RDP 2018-01: A Density-based Estimator of Core/Periphery Network Structures: Analysing the Australian Interbank Market 7. The Core/Periphery Structure of the IBOC Market

7.1 Estimated Core

Figure 8 shows IBOC market core size estimates for every quarter in our sample using three of the estimators evaluated above.[27] As expected, the DB estimator finds a smaller core than the other estimators. Notably, with respect to the CvP estimator, the core found by the DB estimator is much smaller, while that found by the correlation estimator is generally larger. Based on our numerical analysis in Section 6, this suggests that the true-core size is in a region where the DB estimator is likely the most accurate.

Figure 8: Core Size
Figure 8: Core Size

Note: Shaded ranges indicate that our optimisation algorithm found multiple core sizes that optimise the relevant function

The most notable feature of Figure 8 is the fall in the estimated core size that occurred during the 2007–08 financial crisis. Although the size of the fall differs between estimators, all estimators suggest that the typical core size fell during this period.

Based on the DB estimator, the average core size was around eight banks prior to the peak of the crisis (i.e. the average until 2008:Q3) and around five banks afterwards. As expected, the four major banks were almost always estimated to be in the core, both before and after the crisis (Figure 9).

Figure 9: Core Composition
Density-based estimator, sorted by frequency in the core
Figure 9: Core Composition

Notes: Each row is a different bank, for which a dot is placed in every quarter that the bank is in the core; the rows are sorted by the frequency each bank is in the core; banks are not identified to preserve confidentiality

Four of the non-major banks that were often in the core prior to the crisis (i.e. those in rows 6, 7, 9, and 10 in Figure 9) were almost never estimated to be in the core after the crisis. Only one of these banks became inactive (an Australian-owned bank), while the other three (one Australian-owned and two foreign-owned banks) moved from the core to the periphery.

Of these banks that moved to the periphery, their average in-degrees (borrowing links) and out-degrees (lending links) all decreased after the crisis. For two of these three banks (one foreign-owned and one Australian-owned), their average number of borrowing links fell more than 80 per cent between pre- and post-crisis, including a reduction in their borrowing links with the remaining core. This reduction in borrowing links was the major cause of them dropping out of the core. For the other bank, the fall in lending links was the major cause of it dropping out of the core; the average number of this bank's lending links fell more than 80 per cent between pre- and post-crisis.

These falls in the number of in- and out-degrees could be due to either/both supply or demand. Using the foreign-owned banks as an example:

  • the increased perceived risk of foreign-owned banks during the crisis may have reduced the willingness of some banks to lend to these foreign-owned banks (supply) – consistent with the theoretical models of Freixas and Jorge (2008) and Acharya, Gromb and Yorulmazer (2012); and/or
  • the increased stress in the foreign-owned banks' home markets may have prompted their pullback from intermediating in the Australian market (demand).

Unfortunately, the nature of our data does not allow us to determine whether the reductions in degree, and therefore the fall in the core size, are demand or supply driven. What we can conclude, however, is that crises can have long-lasting effects on the IBOC market, and that not all relationships remain reliable during times of stress. Identifying the causes of these banks' reductions in degrees is left for future research.

International studies find both reductions and increases in core size during the crisis. For the Italian overnight market (excluding foreign banks), and using the CvP estimator, Fricke and Lux (2015) find a reduction in the size of the core – from 28 per cent of active banks to 23 per cent. Conversely, Wetherilt et al (2010) find that the core size in the UK overnight market increased during the crisis. They suggest that the UK experience could be due to banks wanting to diversify their borrowing relationships to ensure they could source liquidity even during periods of high stress, or that changes to the UK's reserves management regime may have allowed banks to increase their activity in this market.

7.2 The Changing Relationship between Core and Periphery

In addition to looking at changes in the make-up of the core, we also want to see whether the relationships between the core and periphery changed during the crisis.

Since the ideal CP structure only requires the off-diagonal blocks to be row and column regular, changes in the densities of these blocks (beyond some minimum density) have no effect on the DB estimator. Therefore, looking at changes in the densities of the off-diagonal blocks may provide useful information about changes in the relationships between the core and the periphery.

However, the typical density measure of each off-diagonal block (i.e. the number of links within the block as a proportion of the number of possible links) may be misleading. This is because changes in the composition of the core and periphery may change the density of the off-diagonal blocks, even if none of the banks actually changed their behaviour.[28] As a result, it is difficult to interpret raw changes in the density of the off-diagonal blocks.

