Skip to main content
SpringerLink
Log in
Book cover

International Conference on Complex Networks and their Applications

COMPLEX NETWORKS 2017: Complex Networks & Their Applications VI pp 1100–1110Cite as

Shock Propagation Through Customer-Supplier Relationships: An Application of the Stochastic Actor-Oriented Model

  • Conference paper
  • First Online:

Part of the book series: Studies in Computational Intelligence ((SCI,volume 689))

Abstract

The dynamics of individual firms’ behaviors and the evolution of interfirm network mutually affect each other, and its observation is the consequence of various effects originating from different mechanisms. To untangle these intertwined effects and to quantify how firms interact with their trading partners, we apply the stochastic actor-oriented model (SAOM) to firm data with customer-supplier relationships in Japan. We separate two propagations driven by customers and suppliers, and find that the both types of propagation are statistically significant and crucial factors in the dynamics of firms’ behaviors.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    Following the literature (e.g., [18]), we use the term, firm’s behavior, in a wide sense, which includes intentional decision by a firm (e.g., investment and production) as well as changeable attributes (e.g., firm’s performance, profit and growth rate). In the following, we use behavior and attribute interchangeably.

  2. 2.

    While the application of the SAOM to economic issues is quite rare in the literature, an important exception is [4], in which interbank network formation is empirically examined.

  3. 3.

    The K computer is the first 10-petaflops supercomputer developed by RIKEN and Fujitsu under the Japanese national project. The system has 82944 compute nodes connected by Tofu high-speed interconnects. For more details, see [19].

  4. 4.

    To be precise, \(\lambda \) is the sum of rate \(\lambda _{net.}\) for network change and rate \(\lambda _{beh.}\) for behavior change.

  5. 5.

    To control the average effect of the tendency to have a tie to a high-performance firm, behavior-related popularity is included in the model.

  6. 6.

    For the method to numerically solve the moment equation (2), see the Appendix.

  7. 7.

    Discretization for the growth rate g is as follows: \(z = 1\) for \(g \le - 0.2\), \(z = 2\) for \(-0.2 < g \le -0.05\), \(z = 3\) for \(-0.05 < g \le 0.05\), \(z = 4\) for \(0.05 < g \le 0.2\), \(z = 5\) for otherwise.

  8. 8.

    Imagine that the parameters are partitioned into (\(\theta _0, \theta _1\)), where \(\theta _1\) has d-dimension, and we need to test the null hypothesis \(H_0\): \(\theta _1 = 0\) against \(H_1\):\(\theta _1 \ne 0\). Neyman-Rao test statistics follows the chi-squared distribution with d degrees of freedom under the null hypothesis. See [14].

  9. 9.

    We randomly shuffle \(z_i\) among the nodes while keeping \(x_{ij}\), i.e. the network structure as a null hypothesis. We obtained, by using 100 samples, \(I=-0.0012(0.0014)\) and \(C=0.998(0.019)\) for the Community 1, \(I=-0.0007(0.0018)\) and \(C=0.991(0.022)\) for the Community 2 as average (s.e. in parentheses) compared with Table 4.

References

  1. Chakraborty, A., Kichikawa, Y., Iino, T., Iyetomi, H., Inoue, H., Fujiwara, Y., Aoyama, H.: Hierarchical Clustering of Communities in Japanese Production Network (in preparation)

    Google Scholar 

  2. Dosi, G., Fagiolo, G., Napoletano, M., Roventini, A.: Income distribution, credit and fiscal policies in an agent-based keynesian model. J. Econ. Dyn. Control 37(8), 1598–1625 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dosi, G., Fagiolo, G., Napoletano, M., Roventini, A., Treibich, T.: Fiscal and monetary policies in complex evolving economies. J. Econ. Dyn. Control 52, 166–189 (2015)

    Article  MathSciNet  Google Scholar 

  4. Finger, K., Lux, T.: Network formation in the interbank money market: an application of the actor-oriented model. Soc. Netw. 48, 237–249 (2017)

    Article  Google Scholar 

  5. Gai, P., Haldane, A., Kapadia, S.: Complexity, concentration and contagion. J. Monet. Econ. 58(5), 453–470 (2011)

    Article  Google Scholar 

  6. Gai, P., Kapadia, S.: Contagion in financial networks. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 466, 2401–2423 (2010). The Royal Society

    Article  MathSciNet  MATH  Google Scholar 

  7. Kushner, H., Yin, G.: Stochastic Approximation and Recursive Algorithms and Applications, 2nd edn. Springer, Berlin

    Google Scholar 

  8. LeBaron, B., Tesfatsion, L.: Modeling macroeconomies as open-ended dynamic systems of interacting agents. Am. Econ. Rev. 98(2), 246–250 (2008)

    Article  Google Scholar 

  9. Lux, T., Zwinkels, R.C.: Empirical validation of agent-based models. In: Hommes, C., LeBaron, B. (eds.) Handbook of Computational Economics. Elsevier, Amsterdam (2017)

    Google Scholar 

  10. McFadden, D.: Conditional logit analysis of qualitative choice behavior. In: Zarembka, P. (ed.) Frontiers in Econometrics, pp. 105–142. Academic Press, London (1974)

    Google Scholar 

  11. Ripley, R.M., Snijders, T.A., Boda, Z., Vörös, A., Preciado, P.: Manual for RSIENA. University of Oxford, Department of Statistics, Nuffield College (2015)

