Booms and Banking Crises F. Boissay, F. Collard and F. Smets

Booms and Banking Crises
F. Boissay, F. Collard and F. Smets
Macro Financial Modeling Conference
Boston, 12 October 2013
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Booms and Banking Crises
MFM October 2013 Conference
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Disclaimer
The views expressed in this presentation are our own and do not
necessarily re‡ect those of the European Central Bank or the Eurosystem
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Motivation/Objective
Better understand the dynamics of …nancial and real business cycles
A few features are common to …nancial recessions (i.e. recessions
concomitant with banking crises):
Fact #1: They are rare events
Fact #2: They are deeper and last longer
Fact #3: Unlike other types of recessions, …nancial recessions
follow credit booms
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Motivation/Objective
Financial recession statistics
Recessions
Financial
Other
Severe
2.36
8.93
4.05
4.05
2.32***
-6.84***
1.65
-3.75
2.46***
-9.28***
1.25
-0.89
4.56***
0.01
1.33
0.40
-3.59*
-1.24
-1.69
-2.44
Frequency (%)
Duration (years)
Magnitude (%)
Mild
Credit Boom
% credit growth 2 years before peak (a)
Credit Crunch
% credit growth 2 years after peak (a)
Source: Schularik et al. (2011), data for 14 OECD countries, 1870-2008. Crises de…ned as in Laeven and
Valencia (2008); *,**,***: the di¤erence is statistically signi…cant at 10%, 5%, 1%; (a) HP–…ltered credit.
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Motivation/Objective
In most DSGE models …nancial recessions are big negative shocks
ampli…ed
Can explain Facts #1 & #2
Cannot explain Key Fact #3
Boissay - Collard - Smets
Booms and Banking Crises
crises are not random
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Our Framework
Textbook stochastic optimal growth model (RBC)
Heterogenous banks with intermediation and storage technologies
Interbank market subject to MH and AI
A banking crisis is an interbank market freeze
Spill–over and feedback e¤ects between the interbank market, the
retail corporate loan market, and the real economy
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Main Results
1
Normal times feature productivity–driven business cycles with a small
…nancial accelerator; a crisis every 42 years.
Boissay - Collard - Smets
Booms and Banking Crises
MFM October 2013 Conference
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Main Results
1
Normal times feature productivity–driven business cycles with a small
…nancial accelerator; a crisis every 42 years.
2
The typical banking crisis follows an unusually long sequence of
small, positive, transitory productivity shocks — No need for a
large negative …nancial shock
Boissay - Collard - Smets
Booms and Banking Crises
MFM October 2013 Conference
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Main Results
1
Normal times feature productivity–driven business cycles with a small
…nancial accelerator; a crisis every 42 years.
2
The typical banking crisis follows an unusually long sequence of
small, positive, transitory productivity shocks — No need for a
large negative …nancial shock
3
High productivity generates a credit boom and a ballooning banking
sector
Boissay - Collard - Smets
Booms and Banking Crises
MFM October 2013 Conference
7 / 38 ()
Main Results
1
Normal times feature productivity–driven business cycles with a small
…nancial accelerator; a crisis every 42 years.
2
The typical banking crisis follows an unusually long sequence of
small, positive, transitory productivity shocks — No need for a
large negative …nancial shock
3
High productivity generates a credit boom and a ballooning banking
sector
4
As productivity gains peter out, excess savings arise ("saving glut")
and interest rates fall; counterparty fears rise in the interbank market,
which may lead to a freeze and banking crisis
Boissay - Collard - Smets
Booms and Banking Crises
MFM October 2013 Conference
7 / 38 ()
Main Results
1
Normal times feature productivity–driven business cycles with a small
…nancial accelerator; a crisis every 42 years.
