Introduction
Bank runs have been discussed in much detail on this blog from a variety of perspectives. In the post Incidents from Japan and Britain, we discussed a variety of banks runs, and one of the runs discussed in that post was tied to the Great Recession. More bank runs were discussed in African Banking Crises, with the discussion on the fall of Saambou Bank demonstrating how that particular run was tied to the Dotcom Bubble.
Most recently in A Deeper Dive Into Bank Runs, we became aware of the different categories into which bank runs can be classified into, based on George Kaufman's work in the field. This last discussion, although brief, provides an important change regarding how bank runs are seen. More importantly, it reduces the importance of narrative when looking at bank runs, by introducing different categories to classify bank runs into. In this article we introduce an additional analysis tool that can improve how we understand the bank run phenomena.
Discussion of Scale Free Networks
A network is described as scale free if the characteristics of the network are independent of the size of the network. By size of the network, I mean the number of nodes in the network. This entails that when the size of a network that is described as scale free grows in size, the underlying structure of that particular network remains the same.
A network is scale free because of the distribution of the edges of nodes following what is known as a power law distribution. A noteworthy difference between the normal distribution and the power-law distribution would be that the number of nodes is a lot more when the distribution follows a power law rather than when it follows a normal distribution. The Power Law distribution will be covered in more detail in future time periods. You can learn more about the normal distribution from this particular article.
In scale free networks we often find what is known as the small world principle. According to the American Mathematical Society, the small world principle is a fundamental issue in social networks. It is a basic statement about the abundance of short paths(i.e. the distance from one node to another) in a graph whose nodes are people, with links joining individuals who know one another. By replacing people and individuals with banks in the previous sentence, I provide an application of the definition of the small world principle to a network of banks.
As networks grow overtime, nodes that already have a high number of links have a probability to see new links attached to them when juxtaposed to nodes with a low number of links. This is known as preferential attachment. Scale free networks are known to exhibit preferential attachment.
Preferential attachment looks like an idea that fits well into the analysis of the interbank network, in the sense that banks want to interact with a reliable counterparty that is used by many banks. This is most likely indicative of the fact that the other bank is sufficiently liquid.
Systemic Risk and Graph Generation
One particular implication of the scale-free network to a banking network would be that a small number of highly connected banks serve as financial hubs, and this in turn has consequences for how shocks to a banking would spread through this network.
From a systemic risk perspective, small-world networks are interesting, as it is reasonable to assume that short average path length between banks make them more susceptible to contagion effects. Contagion from a financial perspective is defined as a situation in which a shock that initially affects only a few financial institutions spreads to the rest of the financial system and the economy. To get a firmer grasp on systemic risk, refer to the article Cryptocurrency Regulation and Modern Portfolio Theory.
To generate a scale-free network, we would begin with an initial node and continue to add further nodes to the network until the total number of nodes is reached. In order to demonstrate the generation of scale-free network, we will make use of NetworkX. This particularly library is used to create, manipulate and study the structure, dynamics and functions of complex networks. This generation is presented below.
The code used to produce the networks in the presentation above is given below. The only variable changed in order to produce the four networks is n. You can read more about the other variables here.
As can be seen from the above presentation, as the network gets bigger, the more susceptible the network becomes to the failure of one bank(i.e. contagion). Systemic risk in the form of interbank contagion occurs when the default of interbank one bank leads to the losses and subsequent defaults of other banks. This in turn affects interbank liquidity.
Conclusion
Network structures with a few highly interconnected, and many less interconnected banks turns out to be more resilient than random network structures where on average all banks have equally many interconnections. By understanding the current structure of the interbank market through and article like this and the ideal structure as presented in the previous sentence, policymakers can create policies which encourage a more healthy interbank network structure and thus reduce the risk of bank run occurrence. Complement this article with the following video.
References
Scale-free Networks, futurelearn.com
NetworkX, networkx.org
Finding the Core: Network Structure in interbank markets, dnb.nl
Its a small world afterall, americanmathematicalsociety.org
Financial Contagion During the Covid-19 Pandemic, duke.edu
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