8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
1/18
Credit Rationing and Implicit Contract Theory
Author(s): Joel Fried and Peter HowittSource: Journal of Money, Credit and Banking, Vol. 12, No. 3 (Aug., 1980), pp. 471-487Published by: Ohio State University PressStable URL: http://www.jstor.org/stable/1991722.
Accessed: 19/11/2014 17:36
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at.http://www.jstor.org/page/info/about/policies/terms.jsp
.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of
content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].
.
Ohio State University Pressis collaborating with JSTOR to digitize, preserve and extend access toJournal of
Money, Credit and Banking.
http://www.jstor.org
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/action/showPublisher?publisherCode=ohiosuphttp://www.jstor.org/stable/1991722?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/1991722?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=ohiosup8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
2/18
JOEL FRIED
PETER HOWITT*
CreditRationing ndImplicit
Contract heory
1. INTRODUCTION
THE RECENT URVEYby Baltensperger[S] shows that the
question of why bankers undertakenonprice rationing of credit is still very much
unanswered.Previousattempts o address he questionhave ended up merely assum-
ing the answer. For example, the attempts prior to the 1960s all involved the
assumption hat interest rates could not adjust so as always to clear the marketfor
credit, the attemptby Hodgman [9] did not really addressthe issue of interestrate
determination,and the later attempt by Jaffee and Modigliani [10] involved the
assumptionthat banks cannot charge different rates to all of their customers. The
only analysis in the literature hat is free from this criticism is that of Jaffee and
Russell [11], which focuses on adverse selection concerning default by dishonest
customers.
Meanwhile,recentdevelopments n the theoryof laborcontracts e.g., [1, 2, 3, 4,
7]) have made progress n answering he closely analogousquestionof why firms ay
workersoff rather hanadjustwages. The purposeof the presentpaper s to show how
thesedevelopments an be used andextendedso as to providea tentativeanswer o the
question of why bankersration credit.1
*Financialupportrom heSocialSciences ndHumanities esearch ouncil f Canadas gratefully
acknowledged.
1The nalysis f Koskela 13, chap.6] is theonlyother ttemptn the iteratureo addresshequestion f
credit ationingnthese ermsKoskela'analysis, owever,wasdirected t hemuch arrowerssueof the
conditionsnderwhich he oanrate n anoptimalmplicit ontract ouldbe independentf variationsn
thestates f theworld,which,as theorem below hows, s notsufficiento demonstrateheesistence f
credit ationing.
JOELRIEDnd PETER OWITTre associate professors of economics, Universityof Western
Ontario.
0022-2879/80/0880-0471$00.50/0
t
1980 OhiOState UniVerSitYreSS
JOURNALFMONEY,CREDIT, NDBANKING, O1. 2, nO. 3 (AUgUSt 980)
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
3/18
472
:
MONEY,
CREDIT,
AND
BANKING
In
brief, our
answer
is
that
credit
rationing
exists
as
part
of an
equilibrium
risk-sharing
rrangement
etween
a bank
and
its
customers.
A
borrower
and
lender
can
benefit
not
only
from
trading
oan
contracts
now,
but
also
from an
understand-
ing or
implicit
ontract
oncerning he
amounts
hey
will be
willing
to
trade,
andat
what
prices,
under
various
conditions
in the
future.
By
means
of
such
arrangements
banksand
their
customerscan
share
the
risks
associated
with
an
uncertain
uture.
Thus
their
arrangements
may be
similar to
insurance
contracts
in
which
the less
risk-averse
party
agrees
for a
fee
to bear
some
of
the risks
to
which
the
other
party
would
otherwisebe
exposed.
The
example
thatwe
shall
use is
the
risk of
changing
costs of
funds
to
Snancial
intermediaries.
f
loans
were
always
negotiatedin
spot
auction
markets hen
customers
would
be
exposed
to the
risk
of
fluctuating
nterest
rates
ontheir
oans. A
bank
maybe
willingto
insure he
customer
against
part
of such
risksby a policy of keeping interestratesless variablethanthey would be on spot
auction
markets,
n
return
orwhich
the
customersmay
be
willing
to
compensate he
bank n the
formof a
higher
average
nterestrate.
But
by
damping he
movements
n
interest
rates
these
arrangements
pen up
the
possibility of
nonprice
rationing.
One
merit
of
the
present
answer
is
thatit
directs
attention
back
toward
the issue
often
raised
by
bankers
themselves
when
askedto
explain
why
they
ration
credit;
namely,
theissue
of
customer
relations.
As in
the
market
or
labor,
it is
typical
for
the
relationship
etween
trading
partners n the
market
or
bank
oans to be
involved
and
highly
personal.
The
object
being
traded s
heterogeneous
in
this
case it
involvesthe
trustworthiness f theborrower),andon eitherside of themarket herearenontrivial
costs
involved
in
switching
one's
trading
partner.
Thus
the
normal
arrangement
between
rading
partners,
whether n
an
explicit
contract
or an
implicit
understanding,
will
take into
account
the
advantages
to
both
sides of
maintaininga
continuous
relationship,
as well
as
the
more
immediate
advantages
from
mutually
beneficial
trade.
The
present
answer
depends
crucially
upon the
existence
of
such
customer
relations.
