國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
21
4. Bank Run
The setting of Chen and Hasan (2008) is that as long as all the depositors withdraw at period 1, the bank run will occur, we extend their definition. From Lemma 1 we can learn that deposit contract equilibrium d involve 2 Ω under 1 situation 1 and Ω under situation 1. However in our model, the bank run can only 2 happen when d2 = Ω1 which the depositor of type 1 withdraws at period 1, and the
depositor of type 2 at I withdraws at period 2, while at 21 I withdraws at period 22 1. It makes two types of depositor may withdraw at period 1, and then leads a bank run to occur.
From the foregoing we learn that in Figure 2 the part above the curve represents the scope of VB1>VB2. Because under situation 1 the utility V of the bank is B1
higher, it makes the bank to choose deposit contract d2 = Ω1 , in turn triggering the occurrence of bank runs. From Figure 1 we know that bank runs occur when negative information is revealed, the incidence of runs is 1−θ . On the other hand, the part below the curve represents the scope of VB2 >VB1, and under situation 1 the utility V of the bank is higher, so it makes the bank to choose deposit contract B2
2 2
d = Ω . Bank runs will never happen under such a situation, and the incidence of runs is 0. This is Proposition 2:
【Proposition 2】Only when the bank chooses d2 = Ω1 and negative information is
revealed, bank runs may happen. Nevertheless, when the bank chooses d2 = Ω , 2 bank runs will never happen.
Meanwhile from Proposition 1 we can arrange the following Corollary 1:
‧
【 Corollary 1 】 When the probability θ of the depositor receiving positive information is higher, the probability p of the bank obtaining R is lower, and the precision q of the signal s is higher, the bank is likely to choose d to equal to 2
Ω , therefore bank runs are easier to occur. 1
Proposition 2 states that only when the bank chooses the contract d2 = Ω1 may have two types of the depositor both withdraws at period 1. Nevertheless, the background of economic conditions described by Corollary 1 is the condition that the bank chooses the contract d2 = Ω1. The intuitive reason of Corollary 1 already has an associated discussion before Proposition 1 is inferred. Intuitively, due to
2> 1
Ω Ω , under the condition that the bank chooses the contract d2 = Ω1, because the benefits of withdrawing until the next period is relatively lower, the depositor receiving negative information tends to withdrawing early at period 1.
Next, we discuss the similarities and differences between Chen and Hasan (2008) and our model concerned the situation of bank runs. The former emphasizes there both are an individual minimum threshold success ratio of the investment plan whether the information is revealed or not. When depositors expect the success ratio is less than the minimum threshold, the bank run phenomenon will occur. Besides, the values of two minimum thresholds are uncertain. From another point of view, the bank runs we deduce will occur when the bank proposes the deposit d2 = Ω1 and the depositor receives negative message. Known by Corollary 1, the lower the success ratio p of the investment plan, the more our model is prone to meet with a bank run. So the probability p of the bank obtaining R to both Chen and Hasan (2008) and our model makes an impact of the same direction on the occurrence of bank runs. It is that the lower the probability p of the bank obtaining R, the lower
‧
國立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
23
the expected return got from the depositor withdrawing until the next period, so there is a strong motivation for the depositor to withdraw at period 1. In addition, the bank in our model has policy selection to the deposit contract, and in response to different economic conditions it will then select a deposit contract in advance to avoid a bank run. However, the banking industry is set to be perfectly competitive in Chen and Hasan (2008). It is the disparity between our model and Chen and Hasan (2008).
‧
A bank runs is a phenomenon that the impacts of the panic in financial crisis or relevant negative information about the bank make depositors lose confidence in the solvency of bank, and thus large numbers of depositors seek to withdraw money from banks. Because banks will turn their deposits into other investments, they do not always retain cash meaning that the deposits which banks keep are limited. Once the bank encounters focused and intensive withdrawals, it will fall into crisis of liquidity shortage, probably leading to operational difficulties, even the risk of bankruptcy. It is seen to be a sudden and concentrated hazard. Meanwhile, the bank run is highly contagious. When a bank run occurs, if the bank does not take timely measures or obtain other assistance, it often causes a larger-scale run, thereby resulting in the collapse of the banking system, hence the government will intervene when necessary as a result.
We expand the settings of Chen and Hasan (2008), which originally assume that the bank is perfectly competitive, so the deposit contract is decided by the economic environment. We alter their model and assume that the bank owns the initiative of participating in decision making, and aims for maximizing its own benefits. They originally assume numerous depositors jointly participate in decision making, while there is only one depositor along with the bank as players in our model, and the depositor divided in two types of liquidity preference patterns will make decisions for profit maximization separately.
According to the interactive strategy game equilibrium of the bank and the depositor, the bank may propose two equilibria of the deposit contract for the depositor to accept it or not, and which deposit contract it proposes will depend on different economic conditions the bank faces. After the bank proposes the deposit contract and the depositor accepts it, the depositor in two different types of liquidity