To overcome this problem, we construct a ‘density index’. In particular, we consider only banks that are in the same position in consecutive periods; that is, they are either in the core for two consecutive periods or in the periphery for the same two periods. We then compute the growth in the densities of the relationships between these banks and between the two periods, and use these growth rates to construct our index (Figure 10).

Figure 10: Density Index
Density-based estimator, mean = 100
Figure 10: Density Index

During 2008, the density of the ‘core lends to periphery’ links fell by 40 per cent – the largest year-on-year fall in our sample – and continued to trend down following the crisis (Figure 10). Conversely, the density of ‘periphery lends to core’ links fell slightly during the crisis, but remained around its long-run average in subsequent years.[29]

These trends are consistent with the increased perceived risk that occurred during the crisis. That is, while it is likely that the core banks were perceived as safe, the periphery banks may not have been. So it is plausible that, in such an environment, the core might reduce their exposure to the periphery, with each periphery bank potentially only able to borrow from the core banks with which they have the strongest relationships, if at all.

However, to fully understand the changing relationships between the core and periphery, we must look at lending volumes, not just the number of lending relationships. Although aggregate lending remained elevated during the crisis (Figure 1), there was a large shift in the direction of lending volumes between the core and periphery (Figure 11).[30]

Figure 11: Lending Volumes
Quarterly aggregates
Figure 11: Lending Volumes

To the extent that, prior to the crisis, periphery banks relied on the core banks for their liquidity, if the core stopped providing this liquidity (or the periphery banks feared that they would), the periphery banks would need to source this liquidity from elsewhere (e.g. the RBA's open market operations, the secured lending market, or term funding markets).[31] The resulting changes in the flows between the core and periphery are consistent with the model of Ashcraft et al (2011). In their model, banks that fear a liquidity shortage desire large precautionary deposit balances. Being precautionary, these banks do not expect to need all of the extra liquidity and therefore expect to have a surplus of funds. As their daily liquidity needs unfold (i.e. as the trading day draws to a close and the need for precautionary balances fades), they seek to lend any excess balances in the market. Knowing this, the core banks reduce their demand for liquidity from other sources, expecting to be able to fund any deficit by borrowing from the periphery.

Our findings are consistent with those of other overnight interbank markets. In the Italian market, the financial crisis led to a reduction in the density of ‘core lending to periphery’ links, no clear difference in the density of ‘periphery lending to core’ links, a reduction in core-to-periphery lending volumes, and an increase in periphery-to-core lending volumes (Fricke and Lux 2015). In the UK market, the densities of both off-diagonal blocks fell during the crisis (Wetherilt et al 2010).

As the acute phase of the crisis passed, demand for precautionary balances by the periphery likely waned (Figure 11). However, the data suggests periphery banks never returned to their pre-crisis reliance on the core for their liquidity. Therefore, in addition to having a long-lasting effect on the core/periphery structure of the IBOC market, the crisis has also had a long-lasting effect on the relationships between the core and periphery.


We do not document the results based on the maximum likelihood estimator as it produced core size estimates that were more volatile and larger (on average) than the estimates produced by any of the other three estimators. The maximum likelihood estimator results are available upon request. [27]

For example, suppose all banks remaining in the core had fewer relationships with the periphery after the crisis than they had before the crisis. If the banks that dropped out of the core had a lower-than-average number of links with the periphery (before the crisis), the densities of the off-diagonal blocks may actually increase during the crisis. [28]

In 2008:Q3, our optimisation algorithm for the DB estimator found two CP splits with the minimum error. The core size is the same with both splits, but the alternate split attenuates the 2008 fall in the ‘core lends to periphery’ index (to 32 per cent) while amplifying the fall in the ‘periphery lends to core’ index. The only other quarter where multiple error-minimising splits were found was 2015:Q4. [29]

Figure 11 splits the system into the major banks and non-major banks because the major banks are estimated to be in the core throughout the sample period. It would also be possible to construct a ‘lending volumes index’ for the core and periphery in the same way as the density indices in Figure 10, but this would remove information about relative volumes. [30]

Garvin, Hughes and Peydró (forthcoming) show that as perceived risk increased during the crisis, banks with weak fundamentals and plentiful collateral increased their secured borrowing more than other banks. [31]