[PPT] - Could making banks hold only liquid assets induce bank runs? Karl PowerPoint Presentation

SLIDE 1

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 University

SLIDE 2

Agenda

Contextualization
Model: assumptions (vs Diamond-Dybvig)
Banks (unified and separated system)
Welfare maximization problem
Results
Take-aways

2

SLIDE 3

Contextualization

3

Glass-Steagall Act (Banking Act of 1933)
Repeal of Glass-Steagall Act (1999)

“To provide for the safer and more effective use

f the assets of banks, to regulate interbank

control, to prevent the undue diversion of funds into speculative operations […] .”

SLIDE 4

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"

SLIDE 5

Model

3 periods: 𝑈 = 0

𝑈 = 1 𝑈 = 2

Continuum of consumers: [0; 1]
Single good (costless storage)
Each endowed with 𝑧 in 𝑈 = 0

5

SLIDE 6

Model

In 𝑈 = 0 each consumer is identical
In 𝑈 = 1 they discover their type (patient or

impatient)

Private information
Sequential service constraint
Until now, same assumptions as in Diamond and

Dybvig (1983)

6

SLIDE 7

Model

𝛽 ∶ probability of being impatient
𝛽 is a random variable with density 𝑔
Support: 0,

𝛽 𝛽 < 1

𝛽: maximum proportion of impatient consumers

7

SLIDE 8

What is the difference?

8

Diamond-Dybvig Peck-Shell

Intrinsic uncertainty

SLIDE 9

The utility functions

𝑉𝐽 𝐷𝐽

1, 𝐷𝐽 2 =

𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 ≥ 1

𝛾 𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 < 1

𝑉𝑄 𝐷𝑄

1, 𝐷𝑄 2 =

𝑣 + 𝑣 𝐷𝑄

1 + 𝐷𝑄 2 − 1

9

SLIDE 10

The utility functions

𝑉𝐽 𝐷𝐽

1, 𝐷𝐽 2 =

𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 ≥ 1

𝛾 𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 < 1

𝑉𝑄 𝐷𝑄

1, 𝐷𝑄 2 =

𝑣 + 𝑣 𝐷𝑄

1 + 𝐷𝑄 2 − 1 𝑉𝑄 𝐷𝑄 1, 𝐷𝑄 2

𝐷𝐽

1: consumption available to an impatient in 𝑈 = 1

: incremental utility of:

1 unit of consumption in 𝑈 = 1 for an impatient

10

SLIDE 11

The utility functions

𝑉𝐽 𝐷𝐽

1, 𝐷𝐽 2 =

𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 ≥ 1

𝛾 𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 < 1

𝑉𝑄 𝐷𝑄

1, 𝐷𝑄 2 =

𝑣 + 𝑣 𝐷𝑄

1 + 𝐷𝑄 2 − 1

𝐷𝑄

1: consumption available to a patient in 𝑈 = 1

: incremental utility of:

1 unit of consumption in 𝑈 = 1 for an impatient

11

SLIDE 12

The utility functions

𝑉𝐽 𝐷𝐽

1, 𝐷𝐽 2 =

𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 ≥ 1

𝛾 𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 < 1

𝑉𝑄 𝐷𝑄

1, 𝐷𝑄 2 =

𝑣 + 𝑣 𝐷𝑄

1 + 𝐷𝑄 2 − 1 𝑉𝑄 𝐷𝑄 1, 𝐷𝑄 2

𝐷𝐽

2: consumption available to an impatient in 𝑈 = 2

: incremental utility of:

1 unit of consumption in 𝑈 = 1 for an impatient

12

SLIDE 13

The utility functions

𝑉𝐽 𝐷𝐽

1, 𝐷𝐽 2 =

𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 ≥ 1

𝛾 𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 < 1

𝑉𝑄 𝐷𝑄

1, 𝐷𝑄 2 =

𝑣 + 𝑣 𝐷𝑄

1 + 𝐷𝑄 2 − 1

𝐷𝑄

2: consumption available to a patient in 𝑈 = 2

: incremental utility of:

1 unit of consumption in 𝑈 = 1 for an impatient

13

SLIDE 14

The utility functions

𝑉𝐽 𝐷𝐽

1, 𝐷𝐽 2 =

𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 ≥ 1

𝛾 𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 < 1

𝑉𝑄 𝐷𝑄

1, 𝐷𝑄 2 =

𝑣 + 𝑣 𝐷𝑄

1 + 𝐷𝑄 2 − 1

𝑣 : incremental utility of:

