Description
The purpose of this paper is to present a model that studies the impact of a tightening
monetary policy on banking failure in a developing country.
Journal of Financial Economic Policy
A theory of linkage between monetary policy and banking failure in developing
countries
Raulin L. Cadet
Article information:
To cite this document:
Raulin L. Cadet, (2009),"A theory of linkage between monetary policy and banking failure in developing
countries", J ournal of Financial Economic Policy, Vol. 1 Iss 2 pp. 143 - 154
Permanent link to this document:
http://dx.doi.org/10.1108/17576380911010254
Downloaded on: 24 January 2016, At: 21:35 (PT)
References: this document contains references to 15 other documents.
To copy this document: [email protected]
The fulltext of this document has been downloaded 645 times since 2009*
Users who downloaded this article also downloaded:
Dilip K. Das, (2010),"Financial globalization: a macroeconomic angle", J ournal of Financial Economic
Policy, Vol. 2 Iss 4 pp. 307-325 http://dx.doi.org/10.1108/17576381011100847
Andreas Kern, Christian Fahrholz, (2009),"Global imbalances and a trade-finance-nexus", J ournal of
Financial Economic Policy, Vol. 1 Iss 3 pp. 206-226 http://dx.doi.org/10.1108/17576380911041700
Bruno Funchal, Mateus Clovis, (2009),"Firms' capital structure and the bankruptcy law design", J ournal of
Financial Economic Policy, Vol. 1 Iss 3 pp. 264-275 http://dx.doi.org/10.1108/17576380911041737
Access to this document was granted through an Emerald subscription provided by emerald-srm:115632 []
For Authors
If you would like to write for this, or any other Emerald publication, then please use our Emerald for
Authors service information about how to choose which publication to write for and submission guidelines
are available for all. Please visit www.emeraldinsight.com/authors for more information.
About Emerald www.emeraldinsight.com
Emerald is a global publisher linking research and practice to the benefit of society. The company
manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as
providing an extensive range of online products and additional customer resources and services.
Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee
on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive
preservation.
*Related content and download information correct at time of download.
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
A theory of linkage between
monetary policy and banking
failure in developing countries
Raulin L. Cadet
Center for Research in Economics and Management
(CREM – CNRS UMR 6211), University of Rennes 1, Cedex, France and
University of Quisqueya (UniQ), Port-au-Prince, Haiti
Abstract
Purpose – The purpose of this paper is to present a model that studies the impact of a tightening
monetary policy on banking failure in a developing country.
Design/methodology/approach – The interest rate on treasury bills is included in the model to
measure monetary policy. Since the model considers developing countries with low-income level, the
paper assumes that a secondary market does not exist.
Findings – The model shows that, despite treasury bills constituting an alternative source of pro?t
for banks in developing countries, a tightening monetary policy increases the probability of banking
failure. In addition, the model shows that ef?ciency level explains the asymmetric effect of monetary
policy on the pro?t of the banks.
Practical implications – The policy implication of the results of the paper is that the central bank
should take into account the adverse effect of a tightening monetary policy on banking failure, when
planning policy decisions.
Originality/value – The paper offers insights into the linkage between monetary policy and
banking failure in developing countries.
Keywords Banking, Business failures, Monetary policy, Interest rates, Developing countries
Paper type Research paper
1. Introduction
Some empirical and theoretical papers study the causes of banking crisis. Empirical
studies emphasize the role of the banks conditions as principal factors. Wheelock and
Wilson (2000) ?nd that bank speci?c data are signi?cant factors of the US bank
failures and acquisitions. Arena (2008), for instance, reveals that bank-level
fundamentals signi?cantly affect banking failure in East Asia and in Latin America.
About the macroeconomic conditions, one of the factors of banking crises mentions by
Mishkin (1999) is high interest rates.
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – G21, G33, E52
The author is grateful to Xavier Freixas, Jean-Jacques Durand, Christophe Tave´ra, Marc
Baudry, Gilles Canales, and Steeve Crittenden for helpful discussions and comments. He wishes
to thank the seminar participants at the CREM, in April 2007, the participants at the IBFR
Conference on Business and Finance, in May 2007, and the participants at the 57th Annual
Meeting of the Midwest Finance Association (MFA), in February 2008, for their comments. The
opinions expressed in this paper are those of the author. They do not necessarily re?ect those of
the CREM and the CREGED.
Monetary policy
and banking
failure
143
Journal of Financial Economic Policy
Vol. 1 No. 2, 2009
pp. 143-154
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576380911010254
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
Kraft and Galac (2007) analyze deposits interest rate and banking failure in Croatia,
where interest rates become high because of liberalization and competition. Actually, in
addition to liberalization and competition, a tightening monetary policy may induce
increasing of interest rates. Some researchers analyze the way monetary policy affects
balance sheets and the behavior of banks. For instance, Kashyap and Stein (1995)
examine the impact of monetary policy on bank’s balance sheets. van den Heuvel
(2002) studies the effects of monetary policy in the US states. Golodniuk (2006) studies
lending channel of monetary policy in Ukraine. Bolton and Freixas (2006) analyze the
effects of monetary policy on securities market and bank lending.
van den Heuvel (2002) ?nds that the effects of monetary policy are larger on banks
with low capital level, and on banks with low liquidity level. About liquidity level,
Freedman and Click (2006) reveal that, in developing countries, banks are highly liquid.
Thus, in developing countries, where banks are highly liquid, treasury bills is an
alternative source of pro?t for banks. Actually, Brownbridge (1998), who analyzes
banking failure in Africa, underlines that treasury bills enable banks to earn large
pro?ts. Thus, does a tightening monetary policy reduce the probability of failure of
banks, in developing countries? This question is essential, because a positive answer
would suggest an opposite view to theory regarding the link between interest rate and
asymmetric information. In addition, because of the consequences of bank failures, it
does matter to identify any potential cause of these events, in order to know how to
prevent them.
Hancock (1985) and Goyeau et al. (2002) analyze bank pro?tability and interest
rates. But, they do not analyze banking failure. Even if there is a link between
pro?tability and solvency, they are different. A bank may be solvent in spite of making
losses, if equity is still positive. The empirical results of Goyeau et al. (2002) reveal that
a decrease of interest rate in Europe has a negative effect on some banking systems
whereas some other banking systems still pro?t. However, according to the study of
Hancock (1985), bank pro?t appears to increase with interest rate increasing, which
contradicts Goyeau et al. (2002). Thus, the questions still remain for research:
RQ1. Does bank pro?tability increase when interest rate increase?
RQ2. If some banks pro?t from interest rates increasing whereas some other banks
do not, what can explain this difference?
Beyond these questions, this paper is more concerned about the following:
RQ3. Does a tightening monetary policy reduce probability of bank failure in
developing countries?
RQ4. Does a tightening monetary policy increase pro?t of banks in developing
countries?
I show that, despite treasury bills constitute an alternative source of pro?t for banks in
developing countries, a tightening monetary policy increases the probability of
banking failure. In addition, the model shows that, unlike an inef?cient bank, an
ef?cient bank pro?ts from a tightening monetary policy.
Regarding ?rms, one of the main ?ndings of Bernanke and Gertler (1989) is that a
shortage of money, which increases interest rates, reduces ?rms net worth. However,
there is no theoretical framework about the linkage between monetary policy and
JFEP
1,2
144
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
individual banking failure in developing countries. Those questions are essential, as
banking failure has economic and social consequences. The paper is organized as
follows: after this introduction, Section 2 presents the model, and Section 3 exposes
some concluding remarks.
2. The model
This section presents a model of the banking sector that maximizes pro?t, and an
individual bank which is a price taker. In this model, prices are interest rates on
treasury bills, loans, and deposits. All interest rates are determined by the banking
market, except interest rate on treasury bills. This model assume that interest rate on
treasury bills, which is an exogenous price to the banking sector, is affected by
stochastic shocks. The reaction function of the interest rate on treasury bills to
stochastic shocks is not discussed in this paper. The paper only assumes that any
change in interest rate is due to the response of monetary policy authority to stochastic
shocks that affect the economy.
Since the model considers developing countries with low-income level, I assume that
secondary market does not exist. In these countries, the secondary market is not well
developed or does not exist at all. I show that, in developing countries with low-income
level, a tightening monetary policy increases the pro?t of ef?cient banks whereas
inef?cient banks do not pro?t from it. The model shows that although treasury bills
constitute an alternative source of pro?t for banks in developing countries, an increase
of interest rate on treasury bills increases the probability of banking failure.
