Counter-Cyclical Borrowing Limits

Recently there has been much debate about the role of borrowing limits, mostly in the form of capital requirements, as a regulatory measure against rapid liquidity contractions in the financial sector. Imposing capital conservation buffers has been suggested as a method of implementing counter-cyclical borrowing limits.

It turns out that, within the framework of this paper, the effects of a counter-cyclical borrow-ing limit is ambiguous. The counter-cyclical borrowborrow-ing limit is effective only if the borrowborrow-ing limit increases enough for the low type broker-dealers to borrow even when identified. An equilib-rium potentially exists where the low type broker-dealer borrows up to the borrowing limit at the maximum price the household will accept. The high type broker-dealer borrows less, but at more favorable price.

Figure 4 illustrates the credit market outcome of this equilibrium. The red point represents the equilibrium contract of the low type broker-dealer and the blue point represents the contract of the high type broker-dealer. The debt contract of the high type is such that the low type is exactly indifferent between the two contracts.

q₁

d₁ d^limit

IC^H IC^L q^H(d₁)

q^L(d₁)

d^L_{f loor}

Figure 3.4: A potential credit market equilibrium with counter-cyclical borrowing limits.

However, for this equilibrium to exist, the increase in the borrowing limit must be substantial.

With higher debt limits the supply of assets in fire sale markets decrease and the fire sale discount for the assets will become smaller. As the potential profit margins decrease the low type broker-dealers need to purchase still larger quantities of the assets to become solvent. If the debt limit does not increase beyond the debt floor of the low type broker-dealers the policy will have no effect.

Applying the policy to the example economy shows that the debt limit must increase signifi-cantly for the policy to be effective. Numerically solving the model shows that the debt limit must be greater than 2.1 to be effective. If the debt limit is below 2.1, the policy has no effect and the equilibrium will be as in the example economy.

When the borrowing limit is equal to d^limit = 2.1 the prevailing fire sale price is ρ = 0.883. The debt floor of the low type broker-dealer is 1.993 and thus they can borrow in equilibrium. They will borrow up to the debt limit of 2.1 and the price per unit debt will equal 0.666. The high type broker-dealer will borrow a nominal amount of 0.88 for the price 0.887.

The analysis above shows that a policy of counter-cyclical borrowing limits can be an effective

measure against systemic failures in financial systems. However, it also cautions that for the policy to take effect the magnitude of the counter-cyclicality of the borrowing limit may need to be quite large to be successful. A moderate and mechanical approach to counter-cyclical borrowing limits may result in a completely ineffective policy.

3.4 Discussion

Commitment to Quantity and Collateralized Lending

A question that is not addressed in the main section of this paper is whether it is reasonable to believe that financial institutions can commit to their declared borrowing quantities. While this is a legitimate concern, in the end it seems plausible that the financial institutions could indeed commit. If the institution, for example, was borrowing from commercial paper markets the total quantity of debt they try to secure could be plainly visible. Admittedly, this does not preclude the institution from attempting to secretly secure funds in addition to their committed quantity.

Nevertheless, there is another method to enforce commitment that is reminiscent to transactions via collateralized lending. The financial institutions and their creditors could ensure commitment by hypothecating the assets as collateral. To ensure commitment to the quantity promised, the financial institutions must first sell some their assets to acquire the funds required to payoff their maturing debt, in excess of what they will eventually be able to borrow. Then they can provide their entire remaining portfolio as collateral and ensure commitment to their declared quantity. The implied haircut in this case would be the difference between the value of the assets and the amount of debt they issue. The interest rate would be the inverse of the price per unit of debt. Repurchase agreements and asset-backed commercial paper markets are some examples of such collateralized lending arrangements.⁹

9A detailed description of tri-party repos and their behavior during the crisis can be found in the paper by Krishna-murthy, Nagel and Orlov(2014).

Quantitative Easing

While not the focus of this paper, the analysis of this paper suggests an effect of quantitative easing that is not often discussed. Proposition 6 states that if banks are unconstrained in period zero (I(B) ≤ 0), the government can achieve a perfect information outcome by implementing a government clearing house for loans. This result is predicated on banks being unconstrained because if I(B) > 0 even a very small amount of risky assets needing to be liquidated can gen-erate a discrete drop in the price of the risky asset. Quantitative easing, or the act of providing banks with excess reserves and thus excess liquidity, is equivalent to increasing B in this model.

Increasing B to the point that the banks are unconstrained, can improve the outcome of this policy intervention.

The result need not be confined to this model. Providing ample liquidity to banks may be beneficial as it may allow banks to provide liquidity in various asset markets and help curtail harmful fire sales and stabilize asset prices during a crisis. Even if certain frictions inhibit an immediate and direct effect, quantitative easing may still be useful in conjunction with various other government policies geared toward stabilizing asset markets. The analysis of this paper suggests that even if quantitative easing cannot achieve much on its own, it can help maximize the effects of certain crisis management policies.