1 unit of consumption in 𝑈 = 1 for an impatient
1 unit of consumption in 𝑈 = 2 for a patient

14

SLIDE 15

The utility functions

𝑉𝐽 𝐷𝐽

1, 𝐷𝐽 2 =

𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 ≥ 1

𝛾 𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑗𝑔 𝐷𝐽

1 < 1

𝑉𝑄 𝐷𝑄

1, 𝐷𝑄 2 =

𝑣 + 𝑣 𝐷𝑄

1 + 𝐷𝑄 2 − 1 𝑉𝑄 𝐷𝑄 1, 𝐷𝑄 2

𝛾 𝑣: incremental utility of 1 unit of consumption in 𝑈 = 2 for an impatient: incremental utility of:

1 unit of consumption in 𝑈 = 1 for an impatient
1 unit of consumption in 𝑈 = 2 for a patient

15

SLIDE 16

The utility functions

𝑣 𝐷1 + 𝐷2 − 1 : utility from “left−over” consumption

16

SLIDE 17

The utility functions

17

𝑣(𝑦) 𝐷1 + 𝐷2 − 1 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

SLIDE 18

The utility functions

18

𝑣(𝑦) 𝐷1 + 𝐷2 − 1 𝛾 𝑣 𝑣 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

SLIDE 19

The utility functions

19

𝑣(𝑦) 𝐷1 + 𝐷2 − 1 𝛾 𝑣 𝑣 + 𝑣 𝐷1 + 𝐷2 − 1 𝑣 𝛾 𝑣 + 𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

𝑣 𝐷𝐽

1 + 𝐷𝐽 2 − 1

SLIDE 20

One more assumption

Constant-return-to-scale technologies

𝑗: illiquid (higher-yield technology)
𝑚: liquid (lower-yield technology)

𝑈: 1 2 𝑗 : −1 𝑆𝑗

20

𝑚 : −1 1 −1 𝑆𝑚 1 < 𝑆𝑚 < 𝑆𝑗

SLIDE 21

Recap (What’s new?)

𝛽 ∽ 𝑔

𝛽 𝛽 ∗ 1 0, 𝛽

𝛽

𝑉 𝑦 =
𝑗 (illiquid) returns 𝑆𝑗 in 𝑈 = 2
𝑚 (liquid) returns 𝑆𝑚 in 𝑈 = 2

21

+ 𝑣 𝐷1 + 𝐷2 − 1

r

𝛾 𝑣 𝑣

SLIDE 22

Banks

22

Separated system Unified system (only 𝑚) (both 𝑚 and 𝑗)

SLIDE 23

Contract

𝑡𝑞𝑓𝑑𝑗𝑔𝑗𝑓𝑡 𝛿 𝑑1 𝑨 𝑑𝐽

2(α1)

𝑑𝑄

2 α1

𝛿 = % of endowment in 𝑚 𝑑1 𝑨 = withdrawal in 𝑈 = 1 𝑑𝐽

2 𝛽1 = withdrawal in 𝑈 = 2 if he also withdrew in 𝑈 = 1

𝑑𝑄

2 𝛽1 = withdrawal in 𝑈 = 2 if he did not withdraw

in 𝑈 = 1

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SLIDE 24

Welfare

No entry costs

24

Perfect competition Maximize utility

SLIDE 25

Welfare

Remarks:

𝑑1 𝑨 = 1
𝛿𝑧 ≤

𝛽 ∗ 1

25

Maximum withdrawal in 𝑈 = 1 Maximum investment in 𝑚

SLIDE 26

Welfare

𝛽 ≤ 𝛿𝑧

26

𝛽 All impatient agents satisfied

SLIDE 27

Welfare

𝛽 ≤ 𝛿𝑧
𝛽 > 𝛿𝑧

27

Only 𝛿𝑧 impatient agents satisfied 𝛽 All impatient agents satisfied

SLIDE 28

Welfare

28

𝑋 =

𝛿𝑧

𝑣 + 1 − 𝛽 𝑣 1 − 𝛿 𝑧𝑆𝑗 + 𝑑𝑄

2 𝛽 − 1 + 𝛽𝑣

1 − 𝛿 𝑧𝑆𝑗 + 𝑑𝐽

2 𝛽

𝑔 𝛽 𝑒𝛽 + + 𝛽 − 𝛿𝑧 𝑣 1 − 𝛿 𝑧𝑆𝑗 + 𝑑𝑄

2 𝛽 − 1 + 𝛿𝑧𝑣

1 − 𝛿 𝑧𝑆𝑗 + 𝑑𝐽

2 𝛽

]𝑔 𝛽 𝑒𝛽 +

𝛿𝑧 𝛽

[ 1 − 𝛽 + 𝛿𝑧 𝑣 + 𝛽 − 𝛿𝑧 𝛾 𝑣 + 1 − 𝛽 𝑣 1 − 𝛿 𝑧𝑆𝑗 + 𝑑𝑄

2 𝛽 − 1 +

SLIDE 29

Welfare

29

Nobody is rationed

𝛿𝑧

𝛽 𝑣 + 𝑣 𝐷𝐽

𝑈

+ 1 − 𝛽 𝑣 + 𝑣 𝐷𝑄

𝑈

𝑔 𝛽 𝑒𝛽 𝛽 𝑣 + 𝑣 𝐷𝐽

𝑈

: utility of all impatient agents 1 − 𝛽 𝑣 + 𝑣 𝐷𝑄

𝑈

: utility of all patient agents

SLIDE 30

Welfare

30

𝜷 − 𝜹𝒛 𝐛𝐬𝐟 rationed

𝛿𝑧 𝛽

𝛿𝑧 𝑣 + 𝑣 𝐷𝐽

𝑈

+ 1 − 𝛽 𝑣 + 𝑣 𝐷𝑄

𝑈

+ 𝛽 − 𝛿𝑧 𝛾 𝑣 + 𝑣 𝐷𝑄

𝑈

𝑔 𝛽 𝑒𝛽

𝛿𝑧 𝑣 + 𝑣 𝐷𝐽

𝑈

: utility of all satisfied impatient agents 1 − 𝛽 𝑣 + 𝑣 𝐷𝑄

𝑈

: utility of all patient agents 𝛽 − 𝛿𝑧 𝛾 𝑣 + 𝑣 𝐷𝑄

𝑈

: utility of all rationed impatient agents

SLIDE 31

Welfare

31

𝛽1𝛽2 𝑋 𝛽1 𝑋 𝛽2 𝑔 𝛽 𝛽

𝑋 = 𝑋 𝛽1 𝑄 𝛽1 +𝑋 𝛽2 𝑄 𝛽2 + ⋯

𝑋 =

𝛽

…

𝑔 𝛽 𝑒𝛽 If it was discrete: But it is continuous:

SLIDE 32

Constraints

32

Resource constraint (only 𝑚)

𝛽1𝑑𝐽

2 𝛽1 + 1 − 𝛽1 𝑑𝑄 2 𝛽1 = 𝛿𝑧 − 𝛽1 𝑆𝑚

𝛿𝑧𝑑𝐽

2 𝛽1 + 1 − 𝛿𝑧 𝑑𝑄 2 𝛽1 = 0

𝛽1 ≤ 𝛿𝑧 𝛽1 > 𝛿𝑧

SLIDE 33

Constraints

33

Resource constraint (only 𝑚)

𝛽1𝑑𝐽

2 𝛽1 + 1 − 𝛽1 𝑑𝑄 2 𝛽1 = 𝛿𝑧 − 𝛽1 𝑆𝑚

𝛿𝑧𝑑𝐽

2 𝛽1 + 1 − 𝛿𝑧 𝑑𝑄 2 𝛽1 = 0

𝛽1 ≤ 𝛿𝑧 𝛽1 > 𝛿𝑧

LHS: amount of withdrawals in 𝑈 = 2 RHS: resources that can be withdrawn in 𝑈 = 2

SLIDE 34

Constraints

34

Resource constraint (only 𝑚)

𝛽1𝑑𝐽

2 𝛽1 + 1 − 𝛽1 𝑑𝑄 2 𝛽1 = 𝛿𝑧 − 𝛽1 𝑆𝑚

𝛿𝑧𝑑𝐽

2 𝛽1 + 1 − 𝛿𝑧 𝑑𝑄 2 𝛽1 = 0

𝛽1 ≤ 𝛿𝑧 𝛽1 > 𝛿𝑧

𝛽1𝑑𝐽

2 𝛽1 : withdrawals of impatient agents in 𝑈 = 2

1 − 𝛽1 𝑑𝑄

2 𝛽1 : withdrawals of patient agents in 𝑈 = 2

SLIDE 35

Constraints

35

Resource constraint (only 𝑚)

