Banking Network Amplification Effects on
Cross-Border Bank Flows

Shugo Yamamoto

December 2015
Discussion Paper No.1533

GRADUATE SCHOOL OF ECONOMICS
KOBE UNIVERSITYROKKO, KOBE, JAPANBanking Network Amplification Effects on Cross-Border Bank Flows

Shugo Yamamoto☨
Faculty of Economics, Yamaguchi University
1677-1 Yoshida, Yamaguchi-shi, Yamaguchi, 7538511, Japan
andResearch Fellow, Graduate School of Economics, Kobe University
2-1, Rokkodai-cho, Nada-ku, Kobe City, Hyogo, 6578501, Japan
Abstract
The global factor often referred to as the volatility index (VIX) is said to be the most important
determinant of cross-border bank flows. Contrary to established theory, we investigate the spatial
amplification of the network origins of the aggregate fluctuation effect on cross-border bank flows.
Results show that first, amplification effects from networks of core–core countries can explain a large
share of global shocks, which will replace VIX. Second, because the US is located at the core of the
network, the US amplifies shock originating in other countries. Furthermore, monetary policy shocks
originating in the US have large amplification effects not only the US itself, but also on the rest of
the world. Therefore, domestic shocks apparently propagate throughout the international banking
network, affecting other countries, and generating a sizable global factor.
JEL Classification Code: F30, F34
Keywords: Core–periphery, Global factor, Spatial effect, VIXThis research has been supported by the Grant-in-Aid for Scientific Research (No. 26780186). The
author has had the support and encouragement of Seiichi Fujita, Yoichi Matsubayashi, Shigeto
Kitano and Masahiko Shibamoto of Kobe University. Needless to say, the author is solely responsible
for all errors.
☨ Email: shugo-y@yamaguchi-u.ac.jp1

1.

Introduction
International capital flows are becoming increasingly globalized. The correlation of financial

cycles across countries has increased in recent years. Actually, this correlation is said to be a maincause of the global financial crisis of 2007–08. Therefore, investigating the mechanisms anddeterminants of international capital flows is important.
Typical research in this area resembles that conducted by Calvo et al. (1996), distinguishing
global common factors for capital flows from country-specific factors, and emphasizing theimportance of external global common factors in explaining capital flows in emerging countries.
Along with this opposing axis, many earlier studies investigated international capital flowmechanisms. For instance, using factor analysis, Fratzscher (2012) extracts global common factors
and finds that these factors played an important role in the global financial crisis of 2007–08. Using
dynamic factor analysis, Sarno et al. (2015) find that more than 80% of the variation of capital flow
results from global common factors. Shirota (2015) reports that the contribution of global common
factors increased after the 2000s. However, factor analysis can merely extract common trends.
Interpretations of the meanings of those sets of variables have created much controversy.
Miranda-Agrippino and Rey (2012) report that the global common factor has high correlation withthe volatility index (VIX), which is a proxy for global investor risk sentiment1. While particularly
addressing VIX, Forbes and Warnock (2012) and Bruno and Shin (2015a) assert that global risk
factors played an important role; country-specific characteristics had only a minor role. Evolvingfrom these studies, Bruno and Shin (2015b) and Rey (2015) reveal the positive feedback loops
between fall in VIX, rise in credit, capital flows, leverage, and the further fall in VIX.
From these preceding studies, a great deal of emphasis has been assigned to high interpretabilityof VIX. However, the network origins of aggregate fluctuations are apparently lacking. According toUsing a large cross section of 858 risky asset prices, they find that an important part of the variance of risky returns is explainedby a single global common factor.
1

2

Acemoglu et al. (2012), in a certain network system, micro-shocks might not remain confined towhere they originate. Rather, micro-shocks might propagate throughout an economy, affecting othersectors, and generating a sizable aggregate effect, which is often designated as a cascade effect. Afterthe seminal works of Allen and Gale (2000), Nier et al. (2007), and Haldane and May (2011),
numerous theoretical studies have revealed that the structure of financial networks affects theirreaction to shocks. A network that is incomplete and asymmetric can amplify the shocks as
symbolized by contagion and systemic risk2. To this end, von Peter (2007), IMF (2009) and Minoiu
and Reyes (2013) analyze a network topological perspective of international financial network. They
report that it is asymmetric, with a hierarchical structure. Hoggarth et al. (2010) use input–output
analysis to reveal amplification effects of international banking networks. However, this approach
can not compare the importance between network amplification effects and VIX.
In this study, through network analysis and by application of a spatial econometrics approach, we
explore somewhat further into the identification of a global common factor with consideration of theamplification effect of domestic factors. Then we can integrate the network-related studies with VIX
related studies. Spatial econometric approaches present benefits for investigating spatial
co-movement among dependent variables and the spillover effects of explanatory variables in one
country on the dependent variables of other country3. Using this approach, Dell’Erba et al. (2013)
and Asgharian et al. (2013) study spatial amplification effects of international financial networks onstock price co-movements. Tonzer (2015) assesses the spatial spillover effects of systemic risk. No
report in the relevant literature has described a study investigating the amplification and feedback
effect of international financial network on capital flows. This is actually the first point to be
discussed. Furthermore, among capital flows of several types, we specifically examine cross-border

However, if network system is complete and symmetric, it can improve risk-sharing by spreading and decreasing the shock.
The application of spatial econometrics is common in the field of economic geography. See Lesage and Pace (2009) for details.
Additionally, this approach is different from a gravity approach, which is used to investigate economic integration by bilateral tradeflows based on the economic sizes and distance between two units.
2
3

3

bank flows because the stock of cross-border bank flows accounts for more than 50% of the overall
amount of international holdings, according to Lane and Milesi-Ferretti (2008). As referred to a
spoke–hub distribution paradigm, economically advanced countries are located in the core andemerging countries are located in the periphery of the network system. Therefore, the mechanisms ofcross-border bank flows might differ among core–core and core–periphery networks. This is thesecond point to be discussed. The results can be summarized as follows. First, in contrast toimportant earlier studies, spatial effects from networks of core–core countries can explain a large
share of global shocks. This explanation is expected to replace VIX. Second, because the US is locatedat the network core, the US amplifies shocks that originate in other countries. Furthermore,monetary policy shocks originating in the US have strong amplification effects not only within theUS, but also throughout the rest of the world. Therefore, domestic shocks might be said to propagate
throughout the international banking network, affecting other countries, and producing a sizableglobal factor.
The remainder of the paper is organized as follows. Section 2 presents a description of the spatial
econometric method. Section 3 presents a description of data and descriptive statistics ofinternational banking systems. Section 4 presents a description of empirical results. The final
section presents conclusions.

