Regulating Credit Lines in the Presence of Fire‐Sale Externalities
What this paper finds — and why it matters
This paper provides a contract-theoretic rationale for the special liquidity regulation of bank credit lines—a form of lending that has received little attention in the regulatory literature despite being the most important source of firm liquidity risk management. In the model, banks choose pre-arranged funding (committed before drawdowns accumulate) and ex-post funding (raised as drawdowns occur) to finance firms’ liquidity needs through credit lines. In states with high liquidity needs, banks cannot raise sufficient ex-post funding to meet all drawdowns and renege on some credit lines, forcing liquidations. Because each additional liquidation depresses the equilibrium liquidation value for all liquidated firms—a pecuniary externality—competitive banks choose insufficient pre-arranged funding in the private equilibrium. A minimum requirement on bank pre-arranged funding per committed (undrawn) funds in credit lines restores constrained efficiency, despite making credit lines more costly; welfare improves because more firms receive funding in high-liquidity states. The optimal regulatory ratio is increasing in the frequency of high-liquidity-need states, the value lost in liquidation, and the sensitivity of liquidation values to forced sales, and decreasing in the premium on pre-arranged funding.
Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Q1. Why can banks not fully meet credit line drawdowns in high liquidity need states?
In high liquidity need states, where many firms simultaneously draw on their credit lines, the revenues that banks receive from credit lines (interest payments and fees from the small share of firms that need no drawdown) shrink relative to the total drawdown demand, and the resulting shortfall cannot be fully met through ex-post funding raised from new investors because bank revenues are the collateral for such funding. The model captures the systemic nature of correlated liquidity shocks: when drawdowns are idiosyncratic, banks can cross-subsidize from non-drawing firms and raise ex-post funding easily; when drawdowns are highly correlated, these cross-subsidy revenues vanish and ex-post funding is insufficient, making pre-arranged funding essential for maintaining credit line insurance.
Q2. What is the pecuniary externality and why does it lead to under-provision of pre-arranged funding?
When a bank reneges on a credit line and the borrowing firm is liquidated, the forced sale of the firm’s assets depresses the equilibrium liquidation value—a fire-sale externality that reduces the payoff for all other firms being liquidated simultaneously; competitive banks do not internalize this negative spillover because, individually, each bank takes liquidation prices as given, leading the private equilibrium to feature too little pre-arranged funding and too frequent reneging relative to the constrained social optimum. This is a classic pecuniary externality (Lorenzoni 2008): the externality does not operate through a technological channel but through prices (liquidation values), so it is invisible to competitive agents who treat prices as parametric.
Q3. How does the minimum liquidity requirement on credit lines restore efficiency?
A minimum requirement mandating that banks hold a specified amount of pre-arranged funding per committed (undrawn) credit line funds induces competitive banks to internalize the social value of additional pre-arranged funding—namely, that more pre-arranged funding reduces the number of liquidated firms and raises equilibrium liquidation values—and thereby implements the constrained planner’s solution. This regulatory tool resembles the Basel III LCR (which requires banks to hold liquid assets equal to 5%-30% of undrawn credit lines, depending on the type of credit facility) and the NSFR (which requires stable funding equal to at least 5% of undrawn credit lines); the paper provides the first theoretical justification for precisely this type of regulation for credit lines and characterizes how the optimal ratio depends on economic fundamentals.
Q4. What are the determinants of the optimal regulatory ratio?
The optimal minimum pre-arranged funding requirement per committed funds in credit lines is higher when: (1) the premium on pre-arranged over ex-post funding is lower (making additional pre-arranged funding less costly at the margin); (2) high-liquidity-need states are more frequent (making the insurance value of pre-arranged funding higher in expectation); (3) liquidations are more costly (larger welfare losses per uninsured firm); and (4) liquidation values are more sensitive to the number of liquidations (a steeper fire-sale externality). This comparative statics result is policy-relevant: it implies that the Basel III framework’s one-size-fits-all approach to credit line liquidity ratios cannot be optimal across jurisdictions with different economic fundamentals, and national authorities should calibrate requirements to local conditions.
Key concepts
credit line pre-arranged funding : bank funding committed before credit line drawdowns accumulate; provides insurance against high-liquidity-need states by ensuring the bank can meet drawdowns even when ex-post funding is insufficient; corresponds to equity-like stable funding in Basel III terminology. fire-sale pecuniary externality on liquidation values : the depression of equilibrium firm liquidation values caused by simultaneous forced sales when many firms are liquidated after banks renege on credit lines; not internalized by competitive banks, leading to under-provision of pre-arranged funding in the private equilibrium. optimal credit line liquidity requirement : a minimum ratio of pre-arranged funding to committed (undrawn) credit line funds that restores constrained efficiency by internalizing the fire-sale externality; shown to be an increasing function of the frequency of high-liquidity-need states, liquidation costs, and liquidation-value sensitivity.