HIAS-E-120

An evolution of global and regionalbanking networks:
A focus on Japanese banks’international expansion

Michael Harrison (a), Jouchi Nakajima (b), Mimoza Shabani (c)(a) University of East London(b)
Hitotsubashi University(c)University of East London

April 2022

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
tel:+81 42 580 8668 http://hias.hit-u.ac.jp/
HIAS discussion papers can be downloaded without charge from:https://hdl.handle.net/10086/27202
https://ideas.repec.org/s/hit/hiasdp.html

An evolution of global and regional banking networks:
A focus on Japanese banks’ international expansion*
Michael Harrison† Jouchi Nakajima‡ Mimoza Shabani§
April 2022

Abstract
This paper examines the possible spillover effects of the global and regional crossborder claims of Japanese banks on domestic financial stability. We contribute to theexisting literature by constructing a global banking network and applying theSpinglass methodology to detect communities formed within the network.
Furthermore, we employ a novel spatial econometric approach, namely, a timevarying spatial autoregressive (SAR) model that captures the evolution of spillover
effects over time. Our empirical results point to the dominant role of Japanese banks
in the global banking network and the evolution of the East Asian regional banking
network. Furthermore, our findings show considerable variation in the degree of
influence of both the global and regional banking networks over time.
Keywords: banking networks, spillover effect, spatial autoregression.
JEL Classification: C23, G21, F34, R11.

*

Financial support from the Ministry of Education, Culture, Sports, Science and Technology of the Japanese
Government through Grant-in-Aid for Scientific Research (No.20H00073) and the Hitotsubashi Institute forAdvanced Study is gratefully acknowledged.
†
Royal Docks School of Business and Law, University of East London.
‡
Hitotsubashi Institute for Advanced Study, Hitotsubashi University (E-mail: nakajima-j@ier.hit-u.ac.jp).
§
Royal Docks School of Business and Law, University of East London.

11. Introduction
Japanese banks have undergone a significant international expansion since the Great Financial
Crisis (GFC) of 2007-2009. Indeed, they are the leading global banks in cross-border lending,with their market share increasing from 7.6% in 2007 to nearly 15% in mid-2019, with a totalof nearly $4.5 trillion of foreign claims. The reach of this expansion is documented to haveboth a global and regional dimension. In particular, there has been a surge in overseas activities
in other Asian countries. The increasing international activities of banks offer important
advantages such as risk-sharing and diversification (Allen et al., 2011; Navaretti et al., 2010)
as well as profitability opportunities (Hattori and Suda, 2007). However, the increased
exposure and reliance on overseas activities renders Japanese banks more vulnerable toexternal shocks (Bruno and Shin, 2015). This poses financial stability implications, as a crisis
can be triggered by banks’ international operations rather than domestic fundamentals via
financial linkages. Therefore, one possible source of financial instability resides in the structureof Japanese banks’ cross-border relationships.
The structure of interconnectedness between financial institutions may indeed play a keyrole in understanding how financial spillovers can be transmitted across borders throughlinkages in the banking sector. The GFC highlighted not only that crises can be transmitted toother countries by banking connections (Kalemli-Ozcan et al., 2013) but also revealed theintertwined nature of financial systems (Allen and Babus, 2009). Since then, a growing numberof studies have employed a network-based approach to analyze cross-border contagion and thetransmission of shocks in intertwined banking systems (Haldane and May, 2011; Hale, 2012;
Hale et al., 2016; Tonzer, 2015). In particular, understanding the network structure in whichbanking systems are connected via cross-border financial claims is crucial for assessing
financial stability (Allen and Babus, 2009; Haldane, 2009). From this perspective, whenmonitoring the financial stability of a given country that is characterized by an internationalbanking system, consideration should also be given to the international dimension of its
activities and its interconnections with other banking systems.
To this aim, our study adds to the growing literature on risk contagion1 in internationalbanking at the country level, focusing on the interconnectedness and role of the Japanesebanking system in the international lending market. Although the vulnerability of international

1

Similar to Tonzer (2015), contagion and spillover are used interchangeably to illustrate the transmission offinancial distress (stability) between countries by banking linkages.

2

activities may stem from the side of both assets and liabilities, in this paper, we focus on asset
vulnerabilities in line with the activities undertaken by Japanese banks, which, as suggested byLam (2013), have increased their holdings of foreign assets while holding their short-term
liabilities rather stable. We employ a network analysis approach using cross-border bilateral
data from the BIS-consolidated international banking statistics. In addition, we apply a novel
econometric analysis, a time-varying spatial autoregressive (SAR) technique, to measure therole and degree of influence of the network on the stability of connected countries via crossborder linkages.
To the best of our knowledge, there is no available study of risk contagion ininternational banking that employs a time-varying SAR technique. We further add to theoriginality of the analysis by not only assessing the dominant role of Japanese banks on the
global banking network but also capturing their role within the East Asian regional network.
The empirical analysis takes several steps. We first construct a global network of banks’ crossborder claims consisting of 47 countries available from the BIS banking statistics database overthe 2006-2017 period. The network here consists of nodes, which in this paper are countrylevel banking sectors that are connected via links by means of borrowing and lending to eachother. The network topology results highlight the changing role of Japanese banks within the
network over the sample time period. The relative importance and the level of connectedness,
as well as the centrality of the Japanese banking system, have indeed increased in recent years.
From our constructed global banking network, we apply the Spinglass community
detection algorithm to detect the clusters formed within the network. A community, or cluster,is a group of nodes with strong cross-border claims against each other relative to the claims toother parts of the network. We find that after 2007-2008, the Japanese banking system serves
not only as a global hub but also as a regional hub. Here, we argue that Japanese banks not only
play an important role in the regional network by providing liquidity to other East Asian
countries but also act as a bridge to connect nodes in the network that are not directly related(Allen and Babus, 2009).
To empirically assess the role of the global banking network on the stability of countries’banking systems, we use a Bayesian estimation approach for the standard SAR model andfurther extend it to a time-varying SAR model. We first apply the methodology to a global
network, which consists of 22 countries due to data availability, as well as the regional network,
consisting of five countries. Our empirical results suggest that in the post-2013 period, there3was not only an increase in cross-border lending by global banks but also an increase in theinfluence of the network on banking stability across countries. We also find positive spillover
effects when the model is applied to the regional network. However, the empirical results also
capture the negative spillover effects that arise during periods of financial distress, such as
those during the GFC and the period of the sovereign debt crisis. The dynamic structure of thebanking network, coupled with the role Japanese banks have on both global and regional
networks, provides crucial insights for policymakers in maintaining (or monitoring) financial
stability.
The paper is structured as follows. Section 2 reviews the relevant literature followed by
the background and some stylized facts on the international activities of Japanese banks in
Section 3. Section 4 provides a network analysis for both global and regional banking. Section
5 describes the model and reports the empirical results, including robustness checks. Section 6
provides a conclusion.
2. Literature review
The international banking literature has widely explored the role global banks have intransmitting shocks to and across countries. Peek and Rosengren (1997, 2000) show how ashock originating in the Japanese domestic economy during the 1990s was transmitted overseas
to the U.S. via the banking system. Using bank-level data, these studies suggest that theliquidity shock of the foreign affiliates of Japanese banks in the U.S. negatively affected real
economic activity in the U.S. Furthermore, other studies provide evidence of how global shocks
can be transmitted to individual countries. Schnabl (2012) shows how a liquidity shock
resulting from the Russian default of 1998 was transmitted to Peru. Using a novel dataset on
the interbank market, the study illustrates how the liquidity shock received by internationalbanks led to a decline in lending to Peruvian banks. Consequently, this had a negative impact
on credit provision to Peruvian firms. Alegria et al. (2017) document the spillover effect of the
global liquidity shock, which emerged following the global financial crisis of 2007-2009, on
the Chilean banking system. They show how the tightening of the international lending market
led to Chilean banks that had relied on foreign funding to incur higher borrowing rates.
Similarly, Aiyar (2012) shows how the global credit supply shock, due to the occurrence of the
global financial crisis, had a negative impact on the UK domestic lending market. The
contraction in domestic lending to firms and households was higher for banks that were more
dependent upon foreign funding. Other studies have shown how the GFC (global shock) that4

