Calomiris–Kahn Demandable Debt Model

The Calomiris–Kahn Demandable Debt Model is a foundational agency-theoretic model of commercial banking, depositor monitoring, and endogenous bank runs in business and economics theory, developed by economists Charles W. Calomiris and Charles M. Kahn in their 1991 American Economic Review paper "The Role of Demandable Debt in Structuring Optimal Banking Arrangements." Whereas the classic Diamond–Dybvig model (1983) viewed demandable bank deposits as a household liquidity-insurance mechanism whose vulnerability to bank runs is a coordination failure, Calomiris and Kahn demonstrated that demandable debt paired with a sequential service constraint (first-come, first-served par redemption) is an optimal governance contract designed to discipline bank insiders against moral hazard, fraud, and asset diversion. When a banker manages an opaque portfolio of illiquid commercial loans and retains the ability to abscond with or divert assets at an interim date after observing deteriorating loan quality, passive outside equity or long-term bondholders cannot prevent value destruction, and individual depositors face a free-rider problem in paying the private cost c > 0 to monitor the bank's fundamentals. By promising full par value D₁ on a first-come, first-served basis at the withdrawal window, the bank rewards informed monitors who detect bad fundamentals by allowing them to stand at the front of the redemption queue and extract full par before a bank run forces early court liquidation, aligning private monitoring incentives with socially optimal bank termination.

Liquidity Insurance vs. Agency Discipline in Banking History

Throughout financial history—from medieval Italian deposit banks and nineteenth-century Scottish and American free banks to modern wholesale money-market funding—commercial banks have chosen a uniform balance-sheet architecture: they hold opaque, illiquid, long-term commercial loans on the asset side while issuing short-term, par-redeemable demandable debt subject to a sequential service constraint on the liability side.

Two distinct theoretical traditions in financial economics explain this institutional structure:

1. The Preference-Shock / Liquidity-Transformation Tradition (Diamond–Dybvig Model, 1983): Douglas W. Diamond and Philip H. Dybvig modeled depositors as households facing uninsurable idiosyncratic consumption-timing shocks ("impatient" vs. "patient" consumers). In Diamond–Dybvig, the bank is a passive cooperative machine with zero insider agency friction; demand deposits provide risk sharing over consumption timing, while the sequential service constraint creates an undesirable sunspot-driven multiple-equilibrium bank run that can be eliminated costlessly by suspension of convertibility or government deposit insurance.
2. The Incentive / Agency-Discipline Tradition (Calomiris and Kahn, 1991; Diamond–Rajan Model, 2001): Calomiris and Kahn observed that historically, bank runs were almost never random "sunspot" panics disconnected from asset fundamentals; instead, historical panics clustered around macro-sectoral downturns when bank loan portfolios suffered adverse fundamental shocks, and unconditional suspension of convertibility without court intervention was prohibited by standard banking charters.

Calomiris and Kahn (1991) resolved this puzzle by showing that the fragility of demandable debt is a deliberate disciplinary feature, not an accidental bug. Because bankers possess specialized information about loan performance (delegated monitoring) alongside the physical control to divert, tunnel, or abscond with bank assets when loan returns turn out poorly, depositors need an institutional mechanism that:

• Induces at least a subset of outside depositors to pay an information-gathering cost c > 0 to monitor the banker at an interim date t = 1; and
• Triggers asset seizure and court-supervised liquidation whenever the bank's expected terminal loan value has fallen low enough that the banker would otherwise abscond or divert assets.

Agents, Technology, and the Banker's Absconding Opportunity

Consider a three-date economy (t = 0, 1, 2) populated by a risk-neutral Banker (Insider) and N ≥ 1 risk-neutral Outside Depositors (Investors):

• Initial Endowment and Loan Investment (t = 0): At date t = 0, the banker originates an illiquid commercial loan portfolio using 1 unit of liquid funds supplied by N depositors (1/N each), whose outside storage option yields gross return R₀.
• Stochastic Terminal Loan Realization (t = 2): If the loan portfolio matures undisturbed until date t = 2, it yields either a high payoff X_H (with probability p in the good interim state s_G and q < p in the bad interim state s_B) or a low payoff X_L < X_H.
• Interim Asset Diversion / Absconding Technology (t = 1): At date t = 1, the banker costlessly observes the interim state s ∈ {s_G, s_B} and can unilaterally abscond with the bank's assets, capturing a private non-verifiable benefit A = α L (with α ∈ (0, 1)) and leaving zero for depositors at date t = 2.
• Court-Supervised Liquidation Value at Date t = 1 (L): If depositors force the bank into court receivership at date t = 1 before the banker absconds, the court removes the banker and liquidates the loan portfolio for L > A, where E[X | s_G] > L > A.

