Imperfect Information, Lending
Standards and Capital Requirements
Pedro Gete and Natalie Tiernan
Georgetown University
May 2013
This paper makes three contributions:
1)
2)
Proposes new way to model lending
standards
Studies banks when there is imperfect
information about the economy:
Sometimes growth is persistent,
sometimes not
Banks observe past growth, solve
signal extraction problem to forecast
next period
I
I
3)
Policy implications of imperfect
information + banks' limited liability +
regulators (with same info as banks) that
cover bank losses:
I
I
State-dependent capital requirements
Lean against bank's beliefs:
Tighten if optimism
I
I
Relax if pessimism
1. New way to model lending standards
Why care about lending standards?
I
I
Cause of the crisis: U.S., Spain, U.K.,
Iceland, Ireland, Greece...
Driver of business cycles
Lending Standards are cyclical
Net % of Loan Officers Tightening Standards
Lending Standards for C&I Loans
80
60
40
20
0
-20
1970
1975
1980
1985
1990
1995
2000
2005
2010
How do we model lending standards?
I Borrowers are heterogeneous in
idiosyncratic characteristics (!)
!
I
Pareto [M; ]
Borrowers' income depends on
idiosyncratic and aggregate productivity
yt (!; st+1 ; lt ) = st+1 ! f (lt )
aggregate productivity shock
I
st+1 =
I
!=
I
idiosyncratic productivity
function of loan amount. E.g. use
loan to buy capital: f (lt ) = ql
lt =
t
t
Distribution of Borrowers
Pareto Distribution (M = 1,µ = 2)
0.4
0.35
Probability density
0.3
0.25
0.2
0.15
0.1
0.05
0
1
2
3
ω
4
5
6
Banks
I
I
I
Banks randomly meet borrowers but
cannot observe !
Banks screen and adjust lending
standards to weed out bad borrowers
Set lending standards so no borrower
below M+ gets credit (e.g. minimum
FICO score)
Pareto Distribution (M = 1, µ = 2)
0.4
0.35
Probability density
0.3
0.25
0.2
M+π
0.15
0.1
0.05
0
1
2
3
ω
4
5
6
What do we want to capture?
I
Tighter standards means:
1.
Banks are pickier
Some borrowers that quali ed for
credit now do not qualify
I
2.
3.
Probability of loan default falls
More likely bank will not meet
borrower good enough to lend (bank
reserves will increase)
@Prob Not lending
M
=
@
(M + t )
+1
>0
What determines lending standards?
I
Cost of equity (Ret)
I
Interest on reserves
I
Expectations about the economy (st+1)
I
Recovery rate if borrower defaults
RRt
( (!; lt ; st+1 ))
I
Expected value of borrowers' assets
I
Costs of implementing the standards
(C( t ))
qt+1
qt
What determines lending standards?
1
Ret
max1 E
f t ; lt g 0
b
t+1
Equity =
=
Z1
M+
t
8
>
>
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
>
>
:
M+
Z
b
t+1
Equity
s.t.
t
(RRt
Rdt )dt dG (!) +
M
+
!
e t+1
Z
M+
+
(!; lt ; st+1 )
Rdt dt dG (!) +
t
Z1
RLt lt
!
e t+1
lt dG (!) ;
Rdt dt dG (!)
(!; lt ; st+1 ) =
|
C( t )
9
>
>
>
>
>
>
>
>
>
>
>
>
>
=
>
>
>
>
>
>
>
>
>
>
>
>
>
;
qt+1
lt + st+1 !
qt
{z
lt
qt
}
Value of loan recovered if type ! defaults
Optimal Lending Standards Risk Neutral Bank:
if RRt = RDt and capital requirement constraint binds:
|
(1
) Rdt + Ret lt =
{z
}
Cost of Funds
=
E [qt+1 ]
lt
qt
| {z
}
+
E [st+1 ] (M + t )
|
{z
lt
qt
+
}
Value Borrower Assets Value Borrower Income
+
C0 ( )
| {z t}
Cost Implementing Standards
(M + t )
M
|
{z
Inverse of
+1
}
@Prob Not lending
@
2. Banks under imperfect information
How do we model imperfect information?
I
st
is observable, but not its components
st = zt +
I
zt
t
is persistent:
follows 2-state Markov process
with transition matrix P
zt = zH ; zL
I
t
is not persistent:
t
is i:i:d: Normal
2
2
;
2
Results due to imperfect info
I
Model of lending standards under
imperfect info can explain two facts:
a)
b)
Higher volatility of standards during
the Great Moderation
Rational credit booms/busts driven by
signal extraction problem after a
sequence of good realizations
Example of Rational Overoptimism
"Spain's economic success over the past
years has been most impressive...
