Firm-Bank Macro ABM
Model

Standard macro models compress the financial sector into a single representative bank and the corporate sector into a single representative firm. That compression erases the network structure of credit relationships: which bank lends to which firm, how concentrated those exposures are, and how a default at one firm propagates through its lender's balance sheet to affect credit supply for every other firm that bank serves. Delli Gatti et al. (2005) built the first firm-bank network ABM to show that business-cycle fluctuations can emerge endogenously from the interaction of heterogeneous firm balance sheets and bank lending decisions, without any aggregate shock at all. The key insight was that cross-sectional dispersion in firm net worth, combined with the network topology of credit linkages, generates correlated default clusters that look like recessions even when the only shocks are idiosyncratic. Delli Gatti et al. (2010) extended this into a full macroeconomic framework with endogenous credit supply, firm entry and exit, and bankruptcy cascades that produce fat-tailed output fluctuations matching empirical GDP distributions.

The core mechanism is a balance-sheet amplification loop running through the firm-bank network. A firm's borrowing capacity depends on its net worth (the external finance premium story from Bernanke-Gertler, but applied heterogeneously). When a firm defaults, its bank absorbs a loss, the bank's capital ratio drops, and the bank tightens lending standards or rations credit to all its borrowers. Those borrowers, now credit-constrained, cut investment and production, which reduces aggregate demand, which lowers revenues for other firms, pushing marginal firms toward default. The cascade propagates through the bipartite firm-bank network: each bank failure or capital squeeze affects all firms connected to it, and each wave of firm defaults affects all banks exposed to those firms. The severity depends on network concentration -- a few large banks serving many firms create systemic fragility that a dispersed network does not.

Central banks and financial stability authorities use firm-bank ABMs for stress testing and capital buffer calibration. The Bank of Italy's research department (where Delli Gatti's work originated) has used firm-bank network models to assess the propagation of corporate default shocks through the Italian banking system. The ECB's Eurace model (Cincotti et al. 2010, Deissenberg et al. 2008) includes a detailed firm-bank credit module as part of a full-scale agent-based macroeconomy used for policy experiments. The IMF's Agent-Based Book of Absolution (ABBA) framework (Bookstaber et al. 2018) models firm-bank contagion as one of its core transmission channels for systemic risk assessment. Ashraf et al. (2017) built a banking-focused ABM calibrated to developing economies where the firm-bank channel dominates monetary transmission. Academic use spans from pure network contagion theory (Battiston et al. 2012) to applied regulatory evaluation (countercyclical capital buffers, leverage ratio floors).

The model family has evolved along several axes since the mid-2000s. Early versions used random matching between firms and banks; newer variants use preferential attachment or fitness-based network formation where firms sort to banks based on interest rate offers and relationship length. Bank behavior has moved from mechanical lending rules to active portfolio optimization with risk-weighted capital constraints under Basel-type regulation. The interbank market has been added as a second network layer, allowing contagion to propagate both through direct exposures (firm defaults eroding bank capital) and through interbank funding freezes (distressed banks unable to roll over wholesale funding). The active frontier includes climate transition risk overlays (stranded-asset defaults propagating through bank networks), supply-chain-finance interactions (trade credit as a parallel contagion channel), and central bank digital currency effects on bank funding structure.

The economy is assembled from three agent populations plus a policy block. Firms are the primary production agents: each carries a capital stock, a debt position, a net-worth level, a production technology, and behavioral rules for investment, pricing, and default. Firm heterogeneity comes from idiosyncratic productivity shocks and different initial balance-sheet positions. The firm population is typically 500 to 5,000 agents in research implementations and 30 to 100 in browser-scale toy models. Banks form the second population: each holds a loan portfolio (a set of credit links to specific firms), an equity capital buffer, deposits (passive or from a household sector), and a lending rule that maps the applicant firm's net worth, leverage, and the bank's own capital ratio into a credit decision (approve/reject, interest rate, credit limit). The bank population is typically 5 to 20 agents, deliberately small relative to firms to create concentration and network asymmetry. The third agent is a compact household/consumption sector that absorbs aggregate output and feeds back into firm revenue. The policy block contains a central bank setting the base rate and a prudential regulator setting minimum capital ratios, countercyclical buffers, and leverage ratio floors.

