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Liquidity Performance Evaluation of the Brazilian Interbank Market using a Network-Based Approach
Thiago Christiano Silva, Marcos Soares da Silva
and Benjamin Miranda Tabak
September, 2015
401
ISSN 1518-3548 CGC 00.038.166/0001-05
Working Paper Series Brasília n. 401 September 2015 p. 1-51
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Liquidity Performance Evaluation of the Brazilian InterbankMarket using a Network-Based Approach
Thiago Christiano Silva*
Marcos Soares da Silva**
Benjamin Miranda Tabak***
Abstract
The Working Papers should not be reported as representing the views of the Banco Centraldo Brasil. The views expressed in the papers are those of the authors and not necessarilyreflect those of the Banco Central do Brasil.
In this paper, we employ a comprehensive set of network measurements to assessthe determinant factors of banking liquidity performance in the Brazilian interbanknetwork. In our empirical model, we proxy the banking liquidity performance withthe liquidity coverage ratio as defined in Basel III. We first show that the Brazil-ian interbank network has a core-periphery structure and then find that this peculiarnetwork topology can improve liquidity performance of banks. Considering sev-eral evidences in the literature pointing to the fact that interbank markets seem toself-organize in core-periphery structures, this finding suggest that interbank sys-tems drive themselves to a network organization that enhances the financial systemliquidity. In contrast, we also argue that core-periphery structures can lead to largeliquidity shortfalls in the financial network in case a core bank defaults, implyinga greater systemic risk. Nonetheless, we show that the default probabilities of corebanks are very low in the Brazilian interbank market.
Keywords: liquidity, core-periphery, network topology, financial stability, bankingregulation, Basel IIIJEL Classification: D85, G21, G28, G38.
*Research Department, Banco Central do Brasil, e-mail: [email protected]**Research Department, Banco Central do Brasil, e-mail: [email protected]
***Universidade Catolica de Brasılia, e-mail: [email protected]
3
1 Introduction
The recent international financial crisis has attracted increasing attention of bankregulators and of the banking community to the need of developing new mechanisms formonitoring and liquidity risk management, both for bank-specific and systemic levels.Following this line, Basel III includes guidelines for a a new standard of policy recom-mendations that is aimed at addressing issues related to liquidity. In special, Basel IIIrequires banking institutions to maintain high-quality liquid assets that can be easily con-verted to cash, so as to cover their liquidity needs in scenarios of stressed cash flows fora horizon of 30 days (cf. the liquidity coverage ratio in BCBS (2013)). In addition, banksshould have sufficient liquid assets to ensure long-term liquidity needs by programmingthe liquidity flow for a one-year horizon (cf. the net stable funding ratio in BCBS (2014)).It is expected that the introduction of these new standard will confer more resilience tofinancial institutions against liquidity shocks.
As Bhattacharya and Thakor (1993) draw attention to, the main question about liq-uidity within a financial system concerns the role that banks exert in manipulating andmatching different short-term liabilities and assets maturities. Kashyap et al. (2002) high-light that banks, regularly, operate as liquidity providers, through the use of short-termfunds raised from the public. This fact can cause maturity mismatches, exposing banksto non-diversified shocks, which can ultimately lead them to bankruptcy (Diamond andDybvig (1983)).
Another important topic related to liquidity is of interbank networks. In their sem-inal work, Allen and Gale (2000) show that liquidity shocks can be further amplified inthe financial system via contagion processes that can propagate through interbank rela-tionships. They are pioneers in acknowledging the importance of the interbank networktopology in explaining economic problems that are of interest by the banking industry.Following their research, several works explore the influence of different network topolo-gies in establishing a more robust or fragile financial system. For instance, De Masi andGallegati (2012) use the interbank network to investigate the credit relationships betweenbanks and firms in the Italian market, while Fujiwara et al. (2009) provide a similar studyfor the Japanese interbank market. Castro Miranda et al. (2014), in turn, explore the net-work topology of the Brazilian payments system. Guerra et al. (2014) study how networkinterconnectivity is relevant to explain bank efficiency and Anand et al. (2013) exam-ine the role of macroeconomic fluctuations, asset market liquidity, and network structurein determining contagion in financial systems. Tumminello et al. (2010) investigate theproperties of correlation matrices and hierarchical structures constructed from financialsystems.
A very relevant question is how the network topology formed by financial opera-
4
tions between market participants influences banking liquidity performance.1 In a recentresearch, Lux (2015) models the underlying network formation process of interbank net-works via a dynamical system and shows that the resulting equilibrium state is effectivelyreached when banks are disposed in a core-periphery structure. Reinforcing that empiricalfinding, several works study how real financial markets fit into a core-periphery model,such as those of the USA (Markose et al. (2012)), the Netherlands (in ’t Veld and vanLelyveld (2014)), Germany (Craig and von Peter (2014)), Italy (Fricke and Lux (2015)),among many others. These findings suggest that financial institutions (FI) in interbanknetworks seem to self-organize in core-periphery structures. Core-periphery structurespresent two perceptible mesoscale structures: the core and the periphery. Core membersintermediate financial operations between members of the periphery and are also stronglyconnected to other core members. In contrast, periphery members can only establish afew connections with core members and not among similar peers. Though the theoreticaland structural aspects of core-periphery networks are clear, the consequences that core-periphery structures bring for the banking liquidity performance stand as an importantquestion in the research agenda.
In our framework, the general goal is to explain how liquidity performance of bank-ing institutions behave for different network measurements that extract diverse structuralaspects of the underlying interbank network. We build our model using an empirical dy-namic panel using supervisory and accounting data from 2008 to 2014. For robustness,we introduce controls for variables that capture the current macroeconomic scenario andthe bank-specific characteristics. Another goal of this work is to present a network anal-ysis of the Brazilian interbank network, such as to enable a better understanding of itsunderlying structural properties. Due to bank heterogeneities, we report the results in twogroups of banks: large and non-large. To the best of our knowledge, this is the first pa-per that makes use of a comprehensive set of network measurements to describe bankingliquidity.
We proxy the liquidity performance of banks with an index that is inspired on theliquidity coverage ratio of Basel III (BCBS (2013)). Essentially, the liquidity perfor-mance index measures the amount of liquid resources that is available for an institutionto withstand expected and unexpected cash flows in the next 30 days, under severe stressscenarios that permit us to capture operational requirements that are effectively demandedby the Brazilian jurisdiction. These stress scenarios simulate ruptures in historical trendsof variables related to cash flow estimates. We mold these scenarios by employing pa-rameters that are extracted from historical references of experienced past crises.2
1Krause and Giansante (2012) show that the characteristics of interbank lending network is an importantdeterminant of contagion within financial markets.
2The methodology for building the stress cash flow scenarios has been reported by the Central Bankof Brazil’s Financial Stability Reports since the first semester of 2012 (BCB (2012a)). In general terms,
5
In order to explain the liquidity performance of FIs, we select a comprehensiveset of network measurements to extract structural information of the network from dif-ferent aggregative viewpoints, ranging from local to global perspectives. For clarity, wefollow Silva and Zhao (2015) who classify network measurements into three intuitiveclasses: strictly local, quasi-local, and global network measures. Strictly local measuresare vertex-level indices that only use information of FIs in an isolated manner from theremainder of the network. Quasi-local network indicators, in turn, are vertex-level mea-sures and use both information of the FI itself and also of its direct neighborhood to deriveinformation. Finally, global measurements are network-level indices that make use of allof the network structure.
With respect to strictly local measures, we analyze the Brazilian interbank networkusing the degree and strength measurements. We find that both funding and investmentdiversifications are lower for non-large banks, revealing that these institutions, on av-erage, assume secondary roles in the interbank market. In addition, we verify that theaverage funding amount of large banks is larger than their average investment, becausethey diversify more in the lending perspective.
In what concern quasi-local measures, we employ centrality measures (closenessand betweenness), criticality, and dominance indicators. Our results signal that non-largebanks are peripheral in the sense of centrality measures. In contrast, large banks havethe largest centrality measures, corroborating the fact that they are members of a networkcore. Banks in this core act as intermediaries to other entities; hence, they are easilyreachable from any point in the network. In addition, we show that non-large bankinginstitutions are critical during 2008 in the Brazilian interbank market, but that criticalitydiminishes after that period. Large banks, in contrast, present significant criticality duringthe entire studied period. Two factors contribute to the maintenance of the considerablecriticality of large banks: 1) they have larger out-strength in the interbank market; and2) they are frequently funded by non-large banks, which in turn are more leveraged andpresent lower capital buffers. Furthermore, we find that non-banks do not have an effec-tive dominance as lenders nor borrowers. Opposed to that, the dominance of large banksin both perspectives constantly increases from 2008 to 2014.
With reference to global measures, we utilize the density, diameter, rich-club co-efficient, and assortativity. We show that the Brazilian interbank network is very sparseduring the period under analysis. The network diameter is very small, fluctuating around3 or 4 intermediation chains. We also confirm the existence of a “rich-club” of bankinginstitutions that have large degree. In addition, we find that the interbank network showsa clear disassortative mixing pattern. All of these facts suggest the presence of a solid
it considers the potential cash flow to face stress situations, such as in: 1) wholesale and retail depositsrun-off; 2) market risk stress on liquidity, including firesales, variation on prices, interest rates, foreigncurrencies, and stocks; 3) 30-day contractual cash flows, including private securities and repos.
6
core of large banking institutions that are strongly interconnected to the remainder of thenetwork. Since they can easily reach most banks in the network, they act as liquidityproviders in the interbank market.
Using the network analysis tools previously described, we explain the liquidity per-formance of FIs in the interbank market. We find that banks have moderate cost foradjusting their liquidity performance. Moreover, the short-term adjustment costs for liq-uidity strongly depend on the liquidity performance of banks. For instance, when weconsider all of the banking institutions, we verify that a liquidity shock takes about fourquarters to absorb roughly 95% of its initial impact. Now, when we only consider bankswith low liquidity performances in the analysis, we find that they need about two yearsto recover from an identical liquidity shock. In contrast, banks with high liquidity perfor-mance only take two quarters to recover from that same liquidity shock. Therefore, bankswith better liquidity performances have lower adjustment costs against liquidity shocks.This finding suggests that banks with low liquidity performance that are at the verge ofbecoming illiquid may be very prone to external liquidity shocks, as they take longer torecover or adjust their balance sheets. In this way, they are more susceptible of defaulting.Conversely, banks with high liquidity performance that display the same liquidity posi-tions can better withstand these external liquidity shocks, as they can adjust their balancesheets with more flexibility.
An additional contribution of this paper is that we show how network topology in-fluences liquidity performance of banks. We first show that the Brazilian interbank marketpresents strong evidences of being a core-periphery structure using complex network toolsthat have recently been presented in Silva et al. (2015). Therein, they show that networksthat present a strong disassortative mixing together with the presence of the rich-club ef-fect have core-periphery topology. Using that methodology, we employ the assortativityand the rich-club coefficient as proxies to model the core-periphery topology of the net-work. Interestingly, we find that the organization of banks in a core-periphery structurecan improve the liquidity performance of banks. This is a positive feature because inter-bank networks seem to self-organize in core-periphery structures, implying better bank-ing liquidity performances (cf. Lux (2015)). However, this network structure comes withcosts in terms of financial stability. According to a comparative analysis between differ-ent types of network structures performed by Lee (2013), a core-periphery network witha deficit core bank gives rise to the highest level of systemic liquidity shortage, implyinggreater systemic risk.