originated in the U.S. was transmitted across countries by banking systems. Cetorelli andGoldberg (2011) study the channels by which global banks transmitted shocks to a number of
emerging economies in Asia, Latin America and Europe during 2007-2009. The authors showthat cross-border bank lending significantly declined in the region, resulting in a fall in thedomestic loan supply in emerging markets.
These studies mainly focus on the role of global banks in transmitting shocks abroad;that is, spillovers to host market(s) arise via either the operations of foreign banks or the
reliance of their domestic banks on foreign funding. In this way, the studies indicate thechannels through which a financial shock, global or linked to an individual country, would dry
up credit provision in the host economy when global banks operate. Kamber and Thoenissen(2013) examine the international transmission of financial shocks in an international realbusiness cycle model. They develop a two-country real business cycle model, the UK and U.S.,
to analyze the transmission of shocks during the 2007-2009 financial crisis. They find that
greater exposure to overseas economies by lending to foreign firms leads to greater spillover
effects of foreign financial shocks being transmitted to the home economy. In contrast, Puri etal. (2010), in their study of the spillover of the 2007-2009 crisis to the German lending sector,
find that after the onset of the crisis, one of the main German banks, Landsbanken, was directly
exposed to subprime assets in the U.S., leading the bank to incur major losses. Puri et al. (2010)
find that savings banks that were linked to Landsbanken reduced lending more than othersaving banks with no exposure. Cao et al. (2017) show that a liquidity shock can be transmitted
to the parent bank via exposure to countries in crisis via cross-border ownership bank linkages,
with reference to the European sovereign debt crisis in 2010. Using subsidiary bank-level datato connect banks located in countries experiencing a crisis, such as Greece, Ireland, Italy andPortugal, with banks operating in all other European countries, they find that banks with higher
ownership ties to those banks in the countries experiencing a crisis were associated with a lower
growth lending rate during the crisis than banks with no exposure.
However, these studies examine shock transmission only via direct exposures and do notconsider the characteristics of the wider network created by global banks in which contagions
can spread. The financial network literature that studies the effect of network connections on
financial stability highlights the role of banks with interlinked balance sheets in generating
contagion. Earlier research by Allen and Galle (2000) and Freixas et al. (2000) suggest that thegreater the connections formed—up to a complete network—in the interbank market, the more5

resilient the system is to the propagation of a shock. Neir et al. (2007) extend the model byAllen and Galle (2000) by conducting simulations in a random network. They find anonmonotonic relationship between connectivity and contagion. Other studies have conducteda network analysis of global banks, analyzing the network characteristics of global banking
networks. Minoui and Reyes (2013) use BIS locational data to construct a global network of
the interbank market for the 1978-2009 period. They analyze the features of the network andfind that connectivity is relatively unstable; it rises before a financial crisis and falls thereafter.
A number of studies have analyzed the structure of the global financial market network (Cerutti
and Zhou, 2017; Chinazzi et al., 2013; Hale, 2012; and Hale et al., 2016)2 with reference to the
2007-2009 crisis and found similar results to those of Minoui and Reyes (2013). Cerutti andZhou (2017, 2018), on the other hand, find that while connectivity through the global banking
network declined following the crisis, some parts of the network became more regionallylinked. In particular, Cerutti and Zhou (2018) find that the regionalization trend, for whichconnectivity has increased among noncore banking systems, has been driven by countries suchas Australia, Canada, Hong Kong and Singapore. The study finds that the principal
determinants of the observed regionalization trend in the global banking network are mainly
the retrenchment of European banks and the role of regional factors, such as geographical andcultural factors. Considering these findings, the authors argue that the increased regionalization
process may not be a transitional phenomenon. Therefore, the topology of the regional network
could be vital to analyze in addition to the global banking network when assessing thevulnerability of cross-border linkages to financial stability. The literature on regional network
analysis is very limited. Alves et al. (2013) construct a network of European interbank markets
using the aggregate bilateral exposure among 53 large European banks. Peltonen et al. (2015)
construct a macronetwork including both country banking linkages and sectorial-level linkages,
by which each banking system is linked to the other sectors of the economy, for 14 European
countries. However, to the best of our knowledge, there are no studies that construct a regional
network that focuses on East Asia.
Another strand of literature on network analyses conducts country-specific studies toanalyze financial contagion mainly using simulation techniques to examine the effect of the
failure of an individual bank on financial stability. Upper and Warm (2004) study the German

2

Chinazzi et al. (2013) use international portfolio investment flows to analyze the topology of the financial
network. Hale (2012) and Hale et al. (2016) use syndicated loans to construct a yearly global network of interbank
market, while Cerutti and Zhan (2017) use BIS consolidated data supplemented with bank level data.

6

interbank market, Furfine (2003) studies the linkages of U.S. banks, Wells (2004) focuses on
the UK interbank market, and Imakubo and Soejima (2006) study the Japanese interbank
money market. However, these studies are restricted to an individual country and focus oncountry-level financial linkages and, hence, do not consider the contagion that may arise via
cross-border banking linkages.
Cihak et al. (2011) study the effect of the international financial connectedness of anindividual country’s banking sector on domestic financial stability using both simulation andeconometric techniques. They construct a global banking network using BIS locational dataand estimate the likelihood of a banking crisis in a particular country, taking into account theinterconnectedness of the country’s banking sector in the network. Both methodologies suggest
an “M”-shaped relationship between the interconnectedness of a country’s banking sector andfinancial stability. In this study, the degree of interconnectedness used in the empiricalestimations is a centrality measure obtained from the network analysis.
Tonzer (2015) also incorporates the network structure to study whether cross-borderlinkages facilitate spillovers within a network consisting of 18 country-level banking systems.
The study uses a spatial econometric technique, including a spatial interaction term, to analyze
the spillovers of instability of interconnected banking systems using confidential BIS locational
data. The results suggest that there is a positive spillover effect for banking systems that areconnected via cross-border linkages with countries that have stable banking systems, and viceversa. Therefore, the bilateral positions of cross-border linkages at the country level are an
important indicator of financial stability.
We build on these papers to provide empirical evidence of the role of the global banking
network on the stability of the banking sectors within the network. The originality of ourresearch stems mainly from three aspects. First, the empirical model we employ, to the best of
our knowledge, has not been used in international banking to analyze network spillover effects.
Second, we capture the prominent and increasing role of Japanese banks in the global banking
network in providing liquidity. Third, we provide empirical evidence of the existence of an
East Asian regional network and assess the role Japanese banks play.
3. Japanese banks international expansion background
During the 1980s, Japanese banks were among the largest in the world and dominated theinternational lending market. While their overseas activities were dispersed globally, such as

