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On the distribution of links in financial networks: structural heterogeneity and functional form

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A Correction to this article was published on 08 October 2019

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Abstract

We investigate the distribution of links in three large data sets: one of these covering interbank loans in the electronic trading platform e-MID, and the other two covering a large part of the loans of banks to non-financial companies in the Spanish and Japanese economies, respectively. In contrast to all the previous literature, we do not assume homogeneity of the link distribution over time and across different categories of agents (banks, firms) but apply our hypothesized distributions as regression models. As it turns out, many of the tested sources of heterogeneity turn out to be significant regressors. For instance, we find pervasive time heterogeneity of link formation in all three data sets, and also heterogeneity for different categories of banks/firms that can be identified in the data as well as some explanatory power of balance sheet statistics in the case of the Japanese data set. Across all networks, the Negative Binomial model almost always outperforms all alternative models confirming its good performance as a model of economic count data in many previous applications.

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Change history

  • 08 October 2019

    In the original publication, the article title was incorrectly published as “On the distribution of links in financial networks: structural heterogeneity and functional”.

Notes

  1. Evidence for a Pareto shape of the distribution of firm sizes is provided by, among others, Axtell (2001) and Segarra and Teruel (2012). In contrast, Cabral and Mata (2003) provide evidence for their proximity to a Lognormal distribution. Since both candidates (as well as some others) are strongly right-skewed, statistical discrimination between them can be a delicate problem. In recent literature, Crosato and Ganugi (2007) have attempted an explicit comparison of the Pareto and lognormal distributions and find a better fit of the former.

  2. As proposed by Vuong (1989), one then subtracts \(0.5(K_1 - K_2)\hbox {log} N\) from the differences of the likelihoods (\(K_1\) and \(K_2\) the number of parameters of both alternative models, and N the number of observations).

  3. The overall number of cases of these two categories is too small to consider them separately.

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Acknowledgements

Part of this work has been conducted in the author’s capacity of Bank of Spain Professor in Computational Economics at University Jaume I in Castellon. The almost final version has been completed during a research stay at the University of Kyoto and University of Hyogo in spring 2017 which has been partially supported by a MEXT scholarship within the project ‘Exploratory Challenges on Post-K Computer.’ The Japanese data have been made available by courtesy of Nikkei Media Marketing Inc. and the consortium of EU FP7 Project No. 255987 (FOC-II). The excellent hospitality of my hosts, Hideaki Aoyama and Yoshi Fujiwara, is most gratefully acknowledged. I am also very grateful to them for many stimulating discussions on the topic of this research and the structure of the Japanese data set that forms part of its empirical basis. My thanks for stimulating discussions also extend to Abhijit Chakraborty, Lutz Honvehlmann, Hiroyasu Inoue, Eliza Lungu and Hazem Krichene. Particular thanks go to Lutz Honvehlmann for his extremely able research assistance and to an anonymous reviewer for his or her careful reading of and constructive comments on the current manuscripts.

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  1. Department of Economics, University of Kiel, Kiel, Germany

    Thomas Lux

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Appendix: Histograms and log–log plots of degree distributions

Appendix: Histograms and log–log plots of degree distributions

See Figs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.

Fig. 1
figure 1

Histogram of degrees, e-MID data

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Fig. 2
figure 2

Histogram of degrees, Spanish banks, in bipartite networks

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Fig. 3
figure 3

Histogram of degrees, Spanish banks, one-mode projection

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Fig. 4
figure 4

Histogram of degrees, Spanish firms, in bipartite network

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Fig. 5
figure 5

Histogram of degrees, Japanese banks, in bipartite network

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Fig. 6
figure 6

Histogram of degrees, Japanese banks, from one-mode projection

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Fig. 7
figure 7

Histogram of degrees, Japanese firms, in bipartite network

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Fig. 8
figure 8

Inverse cumulative distribution of degrees for e-MID interbank network in logarithmic representation

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Fig. 9
figure 9

Inverse cumulative distribution of degrees for Spanish banks, from bipartite network

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Fig. 10
figure 10

Inverse cumulative distribution of degrees for Spanish banks, from one-mode projection

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Fig. 11
figure 11

Inverse cumulative distribution of degrees for Japanese banks, from bipartite network

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Fig. 12
figure 12

Inverse cumulative distribution of degrees for Japanese banks, from one-mode projection

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Lux, T. On the distribution of links in financial networks: structural heterogeneity and functional form. Empir Econ 58, 1019–1053 (2020). https://doi.org/10.1007/s00181-018-1569-6

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