1. No category

Wholesale Banking and Bank Runs in
Macroeconomic Modelling of Financial Crises
Mark Gertler, Nobuhiro Kiyotaki and Andrea Prespitino
NYU, Princeton, Federal Reserve Board
A key feature of the recent crisis is banking crisis
Slow run on shadow banks from Summer 2007, followed by
fast run after Lehman failure in Fall 2008
Spreads rose and investments fell
Rapid rise in research that incorporates banking and banking
crisis in macro models
A limitation: Mostly focus on retail banks, while the crisis
centered around wholesale banks
Wholesale funding by …nancial intermediaries expanded significantly before the crisis
What are the driving forces? E¢ ciency gain?
Possibility of run in wholesale funding market?
Retail
Sector
Private Depository Institutions
Money Market Mutual Funds
Mutual Funds
Wholesale Originate : Financing Companies
Sector
Real Estate Investment Trusts
Government Sponsored Enterprises
Securitize : Security Brokers Dealers
ABS Issuers
Hold : GSE Mortgage Pools
Funding Companies
Holding Companies
Figure 3: Intermediation by Sector
Wholesale, Retail and Direct Households Intermediation
350
300
250
200
150
100
1975
1980
1985
1990
Housheolds Intermediation
1995
2000
Retail Banks Intermedaition
2005
2010
2015
2020
Wholesale Banks Intermediation
The graph shows the evolution of credit intermediated by the three different sectors. Nominal data from the flow of
funds are deflated using the CPI and normalized so that the log of the normalized value of real wholesale
intermediation in 1980 is equal to 1. The resulting time series are then multiplied by 100
2
Figure 5: Short Term Wholesale Funding
Short Term Wholesale Funding
250
200
150
100
50
0
2000
2002
2004
2006
2008
ABCP
2010
2012
2014
2016
REPO
The graph shows the logarithm of the real value outstanding. Nominal values from Flow of FUnds are deflated
using the CPI
4
Figure 6: Retail short term Funding
Retail Short Term Funding
180
160
140
120
100
80
60
40
20
0
2000
2002
2004
2006
2008
2010
2012
2014
2016
The graph shows the logarithm of the real value outstanding. Nominal values from Flow of Fnds are deflated using
the CPI and normalized so that the log of the normalized value of retail short term funding in 2001 is equal to 100
5
Spreads and Investment
3
900
2
Percerntage points
0
-100
-1
-600
-2
-3
2003
2004
2005
2006
2007
2008
ABCP Spread
FIN CP Spread
Excess Bond Premium
Residential Investment
Durables
Business Investment
2009
Total Investment
2010
-1100
2011
Billions of 2009 Dollars
400
1
We develop a macro model of wholesale and retail banks and
households
Wholesale banks are better at making business loans
Banks are better in monitoring other banks than households
Financial innovation: better monitoring of other banks ! wholesale banks borrow more from retail banks
leverage of each bank
> net leverage of banking sector "
Improve e¢ ciency: larger steady state output and smaller …nancial accelerator
But wholesale banks are more vulnerable to roll-over risk, or
"bank run"
Basic Model
Capital is either intermediated by banks or held by households
Ktw + Ktr + Kth = K
date t
9
>
>
=
date t+1
8
>
>
<
Ktj capital
Ktj capital
!>
j
j
>
j
>
>
: Zt+1Kt output
F (Kt ) goods ;
F
j
j
(Kth)
=
h
>
2
r
j 2
Kt :
>
w
management cost
=0
Retail bank pays ftr = F r0(Ktj ) fee per unit of capital to
households who provide management service
Wholesale Banks
𝑄𝑡 𝐾 𝑤 𝑡 = 𝑁 𝑤 𝑡 +𝐵𝑡
𝑄𝑡
𝐾𝑟
𝐵𝑡 Interbank Loan
𝑡
Retail Banks
Direct Finance
𝑄𝑡 𝐾 ℎ 𝑡
Deposit
𝐷𝑡
Households
Retail deposit and interbank loan contracts
Short term
Promised rates of returns Rt+1 and Rbt+1 are non-contingent
With run, the return to the creditor is the minimum of the
promised return and total realized debtor bank assets per outstanding credit
In Basic Model, bank run is unanticipated
Households maximize
0
Ut = Et @
1
X
i=0
i
1
ln Cth+iA
subject to:
Cth + Dt + QtKth + F h(Kth)
= ZtW h + RtDt
1
+ (Zt+Qt)Kth 1 + ftr Ktr
!
B
t@
1=E
0
B
t@
1=E
0
1
Ct C
A Rt+1
Ct+1
1
Ct
Zt+1 + Qt+1 C
A
Ct+1 Qt + F h0(Kth)
F r (Ktr )
Many bankers of type j = w; r
j
Each has an i.i.d. survival probability of
Banker consumes wealth upon exit:
j
ct
=
j
nt
Preferences are linear in "terminal" consumption
2
Vtj = Et 4
1
X
i
( j )i 1(1
j
i=1
3
)cjt+i5
Each exiting banker replaced by a new banker with an endowj
j
ment w = nt
Net worth njt of surviving bankers
njt = (Zt + Qt)ktj
1
Rtdjt
1
Rbtbjt
1
Date t
𝑍𝑡 is
realized
Date t+1
B/S of Bank j
Deposit:
Asset:
𝑑𝑡
(𝑄𝑡 +𝑓𝑡 )𝑘𝑡
Interbank
loan: 𝑏𝑡
Net worth:
𝑛𝑡
Continue: 𝑉𝑡
Repay 𝑅𝑡+1 𝑑𝑡
and 𝑅𝑏𝑡+1 𝑏𝑡
Retain 𝑛𝑡+1
Exit or continue
divert
Bankrupt
𝜃[𝑑𝑡 + 𝑛𝑡 + 𝜔max(𝑏𝑡 , 0)]
Incentive constraint
𝜃[𝑑𝑡 + 𝑛𝑡 + 𝜔max(𝑏𝑡 , 0)] ≤ 𝑉𝑡
Consider a bank with
and djt to maximize
j
nt
80
>
>
<B
B
t >@
>
:
Vtj = E
= Et
=
j
t+1
= 1: The bank chooses (Qt +
1
1
j
j
ft )kt
9
>
>
=
j
V
j
j t+1 C
C nj
+
j A t+1>
>
;
nt+1
Rkj t+1-Rbt+1 (Qt+ftj )ktj +(Rbt+1-Rt+1)djt +Rbt+1
j
j
j
(Q
+
f
)k
t
kt
t
t
+
j j
btdt
+
j
bt;
where
j
Rkt+1
Qt+1+Zt+1
=
Qt + ftj
subject to
Vtj
1 + djt + !M ax (Qt + ftj )ktj
djt
1; 0
Wholesale banks
Dtw = 0; if !
QtKtw =
w
t
=
w
bt
< (1
!)
w
kt
w w
t Nt
= Ntw + Bt
w
bt
(1
!)
!
w
kt
(Qt + ftr )Ktr + Bt =
r r
t Nt
r
bt
r
bt
r
bt
Retail banks
r
t
Ntj =
j
(Zt + Qt) Ktj
1
=
RtDtj
1
= Ntr + Dtr
RbtBtj
1
+(1
j
)wj
β
αh
Wh
σr
αr
Wr
θ
σw
αw
Ww
ω
σz
ρz
PARAMETERS
Households
discount rate
Intermediation cost
Endowment
Retail Banks
Survival Probability
Intermediation cost
Endowment
Divertable proportion of assets
Wholesale Banks
Survival Probability
Intermediation cost
Endowment
Shrinkage of divertable proportion of assets
Production
std of dividends
autocorrelation of dividends
.99
.03
.006
.95
.0075
.0008
.25
.9
0
.0004
.5
.05
.9
Q
Kr
Kw
Rb
R
Rwk
φw
φr
Y
Ch
Nr
Nw
STEADY STATE
price of capital
retail intermediation
wholesale intermediation
Annual interbank rate
Annual deposit rate
Annual wholesale return on capital
wholesale leverage
retail leverage
output
consumption
retail banks networth
wholesale banks networth
1
.4
.4
1.052
1.04
1.064
25
10
.0225
.0168
.0785
.0160
Financial Innovation: A Permanent Fall in !
Wholesale banks borrow more from retail banks with higher
leverage
Retail banks reduce business loans
Leverage multiples of individual bank is higher, but
(Qt + ftr ) Ktr + Bt
QtKtw
QtKtw + (Qt + ftr ) Ktr
<
<
w
r
r
Nt + Nt
Nt
Ntw
Economy becomes more e¢ cient with larger net output
Financial accelerator becomes SMALLER
Figure 10: Low Frequency Dynamics in Financial Intermediation
k
w
Proportion of total intermediation
0.5
0.45
0.4
0.35
0.3
0.25
0.2
1980
1985
1990
1995
2000
2005
2010
2000
2005
2010
2000
2005
2010
kr
Proportion of total intermediation
0.6
0.55
0.5
0.45
0.4
0.35
Ratio between WS and Retail short term funding
1980
1985
1990
1995
B/D
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1980
1985
1990
1995
9
Figure 12: A recession before and after financial innovation (NO RUN EQUILIBRIUM)
40
-0.04
-0.3
-0.08
-0.4
4
Ann.  from ss
% from ss
-0.01
-0.02
-0.03
-0.04
0
20
40
ERkw-Rb
2
1
0
20
% from ss
% from ss
-0.2
0.2
0.1
0.05
40
0
Rb-R
20
20
Quarters
40
After Financial Innovation (low )
x 10
0
ERkw-R
20
N
40
r
0
-0.05
-0.1
-0.15
-0.2
0
20
Quarters
40
-0.25
0
Before Financial Innovation (high )
11
40
2
w
-0.4
-0.8
20
4
0
40
-0.6
0
0
-3
6
N
0.15
20
Quarters
0
r
0.6
0
x 10
0
1
0
0.1
40
2
0.2
0.4
20
3
0.8
0
0
4
0
40
0.15
0.05
-3
5
3
0
40
x 10
w
% from ss
20
-3
Q
0.01
0
-0.2
-0.06
0
0.2
% from ss
20
-0.1
Ann.  from ss
0
-0.02
kr
0.25
% from ss
-0.04
0
% from ss
% from ss
% from ss
-0.02
-0.06
kw
y
0
Ann.  from ss
z
0
20
Quarters
40
Wholesale Bank Runs
Ex ante, zero probability of a run
If retail banks do not roll over their interbank credit ("run"),
the wholesale banks sell their capital to households and retail
banks who are less e¢ cient in managing capital
In addition to an equilibrium without run, bank run equilibrium
exists if:
(Zt + Qt ) Ktw 1 < RbtBt
Qt
1
the liquidation price of the bank’s assets
After a bank run at t :
Kth + Ktr = K;
Ntw+1 = (1
Nsw
=
w
h
w
(Zs+Qs) Ksw 1
)ww +
RbsBs
w
w
(1
1
i
+(1-
)ww
w
)ww ; 8 s
Household condition for direct capital holding !
8
1
<X
Qt = Et :
i=1
t;t+i[Zt+i
h
9
=
Kth+i];
h
Kth
t+2
Figure 14: A recession followed by a run on wholesale bankers only
kw
0.8
-0.4
-0.6
-0.15
0
20
-1
40
0
ERkw-Rb
-0.04
0
20
Ann.  from ss
Ann.  from ss
-0.02
0.005
0
40
0
w
20
1
0.1
0
20
Quarters
40
0
20
0.01
0.005
0
40
20
Quarters
N
-0.4
-0.6
-1
40
run on wholesale low 
40
r
-0.1
-0.2
-0.3
0
20
Quarters
recession high 
13
20
0
-0.8
0
0
w
-0.2
0.2
40
ERkw-R
0
N
0.3
20
0.015
2
0
0
Rb-R
0
% from ss
2
-0.02
-0.06
40
4
-2
40
0.4
3
20
x 10
r
4
0
0
-3
6
0.01
% from ss
Ann.  from ss
0
40
0.015
0
% from ss
20
0
-0.04
0.2
Run on Wholesale
-1
0.4
-0.8
0.02
-0.06
0.6
% from ss
-0.2
-0.2
Q
0.02
Ann.  from ss
-0.1
1
% from ss
% from ss
% from ss
-0.05
kr
0
% from ss
y
0
40
-0.4
0
20
Quarters
40
Anticipated Bank Runs
Deposit returns Rbt+1
xbt+1
8
>
>
<
Rbt+1 if no bank run
=>
>
: xbt+1Rbt+1 if bank run
2
Qt+1 +
= M in 1;
Rbt+1Bt
6
4
3
Zt+1 Ktw 7
5
Household attaches the probability of bank run as
pt = p(Et(xbt+1)); p (1) = 0; p0( ) < 0
FONC for interbank loan is
Et[(1-pt)
r
r
(R
t+1
kt+1-Rbt+1)+pt
r
r
(R
t+1
kt+1-xbt+1Rbt+1)]
=0
Figure 15: A recession in the model with anticipated runs
0.06
0.04
0.02
-0.04
-0.06
-0.1
40
0
20
-0.8
40
-0.2
0.015
Ann.  from ss
-0.01
% from ss
0.02
-0.03
-0.4
-0.6
0
20
-0.8
40
0
w
0
20
Quarters
40
0
20
20
Quarters
1.5
1
0
-0.6
-1
40
-0.05
-0.1
-0.15
0
20
Quarters
recession with positive probability of a run on wholesale
14
20
Nr
-0.4
40
Rb-R
0
-0.8
0
40
2
0
40
-0.2
0.1
0
x 10
Nw
0.15
20
0.5
0
0.05
0
0
40
0
-3
0.005
% from ss
% from ss
0.5
0
40
0.01
0.2
1
20
2.5
r
1.5
% from ss
20
0.2
ERkw-Rb
0
-0.04
0
B
0
-0.02
0.3
0.1
Ann.  from ss
Q
% from ss
-0.4
% from ss
20
0.4
-0.2
-0.6
-0.08
0
0.5
% from ss
-0.02
kr
0
% from ss
0.08
0
kw
y
0
% from ss
% from ss
p
0.1
40
-0.2
0
recession
20
Quarters
40
Figure 16: A recession followed by a run in the model with anticipated runs
p
0
0.04
-0.2
-0.05
-0.1
-0.15
0.02
-0.2
40
0
20
Ann.  from ss
Ann.  from ss
-0.06
0.01
0.005
0
40
0
w
20
2
0.3
1
0
20
Quarters
40
0.02
0.006
0.004
0.002
0
0
20
N
0.01
0
40
N
-0.6
-1
40
r
-0.1
-0.2
-0.3
0
20
Quarters
recession followed by anticipated run on wholseale
15
20
0
-0.4
40
0
w
-0.8
20
Quarters
40
0.005
-0.2
0
20
0.015
0
0.2
0
0
ERkw-R
0.008
40
0.1
0
0
40
0.025
% from ss
0.4
20
0.01
r
3
0.4
Rb-R
0.015
% from ss
% from ss
-0.04
0
0
ERkw-Rb
-0.02
% from ss
-1
40
0.02
0
-1
20
0.6
0.2
-0.8
Q
0.02
-0.08
-0.6
Ann.  from ss
20
-0.4
% from ss
0
0.8
% from ss
0.06
kr
0
% from ss
% from ss
% from ss
0.08
0
kw
y
0.1
40
-0.4
recession
0
20
Quarters
40