econ7003 money and banking. hugh goodacre. lectures 1-2. bank runs bank deposits and uncertain...
TRANSCRIPT
![Page 1: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/1.jpg)
ECON7003 Money and Banking. Hugh Goodacre.Lectures 1-2.
BANK RUNS
Bank deposits and uncertain liquidity demand.
The Diamond and Dybvig 1983 model, Spencer, ch. 10 version.
1. Trading risk in a two-individual ‘society’.
2. The bank deposit contract.
Preview:
3. Measures to prevent bank runs.
![Page 2: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/2.jpg)
Withdrawal of deposits on demand normally no problem, despite:
low deposit : asset ratio
high gearing in bank sector
(a) Scale economies:
→ withdrawal demands unlikely to be correlated.
For banking system as a whole, likely to be inversely correlated:
Debits-credits net out!
(b) Tradable money market instruments:
e.g. Certificates of Deposit (CDs).
To meet fluctuations in liquidity needs.
![Page 3: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/3.jpg)
These advantages are basic to bank’s profit through intermediation:
i.e. Asset transformation:
Short-term / instantly withdrawable deposits → long-term / illiquid assets
‘Maturity transformation’
Small-size deposits → large-size assets:‘Size transformation’
Low-risk instrument, i.e. deposit, → high-risk.:‘Risk transformation’
In each case:Interest on asset > interest on liability → bank profit.
![Page 4: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/4.jpg)
BUT:
Loss of confidence in bank
→ withdrawals not motivated by ‘genuine’ liquidity requirement / transactions motive.
May be contagious and → panic.
In panic, those at end of queue may not be paid in full:
Even if bank is solvent and all its assets are liquidated
![Page 5: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/5.jpg)
Costs of liquidation
Loss of:
customer relationships
confidential information, etc.
i.e. Destruction of ‘informational capital’ / intangible assets.
Inevitably undervalued in ‘fire sale’ conditions.
→ Net value > 0 when functioning
may → < 0 if sold off hurriedly.
![Page 6: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/6.jpg)
Asymmetric information problem facing bank:
Bank unable to distinguish between:• withdrawals for ‘genuine’ / transactions purposes• withdrawals through panic
→ cannot pay ‘in sequence’:
Gain time → avoid fire sale
→ liquidate assets at better price.
![Page 7: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/7.jpg)
3-period model of bank runs and measures to prevent them.
Assumption:Bank liabilities all consist of deposits withdrawable on demand.
Each individual has a primary investment of 1 in period 0yields 1 if liquidated and consumed in period 1yields R > 1 if liquidated and consumed in period 2.
i.e. R ≡ 1 + r
![Page 8: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/8.jpg)
Individuals are of 2 types:
Type 1s ‘die’ in period 1having first liquidated their investment and consumed its entire value.
Type 2s survive period 1 but ‘die’ in period 2having by that time liquidated their investment and consumed its entire value.
The overall proportion (p) of type 1s is publicly knownin period 0
i.e. There is no aggregate uncertainy.
but individuals do not find out which type they are until period 1, and this information is private.
i.e. There is individual uncertainy.
![Page 9: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/9.jpg)
i.e. Requirement for liquidation of investment in period 1 drives the demand for liquidity.
‘Cost of early death’ is R – 1.
Because R > 1, type 2s optimally set C1 = 0.
![Page 10: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/10.jpg)
Individual’s expected utility E [U] in period 0:
E [U] = p.U(C11 + C2
1) + (1 – p).U(C12 + C2
2)
Type 1s: Expectation of a constant is a constant →
E[C11] = C1
1 = 1
E[C21] = C2
1 = 0 Type 2s: Expectation that they optimise →
E[C12] = 0
E[C22] = R
→ Substituting:
E [U] = p.U(1 + 0) + (1 – p).U(0 + R)
→ E [U] = p.U(1) + (1 – p).U(R)
![Page 11: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/11.jpg)
‘Society’ of two individuals where p = ½
Learning own type ≡ revelation of type of other !
i.e. Full ‘state verification’ / no informational asymmetry.
→ Socially optimal risk-sharing contract possible in period 0:Type 2 will pay fixed sum (π) to type 1 in period 1.
→ Individual 1 consumes C1 = 1 + π in period 1.
Individual 2 consumes C2 = R(1 – π) in period 2.
Only requirement: Mechanism for enforcing contract.