2.1 The banking sector
I assume that the banking sector is a competitive market. The banking sector has three
assets: loans (L), treasury bills (B), and reserve (R). In the liability side of the sector’s
balance sheet, there are the shareholders equity (K) and deposits (D). The reserve of the
banking sector is a proportion of deposits. The reserve rate is denoted by a. Central
bank requires from the banking sector a capital adequacy which should be superior or
equal to a proportion of risk-weighted assets (denoted by f).
Reserve:
R ¼ aD ð1Þ
Capital requirement:
fðs
l
L þs
b
BÞ # K
where s
l
and s
b
are the risk-weight of loans and treasury bills, respectively. It is
assumed that the risk-weight of loans is identical for all banks. Since treasury bills are
risk-free, s
b
¼ 0. Thus, the capital requirement inequality becomes:
fs
l
X
L # K ð2Þ
The balance sheet identity:
L þ B þ R ¼ K þ D ð3Þ
In the balance sheet identity (equation (3)), I replace reserve (R) by its value from
equation (1). It is assumed that all banks maintain the shareholders equity equal to the
minimum of capital requirement, fs
l
L. One of the propositions proved by Rochet (2004)
Monetary policy
and banking
failure
145
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
is that under deposit insurance, commercial bank’s optimal behavior is to maintain
capital just suf?cient for meeting capital requirement. However, in developing
countries, there is implicit deposit insurance. Thus, K is replaced by its value:
L þ B þaD ¼ fs
l
L þ D Lð1 2fs
l
Þ þ B ¼ Dð1 2aÞ
L ¼
1 2a
1 2fs
l
D 2
1
1 2fs
l
B
ð4Þ
B ¼ Dð1 2aÞ 2Lð1 2fs
l
Þ ð5Þ
Since their reserve rate, a, is superior to the reserve rate imposed by the authority of
supervision, banks can reduce their liquidity to increase treasury bills. In addition, the
banks may still increase loans, despite they increase treasury bills, because banks are
highly liquid in developing countries. Thus, in developing countries, banks do not
necessarily substitute loans to treasury bills, vice versa. In this case, the effect of open
market operations of the central bank, which increases interest rate to sell treasury bills,
is weak on loans, in developing countries. That is the reason why, the ef?cacy of
monetary policy may be weak in these countries.
Each bank of the banking sector has the same cost function of intermediation,
C(D, L). This cost function, is equal to the sum of the cost of the management of
deposits, C
d
(D), and the cost of management of loans, C
l
(L). The cost function satis?es
the assumptions of convexity, such as the decreasing returns to scale. The pro?t
function of the sector is the following (see Appendix 1):
EðpÞ ¼ r
l
ð1 2
pÞL þ r
b
B 2r
d
D 2C
d
ðDÞ 2C
l
ðLÞ 2
pL ð6Þ
Because of the assumptions on C(D, L), the pro?t function is concave in D and L. The
interest rates on loans, deposits, and treasury bills are, respectively, r
l
, r
d
, and r
b
. The
expected default rate of the banking sector is denoted
p. The variable p is a random
variable. All banks face the same marginal costs whereas the expected default rate,
p
i
,
differs from bank to bank[1]. The expected default rate affects the pro?t margin of the
banks, by reducing the interest the banks should received on loans. Second, the
expected default rate causes loss in loans portfolio. These effects of the default rate on
the expected pro?t is take into account in equation (6) by the terms r
l
ð1 2
pÞL and
2
pL. The marginal costs of the banking sector and the marginal cost of any individual
bank are identical[2]. Since interest rate on treasury bills is used as instrument of
monetary policy in most developing countries, it is used in this model as the indicator
of monetary policy.
If equation (5) is replaced in the pro?t function, it becomes:
EðpÞ ¼ r
l
ð1 2
pÞL þ r
b
ð1 2aÞD 2r
b
ð1 2fs
l
ÞL 2r
d
D 2C
d
ðDÞ 2C
l
ðLÞ 2
pL
ð7Þ
Proposition 1. The interest rates on loans and deposits are both positive functions of
the interest rate on treasury bills; and the costs of intermediation increase the interest
rate on loans, and decreases the interest rate on deposits.
Proof. The problem of the banking sector is to maximize pro?t. To resolve it,
banking sector chooses the optimal amounts of loans and deposits. Because of the
assumptions of convexity on the cost function, the maximization of the pro?t is
characterized by the ?rst order conditions:
JFEP
1,2
146
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
›EðpÞ
›L
¼ r
l
ð1 2
pÞ 2r
b
ð1 2fs
l
Þ 2C
0
l
ðLÞ 2
p ¼ 0
r
l
¼
1
1 2
p
r
b
ð1 2fs
l
Þ þ C
0
l
ðLÞ þ
p
 Ã
ð8Þ
›EðpÞ
›D
¼ r
b
ð1 2aÞ 2r
d
2C
0
d
ðDÞ ¼ 0 r
d
¼ r
b
ð1 2aÞ 2C
0
d
ðDÞ ð9Þ
Equation (8) shows that the risk-weighted capital requirement, fs
l
, reduces interest
rates on loans, whereas equation (9) indicates that the reserve rate, a, reduces interest
rate on deposits. Capital requirement constitutes a cost supported by banks, as it
prevents the bank to provide loans to a certain extent. Zarruk and Madura (1992) ?nd a
similar result. The model developed in their paper shows that capital regulation results
in a reduced interest margin. A
The rate of reserve, a, which is equal or superior to the rate of reserve requirement,
is also a cost, as banks do not get return from it. This cost is supported by the
depositors. Indeed, the interest rate paid to depositors is inferior to what it should be if
there was not any reserve in the assets of the banks. Regarding the costs of ?nancial
intermediation, only the customers support them. These costs reduce interest rate they
should receive on deposits, and increase what they should pay on loans.In addition, the
expected default rate is added to the interest rate that banks’customers pay on loans.
Thus, in this model, banks receive a risk prime which is equal to the expected default
rate. This result is coherent with ?nancial economic theory. Higher expected default
rate induce higher interest rate on loans.
2.2 An individual bank
In this subsection, a bank pro?t and its probability of failure are modeled. All variables
are used with the subscript i to indicate that only one bank is considered instead of the
banking sector. The bank is a price taker. Thus, interest rates received on loans and
paid on deposits are those determined by the market (equations (8) and (9)), whereas
the value of the interest rate on treasury bills is decided by central bank, as a reaction
to stochastic shocks that affect the economy. The expected default rate of the bank is
p
i
. The value of p
i
may be different from
p. This subsection models the individual bank
as follows:
Reserve:
R
i
¼ aD
i
ð10Þ
Capital requirement:
fs
l
L
i
# K
i
ð11Þ
The balance sheet identity:
L
i
þ B
i
þ R
i
¼ K
i
þ D
i
In the balance sheet identity, reserve (R
i
) is replaced by its value from equation (10),
and K
i
by its value from equation (11)[3]:
L
i
þ B
i
þaD
i
¼ fs
l
L
i
þ D
i
L
i
ð1 2fs
l
Þ þ B
i
¼ D
i
ð1 2aÞ
B
i
¼ D
i
ð1 2aÞ 2L
i
ð1 2fs
l
Þ
ð12Þ
Monetary policy
and banking
failure
147
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
The pro?t function of the bank is written as follows:
Eðp
i
Þ ¼ r
l
ð1 2p
i
ÞL
i
þ r
b
B
i
2r
d
D
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ 2p
i
L
i
ð13Þ
In the pro?t function (equation (13)), interest rates on loans and deposits are replaced
by their respective value which are in equations (8) and (9). Thus, the pro?t function of
the bank becomes[4]:
Eðp
i
Þ ¼
p 2p
i
1 2
p
L
i
½1 þ r
b
ð1 2fs
l
Þ? þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ
2C
l
ðL
i
Þ þ C
0
l
ðL
i
Þ
1 2p
i
1 2
p
L
ð14Þ
The gap between the expected default rate of the banking sector and the default rate of
an individual bank,
p 2p
i
, is the relative ef?ciency of this bank. Thus, the pro?t of a
bank is a function of the relative ef?ciency of this bank.
Proposition 2. When central bank tightens monetary policy, by increasing interest
rate on treasury bills, depending on bank’s relative ef?ciency, three cases are possible,
regarding pro?t.
