📈 economics

Bank Run Exposure in a Paycheck-to-Paycheck Economy with Loss-Averse Depositors

This paper develops a behavioral model demonstrating how loss-averse, paycheck-to-paycheck depositors can endogenously generate bank run risks through increased liquidity demand, and validates this framework with empirical data showing improved exposure prediction, particularly for small banks in the post-Silicon Valley Bank collapse era.

Original authors: G. Charles-Cadogan

Published 2026-08-13

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: G. Charles-Cadogan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Nervous System of the Bank

Imagine the economy as a giant, bustling city where everyone relies on a central water system to keep their homes running. In this city, the "water" is money, and the "pipes" are banks. For a long time, engineers (the regulators) thought they could predict exactly how much water would flow out of the pipes during a storm. They built safety valves based on the idea that people only take water when they really need it, like filling a bucket for a garden. But what if the people living in the city are actually terrified of running out of water? What if, the moment they hear a rumor that the reservoir might be low, they don't just fill a bucket—they panic, grab every bucket they own, and start screaming for more?

This paper lives in the world of economics, specifically looking at how banks handle the risk of people rushing to withdraw their money all at once, an event known as a "bank run." To understand the story, you need to know three simple things. First, many people live "paycheck-to-paycheck," meaning they have very little savings and rely on their next paycheck arriving on time to pay their bills. Second, humans have a psychological quirk called "loss aversion," which means the pain of losing something (like missing a bill payment) feels much stronger than the joy of gaining the same amount. Third, banks keep a small pile of cash in reserve to handle normal withdrawals, but if everyone tries to take their money out at the same time, that pile isn't enough. The big question is: how does the fear of losing a paycheck turn a normal day into a financial panic?

The Paper's Story: When Fear Becomes a Self-Fulfilling Prophecy

This paper, written by G. Charles-Cadogan, builds a new kind of model to explain why bank runs happen, not just because of bad luck, but because of how our brains work when we are stressed. The author argues that the old ways of measuring bank risk are missing a crucial ingredient: the behavior of people who are one missed paycheck away from disaster.

The "Paycheck-to-Paycheck" Panic
The paper starts with a simple observation: most people get their paychecks directly deposited into their bank accounts. If that paycheck is delayed or reduced, these people can't just wait; they need cash now to buy food or pay rent. Because they are "loss-averse," the thought of missing a payment hurts them more than the joy of saving money helps them. The author suggests that when these people feel a little bit of stress, their fear of losing their income spikes. In the paper's model, this isn't just a feeling; it's a mathematical trigger. When the probability of a "bad state" (like a delayed paycheck) gets high enough in a depositor's mind, their demand for cash explodes.

The "Bank Run Exposure State Space"
The author creates a new concept called the "Bank Run Exposure State Space." Think of this as a weather map for panic. Usually, the weather is calm. But there are specific "stress states" where the combination of a shaky paycheck and a loss-averse brain creates a perfect storm. In these states, the bank's normal safety rules aren't enough. The paper proves that if enough people are in this "panic zone," they can create a bank run even if the bank is actually healthy. It's like a crowd at a concert: if everyone suddenly thinks the exit is blocked, they all push for the door at once, creating a crush, even if the exit was wide open the whole time.

The Math of Fear
To show how this works, the author uses some fancy math involving "martingales" (a way of predicting future values based on current information) and "half-Cauchy distributions" (a way to describe rare, extreme spikes in fear). The model suggests that while most of the time people are calm, their fear can occasionally spike to extreme levels, much like a volcano that is usually quiet but occasionally erupts. The paper simulates these scenarios and finds that if you ignore this "fear factor," you will think banks need much less cash in reserve than they actually do. In fact, the simulations show that ignoring this behavioral fear understates the volatility of cash needs by about 87%.

