Complex Interbank Network Estimation: Sparsity-Clustering Threshold

Abstract

In the “too-interconnected-to-fail” discussion network theory has emerged as an important tool to identify risk concentrations in interbank networks. Therefore, however, data on bilateral bank exposures, i.e. the edges in such a network, is not available but has to be estimated. In this work we report on the possibility of enhancing existing inference techniques with prior knowledge on network topology in order to preserve complex interbank network characteristics. A convenient feature of our technique is that a single parameter $\alpha$ governs the characteristics of the resulting network. In an empirical study we reconstruct the network of about 2100 US commercial banks and show that complex network characteristics can indeed be preserved and, moreover, controlled by $\alpha$. In an outlook we discuss the possibility of developing an $\alpha$-based measurement for the complexity characteristics of observed interbank networks.

Appendix

In order to analyze the “goodness” of our estimation technique, we compute the error terms between observed total payment obligations and claims (i.e. target matrix margins) and the margins of the estimated adjacency matrix. Therefore, we present in Fig. 4 the sum of absolute errors relative to sum of total interbank payment obligations and claims (notice the log-scale). Hence, the graph shows the total (absolute) interbank payment obligations and claims that have not been correctly attributed to individual banks by our estimation technique as a percentage of total interbank value. Since for $\alpha =1$ no interbank links are established the relative error is exactly one in this case. Interestingly, the estimation error remains on about the same level for $0<\alpha <1$. This indicates that even though the number of established links is reduced drastically banks are still able to distribute their interbank assets among a set of sufficiently similar (with respect to our composite measure of similarity) counterparts.