Mapping Economic Risk: How Interconnected Networks Amplify Shocks

by

Author: Denis Avetisyan

A new framework reconstructs the complex web of production and financial relationships to reveal how vulnerabilities cascade through the modern economy.

A multilayer framework models systemic risk by reconstructing networks of interbank relationships, bank-firm credit, and interfirm production-allowing shocks originating in the production network to propagate through firm exposures and ultimately amplify via interbank contagion, culminating in ranked risk profiles that detail contributions to economic losses across each layer-from initial production reduction to compounded bank credit losses and final interbank amplification.
A multilayer framework models systemic risk by reconstructing networks of interbank relationships, bank-firm credit, and interfirm production-allowing shocks originating in the production network to propagate through firm exposures and ultimately amplify via interbank contagion, culminating in ranked risk profiles that detail contributions to economic losses across each layer-from initial production reduction to compounded bank credit losses and final interbank amplification.

This paper presents a multilayer network approach to model systemic risk, integrating input-output and financial linkages to assess contagion and inform stress testing.

Assessing economic resilience demands understanding the complex interplay between production and financial networks, yet detailed data on these interdependencies are often inaccessible due to privacy concerns. This paper, ‘Modeling structure and credit risk of the economy: a multilayer bank-firm network approach’, introduces a novel framework for reconstructing the multilayer structure of an economy-integrating firm-to-firm linkages with bank-firm credit relationships-to model the propagation of shocks. By applying this methodology to the Italian economy, we identify systemically important actors and vulnerabilities, revealing key determinants of systemic risk and enabling detailed network-based stress tests. Could this approach provide regulators with a valuable ‘digital twin’ for proactively mitigating financial instability?

Unveiling the Hidden Threads: Mapping Financial Interdependence

Conventional financial risk assessments frequently operate under the assumption of institutional independence, a simplification that obscures the reality of modern finance. This isolated approach overlooks the crucial fact that financial institutions are deeply interwoven through a complex network of credits, investments, and shared exposures. Consequently, these models struggle to predict or mitigate systemic risks – vulnerabilities that arise not from the failings of individual entities, but from the cascading effects of interconnected failures. A shock to one institution can rapidly propagate through the network, triggering a chain reaction that destabilizes the entire system – a phenomenon largely invisible to models that treat each firm as a solitary unit. Recognizing this interdependence is therefore paramount for a more robust and accurate understanding of financial stability, necessitating methodologies that explicitly map and analyze these complex relationships.

Financial stability isn’t solely about the health of individual institutions; it fundamentally depends on understanding how those institutions relate to one another. A robust assessment requires mapping the intricate network of connections between firms and banks, recognizing that distress in one entity can rapidly propagate through the system. These relationships extend beyond simple creditor-debtor ties, encompassing ownership, supply chains, and shared exposures. Consequently, a comprehensive view moves beyond isolated risk assessments to consider systemic vulnerabilities – the potential for localized shocks to cascade into widespread financial crises. Analyzing this complex web allows for the identification of critical nodes and pathways, offering insights into how shocks might transmit and where interventions could be most effective in bolstering the overall resilience of the financial system.

A novel multilayer network approach was developed to model the intricate relationships driving financial interdependence, encompassing production linkages, credit exposures, and interbank lending patterns. This reconstruction revealed a surprisingly dense network structure, with each institution, on average, directly connected to twenty others within the interbank lending layer and forty within the firm-to-firm production network. These high average node degrees suggest substantial systemic risk, as shocks can propagate rapidly through the financial system. Validation procedures confirmed the reconstructed network accurately reflects the observed patterns of financial relationships, offering a robust framework for assessing and mitigating potential vulnerabilities within the global financial landscape.