In this paper, we also contribute to the literature by providing insights as to how cen-trality and distance network measurements influence the liquidity performance of banks.We relate centrality with how often banks intermediate financial transactions. We findthat central players, in general, have better liquidity performances than those players that
7
are located in the periphery. In addition, we relate how easy liquidity can flow within aninterbank network with the network diameter. We verify that, as the network diametergets larger, the harder is to liquidity to flow from one extreme to the another, leading to adecrease in the overall liquidity performance of banks.
Our results also corroborate that the Brazilian interbank market effectively playsthe role of liquidity provider for its constituent members. We also study how the invest-ments diversification impacts the liquidity performance of banks. We find that banks withless concentrated investments portfolios, on average, present better liquidity positions. Inaddition, we relate market discipline to the positive association we unveil between thedefault probability and the liquidity performance of banks.3 Honga et al. (2014) find sim-ilar results for the US industry. This finding suggests that banks with potential solvencyproblems make strong efforts to emit signals or actions with the purpose of conveyingthe apparent information that their liquidity positions are satisfactory. Intuitively, bankswith relative large default probabilities must maintain larger liquidity buffers against un-expected external shocks because they do not have wide access to the interbank marketand have higher costs for adjusting against external liquidity shocks.
The paper proceeds as follows. In Section 2, we present the employed data set, aswell as some of its structural characteristics. In Section 3, we supply a topological analysisof the Brazilian interbank market by using several complex network measurements thatcapture different aggregative structural viewpoints of the network topology. In Section4, we define the empirical econometric model to explain banking liquidity performance.In Section 5, we discuss the results from our econometric models. In Section 6, wepresent robustness tests to check our empirical model. In Section 7, we explore policyimplications based on our results. Finally, in Section 8, we draw some conclusions.
2 Data
In this paper, we use a unique database with supervisory and accounting data main-tained by the Central Bank of Brazil.4 From this database, we take quarterly informa-tion on Brazilian domestic interbank market exposures, supervisory variables and balancesheet statements. In special, we bring into the analysis all types of unsecured financialinstruments registered in the Central Bank of Brazil. Due to domestic regulatory norms,all securities and credit operations must be registered, characteristics that reinforce thedata representativeness and quality. Among examples of financial instruments, we high-light credit, capital, foreign exchange operations and money markets. The money market
3The computation of the default probability only takes into account credit and market risks, hence itdoes not have a liquidity component.
4The collection and manipulation of the data were conducted exclusively by the staff of the Central Bankof Brazil.
8
comprises operations with public and private securities. Both types of operations areregistered and controlled by different institutions. In order to compose the dataset, theexposures are gathered from several other systems. In special, we have information onoperations with private securities provided by the Cetip,5 on operations between FIs withcredit characteristics supplied by the SCR,6 and on swaps and options registered by theBM&FBOVESPA.7
There is a total of 107 types of active operations based on unsecured financial instru-ments in the Brazilian market. In order to facilitate the understanding of the total amountflowing in each type of market, we aggregate these 107 financial instruments into relevantmacro-groups, as illustrated in Table 1. In order to group different financial instrumentsinto macro-groups, we take into account their total gross amount of active operations, aswell as a logical relationship among them.
Table 1: Relevant macro-groups of financial instruments.
Acronym Brief description of the macro-group # Financial instruments
DI Interfinancial deposits 1Mandatory DI Mandatory interfinancial deposits 10
Credit Credit operations 1Financial bill Financial bills 7
CCB Bank credit bills 1FDS Social development fund shares 1
Swap Swap operations 1Debenture Debentures 1
Transfer Interfinancial transfers 1Others Other financial instruments 83
TOTAL 107
We only use exposures that exist among different financial conglomerates or in-dividual FIs that do not belong to conglomerates. As such, we do not consider intra-conglomerate exposures. The players in the market are all banking institutions, which we
5Cetip is a depositary of mainly private fixed income, state and city public securities and other securitiesrepresenting National Treasury debts. As a central securities depositary, Cetip processes the issue, redemp-tion and custody of securities, as well as, when applicable, the payment of interest and other events relatedto them. The institutions eligible to participate in Cetip include commercial banks, multiple banks, sav-ings banks, investment banks, development banks, brokerage companies, securities distribution companies,goods and future contracts brokerage companies, leasing companies, institutional investors, non-financialcompanies (including investment funds and private pension companies) and foreign investors.
6Among several other types of legal attributions, SCR (Sistema de Informacoes de Credito do BancoCentral), which is operated by the Central Bank of Brazil, holds operations and securities with credit char-acteristics and associated guarantees contracted by FIs.
7BM&FBOVESPA is a Brazilian-owned company that was created in 2008 through the integration ofthe Sao Paulo Stock Exchange (Bolsa de Valores de Sao Paulo) and the Brazilian Mercantile & FuturesExchange (Bolsa de Mercadorias e Futuros). As Brazil’s main intermediary for capital market transactionsthe company develops, implements and provides systems for trading equities, equity derivatives, fixed-income securities, federal government bonds, financial derivatives, spot FX and agricultural commodities.
9
classify in the following macro-segments:
• Banking I: commercial banks, multiple banks with commercial portfolio, or federalsavings banks.
• Banking II: multiple banks without commercial portfolio and investment banks.
• Banking IV: development banks.
In addition, we classify banks in accordance with their relative sizes. For that end,we use a simplified version of the size categories defined by the Central Bank of Brazilin the Financial Stability Report published in the second semester of 2012 (see BCB(2012b)), as follows:8 1) we group together the micro, small, and medium banks into the“non-large” category, and 2) the official large category is maintained as is in our simplifiedversion. Therefore, instead of four segments representing the bank sizes, we only employtwo.
Figure 1a displays the evolution of the number of interbank participants over time.We can see that the total number of participants remains roughly constant throughout theperiod. In special, the number of large banking institutions is, on average, 7.32, while ofnon-large banks, 120.43. Figures 1b, 1c, and 1d portray the total market shares, capitalbuffer, and leverage of large and non-large banks. We can see that large banks detainthe majority of the interbank market, are more liquid, and have a lower leverage thannon-large banks.
Figure 2 displays the total amount of unsecured operations in the Brazilian inter-bank market. Since the amount of transfers is prevalent against all of the others financialinstruments, in Fig. 2a we highlight how the transfers amount compares to the sum ofall of the others financial instruments. In turn, Figure 2b exhibits the evolution of all ofthe financial instruments except transfers. We note a vertiginous increase in the trans-fers amount in September 2010, which is due to transfers of major development banks tolarge banking institutions.9 This finding is consistent with the Financial Stability Reportof the Central Bank of Brazil published in the first semester of 2011 BCB (2011), whichexplains that the large amounts of transfers to banking institutions occurred to overcomethe liquidity shortage of the last international financial crisis.
Except for operations related to transfers, we can also see that interfinancial depositsare the majority and remain roughly constant until the end of 2012, period in which they
8The Financial Stability Report ranks FIs according to their positions in a descending list ordered byFIs’ total assets. The Report builds a cumulative distribution function (CDF) on the FIs’ total assets andclassifies them depending on the region that they fall in the CDF. It considers as large FIs that fall in the0% to 75% region. Similarly, medium-sized FIs fall in the 75% to 90% category, small-sized, 90% to 99%mark, and those above are micro-sized.
9Figure 1b shows a clear evidence of this fact as there is a steep increase in the total market share oflarge banking institutions exactly in September 2010, which is due to these large transfers amounts.
10
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Is
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Large banksNon−large banks
(a) Total number of FIs
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Mar
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hare
s [U
S$]
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Large banksNon−large banks
(b) Total market shares
108
109
1010
Avg
. Cap
ital B
uffe
r [U
S$]
03/2
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Large banksNon−large banks
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Large banksNon−large banks
(d) Average leverage
Figure 1: Aggregate descriptive indicators related to the Brazilian interbank network and to the accountingdata of financial institutions. The y-axis of (b) and (c) are in log-scale.
start to reduce. Exposures related to credit operations, in contrast, assume an expansivebehavior. Exposures due to operations related to financial bills take on significant valuesin the interbank market operations after the start of 2012, which coincides with the declineof operations related to interfinancial deposits.
Figure 3 depicts exposure networks in the Brazilian interbank market for September2008, December 2011, and December 2014. For each of these dates, we apply threefiltering criteria so as to better visualize the amounts that are being lent and borrowedwithin the network. The filters are for exposures larger than USD 10 million, 100 million,and 1 billion. We see a distinctive and much sparser network with exposures larger thanUSD 1 billion in September 2008 in relation to the other networks in December 2011 and2014. These, in turn, seem to be similar to each other. This suggests that, in September2008, the great majority of lending and borrowing operations were in smaller amounts.Moreover, we see that large banks intermediate and also concentrate a large portion ofunsecured financial operations, which hints us to the fact that they are members of a
11
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al A
mou
nt [U
S$]
TransferRemainder
(a) Transfer vs. remainder
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Debenture DI Mandatory DI Financial Bill Credit Swap FDS CCB Others
(b) All instruments, except transfers
Figure 2: Total amount of unsecured exposures in the Brazilian interbank market. We discriminate thecurves using the macro-groups as defined in Table 1.
network core. We will quantitatively confirm this claim using network analysis tools inSection 3.
12
(a) September 2008 (> 10M) (b) September 2008 (> 100M) (c) September 2008 (> 1B)
(d) December 2011 (> 10M) (e) December 2011 (> 100M) (f) December 2011 (> 1B)
(g) December 2014 (> 10M) (h) December 2014 (> 100M) (i) December 2014 (> 1B)
Figure 3: Snapshots of the unsecured exposure network that represents the Brazilian interbank market.The shapes convey the bank macro-segments. The circles denote institutions classified as Banking I, thesquares, Banking II, and diamonds, Banking IV. The colors illustrate the bank control types. The greencolor portrays domestic private institutions; the red color, government-owned institutions; the blue color,private with foreign control institutions; and the black color, private with foreign participation institutions.The vertices’ sizes are proportional to the corresponding institutions’ sizes.
3 Topological analysis of the interbank network
We provide how the network measurements are computed in A. Here we focus inproviding their economic meaning in the context of interbank markets. For the sake ofclarity, we inform the descriptive statistics of the local and quasi-local network measuresin Table 2 and of the global network measures in Table 3.
3.1 Degree (strictly local measure)
We can conceive the in- and out-degree of a vertex as measures for quantifying theliabilities and assets diversification, respectively, of market participants. As these indicesincrease, FIs become more diversified in terms of funding (liabilities side) or investments(assets side). In addition, FIs with large degrees are more susceptible to within-network
13
Tabl
e2:
Sum
mar
yre
sults
for
the
loca
land
quas
i-lo
caln
etw
ork
mea
sure
men
ts.
Type
Net
wor
kM
easu
reA
llB
anks
Lar
geB
anks
Non
-larg
eB
anks
Avg.
Std.
Min
.M
ax.
Avg.
Std.
Min
.M
ax.
Avg.
Std.
Min
.M
ax.
