric estimation in network formation models with homophily and degree homophily Work. Pap., Univ. Tex Austin:
     [Google Scholar]
  99. Yan T, Jiang B, Fienberg SE, Leng C 2019. Statistical inference in a directed network model with covariates. J. Am. Stat. Assoc. 114:857–68
     [Google Scholar]
  100. Yan T, Xu J. 2013. A central limit theorem in the β-model for undirected random graphs with a diverging number of vertices. Biometrika 100:519–24
     [Google Scholar]
  101. Zenou Y. 2016. Key players. The Oxford Handbook of the Economics of Networks Y Bramoullé, A Galeotti, B Rogers 244–74 Oxford, UK: Oxford Univ. Press
     [Google Scholar]
  102. Zheng T, Salganik MJ, Gelman A 2006. How many people do you know in prison? Using overdispersion in count data to estimate social structure in networks. J. Am. Stat. Assoc. 101:409–23
     [Google Scholar]
/content/journals/10.1146/annurev-economics-093019-113859
Loading
Econometric Models of Network Formation
Annual Review of Economics 12, 775 (2020); https://doi.org/10.1146/annurev-economics-093019-113859
/content/journals/10.1146/annurev-economics-093019-113859
/content/journals/10.1146/annurev-economics-093019-113859
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error