Introduction
Previously on the blog, we have viewed the economy as a complex adaptive system. This perspective allows for better design of policies that will help mitigate the effects of systemic risk, which is defined as the risk of cascading failure in the financial sector, caused by linkages within the financial system, resulting in severe economic downturn.
Below we consider the words of Andy Haldane, Executive Director of Monetary Analysis and Statistics at the Bank of England:
“The similarities between the SARS outbreak and failure of Lehman Brothers are striking. An external event strikes. Fear grips the system which, in consequence, seizes. The resulting collateral damage is wide and deep. Yet the triggering event is, in hindsight, found to have been rather modest. The dynamics appear chaotic, both mathematically and metaphorically.
These similarities are no coincidence.
Both events have manifestations of the behavior under stress of a complex, adaptive network. Complex because these networks were a cat’s cradle of interconnections, financial and non-financial. Adaptive because behavior in these networks was driven by interactions between optimizing, but confusing agents. Seizures in the electricity grid, degradation of eco-systems, the spread of epidemics and the disintegration of the financial system- each is essentially a different branch of the same network family tree.”
Viewing the financial system as a complex adaptive network allows for usage of models and insights from network disciplines such as biology and ecology to the financial sphere. This article will therefore discuss some of the fundamental concepts of network science.
Graphs, Nodes and Edges
In network science, a graph is a way of specifying relationships among a collection of items. A graph consists of a set of objects, called nodes, with certain pairs of these objects connected by links called edges. The figure shown below displays the typical way to draw a graph.
In certain situations, we might want to express asymmetric relationships, for example that A points to be but not the other way around. In this type of situation, we define a directed graph to consist of a set of nodes, as before, together with a set of directed edges. Each directed edge is a link from one node to another, and the direction is important. The illustration below shows how a directed graph is drawn.
In this paper, Benjamin Vandermarliere applies network science to study the Russian Interbank System. Vandermarliere views banks as nodes and loans as edges. He applies the definition of a directed edge as follows:
Over a certain period, an issuer lends money to a receiver. This is a directed edge starting from the issuer node and pointing towards the receiver node. In this instance, it does not matter how many times the loan is issued, or how large the loan is.
Example and Code
ARPANET, PATHS, AND BREADTH FIRST SEARCH
It is time to get hands on with our network science knowledge. To do so, we will make use of the ARPANET in December 1970, back when it only had 13 nodes. For those of you who are unfamiliar, the ARPANET is a precursor to the Internet. ARPANET is an example of a communication network in which nodes are computers or other devices that can pass messages and the edges represent direct links through which message can be transmitted.
Now let us presume that we interested in the distance between two nodes in the graph. We can make use of Breadth-First Search (BFS) to achieve this. BFS searches the graph from a starting node, reaching the closest node first. In addition to providing a method for determining distances, it can also serve a useful conceptual framework to organize the structure of a graph.
For example, let us say that we are interested in the distance between MIT and HARVARD. We can make use of BFS to determine this distance. The code used to achieve this is presented below:
In the situation presented above, manually counting the distance between nodes is a much simpler alternative than using a Python class to achieve the same objective. Using BFS is a lot more beneficial however, in a situation where the graph has a lot more nodes and edges.
Conclusion
Considering the financial severity of the Great Recession the wealth of most households worldwide, it is important to find a more robust economic paradigm that can better anticipate boom and bust cycles. Some central banks, like the one in England, already make use of more "elastic" economic frameworks. Ideally, this new economics should satisfy three criteria.
It should be able to factor in that the economy is constantly evolving;
It acceptance of the private sector and government as complementary, rather than mutually exclusive systems; finally
This new economics must be able to facto in the unpredictability of economic events and human behavior.
By applying the complex adaptive network framework on the economic discipline, we are able to satisfy all three requirements. By getting a firm grasp on network science as discussed in this article, we are able to make good progress towards this new economic perspective in the third world. Complement this article with the following video.
References
Rethinking the Financial Network, BankofInternationalSettlements.org
Networks, Crowds and Markets, cornell.edu
Network Science, Wikipedia.com
Network Analysis of the Russian Interbank System, lib.ugent.be
Capitalism 4.0 The Birth of a New Economy in the Aftermath of the Crisis, audible.com
Breadth First Search Implementation in Python, youtube.com
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