2.

Estimation method
The concept of spatial dependence in a regression model is that the values of the dependent

variable at a certain location depend on observations at other locations. In general, spatial
dependence is present whenever the correlation across location units is non-zero and whenever thepattern of non-zero correlations follows a certain spatial ordering. Two representative models of
specifications exist with spatial dependence. One is called the spatial lag model (SLM), which4emphasizes the spatial correlation in the dependent variable. The other is called spatial error model(SEM), which emphasizes the spatial correlation in the error term. Although the model specification
choice presents an important problem, Lesage and Pace (2009) recommend the use of the moregeneral Spatial Durbin Model (SDM). This model provides a general starting point for the discussionof spatial regression model estimates because this model subsumes SEM and SLM. By following
Anselin et al. (2008) and Elhorst (2014), we estimate a panel data version of SDM with slight
extension, as described in Eq. (1).

(1)

Therein,is a dependent variable ofstands for the time-series dimension.

vector.

denotes the cross-sectional dimension.

is a scalar that denotes the spatial autoregressive coefficient,which captures the feedback effect arising from the dependent variable in neighboring locations.
is anvector of spatial weight with an element

strength of the interaction between locationof the matrix, which expresses the(in the row of the matrix) and location(in thecolumn of the matrix). By convention, because one location can not have an interaction with itself,
the diagonal element of

is 0. Also,

denotes the identity matrix of

Kronecker product. Therefore the term
is an

is an

is the corresponding

vector of error terms. As described in this paper, we distinguishthe explanatory variables as domestic and global variables. A domestic variable is. A global variable isdenotes thedenotes a spatial lagged dependent variable.

matrix of location specific dummy and the global constant, andcoefficient vector.

andmatrix of

matrix of. Their difference is based on whether the variables arecommon across the locations or not. Because global variables

have a feature of global

characteristic, they will affect all locations simultaneously without intersection with5.

Consequently, global variables are common across the locations. The coefficient ofvector ofis the. However, the domestic variables differ among locations. Furthermore, there aredomestic variables of two types. The first is a spillover effect to dependent variables of other locations
throughwith coefficientof vector. The second is the impact of explanatory variables on

the dependent variable of the same location with coefficientof vector.

The model can be transformed to an estimable reduced form as shown below.

(2)

The existence of the feedback effect produces a simultaneity problem. Consequently, conventional
OLS estimates of the model parameters are expected to be inconsistent. Aneslin et al. (2008) andElhorst (2014) present the maximum likelihood estimation of the SLM and SEM to include fixed
effect and random effect. Actually, SDM is an extended version of SLM. Therefore, it can produce anestimate using the same procedure4.
After estimating the coefficients, we will interpret our results from reference to Lesage and Pace
(2009) and to Elhorst (2014). Different from the conventional model, the marginal impacts of
explanatory variables are not

,

, and

because a change in explanatory variable in one

location, say location , affects the dependent variable of that location, which in turn affects thedependent variable in nearby locations, which then feedback to the dependent variable of location .
The coefficients ofand, which do not include such a feedback effect, should be interpreted as

immediate effects of change in the explanatory variable on the dependent variable of the same
location. Similarly, the coefficient ofshould be interpreted as an immediate neighborhood effect ofchange in the explanatory variables of a certain location to the dependent variable in the other4

We use the XSMLE of a command to estimate spatial panel model in Stata. See Belotti et al. (2013) for details.

6locations. According to Elhorst (2014), the feedback and amplification effect at given period
expressed as Eqs. (3) and (4). This matrix denotes the partial derivatives of-thand -th

in location 1 up to location

can bewith respect to the. Eq. (3) is used to derive the domestic variable. It

is similar to conventional SDM.

(3)

However, Eq. (4) is for global variables and is similar to SLM.

(4)

The equations presented above include the term.

Therefore it has a feedback and amplification effect. Additionally, it shows that if a particularexplanatory variable in a particular location changes, then not only will the dependent variable inthat location itself change (direct effect), the dependent variables in other locations will also change(indirect effect). These effects differ for different locations in the sample. Therefore, therepresentation of these effects is a problem. For example, if we have
we obtain ancross-section location, thenmatrix including too many results. To simplify the expression of the estimation

results, Lesage and Pace (2009) propose to report two summary measures. The first is a summary
measure of the direct effect, defined as the average direct effect, which is the average of the diagonal
elements of the matrix of Eqs. (3) and (4). The second is a summary measure of indirect effects. It is7defined as the average indirect effect, which is the average of the row sums of the off-diagonal
elements of the matrices of Eqs. (3) and (4).

3.

Data and descriptive statistics

3.1 Data description
As described in this paper, we use panel data of 64 countries including economically developedand emerging countries during 2001–2013 on yearly bases. The choice of the countries depends onthe data availability. The list of the countries is described in the appendix. The dependent variable isexternal positions of the reporting country to the rest of the world. It is taken from locationalbanking statistics of the Bank of International Settlements (BIS)5. As described above, we divide
explanatory variables into domestic and global variables. The domestic variables are net foreign
assets to GDP (NFA/GDP), the real exchange rate against US dollars (REX) and M2 to GDP(M2/GDP). All the data were referred from the World Bank database. We referred to Bruno and Shin(2015a) for the selection of variables6. According to their studies, because the debt side of balance
sheet is mainly invoiced in US dollars, the appreciation of a certain country’s currency against US
dollar will strengthen the balance sheet, which will increase cross-border lending. The appreciation
is expressed by a decrease of the value. Actually, REX is expected to exert a negative effect on thedependent variables. Next, to increase cross-border lending, funds in hand are needed. Also,
NFA/GDP and M2/GDP are expected to have a positive impact on dependent variables. Global
variables include VIX and the growth rate of real GDP of economically advanced countries(AD_RGDP). Global variables have the features of being global characteristics. Therefore, they are
expected to have an equal influence worldwide and to be common across countries. In fact, VIX, often

We use liabilities to all sectors with all instruments which include debt securities, loans and deposits and other instruments.
Notice that, because the format of the original data is external position of the rest of the world to the relevant country, wetransformed to inverse direction.
6 They estimate not lending but borrowing. Therefore, a little difference exists in choice of variables.
58referred as the fear index, is a popular measure of the implied volatility of S&P 500 index options.
The rise of their value implies an increase of the international risk. It is taken from Global liquidity
indicators of BIS. In addition, AD_RGDP is taken from international financial data of the IMF.
Finally, except for NFA/GDP and AD_RGDP, all the variables are log-linearized.

