From Interaction to Business Fluctuations: How Credit Network Explains Cycles
What this paper finds — and why it matters
Layer 1: Overview
This paper investigates how the endogenous structure of credit, deposit, and interbank networks shapes business cycle fluctuations and large financial crises in the U.S. economy. Ciola and Tedeschi build and estimate a microfounded heterogeneous-agents macroeconomic model in which households, firms, and banks interact through decentralized matching in three markets — deposits, credit, and interbank lending — with agents choosing partners based on both posted interest rates and the size of the counterpart, generating a preferential-attachment mechanism that endogenously concentrates the financial sector. The structural parameters governing network formation are estimated on U.S. quarterly interest rate and GDP growth data from 1947 to 2019 via an Extended Method of Simulated Moments (EMSM) procedure combined with a Bayesian Adaptive Random Walk Metropolis–Hastings sampler; the calibrated model reproduces the empirical autocorrelation structure of these series. The model’s key finding is that preferential attachment endogenously concentrates roughly three-quarters of deposits, credit, and interbank transactions into a single hub bank, whose dominance raises markups, suppresses deposit rates, and depresses aggregate capital accumulation relative to the initial symmetric state. Bank runs against this hub — rare but endogenously generated when households reallocate deposits simultaneously — collapse the interbank market completely and produce deep recessions that last multiple quarters, with recovery requiring approximately five years.
Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Q1. What is the model’s core structure and how do agents interact?
The model consists of a fixed number of households (N_H = 1,000), banks (N_I = 10), and firms (N_F = 1,000) who interact in deposit, credit, and interbank markets through a decentralized preferential-attachment matching mechanism in which agents assess both current interest rates and the size of potential counterparts. Households deposit savings in a single bank chosen based on a fitness index combining the bank’s promised deposit rate and its size (used as a proxy for long-run quality), and they search for a new partner each period with probability ζ_H. Firms borrow from one bank at a time, also choosing based on a fitness that weighs the promised profit share against bank size, and switch with probability ζ_F. Banks set interest rates in all three markets to maximize expected profits, exploiting their monopolistic power (higher when they are larger), subject to a balance sheet constraint that links deposits, credit extended to firms, and interbank borrowing. The interbank market exists specifically to cover unexpected deposit withdrawals: when a bank’s deposits fall below its outstanding credit, it borrows in the interbank market or closes credit lines.
Q2. How does the estimation methodology work and what parameters does it identify?
The paper employs the Extended Method of Simulated Moments (EMSM) of Smith (1993) and Gourieroux et al. (1993), which minimizes the weighted distance between the coefficients of a VAR auxiliary model estimated on observed U.S. data and on H simulated time series generated from a given structural parameter vector, with the optimal weighting matrix set to the inverse of the Newey–West covariance of the auxiliary parameter estimates. Because gradients of the criterion function are not analytically available for this nonlinear agent-based model, the authors use a two-step approach: first, a Particle Swarm Optimization (PSO) algorithm explores the parameter space to locate a neighborhood of the global minimum; second, a Bayesian Adaptive Random Walk Metropolis–Hastings (ARWMH) algorithm generates posterior draws from the structural parameter distribution using the chi-square distributional properties of the EMSM criterion function. The estimated structural parameters include the nine network formation parameters {ω_X, ζ_X, ψ_X} for each of the three markets — governing competition intensity, switching probability, and the weight agents assign to counterpart size — while the production coefficient (α = 0.37) and household discount factor (β = 0.997) are calibrated directly to U.S. labor share and real interest rate data. Estimation uses 1947:Q1–2019:Q4 U.S. real GDP growth and real interest rate data; with three VAR lags and d = 9 structural parameters, the overidentification chi-square test can be assessed.
Q3. What are the long-run dynamics and how does the financial network concentrate?
Starting from an equal distribution of agents across banks, the model converges to a pseudo-steady-state in which a single hub bank intermediates approximately three-quarters of deposits, credit lines, and interbank transactions, because the preferential-attachment mechanism is self-reinforcing: larger banks attract more depositors (providing more stable funding), more firms (generating more profit), and more interbank counterparts, which further enlarges their size and attractiveness. This concentration has clear aggregate consequences: as the hub’s monopolistic power grows, it widens the markup over the perfect competition interest rate in the credit market and the markdown below it in the deposit market, reducing the deposit rate paid to households and thereby depressing household capital accumulation. Simulations across 1,000 independent replicas show that the aggregate production level in the pseudo-steady-state is below the initial competitive equilibrium, credit and interbank interest rates rise, and approximately 10% of total capital circulates through the interbank market as periphery banks rely on the hub for liquidity provision.