Testing the Theory with Real Data
The author then tries to test this idea using real-world data from US banks (specifically "Call Reports" filed with the government). Since the government data doesn't show individual people's paychecks, the author uses clever shortcuts, like looking at how many deposits come from regular people (retail) versus big companies (wholesale), and how much the bank lends to consumers.
The results are a bit mixed but interesting. The paper finds that banks with more regular, paycheck-dependent customers do seem to react more strongly to stress, especially during scary times like the Silicon Valley Bank collapse in 2023. However, because the government data is a bit blurry (it's quarterly, not daily), the evidence is described as a "proof-of-concept" rather than a final, definitive proof. The paper suggests that a new, composite way of measuring risk (combining different types of deposits and loans) works slightly better than just looking at retail deposits alone, but the data is still too coarse to see the exact moment a person panics.

What the Paper Rules Out
The paper is very clear about what it is not saying. It argues against the idea that bank runs are purely random events or that they only happen because a bank is actually broke. It also rejects the idea that regulators can simply set a fixed rule for how much cash banks need without considering how people feel about their money. The paper explicitly states that standard models that ignore "loss aversion" are too smooth and miss the sharp spikes in demand that happen when people are scared.

The Bottom Line
In short, this paper suggests that the next time a bank feels shaky, it might not be because of a bad investment, but because the people who hold the money are terrified of missing their next paycheck. The author proposes that banks and regulators need to build a new kind of "fear meter" into their safety plans. While the math is complex and the real-world data is still being refined, the core message is vivid: in a world where everyone lives paycheck-to-paycheck, the fear of losing a single dollar can turn a calm bank into a chaotic scene much faster than anyone expected. The paper doesn't claim to have solved the problem, but it offers a new, more human way to look at the danger.

Technical Summary: Bank Run Exposure in a Paycheck-to-Paycheck Economy with Loss-Averse Depositors

Problem Statement
The paper addresses a gap in the literature regarding bank run exposure in a "paycheck-to-paycheck" economy where liquidity demand is increasingly behavioral, state-dependent, and endogenously amplified. While regulatory frameworks like the Basel III Liquidity Coverage Ratio (LCR) treat deposit outflows as exogenous stress parameters based on average assumptions, they fail to model how depositor fear, paycheck timing, and loss aversion can amplify withdrawals in specific states. The author argues that in a digitally connected economy, income uncertainty translates directly into liquidity demand. When loss-averse depositors assign high subjective probabilities to "bad states" (e.g., delayed or reduced paychecks), withdrawal demand can spike beyond regulatory averages, creating a behavioral liquidity externality that forces banks to hold excess reserves and crowd out productive lending.

Methodology
The paper develops a behavioral asset-pricing model integrating prospect theory with a paycheck-to-paycheck consumption framework.

Theoretical Framework:
- Loss Aversion and Liquidity: The model extends Tobin's liquidity-preference theory by incorporating Kahneman and Tversky's prospect theory. Agents are defined as loss-averse regarding fluctuations in wealth and income relative to a reference point. The value function is piecewise, convex over losses and concave over gains, with a loss-aversion index $\lambda$ .
- Myopic Loss Aversion: Agents live paycheck-to-paycheck with zero wealth and no intertemporal trade-offs. They exhibit "myopic loss aversion," evaluating income every pay period. Consumption ratcheting is embedded, meaning consumption cannot easily be reduced below a reference level, making agents sensitive to income shocks.
- Stochastic Loss Aversion: To capture rare fear states, the model treats loss aversion as a stochastic process. It is modeled as a multiplicative combination of a smooth Hall–CRRA benchmark (based on consumption growth fundamentals) and a heavy-tailed half-Cauchy shock. This allows the median loss aversion to remain near standard estimates (e.g., $\lambda \approx 2.25$ ) while permitting extreme tail realizations that drive stress states.
- Bank Run Exposure State Space: The author defines a "Bank Run Exposure State Space" ( $\Omega_{run}$ ). This is the subset of states where the subjective probability of a bad income state, combined with loss aversion, satisfies a sufficient condition to trigger a run. This condition occurs when the weighted marginal value of a loss state dominates the weighted marginal value of a gain state.
- Martingale Representation: The paper derives a martingale representation for bank run exposure, showing that exposure is not a fixed slope coefficient but a stochastic object driven by liquidity risk and the dynamics of loss aversion.
Empirical Implementation:
- The paper conducts a "proof-of-concept" empirical exercise using public FFIEC Call Report data (2001–2024).
- Since account-level paycheck data is unavailable, the author constructs proxies for loss-averse clientele. They compare a simple "Retail Share" proxy against a regression-weighted composite index ( $LA^{reg}_{bt}$ ) constructed from transaction-deposit share, core-deposit share, and consumer-loan share.
- The empirical specification is a panel regression of changes in cash reserves on liquidity volatility, the loss-aversion proxy, and their interaction, controlling for bank and time fixed effects.