3.2 Weight matrix
Weight matrix

determines the structure of dependence among countries. Therefore, the choiceof data is crucially important. In the field of financial linkage, the representative data source is BIS
and Coordinated Portfolio Investment (CPIS) of IMF. Actually, BIS covers the international banking
activity; CPIS covers international portfolio investment. Both series describe bilateral cross-border
position toward individual recipient countries. Using these data, numerous attempts have been
undertaken to analyze the structure of the international banking network. For instance, to makebilateral financial linkages measures as an explanatory variable, Kalemi-Ozcan et al. (2013) uses
BIS data. Ahrend and Goujard (2014) use both BIS and CPIS data. In spatial estimation, Tonzer(2015) uses BIS data; Dell’Erba et al. (2013) and Asgharian et al. (2013) use CPIS data to construct aweight matrix. However, because the country coverage of the BIS data is limited to economicallyadvanced countries, we use CPIS data as the main data source.
Because we use cross-border bank flows as a dependent variable, the use of data related to capitalflow as a weight matrix might entail some risk of impairing the exogeneity of the estimated model.
To avoid this problem, traditional studies use geographic distances as the weight matrix7. Other
studies, for example, one by Amaral et al. (2014), use trade linkages as a weight matrix to study thespillover of banking crises. However, although the geographic distance and trade linkage, which

7 Two justifications for the use of geographic distances are the following. First, a country’s economic linkage is strong for nearby

countries because of the business cycle synchronization by export and import. Second, it provides a clear identification because
geographic distances are strictly exogenous.

9represent the real side of the economy, might explain some share of real business synchronization,
they might not explain financial linkages because financial transactions need not transport physicalobjects. They merely transmit electronic signals through the international settlement system.
Financial networks have nothing to do with geographic distances. Furthermore, according to Schiavo
et al. (2010), the respective structures of international trade and financial networks differ8. Although
the use of geographic distances is expected to improve the exogeneity problem, it will impair thequality of the proxy of financial networks. Therefore, the weight matrix constructed by CPIS data
presents a contradictory tradeoff between exogeneity problems and goodness of proxy ofinternational banking network. The point here is to use the CPIS data as a proxy of the level ofinteraction in the banking network. However, it is noteworthy that the use of CPIS data rather than
BIS data as a weight matrix can be expected to correct the exogeneity problem to some degree.
Because according to Broner et al. (2013) and Contessi et al. (2013), portfolio investment has
different properties from those of cross-border bank flows.
The weight matrix construction is the following. We use two measures of the weight matrix fromCPIS data9. One is calculated from the total of debt securities. The other is calculated from equity
and investment fund shares. Furthermore, we defined the former matrix as DEBT_WEIGHT and thelatter as EQUITY_WEIGHT. The () element of the matrix

is denoted byand is calculatedusing the following equation.

(5)

This paper exploits complex network analysis to compare international trade and financial networks. According to the study,hierarchical structure is more pronounced in financial networks, which implies that most financial transactions occur through ahandful of countries acting as hubs.
9 Notice that some blank and confidential values exist in CPIS data. We remedy this problem using the following procedure. First,
we assume blank as non-existence of a transaction and assign it zero. Second, we construct a periodic average of weight matrix
without a confidence value. In constructing a sub-period weight matrix, there are several elements of matrix which consist only of
confidence values. In this case, we assigned zero.
8

10

Actually,is the periodic average of portfolio investment from country

during 2001–2013. Additionally, we conduct row normalization: each row of

to country

will sum to 1 10.

3.3 International banking network
Because the international banking network is comparable to a spoke–hub distribution paradigm,
the spatial amplification effect might be different between core and periphery countries. To confirm
this point, we divide all 64 sample countries to two sub-groups: 22 OECD countries that indicate thecore and 42 Non-OECD countries that indicate the periphery. The classification is based on thefollowing two points. The first is whether the country is an OECD country or not. The second is that,to check the validity of the weight matrix based on CPIS data, we must conduct a comparison withBIS consolidated data. Therefore, countries in both groups must coincide11. Although the coverage ofthe countries is limited, because BIS data capture international banking activity, a weight matrix
based on BIS data is more accurate than one based on CPIS data. From Figure 1, which describes the
top 25 network interconnectedness of OECD countries, we compare the weight matrix constructedusing consolidated banking statistics of BIS, Total debt securities, and Equity and investment fundshares12. The figure below portrays a similar asymmetric core–periphery structure. The bulk offinancial transactions occur through the US, UK, Germany, and France which act as hubs, which
implies the validity of using CPIS data as a proxy of the international banking network, which isrepresented by BIS data.

<<Insert Figure 1 here>>This is done for computational simplicity and to clarify the interpretation of the estimate results. See Anselin et al. (2008) for
details.
11 Because of a lack of data in consolidated banking statistics of BIS, we did not include Luxembourg in the group of OECD.
12 This figure is calculated from the numerator part of Eq. (5) of the previous subsection.
10

11

<<Insert Figure 2 here>>

Next, we compare the individual characteristics of OECD and Non-OECD countries. Figure 2
shows the international lending and borrowing of Belgium and Brazil, which are respectively typicalOECD and Non-OECD countries. It is apparent that the lending and borrowing of Belgium has
similar trend behavior. In contrast to this, the lending and borrowing of Brazil has a different trend
behavior, from which we can confirm the divergence of the two lines. This fact implies that borrowing
will induce lending in OECD countries. This observation is not confined to the cases of these twocountries. We can make a generalization of this phenomenon. Figure 3 presents a scatter plot ofinternational lending and borrowing of all 64 countries including OECD and Non-OECD countries13.
According to this figure, the regression estimate of the coefficient of straight line of OECD countries
is 1.107; R-squared is 0.923. In contrast to this, the estimated coefficient in Non-OECD is 0.739;

R-squared is 0.621. Therefore, we can say that the relation between lending and borrowing in OECD
countries is higher than that in Non-OECD countries. From this evidence, we can infer that country
A’s lending to B will spark a chain reaction to B’s lending to C, and so on, in OECD countries. This
inference is in line with results of a study by Broner et al. (2013), which suggest that the correlationof capital flow among economically advanced countries is higher than that among emerging countries.
Therefore, the mechanisms of cross border bank flows might differ between OECD and Non-OECD
countries. This point demands further discussion.

