The interbank market has a natural multiplex network representation. We employ a unique database of supervisory reports of Italian banks to the Banca d'Italia that includes all bilateral exposures broken down by maturity and by the secured and unsecured nature of the contract. We find that layers have different topological properties and persistence over time. The presence of a link in a layer is not a good predictor of the presence of the same link in other layers. Maximum entropy models reveal different unexpected substructures, such as network motifs, in different layers. Using the total interbank network or focusing on a specific layer as representative of the other layers provides a poor representation of interlinkages in the interbank market and could lead to biased estimation of systemic risk.

JEL classification: D85 C49 C63 E51 G21Keywords: Diversification Complex networks Credit networks Expected degree model Modularity Community structure of networks a b s t r a c t Building upon the growing interest for complex network theory, the main ambition of this paper is to contribute to a more effective application of network theory to economic phenomena, and particularly to financial networks. We depart from recent contributions on credit networks in two respects. In the first place, we constrain diversification with the out-and in-degree distribution of nodes, by adopting a suitable extension of the expected degree model for random weighted digraphs. In the second place, we focus on real networks by using this extension as null model for statistical analysis. With the help of statistical inference, we provide a rigorous answer to the following question: do real networks obey our null model? Further, we show that this answer is tightly connected to the existence of clusters or modules, as defined by Newman and Girvan (2004), within networks.

We allow firms and banks to entertain multiple credit connections in a financially constrained production framework, resorting to a random network model whose parameters are calibrated with real data. The calibration is successful since the network model is able to reproduce the degree and strength (debt and loan) distributions of the Japanese credit market. We run simulations over the parameter space using an efficient design, and compare a number of alternative statistical metamodels in order to select the best specification for the relationship between the parameters and a set of endogenous variables of the model. We show that the metamodeling approach can be usefully extended to economic models in order to bridge the gap between micro and macro variables through a rigorous statistical analysis of ABMs, without imposing unrealistic restrictions on the micro model such as the representative agent hypothesis.

We build a statistical ensemble representation of two economic models describing respectively, in simplified terms, a payment system and a credit market. To this purpose we adopt the Boltzmann-Gibbs distribution where the role of the Hamiltonian is taken by the total money supply (i.e. including money created from debt) of a set of * Corresponding author 1 interacting economic agents. As a result, we can read the main thermodynamic quantities in terms of monetary ones. In particular, we define for the credit market model a work term which is related to the impact of monetary policy on credit creation. Furthermore, with our formalism we recover and extend some results concerning the temperature of an economic system, previously presented in the literature by considering only the monetary base as conserved quantity. Finally, we study the statistical ensemble for the Pareto distribution.

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