RDP 2018-01: A Density-based Estimator of Core/Periphery Network Structures: Analysing the Australian Interbank Market 1. Introduction

Seizures in the electricity grid, degradation of eco-systems, the spread of epidemics and the disintegration of the financial system – each is essentially a different branch of the same network family tree. Haldane (2009)

The market for unsecured overnight interbank loans in Australia, known as the interbank overnight cash (IBOC) market, is a pivotal financial market. The average interest rate on these loans is the Reserve Bank of Australia's (RBA) operational target for monetary policy; so the IBOC market is the first step in the transmission of monetary policy to the rest of the financial system and broader economy. As such, its smooth operation is critical, and it is important for the RBA to have detailed knowledge about how it functions, especially in times of stress.

In this paper, we explore the IBOC market through the lens of network theory.^[1] Network theory allows us to identify the lending relationships formed by banks, determine whether these relationships make any of the banks central to the proper functioning of the market, and analyse how these relationships may change during periods of stress. The answers to these questions provide a guide to which interbank relationships are resilient, whether crises can have long-lasting effects on the IBOC market, and how to efficiently manage emergency liquidity provision (e.g. liquidity provision could be more targeted if we know the relationships between the banks).

This paper also has a theoretical contribution. First, we find that several of the IBOC market's network properties are consistent with the core/periphery model (first introduced by Borgatti and Everett (2000) and adjusted to capture the features specific to interbank markets by Craig and von Peter (2014)). The premise of the core/periphery model is that there are two types of banks. ‘Core’ banks are central to the system; they lend to/borrow from all other banks in the core and to some banks outside of the core. ‘Periphery’ banks, instead, lend to/borrow from some core banks, but do not transact directly among themselves. Thus, the removal of a core bank can inhibit the flow of funds and drastically change the structure of the network.

There have recently been several studies that analyse interbank markets with the core/periphery model.^[2] And with real-world networks being unlikely to satisfy the idealiseds core/periphery structure outlined above, various methods have been developed to estimate the underlying core/periphery structure of these networks.^[3] However, as far as we are aware, no-one has evaluated the various estimators' relative accuracies. This paper fills this gap.

We find that existing estimators can provide wildly varying and inaccurate estimates in networks that have either a relatively large or relatively small core (relative to the density of the network, a concept explained in Section 3). We analytically derive the source of this problem, and then derive a new estimator that is immune to this source of inaccuracy. In numerical simulations, our estimator produces lower estimation errors than any of the commonly used estimators when either the true size of the core is known to be relatively small, or when no prior information about the true size of the core is available.

Our new estimator can be used on any network that may have a core/periphery structure. Therefore, given the increasing use of the core/periphery model when analysing networks, our theoretical contribution has broad applicability.

Returning to our empirical contribution, we show that the core/periphery model provides a better explanation of the IBOC market's features than other canonical network models. So we use this model (with our estimator) to analyse the evolution of the market during the 2007–08 financial crisis. Prior to the crisis, the IBOC market had a core of around eight banks – the core typically included the four major Australian banks, three foreign-owned banks, and one other Australian-owned bank. The financial crisis caused the core to shrink to around five banks – the four major banks and one foreign-owned bank – with the core remaining around this size in the years since the crisis. This finding suggests that not all relationships are reliable during times of stress. It also indicates that temporary shocks can have long-lasting effects on the IBOC market, which is important not only for determining the effect of exogenous shocks but also for evaluating the potential effect of any operational changes made by the RBA.

We also look at changes in the relationships between the core and periphery. We find that the number of ‘core lending to periphery’ relationships fell 40 per cent during 2008 (the largest year-on-year fall in our sample) and continued to trend down following the crisis. Conversely, the number of ‘periphery lending to core’ relationships remained broadly unchanged.

Additionally, we uncover a large shift in the direction of lending volumes. The major banks were net lenders to the non-major banks before the crisis. During the crisis, this relationship switched – in 2008 the volume of major banks' loans to non-major banks decreased by 58 per cent, while the volume of loans in the reverse direction increased by 84 per cent. The non-major banks have remained net lenders to the major banks since the crisis, albeit at a lower level than during 2008–09.

Irrespective of whether it was the core actively reducing their exposure to the periphery, or the periphery reducing their reliance on the core (due to fears about the reliability of their funding), these trends are consistent with the predictions of theoretical models of precautionary liquidity demand during periods of heightened risk (Ashcraft, McAndrews and Skeie 2011).

Footnotes

The interconnectedness of the Australian financial system has previously been studied using different data sources. Tellez (2013) analyses Australian banks' large exposures, while Anufriev and Panchenko (2015) estimate interconnectedness from partial correlations between entities' equity returns. Network analyses have been conducted for international interbank markets (see Bech and Atalay (2010) and Wetherilt, Zimmerman and Soramäki (2010), for example), but not for the IBOC market. [1]

Examples include Craig and von Peter (2014) for Germany, Wetherilt et al (2010) and Langfield, Liu and Ota (2014) for the United Kingdom, in ′t Veld and van Lelyveld (2014) for the Netherlands, Martinez-Jaramillo et al (2014) for Mexico, and Fricke and Lux (2015) for Italy. [2]

In any real-world analysis, the model used does not capture everything that influences the data (with the external influences treated as ‘noise’). For example, two banks that would otherwise only interact with the core may also have a direct relationship that developed from their other operations (i.e. outside the IBOC market). Such an idiosyncratic relationship would be noise when trying to identify any core/periphery structure. [3]