<<Insert Figure 3 here>>

4.

Empirical Results

Data are taken from locational banking statistics of the BIS. The scatter plot shows the periodic average of lending andborrowing from 2001 to 2013 with a logarithmic scale.
1312

4.1 Main results of all 64 countries
In this subsection, we examine the empirical results obtained for all 64 countries including OECD
and Non-OECD countries from Tables 1 and 2. In the table, PERIOD OF WEIGHT: 2001-13 stand for
periodic average of weight matrix during 2001–2013. FIXED and RANDOM respectively denote fixed
and random effect models.
including coefficients of both

is a spatial coefficient.
andis the coefficient of explanatory variables. It is referred to as an immediate effect.

stands for theimmediate neighbor effect. A-Dir and A-InD respectively stand for the average direct and indirect
effects. Here, because we are analyzing the component of global common factor, we specificallyexamine the results ofand VIX. Additionally, we specifically examine direct and indirect effects of

M2/GDP, representing a spillover of monetary policy.

<<Insert Table 1 here>>

According to Table 1, the coefficient of

is 0.369–0.421 at the model using DEBT_WEIGHT. It is

0.265–0.290 at the model using EQUITY_WEIGHT. All the estimation results were significant at the
1% level, which indicates that the dependent variable of a certain country has a spatial effect on thedependent variables of the other countries. Next, except for AD_RGDP, all the coefficients offrommodels (1)–(8) in Table 1 are significant at the 1% level. Furthermore, both NFA/GDP and M2/GDP
have a positive impact, although both REX and VIX have a negative impact on international
lending14. Consequently, it is consistent with theoretical hypothesis. For comparison, we check theempirical result of non-spatial case from model (9) and (10), labeled as NO_WEIGHT in Table 1.
From the table, one can confirm that the coefficient of all five variables is significant at the 1% level.
Similarly, NFA/GDP and M2/GDP have a positive impact, whereas REX and VIX have a negative
The decrease of REX reflects appreciation of real exchange rate and increase of VIX indicates reflects increased uncertainty ininternational financial markets.

14

13

impact on international lending. Consequently, except for AD_RGDP, the result of

without spatial

term is consistent with the results of the inclusion of spatial term15. Next, the estimation results ofthe coefficient, which represent an immediate neighborhood effect are as follows. Actually,

M2/GDP is significant at the 1% level. It has a positive sign from models (1)–(8). However, NFA/GDP
is significant only for the model using DEBT_WEIGHT. REX is not significant at all, which indicatesthat M2/GDP. In other words monetary policy has a strong spillover effect on other countries.
From these results, we can calculate direct and indirect effects by applying the estimatedcoefficients to Eqs. (3) and (4) of section 2. Except for AD_RGDP, it is apparent that all average direct
effects are significant at the 1% level and that the sign is consistent with the result of
from the immediate effect of
estimation of. Different, direct effects have an amplification effect. For example, theand the average direct effect of M2/GDP from model (1) are, respectively, 0.485 and

0.508. The difference between two values represents feedback and the amplification effect throughweight matrix. The average direct effect in the table is a summary measure. The element of matrix
varies across countries. The direct effect also varies across countries. Unfortunately, because thesample countries are 64, it cannot be shown here because of a lack of space. Therefore, we will
specifically examine the direct effect of the 5 highest and lowest countries against M2/GDP as an
example. In Figure 4, the bar graph shows a direct effect of each country. The cross line represents
average direct effect. Both are based on model (1). According to the figure, the highest countries are
US, Germany, UK, France, and Japan. The lowest are Ukraine, Pakistan, Vanuatu, Bolivia, andMongolia. In more detail, direct effects of US and Mongolia are, respectively 0.627 and 0.485, whichindicates that US has a large amplification effect but Mongolia has no amplification effect.

<<Insert Figure 4 here>>
The negative coefficient of AD_RGDP in NO_WEIGHT implies that the stagnation of economy will induce monetary expansion
policy, which will increase international lending.
15

14

Next, the average indirect effect of M2/GDP and VIX are significant at the 1% level from models(1)–(8). However, NFA/GDP was found to be significant from models (1)–(6). REX is only significant
for models (7) and (8). Actually, AD_RGDP is not significant at all. Furthermore, different from thedirect effect, the indirect effect has an amplification effect on other countries. For example, theestimation of average direct effect and average indirect effect of M2/GDP from model (1) are,respectively, 0.508 and 1.813. Therefore, the average indirect effect is three times greater, whichindicates a strong spillover effect of monetary policy of certain country to the rest of the world. As isthe case with direct effects, we will specifically examine the indirect effect of 5 highest and lowest
countries against M2/GDP as an example. In Figure 5, the bar graph shows indirect effects of eachcountry. The cross line presents the average indirect effect. Both are based on model (1). According to
the figure, the countries with the most indirect effects are the US, the UK, Germany, France,
Luxembourg. The lowest are Costa Rica, Pakistan, Vanuatu, Bolivia, and Mongolia. The order of thehighest and lowest countries is similar to that shown in Figure 4. In more detail, indirect effects of
the US and Mongolia are, respectively 21.700 and 0.001, which indicates that the indirect effect of
the US is more than 10 times larger than the summary indicator. Consequently, the shock originatedin the US has strong spillover effects on the rest of the world.