2
The typical banking crisis follows an unusually long sequence of
small, positive, transitory productivity shocks — No need for a
large negative …nancial shock
3
High productivity generates a credit boom and a ballooning banking
sector
4
As productivity gains peter out, excess savings arise ("saving glut")
and interest rates fall; counterparty fears rise in the interbank market,
which may lead to a freeze and banking crisis
5
The subsequent …nancial recession is deep and long because of a
credit crunch; credit–to–GDP ratio predicts …nancial recessions
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Related literature
Kiyotaki-Moore (1997), Bernanke-Gertler-Gilchrist (1999),
Christiano-Motto-Rostagno (2013), Gertler-Kiyotaki (2009),
Gertler-Karadi (2010):
6= Full equilibrium non-linearities, such as sudden bank runs
Bianchi (2009), Bianchi-Mendoza (2010):
6= Endogenous interest rates play a key role
Brunnermeier-Sannikov (2012), He-Krishnamurthy (2012):
6= Typical crisis follows a rare, long sequence of positive TFP shocks
6= Typical crisis identi…ed as a bank run, not as a binding borrowing
constraint
Gertler-Kiyotaki (2012)
6= Bank run is market based and rationally expected
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Model setup
Overview
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Representative Household and Firm
Firm: maxfkt ,ht g π t = F (kt , ht ; zt ) + (1
δ)kt
Rt kt
wt ht
Household:
max
fat +τ +1 ,ct +τ ,h t +τ g∞
τ =0
Et
∞
∑ β τ u ( c t + τ , ht + τ )
τ =0
subject to budget constraint
ct + at +1 = rt at + wt ht + π t + χt
Notice that rt 6 Rt (spread) and kt 6 at (credit crunch)
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The Banking Sector
Banks are atomistic, competitive, and price takers
Continuum of heterogeneous 1–period banks p, with cdf µ(p ) over
(0, 1)
Bank p’s net return per unit of corporate loan is pRt
It is bene…cial to relocate funds, but relocation is impaired due to:
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The Banking Sector
Banks are atomistic, competitive, and price takers
Continuum of heterogeneous 1–period banks p, with cdf µ(p ) over
(0, 1)
Bank p’s net return per unit of corporate loan is pRt
It is bene…cial to relocate funds, but relocation is impaired due to:
Asymmetric information: p is private information
Boissay - Collard - Smets
Booms and Banking Crises
MFM October 2013 Conference
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The Banking Sector
Banks are atomistic, competitive, and price takers
Continuum of heterogeneous 1–period banks p, with cdf µ(p ) over
(0, 1)
Bank p’s net return per unit of corporate loan is pRt
It is bene…cial to relocate funds, but relocation is impaired due to:
Asymmetric information: p is private information
Moral hazard: bank p may borrow φt and walk away ("diversion")
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The Banking Sector
Bank p has 4 options:
1. Lend to other banks on the interbank market =) ρt
2. Store goods =) γ
3. Raise funds φt from interbank market and lend to …rm
=) pRt (1 + φt ) ρt φt
4. Raise funds φt from interbank market and walk away =) γ (1 + θφt )
Incentives to divert depend on the corporate loan rate: the
lower Rt , the higher these incentives, and the more counterparty fears
on the interbank market
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The Borrowing Bank’s Problem
Borrowing bank p solves:
max rt (p )
φt
PC :
IC :
pRt (1 + φt )
pRt (1 + φt )
ρt φt
ρt φt > ρt
γ (1 + θφt ) 6 ρt
Pro…ts are fully distributed to household: rt
Boissay - Collard - Smets
Booms and Banking Crises
) p > p t ρt /Rt
) φt = (ρt γ)/θγ
R1
0
rt (p ) dµ (p )
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Interbank Market Equilibrium
Interbank market clearing condition
Supply (+)
z }| {
µ (p t )
with p t
Boissay - Collard - Smets
=
z
Demand bends backward (+ or
(1
|
µ (p ))
{z t }
"extensive margin" ( )
}|
ρt /Rt and φt = (ρt
Booms and Banking Crises
)
φt
|{z}
{
"intensive margin" (+)
γ)/θγ
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Interbank Market Equilibrium
The interbank market freezes when the retail corporate loan rate is below a threshold
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Interbank Market Equilibrium
The interbank market freezes when the retail corporate loan rate is below a threshold
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Interbank Market Equilibrium
The interbank market freezes when the retail corporate loan rate is below a threshold
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Absorption Capacity and Market Freeze
Proposition (Interbank loan market freeze): The interbank loan
market is at work if and only if at 6 at
fk 1 (R + δ 1; zt ), and
freezes otherwise.
The interbank market improves e¢ ciency but freezes when Rt < R
In general equilibrium, Rt is driven by savings (at ) and technology
(zt ). Hence the interbank market freezes when at > a(zt )
Threshold a(zt ) is the banking sector’s "absorption capacity"
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Quantitative Analysis
Calibration
Calibration of the real side is standard
Financial sector (γ, θ, µ(.)) is calibrated so that:
Crisis probability is 2.3%
Average interest rate spread is 1.7%
Average corporate loan rate of 4.4%
The model is solved numerically by a collocation method
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Quantitative Analysis
Optimal savings rule: exogenous versus endogenous crises
Variety of crises: shock–driven (S) and credit boom–driven (U)
History suggests that credit–boom driven crises prevail
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Quantitative Analysis
Typical path to crisis
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Quantitative Analysis
Typical path to crisis
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Quantitative Analysis
Typical path to crisis
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Quantitative Analysis
Intuition
1
At the beginning, a positive shock brings TFP above its mean
Credit demand rises. Return on savings goes up. The household
accumulates assets for consumption smoothing
2
TFP goes down back to mean but remains above it for a long time
Credit demand decreases, while the household keeps on accumulating
savings; interest rates go down
3
As the probability of a crisis increases, the household maintains
savings to hedge against a more likely loss of revenue, which works to
reduce interest rates and to raise the likelihood of a crisis even further
— saving glut externality
4
A crisis breaks out as the corporate loan Rt rate crosses threshold R
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Quantitative Assessment
Financial recession statistics
Financial
Frequency (%)
Recessions
Other
Severe
Mild
2.35
8.94
3.76
3.76
2.08
-12.60
1.39
-4.98
2.22
-11.32
1.04
-3.28
% credit growth 2 years before peak (a)
3.81
0.11
2.33
0.06
Credit Crunch
% credit growth 2 years after peak (a )
-5.09
0.09
-2.97
0.02
Duration (years)
Magnitude (%)
Credit Boom
(a) HP–…ltered credit.
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Welfare
%-Loss in permanent consumption
Financial frictions
FBA – DEA
De…cient institutions
FBA – CEA
Externalities
CEA – DEA
Fin. under-development
DEA – NIM
2.20
1.53
0.61
4.61
FBA: Fist Best Allocation; DEA: Decentralized Equilibrium Allocation
CEA: Constrained E¢ cient Allocation; NIM: No Interbank Market
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Concluding Remarks
Develop a simple quantitative macro-model with banking crises,
where crises are not caused by large, negative, …nancial shocks but
rather by long sequences of small, positive, productivity shocks
Credit booms are conducive to crises
Highlight the role of consumption smoothing and saving glut
externalities
From a policy making perspective:
Framework for both crisis management and crisis prevention
DSGE-based probability of a crisis
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THANK YOU
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Return on Deposits and Corporate Loan Supply
Return on deposits:
rt =
8
R 1 dµ(p )
>
>
< Rt p t p 1 µ(p t ) , if an equilibrium with trade exists
>
>
: Rt
γ
Rt
γ
Rt µ
+
Corporate loan supply
kts =
Boissay - Collard - Smets
R1
γ
Rt
p dµ (p )
, otherwise.
8
>
< at , if an equilibrium with trade exists
>
:
1
µ
γ
Rt
at , otherwise
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Interest Rates
Endogenous and exogenous sources of instability
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Optimal Decision Rules
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Quantitative Analysis
Two counter–factual experiments
Typical paths to crisis without smoothing or externality
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Quantitative Assessment
Dynamics of output and credit gaps around recessions
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Quantitative Assessment
Dynamics of output and credit gaps around recessions
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Crisis Prediction
Type–I and Type–II errors
Model
Probability
(benchmark)
(1)
z
a
—
—
0.03
0.00
0.55
0.00
Type-I errors (%)
Type-II errors (%)
N. warnings
31.43
4.85
30,215
100.00
0.00
0
N. crises
N. obs (simul.)
11,739
468,769
11,739
468,769
R2
F-Test
Boissay - Collard - Smets
Booms and Banking Crises
Probability regressions
(2)
(3)
(4)
Logit
(5)
(a, z )
K /Y
K /Y
0.69
0.00
0.72
0.00
0.38
0.00
72.50
4.11
22,020
56.87
5.55
30,439
36.79
4.92
29,911
35.97
5.16
31,089
11,739
468,769
11,739
468,769
11,739
468,769
11,739
468,769
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Sensitivity Analysis
Financial recession statistics
Baseline
Frequency (%)
Duration (years)
Magnitude (%)
Boissay - Collard - Smets
2.35
2.08
-12.60
σ
ν
θ
λ
10
0.25
0.15
20
σz
0.025
ρz
0.70
Altern.
TFP
4.74
1.75
-10.61
3.45
2.31
-16.33
5.87
1.72
-9.29
5.73
1.84
-12.05
4.56
2.09
-15.40
4.34
2.22
-17.82
2.32
1.99
-10.86
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Endogenous Cycles
Two deterministic versions of the model (constant TFP)
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Model With Both TFP and Financial Shocks
Typical path to crisis
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