(In)Efficient Interbank Networks

• Published date: 01 March 2020
• Author: FABIO CASTIGLIONESI,NOEMI NAVARRO
• Date: 01 March 2020
• DOI: http://doi.org/10.1111/jmcb.12664

DOI: 10.1111/jmcb.12664

FABIO CASTIGLIONESI

NOEMI NAVARRO

(In)Efficient Interbank Networks

Westudy the efficiency properties of the formation of an interbank network.

Banks face a trade-off by establishing connections in the interbank market.

On the one hand, banks improve the diversification of their liquidity risk

and therefore can obtain a higher expected payoff. On the other hand, banks

not sufficiently capitalized have risk-shifting incentivesthat expose them to

the risk of bankruptcy. Connecting to such risky banks negatively affects

expected payoff. We showthat both the optimal and the decentralized net-

works are characterized by a core-periphery structure. The core is made

of the safe banks, whereas the periphery is populated by the risky banks.

Nevertheless, the two network structures coincide only if counterparty risk

is sufficiently low.Otherwise, the decentralized network is underconnected

as compared to the optimal one. Finally, we analyze mechanisms that can

avoid the formation of inefficient interbank networks.

JEL codes:D85, G21

Keywords:interbank network, core-periphery, liquidity coinsurance,

counterparty risk.

IT IS WELL ESTABLISHED THAT banks have incentives to form

bilateral lending relationships. The most intuitive reason is to coinsure future and

uncertain idiosyncratic liquidity shocks (Allen and Gale 2000, Freixas, Parigi, and

Rochet 2000). There is robust evidence that documents how interbank lending plays a

crucial role in providing liquidity insurance both in normal times (Furfine 2001, King

We thank Martin Brown,Sandro Brusco, Fabio Feriozzi, Jiro E. Kondo, Emanuela Sciubba, and Wolf

Wagnerfor helpful comments. We are also grateful to seminar participants at Bank of England, Universidad

Carlos III, Bank of Italy, 1st Swiss Conference on Banking and Financial Intermediation (Champery),

Society for Economic Dynamics (Boston), European Finance Association (Athens), and Association for

Public Economic Theory (Galway) annual meetings where an earlier version of this paper was presented.

The usual disclaimer applies. Castiglionesi acknowledges financial support from the Marie Curie Intra

European Fellowship and Navarro from the Spanish Ministry of Economics, grant ECO2014-53767P.

FABIO CASTIGLIONESI is at Tilburg University (E-mail: fabio.castiglionesi@uvt.nl). NOEMI NAVAR R Ois at

Universit´

e de Bordeaux.(E-mail: navarro.prada@gmail.com).

Received July 5, 2018; and accepted in revised form April 29, 2019.

Journal of Money, Credit and Banking, Vol. 52, Nos. 2–3 (March–April 2020)

C

2019 The Authors. Journal of Money,Credit and Banking published by Wiley Periodicals,

Inc. on behalf of Ohio State University

This is an open access article under the terms of the Creative Commons Attribution License,

which permits use, distribution and reproduction in any medium, provided the original work

is properly cited.

366 :MONEY,CREDIT AND BANKING

2008, Cocco, Gomes, and Martins 2009) and in times of crisis (Furfine 2002). The

overall amount of these bilateral links that banks establish forms what is generally

known as the interbank network.

The 2007/2008 financial crisis witnessed a prominent role played by the interbank

market in initiating and spreading the turmoil. This event prompted a surge of empir-

ical evidence about the actual shape of the interbank network. Sorom¨

aki et al. (2007)

and Bech and Atalay (2010) find that the interbank networks formed by U.S. com-

mercial banks is quite sparse. It consists of a core of highly connected banks, while

the remaining peripheral banks connect to the core banks. An almost identical feature

is found in interbank networks in countries like the UK, Canada, Japan, Austria, and

Germany (see, respectively,Boss et al. 2004, Inaoka et al. 2004, Embree and Roberts

2009, Craig and von Peter 2014, Langfield, Liu, and Ota 2014).

The aim of this paper is to establish under which conditions, if any,a core-periphery

interbank network may be optimal. We then study the decentralized endogenous

network formation game. That is, we investigate if banks have the right incentive

to mimic the optimal network and under which conditions this may occur. Overall,

the objective of the paper is to rationalize the stylized fact on the core-periphery

shape of the interbank networks, and to understand when such a structure may

entail inefficiencies.