Loc
al
Out
-deg
ree
9.03
0.74
7.53
10.3
249
.32
5.46
36.6
356
.86
6.60
0.94
4.94
8.29
In-d
egre
e9.
030.
747.
5310
.32
24.7
12.
0220
.67
30.2
98.
080.
786.
629.
53O
ut-s
tren
gth
(in
USD
Bill
ion)
1.94
0.79
0.80
3.10
30.3
813
.10
9.77
46.1
20.
230.
060.
150.
33In
-str
engt
h(i
nU
SDB
illio
n)1.
940.
790.
803.
1020
.23
9.13
6.32
31.5
10.
840.
290.
421.
25
Qua
si-lo
cal
Ver
tex-
leve
lave
rage
shor
test
path
dist
ance
2.01
0.02
1.96
2.05
1.54
0.06
1.48
1.69
2.04
0.02
1.99
2.08
Clo
sene
ss(×
10−
3 )0.
400.
010.
380.
430.
520.
020.
480.
570.
390.
010.
370.
42B
etw
eenn
ess
(×10−
3 )0.
700.
060.
600.
8410
.09
1.76
5.55
12.4
30.
140.
040.
080.
23C
ritic
ality
0.97
0.17
0.68
1.29
1.54
0.28
0.91
2.27
0.93
0.19
0.63
1.32
Len
derd
omin
ance
0.12
0.02
0.08
0.16
0.13
0.03
0.09
0.18
0.12
0.02
0.08
0.16
Bor
row
erdo
min
ance
0.86
0.04
0.80
0.92
4.47
0.58
3.00
5.73
0.64
0.04
0.59
0.71
14
Table 3: Summary results for the global network measurements.
Network Measure Avg. Std. Min. Max.
Assortativity -0.33 0.04 -0.39 -0.25Rich-club coefficient -0.33 0.04 -0.39 -0.25
Density 0.07 0.01 0.06 0.08Diameter 3.73 0.26 3.00 4.00
Network-level shortest path distance 2.01 0.02 1.96 2.05
events, as they are more susceptible to impacts that connect the origin of the event tothe refereed FI. This is true because there are potentially several paths through which theimpact can travel. Among several examples of possible financial events studied by theliterature, we highlight the occurrence of idiosyncratic or joint defaults. However, thetopological aspects of the network play a crucial role in the propagation of such kinds ofevents. As such, an FI with large degree will not necessarily suffer a larger impact thanan FI with small degree as the interbank connectivity pattern may amplify or reduce theimpact accordingly to the direct or indirect neighborhoods of these FIs.
Figures 4a and 4b depict the evolution of the average out-degree, 〈k(out)〉, and the av-erage in-degree, 〈k(in)〉, respectively, of the Brazilian interbank network. We discriminatethe trajectories by bank sizes. Both funding and investment diversifications are lower fornon-large banks, revealing that these institutions, on average, assume a smaller numberof financial operations than large banks in the unsecured interbank market. Moreover, theslight downward trend for the funding and investment diversifications for non-large bankssuggest that they are concentrating more financial operations on a subgroup of banks.In contrast, the within-network funding and investment portfolios of large banks roughlyassume an upward trend in the studied period. The number of borrowing and lendingoperations largely increases from December 2008 to March 2009. The increase on theborrowing and investment portfolios of banks in this period may be related to the uncer-tainties of financial agents that were brought by the global financial crisis. In this way,banks were less willing to be overly exposed to few banks. After this date, the in- andout-degree of large banks tends to stand still until the end of the sample. Still regardinglarge banks, we see that 〈k(out)〉 > 〈k(in)〉 for all points in the sample, showing that largebanks prefer to diversify more on their investment side rather than their funding side.
3.2 Strength (strictly local measure)
In a network of exposures, the out-strength represents the amount of money that anFI has invested in that market, providing a measure of total exposure or dependence of
15
0
10
20
30
40
50
60
Avg
. Out
−D
egre
e
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(a) Out-degree
5
10
15
20
25
30
35
Avg
. In−
Deg
ree
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(b) In-degree
Figure 4: Evolution of the in- and out-degree of the participants in the Brazilian interbank network. Wediscriminate the trajectories by bank sizes (large or non-large).
that entity to a specific market segment. Note that as the out-strength of an institutionincreases, it is more likely that it will be more and more susceptible to impacts due toits potential higher vulnerability in that market. In contrast, the in-strength symbolizesthe amount of money an FI has received from players of that market segment. As the in-strength of an entity grows larger, it is more likely that it will be more and more dominantin the borrower perspective in the market.
108
109
1010
1011
Avg
. Out
−S
tren
gth
[US
$]
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(a) Out-strength
108
109
1010
1011
In−
Str
engt
h [U
S$]
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(b) In-strength
Figure 5: Evolution of the in- and out-strength of the participants in the Brazilian interbank network. Wediscriminate the trajectories by bank sizes (large or non-large). We report the y-axis in log-scale.
While the degree subsides in determining how diverse are the funding and invest-ment portfolios of an FI, the strength indicates the total amount that is being funded orinvested in the network. Figures 5a and 5b display the average out-strength, 〈s(out)〉, andthe average in-strength, 〈s(in)〉, respectively, in the interbank market. Again, we segregatethe results in accordance with bank sizes. Both for the in- and out-degrees, we see an
16
upward trend during this period, with predominance of amounts invested and funded bylarge banks. In addition, the ratio of the average total amount invested and funded re-mains roughly constant at 〈s(out)〉/〈s(in)〉≈ 1. Putting together this fact with the observationthat the investment diversification is larger than the funding diversification of large banks(remind Fig. 4), we conclude that the average funding that large banks receive is largerthan their average investment in the interbank market. This suggests that large banks pre-fer to diversify more in their investment portfolio management in relation to their fundingportfolio management. We can visualize this fact in Figs 6a and 6b, which depict the av-erage amount lent to each neighbor, 〈s(out)/k(out)〉, and the average amount borrowed fromeach neighbor, 〈s(in)/k(in)〉, in the market.
0
2
4
6
8
10
12x 10
8
Avg
. Out
−S
tren
gth
/ Out
−D
egre
e
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(a) Out-strength / out-degree
0
2
4
6
8
10
12
14
16x 10
8
Avg
. In−
Str
engt
h / I
n−D
egre
e
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(b) In-strength / in-degree
Figure 6: Evolution of the in- and out-strength to in- and out-degree ratios of the participants in theBrazilian interbank network. We discriminate the trajectories by bank sizes (large or non-large). We reportthe y-axis in log-scale.
3.3 Closeness (quasi-local measure)
We can relate the concept of closeness to the efficiency in complex networks (La-tora and Marchiori (2002)), in the sense that efficiency measures how well informationpropagates throughout the network. In this way, FIs with a large closeness indices areefficient in propagating information, both at global and local scale. From a liquidity pointof view, these types of FIs have facility in obtaining funding from other players in themarket, as they play a central role in the network.
Figure 7a shows how the closeness index varies for large and non-large banks in theinterbank market network. We note that the closeness displayed by large banks is largerthan of non-large banks. In addition, the trajectories of the closeness indices for both largeand non-large banks seems to be stable, with considerable fluctuations.
17
3.5
4
4.5
5
5.5
6x 10
−3
Avg
. Clo
sene
ss
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(a) Closeness
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Avg
. Bet
wee
nnes
s
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(b) Betweenness
0
2
4
6
8
10
12
14
Avg
. Dom
inan
ce a
s Le
nder
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(c) Dominance as Lender
0
1
2
3
4
5
6
Avg
. Dom
inan
ce a
s B
orro
wer
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(d) Dominance as Borrower
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
Avg
. Crit
ical
ity
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Large banksNon−large banks
(e) Criticality
Figure 7: Evolution of several quasi-local topological network measurements extracted from the Brazilianinterbank network.
18
3.4 Betweenness (quasi-local measure)
We can understand the betweenness as how active banks are in intermediating fi-nancial operations between different market participants. Banks that are very active inthis function can be regarded as liquidity providers in the financial network.
Figure 7b depicts the betweenness for large and non-large banking institutions thatparticipate in the interbank market. We note that non-large banks are mainly peripheral inthe sense that they almost do not take part in the communication through the shortest pathof other two entities in the network. In contrast, large banks have the largest betweennessvalues and show an upward trend in the period. The increase in the centrality played bylarge banks corroborates the fact that they are members of a network core. Banks in thiscore act as intermediaries to other entities; hence, they are easily reachable from any pointin the network.
3.5 Dominance (quasi-local measure)
We can interpret the dominance as how important one bank is for their neighbors interms borrowing and lending operations. If a bank is dominant, then it is responsible fora large fraction of the funding or investment portfolios of its neighborhoods. The removalof dominant FIs may cause large impacts on their direct neighbors, as they play a centralrole in their funding or investment operations.
Figures 7c and 7d display the dominance of large and non-large banks acting aslenders and borrowers, respectively, in the interbank market. Non-banks do not have aneffective dominance as lenders nor borrowers in any given time of the studied period.However, the dominance as lenders and borrowers of large banks constantly increasesfrom 2008 to 2014. We can give special attention for the interval from September 2008 toDecember 2008, in which the dominance of large banks acting as borrowers and lenderssignificantly increased.
3.6 Criticality (quasi-local measure)
We can conceive the criticality as a quasi-local measure of transmission of liquidityshocks between FIs. Note that, in the spectrum of the criticality, the local importance of anFI is not directly related to its size; rather, it is represented by its creditors’ vulnerabilities,measured by their net liabilities to capital buffer ratios.
Figure 7e reports the criticality indices for large and non-large banks in the periodfrom 2008 to 2014. Except for a large portion of 2008, on average, non-large bankinginstitutions are not critical for the given sample and show a downward trend, suggestingthat their neighbors are not vulnerable to them. Opposed to that, on average, large banks
19
are critical, with a slight upward trend during the studied period, with a prominent peak inDecember 2008. Two factors contribute to the maintenance of the considerable criticalityof large banks: 1) they have larger out-strength in the interbank market; and 2) they arefrequently funded by non-large banks, which in turn are more leveraged and present lowercapital buffers.
3.7 Density (quasi-local measure)
The density give us a sense of how connected the financial network is. Large valuesfor density indicate a high number of financial operations between market participants.
Figure 8a shows the density of the interbank market from 2008 to 2014. The net-work density varies over the interval [6.4%,7.7%]. Interestingly, the network diameterreaches its maximum value in September 2008. Inspecting the exposure network in Fig.3, we verify that there are fewer financial operations that are greater than USD 1 billionin relation to the other network snapshots taken in December 2011 and December 2014,suggesting that banks diversified more their lending portfolios during the crisis period.
We also see that the Brazilian interbank market is very sparse. The sparsenessin these networks may arise because banks incur in operational expenses to maintainrelationships with other counterparties. As such, banks often create relationships withonly a small subset of possible candidates so as to minimize costs (relationship lending).The selection among the candidates follows the banks’ utility functions that normally relyon a tradeoff among past transactions, offered return rates, and market creditworthiness.
3.8 Average network-level shortest path distance (global measure)
In the interbank networks, the network measurement 〈p〉 can be seen as the aver-age length of the intermediation chains that are taking place among the market partici-pants. Longer intermediation chains arise when 〈p〉 is large, which effectively contributeto slowing down the market transactions between participants and consequently harmingthe liquidity allocation between FIs. In contrast, when p is small, the information betweenthe market participants flows quickly in the network, giving rise to a well-functioning liq-uidity allocation in the market.