Systemic risk rankings, based on metrics measuring production loss through supply chains (<span class="katex-eq" data-katex-display="false">ESRI</span>), bank equity loss (<span class="katex-eq" data-katex-display="false">FSRI</span> and <span class="katex-eq" data-katex-display="false">DR</span>), and a combined total risk score, reveal how the failure of individual firms or banks propagates through the economy, with vulnerability scores indicating bank sensitivity to firm failures and marker colors representing bank specialisation.
Systemic risk rankings, based on metrics measuring production loss through supply chains (ESRI), bank equity loss (FSRI and DR), and a combined total risk score, reveal how the failure of individual firms or banks propagates through the economy, with vulnerability scores indicating bank sensitivity to firm failures and marker colors representing bank specialisation.

Deconstructing the System: Reconstructing Financial Networks

The Production Network is reconstructed utilizing the Input-Output Gravity Model, a method adapted from international trade analysis. This model quantifies the flow of goods and services between firms by treating each firm as an ‘economy’ and inter-firm transactions as ‘trade’. The model leverages firm-level data on production inputs and outputs – specifically, the monetary value of goods and services sold from firm i to firm j – and applies a gravity-like equation where the flow is proportional to the ‘size’ of each firm (total output) and inversely proportional to the ‘distance’ – in this case, a proxy for the complexity of the supply chain relationship. This approach allows for the estimation of direct and indirect interdependencies within the production structure, providing a weighted network where edge weights represent the monetary value of transactions.

The Bank-Firm Network reconstruction utilizes an Enhanced Capital Asset Pricing Model (ECAPM) to quantify credit exposures. This model moves beyond traditional CAPM by incorporating firm-specific characteristics and loan portfolio data. Specifically, the ECAPM assesses exposures by analyzing the composition of bank loan portfolios, weighting exposures based on the assets of borrowing firms. This approach allows for the determination of direct credit links between banks and firms, and the overall systemic risk stemming from these interdependencies. The model’s output is a weighted network representing the magnitude of financial connections, essential for analyzing contagion effects and systemic vulnerabilities within the financial system.

The Interbank Network is reconstructed using the Density-Corrected Gravity Model, a methodology that estimates interbank lending and borrowing relationships based on financial institutions’ asset and liability data. This model incorporates balance sheet information – specifically, total assets representing a bank’s lending capacity and total liabilities reflecting its funding needs – to quantify potential exposures. The Density-Correction component adjusts for network density, mitigating biases that arise from highly connected or sparse networks. The resulting network maps the flow of funds between banks, enabling the analysis of contagion risk and systemic vulnerability within the financial system. This approach differs from simpler gravity models by accounting for the overall structure of the interbank market, providing a more accurate representation of financial interdependencies.

Model performance was evaluated using the R-squared metric, quantifying the proportion of variance explained by each model. The Economic Systemic Risk Index (ESRI) model achieved an R-squared value of 0.87, indicating a high degree of explanatory power regarding economic systemic risk. The Financial Systemic Risk Index (FSRI) model demonstrated substantial explanatory power with an R-squared value of 0.73. Notably, the DebtRank (DR) model achieved a perfect score of 1.00, signifying it fully explains the observed variation within the modeled dataset and providing a complete representation of debt-based relationships.

Empirical and reconstructed strength values closely align for individual banks and firms, as demonstrated by the scatter plot with the identity line representing perfect reconstruction, and points colored by specialization (banks) or NACE1 sector (firms).
Empirical and reconstructed strength values closely align for individual banks and firms, as demonstrated by the scatter plot with the identity line representing perfect reconstruction, and points colored by specialization (banks) or NACE1 sector (firms).

Simulating the Cascade: Mapping Shock Propagation and Vulnerability

Shock propagation is modeled within a multilayer network comprising production, bank-firm, and interbank connections to simulate systemic risk. A firm failure in one sector initiates a cascade effect, impacting connected entities across these networks. The simulation tracks how initial capital shocks are transmitted through direct and indirect linkages. Specifically, a reduction in the assets of a failing firm triggers losses for its creditors and counterparties, which then propagate further based on the network structure and interdependencies. The model captures both direct exposures-loans or financial obligations-and indirect exposures arising from shared counterparties and interconnected production relationships, allowing for the quantification of potential systemic impact resulting from localized failures.