7

in Southeast Asia, Latin America and Europe, their dominant presence was in the U.S. (Peekand Rosengren, 1999). However, following the country’s stock market crash in the early 1990s,
Japanese banks faced major financial problems that reduced their ability to maintain theirleading role in international markets. Indeed, Japanese banks had to withdraw from theirinternational activities and significantly reduce their presence in the U.S. market. The
implications of the substantial decline in loan provision activities of Japanese banks were farreaching for the U.S. credit market and the real economy (Peek and Rosengren, 1997, 2000).
In the aftermath of the financial crisis that hit the Japanese economy and subsequently
its banking sector, the country’s main banks ceased their U.S. activities but expanded in the
Asian market. Given the booming economic conditions in Asia during the mid-1990s, Japanesebanks sought an opportunity that could help them revive their financial positions. However, ina dramatic turn of events, the Asian crisis in 1997 proved to be detrimental to the health ofJapanese banks. These trends are evident in Figure 3.1, which shows the foreign claims ofJapanese banks in a number of selected Asian countries. Hong Kong and Singapore were thelargest countries in which Japanese banks had lent during the 1990s. Faced with an increasing
number of nonperforming loans in the Asian market, Japanese banks had to again cease theirinternational operations and return to the domestic market.

8

Figure 3.1: Japanese banks’ cross-border exposure to selected Asian countries$ billion

180
160
140
120
100
80
60
40
20
0
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019
Singapore

Chinese Taipei

Hong Kong SAR

Malaysia

China

Korea

Source: BIS Consolidated Banking Statistics.

Following the retrenchment from foreign activities (markets) in the aftermath of thecrisis, Japanese banks, which had become largely domestically oriented, had fully recoveredby the mid-2000s. Moreover, financial health had improved considerably, so much so thatduring the GFC, it was the Japanese banks that came to the rescue of some of the world’s
largest banks (Shabani et al., 2016; IMF, 2015). While the Japanese economy was indeed hit
by the financial crisis of 2007-2009, mainly via exports, its banking sector proved to be resilient.
In what followed, Japanese banks then revived their overall international position. Indeed, as
seen from Figure 3.2, cross-border lending continued to grow, while other countries, such as
the United Kingdom, France, the United States and Germany, reduced their lending, reflecting
the aftermath of the crisis. In relation to regional activities, Japanese banks also increased theirclaims toward most Asian countries, such as Hong Kong, China and Singapore, as is evident
in Figure 3.1.

9

Figure 3.2: Cross-border claims against all counterparties$ trillion

5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0

GermanyJapan

United Kingdom

United States

FranceSource: BIS Consolidated Banking Statistics.

Figure 3.3 shows the countries and sectors for which Japanese banks have the largest
cross-border exposure, at the end of 2019. The U.S. remains the largest recipient of foreign
claims of Japanese banks at a global level, with a total of $1.8 trillion. Approximately 62% offoreign claims are against the nonbank private sector, including nonbank financial institutions,households and nonfinancial corporations. However, positions with nonbank financial
institutions account for approximately 25% of total foreign claims. In contrast, while Japanesebanks also appear to have large claims, to the size of $618 billion, toward the Cayman Islands,
more than 99% of the claims are against the nonbank private sector, including nonbank
financial institutions.3 Other countries that Japan holds claims against include some of the main
European countries, including France, the UK, and Luxembourg, as well as Asian countries,
such as China, Singapore, and Thailand. Furthermore, Canada and Australia both appear to bein the top 10 countries for which Japanese banks have sizable cross-border claims. Figure 3.3
also reveals that, overall, most of the Japanese cross-border claims are held toward the nonbank

3

Aldasoro et al. (2020) suggest that the large claims that Japanese banks have toward the offshore nonbanking
sector could reflect the banks’ holdings of structured assets, namely, Collateral Loan Obligations (CLOs).
According to FSA (2019) Japanese banks holdings of CLOs amounted to $107 billion, as of the end of 2018.

10

private sector, with the exception of China, where the banking sector is the largest recipient
sector.

Figure 3.3: Consolidated foreign claims of Japanese banks, against counterparty country
and sector, 2019.
100
90
80
70
60
50
40
30
20
10
0

Banks

Official sector

Non‐bank private sector

Source: Authors’ own calculations based on data from BIS; Consolidated Banking Statistic; Ultimate risk basis.
Notes: Foreign claims are presented as a percentage of each sector to the total foreign claims. The figure includes
the top 10 countries that have received the largest amount of cross-border lending from Japanese banks.

The international expansion of Japanese banks is also reflected in the revenue generated
by these activities in proportion to the total revenue activities. Figure 3.4 depicts an increase in
the overseas revenue generated by the country’s largest three banks, namely, Mitsubishi UFJ,
Mizuho and Sumitomo Mitsui. In addition to their resilience during the GFC and hence theirstrong financial position, other domestic factors may explain the surge of overseas activities byJapanese banks. Indeed, the lack of domestic growth opportunities (Lam, 2013) coupled with
the quantitative easing measures undertaken by the Bank of Japan, whereby lowering longterm interest rates and flattening the yield curve, gave banks more incentive to search for yieldabroad. Another proposed argument in the literature is the retrenchment of European banks(Lam, 2013; Cerutti and Zhou, 2018), particularly from Asia, further adding to the incentivesof Japanese banks to increase cross-border lending, especially in the region. The retrenchment

11

of European banks is also captured in Figure 3.4, which shows that the share of overseas
revenue declines in the aftermath of the 2009 financial crisis and the later European Sovereign
Debt crisis.

Figure 3.4: Overseas revenue as a percentage of total revenue for main banks in selected
countries
80
70
60
50
40
30
20
10
0
2006

2007

2008

Japan

2009

2010

Germany

2011

2012
France

2013

2014

2015

United States

2016

2017

2018

2019

United Kingdom

Source: Bloomberg; Authors’ own calculations.
Notes: The share of overseas revenue to total revenue is calculated by using bank-level data for the largest banks
in each country. For Japan, data for Mizuho, Mitsubishi and Sumitomo banks are used to construct the
total overseas revenue generated by these banks to total revenue. Figures for 2006 represent data for only
Mitsubishi and Sumitomo banks, as there are no data available for Mizuho bank. For Germany, due to data
availability, only Commerzbank and Deutsche Bank are used in the calculations. Data for both banks areavailable only from 2009 to 2018. For France, data represent the revenue reported by Societe Generale,
BNP Paribas and Credit Agricole. Data for Credit Agricole for 2009 are not available. For the UnitedStates, data on Bank of America, Citigroup and JPMorgan Chase are obtained and available from 2009.
For the calculations of the United Kingdom, the share of overseas revenue data on Barclays, HSBC andNatwest Group were used. The figure for 2009 represents data for Barclays and HSBC only.