Proof. The partial derivative of the pro?t function of the bank, with respect to
interest rate on treasury bills, is the following:
›Eðp
i
Þ
›r
b
¼
p 2p
i
1 2
p
L
i
ð1 2fs
l
Þ ð15Þ
.
If the relative ef?ciency of the bank is negative, i.e.
p 2p
i
, 0, a tightening of
monetary policy will reduce the bank’s pro?ts:
›Eðp
i
Þ
›r
b
, 0
.
If the relative ef?ciency of the bank is null, i.e.
p 2p
i
¼ 0, a shock of monetary
policy will have no impact on the pro?ts of the bank:
›Eðp
i
Þ
›r
b
¼ 0
.
If the relative ef?ciency of the bank is positive, i.e.
p 2p
i
. 0, its pro?ts will
increase when central bank tightens monetary policy:
›Eðp
i
Þ
›r
b
. 0
The ef?ciency level is a factor that explain the asymmetric effect of monetary policy on
the pro?t of the banks. An inef?cient bank does not pro?t from a tightening monetary
policy, whereas an ef?cient bank. When central bank tightens monetary policy, even if
an ef?cient bank does not buy treasury bills, it should modify the structure of its
balance sheet to maintain its pro?ts at the same level or to increase it. Since the interest
rates increase when the central bank tightens monetary policy, if a bank maintain the
growth of its loans at the same level, the amount of non performing loan may increase.
JFEP
1,2
148
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
For, the increasing of the interest rate on loans induces an increase of asymmetric
information.
Thus, when central bank tightens monetary policy, an ef?cient bank should reduce
the growth of its loans to reduce the effect of asymmetric information. That is the
reason why a tightening monetary policy may induce an increase of the pro?t of an
ef?cient bank. Actually, a tightening monetary policy may also have a neutral impact
on the pro?t of an ef?cient bank. Since an inef?cient bank does not deal well with
asymmetric information, a tightening monetary policy induces a decrease of the pro?t
of such a bank.
Proposition 3. Since it decreases the ef?ciency level of the bank, an increase of
interest rate on treasury bills, which is a tightening monetary policy, increases the
probability of failure of the bank.
Proof. I consider that a bank fails when it is insolvent. Thus, the bank is insolvent
if the sum of shareholders equity and pro?t is negative. The probability of failure of the
bank, which is denoted r, is calculated as follows (see Appendix 2):
r
i
¼ PðK
i
þ Eðp
i
Þ , 0Þ ¼ PðEðp
i
Þ , 2K
i
Þ
r
i
¼ Prob
p 2p
i
1 2
p
L
i
½1 þ r
b
ð1 2fs
l
Þ?
þC
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ 2C
0
l
ðL
i
ÞL
i
1 2p
i
1 2
p
, 2K
i
r
i
¼ Prob p
i
.
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
2
C
0
l
ðL
i
Þ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
þ
pð1 þ r
b
ð1 2fs
l
ÞÞ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
ð16Þ
Equation (16) shows that the probability of failure is the probability that the default
rate of the bank is superior to a threshold which is denoted T, with:
T ¼
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
2
C
0
l
ðL
i
Þ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
þ
pð1 þ r
b
ð1 2fs
l
ÞÞ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
Thus, the probability of the failure of the bank, r
i
, is:
r
i
¼ Prob ðp
i
. TÞ ¼ 1 2Prob ðp
i
# TÞ r
i
¼ 1 2Prob ðp
i
# TÞ ð17Þ
The default rate may be interpreted as an indicator of the ef?ciency level of the bank.
Because the probability of failure is the probability that the expected default rate is
superior to a threshold, ef?ciency level and the probability of failure are linked.
The partial derivative of the probability of failure, with respect to the interest rate
on treasury bills, can now be calculated to verify the impact of a tightening monetary
policy:
Monetary policy
and banking
failure
149
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
›r
i
›r
b
¼ 2
›Probðp
i
Þ # T
›r
b
ð18Þ
›Probðp
i
# TÞ
›r
b
¼
›Probðp
i
# TÞ
›T
›T
›r
b
ð19Þ
›T
›r
b
¼ 2
L
i
ð1 2fs
l
Þð1 2
pÞðK
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
ÞÞ
½1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ?
2
þ
C
0
l
ðL
i
Þð1 2fs
l
Þ
½1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ?
2
þ
pð1 2fsÞ½1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ? 2
pð1 2fs
l
Þ½1 þ r
b
ð1 2fs
l
Þ?
½1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ?
2
ð20Þ
Because of equations (18) and (19), the sign of the impact of the monetary policy
interest rate on the probability of failure, ›r
i
=›r
b
, is the opposite sign of the derivative
of the threshold T, with respect to the interest rate of the monetary policy, ›T=›r
b
.
According to the last result (equation (20)), the sign of ›T=›r
b
depends between the
equity and the total cost of intermediation. Since the paper assumes that all banks
respect the minimum capital requirement, shareholders equity is enough to be higher
than the intermediation costs. Thus, the derivative of the threshold, with respect to r
b
,
is inferior to zero. Thus, the derivative of the probability of failure, with respect to r
b
, is
superior to zero:
›T
›r
b
, 0 ð21Þ
›r
i
›r
b
. 0 ð22Þ
A
The sign of ›r
i
=›r
b
shows that, because it decreases the ef?ciency level of the bank, a
tightening monetary policy increases the probability of failure of this bank.
As underlined previously, the expected default rate is an indicator of the ef?ciency
level of the bank. Indeed, the increasing of interest rates causes the increasing of
asymmetric information. That is the reason why the probability of failure of all banks
increase when the central bank tightens monetary policy. To deal with asymmetric
information an ef?cient bank should reduce the growth of its loan portfolio.
A limitation of my model is that it does not account for time, which limits the
possibility to show the dynamic impact of monetary policy on banking failure.
Although static, the model meets the questions to which it intended to answer; the
model shows that, despite treasury bills constitute an alternative source of pro?t for
banks in developing countries, a tightening monetary policy increases the probability
of banking failure. In addition, the model shows that an ef?cient bank pro?ts from a
tightening monetary policy, whereas an inef?cient bank does not.
JFEP
1,2
150
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
3. Concluding remarks
In this paper, I show that ef?ciency level explains the asymmetry of the effect of
monetary policy on banking pro?t. The level of relative ef?ciency explains why some
banks pro?t from a tightening monetary policy, whereas some other banks do not. In
addition, the model shows that, despite treasury bills constitute an alternative source of
pro?t for banks in developing countries, a tightening monetary policy increases the
probability of banking failure. Actually, an increase of the interest rates induces an
increase of asymmetric information. An ef?cient bank should decrease its loan
portfolio to deal with asymmetric information.
If the interest rate is so high so that loan portfolio should be null, there will be a
banking crisis. There is a threshold of interest rate, which I call a threshold of crisis,
that interest rate on treasury bills should not exceed.
The policy implication of the results of this paper is that, the central bank should
take into account the adverse effect of tightening monetary policy on banking failure,
when planning policy decisions. Actually, although monetary policy intend to stabilize
the price level, it may destabilize the banking sector if the growth of the interest rate is
not moderate.
Notes
1. The default rate is the ratio of loans not reimburse to total loans.
2. Since all banks face the same marginal cost, C
0
d
ðDÞ ¼ C
0
d
ðD
i
Þ and C
0
l
ðLÞ ¼ C
0
l
ðL
i
Þ.
3. Remember that it is assumed that all banks maintain the exact minimum of capital
requirement.
4. See Appendices for details about calculus.
References
Arena, M. (2008), “Bank failures and bank fundamentals: a comparative analysis of Latin
America and East Asia during the 1990s using bank-level data”, Journal of Banking
& Finance, Vol. 32 No. 2, pp. 299-310.
Bernanke, B. and Gertler, M. (1989), “Agency costs, net worth, and business ?uctuations”,
The American Economic Review, Vol. 79, pp. 14-31.
Bolton, P. and Freixas, X. (2006), “Corporate ?nance and the monetary transmission mechanism”,
Review of Financial Studies, Vol. 19, pp. 829-70.
Brownbridge, M. (1998), “Financial distress in local banks in Kenya, Nigeria, Uganda and
Zambia: causes and implications for regulatory policy”, Development Policy Review, Vol. 16,
pp. 173-88.