Systemic risk propagation is fundamentally determined by the architecture of interconnected economic networks. Specifically, the Production Network defines supplier-customer relationships and initial shock transmission points; the Bank-Firm Network maps credit exposures between financial institutions and businesses, dictating the flow of financial distress; and the Interbank Network details liabilities between banks, enabling contagion through wholesale funding markets. Accurate modeling requires representing these networks concurrently, as a failure in one sector can transmit through multiple layers – for example, a firm default stemming from production issues impacting its bank lenders, who then experience losses affecting their interbank counterparties. Ignoring these interdependencies leads to an underestimation of systemic risk, as isolated network analyses fail to capture the complete propagation pathways and amplification effects.

DebtRank is a metric used to assess systemic risk within the Interbank Network by quantifying the amplification of financial shocks. It operates on the principle that a bank’s systemic importance is proportional to its direct and indirect exposures to other banks, weighted by their own systemic importance as determined recursively. Specifically, DebtRank calculates a bank’s contribution to overall systemic risk by considering the total amount of debt it holds from other banks in the network, effectively measuring its potential to transmit shocks. Higher DebtRank values indicate greater susceptibility to contagion, as these institutions are more likely to both receive and propagate financial distress throughout the network, potentially triggering a systemic crisis. The metric differs from simple eigenvector centrality by explicitly incorporating the amount of interbank debt as a measure of systemic contribution.

Quantitative analysis of interbank exposures demonstrates a strong correlation between asset holdings and bank vulnerability. Initial correlation values were measured at 0.22; however, these values increase to 0.41 across different vulnerability quantiles. This indicates that as bank vulnerability increases, the correlation between asset holdings within the interbank network also rises significantly. The observed increase confirms that interconnectedness through interbank lending amplifies systemic risk, as the failure of one institution becomes more likely to propagate through correlated asset holdings to other institutions.

Sector and bank rankings based on systemic risk metrics-including economic stress (<span class="katex-eq" data-katex-display="false">ESRI</span>), financial stability (<span class="katex-eq" data-katex-display="false">FSRI</span>), and debt propagation (<span class="katex-eq" data-katex-display="false">DR</span>)-reveal the relative contribution of each layer to overall systemic importance when a sector experiences a 10% production reduction, with bank specializations indicated by marker color.
Sector and bank rankings based on systemic risk metrics-including economic stress (ESRI), financial stability (FSRI), and debt propagation (DR)-reveal the relative contribution of each layer to overall systemic importance when a sector experiences a 10% production reduction, with bank specializations indicated by marker color.

Beyond Prediction: Implications for Resilience and Regulatory Design

The Economic Systemic Risk Index incorporates a novel metric, the Essentiality Score, designed to pinpoint those firms and sectors whose distress would cascade through the financial system with the most damaging consequences. This score isn’t simply based on size or interconnectedness, but rather a firm’s unique role in facilitating economic activity – how irreplaceable it is in essential transactions. A high Essentiality Score indicates a firm acts as a critical node, meaning its failure wouldn’t just impact immediate counterparties, but would disrupt broader economic functions, potentially triggering widespread instability. Identifying these crucial entities allows for a more focused approach to financial oversight, enabling regulators to prioritize interventions and bolster resilience where it matters most, rather than applying broad-stroke measures across the entire system.