Figure 8b shows the evolution of the network-level shortest path distance in theinterbank market from 2008 to 2014. We can see a downward trend of the network-levelshortest path distance, raveling that the length of intermediation chains between bankstends to get smaller. In this way, the liquidity allocation turns to be more efficient, due tothe fact that banks can communicate with each other easier.
Looking side by side Figs. 8a and 8b, we see an interesting phenomenon. Nor-mally, as networks get sparser, the tendency of the network-level shortest path distance is
20
0.055
0.06
0.065
0.07
0.075
0.08
0.085
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Den
sity
(a) Density
1.85
1.9
1.95
2
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Avg
. Net
wor
k S
hort
est P
ath
(b) Network-level shortest path
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Net
wor
k D
iam
eter
(c) Diameter
Figure 8: Evolution of several global topological network measurements extracted from the Brazilian in-terbank network.
to increase, as there are fewer feasible paths in the network. Interestingly, we verify inour simulations that as the network gets sparser, the network-level shortest path distancedecreases. This suggests that financial institutions are concentrating a large portion oftheir financial operations in a subgroup of banks that in turn have facility in communi-cating with the remainder of the network. This subgroup of vertices is an evidence of acore-periphery structure in the Brazilian interbank market.
3.9 Diameter (global measure)
The diameter indicates the largest intermediation chain that is possible in the finan-cial network.
Figure 8c shows the network diameter of the interbank network from 2008 to 2014.From March 2008 to March 2011, the diameter remains constant at T = 4. After March2011, the network diameter generally oscillates between T = 3 and T = 4, reflecting
21
the steady decrease of network-level shortest path distance observed in Fig. 8b. Note,however, that a smaller network-level shortest path distance will not always reflect in asmaller network diameter, and vice versa.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ric
h−C
lub
Coe
ffici
ent
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
K = 2K = 10K = 20K = 30
(a) Rich-club coefficient
−0.4
−0.38
−0.36
−0.34
−0.32
−0.3
−0.28
−0.26
−0.24
03/2
008
06/2
008
09/2
008
12/2
008
03/2
009
06/2
009
09/2
009
12/2
009
03/2
010
06/2
010
09/2
010
12/2
010
03/2
011
06/2
011
09/2
011
12/2
011
03/2
012
06/2
012
09/2
012
12/2
012
03/2
013
06/2
013
09/2
013
12/2
013
03/2
014
06/2
014
09/2
014
12/2
014
Ass
orta
tivity
(b) Assortativity
Figure 9: Evolution of assortativity and rich-club coefficient, which are global network measurements.When looked together, they give us a sense of how close is a network to a core-periphery structure.
3.10 Rich-club coefficient (global measure)
The rich-club coefficient conveys the notion of associativity between different mar-ket participants. Subgroups or communities of banks that have large rich-club coeffi-cients indicate that they maintain financial operations among every other participant inthat group. It is therefore an indicative of well-connected groups of vertices in the net-work.
Figure 9a portrays the rich-club coefficient for the Brazilian interbank market forfour values of the degree k∈ {2,10,20,30}. We first see that the interbank network indeedhas a “rich club” inside the network, which is mainly composed of those vertices withlarge degrees. As we have seen by the degree measure, these are represented essentially bylarge banks. Moreover, we also verify that the network does not present dense structureswhen we compute the rich-club coefficient with all of the network vertices (large andsmall small degrees). Therefore, while large banks seem to form near-clique structureswith other large banks in a small region, the network as a whole has, in general, sparsestructures.
3.11 Assortativity (global measure)
We can relate a financial network with a highly disassortative pattern with the emer-gence of the two mesoscales structures that are found in core-periphery network struc-
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tures. This occurs because the majority of banks connect with other banks with dissimilardegrees. That is, non-large banks tend to connect to large banks, and vice versa. In thisway, each of them form one mesostructure: the core and the periphery, in which bankswith large degree compose the core and banks with small degree, the periphery.
Figure 9b depicts the network assortativity of the interbank network from 2008to 2014. Although the Brazilian interbank network shows a clear disassortative mixingpattern, we can see two distinct regions in the graph with respect to the assortativitybehavior. First, from December 2007 to December 2012, the network gets more andmore disassortative. Now, from March 2013 onwards, the network starts to becomes lessdisassortative (more assortative).
Nonetheless, we see that the topology of Brazilian interbank market is highly dis-sasortative, which is an indicative of the existence of the two aforementioned mesoscalestructures. With this respect, we see that large banks compose the core because of severalreasons: they have large degrees (degree analysis), are central in the sense that they in-termediate financial operations of other banks (betweenness and closeness analyses), andare tightly interconnected to other large banks (rich-club coefficient analysis with largek). The periphery regions mainly correspond to players that are either only borrowers orlenders and are sparsely interconnected (rich-club coefficient analysis with small k). Allof these facts together give us strong evidences that the Brazilian interbank market has acore-periphery structure.
4 Econometric model
In this section, we define the empirical specification that we employ to identify andassess the determinant factors of liquidity performance in the Brazilian interbank market.We use the following dynamic panel:
LCRi,t = α +β0LPi,t−1 +β1X (1)i,t +β2X (2)
i,t +β3X (3)t +β4Dt +υi + εi,t , (1)
in which LCRi,t portrays the liquidity performance of bank i at time t, which is proxiedby the Liquidity Coverage Ratio of Basel III. We detail its computation in B. X (1)
i,t isfeature vector that carries the network measurements. In our analysis, we control for bank-specific features and external macroeconomic factors that we model using the featuresvectors X (2)
i,t and X (3)t , respectively.10 We also control for time fixed effects using time
dummies Dt . The term υi represents the non-observable individual factors. Finally, the
10We observe that the external macroeconomic factors are global time-dependent events. For a fixedtime, they are homogeneous among banks. Hence, we only use the subscript t in the corresponding featurevector.
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term εi,t is the error term that, by hypothesis, is identically and independently distributedwith zero mean and constant variance σ2
ε , i.e., εi,t ∼ IID(0,σ2ε ).
We expect the liquidity structure of a bank to persist over time, as its balance sheetstructure cannot be quickly adjusted. This is the reason we opt to use a dynamic ratherthan a static panel model. We effectively model the short term adjustment cost by in-cluding the lagged dependent variable LCRi,t−1 among the regressors. The associatedcoefficient β0 represents the speed of adjustment to equilibrium. Short-term adjustmentcosts for banks arise due to rigidities in their balance sheets, which unable them to raiseliquidity in a short notice in response to negative liquidity shocks. Values of β0 between 0and 1 imply persistence of LCR and also stability, as the liquidity performance is dampedover time until it returns to its normal level. As the autoregressive coefficient β0 approx-imates 1, the more rigid or the more inefficient is the bank to raise liquidity in a shortnotice due to external shocks. Conversely, banks with β0 nearing 0 can adjust their liq-uidity needs with relative easiness, as their liquidity positions can be modified with lessinertia on their past positions.
There are three main questions that our empirical model in (1) seeks to test:
• Are the short-term adjustment costs for liquidity (autoregressive coefficient β0) sig-nificant when we have already controlled for network-based measurements, bank-specific controls, and macroeconomic variables? In addition, we seek to investigatehow these costs behave for different financial institutions that participate in the in-terbank market. Institutions with large inertia in this coefficient can have difficultiesto absorb external liquidity shocks, because they may not be able to accommodatetheir liquidity needs in the short run.
• Several papers in the literature show that the network topology plays a key role inestablishing contagion (see Allen and Gale (2000)). On the other hand, interbankmarket serves as an efficient liquidity channel, as liquidity can be readily transferredfrom surplus to deficit banks. Therefore, is the network structure one of the driversof the liquidity performance of banks and does the network topology explains liq-uidity performance?
• Interbank markets are the focus of central banks’ implementation of monetary pol-icy and also have a significant impact on the entire economy. Does financial regula-tion policies adopted by the Central Bank of Brazil in the interbank market improvethe overall liquidity of the financial system? We investigate this by only consideringthe network layer of regulatory assets rather than all of the unsecured assets.
Given the dynamic nature of our empirical model, least squares estimation meth-ods yield biased and inconsistent estimates (cf. Baltagi (2001)). In this way, we use a
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dynamic panel estimation that is able to deal with the biases and inconsistencies of ourestimates. A further challenge for the estimation of LCR is of the presence of potentialendogeneity problems, which can arise when there is correlation between the explanatoryvariables and the error term. Endogeneity can occur as a result of measurement error,autoregression with autocorrelated errors, simultaneity and omitted variables. A commoncause of endogeneity is a loop of causality between the independent and dependent vari-ables of a model, often termed mutual causality. In our model, for instance, we cannotconclude if an increase in the bank’s activeness11 in the interbank market is the maindriver causing the enhancement of its liquidity or if its low liquidity has caused the bankto use the interbank market in a more active manner. That is, there may be mutual causal-ity: network-based measures may explain in part liquidity and the liquidity position mayalso explain the current bank’s network-based measurements.
To address these problems, we employ the Generalized Method of Moments (GMM)for linear dynamic panel-data estimation put forward by Arellano and Bover (1995) andBlundell and Bond (1998). The Blundell–Bond estimator is well suited to account forthe model’s dynamic structure and it also has two additional properties. First, Blinderet al. (2003) show that the Blundell-Bond estimator does not break down in the presenceof unit roots. Second, it accommodates the possible endogeneity between our dependentvariables and some of the explanatory variables in our models by means of appropriateinstruments. In particular, the system GMM estimator uses lagged values of the depen-dent variable in levels and in differences as instruments, as well as lagged values of otherregressors, which could potentially suffer from endogeneity. The latter problem wouldlead to a correlation between those endogenous variables and the error term and hence toinconsistent estimates if not properly taken care of.
With respect to the potential endogeneity of our regressors, we consider that ourexplanatory variables, as well as the lagged dependent variable, are endogenous. Forthose endogenous variables, we make use of their lagged values as instruments, as dis-cussed in Arellano and Bover (1995) and Blundell and Bond (1998). Note that the systemGMM estimator also controls for unobserved heterogeneity and for the persistence of thedependent variable.
All of our reported results are based on the one-step system GMM estimator, usingrobust standard errors. Even though the two-step estimator is asymptotically more effi-cient, the two-step estimates of the standard errors tend to be severely downward biased,as Arellano and Bond (1995) and Blundell and Bond (1998) draw attention to.
Returning to our empirical specification shown in (1), we use the following networkmeasurements to compose the feature vector X (1)
i,t :12
11From a liquidity point-of-view, the activeness of a bank in the interbank market can be measured by itsin-strength in a network of exposures.
12Refer to Section 3 for details.
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• Strictly local measure: in-strength.
• Quasi-local measures: Herfindahl-Hirschman index (HHI) for intra-network assetsand betweenness.
• Global measures: disassortativity,13 rich-club effect with k = 30,14 diameter anddensity.
Note that network measurements are known to be highly correlated to each other.15
As such, we must carefully choose those measures that are not highly correlated, whilestill being able to capture local, quasi-local, and global structural features of the network.The network measurements that compose our feature vector X (1)
i,t satisfy these restrictions.