4. Network analysis
4.1 Data
Network representation of the international banking system requires cross-border bilateralclaims that banking entities have on each other. While the scarcity of data that tracks the foreign
activities of large global banks is well documented in the literature (see, for example, Cerutti
et al., 2011; Hale et al., 2016), the BIS International Banking Statistics reports cross-borderbilateral exposure for BIS reporting banks on an aggregate country basis. The BIS compiles
and reports these data on both a locational and consolidated basis.

12

The Consolidated Banking Statistics (CBS) report consolidates gross foreign claims ofglobal banks headquartered in 31 reporting BIS countries. Global banks can make cross-borderloans directly via their headquarters in the home country, or they can set up deposits taking
foreign affiliates in the form of subsidiaries or branches in various host countries across theglobe. Therefore, foreign claims reported in the CBS consist of cross-border claims on
unaffiliated foreigners (via headquarters) and local claims of foreign affiliates on borrowers in
the country where the affiliate resides. The CBSs are published on an immediate borrower basis
and an ultimate risk basis. The former identifies the location of the immediate counterparty,
whereas the latter records where the ultimate risk lies in the instance that it does not rest with
the immediate counterparty. For example, claims of a UK bank that are guaranteed by aJapanese bank are recorded as claims against the Japanese banks.
The Locational Banking Statistics (LBS), on the other hand, report cross-border claimsof global banks on a residence basis. The dataset captures cross-border assets and liabilities ofbanks located in 47 reporting BIS countries vis-a-vis counterparties in more than 200 recipient
countries. Indeed, data are recorded based on the residency of a reporting bank corresponding
to the national accounts and balance of payment methodology.4 In this way, the external
positions of banking systems are unconsolidated, and hence, the intergroup positions are notnetted out as in the CBS.
Both the CBS and LBS datasets are presented on an aggregate country level rather thanat the individual bank level. Therefore, by “banking system”, we refer to the cross-border
positions, both asset and liabilities, of individual banks that are part of the banking system of
the reporting country. However, the different methodologies used to collect both datasets canindeed help clarify what is meant by a “banking system.” For example, the LBS records thebilateral cross-border lending of banks located in a BIS-reported country regardless of banks’
nationality,5 in which case lending by a Japanese bank’s subsidiary in New York would be
included in the position of banks in the United States. Therefore, the LBS will include thepositions of all banks that operate in the United States and hence are part of the U.S. banking
system. However, in the CBS, the lending of the same Japanese affiliate located in New York4

For a more detail overview of the differences between the consolidated and locational banking statistics, see
McGuire and Tarashev (2008) and Avdjiev et al. (2015).
5
The LBS do not provide information on the bilateral cross-border positions by nationality of reporting banks.

13will be consolidated and reported by the country where the parent entity is located and hence
will be part of the Japanese banking system.
For our paper, the CBS dataset is more suitable mainly for two reasons. First, the CBS
captures the exposure of global Japanese banks on a worldwide consolidated basis,6 and,
therefore, we can gauge the bilateral linkages created by the Japanese banking system. The
dataset not only provides information on the foreign activities of Japanese banks, which allows
us to capture the exposure of the banking system to individual countries, but also the sectorial
exposure, such as the public sector, banks and nonbanks, in that country. The foreign activities
of Japanese banks, and thereby their foreign exposure, can have important implications forfinancial stability in the event of shocks being transmitted from foreign countries. Second, in
an attempt to understand the drivers of bilateral linkages created by Japanese banks, data bybank nationality are needed given that key decisions are usually centralized at the headquarters
level (Fender and McGuire, 2010). Indeed, Schnabel (2012) illustrates the decisive role playedby parent affiliates (i.e., headquarters) of foreign banks located in Peru during the 1998 Russiancrisis.
4.2 Network Description
The intricate structure of cross-border linkages between banking systems can be bestformalized using network analysis. We construct a global banking network for each quarter
from the first quarter of 2006 to the fourth quarter of 2017. Each node in the graph represents
the countries’ banking system, with the edges of the network representing the cross-border
lending and borrowing activities of their banking systems. In this way, the analysis is able tocapture the cross-border exposure each banking system (node) has toward other banking
systems included in the sample. An important feature of the network is the location of the nodes
within the network. That is, the positions of the nodes relative to each other are determined by
the weighted exposure to one another; hence, nodes that are plotted closer together have greater
exposure to one another.
To best capture the position and prominence of nodes in the network, we use the total
degree (also known as the Freeman degree) and eigenvector centrality (often referred to as theprestige score). The total degree counts the number of edges that connect to a particular node;

6

Although the intragroup position of banks is netted out, the data does include those of foreign subsidiaries, themajority of which or wholly owned (Avdjiev and Wooldridge, 2018).

14

therefore, it measures the connectivity of a given node within the network. However, because
it only counts the direct connections it has with other nodes, the total degree measure best
captures local importance (Allen et al., 2020; Zhou et al., 2017). In contrast, Eigenvector
centrality can be used to capture the importance of a node throughout the network by assigninghigher scores to those nodes that are connected to other important nodes in the network.
Therefore, the importance of a node is determined by the importance of the nodes it has directties with. This, on the other hand, would suggest that a banking system that is well connectedwith another important banking system would be more vulnerable to the transmission ofnegative shocks. A high eigenvector centrality score is indicative of a “financial hub” andsupports the concept of global core membership in the financial network (von Peter, 2007;
Minoiu and Reyes, 2013).
Figure 4.1 offers a visual representation of the global banking network for the fourth
quarter of 2017, consisting of 47 countries. This includes both BIS reporting and nonreporting
countries,7 which by way of construction identifies a core-periphery network structure (Cerutti
and Zhou, 2018). A core-periphery banking network structure displays a central dense cluster
surrounded by less connected nodes. Minoiu and Reyes (2013) argue that a great deal of
instability within the network arises from the connections made to the highly concentrated andgreatly exposed areas of the network.

7
Table 1A in the Appendix provides the list of countries included, which consists of 31 reporting countries and
16 nonreporting countries. It is worth noting that bilateral data can only be formed for BIS-reporting countries,
which better captures the borrower/lender relationship/exposure of their representative banking system. However,this is not possible for nonreporting countries due to data limitation and hence the relationship is restricted to only
the borrower counterparty in empirical analyses.

15

Figure 4.1: Network representation of the borrowing and lending of the banking systemsof 47 countries.

Notes: The network is a representation of the cross-border lending and borrowing of 47 banking systems’ countries
for 2017 Q4. The nodes indicate the eigenvector centrality score that each banking system holds.

