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Specification and estimation of network formation and network interaction models with the exponential probability distribution

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  • Chih‐Sheng Hsieh
  • Lung‐Fei Lee
  • Vincent Boucher

Abstract

We model network formation and interactions under a unified framework by considering that individuals anticipate the effect of network structure on the utility of network interactions when choosing links. There are two advantages of this modeling approach: first, we can evaluate whether network interactions drive friendship formation or not. Second, we can control for the friendship selection bias on estimated interaction effects. We provide microfoundations of this statistical model based on the subgame perfect equilibrium of a two‐stage game and propose a Bayesian MCMC approach for estimating the model. We apply the model to study American high school students' friendship networks using the Add Health dataset. From two interaction variables, GPA and smoking frequency, we find that the utility of interactions in academic learning is important for friendship formation, whereas the utility of interactions in smoking is not. However, both GPA and smoking frequency are subject to significant peer effects.

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  • Chih‐Sheng Hsieh & Lung‐Fei Lee & Vincent Boucher, 2020. "Specification and estimation of network formation and network interaction models with the exponential probability distribution," Quantitative Economics, Econometric Society, vol. 11(4), pages 1349-1390, November.
  • Handle: RePEc:wly:quante:v:11:y:2020:i:4:p:1349-1390
    DOI: 10.3982/QE944
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    Cited by:

    1. Yann Bramoullé & Habiba Djebbari & Bernard Fortin, 2020. "Peer Effects in Networks: A Survey," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 603-629, August.
    2. Marco Battaglini & Eleonora Patacchini & Edoardo Rainone, 2019. "Endogenous Social Connections in Legislatures," NBER Working Papers 25988, National Bureau of Economic Research, Inc.
    3. Anton Badev, 2021. "Nash Equilibria on (Un)Stable Networks," Econometrica, Econometric Society, vol. 89(3), pages 1179-1206, May.
    4. Hsieh, Chih-Sheng & König, Michael & Liu, Xiaodong, 2019. "A Structural Model for the Coevolution of Networks and Behavior," CEPR Discussion Papers 13911, C.E.P.R. Discussion Papers.
    5. Áureo de Paula, 2020. "Econometric Models of Network Formation," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 775-799, August.
    6. Boucher, Vincent, 2020. "Equilibrium homophily in networks," European Economic Review, Elsevier, vol. 123(C).
    7. Hsieh, Chih-Sheng & Lin, Xu, 2017. "Gender and racial peer effects with endogenous network formation," Regional Science and Urban Economics, Elsevier, vol. 67(C), pages 135-147.
    8. Áureo de Paula, 2015. "Econometrics of network models," CeMMAP working papers CWP52/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education
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