We build up the attribute vector X (2)i,t , which accounts for defining the bank-specific
properties, using following descriptors:
• Control type: we make distinction between private domestic and foreign institu-tions.
• Size: we distinguish between large and non-large institutions.
• Main activities: we consider three activity segments: wholesale, investmen, anduniversal. The universal activity segment only applies for large banks that holdmultiple portfolios with two or more segments and that operate nationwide.
• Probability of default (PD): we employ the model described in Tudela and Young(2003). Therein, the default probability is modeled via a hybrid model, which em-ploys a combination of the classical Merton structural approach and additional fi-nancial information. The original Merton model relies on several simplifying as-sumptions about the structure of the typical FI’s finances. The event of default isdetermined by the market value of the FI’s assets in conjunction with its liabilitystructure. When the assets value falls below a certain threshold (the default point),the firm is considered to be in default. A critical assumption in the original Mertonstructural model is that the event of default can only take place at the maturity ofthe debt when the repayment is due. In contrast, Tudela and Young (2003) modifiesthis strong and restrictive assumption to allow for defaults to occur at any point intime and not necessarily at debt maturity.
13Inspecting the assortativity evolution in the Brazilian interbank market in Fig. 9b, we see that it assumesstrictly negative values. In this way, for clarity, we opt to use the disassortativity that we define as themodulus or absolute value of the assortativity.
14We select k = 30 so as to capture the connectedness of the network core, which is only composed ofthose FIs with large degree. To select such value, we use both the rich-club coefficient curve in Fig. 9a andthe degree values of the most connected FIs in Fig. 4.
15To name a few, the pairs out- and in-strengths, degree and strength, closeness and betweenness, be-tweenness and degree are often highly correlated.
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• Accounting variables: we use aggregate accounting variables that are extractedfrom FIs’ balance sheets. In special, we characterize FIs in accordance with theirfunding costs, operational costs, and ROE. With regard to the funding costs vari-able, it encompasses expenditures with deposits, repurchase agreements, securi-ties, loans, onlending, sales operations and assets transfers. In turn, operationalcosts include administrative expenditures, such as with personnel (including socialcharges), communications, publicity, energy, and non-recurrent operations.
For the attribute vector X (3)t that holds macroeconomics variables, we use:
• Brazil’s quarterly GDP.
• Domestic policy rate (Selic).
5 Discussion of the results
Tables 4, 5, and 6 report the estimated coefficients of the econometric panel in (1)for the full set of FIs, for the sub-sample comprising only FIs with low liquidity perfor-mance, and for the sub-sample composed of FIs with high liquidity performance, respec-tively. We establish the borders of the sub-samples that only have FIs with low and highliquidity performances using the lower and upper quartiles of the liquidity performanceof banks, respectively.
The consistency of the system GMM estimator depends on the validity of the as-sumption that the error terms do not exhibit serial correlation and on the validity of theinstruments. To address these issues, Arellano and Bond (1995) and Blundell and Bond(1998) present two specification tests that we employ in our simulations. In the first one,termed as the Hansen test, we verify over-identifying restrictions. In essence, it tests theoverall validity of the instruments by analyzing the sample analogue of the moment condi-tions that we use in our estimation process. In the second test, we examine the hypothesisthat the error term is not serially correlated. We test whether the differenced error termhas a second order serial correlation. By construction, the differenced error term proba-bly has a first order serial correlation even if the original error term does not. Failure inrejecting the null hypotheses of both tests should give support to our models.
We note that the autoregressive coefficient suggests a moderate cost for adjustingthe liquidity performance of banks. For all of the banks, on average, a liquidity shockwould take four quarters to absorb roughly 95% of the initial impact. Banks with lowerliquidity performance, however, would need almost two years to recover from an identicalliquidity shock. In contrast, banks with high liquidity performance would need only twoquarters to absorb a liquidity shock. In this way, we see that the short-term adjustment
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Table 4: Estimation results for the liquidity performance of the full sample of banking institutions. Thecoefficients and their corresponding standard deviations (in parentheses) are reported. (***) p < 0.01;(**) p < 0.05; (*) p < 0.10.
Explanatory variable SpecificationsSpec. (1) Spec. (2) Spec. (3)
Liquidityt−10.4895*** 0.4771*** 0.4686***(0.0195) (0.0196) (0.0196)
Disassortativity 1.0230*** 0.9804*** 0.9993***(0.3152) (0.3649) (0.3411)
Rich-club 0.0452* 0.0551*** 0.0419***(0.0238) (0.0137) (0.0110)
[Disassortativity] · [Rich− club] 0.0318** 0.0184*** 0.0626***(0.0117) (0.0032) (0.0104)
Betweenness 0.6194*** 0.5429*** 0.5355*(0.1125) (0.1670) (0.2810)
In-strength 0.0288*** 0.0258*** 0.0234***(0.0074) (0.0073) (0.0074)
HHI-Assets -0.3451*** -0.3362*** -0.3153***(0.0904) (0.0895) (0.0039)
Diameter -0.0996*** -0.1177*** -0.1196***(0.0377) (0.0377) (0.0375)
Density -0.1079* -0.2065*** -0.1883**(0.0063) (0.0757) (0.0579)
PD 0.0073*** 0.0080***(0.0023) (0.0024)
Funding cost -0.04873*** -0.0507***(0.0186) (0.0187)
Adjusted ROE 0.2091*** 0.1864***(0.0072) (0.0072)
Operational cost -0.0089 -0.0091(0.0059) (0.0058)
GDP 0.0163** 0.0158**(0.0077) (0.0076)
Domestic private -0.2598(0.5186)
Foreign -0.3879(0.5450)
Wholesale segment 0.3328***(0.1271)
Investment segment 0.0326(0.1506)
Universal segment 1.4785**(0.5834)
Small-sized FI -0.2019(0.1251)
Constant -0.8804 -0.6468 -0.3021(0.7946) (1.0930) (1.2020)
Bank fixed effects YES YES YESQuarterly dummies YES YES YES
Order 2 Abond 0.4666 0.3462 0.3580Sargan (p-value) 0.48 0.6516 0.7291
Wald test (p-value) 0.0000 0.0000 0.0000Number of instruments 141 153 141
Number of samples 3346 3346 3346
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Table 5: Estimation results for the liquidity performance of the sub-sample of banking institutions with lowliquidity performance. The coefficients and their corresponding standard deviations (in parentheses) arereported. (***) p < 0.01; (**) p < 0.05; (*) p < 0.10.
Explanatory variable Spec. (4) Spec. (5) Spec. (6)
Liquidityt−10.6740*** 0.6979*** 0.7151***(0.0253) (0.0305) (0.0347)
Disassortativity 0.9028*** 0.8459*** 0.8520***(0.2692) (0.2738) (0.2510)
Rich-club 0.0951*** 0.1124*** 0.0833***(0.0231) (0.0287) (0.0175)
[Disassortativity] · [Rich− club] 0.0184*** 0.0196** 0.0154***(0.0094) (0.0079) (0.0013)
Betweenness 0.8813*** 0.8100*** 0.8714***(0.2121) (0.2876) (0.2637)
In-strength 0.0132*** 0.0132** 0.0100*(0.0056) (0.0064) (0.0042)
HHI-Assets -0.1896*** -0.1702** -0.0857(0.0700) (0.0818) (0.0827)
Diameter -0.0950*** 0.0821** 0.2960**(0.0302) (0.0331) (0.1202)
Density -0.2282*** -0.4183*** -0.1883**(0.0618) (0.0894) (0.0579)
PD 0.0036 0.0072(0.0181) (0.0215)
Funding cost -0.0438*** -0.0221***(0.0035) (0.0036)
Adjusted ROE 0.4460*** 0.7015***(0.1203) (0.1337)
Operational cost -0.02396*** -0.0214***(0.0072) (0.0082)
GDP 0.0291*** 0.0225**(0.0089) (0.0109)
Domestic private -1.9553***(0.6996)
Foreign -1.5120**(0.6685)
Wholesale segment 0.1661(0.1041)
Investment segment 0.8372***(0.2334)
Universal segment 0.7979(1.0866)
Small-sized FI 0.3581**(0.1403)
Constant 0.3552 4.1823*** 4.4302***(0.9836) (1.2175) (1.4901)
Bank fixed effects YES YES YESQuarterly dummies YES YES YES
Order 2 Abond 0.4161 0.4374 0.4782Sargan (p-value) 0.1739 0.2036 0.3647
Wald test (p-value) 0.0000 0.0000 0.0000Number of instruments 134 162 151
Number of samples 645 645 645
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Table 6: Estimation results for the liquidity performance of the sub-sample of banking institutions with highliquidity performance. The coefficients and their corresponding standard deviations (in parentheses) arereported. (***) p < 0.01; (**) p < 0.05; (*) p < 0.10.
Explanatory variable Spec. (7) Spec. (8) Spec. (9)
Liquidityt−10.3808*** 0.3913*** 0.3842***(0.0041) (0.0483) (0.0496)
Disassortativity 0.5488*** 0.5713*** 0.6973***(0.1428) (0.1635) (0.2179)
Rich-club 0.0011* 0.0025 0.0044(0.0004) (0.0019) (0.0067)
[Disassortativity] · [Rich− club] 0.0084*** 0.0096* 0.0054***(0.0020) (0.0052) (0.0013)
Betweenness 0.0291*** 0.0204*** 0.0534***(0.0081) (0.0072) (0.0042)
In-strength -0.0009*** -0.0027* -0.0010*(0.0002) (0.0015) (0.0026)
HHI-Assets -0.0114*** -0.0048 -0.0196(0.0034) (0.0329) (0.0356)
Diameter -0.0037*** -0.0107 -0.0087(0.0008) (0.0175) (0.0179)
Density -0.3901* -0.6785* -0.6760**(0.0451) (0.3725) (0.3794)
PD 0.0009 0.0015(0.0017) (0.0018)
Funding cost -0.0009*** -0.0009***(0.0003) (0.0003)
Adjusted ROE 0.0006*** 0.0008(0.0002) (0.0006)
Operational cost -0.0000 -0.0015(0.0000) (0.0024)
GDP 0.0057* 0.0059*(0.0035) (0.0036)
Domestic private 0.0546(0.0742)
Foreign -0.0363(0.0706)
Wholesale segment 0.0708(0.0576)
Investment segment 0.0170(0.0358)
Universal segment -0.2786(0.2522)
Small-sized FI -0.0528(0.0414)
Constant 0.9897*** 0.4754*** 0.4959(0.0594) (0.0607) (1.2020)
Bank fixed effects YES YES YESQuarterly dummies YES YES YES
Order 2 Abond 0.4656 0.615 0.7253Sargan (p-value) 0.2495 0.3314 0.5332
Wald test (p-value) 0.000 0.0000 0.0000Number of instruments 151 145 159
Number of samples 505 505 505
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costs for liquidity are significant. In special, banks with lower liquidity performance havemore difficulty in accommodating their balance sheets when external liquidity shockshappen.
The in-strength can be understood as a proxy of how active is a bank in the interbankmarket when it comes to borrowing resources. We expect that, on average, if banks aregetting funded by large amounts in the interbank market, they will have better liquiditypositions. In fact, we see that the Brazilian interbank market effectively plays the roleof liquidity provider for its members, as we can infer from the positive and statisticallysignificant coefficient associated to the in-strength.