Interaction happens through two primary channels and one feedback loop. The credit market is a directed bipartite network: each firm has one or more lending relationships with banks, and each bank has a portfolio of firm exposures. In each period, firms that need external finance apply to banks (either their existing relationship bank or by shopping across banks); banks evaluate applications against their lending criteria and capital position, and either extend credit or reject. The goods market closes the macro loop: firms produce using capital financed by bank credit, sell output at prices set by a markup rule, and the resulting revenue determines whether the firm can service its debt. Aggregate demand depends on total household income (wages from firm production) and total investment spending (credit-financed capital purchases). The feedback loop runs: credit supply determines investment, investment determines output, output determines firm revenue, revenue determines debt service capacity, debt service failures determine bank losses, bank losses determine credit supply.

State variables update each period in a fixed sequence: (1) productivity shocks arrive at the firm level, (2) firms set desired production and compute financing needs, (3) the credit market operates -- firms apply for loans, banks screen and allocate credit, interest rates are set, (4) production occurs and goods are sold, (5) firms compute profits and service debt, (6) defaults are realized and losses allocated to banks, (7) bank capital is updated, failed banks are resolved or recapitalized, (8) the prudential regulator checks its rule and adjusts buffers, (9) the central bank updates the policy rate, (10) firm entry and exit occur (bankrupt firms are removed, new firms enter with initial endowments). This sequential structure makes the propagation path from an idiosyncratic firm shock to an aggregate credit crunch traceable step by step.

The Bank of Italy has used firm-bank network ABMs to assess how corporate default shocks propagate through the Italian banking system, where relationship lending and geographic concentration create significant network effects. Delli Gatti et al. (2010) calibrated their model to Italian firm-level data from the CERVED database and showed that the observed fat tails in Italian GDP growth could be explained by cascade dynamics through the firm-bank network without invoking any aggregate shock. The ECB's Eurace project (Cincotti et al. 2010, Deissenberg et al. 2008) built a full-scale agent-based macroeconomy with a detailed credit module used for policy experiments on capital requirements, monetary policy transmission, and fiscal stabilization in the euro area.

The IMF's ABBA framework (Bookstaber et al. 2018) uses firm-bank contagion as one of its core channels for systemic risk assessment. The framework models how shocks to specific sectors (energy, real estate, manufacturing) propagate through bank exposures to affect credit supply economy-wide. This has been applied to country-level Financial Sector Assessment Programs (FSAPs) where traditional stress tests (top-down, no network) miss the feedback effects. Ashraf et al. (2017) calibrated a banking ABM to Bangladesh and showed that monetary policy transmission operates primarily through the bank lending channel in economies with thin capital markets, and that the heterogeneity of bank balance sheets creates substantial variation in pass-through rates.

The model breaks down when the corporate sector finances primarily through capital markets rather than bank lending. In the US, where large firms issue bonds directly and bank lending is a smaller share of total corporate debt, the firm-bank network channel is weaker than in bank-dependent economies (continental Europe, Japan, most developing countries). The model also fails when the dominant shock is a pure demand shock that hits all firms symmetrically -- the network structure adds nothing when there is no cross-sectional variation in the initial impact. For settings where interbank contagion dominates over firm-bank contagion (e.g., the 2008 wholesale funding freeze), a pure interbank network model (Gai-Kapadia 2010) is more appropriate than the firm-bank specification.

Key Papers

• Delli Gatti et al. (2005) -- first firm-bank network ABM with endogenous business cycles from balance-sheet interactions
• Delli Gatti et al. (2010) -- extended framework with firm entry/exit, bankruptcy cascades, and fat-tailed output fluctuations
• Cincotti et al. (2010) -- Eurace credit module: full-scale agent-based macroeconomy with detailed firm-bank credit channel
• Ashraf et al. (2017) -- banking ABM calibrated to developing economies, monetary policy transmission through heterogeneous banks
• Bookstaber et al. (2018) -- IMF ABBA framework with firm-bank contagion as a core systemic risk channel
• Battiston et al. (2012) -- network topology and systemic risk: too-connected-to-fail analysis in firm-bank networks

Named Variants

• Interbank market extension (two-layer network: firm-bank + bank-bank)
• Supply-chain-finance overlay (trade credit as parallel contagion channel)
• Preferential attachment network formation (endogenous topology)
• Climate transition risk variant (stranded-asset defaults propagating through bank networks)
• Basel III countercyclical buffer calibration (dynamic capital requirements)

Open Questions

• What network topology minimizes systemic risk for a given level of credit intermediation efficiency?
• How should countercyclical capital buffers be calibrated when the firm-bank network topology is itself endogenous to the regulatory regime?
• Can firm-bank ABMs be estimated on real credit-register data (e.g., European AnaCredit) to produce quantitative rather than qualitative policy guidance?