Multilayer overlaps and correlations in the bank-firm credit network of Spain

Abstract

We investigate the structural dependencies in the bank-firm credit market of Spain under a multilayer network perspective. In particular, the original bipartite network is decomposed into different layers representing different industrial sectors. We then study the correlations between layers based on normalized measures of overlaps of links and weights of banks between layers. To assess the statistical significance of such correlations, we compare the observed values with the expected ones obtained from random graph models specifying only global constraints, i.e. the total degree or the total strength in single layers, and from configuration models capturing the intrinsic heterogeneity in the local constraints like the observed degree sequence and/or strength sequence in single layers. We find that, first, the raw dependencies between layers of the observed network are highly heterogeneous. Second, when evaluated against the null models, on the one hand, the rescaled correlations after filtering out the effects of the global constraints typically display no significant difference to the observed correlations. In addition, in the binary version, almost all correlations are still present after subtracting the effects of the observed degree sequences in all layers. On the other hand, the observed correlations are partially explained by the local constraints maintained in the weighted configuration models. All in all, comparing the observed network with all referenced null models, we find that the multilayer credit network under scrutiny has a significant, non-random structure of correlations that cannot be explained by more primitive network properties alone. In the binary case, such a non-random structure is, for instance, typically observed in the pairs of layers that have high levels of overlaps and correlations. In contrast, in the weighted case, patterns are found in different pairs of layers that have various levels of overlaps and correlations.

The multilayer architecture of the global input-output network and its properties

“…In following, we will briefly explain the methods used to measure the overall overlaps and correlations between layers. Following Gemmetto and Garlaschelli (2014);Gemmetto et al (2016); Luu and Lux (2019), we define the overall (normalized) degree of overlaps between every pair of layers α and β in the binary version as…”

“…In particular, if trade links are strong in a particular layer, do they also exist and tend to form intensive relations in the other layers? To answer this question, we measure the overall overlap coefficient and Pearson correlation coefficient for every pair of layers (Gemmetto and Garlaschelli, 2014;Gemmetto et al, 2016;Luu and Lux, 2019). In general, when comparing layer vs. layer, we find that some clusters of layers exhibit a relatively higher level of similarity (see Figures ( 5) and ( 6) as well as the dendrograms shown in Figures ( 13) and ( 14) in the Appendix).…”

“…For example, in the financial system, banks often interact among themselves via different channels and various markets (e.g. see Leon et al, 2014;Poledna et al, 2015;Bargigli et al, 2015;Luu and Lux, 2019). It has been also shown in recent studies that focusing on a single layer or on a combined layer may lead to a wrong assessment of systemic risk or underestimate the importance of the inter-plays among different propagation channels of shocks (Kok and Montagna, 2013;Poledna et al, 2015).…”

Contagion in economic networks: a data-driven machine learning approach

“…In this section, we show that the model is also able to reproduce a handful of key stylized facts of bipartite bank-firm credit networks reported in the related literature (Masi et al (2011), Masi and Gallegati (2012), Bottazzi, Sanctis and Vanni (2020), Luu and Lux (2019)):…”

“…Table 5 brings some statistics of the financial networks. They present some characteristics reported by other empirical studies on financial networks, such as disassortative behavior (e.g., Bottazzi, Sanctis and Vanni (2020)), sparseness (e.g., Souza et al (2016)), and a distribution of banks' degrees wider than that of firms in the bank-firm network (e.g., Luu and Lux (2019)). In each period t, we combine both networks to create the overall matrix of exposures A t ∈ NB t × (NB t + NF t )), where NB t is the number of banks at t, NF t is the number of firms at t, and A i jt is the net exposure of i towards j at t. Recalling that creditors can be only banks, and debtors can be either firms or banks.…”