Karl Shell James Peck Presentation by Ludovico Genovese and Alessandro Pistoni Cornell University The Ohio State University Agenda Contextualization Model assumptions vs Diamond ID: 581279
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Slide1
Could making banks hold only liquid assets induce bank runs?
Karl Shell James Peck
Presentation by Ludovico Genovese and Alessandro Pistoni
Cornell University
The Ohio State UniversitySlide2
Agenda
ContextualizationModel: assumptions (vs Diamond-Dybvig)Banks
(unified and separated system)Welfare
maximization problemResultsTake-
aways
2Slide3
Contextualization
3
Glass-Steagall Act (Banking Act of 1933)
Repeal of Glass-Steagall
Act (1999)
“To
provide for the
safer
and
more effective
use of the assets of banks, to
regulate interbank
control, to prevent the undue diversion of funds into
speculative operations
[
…]
.”Slide4
Is Glass-Steagall’s
repeal to blame?
4
Could making banks hold only liquid assets induce bank runs
? (PS, April 2010)
"Maybe we ought to have a
two-tier
financial system
."
Paul Volcker (March 2009)
"This
institutions should
not be taking extraordinary risks
in the market place
represented
by
hedge
funds, equity
funds, large-scale
proprietary trading
.
Those
things would put their
basic
functions in jeopardy"Slide5
Model
3 periods:
5Slide6
Model
3 periods:
Continuum of consumers:
6Slide7
Model
3 periods:
Continuum of consumers:
S
ingle good (costless storage)
7Slide8
Model
3 periods:
Continuum of consumers:
S
ingle good (costless storage)
Each endowed with
in
8Slide9
Model
I
each consumer is identical
9Slide10
Model
I
each consumer is identical
In
they discover their type (patient or impatient)
10Slide11
Model
I
each consumer is identical
In
they discover their type (patient or impatient)
P
rivate
information
11Slide12
Model
I
each consumer is identical
In
they discover their type (patient or impatient)
P
rivate
information
Sequential service constraint
12Slide13
Model
I
each consumer is identical
In
they discover their type (patient or impatient)
P
rivate
information
Sequential service constraint
Until now, same assumptions as in Diamond and
Dybvig
(1983)
13Slide14
Model
14Slide15
Model
proportion of impatient agents
15Slide16
Model
probability of being
impatient
16Slide17
Model
probability of being impatient
is a random variable with density
17Slide18
Model
probability of being impatient
is a random variable with density
Support:
18Slide19
Model
probability of being impatient
is a random variable with density
Support:
19Slide20
Model
probability of being impatient
is a random variable with density
Support:
: maximum proportion of impatient consumers
20Slide21
What is
the difference?
21Diamond-
DybvigSlide22
What is
the difference?
22
Diamond-
Dybvig
Peck-ShellSlide23
What is
the difference?
23
Diamond-
Dybvig
Peck-Shell
Intrinsic uncertainty
Slide24
The utility functions
24Slide25
The utility functions
consumption
available to
an impatient
in
unit of consumption in
for an impatient
25Slide26
The utility functions
consumption available to
a patient in
unit of consumption in
for an impatient
26Slide27
The utility functions
consumption
available to
an impatient
in
unit of consumption in
for an impatient
27Slide28
The utility functions
consumption
available to
a
patient in
unit of consumption in
for an impatient
28Slide29
The utility functions
unit of consumption in
for an impatient
unit of consumption in
for a patient
29Slide30
The utility functions
unit of consumption in
for an impatient
unit of consumption in
for a patient
30Slide31
The utility functions
unit of consumption in
for an impatient
unit of consumption in
for a patient
31Slide32
The utility functions
32Slide33
The utility functions
33
Slide34
The utility functions
34
Slide35
The utility functions
35
Slide36
One more
assumption
Constant-return-to-scale technologies
36Slide37
One more
assumption
Constant-return-to-scale technologies
: illiquid (higher-yield technology)
37Slide38
One more
assumption
Constant-return-to-scale technologies
: illiquid (higher-yield technology)
:
38Slide39
One more
assumption
Constant-return-to-scale technologies
: illiquid (higher-yield technology)
: liquid (lower-yield
technology)
:
39Slide40
One more
assumption
Constant-return-to-scale technologies
: illiquid (higher-yield technology)
:
liquid (lower-yield technology)
:
40
:
Slide41
One more
assumption
Constant-return-to-scale technologies
: illiquid (higher-yield technology)
:
liquid (lower-yield technology)
:
41
:
Slide42
One more
assumption
Constant-return-to-scale technologies
: illiquid (higher-yield technology)
:
liquid (lower-yield technology)
:
42
:
Slide43
Recap (What’s new?)
