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Traditionally, aggregate liquidity shocks are modelled as exogenous events. Extending our previous work (Cao & Illing, 2007), this paper analyses the adequate policy response to endogenous systemic liquidity risk. We analyse the feedback between lender of last resort policy and incentives of private banks, determining the aggregate amount of liquidity available. We show that imposing minimum liquidity standards for banks ex ante are a crucial requirement for sensible lender of last resort policy. In addition, we analyse the impact of equity requirements and narrow banking, in the sense that banks are required to hold sufficient liquid funds so as to pay out in all contingencies. We show that such a policy is strictly inferior to imposing minimum liquidity standards ex ante combined with lender of last resort policy.

The paper models the interaction between risk taking in the financial sector and central bank policy for the case of pure illiquidity risk. It is shown that, when bad states are highly unlikely, public provision of liquidity may improve the allocation, even though it encourages more risk taking (less liquid investment) by private banks. In general, however, there is an incentive of financial intermediaries to free ride on liquidity in good states, resulting in excessively low liquidity in bad states. In the prevailing mixed-strategy equilibrium, depositors are worse off than if banks would coordinate on more liquid investment. In that case, liquidity injection will make the free riding problem even worse. The results show that even in the case of pure illiquidity risk, there is a serious commitment problem for central banks. We show that unconditional free lending against good collateral, as suggested by the Bagehot Rule, fails to address the moral hazard problem: Even though we consider a model with pure illiquidity risk, it turns out that such a policy will encourage banks to behave naughty, providing insufficient level of liquidity.