Countries that depict a higher degree of centrality are France, Spain, Switzerland, theUK and the U.S. at a value of 70 based on a Freeman degree, followed by Belgium, Denmark
and Japan at a value of 69. Therefore, their banking systems are connected to approximately
34-35 other banking systems in the network sample via cross-border financial claims. The
eigenvector centrality measure indicates that the U.S., UK, Germany and Japan are the mostinfluential banking systems in the network. The prominent role of the U.S. reflects the exposureof its banking system to European countries, which are part of the core network. Japan, on theother hand, seems to be more exposed (connected) not only to core countries but also to noncore
and offshore centers such as Bahrain, Hong Kong, Singapore and Panama. This can beobserved from the visual depiction in Figure 4.1, as well as by the argument put forward in
Section 2. Both measures discussed so far suggest that countries such as Japan, the U.S.,
Switzerland, the UK and other European countries such as France, Spain and Denmark fit wellwith the definition of “financial hub” proposed by von Peter (2007). Indeed, a banking hub is16

exposed to many other nodes, including other hubs, and will likely facilitate the distribution ofliquidity across the network (von Peter, 2007). Furthermore, a banking hub may serve as anintermediary in the network by connecting nodes that are not directly connected.
The intermediary role of banking systems, which act as a bridge between unconnectedbanking systems via the shortest path, can be best captured by the betweenness measure. Higher
values denote a greater scope for intermediation. Countries including France, Spain,
Switzerland, the U.S. and the UK are associated with the highest betweenness score of 11.68.
This is followed by Japan, scoring 10.01. The high ranking of the European countries is
intuitive given their regional position. The finding on Japan, however, suggests that thecountry’s banking system could indeed act as an intermediary in channeling funds between thecore of the network and the East Asian region. This is also supported by the visual depictionof the network representation, Figure 4.1, in which Japan is clearly located between the East
Asian region and the core members of the network.
A further point to our analysis is the detection of communities in the constructed global
banking network. Community, as well as the measures of centrality analyzed above, are indeed
the most important components of network structure put forward in the literature (see Allen etal., 2020). Furthermore, from a financial stability perspective, it is necessary to examine
communities within the network, as their increased density can be reflective of a concentrated
pocket of systematic risk (Allen and Babus, 2009; Minoiu and Reyes, 2013, Garratt et al., 2011).
To achieve this, we run a community detection process,8 in which a cluster is a group of
nodes with strong financial claims against each other compared to claims to other parts of the
network. We employ the Spinglass community detection process using a semi-supervised
method to partition the graph by accounting for how potential clusters interact with adjacentclusters. Here the aim is to minimize edge betweenness between communities rather thansplitting the graph into a predetermined number of clusters. (See Appendix 1 for a more detailon the detection process)We detect six communities within our global banking network as of the last quarter of
2017, as shown in Figure 1A in the Appendix. Figure 4.2 illustrates the countries that arelocated in Community A, which includes core banking systems such as those of Japan,
Switzerland and the U.S. as well as offshore centers such as Bahrain and Panama, together with

8

Cluster and communities are used interchangeably in this paper.

17

a number of East Asian countries. Given the diverse nature and relatively large number ofbanking systems that are located within this cluster, 15 in total, the community might have amodular structure of its own. That is, a large cluster may contain several smaller clusters, andhence, we can identify those banking systems that are more connected via cross-border linkages
within the same community.

Figure 4.2: Graphical representation of Community A

Notes: The above graph is a representation of cross-border claims of the banking systems that fall withinCommunity A. The two shaded areas represent the two subcommunities detected using the Spinglass
algorithm.

The results suggest that there are two subclusters in Community A, as illustrated by thetwo shaded clusters in Figure 4.2. Countries such as the U.S., Switzerland, Bahrain, Panama,
Mexico and Turkey are located in the same subcluster, indicated by the blue-shaded node.
Japan, India, Indonesia, Malaysia, Singapore, South Korea, Chinese Taipei, Hong Kong SAR
and China are located in the same subcluster, denoted by the red-shaded area. These findings
are rather intuitive, in which regional factors are evident, especially in the case of Japan being
most connected with and hence exposed to other East Asian countries. Therefore, thisobservation reinforces our argument derived from the visual depiction of the global network
shown in Figure 4.1, which hints at the presence of a regional geographic community.

18

The estimated results support the regionalization argument put forward in the literature
for which borrowing and lending relationships within the same region, especially towardnoncore banking systems, have increased since the 2007-2009 financial crisis (Cerruti andZhou, 2017; IMF 2015). In particular, our findings suggest that Japan, a core member of the
global network, also has a prominent role within the regional banking network. Indeed,Japanese banks’ overseas expansion, as measured here by the outstanding cross-borderfinancial claims, is associated with the increase in regional interlinkages within the identified
East Asian subcluster.
5. Empirical Analysis
5.1 The model
The global network created by means of banking systems forming international lending andborrowing relationships with each other could facilitate the transmission of shocks through the
network. Indeed, given the intertwined nature of network creation, banking systems can beprone to both direct and indirect (stability spillover) effects. The banking stability of a country
could therefore be threatened by the international exposure of its banking system via crossborder claims or by factors that affect the stability of the banking systems within the network
rather than domestic fundamentals.
One of the most popular econometric models for network analysis that allows the captureof direct and indirect effects of financial spillovers is the spatial autoregressive (SAR) model(LeSage and Pace, 2009). Suppose we analyze some economic variables in a network of 𝑛countries over time 𝑡

1, … , 𝑇. Define 𝒚 as a 𝑛

countries and 𝑾 as a 𝑛𝑛 weighting matrix. Then, a standard SAR model is formulated as𝒚where 𝑿 is a 𝑛
is a 𝑘

1 vector of the dependent variable for 𝑛

𝜌𝑾 𝑦

𝑿𝜷

𝜺,

(1)

𝑘 matrix of explanatory variables, 𝜷 is a 𝑘

1 vector of coefficients, and 𝜺

1 vector of disturbances. We assume each of the disturbances 𝜺

𝜀 ,…,𝜀′follows a normal distribution, 𝜀 ~ 𝑁 0, 𝜎 , with a mutual independence between 𝜀 and 𝜀 ,for simplicity. Then, equation (1) leads to the following formulation of the dependent variable
for the 𝑖-th country:
𝑦

𝜌𝒘 𝒚

𝒙 𝜷

𝜀 ,

𝜀 ~ 𝑁 0, 𝜎 ,where 𝒘 and 𝒙 are the 𝑖-th row of 𝑾 and 𝑿 , respectively.

19

(2)

In our analysis, 𝑦 is a measure of banking stability proxied by the Z-score of country 𝑖
at time 𝑡 . For the weighting matrix, 𝑾 , the rows of the weighting matrix represent theoutstanding cross-border claims of country 𝑖 to country 𝑗 at time 𝑡, and the columns represent
the outstanding cross-border claims of country 𝑗 on country 𝑖. 𝑾 is row-normalized and hencemeasures the relative weight of cross-border claims between country 𝑖 and 𝑗 at time 𝑡. For the
explanatory variable 𝑿 , to take into account a decline in the Z-score for most of the countries
at the time of GFC, we use a GFC dummy variable that takes one at the fourth quarter in 2008and zero for other periods.
The key parameter in the SAR model is the spatial parameter, denoted by 𝜌 in equations(1) and (2). If 𝜌

0, the network, the weighting matrix 𝑾 affects the dependent variable 𝒚𝒕 .

