Author: Yijie Zhou, Data Analyst Intern at FNA
The latest dashboard on FNA’s G20 Monitor applies the notion of trophic analysis to financial and economic networks. With the tool, financial institutions can better understand their position and functionality within the networks and shed light on policy and regulation problems.
In this blog, FNA Data Analyst Intern, Yijie Zhou, explores how trophic analysis, an idea originating from food webs, applies to finance and economics and what we’ve learnt from the findings.
Trophic Levels in Food Webs
Different animals or organisms each have their unique position and importance in an ecosystem. The complex interactions between each item in an ecosystem form a food can be decomposed into different layers using a measure called trophic levels. We illustrate this briefly in Figure 1.
Here, each layer has its own functionality, from microorganisms to herbivores, to apex predators, with the food web showing the flow of nutrition and energy between species.
|Figure 1: Typical example of a food web|
Trophic Level in Financial and Economic Networks
We applied a newly improved version of the trophic level (Mackay et al, 2020) and its relative concepts of trophic incoherence to investigate the production network. The production network, constructed using the publicly available dataset – World input-output dataset. The dataset provides information on transactions of monetary goods between 56 sectors in 43 countries. We show an example of trophic analysis on the production network of the USA in 2013. For visualization purposes, we apply filters to nodes and highlight the largest 20 nodes.
Figure 2 adopts a trophic layout where the y axis shows the trophic levels we compute for each node and x axis represents the output of spring-electrical model which makes sure each node maintains a suitable distance from each other.
A directed link in the graph indicates a flow of monetary goods from the supplier (seller) to the consumer (buyer). Figure 2 shows two heavy links indicating a large number of transactions between mining and the manufacture of coke and petroleum products and between crop/animal production and Manufacture of foods. We have filtered links with small transaction amounts to provide a clearer visualization.
The node size demonstrates the value of PageRank (Page et.al, 1999) a well known centrality measure indicating the importance of individual nodes. From the figure, the trophic levels and Pagerank tells a different story. Nodes like Retail trade have a high trophic level but not necessarily have a high PageRank value. While centrality measures focus more on the node importance from the connection perspective, trophic levels focus more on the position of the nodes in the overall direction flow.
The node colours represent the four categories of classification of the economy sector. In the example of the USA production network, we have primary sectors like ‘Mining and quarrying‘ in the bottom of the trophic structure having the lowest trophic levels. In the middle, secondary and tertiary sectors are mixed as they are the main consumers of primary sectors and also important suppliers of quaternary sectors like ‘Healthcare’ and ‘Public defence’.
Trophic levels are node level statistics, but we can also use it to compute the trophic incoherence, a network-level measure, capturing the cycles within the graph (0 means the graph does not have cycles and 1 means all pairs of nodes connected). The trophic incoherence of the production network in Figure 2 is 0.78 meaning that there are many feedforward and feedback loops in it.
|Figure 2: Trophic structure of the production network of the USA in 2013.|
We can further adjust the scale of our analysis and look into a group of countries. We compare the 2014 trophic structure of USA-KOR-CHINA and 5 EU countries (before Brexit) in Figure 3. Here, we observe that EU countries are more clustered and united compared to the US-Asia relationship, implying that international transactions in the EU are more frequent between countries as well as related sectors than those of USA-CHINA-KOR. Moreover, we also see from the figure that China and the USA are located at the top-side of the layout, highlighting their role as consumers in the regional production network.
With the trophic layout and results of trophic analysis, we can better understand the hierarchy of the production network and the overall directional flow of the monetary goods in a given economy. This could also shed light on the study of shock propagation along the supply chain and the integration of regional economic systems. In the context of financial networks, trophic analysis has already been used to study systemic risk (Sansom et al 2020). This new dashboard is now available within the FNA G20 Monitor.
|Figure 3: Trophic structure of two groups of countries.|
(2) http://www.wiod.org/home. Note that we only use the square production matrix and we do not take into account the information about final demands of households and governments.
Johnson, S., Dom ́ınguez-Garc ́ıa, V., Donetti, L., Mu ̃noz, M.A., 2014. Trophic coherence determines food-web stability. Pro-ceedings of the National Academy of Sciences 111, 17923–17928.
MacKay, R.S., Johnson, S. and Sansom, B., 2020. How directed is a directed network?. Royal Society open science, 7(9), p.201138.
Page, L., Brin, S., Motwani, R. and Winograd, T., 1999. The PageRank citation ranking: Bringing order to the web. Stanford InfoLab.
Sansom, B., Johnson, S. and MacKay, R.S., 2021 Trophic Incoherence Drives Systemic Risk in Financial Exposure Networks.