![Page 12: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/12.jpg)
Deriving optimal scale of transfer (π):
We need to find the value of π which maximises total social utility (SU) ≡ U(C1) + U(C2)
Express period 2 budget constraint i.t.o. C1:
C1 = 1 + π
→ π = C1 - 1
Substituting into C2 = R(1 – π) we have:
C2 = R[1 – (C1 – 1)]
= R(2 – C1) = 2R – RC1
Substituting into expression for total social utility, we have:
SU = U(C1) + U(2R – RC1)
![Page 13: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/13.jpg)
Differentiating SU and setting to zero to maximise, we have:
SU = U(C1) + U(2R – RC1)
→ dSU / dC1 = MU1 – R.MU2 = 0
→ MU1 / MU2 = R = 1 + r
i.e. MRS (in consumption) = MRT (through investment)
We define the values which solve these equations as:
C1*, C2*, and π*
![Page 14: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/14.jpg)
C2
2 C1
2R ← Vertical intercept:Period 2 social budget constraint:
C2 = R(2 – C1)Solving for C1 = 0:
C2 = 2R
Horizontal intercept:Maximum possible consumption by both types (‘social’ consumption) is 2. ↓
Social budget line
![Page 15: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/15.jpg)
C2
R
2 C1
1
2R
Allocation point under autarchy / no trading of risk
i.e. Social level of consumption under autarchy is:
1 + R
A
![Page 16: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/16.jpg)
C2
2 C1
2R
450
450 line indicates complete absence of risk between ‘states’ / outcomes
![Page 17: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/17.jpg)
C2
R
2 C1
1
2R
450
With trading in risk / contract to pay π, ‘social IC’ reaches tangency with BC at A'
A' is closer to the 450 line, indicating a reduction in risk
With no trading in risk, ‘social indifference curve’ cuts BC at A
A'
A
It is on a higher social IC curve, showing that trading in risk results in a socially preferable outcome to autarchy.
![Page 18: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/18.jpg)
C2
C2*
2
A
C1
1
2R
450
A'Rπ*
π*
At A', individual 1 consumes C1*
due to receiving π*
At A', individual 2 consumes C2*
due to loss of Rπ*
C1*
R
Note: C2* > C1*
![Page 19: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/19.jpg)
BUT:
Society of more than two individuals:
Information on own type remains private in period 1:
→ life expectancy and liquidity requirements no longer publicly revealed.
→ asymmetric information problem in designing contract for trading risk.
![Page 20: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/20.jpg)
An intermediary / bank now offers a deposit contract capable of achieving same degree of insurance as in the two-individual case.
i.e. :
All type 1s will consume C1* = 1 + π in period 1.
All type 2s will consume C2* = R(1 – π) in period 2.
C2* > C1* → type 2s still have motive to set C1 = 0
![Page 21: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/21.jpg)
BUT: Bank can only fulfil this contract if only type 1s withdraw their deposits in period 1.
i.e. for ‘genuine’ liquidity requirement.
Fragility of this result:
In period 1 liabilities > assets
→ bank relies on type 2s not withdrawing.
![Page 22: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/22.jpg)
Period 1 liabilities > assets:
Recall the assumption: All the bank’s assets / funds are sourced from its depositors.
Let there be N depositors, then the funds available to the bank for distribution to depositors in period 1 are:
N.1 = N
The bank’s liabilities to depositors in period 1 are: N.C1*
And N.C1* > N !
![Page 23: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/23.jpg)
Let p = ½
‘Good’ outcome period 1:
Type 2s will optimise by setting C12 = 0
Only type 1s withdraw deposits in period 1.
→ Liquidity demand in period 1 is:
pNC1* + (1 – p)N.0
= ½NC1* < N
i.e. Bank’s liabilities do not exceed its assets.All deposit withdrawal demands can be met.
![Page 24: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/24.jpg)
‘Bad’ outcome period 1:
Type 2s fear a bank run / begin to withdraw deposits in period 1.
If all do so (‘bank panic’), type 2 liquidity demand in period 1 is:
(1-p).NC1* = ½NC1*.
→ Total liquidity demand:
½NC1* + ½NC1*
= NC1* > N
i.e. Bank’s assets insufficient to meet liabilities.Some depositors get 0.
![Page 25: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/25.jpg)
Deposit : liability ratio of banks in period 1:
N : N.C1*
i.e. 1 : C1*
Assumption: No deposit insurance arrangements are in place.
Maximum proportion of depositors who can withdraw their deposits in period 1 in the presence of a run:
Deposits divided by liabilities:
N / NC*
i. e. deposits : liabilities ratio (1 : C1*) expressed as a fraction:
f = 1 / C1*
C1* > 1
→ f < 1
![Page 26: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/26.jpg)
Fraction of depositors who get nothing through being last in the queue:
1 – f= 1 - 1 / C1*
= (C1* - 1) / C1*
We have: C1* = 1 + π
Substituting: 1 – f = (1 + π – 1) / C1* = π / C1*
i.e. Fraction who receive nothing is π / C1*
![Page 27: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/27.jpg)
i.e. Intermediation / bank deposits offer solution to informational problems of trading in risk of early death.
BUT
That solution is not robust to fear of bank’s insolvency:
Such fear may → self-fulfilling prophecy / fear becomes general (‘panic’).
‘Sequential service constraint’ / bank cannot meet all withdrawal demands / ‘last in queue’ get nothing.
Expectations of run may → actual run, with no change in fundamentals.
Banks are inherently ‘fragile’.
If fear is contagious, may threaten whole banking system.
![Page 28: ECON7003 Money and Banking. Hugh Goodacre. Lectures 1-2. BANK RUNS Bank deposits and uncertain liquidity demand. The Diamond and Dybvig 1983 model, Spencer,](https://reader036.vdocuments.us/reader036/viewer/2022062312/5515dc82550346d46f8b4b00/html5/thumbnails/28.jpg)
Preview: The ‘good’ and ‘bad’ outcomes will be defined as Nash equilibria.
Measures to prevent bank runs.
Influence expectations / provide confidence.
Make ‘good’ Nash equilibrium unique.
3 possible solutions:
Action by banks themselves:Suspend convertibility
Government actions:Government-backed deposit insuranceLender of last resort facility