Freedman, P.L. and Click, R.W. (2006), “Banks that don’t lend? Unlocking credit to spur growth
in developing countries”, Development Policy Review, Vol. 24 No. 3, pp. 279-302.
Golodniuk, I. (2006), “Evidence on the bank-lendind channel in Ukraine”, Research in
International Business and Finance, Vol. 20, pp. 180-99.
Goyeau, D., Sauviat, A. and Tarazi, A. (2002), “Rentabilite´ bancaire et taux d’inte´reˆt de marche´:
une application aux principaux syste`mes bancaires europe´ens sur la pe´riode 1988-1995”,
Revue d’Economie Politique, Vol. 112 No. 2, pp. 275-91.
Hancock, D. (1985), “Bank pro?tability, interest rates, and monetary policy”, Journal of Money,
Credit, and Banking, Vol. 17 No. 2, pp. 189-202.
Monetary policy
and banking
failure
151
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
Kashyap, A.K. and Stein, J.C. (1995), “The impact of monetary policy on bank balance sheet”,
Carnegie-Rochester Conference Series on Public Policy, Vol. 42, pp. 151-95.
Kraft, E. and Galac, T. (2007), “Deposit interest rates, asset risk and bank failure in Croatia”,
Journal of Financial Stability, Vol. 2, pp. 312-36.
Mishkin, F.S. (1999), “Global ?nancial instability: framework, events, issues”, The Journal of
Economic Perspectives, Vol. 13 No. 4, pp. 3-20.
Rochet, J.C. (2004), “Capital requirements and the behavior of commercial banks”, Credit,
Intermediation and the Macroeconomy: Models and Perspectives, Oxford University Press,
Oxford.
van den Heuvel, S.J. (2002), “Banking conditions and the effects of monetary policy: evidence
from US states”, mimeo, University of Pennsylvania, Philadelphia, PA.
Wheelock, D.C. and Wilson, P.W. (2000), “Why do banks disappear: the determinants of US
bank failures and acquisitions”, Review of Economics and Statistics, Vol. 82 No. 1,
pp. 127-38.
Zarruk, E.R. and Madura, J. (1992), “Optimal bank interest margin under capital regulation
and deposit insurance”, Journal of Financial and Quantitative Analysis, Vol. 27 No. 1,
pp. 143-9.
Appendix 1. Pro?t function of the bank
The pro?t function of the bank is written as follows:
Eðp
i
Þ ¼ r
l
ð1 2p
i
ÞL
i
þ r
b
B
i
2r
d
D
i
2C
l
ðL
i
Þ 2C
d
ðD
i
Þ 2p
i
L
i
ðA1Þ
In the pro?t function (equation (A1)) I replace interest rates on loans and deposits by their
respective value which are in equations (8) and (9). Thus, the pro?t function of the bank
becomes:
Eðp
i
Þ ¼
1
1 2
p
ðr
b
2r
b
fs
l
þ C
0
l
ðL
i
Þ þ
pÞð1 2p
i
ÞL
i
 Ã
þ r
b
ð1 2aÞD
i
2r
b
ð1 2fs
l
ÞL
i
2r
b
ð1 2aÞD
i
þ C
0
d
ðD
i
ÞD
i
2C
l
ðL
i
Þ 2C
d
ðD
i
Þ 2p
i
L
i
Eðp
i
Þ ¼
1
1 2
p
r
b
L
i
2r
b
fs
l
L
i
þ C
0
l
ðL
i
ÞL
i
þ
pL
i
2r
b
p
i
L þ r
b
fs
l
p
i
L
i
2C
0
l
ðL
i
Þp
i
L
i
2pp
i
L
i
Â
2r
b
ð12fs
l
Þð12
pÞL
i
þ C
0
d
ðD
i
Þð12
pÞD
i
2C
l
ðL
i
Þð1 2
pÞ 2C
d
ðD
i
Þð1 2
pÞ 2p
i
ð1 2
pÞL
i
Ã
Eðp
i
Þ ¼
1
1 2
p
r
b
L
i
2r
b
fs
l
L
i
þ C
0
l
ðL
i
ÞL
i
þ
pL
i
2r
b
pL
i
þ r
b
fs
l
p
i
L
i
2C
0
l
p
i
L
i
2pp
i
L
i
Â
2r
b
L
i
þ r
b
pL
i
þ r
b
fs
l
pL
i
2r
b
fs
l
pL
i
þ C
0
d
ðD
i
ÞD
i
2C
0
d
ðD
i
Þ
pD
i
2C
l
ðL
i
Þ þ C
l
ðL
i
Þ
p
2C
d
ðD
i
Þ þ C
d
ðD
i
Þ
p 2pL
i
þ pp
i
L
i
Ã
Eðp
i
Þ ¼
1
1 2
p
L
i
ð
p 2p
i
Þ þ r
b
L
i
ð
p 2p
i
Þ 2r
b
fs
l
L
i
ð
p 2p
i
Þ
Â
þC
0
d
ðD
i
ÞD
i
ð1 2
pÞ 2C
0
l
ðL
i
Þð1 2p
i
ÞL
i
2C
d
ðD
i
Þð1 2
pÞ 2C
l
ðL
i
Þð1 2
pÞ
Ã
Eðp
i
Þ ¼
p 2p
i
1 2
p
L
i
½1 þ r
b
ð1 2fs
l
Þ? þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ 2C
0
l
ðL
i
ÞL
i
1 2p
i
1 2
p
ðA2Þ
JFEP
1,2
152
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
Appendix 2. The probability of banking failure
r
i
¼ PðK
i
þ Eðp
i
Þ , 0Þ ¼ PðEðp
i
Þ , 2K
i
Þ
r
i
¼ Prob
p 2p
i
1 2
p
L
i
½1 þ r
b
ð1 2fs
l
Þ? þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
2C
0
l
ðL
i
ÞL
i
1 2p
i
1 2
p
, 2K
i
r
i
¼ Prob
p 2p
i
1 2
p
L
i
½1 þ ð1 2fs
l
Þr
b
? , 2K
i
2C
0
d
ðD
i
ÞD
i
þ C
d
ðD
i
Þ þ C
l
ðL
i
Þ
þC
0
l
ðL
i
ÞL
i
1 2p
i
1 2
p
r
i
¼ Prob
p 2p
i
, 2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ
þC
0
l
ðL
i
Þ
1 2p
i
1 þ r
b
ð1 2fs
l
Þ
ðA3Þ
r
i
¼ Prob 2
p
i
, 2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ
þC
0
l
ðL
i
Þ
1 2
p
i
1 þ r
b
ð1 2fs
l
Þ
2
p
r
i
¼ Prob 2
p
i
þ C
0
l
ðL
i
Þ
p
i
1 þ r
b
ð1 2fs
l
Þ
,
2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ
þC
0
l
ðL
i
Þ
1
1 þ r
b
ð1 2fs
l
Þ
2
p
ðA4Þ
r
i
¼ Prob 2
p
i
1 þ C
0
l
ðL
i
Þ
1
1 þ r
b
ð1 2fs
l
Þ
,
2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
£
1 2
p
1 þ r
b
ð1 2fs
l
Þ
þ C
0
l
ðL
i
Þ
1
1 þ r
b
ð1 2fs
l
Þ
2
p
r
i
¼ Prob 2
p
i
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
1 þ r
b
ð1 2fs
l
Þ
, 2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
£
1 2
p
1 þ r
b
ð1 2fs
l
Þ
þ C
0
l
ðL
i
Þ
1
1 þ r
b
ð1 2fs
l
Þ
2
p
Monetary policy
and banking
failure
153
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
r
i
¼ Prob 2
p
i
, 2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
þ
C
0
l
ðL
i
Þ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
2
pð1 þ r
b
ð1 2fs
l
ÞÞ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
r
i
¼ Prob 2
p
i
.
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
2
C
0
l
ðL
i
Þ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
þ
pð1 þ r
b
ð1 2fs
l
ÞÞ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
Corresponding author
Raulin L. Cadet can be contacted at: [email protected]
JFEP
1,2
154
To purchase reprints of this article please e-mail: [email protected]
Or visit our web site for further details: www.emeraldinsight.com/reprints
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
doc_265151886.pdf
The purpose of this paper is to present a model that studies the impact of a tightening
monetary policy on banking failure in a developing country.
