RDP 2019-10: Emergency Liquidity Injections 7. Conclusion

This paper models a liquidity crisis in the banking system and compares different types of emergency liquidity injections. A crisis occurs when there is an exogenous system-wide withdrawal of funding liquidity that forces banks to sell securities, causing securities price depression to the point that banks cannot survive the withdrawal. The banking system's level of pre-crisis exposures to securities with liquidity risk determines (inversely) how large the outflow must be to cause bank failures, and hence the likelihood of a crisis occurring.

A secured lending policy can mitigate banks' fire selling of securities, because banks must use those securities as collateral for borrowing from the authority. The positive effect of the constraint essentially offsets banks' fire sale externalities – neither are factored into banks' profit maximisation – and so does not incentivise liquidity risk-taking. Accordingly, relative to an unsecured lending policy, a secured lending policy can reduce banks' losses on illiquid securities without greater incentives for liquidity risk-taking. Under either lending policy, banks' incentive to take liquidity risk is decreasing in the interest rates on emergency lending. For penalising interest rates to not cause further bank failures, however, lending must be for long enough terms that the liquidity distress has subsided before repayments are due. Liquidity injections via asset purchases involve no ex post repayments, and therefore, relative to lending policies, have less ability to save banks and disincentivise liquidity risk-taking.

The model presented here is general in several dimensions that could be restricted for applications in more complex settings. There is a continuum of banks and an authority that all react optimally to each other, with continuous liquidity shocks and investment choices, and endogenous market liquidity and crisis probability. By simplifying aspects of the model, such as discretising variables or agents, it could be applied to a wide variety of other settings. For example, the endogenous crisis probability may be suitable for analysing financial cycles. This is left to future work.