1.4 Bank runs

Bank Run

A bank run occurs when a large portion of a bank’s customers withdraws money in a short period of time driven by fears of bank failure. As bank runs progress, they may become self-fulfilling prophecies, as the chance of sudden bankruptcy increases. In case a bank lacks liquidity, it may use lenders of last resort such as the discount window to prevent bankruptcy.

Intuition

In fractional-reserve banking systems, banks only keep part of the money that its customers deposit, and loan out the rest of the money. As such, if enough customers withdraw over a short period of time, the bank may not have enough liquidity to satisfy all of the withdrawals. This could be prevented by suspension of payments, which albeit generally a temporary measure while banks sell loans, may be a potential situation for bankruptcy.

Bank runs may also happen as a result of self-fulfilling prophecies. Customers may believe that the bank is inept in some way and may withdraw their money. Since the bank cannot react on time, a bank run occurs.

We can formulate bank run problems based on the Prisoner’s Dilemma: suppose that two investors deposit a $D$ dollars in a bank. The bank has invested $2D$ into a long-term project, yielding $2R$ upon maturity ($R>D$). If the bank is forced to liquidate the project before completion, it will recover $2r$, where $D>r>\frac{D}{2}$. We can create a table to help us with the cases of this problem:

• Before maturity:
  • One of the investors withdraws: the one that withdraws gets $D$, whereas the other gets $2r-D$.
  • Both investors withdraw: each investor receives $r$.
• After maturity:
  • One of the investors withdraws: the one that withdraws gets $D$, whereas the other gets $2R-D$.
  • Both investors withdraw: each investors receives $D$ and the bank profits $2R-2D$.
  • None of the investors withdraws: both investors get $R$.

Here, there are two Nash equilibria:

1. Both investors withdraw and get $r$ each.
2. Both investors keep their money in the bank and get $R$ each.

Option 1 leads to a bank run, since the investors did not get the full quantity of their money $D$ back. However, the FDIC insures deposits up to some limit such that the minimum amount of money an investor gets is always $D$. Also, if the bank has some backup money, it may also be able to pay off the original investment.

The FDIC’s establishment, although beneficial, greatly downplays the credibility of banks, as depositors have weaker incentives to monitor the quality of banks.

Example

Bank Runs During the Great Depression

During the Great Depression, different federal banks in Mississippi had different approaches to banking panics:

• Federal Bank of Atlanta (in the south of MS) believed the FED should serve as a lender of last resort, responding to the panics with large infusions of cash.
• Federal Bank of St. Louis (in the north of MS) believed in the real bills doctrine, only lending backed money and therefore being tougher on discount.

However, at the end, economic characteristics were similar in both parts of Mississippi, and although quality of bank assets was higher in banks governed by the St. Louis fed, more banks were suspended, and lending and trade declined more.

Since the panic was due to illiquidity, FED’s action should’ve been aggressive on a national scale.