Bubbles, Banks and Financial Stability
Kosuke Aoki and Kalin Nikolov
University of Tokyo & ECB

29 May 2012, CIGS

Aoki & Nikolov (Tokyo & ECB)

Bubbles, Banks and Financial Stability

2012/05/29, CIGS

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Introduction

Bursting bubbles: an important factor in many banking and economiccrisis- Subprime/Japan/Scandinavia
But occationally busts can occur without a crisis - ‘Dot Com’ bubbleof 1998-2000
Aim of the Paper:
Build a limited commitment economy with explicit financial
intermediation
Model’s impolications for the interaction of bubbles and bank balance
sheetsAoki & Nikolov (Tokyo & ECB)

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The Economic Questions

1Who holds the bubble?

2

How does the real impact of the bubble depend on who holds it?

3

How does the financial safety net affect bubbly equilibria?

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Brief Answers

Question 1 : Who holds the bubble?
Answer:No financial safety net: savers
Banks hold bubbles if financial safety net exists

Question 2: Real impact of the bubble
Answer: Bubbles held by banks lead to bigger output fluctuations.

Question 3: financial safety net and bubbly equilibria
Answer: (1) bubbles are bigger; (2) more fragile bubbles can exist.

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Rational Bubbles: A (very) brief survey

General economic problem: how to create efficient means of saving
OLG (no credit constraints)
Samuelson (1958)
Tirole (1985), Weil (1987)

Models with credit/resaleability constraints
Woodford (1990)
Kiyotaki-Moore (2008)
Caballero and Krishnamurthy (2006)
Martin and Ventura (2011), Farhi and Tirole (2011), Hirano andYanagawa (2011)

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Rational bubbles in a credit constrained economy

Inside liquidity created from private intermediation- debt for borrowers- stores of value for lenders
Limited commitment - too little inside liquidity- inefficient stores of value- low interest rates
Bubbles- replace inefficient stores of value- but: fragile

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Our contribution

Modelling financial intermediaries explicitly
Result: multiple asset holders with different economic roles
This matters: asset price bubbles have a different real impact
depending on who holds them

Impact of moral hazard on bubbly equilibria

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Entrepreneurs
Utility∞E0 ∑ βt ln ctt =0Production function
yt +1 = aht ,a = aH , aL ,aH > aL

Budget constraint: when becomes a borrower;
ct + wt ht − lt +µt mte 6 (1 − τ t ) yt − Rtl −1 lt −1 + µt mte−1|{z}|{z}investment

loan

when becomes a saver;
ct + wt ht + dt +µt mte 6 (1 − τ t ) yt + Rtd−1 dt −1 + µt mte−1|{z}depositBorrowing constraint
Rtl lt + Et Υt +1 ≤ θyt +1 ,Aoki & Nikolov (Tokyo & ECB)

0<θ<1Bubbles, Banks and Financial Stability

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8 / 26Entrepreneurs’ behavior: low productivity

In equilibrium, the productives borrow and the unproductives save.
log utility =⇒ consumption is (1 − β) share of wealth
The unproductives allocate savings between deposit, bubbles and own
production (if they produce)
#
"
#"
#"
1 − τ t +1
1 − τ t +1 aL
1 − τ t +1 µ t +1d= Et
R t ≥ Et
Et
µt
ctL+1ctL+1ctL+1 wt
whereµ t +1 =Aoki & Nikolov (Tokyo & ECB)µt +1 w.p. π
0 w.p. 1 − π

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Entrepreneurs’ behavior: high productivity

When borrowing constraints bind (aH /wt > Rtl ), the productives
borrow up to the limit. Leveraged rate of return isaHaH (1 − θ̃ t )
>
> Rtl
wt
wt − θ̃ t aH /Rtl
where
θ̃ t =

θ − Et τ t + 1≤θ
1 − Et τ t + 1

The productives do not buy bubbles

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BanksRisk neutral, exit with probability 1 − γBudget constraints and state evolution
ctB + lt +µ t mt
| {z }

bubble purchase=nt +dt|{z}net worthnt +1 = Rtl lt + µt +1 mt − Rtd dt
Borrowing constraint( 1 − λ ) dt 6| {z }

diversion value

V (nt )
| {z },

0<λ<1

continuation value of the bank

Constraint binds when Rtl > Rtd . V (nt ) given by
V (nt ) = βEt [γV (nt +1 ) + (1 − γ) nt +1 ]Aoki & Nikolov (Tokyo & ECB)

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Banks’ behaviour
Risk neutrality implies thatV (nt ) = φt ntβ (1 − γ) + γEt φt +1 Rtl
φt = l R d > 1.
t
1 − β (1 − γ) + γEt φt +1 R1t −−λExpectation of high future leverage allows the bank to borrow more
(i.e. high leverage today)
Deposits (under a binding collateral constraint on banks)
Dt =φtγ Nt(1 − λ )| {z }≈leverage

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Banks’ behabiour (cont)Banks’ portfolio choice between bubbles and loansµ̃t +1≤ Et [( 1 − γ + γφt +1 )]Rtl
Et (1 − γ + γφt +1 )µtwhereµ̃t +1 =µbt+1 with prob. π
ρt +1 µt with prob. 1 − πρ captures the financial safety net

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Workers: (passive role)

Utility∞

U = E0 ∑ β tt =01+ ηhctw − t1+η!