Asymmetric Information and Costly Depositor Monitoring at Date t = 1

Why cannot a court contractually mandate liquidation at date t = 1 whenever state s_B occurs? First, the interim fundamental state s ∈ {s_G, s_B} is non-verifiable by a court at date t = 1; a court can only verify whether the bank has honored or defaulted on a depositor's cash withdrawal demand. Second, observing a private signal σ_i of s at date t = 1 requires an outside depositor i to pay a private monitoring cost c > 0.

Why Simple Equity or Long-Term Debt Fails to Prevent Absconding

Suppose the banker financed the loan portfolio by issuing passive outside equity or long-term debt maturing at date t = 2 with face value F₂ ∈ (X_L, X_H). At date t = 1:

• Good Interim State (s_G): The banker's expected continuation residual is p(X_H − F₂) ≥ A, so the banker continues operating honestly to date t = 2.
• Bad Interim State (s_B): The banker's legitimate continuation value falls to q(X_H − F₂) < A. Without investor intervention at date t = 1, the banker absconds at date t = 1 in state s_B, inflicting a deadweight loss L − A > 0 and leaving depositors with nothing.

The Depositor Free-Rider Problem Under Pro-Rata Liquidation

If the contract allows any investor to call the bank into pari passu (equal-priority) bankruptcy at date t = 1 yielding L/N per investor, a monitor who pays c > 0 in state s_B nets L/N − c, while every non-monitoring depositor receives L/N for free, causing monitoring to collapse under free-riding.

Mechanics of the First-Come, First-Served Redemption Queue

Calomiris and Kahn (1991) demonstrated that demandable debt with a sequential service constraint solves both the banker's absconding problem and the multi-depositor monitoring free-rider problem simultaneously. Under a demandable debt contract:

1. Any depositor may demand redemption at date t = 1 for a fixed interim par value D₁ satisfying:

1. Sequential Service (First-Come, First-Served): Depositors arriving at the withdrawal window at date t = 1 are paid the full par value D₁ in the order of arrival until either all withdrawal demands are met or the bank hits a charter bankruptcy / closure threshold k̄ of withdrawals (where k̄ · D₁ ≤ L), at which point the bank is closed and placed into court receivership.
2. Continuation Payoff (D₂): If fewer than k̄ depositors demand withdrawal at date t = 1, the bank continues to date t = 2 and promises non-withdrawing depositors a terminal face value D₂ > D₁ paid out of X.

Rewarding Informed Monitors via Queue Priority

Why does setting D₁ > L/N under first-come, first-served redemption incentivize private monitoring at date t = 1?

• When a Monitor Observes the Good Signal (s_G): In state s_G, the banker does not abscond (p(X_H − D₂) ≥ A), so waiting until date t = 2 yields an expected payout E[R₂ | s_G] > D₁. Thus, an informed depositor who observes s_G chooses not to withdraw at date t = 1, allowing the bank's high-return illiquid loans to mature without costly early liquidation.
• When a Monitor Observes the Bad Signal (s_B): In state s_B, the monitor knows that if the bank is not liquidated at date t = 1, the banker will abscond. Because the monitor acquires information at date t = 1 before uninformed depositors, the monitor rushes to the front of the withdrawal queue, demands redemption, and receives full par value D₁ > L/N.
• Information Externality and the Fundamental Bank Run: Once the informed monitors withdraw and the queue reaches the threshold k̄, the bank is forced into court receivership at date t = 1. In liquidation, the M informed monitors at the front of the line receive D₁, while the N − M uninformed depositors at the back of the line split the remaining liquidation value L − M · D₁, receiving (L − M · D₁)/(N − M) < L/N < D₁.

Equilibrium Condition for Endogenous Monitoring

The difference between the front-of-the-line par payout D₁ and the back-of-the-line residual liquidation payout (L − M · D₁)/(N − M) is an endogenous prize transferred from uninformed depositors to informed monitors in bad states s_B. In an interior equilibrium where M out of N depositors pay the monitoring cost c > 0 and N − M depositors remain passive, the interim par value D₁* is set so that the expected gain from jumping to the front of the queue in state s_B compensates each monitor for c:

Passive uninformed depositors willingly accept back-of-the-line subordination in state s_B because they save the monitoring cost c while benefiting from the monitors' public good: in state s_B, the monitors' run forces early court liquidation (saving L − M · D₁* > 0 for uninformed depositors instead of losing 100% of their funds to banker absconding), while in state s_G the monitors stay quiet and allow all depositors to earn the high date-2 return.

Signal Aggregation via Withdrawal Thresholds (k̄ ≥ 2)

In the general version of Calomiris and Kahn (1991), individual monitors do not observe the bank's interim state s ∈ {s_G, s_B} with perfection; instead, each monitoring depositor i ∈ {1, ..., M} pays c > 0 and observes an independent noisy binary signal σ_i ∈ {0, 1}, where a bad signal (σ_i = 1) occurs with high probability β_B in state s_B and low false-positive probability β_G < β_B in state s_G.