<<Insert Figure 5 here>>

Finally in this subsection, we check the weight matrix robustness. The international banking
system structure presents the possibility of structural change over time. Therefore, the weightmatrix ofmight not be stable throughout the sample period. To check this point, we divide thesample period of weight matrix to 2 sub-periods. The results are presented in Table 2. On the left
15

side of the table, PERIOD OF WEIGHT: 2001-05 stand for periodic average of weight matrix during
2001–2005. On the right side of the table, PERIOD OF WEIGHT: 2009-13 stand for periodic averageof weight matrix from 2009–2013. Other notations show similar results to those of Table 1. According
to Table 2, the value of coefficientis 0.267–0.497. Although the range of the value is wide, we cansay approximately that the coefficient is stable throughout the entire sample period. Furthermore,
not only the other estimated coefficients, but also the significance level and sign are similar.
Therefore, it can be said that the weight matrices of both DEBT_WEIGHT and EQUITY_WEIGHT
are stable through all sample periods.16<<Insert Table 2 here>>

4.2 Importance of the US
The results of the previous subsection showed that the US is located at the core of theinternational banking system. Therefore, the US can be expected to play an important role in thespillover and amplification effects. In this subsection, by particularly addressing indirect effect of the
impact of M2/GDP as an example, we conduct a simple simulation to analyze the importance of the
US in the international banking network. The starting point of the simulation is to assume that thebilateral lending and borrowing of a certain country with the US suddenly vanishes to zero, whichindicates that we set up the row and column of the US in weight matrix

to zero. Then we cancalculate the indirect effect of each country similarly, but without the US (WITHOUT US). The
results are shown in Figure 6. For comparison, the result of Figure 5, which is labeled as WITH US,
is also shown in Figure 6. The order of the countries is based on Figure 5. We delete the US as thefigure shows. Therefore, the number of the countries is four. According to the figure, the indirect
Because we make row normalization and because each row ofwill sum to 1, the relative position of the country is important.
This result demonstrates that the relative structure of international banking network is stable during our sample period.
16

16

effect of each country decreased drastically by eliminating the row and column of the US element tozero. For example, the indirect effect of UK decreased from 13.421 to 3.705. Furthermore, theindirect effect of Germany decreased from 11.064 to 2.526. Therefore, it can be said that the US plays
an important role in the spillover and amplification of shocks that originate in other countries.

<<Insert Figure 6 here>>

4.3. Comparison between OECD and Non-OECD
Comparing the international banking system to a spoke–hub distribution paradigm illustrates
that the spatial amplification effect might be different between core and periphery countries. To
confirm this point, using the definition presented in section 3.3, we divide all 64 sample countries totwo sub-groups: 22 OECD countries that denote the core and 42 Non-OECD countries that denotethe periphery.
The results of OECD and Non-OECD countries are presented respectively in Tables 3 and 4.
According to Table 3, the coefficient ofTable 4, the coefficient of

is 0.521–0.630 in OECD countries. However, according toof Non-OECD countries is 0.239–0.334. Therefore, we can infer that the

spatial coefficient of OECD countries is about two times higher than Non-OECD countries. However,
the interpretability of the coefficient of

anddecreased drastically in OECD countries. It isnoteworthy that global explanatory variables of VIX and AD_RGDP have almost no interpretability
in OECD countries. In comparison, the respective interpretabilities of VIX and the other coefficientsin Non-OECD countries are strongly significant and similar with the results obtained for all 64
countries of Table 1.

<<Insert Table 3 here>>17

<<Insert Table 4 here>>

Next, the interpretability of both average direct and indirect effects of OECD countries also
decreased. In stark contrast to this, in Non-OECD countries, average direct effects of NFA/GDP, REX,
M2/GDP, VIX are significant at the 1% level from models (29)–(36) of Table 4. Furthermore, theaverage indirect effects of REX, M2/GDP, VIX are almost significant at the 1% level from models(29)–(36). Results from average indirect effects imply that OECD countries can be described as alarge closed economy model that is unaffected by the explanatory variables of other countries.
Similarly, because Non-OECD countries are affected by explanatory variables of other countries,
they can be described as small open economies.
Some points of empirical results of this subsection must be mentioned briefly here. First, in OECD
countries, the coefficient ofis higher than it is in Non-OECD countries. Second, in OECD

countries, VIX has almost no interpretability. Furthermore, according to section 3.3, one is remindedthat the correlation of lending and borrowing of OECD countries is higher than that of Non-OECD
countries. Therefore, these three important pieces of evidence indicate that not a global common
factor represented by VIX but a high spatial coefficient ofis the major factor of high correlation ofinternational lending in OECD countries17. This point stands in stark contrast with importantearlier studies that explained global common factor by VIX.
Finally, to clarify the identity of VIX in OECD countries, we conduct an additional empirical test.
In the last parts of Tables 3 and 4, which show models (27), (28), (37), (38), and NO_WEIGHT
respectively describe non-spatial estimation of OECD and Non-OECD countries. According to thisnon-spatial estimation, the coefficient of VIX is significant at the 1% level in both OECD and

As a robustness check, although a risk of impairing the exogeneity of the estimated model exists, we additionally estimate thesame model using the weight matrix constructed from BIS consolidated data of 22 OECD countries. According to the results,
is0.532–0.558. Neither VIX nor AD_RGDP is significant.
17

18

Non-OECD countries. However, as described previously, inclusion of the spatial term will drasticallydecrease the interpretability of VIX in OECD countries, which implies omitted variable biases in
non-spatial estimation. Therefore, we can infer that, in OECD countries, the identity of global
common shock is explained by the high spatial coefficient of
the coefficient of. However, in Non-OECD countries,

is low. Moreover, VIX still has strong interpretability. Consequently, themechanisms of international lending in core and periphery countries differ.

5.

