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Specification and Estimation of Network Formation and Network Interaction Models with the Exponential Probability Distribution

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  • Hsieh, Chih-Sheng
  • Lee, Lung fei

Abstract

In this paper, we model network formation and network interactions under a unified framework. The key feature of our model is to allow individuals to respond to incentives stemming from interaction benefits on certain activities when they choose friends (network links), while capturing homophily in terms of unobserved characteristic variables in network formation and activities. There are two advantages of this modeling approach: first, one can evaluate whether incentives from certain interactions are important factors for friendship formation or not. Second, in addition to homophily effects in terms of unobserved characteristics, inclusion of incentive effects in the network formulation also corrects possible friendship selection bias on activity outcomes under network interactions. A theoretical foundation of this unified model is based on a complete information cooperative game. A tractable Bayesian MCMC approach is proposed for the estimation of the model. We apply the model to empirically study American high school students' friendship networks with the Add Health data. We consider two activity variables, GPA and smoking frequency, and find a significant incentive effect from GPA, but not from smoking, on friendship formation. These results suggest that the benefit of interactions in academic learning is an important factor for friendship formation, while the interaction benefit in smoking is not, even though homophily in smoking behavior is important for a smoker to link to other smokers. On the other hand, from the perspective of network interactions, both GPA and smoking frequency are subject to significant positive interaction (peer) effects.

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  • Hsieh, Chih-Sheng & Lee, Lung fei, 2017. "Specification and Estimation of Network Formation and Network Interaction Models with the Exponential Probability Distribution," MPRA Paper 60726, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:60726
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    Cited by:

    1. Marco Battaglini & Eleonora Patacchini & Edoardo Rainone, 2019. "Endogenous Social Connections in Legislatures," NBER Working Papers 25988, National Bureau of Economic Research, Inc.
    2. Charroin, Liza & Fortin, Bernard & Villeval, Marie Claire, 2022. "Peer effects, self-selection and dishonesty," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 618-637.
    3. 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.
    4. Áureo de Paula, 2020. "Econometric Models of Network Formation," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 775-799, August.
    5. Áureo de Paula, 2015. "Econometrics of network models," CeMMAP working papers CWP52/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Anton Badev, 2021. "Nash Equilibria on (Un)Stable Networks," Econometrica, Econometric Society, vol. 89(3), pages 1179-1206, May.
    7. Boucher, Vincent & Del Bello, Carlo & Panebianco, Fabrizio & Verdier, Thierry & Zenou, Yves, 2020. "Education Transmission and Network Formation," CEPR Discussion Papers 14997, C.E.P.R. Discussion Papers.
    8. Liza Charroin & Bernard Fortin & Marie Claire Villeval, 2022. "Peer effects, self-selection and dishonesty," Post-Print hal-03712450, HAL.
    9. Chih-Sheng Hsieh & Michael D. Konig & Xiaodong Liu, 2022. "A Structural Model for the Coevolution of Networks and Behavior," The Review of Economics and Statistics, MIT Press, vol. 104(2), pages 355-367, May.
    10. Boucher, Vincent, 2020. "Equilibrium homophily in networks," European Economic Review, Elsevier, vol. 123(C).
    11. 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.

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    Keywords

    Social Networks; social interaction; selectivity; spatial autoregression; Bayesian estimation;
    All these keywords.

    JEL classification:

    • 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
    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth

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