Journal of Financial Economic Policy
A theory of linkage between monetary policy and banking failure in developing
countries
Raulin L. Cadet
Article information:
To cite this document:
Raulin L. Cadet, (2009),"A theory of linkage between monetary policy and banking failure in developing
countries", J ournal of Financial Economic Policy, Vol. 1 Iss 2 pp. 143 - 154
Permanent link to this document:
http://dx.doi.org/10.1108/17576380911010254
Downloaded on: 24 January 2016, At: 21:35 (PT)
References: this document contains references to 15 other documents.
To copy this document: [email protected]
The fulltext of this document has been downloaded 645 times since 2009*
Users who downloaded this article also downloaded:
Dilip K. Das, (2010),"Financial globalization: a macroeconomic angle", J ournal of Financial Economic
Policy, Vol. 2 Iss 4 pp. 307-325 http://dx.doi.org/10.1108/17576381011100847
Andreas Kern, Christian Fahrholz, (2009),"Global imbalances and a trade-finance-nexus", J ournal of
Financial Economic Policy, Vol. 1 Iss 3 pp. 206-226 http://dx.doi.org/10.1108/17576380911041700
Bruno Funchal, Mateus Clovis, (2009),"Firms' capital structure and the bankruptcy law design", J ournal of
Financial Economic Policy, Vol. 1 Iss 3 pp. 264-275 http://dx.doi.org/10.1108/17576380911041737
Access to this document was granted through an Emerald subscription provided by emerald-srm:115632 []
For Authors
If you would like to write for this, or any other Emerald publication, then please use our Emerald for
Authors service information about how to choose which publication to write for and submission guidelines
are available for all. Please visit www.emeraldinsight.com/authors for more information.
About Emerald www.emeraldinsight.com
Emerald is a global publisher linking research and practice to the benefit of society. The company
manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as
providing an extensive range of online products and additional customer resources and services.
Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee
on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive
preservation.
*Related content and download information correct at time of download.
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
A theory of linkage between
monetary policy and banking
failure in developing countries
Raulin L. Cadet
Center for Research in Economics and Management
(CREM – CNRS UMR 6211), University of Rennes 1, Cedex, France and
University of Quisqueya (UniQ), Port-au-Prince, Haiti
Abstract
Purpose – The purpose of this paper is to present a model that studies the impact of a tightening
monetary policy on banking failure in a developing country.
Design/methodology/approach – The interest rate on treasury bills is included in the model to
measure monetary policy. Since the model considers developing countries with low-income level, the
paper assumes that a secondary market does not exist.
Findings – The model shows that, despite treasury bills constituting an alternative source of pro?t
for banks in developing countries, a tightening monetary policy increases the probability of banking
failure. In addition, the model shows that ef?ciency level explains the asymmetric effect of monetary
policy on the pro?t of the banks.
Practical implications – The policy implication of the results of the paper is that the central bank
should take into account the adverse effect of a tightening monetary policy on banking failure, when
planning policy decisions.
Originality/value – The paper offers insights into the linkage between monetary policy and
banking failure in developing countries.
Keywords Banking, Business failures, Monetary policy, Interest rates, Developing countries
Paper type Research paper
1. Introduction
Some empirical and theoretical papers study the causes of banking crisis. Empirical
studies emphasize the role of the banks conditions as principal factors. Wheelock and
Wilson (2000) ?nd that bank speci?c data are signi?cant factors of the US bank
failures and acquisitions. Arena (2008), for instance, reveals that bank-level
fundamentals signi?cantly affect banking failure in East Asia and in Latin America.
About the macroeconomic conditions, one of the factors of banking crises mentions by
Mishkin (1999) is high interest rates.
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – G21, G33, E52
The author is grateful to Xavier Freixas, Jean-Jacques Durand, Christophe Tave´ra, Marc
Baudry, Gilles Canales, and Steeve Crittenden for helpful discussions and comments. He wishes
to thank the seminar participants at the CREM, in April 2007, the participants at the IBFR
Conference on Business and Finance, in May 2007, and the participants at the 57th Annual
Meeting of the Midwest Finance Association (MFA), in February 2008, for their comments. The
opinions expressed in this paper are those of the author. They do not necessarily re?ect those of
the CREM and the CREGED.
Monetary policy
and banking
failure
143
Journal of Financial Economic Policy
Vol. 1 No. 2, 2009
pp. 143-154
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576380911010254
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
Kraft and Galac (2007) analyze deposits interest rate and banking failure in Croatia,
where interest rates become high because of liberalization and competition. Actually, in
addition to liberalization and competition, a tightening monetary policy may induce
increasing of interest rates. Some researchers analyze the way monetary policy affects
balance sheets and the behavior of banks. For instance, Kashyap and Stein (1995)
examine the impact of monetary policy on bank’s balance sheets. van den Heuvel
(2002) studies the effects of monetary policy in the US states. Golodniuk (2006) studies
lending channel of monetary policy in Ukraine. Bolton and Freixas (2006) analyze the
effects of monetary policy on securities market and bank lending.
van den Heuvel (2002) ?nds that the effects of monetary policy are larger on banks
with low capital level, and on banks with low liquidity level. About liquidity level,
Freedman and Click (2006) reveal that, in developing countries, banks are highly liquid.
Thus, in developing countries, where banks are highly liquid, treasury bills is an
alternative source of pro?t for banks. Actually, Brownbridge (1998), who analyzes
banking failure in Africa, underlines that treasury bills enable banks to earn large
pro?ts. Thus, does a tightening monetary policy reduce the probability of failure of
banks, in developing countries? This question is essential, because a positive answer
would suggest an opposite view to theory regarding the link between interest rate and
asymmetric information. In addition, because of the consequences of bank failures, it
does matter to identify any potential cause of these events, in order to know how to
prevent them.
Hancock (1985) and Goyeau et al. (2002) analyze bank pro?tability and interest
rates. But, they do not analyze banking failure. Even if there is a link between
pro?tability and solvency, they are different. A bank may be solvent in spite of making
losses, if equity is still positive. The empirical results of Goyeau et al. (2002) reveal that
a decrease of interest rate in Europe has a negative effect on some banking systems
whereas some other banking systems still pro?t. However, according to the study of
Hancock (1985), bank pro?t appears to increase with interest rate increasing, which
contradicts Goyeau et al. (2002). Thus, the questions still remain for research:
RQ1. Does bank pro?tability increase when interest rate increase?
RQ2. If some banks pro?t from interest rates increasing whereas some other banks
do not, what can explain this difference?
Beyond these questions, this paper is more concerned about the following:
RQ3. Does a tightening monetary policy reduce probability of bank failure in
developing countries?
RQ4. Does a tightening monetary policy increase pro?t of banks in developing
countries?
I show that, despite treasury bills constitute an alternative source of pro?t for banks in
developing countries, a tightening monetary policy increases the probability of
banking failure. In addition, the model shows that, unlike an inef?cient bank, an
ef?cient bank pro?ts from a tightening monetary policy.
Regarding ?rms, one of the main ?ndings of Bernanke and Gertler (1989) is that a
shortage of money, which increases interest rates, reduces ?rms net worth. However,
there is no theoretical framework about the linkage between monetary policy and
JFEP
1,2
144
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
individual banking failure in developing countries. Those questions are essential, as
banking failure has economic and social consequences. The paper is organized as
follows: after this introduction, Section 2 presents the model, and Section 3 exposes
some concluding remarks.
2. The model
This section presents a model of the banking sector that maximizes pro?t, and an
individual bank which is a price taker. In this model, prices are interest rates on
treasury bills, loans, and deposits. All interest rates are determined by the banking
market, except interest rate on treasury bills. This model assume that interest rate on
treasury bills, which is an exogenous price to the banking sector, is affected by
stochastic shocks. The reaction function of the interest rate on treasury bills to
stochastic shocks is not discussed in this paper. The paper only assumes that any
change in interest rate is due to the response of monetary policy authority to stochastic
shocks that affect the economy.
Since the model considers developing countries with low-income level, I assume that
secondary market does not exist. In these countries, the secondary market is not well
developed or does not exist at all. I show that, in developing countries with low-income
level, a tightening monetary policy increases the pro?t of ef?cient banks whereas
inef?cient banks do not pro?t from it. The model shows that although treasury bills
constitute an alternative source of pro?t for banks in developing countries, an increase
of interest rate on treasury bills increases the probability of banking failure.
