CRIEFF Discussion Paper Number 0703
Banks,
depositors and liquidity shocks: long term vs. short term interest rates in a
model of adverse selection.
Geethanjali Selvaretnam
Abstract
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.
JEL Classifications: D82; G21
Keywords:
adverse selection, interest rates, liquidity shock, private information
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