We have several evidences from Section 3 that the Brazilian interbank network has acore-periphery structure. Now we verify how the core-periphery topology affects bankingliquidity performance. Note that core-periphery structure seems to be a common findingin several domestic interbank networks, implying that our results may have wide implica-tions. Recall that we can check the core-periphery topological property by inspecting theinteraction among the disassortativity and rich-club coefficients. Besides the interactionsbetween these two network measurements, we also report their individual coefficients, sothat we can understand which one prevails. We can clearly see that the core-peripherystructure seems to enhance the liquidity performance of banks due to the positive signand statistically significant values of the aforementioned variables.
We also see that the disassortativity prevails over the rich-club coefficient, implyingthat the existence of two mesoscale structures, the core and the periphery, leads marketparticipants to much better liquidity performances in relation to the existence of a near-clique structures inside the core and sparse structures between periphery-periphery andperiphery-core. We give an intuition behind that in the following. We can conceive thestrong interconnectedness between core members as a mechanism of resilience and re-dundancy of the financial system in terms of liquidity shortages. This is true becauseperipheral members can easily exchange between core members as they are easily reach-able and can reach any other participants in the network. In contrast, the existence of thetwo mesoscale structures contributes to the rapid liquidity flow inside the network, as thecore shortens the effective network distance between borrowers and lenders in the periph-ery. By reducing the rich-club effect inside the network, we may reduce the redundancyinside the core, however, we still can find other similar core members to reaccommodateor rearrange the financial operations. Now the reduction in the network dissasortative pat-tern may lead to the degradation of the structural properties of the core and the periphery.Eventually, these two mesoscale structures may cease to exist. In this case, the liquidityflow would decrease as core members would be less central and therefore their shortestpath distances would increase. This would happen because, in a core, large banks areeasily reachable by all of the market members in the network and effectively play the role
31
of liquidity providers. When this core cannot easily communicate with the remainder ofthe network anymore, liquidity on average would take longer to flow inside the network.In this way, periphery members with low liquidity performance that assume debtor po-sitions in the interbank market would not be able anymore to gather funds directly fromcore banks that play the role of liquidity distributors.
Centrality also plays an important role in explaining liquidity performance of banks.We can see that by inspecting the coefficient of the betweenness, which is positive andstatistically significant. In special, we see that banks that intermediate more financialoperations are likely to have better liquidity performance. Large banks are the ones withlarger centrality or betweenness indices. Periphery members are often only borrowers orlenders in the interbank market; hence, they do not intermediate financial operations.
Even though the magnitude of the betweenness coefficient is large, the disassortativepattern of the network is stronger in providing better liquidity performance for banksbecause of its large coefficient. Interestingly, in the results for only banks with highliquidity performance, we see that the rich-club effect is insignificant. This may happenbecause almost all of the banks with high liquidity performance are large banks, which inturn are members of a core. In this way, the “rich-club” effect turns out to be insignificantin this configuration. In contrast, the disassortativity seems to be a very important factorregardless of the sample we use in our simulations. We also see that the betweenness in thesample of only banks with low liquidity performance plays a much important importantrole in enhancing liquidity performance that in the sample that is composed of only bankswith high liquidity performance. Therefore, centrality plays a key role for members thatare roughly at the periphery. However, it is not very relevant when we analyze banks withhigh liquidity performance.
Diversification is an essential element in what concerns liquidity performance ofbanks. We can see that banks, whose relationships in their active interbank operationsare less concentrated, on average, present better liquidity positions. This is captured bythe statistically significant negative coefficient of the HHI-index, which measures the as-sets concentration of banks. With respect to the network members, we see that largeinstitutions present diversified portfolios both in the borrowing and lending perspective.Non-large financial institutions, in contrast, on average, often present more concentratedborrowing and lending portfolios.
In addition, as the network diameter increases, the efficiency of liquidity transfersis reduced as the number of intermediation chains gets larger. With this respect, the lesslikely are the occurrences of interbank operations related to liquidity shortfalls when thenetwork diameter is small. As we have seen, the Brazilian interbank market shows, onaverage, a small network diameter of 4. This characteristic means that banks that arenot connected to the core of interbank market have more difficulty in gathering resources
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from large banks, for large banks are the central players in distributing liquidity in thefinancial market.
From a theoretical point-of-view, if a financial institution has a probability of defaulthigher than the average of its peers, then other agents would see it as a risky institution.As such, they would demand higher yields in financial operations so as to counterbalancethe higher assumed risks. Another effect of having relative high probability of default isthat the institution suffers from credit restriction. Other institutions, besides establishinghigher prices to accept financial contracts, limit the amount that they are willing to lendto that risky institution. In view of this, that institution would have difficulty in fundingitself and hence to adjust its liquidity. Interestingly, however, we verify a positive as-sociation between the default probability and the liquidity performance of banks. Thisfact suggests that banks with potential solvency problems make strong efforts to emitsignals or actions with the purpose of conveying the apparent information that their liq-uidity positions are satisfactory. Intuitively, banks with relative large default probabilitiesmust maintain larger liquidity buffers against unexpected external shocks because they donot have wide access to the interbank market and have higher costs for adjusting againstexternal liquidity shocks.
We can also observe that the funding costs have negative association with liquidityperformance. As such, banks with liquidity shortfalls have to pay more expensively forgathering funds in the interbank market. This feature suggests that market discipline iseffective in the credit market. Likewise, banks that have higher operational costs hold,on average, low liquidity performances. The banking liquidity conditions are procyclical,i.e., the liquidity of banks increases in economic expansionary periods, while it contractsin recessions. As we expect, large banks whose activities are related to investment andwholesale credit or that are public are consistently more liquid than banks that are private,foreign, or small.
6 Robustness tests
In this section, we perform robustness tests with a focus on regulatory assets thatare determined by the Central Bank of Brazil. These regulatory assets are used as a part ofCentral Bank of Brazil’s regulatory policies to promote liquidity in the financial system.Among these regulatory assets, we can highlight:
• DPGE (Time Deposit with Special Guarantee): the DPGE is a fixed income se-curity representing time deposits created to assist small- and mid-sized financialinstitutions to raise funds. Thus, DPGE confer to holders the right to credit againstthe issuer. Probably, it is one of the main instruments used by the Central Bank of
33
Brazil in promoting liquidity in the financial system. It was created in April 2009by the National Monetary Council (CMN) in its Resolution no. 3692. ThroughResolution no. 4415, in 2012, the CMN also created a new type of regulatory assetknown as DPGE II. This version is distinguished from the DPGE because it is eli-gible for the Credit Guarantee Fund (FGC). In addition, terms should be adjustableto the respective bank loans to which they are pegged.
• Adjustment of reserve requirements: the Central Bank of Brazil can effectively in-ject liquidity in the financial system by decreasing the reserve requirement levels inperiods of distress.
• Mandatory interfinancial deposits: there are several types of mandatory interfinan-cial deposits. In general terms, they enable funds exchanges between financial insti-tutions in order fulfill specific requirements. For instance, the financial instrument“interfinancial deposit linked to microfinance operations” can be used by financialinstitutions to fulfill the minimum requirements in microfinance operations. Thesefinancial instruments are mainly used to force liquidity to flow in the interbank mar-ket, as they encourage financial transactions in which one of the parts is small- ormid-sized institutions.
• Special types of financial bills: Instrument that allows fundraising term extensionfor financial institutions. Thus, they provide better management of financial in-stitutions’ assets and liabilities. One of the main advantages of financial bills isthe minimum maturity period to maturity, without possibility of partial or total re-demption before that period. Another characteristic is that the financial asset has aminimum nominal unit value. Some special types of financial bills are eligible debtinstruments for composing the regulatory capital of financial institutions.
As robustness exercises, we perform two re-estimations of the discussed economet-ric model. We again focus only on unsecured financial instruments. In the first, we re-runthe model without considering these regulatory assets. In contrast, in the second model,we only consider the network layer constituted of regulatory assets.
Table 7 reports the estimates for the panel when we employ the network composedof all of the unsecured assets but regulatory assets. Note that, by removing regulatoryassets, we are effectively leaving behind contracts that are induced by the Central Bank ofBrazil, and not the FIs themselves. This network layer, thus, is constituted of financial re-lationships that are solely due to strategies of each of the network participants. InspectingSpecifications (10), (11), and (12) informed in Table 7, we note that the cost of adjust-ing banking liquidity maintains significant and does not suffer considerable changes inrelation to the estimated liquidity cost when all of the unsecured assets are brought into
34
the analysis. These results, however, suggest that the interbank network loses efficiencyas to its ability to transmit regular flows of liquidity resources when we exclude financialoperations induced by regulatory policies of the Central Bank of Brazil. This observationsuggests that the regulatory policies performed by the Central Bank of Brazil do help inpromoting a more liquid financial system.
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Figure 10: Fraction of active operations due to regulatory assets against total unsecured assets.
We now analyze how the network topology changes due to the removal of regula-tory assets. As Fig. 10 reveals, we first note that the total amount of regulatory assets inthe network is not representative in relation to the total amount of unsecured assets. Thenetwork topology, however, seems to change in a more significative way. Figure 11 por-trays the percentage changes observed in the network density, and the in- and out-degreesof large and non-large banking institutions.
While the network layer of regulatory assets represents, on average, only 3% ofthe total unsecured assets, the network density seems to reduce in an amplified way. Inorder to better analyze the reason of the network density reduction, we inspect the per-centage changes in the in- and out-degree of the network members. Interestingly, for largebanking institutions, we see that the active funding operations assumes a large reductionof [10,11]%, revealing that an expressive portion of the large FI’s relationships is exclu-sively due to regulatory assets. In the other perspective, the number of active investmentoperations only reduces [2,3]%, showing that large banks, on average, only assume in-vestor positions with other banks with contracts that have one or more regulatory assetsand at least another unsecured asset. That is, they seem to not invest in peers with onlyregulatory assets in the relationship. For non-large banking institutions, we see that boththe funding and investment operations uniformly reduce to about [6,7]% of the originalnumber when all of the unsecured assets are considered.
Analyzing the global network structure, we see that the network assortativity doesnot have a perceptible change. This fact indicates that the network relationships corre-
35
Table 7: Estimation results for the liquidity performance of banking institutions when regulatory financialinstruments are excluded. The coefficients and their corresponding standard deviations (in parentheses) arereported. (***) p < 0.01; (**) p < 0.05; (*) p < 0.10.