2.1 The banking sector
I assume that the banking sector is a competitive market. The banking sector has three
assets: loans (L), treasury bills (B), and reserve (R). In the liability side of the sector’s
balance sheet, there are the shareholders equity (K) and deposits (D). The reserve of the
banking sector is a proportion of deposits. The reserve rate is denoted by a. Central
bank requires from the banking sector a capital adequacy which should be superior or
equal to a proportion of risk-weighted assets (denoted by f).
Reserve:
R ¼ aD ð1Þ
Capital requirement:
fðs
l
L þs
b
BÞ # K
where s
l
and s
b
are the risk-weight of loans and treasury bills, respectively. It is
assumed that the risk-weight of loans is identical for all banks. Since treasury bills are
risk-free, s
b
¼ 0. Thus, the capital requirement inequality becomes:
fs
l
X
L # K ð2Þ
The balance sheet identity:
L þ B þ R ¼ K þ D ð3Þ
In the balance sheet identity (equation (3)), I replace reserve (R) by its value from
equation (1). It is assumed that all banks maintain the shareholders equity equal to the
minimum of capital requirement, fs
l
L. One of the propositions proved by Rochet (2004)
Monetary policy
and banking
failure
145
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
is that under deposit insurance, commercial bank’s optimal behavior is to maintain
capital just suf?cient for meeting capital requirement. However, in developing
countries, there is implicit deposit insurance. Thus, K is replaced by its value:
L þ B þaD ¼ fs
l
L þ D Lð1 2fs
l
Þ þ B ¼ Dð1 2aÞ
L ¼
1 2a
1 2fs
l
D 2
1
1 2fs
l
B
ð4Þ
B ¼ Dð1 2aÞ 2Lð1 2fs
l
Þ ð5Þ
Since their reserve rate, a, is superior to the reserve rate imposed by the authority of
supervision, banks can reduce their liquidity to increase treasury bills. In addition, the
banks may still increase loans, despite they increase treasury bills, because banks are
highly liquid in developing countries. Thus, in developing countries, banks do not
necessarily substitute loans to treasury bills, vice versa. In this case, the effect of open
market operations of the central bank, which increases interest rate to sell treasury bills,
is weak on loans, in developing countries. That is the reason why, the ef?cacy of
monetary policy may be weak in these countries.
Each bank of the banking sector has the same cost function of intermediation,
C(D, L). This cost function, is equal to the sum of the cost of the management of
deposits, C
d
(D), and the cost of management of loans, C
l
(L). The cost function satis?es
the assumptions of convexity, such as the decreasing returns to scale. The pro?t
function of the sector is the following (see Appendix 1):
EðpÞ ¼ r
l
ð1 2
pÞL þ r
b
B 2r
d
D 2C
d
ðDÞ 2C
l
ðLÞ 2
pL ð6Þ
Because of the assumptions on C(D, L), the pro?t function is concave in D and L. The
interest rates on loans, deposits, and treasury bills are, respectively, r
l
, r
d
, and r
b
. The
expected default rate of the banking sector is denoted
p. The variable p is a random
variable. All banks face the same marginal costs whereas the expected default rate,
p
i
,
differs from bank to bank[1]. The expected default rate affects the pro?t margin of the
banks, by reducing the interest the banks should received on loans. Second, the
expected default rate causes loss in loans portfolio. These effects of the default rate on
the expected pro?t is take into account in equation (6) by the terms r
l
ð1 2
pÞL and
2
pL. The marginal costs of the banking sector and the marginal cost of any individual
bank are identical[2]. Since interest rate on treasury bills is used as instrument of
monetary policy in most developing countries, it is used in this model as the indicator
of monetary policy.
If equation (5) is replaced in the pro?t function, it becomes:
EðpÞ ¼ r
l
ð1 2
pÞL þ r
b
ð1 2aÞD 2r
b
ð1 2fs
l
ÞL 2r
d
D 2C
d
ðDÞ 2C
l
ðLÞ 2
pL
ð7Þ
Proposition 1. The interest rates on loans and deposits are both positive functions of
the interest rate on treasury bills; and the costs of intermediation increase the interest
rate on loans, and decreases the interest rate on deposits.
Proof. The problem of the banking sector is to maximize pro?t. To resolve it,
banking sector chooses the optimal amounts of loans and deposits. Because of the
assumptions of convexity on the cost function, the maximization of the pro?t is
characterized by the ?rst order conditions:
JFEP
1,2
146
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
›EðpÞ
›L
¼ r
l
ð1 2
pÞ 2r
b
ð1 2fs
l
Þ 2C
0
l
ðLÞ 2
p ¼ 0
r
l
¼
1
1 2
p
r
b
ð1 2fs
l
Þ þ C
0
l
ðLÞ þ
p
 Ã
ð8Þ
›EðpÞ
›D
¼ r
b
ð1 2aÞ 2r
d
2C
0
d
ðDÞ ¼ 0 r
d
¼ r
b
ð1 2aÞ 2C
0
d
ðDÞ ð9Þ
Equation (8) shows that the risk-weighted capital requirement, fs
l
, reduces interest
rates on loans, whereas equation (9) indicates that the reserve rate, a, reduces interest
rate on deposits. Capital requirement constitutes a cost supported by banks, as it
prevents the bank to provide loans to a certain extent. Zarruk and Madura (1992) ?nd a
similar result. The model developed in their paper shows that capital regulation results
in a reduced interest margin. A
The rate of reserve, a, which is equal or superior to the rate of reserve requirement,
is also a cost, as banks do not get return from it. This cost is supported by the
depositors. Indeed, the interest rate paid to depositors is inferior to what it should be if
there was not any reserve in the assets of the banks. Regarding the costs of ?nancial
intermediation, only the customers support them. These costs reduce interest rate they
should receive on deposits, and increase what they should pay on loans.In addition, the
expected default rate is added to the interest rate that banks’customers pay on loans.
Thus, in this model, banks receive a risk prime which is equal to the expected default
rate. This result is coherent with ?nancial economic theory. Higher expected default
rate induce higher interest rate on loans.
2.2 An individual bank
In this subsection, a bank pro?t and its probability of failure are modeled. All variables
are used with the subscript i to indicate that only one bank is considered instead of the
banking sector. The bank is a price taker. Thus, interest rates received on loans and
paid on deposits are those determined by the market (equations (8) and (9)), whereas
the value of the interest rate on treasury bills is decided by central bank, as a reaction
to stochastic shocks that affect the economy. The expected default rate of the bank is
p
i
. The value of p
i
may be different from
p. This subsection models the individual bank
as follows:
Reserve:
R
i
¼ aD
i
ð10Þ
Capital requirement:
fs
l
L
i
# K
i
ð11Þ
The balance sheet identity:
L
i
þ B
i
þ R
i
¼ K
i
þ D
i
In the balance sheet identity, reserve (R
i
) is replaced by its value from equation (10),
and K
i
by its value from equation (11)[3]:
L
i
þ B
i
þaD
i
¼ fs
l
L
i
þ D
i
L
i
ð1 2fs
l
Þ þ B
i
¼ D
i
ð1 2aÞ
B
i
¼ D
i
ð1 2aÞ 2L
i
ð1 2fs
l
Þ
ð12Þ
Monetary policy
and banking
failure
147
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
The pro?t function of the bank is written as follows:
Eðp
i
Þ ¼ r
l
ð1 2p
i
ÞL
i
þ r
b
B
i
2r
d
D
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ 2p
i
L
i
ð13Þ
In the pro?t function (equation (13)), interest rates on loans and deposits are replaced
by their respective value which are in equations (8) and (9). Thus, the pro?t function of
the bank becomes[4]:
Eðp
i
Þ ¼
p 2p
i
1 2
p
L
i
½1 þ r
b
ð1 2fs
l
Þ? þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ
2C
l
ðL
i
Þ þ C
0
l
ðL
i
Þ
1 2p
i
1 2
p
L
ð14Þ
The gap between the expected default rate of the banking sector and the default rate of
an individual bank,
p 2p
i
, is the relative ef?ciency of this bank. Thus, the pro?t of a
bank is a function of the relative ef?ciency of this bank.
Proposition 2. When central bank tightens monetary policy, by increasing interest
rate on treasury bills, depending on bank’s relative ef?ciency, three cases are possible,
regarding pro?t.
Proof. The partial derivative of the pro?t function of the bank, with respect to
interest rate on treasury bills, is the following:
›Eðp
i
Þ
›r
b
¼
p 2p
i
1 2
p
L
i
ð1 2fs
l
Þ ð15Þ
.