Therefore, a positive sign of 𝜌 would reflect the stability of the banking system being positively
related to the stability of the countries connected via cross-border linkages. The value of 𝜌
reflects the degree of spatial dependence in banking stability across countries.
Given the dynamic structure of the global banking network, we extend the SAR model
to a time-varying SAR model by allowing the spatial parameter 𝜌 to vary over time:
𝒚

𝜌𝑾𝒚

𝑿𝜷

𝜺,

(3)

where 𝜌 follows the random-walk process:𝜌𝜌𝜂 , 𝜂 ~ 𝑁 0, 𝑣 .

(4)

The time-varying spatial parameter 𝜌 measures the degree of influence of the network on thedependent variable 𝒚 . In the standard SAR model, nonzero 𝜌 means that the network affects
the dependent variable, and the increase in the weight on a specific country (say, Japan) overtime implies that the country has a more key role in the international banking network, which
affects the dependent variable more than in the past. Furthermore, if the time-varying versionof the spatial parameter, 𝜌 , has been increasing over time, it indicates that the influence of the
network has generally become stronger; therefore, the country’s role has become even more
relevant. In other words, we can divide the increase in the country’s role in the network into
two factors: (i) the increase in the weighing matrix, and (ii) the increase in the influence of the
network matrix in general (for all entities in the network), measured by changes in (i) thecomposition of the weighting matrix 𝑾 , and (ii) the time-varying coefficient 𝜌 .

20

The standard SAR model is usually estimated by the maximum likelihood (ML) method
or instrument variable (IV) method. However, the latent variables in the time-varying SAR
model are high dimensional, which makes the use of ML and IV methods challenging.
Therefore, we take a Bayesian estimation approach. The Bayesian approach for the standard
SAR model is developed in, e.g., LeSage and Pace (2009) and Ohtsuka et al. (2010). We extend
it for the time-varying SAR model (see Appendix 2 for a detail on the estimation method).
5.2 Results of the global banking network
As a first step in the analysis, we estimate (1) the standard (non-time-varying) SAR model. The
model is estimated using sample data from 2006 Q1 to 2017 Q4. As discussed in section 3, 𝑊
is a 𝑛𝑛 matrix constructed using BIS consolidated banking statistics. Due to data limitations,

we can only include 22 countries when estimating the model. The countries included in theanalysis are Australia, Austria, Belgium, Brazil, Chile, Denmark, France, Germany, Greece,
Ireland, Italy, Japan, Mexico, the Netherlands, Panama, Portugal, Spain, Sweden, Switzerland,
Turkey, the United Kingdom, and the United States. The dependent variable, 𝑦 , is the bankZ-score, obtained from the Global Financial Development Database,9 available from the World
Bank. The bank Z-score variable measures the riskiness of a country’s banking system, forwhich higher values indicate that the banking system is farther away from default.
We first estimate the standard version of the SAR model described by equation (1). The
estimated spatial parameter (𝜌) is 0.535 with a 95% interval (0.471, 0.593). The statisticallysignificant parameter indicates that banking stability across countries in the network is spatiallydependent. That is, the value and sign of (𝜌) is an indication of whether there is an amplification(a negative 𝜌) or stabilization (a positive 𝜌) effect on banking stability occurring in the eventof a shock in the network. Hence, the stability of a banking system is positively related to thestability of the banking systems connected via cross-border claims
Next, we estimate the time-varying SAR model defined by equations (2) and (3). Figure
5.1 reports the results of the time-varying spatial parameter (𝜌 ). The solid line indicates themean estimate, and the dashed lines indicate the 95% interval. The figure also reports theestimated time-invariant spatial parameter from the standard SAR model for comparison. The
estimated time-varying spatial correlation has increased over time and captures both the GFC

9Because the data are only available on an annual basis, the Z-score variable is linearly interpolated for thebaseline model using quarterly series.

21and the European Sovereign Debt crisis. Indeed, the spatial parameter increased in the 2006 to2008 period, then exhibited a relatively stable trend, and again increased around the 2015 to2017 period. This finding points to relevant changes in spatial dependence in banking stability
across countries over time. Indeed, a lower spatial parameter (𝜌 ), evident during the financial
crisis, is associated with a higher degree of instability (riskiness) of those banking systems thatare connected via cross-border claims. In the post-2013 period, we observe that not only has
there been an increase in the cross-border lending of international banks, associated with anincrease in the weighing matrix, 𝑊 , , but also the influence of the network on banking stability(more prone to positive spillovers banking systems are) across countries has increased.

Figure 5.1: The estimated time-varying spatial parameter (𝝆𝒕 , left) in the time-varying SAR

model and the time-invariant spatial parameter (𝝆, right) in the standard SAR model for thequarterly series
1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0

0.0

‐0.2

‐0.2

‐0.4
2006

‐0.4
2008

2010

2012

2014

2016

[Time‐invariant]Note: The solid line and the diamond are mean estimates, and the dashed lines and bars are 95% intervals.

Furthermore, focusing on Japan’s contribution in the network to banking stability, Figure
5.2 shows the sum of weights that Japan contributes to the other countries in the weighting
matrix 𝑊 , . It is evident that the contribution slightly increases after the GFC and clearly hikes
after 2014. As noted above, Japan’s role in the network can be divided into two factors. Thisfinding indicates both increases in the weighting matrix and the influence of the network matrix
measured by the time-varying spatial coefficient for Japan’s increasing role in the network.

22

Figure 5.2: The sum of weights that Japan contributes to other countries in the weighting
matrix
1.4

%

1.2
1.0
0.8
0.6
0.4
0.2
0.0
2006

2008

2010

2012

2014

2016

5.3 Results of regional network
In this section, we present the results of the SAR models using a weighting matrix that
represents the exposure of the regional (community) network identified in Section 3. In doing
so, we attempt to capture any effects (spillover) on stability that could arise from such exposure.
In other words, 𝑊 here represents the outstanding cross-border claims of countries located in
the regional network. We focus on the East Asian subcluster of Community A, and due to data
limitations, the weighting matrix 𝑊 captures only the claims of five East Asian countries,
namely, Japan, Hong Kong, Korea, Singapore and Chinese Taipei. Furthermore, data on crossborder claims used to construct the row standardized matrix, 𝑊 , for the five countries are notcomplete, as reported in the BIS database. To construct a bilateral claims matrix for thosequarters in which we have missing values, we use the mean of other nonmissing values in thesame column in the matrix.
The estimated spatial parameter in the standard (time-invariant) SAR model using
quarterly series is 0.210 with 95% intervals (0.029, 0.354), which indicates that the spatial
parameter (𝜌) is significant and positive for the regional network. This implies the positive
stabilization effect the regional network has on banking stability across the region. However,
the result of the time-invariant model suggests that the degree of spatial dependence is, on
average, less in the case of the regional network.