Explanatory variable Spec. (10) Spec. (11) Spec. (12)
Liquidityt−10.4802*** 0.4414*** 0.4476***(0.0209) (0.0214) (0.0216)
Liquidityt−2-0.0410** -0.0599*** -0.0521***(0.0185) (0.0285) (0.0185)
Disassortativity 0.9186*** 0.8883*** 0.8417***(0.1762) (0.1648) (0.1731)
Rich-club 0.0419* 0.0492*** 0.0446***(0.0212) (0.0127) (0.0109)
[Disassortativity] · [Rich− club] 0.0102* 0.0117* 0.0084(0.0053) (0.0060) (0.0047)
Betweenness 0.5212*** 0.5681*** 0.5932**(0.1022) (0.1480) (0.2351)
In-strength -0.0120** -0.0130** -0.0137**(0.0062) (0.0063) (0.0062)
HHI-Assets -0.0093 -0.0002 0.0059(0.0486) (0.0476) (0.0469)
Diameter 0.0839 -0.0327 -0.0198(0.0534) (0.0613) (0.0604)
Density 0.0408 -0.0259 0.0495(0.0560) (0.0738) (0.0743)
PD 0.0067*** 0.0071***(0.0017) (0.0017)
Funding cost -0.0010*** -0.0010***(0.0002) (0.0002)
Adjusted ROE 0.0678 -0.1426(0.1355) (0.1341)
Operational cost -0.0017 -0.0025(0.0048) (0.0047)
GDP 0.0206*** 0.0189***(0.0064) (0.0063)
Domestic private -0.3857(0.2642)
Foreign -0.1681(0.2440)
Wholesale segment 0.4248***(0.0992)
Investment segment 0.0878(0.1213)
Universal segment 1.6780***(0.4405)
Small-sized FI -0.0984(0.0289)
Constant -1.1647** -3.5301*** -3.4532***(0.5233) (0.8777) (0.8858)
Bank fixed effects YES YES YESQuarterly dummies YES YES YES
Order 2 Abond 0.1384 0.1729 0.1682Sargan (p-value) 0.6470 0.8093 0.7751
Wald test (p-value) 0.0000 0.0000 0.0000Number of instruments 141 151 149
Number of observations 3145 3145 3145
36
lation is maintained by the removal of regulatory assets. The network diameter does notchange as well. Using these two facts, we can see that the network, though sparser, doesnot change in a structural sense.
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Figure 11: Percentage changes on the network density and in- and out-degree when we remove establishedcontracts that are due regulatory assets determined by the Central Bank of Brazil.
Another interesting robustness exercise is to study how the network layer composedof only regulatory assets explain liquidity performance of banks. We re-run our economet-ric model using only that network layer. Table 8 reports the results. An interesting findingis that the assortativity of this network layer is negatively related to liquidity performanceof banks, meaning that regulatory assets incentive the formation of less concentrated fi-nancial networks that normally occur in core-periphery networks (strongly disassortativenetworks). This happens because banks are less willing to connect only to core banks, andhence they diversify more. In this way, the network topology formed by regulatory assetscontributes to decreasing the systemic risk that is inherently embodied in a core-peripherystructure. We can say therefore that the introduction of regulatory assets help at a largeextent small- and micro-sized banks to adjust their liquidity positions.
37
Table 8: Estimation results for the liquidity performance of banking institutions when only regulatoryfinancial instruments are included. Specification (13) employs the entire sample, while Spec. (14), only non-large banks. Specification (15) utilizes the entire sample and an interactive dummy for small- and micro-sized banks. The coefficients and their corresponding standard deviations (in parentheses) are reported.(***) p < 0.01; (**) p < 0.05; (*) p < 0.10.
Explanatory variable Spec. (13) Spec. (14) Spec. (15)
Liquidityt−10.4538*** 0.4490*** 0.2215***(0.0309) (0.0324) (0.0219)[
Liquidityt−1]· [Small−Sized]
0.7524***(0.0231)
Disassortativity -0.0151** -0.0177** -0.0124**(0.0073) (0.0079) (0.0049)
Rich-club 0.0521 0.0895 0.0976(0.0269) (0.0582) (0.0901)
[Disassortativity] · [Rich− club] 0.0009* 0.0015 0.0021(0.0004) (0.0011) (0.0029)
Betweenness 0.4216 0.4986 0.4656(0.3281) (0.4198) (0.2973)
Density 0.1439** 0.1370** 0.1034**(0.0612) (0.0667) (0.0412)
In-Strength 0.0025 0.0013 0.0022(0.0075) (0.0097) (0.0050)
HHI-Assets 0.0492 0.0312 0.0138(0.0862) (0.0964) (0.0580)
Diameter -0.0232 0.0228 -0.0198(0.0281) (0.0302) (0.0189)
Funding cost -0.0258*** -0.0252*** -0.0164***(0.0044) (0.0046) (0.0030)
Adjusted ROE -0.4458*** -0.5101*** -0.2654**(0.1664) (0.1794) (0.1121)
PD 0.0155 0.0242* 0.0003(0.0118) (0.0134) (0.0079)
Size 1.8045*** 2.4010*** -4.7214***(0.7210) (0.8861) (0.5258)
Selic 0.0463*** 0.0493*** 0.0278***(0.0149) (0.0161) (0.101)
GDP 0.0305*** 0.0321*** 0.0221***(0.0106) (0.0113) (0.0071)
Domestic private 0.1789 0.1512 0.2386(0.2411) (0.2471) (0.1625)
Foreign -0.0724 -0.1484 0.0832(0.2619) (0.2730) (0.1762)
Credit segment -0.3048** -0.3957** -0.3911***(0.1552) (0.1673) (0.1045)
Wholesale segment -0.0193 -0.0424 0.0262(0.1508) (0.1563) (0.1015)
Banking I 1.0894 1.3272** 0.7637*(0.5980) (0.6230) (0.4026)
Constant -12.7048*** -14.9696*** 9.1578***(2.6624) (3.1830) (1.9194)
Bank fixed effects YES YES YESQuarterly dummies YES YES YES
Order 2 Abond 0.3617 0.3768 0.1752Sargan (p-value) 0.3158 0.5094 0.5597
Wald test (p-value) 0.0000 0.0000 0.0000Number of instruments 149 163 151
Number of observations 1649 1503 1649
38
7 Policy implications
The large failure cascades that occurred in financial systems over the world sincethe financial crisis in 2008 have taught some lessons for financial regulators. A clearlesson from the global financial crisis is that not only capital requirements are enough butthere is also a need for liquidity requirements as well. When financial markets suffer fromfinancial instability and huge asymmetric information, liquidity becomes a very relevantpolicy issue.
The development of Basel III can be seen as a response from international financialregulators. It comprehends a set of reform measures, that were developed by the BaselCommittee on Banking Supervision and its aims are at strengthening regulation, supervi-sion and risk management of the banking sector. The main goals of these reforms wereto improve the banking sector’s ability to absorb shocks, to refine risk management andgovernance, and to strengthen banks’ transparency and disclosures (BCBS (2010)).
The idea of these reforms to financial regulation was to increase the resilience atthe bank level, which in turn can reduce systemic risk. It is important to stress that liq-uidity has played a major role in the development of the crisis and therefore it should beaddressed by financial regulation. Our main result suggest that there is a group of banksthat have difficulties in adjusting their liquidity after a liquidity shock, which affects theirperformance. Thus, imposing minimum liquidity ratios seems to be a relevant regulationpolicy that has to be implemented. The Brazilian financial regulators have been improvingthese requirements to comply with Basel III.
Our results suggest that a core-periphery structure is prevalent in the Brazilian in-terbank market, which can amplify the propagation of liquidity shocks. As such a betterunderstanding of how this particular network structure emerges and why they are so com-mon across countries goes beyond the scope of this paper and is left for further research.We can infer from our results, nonetheless, that this topology is the result of liquiditymanagement by banks and financial intermediaries in the financial system.
In line with the findings of Krause and Giansante (2012), our results suggest that,when designing regulation, one should also consider financial linkages between banks.Recent research has discovered a core-periphery structure in interbank markets for a vari-ety of countries.16 One of the reasons for this trend is that such a topology may facilitateliquidity management. However, it also poses challenges for financial regulators. Also,Capponi and Chen (2015) find that from a policy perspective in a core-periphery structureit is better to design regulation that targets systemically important banks rather than maxi-mizing the total liquidity of the system, which is preferred if the network is random. Theseresults suggest that the network topology matters for the design of appropriate regulation.
16See Fricke and Lux (2015), Langfield et al. (2014), in ’t Veld and van Lelyveld (2014), and amongothers.
39
8 Conclusion
In this paper, we investigate the roles FIs play within the Brazilian interbank marketusing a comprehensive set of network measurements borrowed from the complex networktheory. One prominent advantage of employing network-based theory is that it is able tocapture topological and structural characteristics of the players’ relationships from thedata representation itself. Our results indicate that the Brazilian interbank network showsstrong disassortative mixing patterns, revealing that highly-connected FIs frequently con-nect to others FIs with very few connections. Moreover, our analysis confirm that theinterbank market also presents the “rich-club” effect, which captures the existence of asubgroup of banks that are strongly interconnected. Putting these two evidences together,we conclude that the Brazilian interbank network effectively has a core-periphery struc-ture. This finding is in line with several domestic interbank networks that we find in theliterature (Craig and von Peter (2014); Fricke and Lux (2015); in ’t Veld and van Lelyveld(2014)).
Moreover, we analyze the liquidity performance determinants of financial institu-tions in terms of network measurements, controlling for bank-specific and macroeco-nomic factors. One of our main findings is that the core-periphery structure is able toenhance, in general, the liquidity performance of banks. Having in mind that several ev-idences point to the fact interbank markets seem to self-organize in core-periphery struc-tures (cf. Lux (2015)), this finding is a positive point as interbank systems seem to drivethemselves to an organization that is optimal or at least improves the overall liquidity ofthe system. However, this optimality has a cost in terms of financial stability. Accord-ing to a comparative analysis between different types of network structures performed byLee (2013), a core-periphery network with a deficit core bank gives rise to the highestlevel of systemic liquidity shortage, implying greater systemic risk. In this way, the bank-ing system may become more vulnerable if a core bank defaults. With this observation inmind, several questions may arise. First, should these core banks have additional liquidityrequirements such as to prevent their failures? Second, should regulators limit pairwisefinancial exposures?17 If we consider that, in a core-periphery structure, members of theperiphery concentrate financial operations on a small subset of core banks, by limitingpairwise financial exposures we would be effectively forcing periphery members to con-nect between themselves; hence, distancing the network structure from a core-peripherytopology.
Our results also show a positive and statistically significant relation among the bank-
17In the Brazilian case, the Financial Stability Report published by Central Bank of Brazil in the firstsemester of 2015 (BCB (2015)) indicates a solid financial system with the majority of the banks, speciallycore banks, showing well-capitalized profiles with high solvency. Moreover, stress tests show that theshort-term liquidity risk and systemic risk of the financial system are low.
40
ing liquidity performance and centrality. This finding suggests that members that interme-diate several financial operations, in general, have better liquidity positions. In addition,our results show that the access to the interbank credit is conducted with short distancesfrom the borrowing banks and the large lending banks. Another relevant factor that facil-itates the gathering of credit is the level of diversification of the funding sources, with aclear advantage for banks with larger in-strength measures.
Finally, it is essential to highlight that the interbank market is able to assess thecredit rating of debtor financial institutions, which is captured by our model by the pos-itive association between less liquidity banks and funding costs. Such fact corroboratesthe thesis that the market discipline efforts is effective. Interestingly, we also find a ro-bust positive association between the default probability and the liquidity performanceof banks. This fact suggests that banks with potential solvency problems make strongefforts to emit signals or actions with the purpose of conveying the apparent informationthat their liquidity positions are satisfactory. Intuitively, banks with relative large defaultprobabilities must maintain larger liquidity buffers against unexpected external shocksbecause they do not have wide access to the interbank market and have higher costs foradjusting against external liquidity shocks.