If the relative ef?ciency of the bank is negative, i.e.
p 2p
i
, 0, a tightening of
monetary policy will reduce the bank’s pro?ts:
›Eðp
i
Þ
›r
b
, 0
.
If the relative ef?ciency of the bank is null, i.e.
p 2p
i
¼ 0, a shock of monetary
policy will have no impact on the pro?ts of the bank:
›Eðp
i
Þ
›r
b
¼ 0
.
If the relative ef?ciency of the bank is positive, i.e.
p 2p
i
. 0, its pro?ts will
increase when central bank tightens monetary policy:
›Eðp
i
Þ
›r
b
. 0
The ef?ciency level is a factor that explain the asymmetric effect of monetary policy on
the pro?t of the banks. An inef?cient bank does not pro?t from a tightening monetary
policy, whereas an ef?cient bank. When central bank tightens monetary policy, even if
an ef?cient bank does not buy treasury bills, it should modify the structure of its
balance sheet to maintain its pro?ts at the same level or to increase it. Since the interest
rates increase when the central bank tightens monetary policy, if a bank maintain the
growth of its loans at the same level, the amount of non performing loan may increase.
JFEP
1,2
148
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
For, the increasing of the interest rate on loans induces an increase of asymmetric
information.
Thus, when central bank tightens monetary policy, an ef?cient bank should reduce
the growth of its loans to reduce the effect of asymmetric information. That is the
reason why a tightening monetary policy may induce an increase of the pro?t of an
ef?cient bank. Actually, a tightening monetary policy may also have a neutral impact
on the pro?t of an ef?cient bank. Since an inef?cient bank does not deal well with
asymmetric information, a tightening monetary policy induces a decrease of the pro?t
of such a bank.
Proposition 3. Since it decreases the ef?ciency level of the bank, an increase of
interest rate on treasury bills, which is a tightening monetary policy, increases the
probability of failure of the bank.
Proof. I consider that a bank fails when it is insolvent. Thus, the bank is insolvent
if the sum of shareholders equity and pro?t is negative. The probability of failure of the
bank, which is denoted r, is calculated as follows (see Appendix 2):
r
i
¼ PðK
i
þ Eðp
i
Þ , 0Þ ¼ PðEðp
i
Þ , 2K
i
Þ
r
i
¼ Prob
p 2p
i
1 2
p
L
i
½1 þ r
b
ð1 2fs
l
Þ?
þC
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ 2C
0
l
ðL
i
ÞL
i
1 2p
i
1 2
p
, 2K
i
r
i
¼ Prob p
i
.
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
2
C
0
l
ðL
i
Þ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
þ
pð1 þ r
b
ð1 2fs
l
ÞÞ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
ð16Þ
Equation (16) shows that the probability of failure is the probability that the default
rate of the bank is superior to a threshold which is denoted T, with:
T ¼
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
2
C
0
l
ðL
i
Þ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
þ
pð1 þ r
b
ð1 2fs
l
ÞÞ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
Thus, the probability of the failure of the bank, r
i
, is:
r
i
¼ Prob ðp
i
. TÞ ¼ 1 2Prob ðp
i
# TÞ r
i
¼ 1 2Prob ðp
i
# TÞ ð17Þ
The default rate may be interpreted as an indicator of the ef?ciency level of the bank.
Because the probability of failure is the probability that the expected default rate is
superior to a threshold, ef?ciency level and the probability of failure are linked.
The partial derivative of the probability of failure, with respect to the interest rate
on treasury bills, can now be calculated to verify the impact of a tightening monetary
policy:
Monetary policy
and banking
failure
149
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
›r
i
›r
b
¼ 2
›Probðp
i
Þ # T
›r
b
ð18Þ
›Probðp
i
# TÞ
›r
b
¼
›Probðp
i
# TÞ
›T
›T
›r
b
ð19Þ
›T
›r
b
¼ 2
L
i
ð1 2fs
l
Þð1 2
pÞðK
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
ÞÞ
½1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ?
2
þ
C
0
l
ðL
i
Þð1 2fs
l
Þ
½1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ?
2
þ
pð1 2fsÞ½1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ? 2
pð1 2fs
l
Þ½1 þ r
b
ð1 2fs
l
Þ?
½1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ?
2
ð20Þ
Because of equations (18) and (19), the sign of the impact of the monetary policy
interest rate on the probability of failure, ›r
i
=›r
b
, is the opposite sign of the derivative
of the threshold T, with respect to the interest rate of the monetary policy, ›T=›r
b
.
According to the last result (equation (20)), the sign of ›T=›r
b
depends between the
equity and the total cost of intermediation. Since the paper assumes that all banks
respect the minimum capital requirement, shareholders equity is enough to be higher
than the intermediation costs. Thus, the derivative of the threshold, with respect to r
b
,
is inferior to zero. Thus, the derivative of the probability of failure, with respect to r
b
, is
superior to zero:
›T
›r
b
, 0 ð21Þ
›r
i
›r
b
. 0 ð22Þ
A
The sign of ›r
i
=›r
b
shows that, because it decreases the ef?ciency level of the bank, a
tightening monetary policy increases the probability of failure of this bank.
As underlined previously, the expected default rate is an indicator of the ef?ciency
level of the bank. Indeed, the increasing of interest rates causes the increasing of
asymmetric information. That is the reason why the probability of failure of all banks
increase when the central bank tightens monetary policy. To deal with asymmetric
information an ef?cient bank should reduce the growth of its loan portfolio.
A limitation of my model is that it does not account for time, which limits the
possibility to show the dynamic impact of monetary policy on banking failure.
Although static, the model meets the questions to which it intended to answer; the
model shows that, despite treasury bills constitute an alternative source of pro?t for
banks in developing countries, a tightening monetary policy increases the probability
of banking failure. In addition, the model shows that an ef?cient bank pro?ts from a
tightening monetary policy, whereas an inef?cient bank does not.
JFEP
1,2
150
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
3. Concluding remarks
In this paper, I show that ef?ciency level explains the asymmetry of the effect of
monetary policy on banking pro?t. The level of relative ef?ciency explains why some
banks pro?t from a tightening monetary policy, whereas some other banks do not. In
addition, the model shows that, despite treasury bills constitute an alternative source of
pro?t for banks in developing countries, a tightening monetary policy increases the
probability of banking failure. Actually, an increase of the interest rates induces an
increase of asymmetric information. An ef?cient bank should decrease its loan
portfolio to deal with asymmetric information.
If the interest rate is so high so that loan portfolio should be null, there will be a
banking crisis. There is a threshold of interest rate, which I call a threshold of crisis,
that interest rate on treasury bills should not exceed.
The policy implication of the results of this paper is that, the central bank should
take into account the adverse effect of tightening monetary policy on banking failure,
when planning policy decisions. Actually, although monetary policy intend to stabilize
the price level, it may destabilize the banking sector if the growth of the interest rate is
not moderate.
Notes
1. The default rate is the ratio of loans not reimburse to total loans.
2. Since all banks face the same marginal cost, C
0
d
ðDÞ ¼ C
0
d
ðD
i
Þ and C
0
l
ðLÞ ¼ C
0
l
ðL
i
Þ.
3. Remember that it is assumed that all banks maintain the exact minimum of capital
requirement.
4. See Appendices for details about calculus.
References
Arena, M. (2008), “Bank failures and bank fundamentals: a comparative analysis of Latin
America and East Asia during the 1990s using bank-level data”, Journal of Banking
& Finance, Vol. 32 No. 2, pp. 299-310.
Bernanke, B. and Gertler, M. (1989), “Agency costs, net worth, and business ?uctuations”,
The American Economic Review, Vol. 79, pp. 14-31.
Bolton, P. and Freixas, X. (2006), “Corporate ?nance and the monetary transmission mechanism”,
Review of Financial Studies, Vol. 19, pp. 829-70.
Brownbridge, M. (1998), “Financial distress in local banks in Kenya, Nigeria, Uganda and
Zambia: causes and implications for regulatory policy”, Development Policy Review, Vol. 16,
pp. 173-88.
Freedman, P.L. and Click, R.W. (2006), “Banks that don’t lend? Unlocking credit to spur growth
in developing countries”, Development Policy Review, Vol. 24 No. 3, pp. 279-302.
Golodniuk, I. (2006), “Evidence on the bank-lendind channel in Ukraine”, Research in
International Business and Finance, Vol. 20, pp. 180-99.