Conclusion
The correlation of cross-border bank flows across countries has increased remarkably since themid-1990s. Over the past few years, a considerable number of studies have emphasized analyses ofglobal common factors. Miranda-Agrippino and Rey (2012) report high correlation between the global
common factor and VIX, which is a proxy for the risk sentiment of global investors. Bruno and Shin(2015b) and Rey (2015) propose a structural interpretation of the factor and explain the amplification
effect of VIX in cross-border banking flows. They are positive feedback loops between the fall in VIX,
rise in credit, capital flows, and leverage, and further declines in VIX.
However, because international banking networks are strongly interconnected and because its
density is high and complex, the possibility exists that local micro-shocks will amplify and become
global common shocks. In this study, by applying a spatial econometrics approach, we investigate thespatial amplification effects of international banking networks on cross-border bank flows. The
conclusions are summarized as follows. First, in a core–core relation that includes only OECD
countries, spatial amplification effects from international banking networks can explain much of the
global common factor. This amplification is expected to replace VIX in terms of analytical importance.
This result stands in stark contrast to those of major preceding studies as described above. Second,in a core–periphery relation that includes both OECD and Non-OECD countries, both spatial effects
19and VIX explain the global common factor. Therefore, the possibility exists that interaction between
VIX and spatial feedback effects will further strengthen the global common factor and boost
cross-border bank flows. Furthermore, our study integrates network-related studies with VIX
related studies. Third, monetary policy shocks originating in the US have a large amplification effectnot only in one’s own country, but also throughout the rest of the world. Therefore, to stabilize theinternational financial system, the FRB must consider the rest of the world. Fourth, because the US
is located at the center of the core of the international banking network, the US can amplify shocks
originating in other countries. Therefore, not only the monetary policy of core country, but also themere existence of core country is playing an important role in the amplification of cross-border bankflows, which underscores the importance of financial regulation, especially for core countries.
Furthermore, to expand the discussion of post-crisis banking regulation, we must apply implications
from the theory of financial networks such as those proposed by Nier et al. (2007) and Haldane andMay (2011).
As a final remark, because global common factors are a complex of diverse shocks, the effects andtheir analyses are extremely complicated. We investigate this topic from a network perspective.
Furthermore, it is apparent that domestic shocks can propagate throughout the internationalbanking network, affecting other countries, and constituting a sizable global factor.

Appendix: List of countries
64 countries are listed below. OECD countries defined in section 3.3 are underlined.
Argentina, Australia, Austria, Bahamas, Bahrain, Belgium, Bolivia, Brazil, Bulgaria, Chile, Hong
Kong, Macao, Colombia, Costa Rica, Cyprus, Czech Republic, Denmark, Egypt, Estonia, Finland,
France, Germany, Greece, Hungary, Iceland, India, Indonesia, Ireland, Italy, Japan, Kazakhstan,
Korea, Kuwait, Latvia, Lebanon, Lithuania, Luxembourg, Malaysia, Malta, Mauritius, Mexico,
20

Mongolia, Netherlands, Pakistan, Panama, Philippines, Poland, Portugal, Romania, Russian,Singapore, Slovenia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, Ukraine, United
Kingdom, United States, Uruguay, Vanuatu, Venezuela

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23

BIS

Total debt securities

Equity and investment fundFigure 1. Top 25 network interconnectedness of the OECD countries.
Note: Data were obtained from consolidated banking statistics of BIS, Total debt securities andequity and investment fund shares. We use the numerator part of Eq. (5) for calculations.
Abbreviations are the following: AU, Australia; AT, Austria; BE, Belgium; CL, Chile; DK, Denmark;FI, Finland; FR, France; DE, Germany; GR, Greece; IE, Ireland; IT, Italy; JP, Japan; KR, Korea; MX,
Mexico; NL, Netherland; PT, Portugal; ES, Spain; SE, Sweden; CH, Switzerland; TR, Turkey; UK,
United Kingdom; US, United States24Belgium

BrazilFigure 2. Lending and borrowing of Belgium and Brazil to the rest of the world.
Note: Data were obtained from BIS locational banking statistics.

25

BORROWING

16

11

6
6

11
LENDINGOECD

16

Non-OECD

Figure 3. Scatterplots of lending and borrowing of OECD and Non-OECD countries to the rest of theworld
Note: Scatter plot shows the periodic average of lending and borrowing during 2001–2013 with alogarithmic scale. Data are from BIS locational banking statistics.

26

Estimated Value

0.65

0.60

0.55

0.50

0.45
US

Germany

UK

FranceJapan←highest
lowest→Dir

UkrainePak istanVanuatu

Bolivi a

Mongolia

A-Dir

Figure 4. Direct effects of five highest and lowest countries against M2/GDP.
Note: Dir denotes direct effect of five highest and lowest countries. A-Dir denotes the average direct
effect. Eq. (3) of section 2. The results from model (1) in Table 1 are used for calculations.

27

25

Estimated Value

20
15
10
5
0
US

UK

Germany

FranceLuxembourg←highest
lowest→InD

Costa Rica

Pak istanVanuatu

Bolivi a

Mongolia

A-InD

Figure 5. Indirect effects of the five highest and lowest countries against M2/GDP.
Note: InD denotes indirect effects of the five highest and lowest countries and A-InD denotes averageindirect direct effect. Eq. (3) of section 2 and the results from model (1) in Table 1 are used for
calculations.

28

Figure 6. Indirect effects of WITH US and WITHOUT US of the four highest countries against
M2/GDP.
Note. WITHOUT US is calculated as setting up the row and column of US in weight matrix

tozero. WITH US is taken from Figure 5. The order of the countries is based on Figure 5 and we delete
US as the figure shows. Therefore, four countries are shown.

29

Table 1. Main results of all 64 countries
Interval:
Weight:Type:
Model:ρβ
NFA/GDPREX
M2/GDPVIX
AD_RGDPθ
NFA/GDPREX
M2/GDP
A-Dir NFA/GDP
REX
M2/GDPVIX
AD_RGDPA-InD NFA/GDP
REX
M2/GDPVIX
AD_RGDPR-sq within
betweenoverall

DEBT_WEIGHT
FIXED
(1)
0.395
0.170
-0.3570.485-0.292
0.231
0.038
0.891
0.174
-0.3510.508-0.2940.530-0.0791.813-0.198
0.613
0.206
0.224

(2)
*** 0.369*** 0.175*** -0.355*** 0.489*** -0.257
0.013
**
0.286
0.086
*** 1.033*** 0.180*** -0.348*** 0.511*** -0.257
0.015*** 0.587-0.023*** 1.920*** -0.145
0.009
0.618
0.201
0.219

RANDOM
***
***
***
***
***
***
***
***
***
***
***
***
***
***

(3)
0.421
0.166
-0.3180.544-0.290
0.175
0.100
0.888
0.170
-0.3140.568-0.2920.449-0.0901.843-0.205
0.613
0.238
0.254

(4)
*** 0.401*** 0.171*** -0.318*** 0.546*** -0.257
0.011
0.216
0.123
*** 0.987*** 0.174*** -0.314*** 0.571*** -0.258
0.013*** 0.478-0.049*** 1.967*** -0.165
0.008
0.617
0.232
0.249