Calomiris and Kahn proved that the optimal banking charter specifies both a liquid reserve buffer (to pay off isolated false-positive withdrawals at D₁ without liquidating core loans) and a multi-withdrawal bankruptcy threshold k̄ ∈ {2, ..., M}. Whenever fewer than k̄ monitors receive bad signals and withdraw at date t = 1, the bank pays them D₁ out of liquid reserves and continues operating to date t = 2; whenever k̄ or more monitors receive bad signals σ_i = 1 and line up at the teller window, the withdrawal queue hits k̄, exhausting liquid reserves and triggering court-supervised liquidation of the bank. Thus, the sequential withdrawal queue acts as a statistical likelihood-ratio test that aggregates decentralized private signals across wholesale depositors before triggering bank closure.

Nineteenth-Century Clearinghouses and Wholesale Funding Runs

Calomiris and Kahn supported their model with institutional evidence from nineteenth-century banking regimes and clearinghouses:

• Prohibition of Unconditional Suspension Clauses: In pre-deposit-insurance banking charters across the United States and Britain, individual banks were forbidden from writing unconditional suspension-of-convertibility clauses into demand notes or deposits. When temporary suspensions occurred during panics under clearinghouse supervision, clearinghouses audited member banks, issued clearinghouse loan certificates, and closed insolvent banks whose fundamentals were in state s_B.
• Empirical Predictability of Historical Bank Runs: Contrasting with pure sunspot theories, empirical studies by Gorton (1988) and Calomiris and Gorton (1991) demonstrated that nineteenth-century U.S. banking panics occurred systematically whenever leading macroeconomic indicators crossed a threshold indicating adverse loan-portfolio fundamentals.

How does the Calomiris–Kahn model differ from the Diamond–Dybvig model of bank runs?

In the Diamond–Dybvig model (1983), bank management is honest, demand deposits exist to insure households against idiosyncratic liquidity preference shocks, and bank runs are welfare-destroying sunspot coordination failures. In the Calomiris–Kahn model (1991), bankers face moral hazard (the ability to abscond with or divert assets at an interim date), and demandable debt with first-come, first-served sequential service is an optimal disciplinary contract: it rewards informed depositors who pay monitoring cost c > 0 with full par value D₁ > L/N at the front of the withdrawal line, triggering early bank liquidation when fundamentals are bad.

Why is the sequential service constraint (first-come, first-served) essential in Calomiris–Kahn?

If a bank liquidated on a pro-rata (pari passu) basis where every depositor received an equal share L/N regardless of arrival order, no individual depositor would pay the private monitoring cost c > 0, because non-monitoring depositors would receive the same payout L/N for free. By setting the demand-deposit par value above the average liquidation value (D₁ > L/N) and paying on a first-come, first-served basis, sequential service transfers a positive queue prize D₁ − L/N from passive uninformed depositors to informed monitors in bad states, reimbursing monitors for their information cost c.

Why do informed depositors not run on the bank in the good fundamental state (s_G)?

In the good interim state s_G, the expected terminal loan payoff is high enough that the banker has no incentive to abscond, and the expected date-2 payout to depositors E[R₂ | s_G] exceeds the date-1 withdrawal par value D₁. Consequently, an informed depositor who pays c and observes s_G prefers to leave funds in the bank until date t = 2 rather than withdrawing D₁ at date t = 1.

What is the moral-hazard cost of government deposit insurance in the Calomiris–Kahn framework?

While government deposit insurance eliminates retail bank runs in the Diamond–Dybvig framework, in the Calomiris–Kahn framework unconditional deposit insurance guarantees that depositors receive par value D regardless of whether they monitor or stand at the front of the queue. This eliminates depositors' incentive to pay the monitoring cost c, removing market discipline on bank insiders and encouraging excessive risk-taking unless replaced by prudential supervision and bank capital requirements.

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2. Diamond, D. W., & Dybvig, P. H. (1983). "Bank Runs, Deposit Insurance, and Liquidity." Journal of Political Economy, 91(3), 401–419. https://doi.org/10.1086/261155
3. Diamond, D. W. (1984). "Financial Intermediation and Delegated Monitoring." The Review of Economic Studies, 51(3), 393–414. https://doi.org/10.2307/2297430
4. Gorton, G. (1988). "Banking Panics and Business Cycles." Oxford Economic Papers, 40(4), 751–781. https://doi.org/10.1093/oxfordjournals.oep.a041885
5. Diamond, D. W., & Rajan, R. G. (2001). "Liquidity Risk, Liquidity Creation, and Financial Fragility: A Theory of Banking." Journal of Political Economy, 109(2), 287–327. https://doi.org/10.1086/319552