Money flow networks: Evidence from Japan

Yoshi Fujiwara, Hiroyasu Inoue, Takayuki Yamaguchi, Hideaki Aoyama, Takuma Tanaka, Kentaro Kikuchi 09 August 2021

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Real-time monitoring of the real economy provides us with a useful tool for understanding the present as well as predicting the future. Monitoring tools that utilise massive amounts of data, in particular on daily or even shorter timescales, have recently become widely available (e.g. Diebold 2021). In this setting, we utilise big data of bank accounts of firms to understand the money flow in a regional economy comprising of the firms and their supplier-customer relationship. This opens up a variety of possibilities for applications such as capturing dynamics under booms and busts of the regional economy, detecting abrupt change due to natural disasters or pandemics, or estimating the possible impact of defaults of firms (to name a few). To the best of our knowledge, such a study has not been conducted to date. This is because such data are not available due to privacy issues, even for academic purposes. Here we report a first step in making such a study feasible on a region-wide scale in collaboration with a regional bank in Japan.

We shall show that firms' accounts in a bank can provide an ideal tool for understanding the structure of money flow behind the economic activities (Fujiwara et al. 2021). Our approach is built upon the complex network comprised of firms as nodes and money flow as links (see Aoyama et al. 2017 for a broader perspective).

Data: A unique opportunity to study money flow

Our data set is comprised of all the bank transfers that are sent from or received by the bank accounts of firms in a regional bank. The regional bank is ‘Shiga Bank, Ltd’, the largest bank in the target prefecture in Japan, which is mid-sized in terms of its population (more than a million) and economic activity. All the account data are anonymous and encrypted, while several attributes such as geographical locations are given to the accounts owned by firms under anonymity. The period covered in our study is from March 2017 to July 2019 (29 months). There were 30,000 accounts of firms, and 2.4 million remittances among them, amounting to ¥2.1 billion in total.

From the data, we constructed a network that is mathematically a graph comprising of nodes and links of the firms' accounts and money flow from one account to another. Obviously, the flow data contains direction and amount of money. Such a graph is called a directed and weighted network. Processing the data set results in 280,000 directed links with the distribution for the weight (amount of flow) being highly skewed. In other words, there were ‘a few giants and many dwarves’. (Note that money flows from customers to suppliers, in the opposite direction of goods/services).

Locating the upstream, downstream, and core of money flow

One of the crucial features in the network is how money flows from upstream to downstream and circulates in the regional economy. Here we define the direction of the flow from customers to suppliers – namely the payment – as being opposite to the flow of goods and services. It is known that social networks often have the so-called ‘bow tie’ structure. At the centre lies a giant core called the ‘giant strongly connected component’ (GSCC), in which any pair of nodes is mutually reachable by at least one path of connected links, essentially meaning an overall pattern of circulation. There are nodes that cannot be reached, but can reach the core, called ‘IN components’. The opposite is true for ‘OUT components’. The IN and OUT components are the upstream and downstream of the circulation, corresponding to the customers and suppliers, respectively. What remains for the rest of the nodes occupies only a tiny portion, called the ‘tendril’ (or TE).

Figure 1 Money flow among firms’ accounts forms a walnut structure

We found that the entire shape does not look like a bow tie but like a ‘walnut’ – in the sense that IN and OUT are two mutually disjointed thin skins enveloping the core of the giant strongly connected component, rather than being two wings elongating from the centre. This feature is quite similar to what we had found in the production network in Japan at a nationwide scale but is different from many social networks such as the World Wide Web. 