Q4. How do cyclical fluctuations and crises emerge endogenously?
Business cycles arise from the continuous reallocation of household deposits across banks, which generates endogenous liquidity shocks that do not require an exogenous crisis trigger: when a critical mass of households simultaneously reallocates away from the hub — a rare but endogenous event driven by the stochastic matching process — the hub faces a severe liquidity shortage, must close credit lines and interbank lending, and produces a systemic economic contraction. In a representative 100-year simulation, aggregate production fluctuates around a stable trend with mild recessions most of the time, but the model occasionally generates a catastrophic bank run against the hub. When this occurs, the hub’s weighted degree in all three markets collapses to near zero within one or two quarters, the interbank market freezes completely, and firm production stops because firms cannot immediately reallocate their credit demand to alternative banks. The impulse response to a sudden reduction in hub deposit centralization shows that aggregate production falls sharply in the short run (as credit contracts) and only surpasses its pre-run level after approximately five years (20 quarters).
Q5. What does the VAR impulse response analysis reveal about recovery dynamics?
An estimated VAR on all simulations — with aggregate production and the volume, centralization, and interest rates of each of the three markets as endogenous variables — shows that a negative shock to deposit market centralization (i.e., a bank run against the hub) triggers an immediate spike in deposit interest rates (as competing banks compete for the displaced funds), a contraction in credit and interbank supply (as periphery banks lack sufficient liquidity to expand), and a rise in credit interest rates (as the pool of surviving credit lines is concentrated in the most profitable projects). In the medium run, higher deposit rates promote household capital accumulation, which ultimately expands the aggregate supply of productive capital; at the same time, the dissolution of the old hub reduces the sector’s average monopolistic markup, permanently lowering credit market interest rates. This self-correcting mechanism underlies the five-year recovery window and also illustrates why prompt policy intervention during hub-collapse crises is particularly effective — early stabilization prevents the reinforcing deposit-withdrawal spiral that deepens the contraction.
Q6. What is the paper’s contribution relative to existing macroeconomic network literature?
The paper makes three distinct contributions over prior agent-based macroeconomic network models: first, it treats households as active depositors whose reallocation choices generate endogenous liquidity shocks rather than simply passive shock absorbers; second, it models banks as profit-maximizing agents that optimally set interest rates exploiting market power rather than assuming perfect competition or regulatory constraints; and third, it produces a Bayesian estimator of all structural parameters rather than relying on calibration to observed moments. Prior work in this tradition (Delli Gatti et al. 2010; Riccetti et al. 2013; Lenzu and Tedeschi 2012) typically either omits households from the deposit market or assumes exogenous mechanisms of crisis formation. By endogenizing all three sources of network dynamics — deposit, credit, and interbank — and estimating the model on U.S. data, the paper provides a framework in which large financial crises emerge as intrinsic system properties rather than imposed scenarios, and quantifies the structural parameters driving them.
Key Concepts
preferential attachment : a matching mechanism in which agents preferentially form links with larger counterparts; in this model it causes households and firms to favor large banks, endogenously concentrating the financial sector into a hub-and-spoke structure with a dominant hub bank.
hub bank : the single largest financial intermediary that endogenously emerges in the model’s long-run equilibrium, intermediating approximately three-quarters of deposits, credit lines, and interbank transactions; its size confers monopolistic power but makes it the systemic node whose failure triggers economy-wide crises.
Extended Method of Simulated Moments (EMSM) : the estimation strategy used to identify the nine network formation structural parameters; it minimizes the weighted distance between VAR coefficients estimated on observed U.S. data and on model-simulated data, with a Bayesian ARWMH sampler used to generate the posterior distribution given the chi-square-distributed criterion function.
endogenous bank run : the crisis mechanism in this model — a simultaneous reallocation of household deposits away from the hub, triggered by the stochastic matching process rather than an external shock, that freezes the interbank market and produces a deep recession lasting approximately five years (20 quarters) in impulse response analysis.