When a central bank implements the LOLR policy in a financial crisis, bank creditors often infer a bank's quality from whether or not it borrows from the central bank. We establish a formal model to study the optimal LOLR policy in the presence of this signaling effect, assuming that the central bank aims to encourage central bank borrowing to avoid inefficiencies caused by contagion. In our model, there are two types of banks: a high quality type with high expected asset returns and a low quality type with lower returns. Both types of banks need to roll over their short-term debts. A central bank offers to lend to both types of banks. After private creditors observe whether banks borrow from the central bank, banks try to borrow from the private market. We find that there may exist a separating equilibrium where only low quality banks borrow from the central bank; and two pooling equilibria where both types of banks do and do not borrow from the central bank. Our major results are as follows: (1) Considering the signaling effect, the central bank should set its lending rate lower than the prevailing market rate to induce both types of banks to borrow from the central bank. (2) Hiding the identity of banks borrowing from the central bank will encourage banks to borrow from the central bank. (3) The central bank may serve as a coordinator for the realization of its favored equilibrium.