As future work, we can further study specific mechanisms related to liquidity short-falls of banks, controlling the maturity of the employed financial assets in transactionswhose finality is to adjust the liquidity of banks.
41
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Appendix A Topological analysis of the interbank network
In the process of analyzing the network, we extract some network measures from thegraph G = 〈V ,E 〉 constructed from the lending and borrowing operations of the interbankmarket banks. To build up such network, V denotes the set of vertices (FIs) and E , the setof edges (operations). The cardinality of V , V = |V |, represents the number of verticesor banks in the network, while E = |E |, the number of edges. The matrix A denotesthe exposures or assets matrix (weighted adjacency matrix), in which the (i, j)-th entryrepresents the exposure amount of the FI (vertex) i towards j. The set of edges E is givenby the following filter over A: E = {Ai j > 0 : (i, j) ∈ V 2}. In our analysis, there is nonetting between i and j.18 As such, if an arbitrary pair of FIs owe to each other, thentwo directed independent edges linking each other in opposed directions will emerge. Aninteresting property of maintaining the gross exposures in the network is that, if an FIdefaults, its debtors remain liable for their debts. We also define the matrix of liabilitiesbetween the FIs as L = AT , where T is the transpose operator.
Next, we present the network measurements that we use to extract topological in-formation of the interbank network. We follow Silva and Zhao (2015) and classify thesemeasures with respect to the type of information the index makes use in its computation,as follows: local, quasi-local, and global measures.
A.1 Strictly local measures
Strictly local measures are related to the inherent characteristic of a vertex itself.In this way, measures qualified as strictly local do not take into account the neighboringfeatures. We present some of these network measures in the following.
A.1.1 Degree
The degree or valency of a vertex i ∈ V , indicated by ki, is related to its connectiv-ity, or number of links, to the remainder of the network. In directed graphs, this notioncan be further extended into the in-degree, k(in)i , and the out-degree, k(out)
i , in a way thatthe identity ki = kin
i + kouti holds. The feasible values of ki are within the discrete-valued
interval {0, . . . ,V − 1} if self-loops are not allowed, and {0, . . . ,V} if self-loops are per-mitted. When ki = 0, vertex i is disconnected from the remainder of the graph. In thiscase, we say that vertex i is a singleton. Conversely, when ki is large, we say that vertex i
is a hub.The out- and in-degree of vertex i ∈ V are defined as follows:
18Pairwise exposures are not netted out so as to maintain consistency with the Brazilian law, becausefinancial compensation is not always legally enforceable.
45
k(out)i = ∑
j∈V1{Ai j>0}, (2)
k(in)i = ∑j∈V
1{A ji>0}, (3)
in which 1{K} represents the indicator or Kronecker function that yields 1 if K, a logicalexpression, evaluates to true, and 0, otherwise. In a network of exposures, the out-degreek(out)
i represents the number of FIs in which participant i has invested (is exposed to).With a similar reasoning, the in-degree k(in)i symbolizes the number of participants thatare funding i in the market (they are exposed to i).
A.1.2 Strength
The strength of a vertex i ∈ V , indicated by si, represents the total sum of weightedconnections of i towards its neighbors. Likewise the degree, the notion of strength canbe further decomposed into the in-strength, s(in)i , and out-strength, s(out)
i , such that theidentity si = sin
i + souti holds. The feasible values of si corresponds to the continuous
interval [0,∞).The out- and in-strength of vertex i ∈ V are defined as:
s(out)i = ∑
j∈VAi j, (4)
s(in)i = ∑j∈V
A ji. (5)
A.2 Quasi-local measures
Given a reference vertex, quasi-local measures take into account the neighborhood’sstructural or topological characteristics to render information.
A.2.1 Closeness
We compute the closeness of vertex i, εi, in accordance with the following expres-sion (Latora and Marchiori (2001)):
εi =1
V (V −1) ∑j∈Vj 6=i
1pi j
, (6)
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i.e., it is the sum of the reciprocal of all of the shortest path lengths starting from i. Forcentral vertices, the average shortest path distance is expected to be small, resulting in alarge closeness index. Opposed to that, for peripheral vertices, we expect shortest pathsto the remainder of the network to be relatively large, yielding a small closeness value.
A.2.2 Betweenness
The betweenness of vertex i, Bi, is a centrality measure that quantifies the fractionof shortest paths between all pairs of vertices (k, j) ∈ V 2, k 6= j 6= i, in a network suchthat i is one of the intermediate vertices in the path. Mathematically, we evaluate thebetweenness as follows (Freeman (1977)):
Bi = ∑(k, j)∈V 2,k 6= j 6=i
σk j(i)σk j
, (7)
in which σk j quantifies the number of shortest paths starting from k and ending in j andσk j(i) denotes the number of shortest paths starting from k and ending in j such that i isan intermediate vertex, i.e., is a member of the geodesic path.
A.2.3 Dominance
The dominance of vertex i ∈ V , Di, measures the relative importance of i on itsneighbors’ operations. The dominance of i as a lender and as a borrower is given by:
D(lender)i = ∑
j∈V
Ai j
s(in)j
, (8)
D(borrower)i = ∑
j∈V
A ji
s(out)j
, (9)
i.e., the lender dominance of i evaluates the fraction of funding to be received by i’s neigh-borhood, while the borrower dominance of i captures the fraction received by i against thetotal amount invested in the market by its neighbors.
A.2.4 Criticality
The criticality of the FI i∈V , Ci, quantifies the impact of the i’s liabilities toward itscounterparties’ liquid assets. It is the sum of the vulnerabilities of its creditors regardingtheir exposures to the FI and is given by:
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Ci = ∑j∈V
V ji = ∑j∈V
Li j
E j, (10)
in which V ji = Li j/E j quantifies the vulnerability of j with respect to the funding depen-dence on i, E j indicates the readily available resources or capital buffer of bank j ∈ V .We use as capital buffer the tier 1 capital of banks.
A.3 Global measures
Global measures make use of all the relationships contained in the network to deriveinformation. We show some in the following.
A.3.1 Density
The network density D, also known as network connectivity, for a directed network,is defined as:
D =E(V2
) = 2EV (V −1)
, (11)
in which V and E represent the total number of vertices and edges, respectively. Thedensity assumes values in the interval [0,1]. When D = 0, we say that G is an emptygraph. Conversely, when D = 1, G is said to be a complete or maximal clique graph.Often in the literature, we classify networks as sparse when D assumes values near 0.Conversely, when D approaches 1, we term the network as dense. As a rule of thumb,when the number of edges in the networks is of the order of the number of vertices, i.e.,E = O(V ), we consider the network as sparse.
A.3.2 Average network-level shortest path distance
The average network-level shortest path distance 〈p〉 is given by:
〈p〉= 1V ∑
i∈V〈pi〉, (12)
in which 〈pi〉 represents the vertex-level average shortest path distance of vertex i that wecompute as follows:
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〈pi〉=1
V −1 ∑j∈Vj 6=i
pi j, (13)
The domain of 〈p〉 is [0,V − 1]. In the interbank networks, the network measure-ment 〈p〉 can be seen as the average length of the intermediation chains that are takingplace among the market participants. In average, as p grows larger, longer intermediationchains will emerge, slowing down the market transactions between participants and con-sequently harming the liquidity allocation between FIs. In contrast, when p is small, theinformation between the market participants flows quickly in the network, giving rise toa well-functioning liquidity allocation in the market.
A.3.3 Diameter
The network diameter T is given by:
T = max(i, j)∈V 2
pi j, (14)
i.e., T is the largest geodesic distance of any pairs of vertices in the network. The feasiblevalues that T may assume are [0,V − 1]. We can interpret the diameter as the largestintermediation chain in the network.
A.3.4 Rich-club coefficient
The rich-club coefficient measures the structural property of complex networkscalled “rich-club” phenomenon. This property refers to the tendency of vertices withlarge degree (hubs) to be tightly connected to each other, thus forming clique or near-clique structures. This phenomenon has been discussed in several instances in both socialand computer sciences. Essentially, vertices with a large number of links, usually knownas rich vertices, are much more likely to form dense interconnected subgraphs (clubs)than vertices with small degree. Considering that E>k is the number of edges among theN>k vertices that have degree larger than a given threshold k≥ 0, the scaled version of therich-club coefficient is expressed as (da F. Costa et al. (2005)):
φ(k) =2E>k
N>k (N>k−1), (15)
in which the factor N>k(N>k−1)/2 represents the maximum feasible number of edges that
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can exist among N>k vertices.
A.3.5 Assortativity
Assortativity is a network-level measure that, in a structural sense, quantifies thetendency of vertices to link with similar vertices in a network. The assortativity coefficientr is computed as the Pearson’s correlation of degrees of vertices in each connected pair.Positive values of r indicate that edges in the network have vertices in the endpoints withsimilar degrees, while negative values indicate endpoints with different degrees (Newman(2003)). In general r ∈ [−1,1]. When r = 1, the network has perfect assortative mixingpatterns, while, it is completely disassortative in the case r =−1. Considering that iu andku represent the origin and destination of the u-th edge of a non-empty graph, respectively,and that l = ∑(i, j)∈V 2 Ai j denotes the total edge weight of the adjacency matrix (in ourcontext, it is the exposures matrix), the assortativity r is evaluated as follows (Newman(2002)):
r =l−1
∑u∈E iuku−[
l−1
2 ∑u∈E (iu + ku)]2
l−1
2 ∑u∈E (i2u + k2u)−
[l−1
2 ∑u∈E (iu + ku)]2 . (16)
According to Silva and Zhao (2012, 2015), understanding the assortative mixingpatterns in complex networks is important for interpreting vertex functionality and foranalyzing the global properties of the network components.
Appendix B Liquidity performance
We define banking liquidity as the ability of FIs to honor their short-run liabilities,to how ease they can convert assets to money and to raise funds, or even to roll-over oremit short-term debts. The inadequate structure of resources held by FIs relates to theirliquidity risk, which also encompasses the difficulties for obtaining credit or for raisingfunds with interest rates comparable to the market reference. The inadequate structureof resources is a risk factor that is associated with the structure of liabilities held by anentity. It measures how adequate this structure is in terms of funding needs, bearing inmind the aspects of possible mismatches with the concentration and the volatility of thefunding sources held by FIs.
We evaluate liquidity performance by means of banks’ liquidity coverage ratios(LCR). LCR measures the amount of liquid resources that is available for an institutionto withstand expected and unexpected cash flows in the next 30 days, under severe stress
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scenarios. These stress scenarios simulate ruptures in historical trends of variables re-lated to cash flow estimates. We mold these scenarios by employing parameters that areextracted from historical references of experienced past crises. In these situations, it isassumed that these sudden adverse shocks will raise the disbursements of FIs above theexpected levels.
The liquidity index LCR is given by the ratio of the liquidity buffer and the stressedcash flow for a horizon of 30 days. The liquidity buffer is the amount each bank can raisein short time and is basically composed of unencumbered sovereign bonds. The stressedcash flow is the potential cash flow each bank would need to face stress situations, suchas retail and wholesale deposit run-off, market stress, and potential losses on liquid assetsand derivative positions.
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