Key Contributions

Bank Run Exposure State Space: The paper formally identifies a specific set of stress states where loss aversion and high subjective probabilities of bad income shocks jointly support a bank run. This distinguishes the model from Diamond-Dybvig (which relies on coordination failures) and Goldstein-Pauzner (which relies on private signals about fundamentals).
Endogenous Probability of Runs: Unlike models where run probabilities are implicit or based on first-order conditions of expected utility, this paper derives run probabilities using a "stopped-process" approach. It links the probability of suspension of convertibility to the withdrawal sequence, reserve constraints, and subjective bad-state probabilities.
Martingale Representation of Exposure: The paper demonstrates that bank run exposure has a martingale representation. It shows how a static liquidity-risk slope transforms into a dynamic exposure coefficient driven by a stochastic loss-aversion process (modeled as a half-Cauchy SDE).
Behavioral Liquidity Externality: The model formalizes how loss-averse liquidity demand alters equilibrium reserve holdings, potentially crowding out positive-net-present-value lending.

Results

Theoretical: The model shows that sufficiently high subjective bad-state probabilities endogenously increase liquidity demand. When loss aversion exceeds a critical threshold ( $\lambda > \lambda_c$ ), the trade-off between income and risk changes, supporting a run. The half-Cauchy specification for loss aversion successfully generates rare, extreme spikes in fear that are central to run exposure while maintaining stability in ordinary states.
Empirical:
- Using public Call Report data, the regression-weighted composite proxy ( $LA^{reg}_{bt}$ ) modestly improves the model fit ( $R^2$ ) relative to a simple retail-share benchmark.
- The interaction between liquidity volatility and the loss-aversion proxy is generally positive but statistically imprecise in the quarterly public data, a limitation the author attributes to the coarseness of the data (quarterly vs. daily/pay-cycle).
- Small Banks: There is suggestive evidence of stronger amplification among small banks (assets < $1 billion), particularly when interacting with the Post-Silicon Valley Bank (SVB) event window.
- SVB Event: The retail-share proxy captures a marginally significant positive amplification signal in the Post-SVB window, whereas the composite proxies improve overall fit but do not yield sharper event-specific coefficients.
- Reserve Volatility: Simulations indicate that omitting latent loss aversion understates the volatility of reserve needs by approximately 87.3%, making reserve demand appear artificially smooth.

Significance and Claims
The paper claims to be the first to introduce a bank run model based on a martingale exposure representation combined with consumption ratcheting and loss aversion in a paycheck-to-paycheck economy.

The author is modest regarding the empirical findings, explicitly stating that the Call Report exercise is a "proof-of-concept" and an "operational demonstration" rather than a definitive test. They argue that public quarterly filings cannot observe the account-level mechanisms (paycheck timing, overdrafts, direct-deposit disruptions) required to sharply estimate the behavioral model. Consequently, the primary empirical contribution is methodological: it demonstrates that the exposure regression can be operationalized with public data and that balance-sheet proxies spanning transaction deposits, core funding, and consumer loans carry slightly more explanatory content than retail share alone.

The paper concludes that the framework highlights how behavioral liquidity demand alters equilibrium reserve holdings. It suggests that regulators and banks should treat bank run exposure as an estimable monitoring statistic, noting that liquidity-only models may significantly understate the volatility of cash demand before a suspension of convertibility is observed. The author emphasizes that a more theory-consistent implementation would require internal bank account-level data.

The Nervous System of the Bank

The Paper's Story: When Fear Becomes a Self-Fulfilling Prophecy

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