PERIOD OF WEIGHT: 2001-13
EQUITY_WEIGHTFIXEDRANDOM
(5)
(6)
(7)
(8)
***
0.269 *** 0.265 ***0.290 *** 0.286***
0.173 *** 0.179 ***0.168 *** 0.172*** -0.332 *** -0.324 ***-0.282 *** -0.279***
0.472 *** 0.479 ***0.519 *** 0.523*** -0.327 *** -0.277 ***-0.311 *** -0.268
0.015
0.012
**
0.052
0.077
0.029
0.046
-0.094-0.051-0.255-0.242***
1.467 *** 1.565 ***1.315 *** 1.382***
0.174 *** 0.180 ***0.168 *** 0.173*** -0.327 *** -0.318 ***-0.283 *** -0.280***
0.500 *** 0.508 ***0.546 *** 0.551*** -0.328 *** -0.278 ***-0.312 *** -0.269
0.016 **
0.014***
0.150 **
0.185 **
0.122
0.136
-0.181-0.153-0.496 ** -0.479***
2.195 *** 2.290 ***1.991 *** 2.097*** -0.124 *** -0.098 ***-0.124 *** -0.103
0.006
0.005
0.620
0.623
0.620
0.623
0.226
0.212
0.267
0.259
0.243
0.230
0.282
0.275

NO_WEIGHTFIXEDRANDOM
(9)
(10)
***
***
***
***
***

0.253 ***
-1.095 ***0.875 ***
-0.421 ***-0.029 ***0.212 ***
-0.654 ***1.114 ***
-0.439 ***-0.033 ***

0.509
0.181
0.185

0.491
0.249
0.254

***
***
***
***
***

**
***
***

Note: PERIOD OF WEIGHT: 2001-13 stand for periodic average of weight matrix during 2001–2013. DEBT_WEIGHT and EQUITY_WEIGHT
denote weight matrices. NO_WEIGHT denotes non-spatial panel estimation. FIXED and RANDOM respectively denote fixed and random effectmodels. *** and ** respectively denote significance of 1% and 5% levels.

30

Table 2. Robustness of the weight matrix

Interval:
Weight:Type:
Model:ρβ
NFA/GDPREX
M2/GDPVIX
AD_RGDPθ
NFA/GDPREX
M2/GDP
A-Dir NFA/GDP
REX
M2/GDPVIX
AD_RGDPA-InD NFA/GDP
REX
M2/GDPVIX
AD_RGDPR-sq within
betweenoverall

PERIOD OF WEIGHT:2001-05
DEBT_WEIGHTEQUITY_WEIGHTFIXEDRANDOMFIXEDRANDOM
(11)
(12)
(13)
(14)
0.453 ***
0.497 ***
0.267 ***
0.295 ***
0.160 ***
0.160 ***
0.179 ***
0.169 ***
-0.301 *** -0.292 ***-0.286 *** -0.232 ***0.528 ***
0.587 ***
0.502 ***
0.546 ***
-0.229 *** -0.235 ***-0.273 *** -0.263 ***
0.001
0.000
0.012
0.010
0.061
0.018
0.089
0.048
-0.516 **-0.305-0.297-0.446 ***0.439 **
0.426 **
1.338 ***
1.203 ***
0.162 ***
0.162 ***
0.180 ***
0.170 ***
-0.306 *** -0.298 ***-0.283 *** -0.234 ***0.546 ***
0.608 ***
0.525 ***
0.569 ***
-0.231 *** -0.237 ***-0.273 *** -0.264 ***
0.003
0.001
0.014
0.012
0.272 **
0.197
0.202 ***
0.141
-1.136 *** -0.928 ***-0.473-0.748 ***1.244 ***
1.385 ***
2.004 ***
1.895 ***
-0.187 *** -0.224 ***-0.097 *** -0.106 ***
0.002
0.001
0.005
0.005
0.608
0.608
0.625
0.624
0.112
0.166
0.340
0.388
0.141
0.185
0.352
0.398

PERIOD OF WEIGHT:2009-13
DEBT_WEIGHTEQUITY_WEIGHTFIXEDRANDOMFIXEDRANDOM
(15)
(16)
(17)
(18)
0.378 ***
0.343 ***
0.327 ***
0.294 ***
0.142 ***
0.148 ***
0.150 ***
0.160 ***
-0.309 *** -0.297 ***-0.252 *** -0.264 ***0.401 ***
0.503 ***
0.383 ***
0.478 ***
-0.256 *** -0.258 ***-0.250 *** -0.258 ***
0.013
0.008
0.011
0.007
0.168 **
0.109
-0.002-0.001-0.075-0.361 **-0.456 **-0.626 ***1.244 ***
0.968 ***
1.436 ***
1.181 ***
0.146 ***
0.149 ***
0.151 ***
0.160 ***
-0.304 *** -0.299 ***-0.255 *** -0.271 ***0.429 ***
0.524 ***
0.417 ***
0.504 ***
-0.257 *** -0.258 ***-0.252 *** -0.259 ***
0.015
0.009
0.013
0.009
0.377 ***
0.243
0.085
0.067
-0.258-0.723 ***-0.746 *** -1.002 ***2.203 ***
1.668 ***
2.267 ***
1.799 ***
-0.148 *** -0.127 ***-0.118 *** -0.102 ***
0.009
0.004
0.006
0.003
0.635
0.633
0.633
0.631
0.187
0.224
0.203
0.239
0.202
0.240
0.218
0.254

Note: On the left side of the table, PERIOD OF WEIGHT: 2001-05 stands for periodic average value of the weight matrix during 2001–2005. On
the right side of the table, PERIOD OF WEIGHT: 2009-13 stands for the average value of weight matrix during 2009–2013. DEBT_WEIGHT
and EQUITY_WEIGHT respectively denote the weight matrices. NO_WEIGHT denotes non-spatial panel estimation. FIXED and RANDOM
respectively denote fixed and random effect models. *** and ** respectively denote significance of 1% and 5% levels.
31

Table 3. Results of OECD countries
Interval:
Weight:Type:
Model:ρβ
NFA/GDPREX
M2/GDPVIX
AD_RGDPθ
NFA/GDPREX
M2/GDP
A-Dir NFA/GDP
REX
M2/GDPVIX
AD_RGDPA-InD NFA/GDP
REX
M2/GDPVIX
AD_RGDPR-sq within
betweenoverall

DEBT_WEIGHT
FIXED
(19)
0.636 ***
0.264 **
-0.607 ***0.136-0.094-0.6540.311
0.582 **
0.217
-0.599 ***0.205-0.101-1.200-0.053
1.795 **
-0.169
0.744
0.280
0.295