𝛽1𝑑𝐽

2 𝛽1 + 1 − 𝛽1 𝑑𝑄 2 𝛽1 = 𝛿𝑧 − 𝛽1 𝑆𝑚

𝛿𝑧𝑑𝐽

2 𝛽1 + 1 − 𝛿𝑧 𝑑𝑄 2 𝛽1 = 0

𝛽1 ≤ 𝛿𝑧 𝛽1 > 𝛿𝑧

𝛿𝑧𝑑𝐽

2 𝛽1 : withdrawals of satisfied impatient agents

in 𝑈 = 2 1 − 𝛿𝑧 𝑑𝑄

2 𝛽1 : withdrawals in 𝑈 = 2 of who did not

withdrawn in 𝑈 = 1

SLIDE 36

Constraints

36

Resource constraint (only 𝑚)

𝛽1𝑑𝐽

2 𝛽1 + 1 − 𝛽1 𝑑𝑄 2 𝛽1 = 𝛿𝑧 − 𝛽1 𝑆𝑚

𝛿𝑧𝑑𝐽

2 𝛽1 + 1 − 𝛿𝑧 𝑑𝑄 2 𝛽1 = 0

𝛽1 ≤ 𝛿𝑧 𝛽1 > 𝛿𝑧

𝛿𝑧 : total 𝑚 invested 𝛽1 ∙ 1: total amount of withdrawals of impatient agents in 𝑈 = 1 𝑆𝑚: returns on asset 𝑚

SLIDE 37

Constraints

37

Incentive compatibility constraint

𝛽

𝑣 𝐷𝑄

2 𝑔 𝑞 𝛽 𝑒𝛽 ≥ 𝛽

𝑣 𝐷𝐽

2 𝑔 𝑞 𝛽 𝑒𝛽

SLIDE 38

Constraints

38

Incentive compatibility constraint

𝛽

𝑣 𝐷𝑄

2 𝑔 𝑞 𝛽 𝑒𝛽 ≥ 𝛽

𝑣 𝐷𝐽

2 𝑔 𝑞 𝛽 𝑒𝛽

𝑣 𝐷𝑄

2 = expected utility of a patient that does not withdraw

in 𝑈 = 1 𝑣 𝐷𝐽

2 = expected utility of a patient that withdraws in 𝑈 = 1

𝑔

𝑞 𝛽 = density of 𝛽 from a patient consumer’s point of view

SLIDE 39

Maximization problem

39

𝑛𝑏𝑦

𝛿, 𝑑𝐽

2 𝛽1 , 𝑑𝑄 2 𝛽1

𝑋

𝑡. 𝑢. 𝐽𝐷𝐷 𝑏𝑜𝑒 (𝑆𝐷)

SLIDE 40

Results

40

THEOREM 3.1 i) 𝑑𝐽

2 𝛽1 = 𝑑𝑄 2 𝛽1 − 1

A bank will never invest more than 𝛽 in 𝑚 and there is full consumption smoothing ii) Optimal contract 𝛿𝑧 < 𝛽

SLIDE 41

Results

41

Consumption Smoothing (i.e. 𝐷𝑄

𝑈𝑃𝑈 = 𝐷𝐽 𝑈𝑃𝑈)

PROOF ICC Now, RC C.S. 𝑑𝐽

2 𝛽1 = 𝑑𝑄 2 𝛽1 − 1

i) Maximizing W sub. only to the RC, we obtain:

SLIDE 42

Results

42

PROOF ii) 𝜖𝑋 𝜖𝛿

𝛿= 𝛽/𝑧

< 0 Plugging RC and C.S. conditions in W Investing more than 𝛽 in 𝑚 is sub-optimal

SLIDE 43

Results

43

Assuming that a patient does not run if indifferent, 𝐷𝑄

𝑈𝑃𝑈 = 𝐷𝐽 𝑈𝑃𝑈

NO RUN THEOREM 3.2 i) There exists an optimal contract for the unified bank, also socially optimal ii)

SLIDE 44

Results

44

PROOF i) Setting the RC and the C.S. to hold is sufficient for ii)

𝛿, 𝑑𝐽

2 𝛽1 , 𝑑𝑄 2 𝛽1

𝑛𝑏𝑦 to have a solution 𝑋

Patient agents are indifferent between running and

not running 𝐷𝑄

𝑈𝑃𝑈 = 𝐷𝐽 𝑈𝑃𝑈

Under the optimal contract

No run equilibrium

SLIDE 45

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

ffer policy advise, moral hazard should be included.”

45

SLIDE 46

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.2010.04.006

Diamond, D. W., & Dybvig, P. H. (1983). Bank Runs, Deposit

Insurance, and Liquidity. Journal of Political Economy, 91(3), 401-419. doi:10.1086/261155

Experience 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/docvie w/t53.d54.00048-stat-0162-100089?accountid=10267

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