(
illiquid
)
returns
in
(liquid)
returns
in
43
Slide44
Banks
44Slide45
Banks
45
Separated system
(only
)
Slide46
Banks
46
Separated system
Unified system
(only
)
(
both
and
)
Slide47
Banks
47
Separated system
Unified system
(only
)
(
both
and
)
Slide48
Contract
48Slide49
Contract
49Slide50
Contract
50Slide51
Contract
51Slide52
Welfare
No entry costs
52Slide53
Welfare
No entry costs
53
Perfect competitionSlide54
Welfare
No entry costs
54
Perfect competition
Maximize utilitySlide55
Welfare
Remarks:
55
Maximum withdrawal in
Slide56
Welfare
Remarks:
56
Maximum withdrawal in
Maximum investment in
Slide57
Welfare
57
All impatient agents satisfiedSlide58
Welfare
58
Only
impatient agents satisfied
All impatient agents satisfiedSlide59
Welfare
59
Slide60
Welfare
60
Slide61
Welfare
61
Slide62
Welfare
62
Nobody is rationed
: utility of all impatient agents
Slide63
Welfare
63
Nobody is rationed
: utility of all impatient agents
:
utility of all patient agents
Slide64
Welfare
64
rationed
: utility of all satisfied impatient agents
Slide65
Welfare
65
rationed
: utility of all satisfied impatient agents
:
utility
of all patient agents
Slide66
Welfare
66
rationed
: utility of all satisfied impatient agents
:
utility of all patient agents
: utility of all
rationed im
patient
agents
Slide67
Welfare
67
If it was discrete:Slide68
Welfare
68
+
If it was discrete:Slide69
Welfare
69
+
If it was discrete:
But it is continuous
:Slide70
Constraints
70
Resource constraint (only
)
Slide71
Constraints
71
Resource constraint (only
)
Slide72
Constraints
72
Resource constraint (only
)
Slide73
Constraints
73
Resource constraint (only
)
LHS
: amount of withdrawals in
Slide74
Constraints
74
Resource constraint (only
)
LHS: amount of withdrawals in
R
HS
:
resources that can be withdrawn
in
Slide75
Constraints
75
Resource constraint (only
)
: withdrawals of impatient agents in
Slide76
Constraints
76
Resource constraint (only
)
: withdrawals of impatient agents in
:
withdrawals of
patient agents in
Slide77
Constraints
77
Resource constraint (only
)
: withdrawals
of satisfied impatient agents
in
Slide78
Constraints
78
Resource constraint (only
)
:
withdrawals of satisfied impatient agents
in
: withdrawals
i
of who did not
withdrawn in
Slide79
Constraints
79
Resource constraint (only
)
:
total
invested
Slide80
Constraints
80
Resource constraint (only
)
:
total
invested
: total amount of withdrawals
of
impatient
agents
in
Slide81
Constraints
81
Resource constraint (only
)
:
total
invested
: total amount of withdrawals
of
impatient
agents
in
:
returns
on asset
Slide82
Constraints
82
Incentive compatibility constraint
Slide83
Constraints
83
Incentive compatibility constraint
expected utility of a patient that does not withdraw
in
Slide84
Constraints
84
Incentive compatibility constraint
expected utility of a patient that does not withdraw
in
expected utility of a patient that withdraws in
Slide85
Constraints
85
Incentive compatibility constraint
expected utility of a patient that does not withdraw
in
expected utility of a patient that withdraws in
density of
from a patient consumer’s point of view
Slide86
Maximization problem
86
Slide87
Results
87
THEOREM 3.1
i)
A bank will never invest more than
in
and there is full
c
onsumption smoothing
ii) Optimal
contract
Slide88
Results
88
Consumption Smoothing(i.e.
)
PROOF
i
)
Maximizing W sub. only to the RC, we obtain:Slide89
Results
89
Consumption Smoothing(i.e.
)
PROOF
ICC
Now,
RC
C.S.
i
)
Maximizing W sub. only to the RC, we obtain:Slide90
Results
90
PROOF
ii)
Plugging RC and C.S. conditions in W
Investing more than
in
is sub-optimal
Slide91
Results
91
THEOREM 3.2
i)
There exists an optimal contract for the unified bank,
also socially optimal Slide92
Results
92
Assuming that a patient does not run if indifferent,
NO RUN
THEOREM 3.2
i
)
There exists an optimal contract for the unified bank,
also socially optimal
i
i)Slide93
Results
93
PROOFi
)Setting the RC and the C.S. to hold is sufficient for
Slide94
Results
94
PROOFi
)Setting the RC and the C.S. to hold is sufficient for
i
i)
P
atient
agents are
indifferent between running
and
not running
Under the optimal contract Slide95
Results
95
PROOFi
)Setting the RC and the C.S. to hold is sufficient for
i
i)
P
atient
agents are
indifferent between running
and
not running
Under the optimal contract
No r
un equilibrium
Slide96
Take-aways
“The unified system optimally resolves the trade-off between liquidity and economic growth; in doing so it maximizes social welfare”
“Our Analysis in its present state does not prove that imposing Glass-Steagall
restrictions would be a mistake, although it does suggest that one should be skeptical about the purported stability benefits. Before using the model to offer policy advise, moral hazard should be included.”
96Slide97
Sources
Peck, J., & Shell, K. (2010). Could making banks hold only liquid assets induce bank runs? Journal of Monetary Economics, 57(4),
420-427. doi:10.1016/j.jmoneco.2010.04.006Diamond, D. W., & Dybvig, P. H. (1983). Bank Runs, Deposit Insurance, and Liquidity. Journal of Political Economy, 91
(3), 401-419. doi:10.1086/261155Experience News & Events. (n.d.). Retrieved November 12, 2016, from http://www.stern.nyu.edu
/experience-stern/news-events/uat_025245
Glass-
Steagall
Act:
http://congressional.proquest.com:80/congressional/docview/t53.d54.00048-stat-0162-100089?accountid=10267
97