23

When looking at the results of the time-varying estimates reported in Figure 5.3, it isevident that the spatial correlation (𝜌 ) varies significantly over time. The degree of spatial
dependence reflects the financial crisis during the period 2008 to 2009, for which banking
instability in the region increased during this period. Notably, the spatial parameter increased
until 2008 and then decreased until approximately 2011. However, thereafter, the spatial
parameter increased significantly, with the trend becoming more pronounced, as depicted in
the left panel of Figure 5.3.
The results confirm the argument put forward in this paper by providing empiricalevidence not only of the increased regional interlinkages but also of the spatial effect thesehave on banking stability. The results suggest an overall positive spillover effect on banking
stability, but they also capture the dynamics of the banking network. That is, during financial
distress, such as the time period associated with the GFC and the sovereign debt crisis, thespillovers could have the reverse (and hence negative) feedback on home banking stability.
Moreover, the increasing exposure and the influence of the regional network on Japanese banks
could be an important aspect for policymakers. That is, regulatory policies and risk monitoringshould take into account the increasing exposure and role of Japanese banks not only as leading
global liquidity providers but also due to the crucial role they play in the region.

Figure 5.3: The estimated time-varying spatial parameter (𝝆𝒕 , left) in the time-varying
SAR model and the time-invariant spatial parameter (𝝆, right) in the standard SAR
model for the regional network.
0.8

1.0

0.6

0.8

0.4

0.6

0.2

0.4

0.0

0.2

‐0.2

0.0

‐0.4

‐0.2

‐0.6
2006

‐0.4
2008

2010

2012

2014

2016

[Time‐invariant]Note: The solid line and the dot are mean estimates, and the dashed lines and bars are 95% intervals.

24

5.4. Robustness
In this section, we present the results of two robustness tests for the global banking network
analysis.10 We exclude Panama from the original dataset, which is an offshore financial center,as identified by the IMF (2000). Offshore financial centers are those in which financial services
are mainly conducted vis-à-vis nonresident, i.e., borrowing and lending to nonresidents. The
services offered by offshore centers are favorable given low or zero taxation (IMF, 2000). For
this reason, in the first robustness test, we exclude Panama and estimate the model using thefirst quarterly series. The second robustness test examines an estimation using annual series tocompare its result with the baseline estimation in which we use quarterly series with theoriginally annual series of Z-scores linearly interpolated. We estimate the annual model forboth datasets, including and excluding Panama.
The results of the spatial correlation using quarterly series are presented in Figure 5.4.
As evident, the spatial parameter 𝜌 is statistically significant and positive in all specifications.
Furthermore, the findings are in line with the results above, for which the degree of spatial
dependence remains nearly within the same range. Looking at the estimated degree of spatial
parameter 𝜌 , it is evident that the role played by Panama in the network is rather minor.

Figure 5.4: The estimated time-varying spatial parameter (𝝆𝒕 , left) in the time-varying SAR

model and the time-invariant spatial parameter (𝝆, right) in the standard SAR model for thequarterly series.
1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0

0.0
Including Panama

-0.2
-0.4
2006

Excluding Panama
2008

2010

2012

2014

-0.2
-0.4

2016

Including Excluding
Panama Panama[Time‐invariant]Notes: Solid lines show the mean estimate and 95% intervals for the dataset including Panama and dashed lines
excluding Panama. Dots are mean estimate and bars 95% intervals.
10

Hence, the robustness tests are based on a network consisting only 21 countries.

25

Figure 5.5 presents the result for the annual series. As expected, the estimated time
variance (𝜌 ) does not reflect the same trend in fluctuations, but the degree of spatial
dependence remains consistent. That is, the estimated statistical significance (𝜌 ) is positive,
pointing to the increased stability across countries and the positive influence the network has
on stability.
Figure 5.5: The estimated time-varying spatial parameter (𝝆𝒕 , left) in the time-varying
SAR model and the time-invariant spatial parameter (𝝆, right) in the standard SAR
model for the annual series.
1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0

0.0
Including Panama

-0.2
-0.4
2006

Excluding Panama

-0.2
-0.4

2008

2010

2012

2014

2016

Including Excluding
Panama Panama[Time‐invariant]Notes: Solid lines show the mean estimate and 95% intervals for the dataset including Panama and dashed lines
excluding Panama. Dots are mean estimate and bars 95% intervals.

6. Conclusion
The international activities of global banks could have financial stability implications for both
host and domestic economies via cross-border claims. While the existing literature provides
some evidence on the financial spillover effects arising from the nature of highlyinterconnected banking systems (see, for example, Tonzer, 2015), there is a lack of empiricalevidence that takes into account the spatial dependence of banking stability in a time-varying
setting. This paper fills this gap by focusing on the international lending of Japanese banks andattempts to capture the role of both the global and regional banking networks in explainingbanking stability. We also provide empirical evidence of the prominent role Japanese banks
have on the global banking network in providing liquidity via cross-border lending, thereby
contributing to overall banking stability.

26

We use bilateral country-level bank data obtained from the BIS, and as a first step in theanalysis, we employ a network analysis at both the global and regional levels. To this end, weconstruct global banking networks consisting of 47 countries. Our findings suggest that thelevel of connectedness and the centrality of the Japanese banking system have indeed increasedin the last few years. From a network analysis perspective, the larger the connectedness of aparticular banking system within the network is, the larger the risk of spillover effects borneby the network. We further find that Japan is part of a regional community that consists of anumber of East Asian countries, such as Indonesia, Malaysia, Singapore, South Korea, Chinese
Taipei, Hong Kong SAR and China. Employing the Spinglass community detection
methodology, we provide empirical evidence of a rising regionalization trend, consistent withthe argument put forward by Cerutti and Zhou (2017, 2018) and the IMF (2015).
Our overall results suggest that there are positive spillover effects of banking stability
arising from cross-border lending activities within both global and regional networks. However,the coefficient associated with the estimated spatial parameter is of greater magnitude than in
the regional analysis. This suggests that spillovers are more pronounced at the global level.
However, when considering the spatial parameter over time for the regional network, weobserved a steady increase after 2014, suggesting a more prominent role played by Japanesebanks in the region. This, on the other hand, would mean that in the event of a financial crisis,
the spillover effects would be negative, thereby increasing the instability of banking systems
connected via cross-border claims.

27

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Zhou, X., F. Liu, J. Wang, T. Li, 2017. Evaluating influential nodes in social networks by local
centrality with a coefficient. International Journal of Geo-Information, 6, 35.

