This paper establishes a theoretical model to examine the LOLR policy when a central bank cannot distinguish between solvent and insolvent banks. We study two cases: a case where the central bank cannot screen insolvent banks and a case where the central bank can only imperfectly screen insolvent banks. The major results that our model produces are as follows: (1) It is impossible for any separating equilibrium to exist because insolvent banks always have an incentive to mimic solvent banks to gamble for resurrection. (2) The pooling equilibria in which, on one hand, all the banks borrow from the central bank and, on the other hand, all the banks do not borrow from the central bank, could exist given certain market beliefs off the equilibrium path. However, neither of the equilibria is socially efficient because insolvent banks will continue to hold their unproductive assets, rather than efficiently liquidating them. (3) When the central bank can screen banks imperfectly, the pooling equilibrium where all the banks borrow from the central bank becomes more likely, and the pooling equilibrium where all the banks do not borrow from the central bank becomes less likely. (4) Higher precision in central bank screening will improve social welfare not only by identifying insolvent banks and forcing them to efficiently liquidate their assets, but also by reducing moral hazard and deterring banks from choosing risky assets in the first place. (5) If a central bank can commit to a specific precision level before the banks choose their assets, rather than conducting a discretionary LOLR policy, it will choose a higher precision level to reduce moral hazard and will attain higher social welfare.
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