Reciprocity in Interbank Markets

TL;DR

This paper introduces a statistical model for weighted reciprocity in interbank networks, revealing how reciprocity patterns change over time and impact network structure analysis.

Contribution

It develops an exponential random graph model accounting for reciprocal links at both topological and weighted levels, providing exact solutions and applying it to real interbank data.

Findings

Higher-than-expected reciprocity before the financial crisis

Reciprocity diminishes during the crisis, especially among smaller banks

Neglecting reciprocity can lead to incorrect inferences about network triads

Abstract

Weighted reciprocity between two agents can be defined as the minimum of sending and receiving value in their bilateral relationship. In financial networks, such reciprocity characterizes the importance of individual banks as both liquidity absorber and provider, a feature typically attributed to large, intermediating dealer banks. In this paper we develop an exponential random graph model that can account for reciprocal links of each node simultaneously on the topological as well as on the weighted level. We provide an exact expression for the normalizing constant and thus a closed-form solution for the graph probability distribution. Applying this statistical null model to Italian interbank data, we find that before the great financial crisis (i) banks displayed significantly more weighted reciprocity compared to what the lower-order network features (size and volume distributions) would predict (ii) with a disappearance of this deviation once the early periods of the crisis set in, (iii) a trend which can be attributed in particular to smaller banks (dis)engaging in bilateral high-value trading relationships. Moreover, we show that neglecting reciprocal links and weights can lead to spurious findings of triadic relationships. As the hierarchical structure in the network is found to be compatible with its transitive but not with its intransitive triadic sub-graphs, the interbank market seems to be well-characterized by a hierarchical core-periphery structure enhanced by non-hierarchical reciprocal trading relationships.