Goyeau, D., Sauviat, A. and Tarazi, A. (2002), “Rentabilite´ bancaire et taux d’inte´reˆt de marche´:
une application aux principaux syste`mes bancaires europe´ens sur la pe´riode 1988-1995”,
Revue d’Economie Politique, Vol. 112 No. 2, pp. 275-91.
Hancock, D. (1985), “Bank pro?tability, interest rates, and monetary policy”, Journal of Money,
Credit, and Banking, Vol. 17 No. 2, pp. 189-202.
Monetary policy
and banking
failure
151
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
Kashyap, A.K. and Stein, J.C. (1995), “The impact of monetary policy on bank balance sheet”,
Carnegie-Rochester Conference Series on Public Policy, Vol. 42, pp. 151-95.
Kraft, E. and Galac, T. (2007), “Deposit interest rates, asset risk and bank failure in Croatia”,
Journal of Financial Stability, Vol. 2, pp. 312-36.
Mishkin, F.S. (1999), “Global ?nancial instability: framework, events, issues”, The Journal of
Economic Perspectives, Vol. 13 No. 4, pp. 3-20.
Rochet, J.C. (2004), “Capital requirements and the behavior of commercial banks”, Credit,
Intermediation and the Macroeconomy: Models and Perspectives, Oxford University Press,
Oxford.
van den Heuvel, S.J. (2002), “Banking conditions and the effects of monetary policy: evidence
from US states”, mimeo, University of Pennsylvania, Philadelphia, PA.
Wheelock, D.C. and Wilson, P.W. (2000), “Why do banks disappear: the determinants of US
bank failures and acquisitions”, Review of Economics and Statistics, Vol. 82 No. 1,
pp. 127-38.
Zarruk, E.R. and Madura, J. (1992), “Optimal bank interest margin under capital regulation
and deposit insurance”, Journal of Financial and Quantitative Analysis, Vol. 27 No. 1,
pp. 143-9.
Appendix 1. Pro?t function of the bank
The pro?t function of the bank is written as follows:
Eðp
i
Þ ¼ r
l
ð1 2p
i
ÞL
i
þ r
b
B
i
2r
d
D
i
2C
l
ðL
i
Þ 2C
d
ðD
i
Þ 2p
i
L
i
ðA1Þ
In the pro?t function (equation (A1)) I replace interest rates on loans and deposits by their
respective value which are in equations (8) and (9). Thus, the pro?t function of the bank
becomes:
Eðp
i
Þ ¼
1
1 2
p
ðr
b
2r
b
fs
l
þ C
0
l
ðL
i
Þ þ
pÞð1 2p
i
ÞL
i
 Ã
þ r
b
ð1 2aÞD
i
2r
b
ð1 2fs
l
ÞL
i
2r
b
ð1 2aÞD
i
þ C
0
d
ðD
i
ÞD
i
2C
l
ðL
i
Þ 2C
d
ðD
i
Þ 2p
i
L
i
Eðp
i
Þ ¼
1
1 2
p
r
b
L
i
2r
b
fs
l
L
i
þ C
0
l
ðL
i
ÞL
i
þ
pL
i
2r
b
p
i
L þ r
b
fs
l
p
i
L
i
2C
0
l
ðL
i
Þp
i
L
i
2pp
i
L
i
Â
2r
b
ð12fs
l
Þð12
pÞL
i
þ C
0
d
ðD
i
Þð12
pÞD
i
2C
l
ðL
i
Þð1 2
pÞ 2C
d
ðD
i
Þð1 2
pÞ 2p
i
ð1 2
pÞL
i
Ã
Eðp
i
Þ ¼
1
1 2
p
r
b
L
i
2r
b
fs
l
L
i
þ C
0
l
ðL
i
ÞL
i
þ
pL
i
2r
b
pL
i
þ r
b
fs
l
p
i
L
i
2C
0
l
p
i
L
i
2pp
i
L
i
Â
2r
b
L
i
þ r
b
pL
i
þ r
b
fs
l
pL
i
2r
b
fs
l
pL
i
þ C
0
d
ðD
i
ÞD
i
2C
0
d
ðD
i
Þ
pD
i
2C
l
ðL
i
Þ þ C
l
ðL
i
Þ
p
2C
d
ðD
i
Þ þ C
d
ðD
i
Þ
p 2pL
i
þ pp
i
L
i
Ã
Eðp
i
Þ ¼
1
1 2
p
L
i
ð
p 2p
i
Þ þ r
b
L
i
ð
p 2p
i
Þ 2r
b
fs
l
L
i
ð
p 2p
i
Þ
Â
þC
0
d
ðD
i
ÞD
i
ð1 2
pÞ 2C
0
l
ðL
i
Þð1 2p
i
ÞL
i
2C
d
ðD
i
Þð1 2
pÞ 2C
l
ðL
i
Þð1 2
pÞ
Ã
Eðp
i
Þ ¼
p 2p
i
1 2
p
L
i
½1 þ r
b
ð1 2fs
l
Þ? þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ 2C
0
l
ðL
i
ÞL
i
1 2p
i
1 2
p
ðA2Þ
JFEP
1,2
152
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
Appendix 2. The probability of banking failure
r
i
¼ PðK
i
þ Eðp
i
Þ , 0Þ ¼ PðEðp
i
Þ , 2K
i
Þ
r
i
¼ Prob
p 2p
i
1 2
p
L
i
½1 þ r
b
ð1 2fs
l
Þ? þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
2C
0
l
ðL
i
ÞL
i
1 2p
i
1 2
p
, 2K
i
r
i
¼ Prob
p 2p
i
1 2
p
L
i
½1 þ ð1 2fs
l
Þr
b
? , 2K
i
2C
0
d
ðD
i
ÞD
i
þ C
d
ðD
i
Þ þ C
l
ðL
i
Þ
þC
0
l
ðL
i
ÞL
i
1 2p
i
1 2
p
r
i
¼ Prob
p 2p
i
, 2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ
þC
0
l
ðL
i
Þ
1 2p
i
1 þ r
b
ð1 2fs
l
Þ
ðA3Þ
r
i
¼ Prob 2
p
i
, 2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ
þC
0
l
ðL
i
Þ
1 2
p
i
1 þ r
b
ð1 2fs
l
Þ
2
p
r
i
¼ Prob 2
p
i
þ C
0
l
ðL
i
Þ
p
i
1 þ r
b
ð1 2fs
l
Þ
,
2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ
þC
0
l
ðL
i
Þ
1
1 þ r
b
ð1 2fs
l
Þ
2
p
ðA4Þ
r
i
¼ Prob 2
p
i
1 þ C
0
l
ðL
i
Þ
1
1 þ r
b
ð1 2fs
l
Þ
,
2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
£
1 2
p
1 þ r
b
ð1 2fs
l
Þ
þ C
0
l
ðL
i
Þ
1
1 þ r
b
ð1 2fs
l
Þ
2
p
r
i
¼ Prob 2
p
i
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
1 þ r
b
ð1 2fs
l
Þ
, 2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
£
1 2
p
1 þ r
b
ð1 2fs
l
Þ
þ C
0
l
ðL
i
Þ
1
1 þ r
b
ð1 2fs
l
Þ
2
p
Monetary policy
and banking
failure
153
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
r
i
¼ Prob 2
p
i
, 2
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
þ
C
0
l
ðL
i
Þ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
2
pð1 þ r
b
ð1 2fs
l
ÞÞ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
r
i
¼ Prob 2
p
i
.
K
i
þ C
0
d
ðD
i
ÞD
i
2C
d
ðD
i
Þ 2C
l
ðL
i
Þ
L
i
1 2
p
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
2
C
0
l
ðL
i
Þ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
þ
pð1 þ r
b
ð1 2fs
l
ÞÞ
1 þ r
b
ð1 2fs
l
Þ þ C
0
l
ðL
i
Þ
Corresponding author
Raulin L. Cadet can be contacted at: [email protected]
JFEP
1,2
154
To purchase reprints of this article please e-mail: [email protected]
Or visit our web site for further details: www.emeraldinsight.com/reprints
D
o
w
n
l
o
a
d
e
d
b
y
P
O
N
D
I
C
H
E
R
R
Y
U
N
I
V
E
R
S
I
T
Y
A
t
2
1
:
3
5
2
4
J
a
n
u
a
r
y
2
0
1
6
(
P
T
)
doc_265151886.pdf