Modeling structure and credit risk of the economy: a multilayer bank-firm network approach

TL;DR

This work develops an unified framework, combining state-of-the art techniques to reconstruct the whole multilayer structure of the economy from balance sheet information of banks and firms, as well as dynamics of shock propagation from the inter-firm to the interbank layers.

Abstract

Assessing the resilience of the economy requires accounting for its intrinsic multi-layer nature, by assessing for instance how disruptions at the firm level spread through the production network and propagate to the banking sector. Methods exist to measure the reverberation of shocks over the multilayer network of supply-customer relations among firms, corporate loans of banks and their interbank market exposures. However, empirical network data are often privacy protected and thus inaccessible to researchers and regulators. In this work we develop an unified framework, combining state-of-the art techniques to reconstruct the whole multilayer structure of the economy from balance sheet information of banks and firms, as well as dynamics of shock propagation from the inter-firm to the interbank layers. We showcase application of our methodology using data of the Italian economy. We identify the most systemically important firms and industries, as well as the most vulnerable banks, further assessing the determinants of systemic risk -- obtaining results coherent with the empirical literature on network contagion. Overall, our framework allows performing detailed network-based stress tests on a digital twin of the economy, without requiring detailed network information that is difficult to acquire.

Figures (13)

• Figure 1: Schematic overview of the multilayer bank-firm systemic-risk framework. (A) Network reconstruction: starting from balance-sheet information for banks and firms in our sample, three interconnected networks are reconstructed independently: the interbank market layer (top, blue links), the bank-firm credit network (middle, green links), and the interfirm production network layer (bottom, red links). (B) Shock propagation: Once the multilayer network is reconstructed, we simulate the spreading of a shock originating in the interfirm layer. The shock first diffuses through interfirm production links, according to ESRI dynamics (left), then is transmitted to the bank layer via firm exposures to banks, according to FSRI (center), and finally amplified through interbank contagion following DR dynamics (right). (C) Systemic-risk analysis: the cumulative effects of the shock propagation are summarized through ranked risk profiles, showing how successive layers contribute to economic losses: reduction of production (ESRI, left), additional bank credit losses (ESRI+FSRI, middle), and interbank amplification (ESRI+FSRI+DR, right).
• Figure 2: CCDF of bank variables (A) and firm variables (B) extracted from the balance sheets of our 2023 sample of the Italian economy.
• Figure 3: Scatter plots of node degrees versus strength used in the reconstruction procedure. Each point represents an individual bank or firm, colored according to their specialization or NACE1 sector, respectively.
• Figure 4: Scatter plots of empirical versus reconstructed strength values, where each point represents an individual bank or firm, while the identity (solid line) serves as a reference for perfect reconstruction. Banks are colored according to their specialization while firms to their NACE1 sector.
• Figure 5: Ranking plots in terms of systemic risk metrics, with nodes placed in descending order of the corresponding scores. (A) Ranking based on ESRI scores of firms, where for each firm $i$ the initial condition is given by its complete production shutdown ($\psi_i=0.0$), while all other firms remain active. ESRI of $i$ thus measures the fraction of total production lost in the interfirm layer through supply-chain contagion, due to the default of $i$. (B) Ranking based on FSRI scores of firms: FSRI of $i$ measures the fraction of total bank equity lost in the bank-firm layer due to the results of the ESRI dynamics with the same initial condition as before. (C) Ranking based on DR scores of firms: DR of $i$ measures the fraction of total bank equity lost in the interbank layer due to the results of the FSRI dynamics with the same initial condition as before. (D) Ranking based on total systemic risk scores of firms (ESRI+FSRI+DR), highlighting the total impact of firms default on the overall economy. Total impact of $i$ thus measures the fraction of total firm production and bank equity lost due to the default of $i$, subsequent supply chain contagion, bank loans devaluation and re-evaluation of interbank claims. (E) Ranking based on vulnerability scores of banks, obtained by averaging over shutdowns of all individual firms as initial conditions. Vulnerability of $\alpha$ thus measures how much the bank can be affected by economic losses, in terms of equity losses. Marker colors denote bank specialisation.