RANDOM
(20)
0.630
0.269
-0.6030.134-0.0760.005-0.640
0.307
0.614
0.226
-0.5970.204-0.0810.007-1.142-0.1241.827-0.123
0.011
0.747
0.281
0.295

***
**
***

**
***

**

(21)
0.625 ***
0.229
-0.436 ***0.184-0.110 **-0.516
0.284
0.651
0.204
-0.4260.254-0.116

**
***
**
**

-0.6360.074
1.845 **
-0.173 **
0.739
0.317
0.338

(22)
0.617
0.235
-0.4320.182-0.0860.007-0.501
0.281
0.691
0.203
-0.4260.257-0.091
0.009-0.860-0.0031.996-0.132
0.013
0.743
0.319
0.340

PERIOD OF WEIGHT: 2001-13
EQUITY_WEIGHTFIXEDRANDOM
(23)
(24)
(25)
(26)
***
0.548 ***
0.533 ***
0.538 ***
0.521
0.300 **
0.312 **
0.259
0.273
***
-0.635 *** -0.627 ***-0.425 *** -0.418
0.146
0.144
0.209
0.206
-0.072-0.048-0.104-0.074
0.010
0.012
0.386
0.288
0.314
0.194
0.316
0.324
0.279
0.290
**
0.275
0.397
0.453
0.600
0.343 ***
0.342 ***
0.297 **
0.294***
-0.622 *** -0.615 ***-0.415 *** -0.408
**
0.173
0.178
0.247 **
0.253
-0.075-0.049-0.108-0.077
0.012
0.014
1.446
1.068
1.278
0.728
0.095
0.052
0.121
0.104
***
0.710
0.976
1.065
1.406
-0.084-0.046-0.111-0.071
0.013
0.014
0.746
0.748
0.739
0.742
0.294
0.298
0.340
0.346
0.305
0.310
0.359
0.366

NO_WEIGHTFIXEDRANDOM
(27)
(28)
***
**
***

0.396 **
-1.372 ***0.692 ***
-0.155 **-0.0080.304-0.683 ***1.086 ***
-0.243 ***-0.014

0.661
0.306
0.304

0.617
0.393
0.395

**
***
**

**

Note: PERIOD OF WEIGHT: 2001-13 stand for periodic average of weight matrices during 2001–2013. DEBT_WEIGHT and EQUITY_WEIGHT
denote weight matrices. NO_WEIGHT denotes non-spatial panel estimation. FIXED and RANDOM respectively denote fixed and random effectmodels. *** and ** respectively denote significance of 1% and 5% levels.

32

Table 4. Results of Non-OECD countries
Interval:
Weight:Type:
Model:ρβ
NFA/GDPREX
M2/GDPVIX
AD_RGDPθ
NFA/GDPREX
M2/GDP
A-Dir NFA/GDP
REX
M2/GDPVIX
AD_RGDPA-InD NFA/GDP
REX
M2/GDPVIX
AD_RGDPR-sq within
betweenoverall

DEBT_WEIGHT
FIXED
(29)
0.334
0.228
-0.5510.683-0.2900.000
0.049-0.2490.594
0.232-0.5550.720-0.2930.199-0.5841.262-0.149
0.534
0.214
0.230

***
***
***
***
***
***
**
***
***
***
***
***
***
**
***
***

RANDOM
(30)
0.331
0.225
-0.5490.678-0.314-0.0060.045-0.2540.582
0.229-0.5530.712-0.317-0.0040.185-0.6241.169-0.150-0.002
0.534
0.217
0.233

***
***
***
***
***

***
***
***
***
***
***
***
***
***

(31)
0.319
0.243
-0.3430.710-0.2824.337
0.031-0.5270.444
0.245-0.3570.737-0.2840.000
0.163-0.9230.895-0.125
0.537
0.294
0.314

***
***
***
***
***
***
***
**
***
***
***
***
***
***
***
***
***

(32)
0.316
0.239
-0.3400.703-0.320-0.0100.026-0.5240.434
0.241-0.3550.730-0.323-0.0080.147-0.9340.887-0.140-0.003
0.536
0.303
0.319

PERIOD OF WEIGHT: 2001-13
EQUITY_WEIGHTFIXEDRANDOM
(33)
(34)
(35)
(36)
***
0.293 ***
0.289 ***
0.241 ***
0.239***
0.194 ***
0.190 ***
0.216 ***
0.212***
-0.335 *** -0.334 ***-0.281 *** -0.281***
0.582 ***
0.576 ***
0.678 ***
0.670***
-0.260 *** -0.298 ***-0.277 *** -0.323
0.000 *** -0.010
3.059 *** -0.012-0.030-0.035-0.014-0.020***-0.767 *** -0.769 ***-0.804 *** -0.794**
1.288 ***
1.278 ***
1.057 ***
1.051***
0.194 ***
0.190 ***
0.217 ***
0.212***
-0.359 *** -0.357 ***-0.301 *** -0.302***
0.648 ***
0.637 ***
0.721 ***
0.713***
-0.263 *** -0.301 ***-0.279 *** -0.324
0.000 *** -0.008
0.000 *** -0.010
**
0.045
0.033
0.054
0.041
***
-1.125 *** -1.146 ***-1.093 *** -1.097***
1.997 ***
1.913 ***
1.480 ***
1.481***
-0.107 *** -0.113 ***-0.082 *** -0.094-0.003-0.003
0.589
0.589
0.585
0.585
0.225
0.224
0.249
0.248
0.240
0.239
0.264
0.264

NO_WEIGHTFIXEDRANDOM
(37)
(38)
***
***
***
***
***

0.243 ***
-1.056 ***0.883 ***
-0.54 ***
-0.039 ***0.215 ***
-0.542 ***1.103 ***
-0.539 ***-0.046 ***

0.474
0.207
0.208

0.451
0.279
0.281

***
***
***
***
***
***

***
***
***

Note: PERIOD OF WEIGHT: 2001-13 stand for periodic average of weight matrices during 2001–2013. DEBT_WEIGHT and EQUITY_WEIGHT
denote weight matrices. NO_WEIGHT denotes non-spatial panel estimation. FIXED and RANDOM respectively denote fixed and random effectmodels. *** and ** respectively denote significance of 1% and 5% levels.

33