    Google Scholar 

  12. Rosvall, M., Bergstrom, C.T.: Maps of random walks on complex networks reveal community structure. Proc. Natl. Acad. Sci. 105(4), 1118–1123 (2008)

    Article  Google Scholar 

  13. Rosvall, M., Bergstrom, C.T.: Multilevel compression of random walks on networks reveals hierarchical organization in large integrated systems. PloS One 6(4), e18209 (2011)

    Article  Google Scholar 

  14. Schweinberger, M.: Statistical modelling of network panel data: goodness of fit. Br. J. Math. Stat. Psychol. 65(2), 263–281 (2012)

    Article  MathSciNet  Google Scholar 

  15. Snijders, T., Steglich, C., Schweinberger, M.: Modeling the co-evolution of networks and behavior. In: van Montfort, K., Oud, H., Satorra, A. (eds.) Longitudinal Models in the Behavioral and Related Sciences, pp. 41–71. Lawrence Erlbaum, New Jersey (2007)

    Google Scholar 

  16. Snijders, T.A.: Stochastic actor-oriented models for network change. J. Math. Sociol. 21(1–2), 149–172 (1996)

    Article  MATH  Google Scholar 

  17. Snijders, T.A., van de Bunt, G.G., Steglich, C.E.: Introduction to stochastic actor-based models for network dynamics. Soc. Netw. 32(1), 44–60 (2010). (Dynamics of Social Networks)

    Article  Google Scholar 

  18. Steglich, C., Snijders, T.A., Pearson, M.: Dynamic networks and behavior: separating selection from influence. Sociol. Methodol. 40(1), 329–393 (2010)

    Article  Google Scholar 

  19. Yamamoto, K., Uno, A., Murai, H., Tsukamoto, T., Shoji, F., Matsui, S., Sekizawa, R., Sueyasu, F., Uchiyama, H., Okamoto, M., Ohgushi, N., Takashina, K., Wakabayashi, D., Taguchi, Y., Yokokawa, M.: The K computer operations: experiences and statistics. Procedia Comput. Sci. 29, 576 – 585 (2014). (2014 International Conference on Computational Science)

    Google Scholar 

Download references

Acknowledgements

We are grateful to Thomas Lux for introducing us to the SAOM literature and to Hideaki Aoyama for his constructive suggestions. This study was supported in part by the Project “Large-scale Simulation and Analysis of Economic Network for Macro Prudential Policy” undertaken at Research Institute of Economy, Trade and Industry (RIETI), MEXT as Exploratory Challenges on Post-K computer (Studies of Multi-level Spatiotemporal Simulation of Socioeconomic Phenomena), Grant-in-Aid for Scientific Research (KAKENHI) by JSPS Grant Numbers, 17H02041. This research used computational resources of the K computer provided by the RIKEN AICS through the HPCI System Research project (Project ID: hp170242).

Author information

Authors and Affiliations

  1. Research Institute of Economy, Trade and Industry (RIETI), 1-3-1, Kasumigaseki Chiyoda-ku, Tokyo, 100-8901, Japan

    Yoshiyuki Arata

  2. Graduate School of Simulation Studies, University of Hyogo, Kobe, 650-0047, Japan

    Abhijit Chakraborty, Yoshi Fujiwara, Hiroyasu Inoue & Hazem Krichene

  3. RIKEN Advanced Institute for Computational Science, 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo, 650-0047, Japan

    Masaaki Terai

Authors
  1. Yoshiyuki Arata
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abhijit Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yoshi Fujiwara
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hiroyasu Inoue
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hazem Krichene
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Masaaki Terai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yoshiyuki Arata .

Editor information

Editors and Affiliations

  1. University of Lyon 2, Lyon, France

    Chantal Cherifi

  2. University of Burgundy, Dijon, France

    Hocine Cherifi

  3. École Normale Supérieure de Lyon, Lyon, France

    Márton Karsai

  4. University College London, London, United Kingdom

    Mirco Musolesi

Appendix

Appendix

To obtain the solution of the moment equation (2), we use the following updating rule (stochastic approximation, see [7, 11]):

$$\begin{aligned} \varvec{\theta }_{n+1} = \varvec{\theta }_n - \alpha _n \mathbf {D}^{-1}_n (\frac{\sum _{i = 1}^{N^{sim}} \mathbf {S}^{sim}_{\varvec{\theta }_n, i} }{N^{sim} } - \ \mathbf {S}^{obs}) \end{aligned}$$

where \(\mathbf {S}^{sim}_{\varvec{\theta }_n, i}\) is an independent sample based on \(\varvec{\theta }\) and \(N^{sim}\) is the number of the independent samples. \(\theta _n\) converges to the solution of the moment equation (2) as n goes to \(\infty \). Since it is easy to generate independent samples by parallel computer, we generate \(N^{sim} = 512\) samples and obtain faster convergence.

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Arata, Y., Chakraborty, A., Fujiwara, Y., Inoue, H., Krichene, H., Terai, M. (2018). Shock Propagation Through Customer-Supplier Relationships: An Application of the Stochastic Actor-Oriented Model. In: Cherifi, C., Cherifi, H., Karsai, M., Musolesi, M. (eds) Complex Networks & Their Applications VI. COMPLEX NETWORKS 2017. Studies in Computational Intelligence, vol 689. Springer, Cham. https://doi.org/10.1007/978-3-319-72150-7_89

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-72150-7_89

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72149-1

  • Online ISBN: 978-3-319-72150-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation