Financial Intermediation and Credit Policy
In
Business Cycle Analysis
Mark Gertler and Nobuhiro Kiyotaki
NYU and Princeton
October 2009
0
Old Motivation (for BGG 1999)
• Great Depression
• Emerging market crises over the past quarter century
.
1
New Motivation (for GK 2009)
• Global economy during Bernanke’s tenure as Fed Chair
2
Figure 1: Selected Corporate Bond Spreads
Basis points
NBER
Peak
Quarterly
800
Q4.
Avg. Senior Unsecured
Medium-Risk Long-Maturity
Baa
600
400
200
0
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
Note: The black line depicts the average credit spread for our sample of 5,269 senior unsecured
corporate bonds; the red line depicts the average credit spread associated with very long maturity
corporate bonds issued by firms with low to medium probability of default (see text for details);
and the blue line depicts the standard Baa credit spread, measured relative to the 10-year Treasury
yield. The shaded vertical bars denote NBER-dated recessions.
37
100
0.02
50
0.01
0
0
real GDP growth (right)
−50
−0.01
lending standards (left)
−100
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
−0.02
Challenges for Writing a Handbook Chapter
• Much of the relevant literature predates August 2007
• Most of the work afterwards is still in preliminary working paper form.
3
Our Approach: Look both Forward and Backward
• Present Canonical Framework relevant to thinking about current crisis.
— Not a comprehensive or complete description
— Only a first pass at organizing thinking
— Goal is to lay out issues for future research
• Build heavily on earlier research.
4
Aspects of the Current Crisis We Try to Capture
• Disruption of Financial Intermediation
— Much of the recent macro literature has emphasized credit frictions on nonfinancial borrowers and has treated intermediaries largely as a veil.
• Unconventional Monetary Policy
5
Unconventional vs. Conventional Monetary Policy
Conventional: The central bank adjusts the short term rate to affect the market
structure of interest rates.
Unconventional: The central bank lends directly in private credit markets.
Section 13.3 of the Federal Reserve Act: "In unusual and exigent circumstances.. the
Federal Reserve may lend directly to private borrowers to the extent it judges the loans
to be adequately secured."
6
Federal Reserve Assets
Trillions
of Dollars
3
2.5
2
1.5
1
Repo
Treasury Securities
Other
AMLF
Maiden Lane I, II, III
Other Credit (&AIG ext)
PDCF, Other Broker-dealer
TAF
Primary Credit
Currency Swaps
3
Agency MBS
Agency Debt
TALF
CPFF
2.5
2
1.5
1
0.5
0.5
0
Aug-07
0
Oct-07
Dec-07
Feb-08
Apr-08
Jun-08
Aug-08
Oct-08
Dec-08
Feb-09
Apr-09
Federal Reserve Liabilities
2.5
2
1.5
1
Trillions of
Dollars
2.5
Treasury, SFA
2
Reserve Balances
Treasury, ga
Reverse Repo
Other
Currency
1.5
1
0.5
Source:
H41,
0
BloombergAug-07
0.5
0
Oct-07
Dec-07
Feb-08
Apr-08
Jun-08
Aug-08
Oct-08
Dec-08
Feb-09
Apr-09
Liquidity Facilities
CPFF and Commercial Paper Outstanding
Billions of Dollars
Billions of Dollars
1,900
500
Federal Reserve
Net Holdings
(right axis)
1,800
1,700
400
300
1,500
400
AA Asset-Backed
Dec-08
200
0
Mar-09
-100
Mar-08
700
600
500
400
300
200
100
100
Unsecured CPFF Fee
AA Non-Financial
0
-100
Jun-08
Sep-08
Dec-08
Mar-09
Source: Federal Reserve Board, Haver, Bloomberg
Overnight Financing Spreads
Billions of Dollars
Billions of Dollars
150
150
200
Agency Debt
150
150
100
Schedule 1
50
50
Apr 16:
0.0
Apr 17:
8.0
Apr 17:
0.0
50
0
0
Dec-08
250
Agency MBS
100
100
Basis Points
Basis Points
250
200
Apr 15:
20.6
Schedule 2
Sep-08
Apr 17:
6.0
0
TSLF Schedule 1 & 2 Total Outstanding
Jun-08
500
AA Financial
100
Apr 17:
1473.7
Sep-08
200
Source: Federal Reserve Board, Haver, FDIC
0
Mar-08
Apr 17:
143.0
Apr 17:
61.0
Apr 17:
27.0
ABCP CPFF Fee
A2/P2/F2
Non-Financial
300
Apr 17:
235.8
FDIC
TLGP
(right axis)
Jun-08
Basis Points
Basis Points
700
600
Mar 31:
336.3
Total
(left axis)
1,600
1,400
Mar-08
3-month CP Rates over OIS
Mar-09
-50
Mar-08
50
0
-50
Jun-08
Sep-08
Dec-08
Mar-09
Note: Spreads are between overnight agency debt and
MBS and Treasury general collateral repo rates
Source: Bloomberg
Source: Federal Reserve Board
100
Agency MBS to Average 5y and 10y Yields
Agency MBS Transactions
Billions of Dollars
Billions of Dollars
300
300
Outright
Purchases
Apr 15:
287.2
200
Basis Points
Basis Points
300
250
Fannie Mae
100
200
250
100
200
0
150
Mar-08
200
Apr 17:
176.4
150
Temporary OMO
Accepted
Apr 17:
0.0
0
Mar-08
Jun-08
Sep-08
Source: Federal Reserve Board, Haver
Dec-08
Mar-09
100
Jun-08
Sep-08
Source: FRB, Haver, Bloomberg
Dec-08
Mar-09
Note: Spreads are agency 30 year on-the-run
coupon to average of 5 and 10 year yields
What We Do
• Develop a quantitative DSGE model that allows for financial intermediaries that
face endogenous balance sheet constraints.
• Use the model to simulate a crisis that has some of the features of the current
downturn.
• Assess how unconventional monetary policy (direct central bank intermediation.)
could moderate the downturn.
• Discuss Open Issues and Extensions
7
Model: Physical Environment
• Firm dispersed across islands, with perfectly mobile labor:
Yt = AtKtαL1−α
t
• I.I.D. prob. π i of arrival of investment opportunities across islands.
Kt+1 = [ψ t(It + π i(1 − δ)Kt)] + [(1 − π i)ψ t(1 − δ)Kt]
= ψ t[It + (1 − δ)Kt]
• Resource Constraint
Yt = Ct + [1 + f (
• Preferences
Et
∞
X
i=0
It
It−1
)]It + Gt
β i[ln(Ct+i − hCt+i−1) −
χ
1+ϕ
Lt+i ]
1+ϕ
8
Beginning of the period
Retail financial
market
Households
Banks
Deposit
During the period
New and
old loans
Bank with fund
shortage
Firms with new
investment
opportunity
Investing regions
Interbank market
Non-investing
regions
Banks with
surplus fund
Old
loans
Firms without
new investment
opportunities
Households
• Within each household, 1 − f "workers" and f "bankers".
• Workers supply labor and return their wages to the household.
• Each banker manages a financial intermediary and also transfers earnings back to
household..
• Perfect consumption insurance within the family.
9
Households (con’t)
To limit bankers’ ability to save to overcome financial constraints:
1 )
• With i.i.d prob. 1 − σ, a banker exits next period. (average survival time = 1−σ
• Upon exiting, a banker transfers retained earnings to the household and becomes
a worker.
• Each period, (1 − σ)f workers randomly become bankers, keeping the number in
each occupation constant
• Each new banker receives a "start up" transfer from the family.
10
Households (con’t)
max Et
∞
X
i=0
β i[ln(Ct+i − hCt+i−1) −
χ
1+ϕ
Lt+i ]
1+ϕ
s.t.
Ct = WtLt + Πt + Tt + RtDt − Dt+1
• Dt ≡ short term bonds (intermediary deposits and government debt)
• Πt ≡ payouts to the household from firm ownership net the transfer it gives to
its new bankers.
11
Financial Intermediaries:
Case of No Idiosyncratic Risk (i.e. π = 1)
(equivalent to π < 1 with perfect interbank market)
• Intermediary Balance Sheet
Qtst = nt + dt
• Evolution of Net Worth
nt+1 = Rkt+1Qtst − Rt+1dt
= (Rkt+1 − Rt+1)Qtst + Rt+1nt
12
Financial Intermediaries (con’t)
Vt = max Et
= max Et
X
(1 − σ)σ iΛt,t+i(nt++i)
i=1
X
(1 − σ)σ iΛt,t+i[(Rkt+i − Rt+i)Qt+ist+i
i=1
+ Rt+int+i]
• With Frictionless Capital Markets:
EtΛt,t+1+i(Rkt+1+i − Rt+1+i) = 0
• With Capital Market Frictions:
EtΛt,t+1+i(Rkt+1+i − Rt+1+i) ≥ 0
13
Financial Intermediaries (con’t)
• Agency Problem: After the banker/intermediary borrows funds at the end of
period t, it may divert the fraction θ of total assets back to its family.
• If the intermediary does not honor its debt, depositers can liquidate the intermediate and obtain the fraction 1 − θ of initial assets
• Incentive Constraint:
Vt ≥ θQtst
14
Financial Intermediaries (con’t)
One can show:
Vt = μtQtst + ν tnt
with
ν t = EtΩt+1
μt = EtΛt,t+1(Rkt+1 − Rt+1)Ωt+1
where Ωt+1 is the shadow value of a unit of net worth at t + 1.
Ωt+1 = 1 − σ + σ(ν t+1 + φt+1μt+1)
15
Financial Intermediaries (con’t)
• Re-writing the incentive constraint:
μtQtst + ν tnt ≥ θQtst
• =⇒Endogenous leverage constraint:
Qtst ≤ φtnt
with
• φt = Maximum leverage ratio
νt
φt =
θ − μt
16
Financial Intermediaries (con’t)
• Since the leverage ratio φt does not depend on firm-specific factors, we can
aggregate:
QtSpt = φtNt
Spt ≡ total assets privately intermediated
Nt ≡ total intermediary capital
• Evolution of Net Worth::
Nt = σ[(Rkt − Rt)φt + R]Nt−1 + ξRktQt−1St−1
where ξ is the fraction of gross assets transferred to new entrepreneurs
17
Credit Policy
(Case of Direct Lending)
• Central bank intermediation supplements private intermediation:
QtSt = QtSpt + QtSgt
• The central bank issues government debt that pays Rt+1 and then lends to nonfinancial firms at Rkt+1.
• Efficiency cost of τ per unit of gov’t credit provided.
• Unlike private intermediaries, the central bank is not "balance-sheet" constrained.
18
Credit Policy (con’t)
QtSgt = ϕtQtSt
=⇒
QtSt = QtSpt + QtSgt
= φtNt + ϕtQtSt
=⇒
QtSt =
1
φtNt
1 − ϕt
QtSt is increasing in the intensity of credit policy, as measured by ϕt.
19
Non-financial Firms
• Goods Producers:
— Issue state-contingent claims (equity)
St = Kt+1
Rkt+1 = ψ t+1[Zt+1 + (1 − δ)Qt+1]/Qt
Yt
with Zt = α K
t
• Hire Labor
(1 − α)
Yt
Lt
20
Non-financial Firms (con’t)
• Capital producers:
max Et
∞
X
Λt,τ
τ =t
(
"
Qiτ Iτ − 1 + f
Ã
Iτ
Iτ −1
!#
Iτ
)
— Investment increasing in Qt :
Qit = 1 + f
Ã
It
It−1
!
It
It
It+1 2 0 It+1
0
+
f(
) − EtΛt,t+1(
) f(
)
It−1 It−1
It
It
21
Government Budget Constraint and Credit Policy
• Government Budget Constraint
G + τ ψ tQtKt+1 = Tt + (Rkt − Rt)Bgt−1
• Credit Policy (contingent on a "crisis")
ψ t = ν[Et(Rkt+1 − Rt+1) − (Rk − R)]
22
β
γ
χ
ϕ
πi
θ
ξ
σ
α
δ
If ”/f 0
G
Y
Table 1: Parameter Values for Baseline Model
Households
0.990 Discount rate
0.500 Habit parameter
5.584 Relative utility weight of labor
0.333 Inverse Frisch elasticity of labor supply
Financial Intermediaries
0.250 Probability of new investment opportunities
0.383 Fraction of assets divertable: Perfect interbank market
0.129 Fraction of assets divertable: Imperfect interbank market
0.003 Transfer to entering bankers: Perfect interbank market
0.002 Transfer to entering bankers: Imperfect interbank market
0.972 Survival rate of the bankers
Intermediate good firms
0.330 Effective capital share
0.025 Steady state depreciation rate
Capital Producing Firms
1.000 Inverse elasticity of net investment to the price of capital
Government
0.200 Steady state proportion of government expenditures
41
Figure 1. Crisis Experiment: Perfect Interbank Market
ψ
0
−3
5
−0.02
0
−0.04
−5
E(rk)−r
r
x 10
0.02
0.01
−0.06
0
10
20
30
40
−10
0
10
20
30
40
0
0
10
c
y
0
30
40
30
40
30
40
investment
0
0.02
20
0.1
−0.02
−0.02
0
−0.04
−0.04
−0.1
−0.06
0
10
20
30
40
−0.06
0
10
k
20
30
40
0
10
labor
0
20
q
0.04
0.1
0.02
−0.1
0
0
−0.2
0
10
20
30
40
−0.02
0
10
20
30
40
−0.1
0
net worth
0
−0.2
Perfect Interbank Market
−0.4
RBC
−0.6
0
10
20
30
40
10
20
Figure 3. Lending Facilities: Perfect Interbank Market
ψ
0
E(rk)−r
r
0.01
0.015
−0.02
0
0.01
−0.04
−0.01
0.005
−0.06
0
10
20
30
40
−0.02
0
10
20
30
40
0
10
c
y
0
20
30
40
30
40
30
40
investment
0
0.02
0.1
−0.02
0
−0.02
−0.04
−0.04
−0.06
0
−0.1
0
10
20
30
40
−0.06
0
10
k
20
30
40
0
10
labor
20
q
0
0.02
0
−0.05
0
−0.1
0
10
20
30
40
−0.02
−0.05
0
net worth
10
20
30
40
−0.1
0
10
20
fraction of government assets
0
0.2
−0.2
νg=0
0.1
−0.4
RBC
0
10
20
30
40
0
0
10
20
30
40
νg=100
Liquidity Risk (πi < 1) and Imperfect Interbank Market
• Asset returns on "investing" islands exceed returns on "non-investing" islands
• The spread between inter-island returns increases during a crisis.
23
Liquidity Risk (πi < 1), con’t
• for h = i, n
h
h
h
Qh
t st = nt + bt + dt.
where bh
t is interbank borrowing
• net worth:
h
h
−1
h
nh
t = [Zt + (1 − δ)Qt ]ψ tQt−1 st−1 − Rbtbt−1 − Rtdt−1,
[Zt + (1 − δ)Qh
h−1h
t ]ψ t
Rkt =
h−1
Qt−1
24
Liquidity Risk (πi < 1), con’t
• objective
Vt = Et
∞
X
(1 − σ)σ i−1Λt,t+inh
t+i,
i=1
h after.
,
b
• the bank chooses dt before liquidity risk realized; sh
t t
• incentive constraint
h
h h
h
V (sh
t , bt , dt) ≥ θ(Qt st − ωbt ).
where ω
[0, 1] measures the efficiency of the interbank market
25
Perfect Interbank Market (ω = 1)
• arbitrage → Qit = Qn
t = Qt ⇒
0
Zt+1 + (1 − δ)Qt+1
hh
EtRkt+1 = EtRkt+1 = ψ t+1
Qt
• incentive constraint
Qtst − bh
t = φtnt
νt
where φt = θ−μ
= the case of no liquidity risk
t
26
Perfect Interbank Market (ω = 1)
• aggregating and given bit + bn
t = 0,
QtSt = φtNt
liquidity risk and a perfect interbank market ⇔ no liquidity risk case
• results from perfect arbitrage in the inter-bank market
EtΛt,t+1Rkt+1Ωt+1 = EtΛt,t+1Rbt+1Ωt+1 > EtΛt,t+1Rt+1Ωt+1.
27
Imperfect Interbank Market (ω = 0)
• Imperfect arbitrage → Qit < Qn
t →A lower asset price on the investing island, of
course, means a higher expected return.
• Let μh
t ≡ be the excess value of assets on a type h island
μit > μn
t ≥ 0.
with
0
0
h
hh
h
μt = Et0 Λt,t+1(Rkt+1 − Rt+1)Ωt+1;
h
h = i.n
28
Imperfect Interbank Market (ω = 0)
QitSti = φitNti
n
n n
Qn
t St ≤ φt Nt ,
and
n
n n n
(Qn
t St − φt Nt ) μt = 0,
with
φh
t =
νt
θ − μh
t
→
0
0
0
0
ih Ωh
nh Ωh
>
E
Λ
R
EtΛt,t+1Rkt+1
t
t,t+1
t+1
kt+1 t+1
0
0
h
h
≥
0
0
h
EtΛt,t+1Rbt+1Ωh
t+1 = EtΛt,t+1Rt+1Ωt+1.