GDP growth is likely to remain above the
euro-area average of just below 2% for
several more years, allowing Spain to
climb past Italy and Germany in the
rankings of GDP per capita by 2020"
Research Department of Deutsche Bank (2007)
Booms/Busts
I
I
I
Fluctuations in beliefs=) uctuations in
lending standards
Expect higher aggregate
productivity=)lower screening intensity
Problem: banks may be reacting to i.i.d.
shocks
Data and model
A) Credit
35
30
% deviation from trend
25
20
15
10
5
0
Model
Worst Boom-Bust
Abrupt Boom-Bust
Smooth Boom-Bust
-5
-10
-2
-1.5
-1
-0.5
0
0.5
Pe riods from pe ak
1
1.5
2
C) Lending Standards
0.3
0.28
0.26
0.24
0.22
0.2
0.18
0.16
0.14
0.12
-2
-1.5
-1
-0.5
0
0.5
Periods from pe ak
1
1.5
2
D) Non-Performing Loans
20
% of total loans, dev. from trend
15
Model
Worst Boom-Bust
Abrupt Boom-Bust
Smooth Boom-Bust
10
5
0
-5
-10
-2
-1.5
-1
-0.5
0
0.5
Periods from pe ak
1
1.5
2
E) Return on Assets
0.8
0.6
%, deviation from trend
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-2
Model
Worst Boom-Bust
Abrupt Boom-Bust
Smooth Boom-Bust
-1.5
-1
-0.5
0
0.5
Periods from peak
1
1.5
2
Likelihood of booms/busts driven by wrong
beliefs
B) Likelihood of Belief-Driv en Boom-Bust
5
4.5
3.5
L
Pr(z = z ∩ η < (s -z )) in %
4
t
L
t
3
2.5
2
1.5
1
0.5
0
-2
-1.5
-1
-0.5
0
0.5
Periods from peak
1
1.5
2
3. Macroprudential Policy
I
I
With imperfect information, iid shocks
matter next period
Two possible errors:
PDF of Conditional Densities
50
H
f (s | z )
t
45
L
f (s | z )
t
40
35
30
25
20
15
10
5
0
-0.05
0
s
t
0.05
I
I
I
Regulator does not have superior info
relative to banks
But Regulator faces unlimited liability:
pay for losses above bank's capital
Regulator is more conservative with
lending standards
Banks lower standards when optimistic
A) Lending Standards
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.2
0.4
0.6
Prior of z being in high state
t
0.8
1
I
I
Policymaker chooses capital
requirements following Value at Risk:
Keep size of loss in a certain probability
Macroprudential tools should lean
against banks' beliefs
I
When optimism, tighten policy
Raising capital requirements:
1.
Increases the weight of equity, which is
more expensive than debt
I
2.
Bank needs to be pickier to ensure
breakeven
Lower leverage implies smaller loans
and less reward to high lending standards
A) Probability banks lose > 50% of capital
25
Capital req. is 3.75%
Capital req. is 4%
Capital req. is 4.25%
15
t
Pr(s <s*|p)
20
10
5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Prior of z being in high state
t
0.8
0.9
Capital requirements s.t. probability of ba nk losses is 2%
6.5
Capital Req. (%)
6
5.5
5
Losses > 50%
4.5
4
3.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Prior of z being in high state
t
0.8
0.9
I
I
Higher capital requirements increase
lending standards and reduce potential
losses
Large losses happen less often, thus a
VaR framework demands lower capital
requirements as loss tolerance rises
Capital requirements s.t. probability of bank losses is 2%
6.5
6
Losses > 50%
Losses > 65%
Capital Req. (%)
5.5
5
4.5
4
3.5
3
0.1
0.2
0.3
0.4
0.5
0.6
Prior of z being in high state
t
0.7
0.8
0.9
Conclusions
I
I
Wm. McC. Martin, Jr. (1955):
"The job of the Federal Reserve is to
take away the punch bowl just as the
party gets going"
Our version:
One job of the macro regulator is to curb
enthusiasm when banks think times are
good
Appendix
Imperfect Info and Volatility
I
I
I
Dynamics of lending standards depend
on information content of economic
news 2
In noisy times, smaller changes
Model prediction matches new fact:
larger volatility in lending standards
since Great Moderation
A new fact:
Std. Dev.: 1967-1983: 16.25
Std. Dev. 1990-2011: 23.28
Net % of Loan Officers Tightening Standards
Lending Standards for C&I Loans
80
60
40
20
0
-20
1970
1975
1980
1985
1990
1995
2000
2005
2010
I
I
I
Data for lending standards:
1967Q1-1983Q4 and 1990Q2-2008Q3
1990Q2-2008Q3 is less noisy (estimated
two state Markov switching model à la
Hamilton 1989)
Identify technology shock using long run
restrictions in VAR (Blanchard-Quah)
only tech shocks have permanent
effect on the level of output
I
In data: higher reaction in less noisy times
Change in Net % of Loan Officers Tightening Standards
Lending Standards for C&I loans after Positiv e Tech Shock
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
1990Q2-2008Q3
1967Q1-1983Q4
0
2
4
6
8
10
12
14
16
Model IRs to TFP shock for different amounts of
noise
B) Lending Standards
0.3
0.28
0.26
0.24
0.22
0.2
0.18
0.16
0.14
0.12
-1
Low Noise
High Noise
0
1
2
3
4
5
6
7
8