Monetary policy under subjective beliefs of banks: optimal central bank collateral requirements

We study how the subjective beliefs about loan repayment on the side of liquidity-constrained banks affect the central bank's choice of collateral standards in its lending facilities. Optimism on the side of banks, entailing a higher collateral value of bank loans, can lead to excessive lending and bank default. Pessimism, though, can entail insufficient lending and productivity losses. With an appropriate haircut on collateral, the central bank can perfectly neutralize the banks' belief distortions and always induce the socially optimal allocation. Under uncertainty about beliefs, the central bank's incentives to set looser collateral standards increase. This reduces the risk of deficient bank lending if sufficiently pessimistic beliefs realize. In extreme cases, monetary policy aims at mitigating productivity losses only, instead of also avoiding bank default.