No collateralisable assets —> cannot borrow
Do not save in equilibrium due to low interest rate
Labour supply
hts = wtηAoki & Nikolov (Tokyo & ECB)

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Government

The government only spends money on bailing out banks
Balanced budget
τ t Zt = ρt mtb−1 µt −1

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Bubbles and the rates of return
deterministic steady stateIn equilibrium bubbles must be (a) attractive to hold and (b)affordable
Bank-held bubbles
Rtd < bubble return = Rtl 6 1
Saver-held bubbles
Rtd = bubble return 6 1
Banks choose not to buy bubbles when Rtl > Rtd = bubble return

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Who holds the bubble: stochastic steady state

Base line case: ρ = 0
π = 0.965
0

Aoki & Nikolov (Tokyo & ECB)

% of bubbles held by banks
π = 0.975 π = 0.985 π = 0.995
00.016
0Bubbles, Banks and Financial Stability

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Introducing the government financial safety net

Consider ρ > 0
What effect does it haveon bank’s bubble holdings?
on bubble size?
on bubble amplification?

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Impact of the safety net
Banks’ bubble holdings as % of total

ρ = 0.00
ρ = 0.25
ρ = 0.50
ρ = 0.75

π = 0.965
1.000
1.000

π = 0.975
0.000
0.000
0.312
1.000

π = 0.985
0.016
0.068
0.183
0.660

π = 0.995
0.000
0.000
0.0000.016

ρ = 0: banks hold few bubbles at intermediate values of π(risk-sharing)ρ >> 0: banks’ bubble holding grows at low values of π(risk-shifting)Aoki & Nikolov (Tokyo & ECB)

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Impact of the safety net
bubble size as % of GDP

ρ = 0.00
ρ = 0.25
ρ = 0.50
ρ = 0.75

π = 0.965
0.008
0.361

π = 0.975
0.118
0.118
0.245
0.411

π = 0.985
0.463
0.467
0.475
0.511

π = 0.995
0.674
0.674
0.674
0.676

High π: ρ has little effect on bubble sizeρ ↑ ⇒ bubble size ↑ dramatically at low values of π

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Effects of bubble holdings on banks% of bubbles held by banks
Bubble to GDP ratioE(Bubble Return|bank) - R lE(Bubble Return|saver) - R dBank NW/GDP (pre-crash)
Bank Loss/GDP% fall in bank NW

ρ = 0.00
0.000
0.296
-0.002
0.010
0.055
0.000
0.000

ρ = 0.25
0.081
0.348
0.005
0.010
0.063
0.021
0.337

ρ = 0.500.237
0.396
0.009
0.009
0.074
0.047
0.630

ρ = 0.75
0.881
0.442
0.009
0.001
0.116
0.097
0.842

The percentage fall in bank net worth is computed after the receipt ofgovernment assistance.
Lage increase in net worth before crash and loss after crash

Aoki & Nikolov (Tokyo & ECB)

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2012/05/29, CIGS

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How do bubbles affect the economy?

Decomposition of output
Y = aL HtL + aH HtH

i
1 h L
=a ( βZt + γNt ) − aL µt + aH − aL ( βst Zt + Lt )
wt

(1)
(2)

w : production cost
1st term: liquidity effect
2nd term: crowding out
3rd term: reallocation
share of productives
credit supply

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Effects of bubbles on the economy1

Bank bubble holdings (% of total)
Total Y ↑ relative to ’no bubble’ SS(1) Liquidity effect(2) Bubble ’crowding out’ effect(3) Investment composition effect...of which(3.1.) Productive net worth(3.2.) Bank lending(4) Labour costs

ρ=00.00
1.03
19.64- 19.540.95

ρ = 1/3
0.11
1.32
20.01
- 19.671.04

ρ = 2/3
1.00
3.11
21.78
- 19.99
1.65

0.31
0.64
- 0.020.34
0.70- 0.060.54
1.11- 0.32

Output larger when banks hold bubbles
high contribution of liquidity effect and increase in bank lending
1 Percentage point contributions of each channel to total increase in output
relative to bubbleless SS
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Costs of funds and bubble holding2

Bank net worth (% increase)
Bank lending
Lending-Deposit spread

ρ=014.43
13.03
0.02

ρ = 1/3
25.03
14.35- 0.01

ρ = 2/3
113.7
22.69- 0.22

Increase in net worth due to bubble risk premiumThis results in increase in credit supply...
and decline in spread

2 percentage point deviation from bubbleless steady state
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Dynamics
OutputBank capital

1.035

2.4

1.03

2.2
2

1.025

1.8

1.02

1.6
1.015
1.4
1.01
1.2
1.005

110.8

0.995

0.6

0.99

0.4
1112131

Saver bubbl e

41

11121

Bank bubbl e

Saver bubbl e

Loans

3141

Bank bubbl eAggregate investment

1.25

1.03

1.025
1.2
1.02
1.15
1.015

1.1

1.01

1.005
1.05
1
10.995

0.95

0.99
11121

Saver bubbl e

31

41

111

Bank bubbl e

21

Saver bubbl e

31

41

Bank bubbl eFigure 3: Comparing a bank-held (solid line) and a saver-held (dashed line) bubble

Large expansion and severe contraction under bank bubble
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Conclusions

Bubbles held by banks have a more amplified impact on the economy
while they survive
when they burst

Banks invest in bubbles
when their risk is underwritten by the government

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