Bank Runs

1
Bank Runs

• Based on Itay Goldsteins notes

2
Panic-Based Bank Runs, Diamond and Dybvig JPE 1983

• Banks create liquid claims on illiquid assets
  using demand-deposit contracts
• (A) enabling investors with early liquidity needs
  to participate in long-term contracts
• (B) provide risk sharing.
• The drawback these contracts expose banks to
  panic-based runs

3
Preferences

• Three periods (0,1,2), one good, continuum 0,1
  of agents
• Each agent is born in period 0 with an endowment
  of 1
• Consumption occurs only in period 1 or 2
• Agents are of two types
• Impatient -- probability enjoy utility
• Patient probability enjoy utility

4
Risk aversion coefficient
5
Technology

• 1 unit of input in period 0 produces 1 unit of
  output in period 1 or R units of output in period
  2 with probability , or 0 otherwise.
• is distributed uniformly over 0,1, revealed
  in period 2
• is increasing in

6
Technology (continued)

• The technology yields on average higher returns
  in the long run
• In autarky, impatient agents consume in period 1,
  while patient agents consume in period 2

7
Resource constraints

• Period 1 consumption of impatient agents
• Period 2 consumption of patient agents
• With probability

8
First-best allocation if types are verifiable

• Planner maximizes expected utility
• First-order condition
• Result

Note that at
9
The Role of Banks overcome the fact that types
are not verifiable

• Bank deposit Payments are
• Period 1 if depositors get
• If
• Depositors get

with
with
10
Depositors contract (continued)

• Period 2
• If
• Depositors get
• If
• Depositors get 0

11
Banks maximize agents expected utility (free
entry in the banking sector)

• Suppose that the bank sets
• Assume that incentive compatibility holds

Good Equilibrium Agents work according to their
types ---first best allocation is achieved
Bad Equilibrium Bank run. All agents demand
early withdrawal.
Of agents consume
, the rest consume 0.
This is worse than Autarky! The optimal deposit
contract under the assumption that runs never
occur
12
Source of Fragility

• The source of fragility is strategic
  complementarities among depositors when
  the incentive to withdraw early increases with
  the number of other depositors who withdraw
  early.
• The run depletes the banks resources and hurts
  those who stay.
• This is reverses when

13
Goldstein and Pauzner , Journal of Finance 2005

• Apply the global-game approach to the
  Diamond-Dybvig model.
• At the limit, threshold signal is
  defined by

Is increasing in