Network-based models are rapidly becoming indispensable for regulatory stress testing, offering a dynamic alternative to static, firm-by-firm analyses. These models simulate the cascading effects of adverse shocks – such as market crashes or commodity price fluctuations – across the interconnected financial system. By mapping relationships between institutions – including lending, derivatives exposures, and shared ownership – policymakers can identify vulnerabilities that might otherwise remain hidden. Instead of evaluating institutions in isolation, these tools reveal how a failure at one firm could propagate through the network, potentially triggering a systemic crisis. The resulting data provides crucial insights into the system’s resilience, allowing regulators to proactively adjust capital requirements, refine resolution strategies, and ultimately strengthen the financial system against future instability. This proactive, systemic approach represents a significant advancement in financial oversight, moving beyond reactive measures to anticipate and mitigate risk before it materializes.

Identifying systemic vulnerabilities and critical institutions allows for a shift towards more precise regulatory strategies. Rather than broad-stroke regulations that may stifle economic activity without addressing core risks, policymakers can now implement targeted interventions focused on bolstering the resilience of entities and sectors most likely to trigger cascading failures. This approach moves beyond simply increasing capital requirements across the board; it enables regulators to address specific weaknesses within the financial network, such as interconnectedness or reliance on short-term funding. By concentrating resources on the institutions and practices that pose the greatest systemic threat, regulators can achieve greater financial stability with potentially less economic disruption.

Conventional financial risk assessments often examine institutions in isolation, failing to account for the intricate web of interconnectedness that defines modern financial systems. This research transcends such limitations by employing network-based models that map the complex relationships between firms and sectors, revealing how a disruption in one area can cascade throughout the entire system. By embracing this holistic perspective, policymakers gain a more accurate understanding of systemic vulnerabilities and can proactively design interventions that address the root causes of potential crises, rather than merely reacting to symptoms. This shift towards systemic thinking promises a more robust and resilient financial landscape, better equipped to withstand future shocks and foster sustained economic stability.

Firm size, market share, and essentiality significantly determine a firm's exposure to supply-chain risk ([ESRI]) as revealed by both OLS and quantile regressions.
Firm size, market share, and essentiality significantly determine a firm’s exposure to supply-chain risk ([ESRI]) as revealed by both OLS and quantile regressions.

The pursuit of systemic risk assessment, as detailed in this framework, resembles less a quest for definitive answers and more an exercise in controlled persuasion. This study doesn’t reveal economic vulnerabilities so much as coax them into visibility through the layered network reconstruction. It’s a delicate dance with chaos, attempting to map the whispers of interdependence before they become a roar. As Richard Feynman observed, “The first principle is that you must not fool yourself – and you are the easiest person to fool.” This work, by meticulously tracing financial and production links, attempts to avoid that self-deception, acknowledging that any model – even one as detailed as this multilayer network – is merely a temporary spell, effective until confronted by the unpredictable reality of production and financial contagion.

What Lies Ahead?

The reconstruction of economic reality, as attempted here with multilayer networks, remains a fundamentally… optimistic endeavor. The illusion of capturing ‘interdependence’ through node linkages is comforting, yet ignores the infinitely more complex web of tacit understandings, regulatory loopholes, and sheer luck that truly governs financial flows. Stress testing, thus, becomes a ritualistic exorcism-a performance of control over chaos that invariably fails to account for the novel forms of panic that will inevitably emerge.

Future iterations of this framework will undoubtedly involve more layers, more nodes, and more computationally intensive simulations. Yet, the core problem persists: the map is never the territory. The true vulnerabilities aren’t structural; they are behavioral. A more fruitful, if considerably less elegant, path lies in acknowledging that economic agents aren’t rational actors responding to stimuli, but storytellers seeking narratives that justify their pre-existing biases. Modeling, then, isn’t about prediction, but about providing more convincing fables.

Ultimately, the success of this approach-and all approaches, really-will be measured not by its accuracy, but by its usefulness in obscuring the fundamental unknowability of the economic system. The goal isn’t to understand risk, but to manage the perception of risk-a subtle, but critical, distinction. Regression is a prayer, and the p-value a superstition, but sometimes, that is enough.

Original article: https://arxiv.org/pdf/2603.09854.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

See also:

2026-03-11 07:36