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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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    2. Marco Battaglini & Eleonora Patacchini & Edoardo Rainone, 2019. "Endogenous Social Connections in Legislatures," NBER Working Papers 25988, National Bureau of Economic Research, Inc.
    3. Alejandra Agustina Martínez, 2023. "Raise your Voice! Activism and Peer Effects in Online Social Networks," Working Papers 277, Red Nacional de Investigadores en Economía (RedNIE).
    4. Zenou, Yves & Biavaschi, Costanza & Giulietti, Corrado, 2021. "Social Networks and (Political) Assimilation in the Age of Mass Migration," CEPR Discussion Papers 16182, C.E.P.R. Discussion Papers.
    5. David Agrawal & Marie-Laure Breuillé & Julie Le Gallo, 2020. "Tax competition with intermunicipal cooperation," Post-Print hal-02949334, HAL.
    6. Boucher, Vincent & Dedewanou, F. Antoine & Dufays, Arnaud, 2022. "Peer-induced beliefs regarding college participation," Economics of Education Review, Elsevier, vol. 90(C).
    7. Áureo de Paula, 2015. "Econometrics of network models," CeMMAP working papers CWP52/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. 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.
    9. Alejandra Agustina Martínez, 2023. "Raise your voice! Activism and peer effects in online social networks," Discussion Papers 2023-05, Nottingham Interdisciplinary Centre for Economic and Political Research (NICEP).
    10. Anton Badev, 2021. "Nash Equilibria on (Un)Stable Networks," Econometrica, Econometric Society, vol. 89(3), pages 1179-1206, May.
    11. 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.
    12. Vincent Boucher & Carlo L. Del Bello & Fabrizio Panebianco & Thierry Verdier & Yves Zenou, 2023. "Education Transmission and Network Formation," Journal of Labor Economics, University of Chicago Press, vol. 41(1), pages 129-173.
    13. Áureo de Paula, 2020. "Econometric Models of Network Formation," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 775-799, August.
    14. Boucher, Vincent, 2020. "Equilibrium homophily in networks," European Economic Review, Elsevier, vol. 123(C).
    15. 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.
    16. Liza Charroin & Bernard Fortin & Marie Claire Villeval, 2022. "Peer effects, self-selection and dishonesty," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03712450, HAL.
    17. Liza Charroin & Bernard Fortin & Marie Claire Villeval, 2022. "Peer effects, self-selection and dishonesty," Post-Print hal-03712450, HAL.

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

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