We model an interbank networkcomposed of several banks that anticipate how the

structure of the network affects their payoff. Participating in the interbank network

is beneficial because it allows banks to increase the expected payoff. We posit that

such expected payoff is increasing in the number of links that a bank establishes

in the network. The rationale behind this assumption is the ability of the interbank

network to reduce liquidity risk by coinsuring future idiosyncratic liquidity shocks.

The higher the number of connections in the network are, the higher the probability to

find coinsurance is, the less resources have to be invested in liquid low-returnassets,

and the more resources can be invested in illiquid high-return investment projects

thus increasing depositors’ payoff (Castiglionesi, Feriozzi, and Lorenzoni 2019).

The benefit howeverhas to take into account the potential cost of participating in the

interbank network. Such cost is captured by assuming that banks face a standard moral

hazard problem (Holmstr¨

om and Tirole 1997). Each bank is financed by depositors

and shareholders. The former supply their funds and expect to break even, the latter

provide capital and decide the type of investment the bank chooses. Shareholders

have two types of investment projects in which they can invest the bank’s resources.

Although one project is risk-free, that is, it guarantees a certain return, the other project

is risky because it has the same payoff of the safe project if it succeeds but it delivers

nothing if it fails. The risky project however gives private benefits to the bank’s

shareholders, therefore it represents a gambling project from the depositors’ point of

view.1Shareholders are protected by limited liability, so they find it convenient to

invest in the gambling project when the bank is poorly capitalized. We assume that a

1.Throughout the paper, we use the expressions risk-free and safe bank (or project) as synonymous.

Similarly for risky and gambling bank (or project).

FABIOCASTIGLIONESIANDNOEMI NAVARRO:367

bank, by establishing a link with banks that invest in the risky project, reduces the ex

ante probability of serving its own depositors. In particular, we assume that the higher

the ratio between the number of neighboring banks that invest in the risky project

over the total neighboring banks, the lower the probability to serve the depositors is.

We refer to the risk of making connections in the interbank network as counterparty

(or solvency) risk.

Weanalyze the trade-off of participating in an interbank market in which the benefit

of a reduced liquidity risk has to be weighted against the counterparty risk. First, we

characterize the optimal interbank network as the solution of the planner’s problem.

The planner can avoid the moral hazard problem in all banks only if a sufficient

amount of bank capital is available in the economy.In this case, the first-best network

is characterized by a fully connected structure. Otherwise, if bank capital in the

economy is scarce, the planner has to allow some banks to gamble and a constrained

first-best (CFB) network is obtained.

The presence of banks investing in the risky project implies that the CFB network

does not necessarily coincide with the fully connected one. Indeed, the CFB net-

work is characterized by a core-periphery structure. The core includes all the banks

that invest in the safe project and form a complete network structure among them-

selves. The periphery includes all the gambling banks that can be connected among

themselves and/or with the core banks according to the parameters’ value. With an

additional assumption on the benefit of participating in the network, we are able to

fully characterize the conditions under which risky banks should or should not be

connected among themselves and with the core (safe) banks.

Second, we analyze the decentralized interbank network formation adopting the

equilibrium notion of pairwise stability. Also in this case a core-periphery structure

emerges as an equilibrium outcome. Nevertheless, the connectivity in the decen-

tralized network does not necessarily coincide with the CFB network. We show

that the structure of the decentralized interbank network is the same as the CFB

one if the counterparty risk is sufficiently low. Otherwise, when the counterparty

risk is not low enough, the decentralized network does not coincide with the CFB

network. The reason is that the planner finds it optimal to link a safe bank with

a gambling bank when the expected losses of the former (because of counterparty

risk) are lower than the expected gains of the latter (represented by the higher ex-

pected payoff due to a higher liquidity coinsurance). However, these expected gains

are not internalized by the safe banks that severe the link with the gambling banks

even when this is not efficient. The decentralized network has an inefficiently low

degree of connectivity compared to the CFB network when counterparty risk is

sufficiently high.

Finally, we analyze possible mechanisms that could prevent the formation of in-

efficient networks. In particular, we allow for decentralized bank capital transfers

before the shareholders take the investment decision. Banks investing in the safe

project may find it convenient to transfer part of their bank capital to the neighbor-

ing gambling banks to change their investment decision and therefore to achieve

a higher expected payoff. We show that if the probability of success of the bank’s