0
0
h
h
29
Credit Policy with Imperfect Inter-bank Market
h = Qh(S h + S h )
Qh
S
t t
t
pt
gt
h = ϕhS h
Sgt
t t
where ϕh
t may be thought of as an instrument of central bank credit policy.
QitSti =
n
Qn
t St =
1
iN i
φ
t t
1 − ϕit
1
nN n
φ
t t
1 − ϕn
t
if f
μn
t > 0.
n∗
n n
n n n∗
n
Qn
t St = Qt Spt + ϕt Qt St , if f μt = 0
with Stn∗ ≡ asset demand consistent with μn
t = 0.
30
Figure 2. Crisis Experiment: Imperfect Interbank Market
ψ
0
−3
5
−0.02
0
−0.04
−5
−0.06
0
10
20
30
40
−10
r
x 10
spread
0.06
0.04
0.02
0
10
20
30
40
0
c
y
0.02
0
0
0.1
−0.02
0
−0.04
−0.1
0
10
0
10
20
30
investment
40
−0.02
−0.04
−0.06
0
10
20
30
40
−0.06
0
10
k
20
30
40
−0.2
labor
20
30
40
30
40
q
0
0.05
0.02
−0.05
−0.1
0
−0.15
−0.02
0
10
20
30
40
0
−0.05
−0.1
0
10
20
30
40
net worth
0
−0.2
Imperfect Interbank Market (πi=0.25)
−0.4
RBC
−0.6
0
10
20
30
40
Perfect Interbank Market
0
10
20
Figure 4. Lending Facilities: Imperfect Interbank Market
ψ
spread
r
0.01
0.06
−0.02
0
0.04
−0.04
−0.01
0.02
0
−0.06
0
10
20
30
40
−0.02
0
10
y
20
30
40
0
0
10
c
20
30
40
30
40
30
40
investment
0
0.1
−0.02
−0.02
0
−0.04
−0.04
−0.1
0
−0.06
0
10
20
30
40
−0.06
0
10
k
20
30
40
0
10
labor
20
q
0
0.05
−0.1
0.02
0
0
−0.05
−0.1
−0.02
−0.2
−0.2
0
10
20
30
40
0
net worth
10
20
30
40
0
10
20
fraction of government assets
0.06
−0.2
νg=0
0.04
−0.4
RBC
−0.6
0.02
−0.8
0
0
10
20
30
40
νg=100
0
10
20
30
40
Discount Window Policy with Imperfect Inter-bank Market
h = nh + bh + mh + d .
Qh
s
t
t t
t
t
t
with mh
t ≥ 0.
³
´
h
h
h
h
h
h
V (st , bt , mt , dt) ≥ θ Qt st − ωg mt .
31
Discount Window Policy with Imperfect Inter-bank Market
define
0
μmt = EtΛt,t+1(Rmt+1 − Rt+1)Ωh
t+1.
h0
→discount rate set according to
μmt = ωg μit
→set Rmt+1 > Rbt+1 = Rt+1 (Bagehot’s principle)
in the aggregate
i = φi N i + ω M .
QitSpt
g t
t t
32
Equity Injections (case of perfect interbank market)
st = spt + sget
Qtst = nt + bh
t + dt + ngt
ngt = Qtsget
33
Equity Injections (case of perfect interbank market)
μgt = EtΛt,t+1(Rgkt+1 − Rt+1)Ωt+1
where Rgkt+1 ≡ ross return on a unit of government equity injected at time t is:
Zt+1 + (1 − δ)Qt+1
Rgkt+1 = ψ t+1
Qgt
with, Qgt º Qt.
nt = [Zt+(1−δ)Qt]ψ tspt−1−Rbtbt−1−Rtdt−1+(Qgt−Qt)[sget−(1−δ)ψ tsget−1]
where (Qgt −Qt)(sgt −sgt−1) is the "gift" to the basnk from new government equity
purchases.
34
Equity Injections (case of perfect interbank market)
V (st − sget, , bt, dt) ≥ θ(Qt(st − sget) − bt).
→
QtSt = φtNt + Ngt
Nt = (σ+ξ)[Zt+(1−δ)Qt]ψ tSpt−1−σRtDt−1+.(Qgt−Qt)[Sget−(1−δ)ψ tSget−1]
35
.Issues
1. Idiosyncratic Asset Risk and Default
2. Illiquidity and Market Thinness
3. Maturity Structure
4. Bank Equity
5. Capital Requirements and Regulation,
and so on....
36