IDEAS home Printed from https://ideas.repec.org/p/swe/wpaper/2018-10.html
   My bibliography  Save this paper

Estimation of a Scale-Free Network Formation Model

Author

Listed:
  • Anton Kolotilin

    (School of Economics, UNSW Business School)

  • Valentyn Panchenko

    (School of Economics, UNSW Business School)

Abstract

Growing evidence suggests that many social and economic networks are scale free in that their degree distribution has a power-law tail. A common explanation for this phenomenon is a random network formation process with preferential attachment. For a general version of such a process, we develop the pseudo maximum likelihood and generalized method of moments estimators. We prove consistency of these estimators by establishing the law of large numbers for growing networks. Simulations suggest that these estimators are asymptotically normally distributed and outperform the commonly used non-linear least squares and Hill (1975) estimators in finite samples. We apply our estimation methodology to a co-authorship network.

Suggested Citation

  • Anton Kolotilin & Valentyn Panchenko, 2018. "Estimation of a Scale-Free Network Formation Model," Discussion Papers 2018-10, School of Economics, The University of New South Wales.
    • Handle: RePEc:swe:wpaper:2018-10
    as

    Download full text from publisher

    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2018-10.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    2. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    3. H. Bauke, 2007. "Parameter estimation for power-law distributions by maximum likelihood methods," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(2), pages 167-173, July.
    4. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(2), pages 255-258, September.
    5. Matthew O. Jackson & Brian W. Rogers, 2007. "Meeting Strangers and Friends of Friends: How Random Are Social Networks?," American Economic Review, American Economic Association, vol. 97(3), pages 890-915, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tomson Ogwang, 2011. "Power laws in top wealth distributions: evidence from Canada," Empirical Economics, Springer, vol. 41(2), pages 473-486, October.
    2. Ogwang, Tomson, 2013. "Is the wealth of the world’s billionaires Paretian?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 757-762.
    3. Junho Na & Jeong-dong Lee & Chulwoo Baek, 2017. "Is the service sector different in size heterogeneity?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 95-120, April.
    4. Barunik, Jozef & Vacha, Lukas, 2010. "Monte Carlo-based tail exponent estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4863-4874.
    5. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    6. Rafael González-Val, 2012. "A Nonparametric Estimation of the Local Zipf Exponent for all US Cities," Environment and Planning B, , vol. 39(6), pages 1119-1130, December.
    7. Rafael González-Val, 2021. "The Probability Distribution of Worldwide Forest Areas," Sustainability, MDPI, vol. 13(3), pages 1-19, January.
    8. Luis Garicano & Claire Lelarge & John Van Reenen, 2016. "Firm Size Distortions and the Productivity Distribution: Evidence from France," American Economic Review, American Economic Association, vol. 106(11), pages 3439-3479, November.
    9. Rafael González‐Val, 2019. "Historical urban growth in Europe (1300–1800)," Papers in Regional Science, Wiley Blackwell, vol. 98(2), pages 1115-1136, April.
    10. Christian Schluter, 2021. "On Zipf’s law and the bias of Zipf regressions," Empirical Economics, Springer, vol. 61(2), pages 529-548, August.
    11. Christian Schluter, 2018. "Top Incomes, Heavy Tails, and Rank-Size Regressions," Econometrics, MDPI, vol. 6(1), pages 1-16, March.
    12. Daniel Fricke & Thomas Lux, 2015. "On the distribution of links in the interbank network: evidence from the e-MID overnight money market," Empirical Economics, Springer, vol. 49(4), pages 1463-1495, December.
    13. Coronel-Brizio, H.F. & Hernández-Montoya, A.R., 2010. "The Anderson–Darling test of fit for the power-law distribution from left-censored samples," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3508-3515.
    14. Paul Sheridan & Yuichi Yagahara & Hidetoshi Shimodaira, 2008. "A preferential attachment model with Poisson growth for scale-free networks," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 747-761, December.
    15. Christian Schluter & Mark Trede, 2019. "Size distributions reconsidered," Econometric Reviews, Taylor & Francis Journals, vol. 38(6), pages 695-710, July.
    16. Iglesias, Emma M. & Linton, Oliver, 2009. "Estimation of tail thickness parameters from GJR-GARCH models," UC3M Working papers. Economics we094726, Universidad Carlos III de Madrid. Departamento de Economía.
    17. Yan, Qiang & Wu, Lianren & Zheng, Lan, 2013. "Social network based microblog user behavior analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1712-1723.
    18. Alonso Rodríguez-Navarro & Ricardo Brito, 2019. "Probability and expected frequency of breakthroughs: basis and use of a robust method of research assessment," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(1), pages 213-235, April.
    19. Rashidisabet, Homa & Ajilore, Olusola & Leow, Alex & Demos, Alexander P., 2022. "Revisiting power-law estimation with applications to real-world human typing dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    20. Rafael González-Val, 2021. "The Spanish spatial city size distribution," Environment and Planning B, , vol. 48(6), pages 1609-1631, July.

    More about this item

    Keywords

    law of large numbers; consistency; degree distribution; scale-free network;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:swe:wpaper:2018-10. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Hongyi Li (email available below). General contact details of provider: https://edirc.repec.org/data/senswau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.