Figure 1 presents a schematic diagram. The result shows that the OUT component is relatively large, meaning that suppliers are dominant in the region

Figure 2 Walnut structure and location of upstream, downstream, and core

To locate the upstream, downstream, and core of the flow for individual firm accounts, it is possible to quantify the location of each account by employing a mathematical tool often used in physics.  Each node's position can be measured by a kind of height (the ‘Hodge potential’) in the stream. Figure 2 shows the histogram for the heights of all the nodes. While the OUT component (suppliers) is clearly separated from the others, the giant strongly connected component and IN component (customers) have significant overlap. This result means that that the firms producing intermediate production goods (OUT) are relatively independent from the core and the firms involved in final consumption goods (IN). This is quite different from our previous study on the nationwide production network. This finding implies that the region under study has an industrial structure that is different from the urban areas of Tokyo and Osaka, which dominate the nationwide production network. If one could perform a systematic analysis in different regions of Japan, one can obtain valuable information on heterogeneous characteristics of regions.

Revealing ‘principal components’ of flow and regional activities

The money flow takes place in localised regions and mutually connected geographical areas in the region. Firms send and receive money to and from others with only certain and a small number of destinations and sources. For example, a firm in a suburban town has transactions frequently with supplier firms and customers in the same area as well as a neighbouring large city, but only infrequently with other areas that are more remote. Because the bank accounts are associated with their geographical areas by their addresses, one can construct a matrix of remittances by summing them in geographically disjointed areas depending on the areas of the location of the source and destination of remittance.

Figure 3 Revealing a component: Source (left) and destination (right)

While such a matrix is large, one can expect that the matrix can be decomposed into a relatively small number of components, each representing principal and frequent flow from one area to another. We used a mathematical method (called non-negative matrix factorisation) precisely for the purpose of revealing those principal components. We found that there are roughly a dozen components that can explain the matrix with good accuracy. Figure 3 displays two such selected components which are depicted on a geographical map. Each component provides us with a pair of sources and destinations as important sender and receiver pairs. It is clear that the left-hand side (sources) and right-hand (destinations) are both concentrated in a particular city, representing that this component is mainly intra-city flow. We found that other components correspond to intra-city and inter-city money flow (Fujiwara et al. 2021).

Looking ahead

The network structure uncovered in our study is useful for several purposes. Because the financial information of small and medium-sized enterprises is often difficult to access, the credit risk management of banks will be improved by utilising the information obtained from the network. Information on the network structure will be also useful in promoting the regional economy, in watching the overall flow of the network, and assessing temporal changes in the network. Finally, studying the network of money flows can enable the prediction of occurrences following an economic shock due to pandemics or other disasters. The study for the case of Covid-19 proves that this direction is very promising for the real-time monitoring of the real economy (Yamaguchi et al. 2020).

Editor’s note: The main research on which this column is based first appeared as a Discussion Paper of the Research Institute of Economy, Trade and Industry (RIETI) of Japan.

References

Aoyama, H, Y Fujiwara, Y Ikeda, H Iyetomi, W Souma and H Yoshikawa (2017), Macro-Econophysics: New Studies on Economic Networks and Synchronization, Cambridge, UK: Cambridge University Press.

Diebold, F (2021), “Measuring real activity in real time: Exiting the Great Recession and entering the pandemic recession”, VoxEU.org, 22 January.

Fujiwara, Y, H Inoue, T Yamaguchi, H Aoyama, T Tanaka and K Kikuchi (2021), "Money flow network among firms' accounts in a regional bank of Japan", EPJ Data Science 10(19).

Yamaguchi, T, K Tsuji, Y Nakagawa, T Tanaka and K Kikuchi (2020), "Sector-wise impact of the COVID-19 pandemic on transactions among firms: A real-time analysis of financial big data", Shiga University, The Institute for Economics & Business Research Discussion Paper Series J-1.

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Topics:  Financial regulation and banking

Tags:  Japan, monetary flow, banking, banks, economic geography, network theory

Professor at the Graduate School of Simulation Studies, University of Hyogo

Associate Professor, Graduate School of Simulation Studies, University of Hyogo

Assistant Professor, The Center for Data Science Education and Research, Shiga University

Emeritus Professor, Kyoto University / Senior Visiting Scientist, RIKEN iTHEMS

Associate Professor, Graduate School of Data Science, Shiga University

Associate Professor, Faculty of Economics, Shiga University

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