31

Appendix Table and Figure
Table 1A: Countries included in the analysis and network measures for 2017 Q4Country

Betweenness

Australia
Austria
BahamasBahrainBelgium
BermudaBrazilCanadaChile
China
Chinese Taipei
CyprusDenmark
FinlandFranceGermany
GreeceGuernsey
Hong Kong SAR
India
Indonesia
IrelandIsle of Man
Italy
Japan
JerseyLuxembourg
Malaysia
MexicoNetherlands
New Zealand
NorwayPanamaPhilippines
Portugal
RussiaSingapore
South Africa
South Korea
Spain
SwedenSwitzerland
TurkeyUnited Kingdom
United States
Vietnam

8.676
7.365
0.000
0.000
10.628
0.000
1.795
7.320
0.669
0.000
1.672
0.000
6.774
1.648
11.32810.147
1.337
0.000
0.000
0.000
0.000
6.532
0.000
4.101
10.853
0.000
0.000
0.000
0.380
6.844
0.000
0.000
2.256
0.000
6.619
0.000
0.000
0.000
6.159
11.328
5.194
11.3284.292
11.3289.426
0.000

Total Degree Eigenvector Centrality Community
69
68
20
17
69
21
53
59
46
23
60
19
68
43
70
68
56
18
24
21
22
67
18
59
69
20
26
19
37
59
18
23
50
18
63
20
24
23
64
70
63
70
58
70
69
17

32

0.084
0.033
0.018
0.004
0.045
0.016
0.053
0.099
0.034
0.108
0.034
0.006
0.016
0.022
0.201
0.240
0.009
0.009
0.142
0.051
0.021
0.086
0.002
0.092
0.212
0.015
0.114
0.017
0.062
0.100
0.050
0.028
0.010
0.008
0.015
0.017
0.083
0.010
0.054
0.079
0.030
0.068
0.020
0.425
0.739
0.006

B
C
F
A
E
E
F
E
F
A
A
D
E
E
E
E
D
E
A
A
A
D
D
D
A
E
E
A
A
E
B
E
A
E
D
C
B
A
A
D
E
A
A
D
A
C

Figure 1A: Global banking network, by community color

Notes: The above graph is a representation of the bilateral cross-border claims of 47 banking systems’ countries
for 2017 Q4. We detect six communities within the global network, denoted by different shades of color.

33

Appendix 1: Cluster Spinglass community detection approach
We select the Spin-Glass community detection approach as this is best suited to the analysis of
networks, where communities can overlap. Furthermore, this approach remedies a common
deficit of the Newman and Girvan (2006) method, in that the latter often produced results withsimilar modularity scores but very different compositions (Eaton and Mansbach, 2012). The
Spin-Glass approach allows for a semi-supervised approach; the number of selected spin states
denotes the maximum number of regional communities which the algorithm is permitted
partition the global network (a graph 𝐺) into. In our analysis, we set this value at six to reflect
the six inhabited continents.
We consider a graph notation 𝐺

𝑉, 𝐴 , where 𝑉

𝑣 ,𝑣 ,…,𝑣

are vertices

representing BIS reporting and counterparty countries. 𝐴 is an adjacency matrix which
specifies the presence of claims (denoted by 𝑒 ) between countries 𝑣 , 𝑣 . Initially theapproach follows the Newman-Girvan approach which seeks to minimise edge betweenness
centrality and removes the highest valued edges to reveal communities within the network.
We define
1
2

𝑚

,

𝐴, ,

and the modularity of the graph:
𝑄 𝐶

1
2𝑚

𝐴

,

𝑃 𝛿 𝐶 ,𝐶 ,where 𝑄 denotes the modularity of a pair of communities. Note that 𝛿 𝐶 , 𝐶 takes on the valueof one if 𝑣 and 𝑣 belong to the same community (such that 𝐶

𝐶 ), and zero otherwise.

To identify modularity (𝑄) the Spin-Glass method takes on the approach found in the‘Potts Model,’ which is a multi-spin approach over a range of possible values (equal to 2𝑚).
These spins generate the probability values (such as 𝐴 in the above expression). Here the∑ 𝐴 , which substitutes into the following

degree of each reporting country is given as: 𝑑to give the probability values:
𝑃

𝑑𝑑
.
2𝑚

34

The Potts model allows for the estimation of up to 𝑘 communities but supports natural
identification of 𝑞 communities such that 𝑞𝑘 (see Easton and Mansbach, 2012).

The Potts Model employs a Hamiltonian cycle to examine clusters (𝐶) to which vertices
𝑣 , 𝑣 belong. This is obtained in probabilistic terms, within the Hamiltonian function. The
functions ground state is:
𝐻 𝐶

𝑎 𝐴 𝛿 𝐶 ,𝐶

𝑐 𝐴

1

𝑏

𝛿 𝐶 ,𝐶1𝐴𝑑𝛿 𝐶 ,𝐶1𝐴

1

𝛿 𝐶 ,𝐶.

Here the first line captures internal links within a community, the second captures
missing links within a community, the third captures links outside the community and finallythe fourth term reflects external missing links (Reichardt and Bornholdt, 2006). Over all thisseeks to reward connections within communities and to minimise instances of connections
outside of communities. When examining deviations from a global network, we employ ageneral probability function (𝛾𝑃 ) to express the Hamiltonian function in the following
reduced form:
𝐻 𝐶

𝐴

35

𝛾𝑃 𝛿 𝐶 , 𝐶 .

Appendix 2: Bayesian estimation method for the time-varying SAR model
For the estimation of the time-varying SAR model, we take the Bayesian estimation approach,because a likelihood of the model includes many integrals, which is computationallychallenging to evaluate directly. We construct a Markov chain Monte Carlo (MCMC)
algorithm, which has been a major strategy to estimate time-varying parameter models in
econometrics (e.g., Koop, 2003). Under certain prior probability distributions, the MCMC
algorithm produces the sample drawn from posterior distribution of parameters including
unobserved latent variables, in our case the time-varying spatial parameter 𝜌 .
We consider the posterior distribution given the data 𝒚

𝒚 , … , 𝒚 . Let 𝝆

𝜌 , … , 𝜌 . We set the prior probability density for 𝜷, 𝑣 . Given the data 𝒚, we generatesample from the posterior distribution 𝜋 𝝆, 𝜷, 𝑣 | 𝒚 using the MCMC method. We apply thefollowing MCMC algorithm:
1. Initialize 𝝆, 𝜷, 𝑣 .
2. Generate 𝝆 conditional on 𝜷, 𝑣 .
3. Generate 𝜷 conditional on 𝝆, 𝑣 .
4. Generate 𝑣 conditional on 𝝆, 𝜷 .
5. Go to 2, until the MCMC converges.
We iterate this MCMC algorithm for 10,000 times in our analysis, after discarding 1,000
samples as a burn-in period.
In Step 2, we use a single-move sampler with the random-walk Metropolis-Hasting (MH)algorithm. Conditional on 𝜷, 𝑣 and 𝜌,𝜌, we derive a posterior distribution of 𝜌 .

Because it forms a non-standard density function, we draw a candidate for the next sample 𝜌∗ ,as 𝜌∗ ~ 𝑁 𝜌 , 𝑞 , where 𝜌 in the current state. Then, we accept 𝜌∗ with a probability of theMH algorithm. If rejected, we use 𝜌 for the next sample. The variance 𝑞 of the proposal
distribution is tuned as an acceptance ratio is roughly 30%. We apply this method for each of𝜌 , … , 𝜌 , sequentially.
In Step 3, we set a prior distribution 𝜷 ∼ 𝑁 𝟎, 𝑰 , and obtain the posterior distributionof 𝜷, which forms a normal distribution given 𝝆, 𝑣 . In Step 4, we set a prior distribution𝑣 ∼ 𝐼𝐺 2, 0.02 , where 𝐼𝐺 denotes an inverse gamma distribution, and obtain the posterior
distribution of 𝑣 , which also forms the inverse gamma distribution given 𝝆, 𝜷 .

36