Banks, depositors and liquidity shocks: long term vs. short term interest rates in a model of adverse selection
This model takes into consideration the fact that depositors have private information about their probability of having to withdraw early. The banks can offer a menu of contracts with different combinations of long and short term interest rates to those who withdraw early and wait respectively. This is a principal- agent model of a bank in a competitive market and depositors where depositors are either low or high type which indicates the probability of early withdrawal. Therefore they will consider the long-term and short-term returns in their investment decision. We find the contracts that the banks offer that can be sustained as equilibrium - symmetric pooling equilibrium where only one contract is offered and a separating equilibrium where two contracts are offered. It is found that found return of more than one can never be sustained. Further, there is no symmetric pooling equilibrium when both types withdraw with some probability. However a symmetric pooling equilibrium can be sustained if the proportion of low type agents is high enough and they never withdraw early. There is a separating equilibrium if the proportion of low type agents is sufficiently high.
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