In
particular, he
analysis
below
implies
that if
there
were no
costs
to
switching
trading
partners
hen
credit
rationing
could
never
occur,
because
there
would
be
no
incentive
for
anyoneto
enter
nto
such
risk-sharing
rrangements
t
all.2
Furthermore,heanalysisoffersanexplanationof whythere s atendency orbanks o
ration east
heavily
those
customerswith
the
longest
standing
relationship.
The
answer o
why
nonprice
credit
rationing
xists also
directs
attention
away
from
the
issue
most
heavily
stressed
by
recent
authors,
namely
thatof
default
risk.3
This
is
2As
pointed
out
below,
these
switchingcosts
may
be
voluntarily
mposed
n an
explicit
contract.
The
use
of
customer
elations s an
attempt o
lend
realism o
the
analysisby
generating
witching
costs
without
he
necessityof
explicit
contracts.
3Data
compiledby
MerrillLynch
Royal
SecuritiesLtd.
fromthe
financial
statements
of the
Canadian
banks ndicate
hat
over the
last
decade,
the
average
valueof
defaults
constituted
ess than
S
percentof
total
loansfortheCanadian ankingsystem.Further,no individualbankhadloanlosses greater
han .7
percent
of its
loan
portfolio.
Datafor the
U . S
indicatesimilar
qualitative
esults
We
would
like to
thankM
Jensen
of the
Universityof
Western
Ontariofor
pointingout
these
figures to
us.
That
bankshave
low
default
rates
neednot
implythat
heyration
on
thebasis
of
defaultrisk.
It
couldalso
meanthat
banks
have a
comparative
advantage n
lending
to a
class of
customer
hat
has a
historically ow
probability f
default:
.e.,
in the
absence
of
interest
rate
regulations,abank
would
require
ahigher
(lower)
loan
rate rom
a
risky
ndividual
riskless
usiness
firm) han
would, say,
a
finance
company.This
may
meanthat
much
that
appears o
be
credit
rationing
s
simply
market
egmentation
basedupon
comparative
advantage.
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
4/18
JOELFRIED AND PETER HOWITT : 473
not to suggest thatbanksdo not spend a greatdeal in an attempt o screenout potential
defaulters. ndeed, the cost of screeningout potentialdefaulters s an important artof
the answer. However, our analysis does not imply thatthose customersmost heavily
rationedwill necessarily be those with the highest probabilityof defaultingor that
customerswith a negligible probabilityof default will never be rationed.4
The rest of the paper s organizedas follows. Section 2 lays out a model of implicit
contracts, ormallyquite similar o thatof Azariadis[2] and demonstrates ome basic
results, including the results that credit rationing may exist under some circum-
stances, andthat ong-established ustomersare less likely thanothers o be rationed.
Section 3 discusses the natureof such rationing,especially with respectto the issues
of whetheror not it is consistentwith the universalpursuitof self-interest,and n what
sense the results depend upon the existence of customer relations. Section 4
digressesbriefly o show how the argument ould be amended o includeexplicitly the
rlskof default. Section 5 characterizes he natureof equilibrium arrangements, ith
particular ttention o the influence of variousexogenous variablesupon the interest
rates chargedby banks and upon the indicence of credit rationing. Section 6 adds
some concluding comments.
2. THE MODEL
We shall consider implicit contracts between a particularbank and its several
customers. The randomvariable whose fluctuations ntroducean element of risk is
the bank's cost of funds i. This can be thoughtof as some economy-wide (real) rate
of interest. The set l C R+ is the set of all possible values of this interestrate, and
its randombehavior is believed by all concernedto be governed by the probability
distributionq(i), where q(i) > O for all i E I. Since the values of i define for our
purposes the states of the world, we shall use the expression in state i to mean
when the cost of funds to banks-- the interestratequals i.
The bank has two classes of customers, indexed by k = O, 1. Class Ocustomers
are those with whom it has a long-establishedrelationship;we call them the old
customers. Class 1 customersare new. All customerswithin a particular lass are
identical. Formally, the only difference between the two classes is that, from the
bank's viewpoint, lending to an old customer is less costly than lending to a new
customer or two reasons. First, old customersmay be supposed already o have an
accountwith this particular ank, which may producesome economies in administer-
ing loans. This factor is much stressed by the literatureemphasizing the joint-
product atureof the bankingenterprise e.g., [8]).5 Second, partof this administra-
4It should be stressed that, if financial intermediaries an successfully identify borrowerswith high
potentialdefaultrisks, then, in the absenceof interest ateregulations,defaultriskcannotbe used to explain
nonprice ationing.This is because nothingprecludes he intermediaryrom charginga differential o high
risk customers to reflect this higher expected cost. The reason Jaffee and Russell [11] get nonprice
rationing s because they implicitly suppose that screeningcosts are infinite, and thus the lender cannot
screen out dishonest borrowers.
sAnother reason for administrativeeconomies for customers with established accounts is that the
effective cost of funds to the bank is lower in an intertemporal ontext. That possibility is not directly
explored in this paper.
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
5/18
474 :
MONEY, CREDIT,AND BANKING
tive cost
takes the form of
screeningthecustomer o
ensurethat he is a
good risk. 6
This cost
may be incurredon every loan
to a new
customer but not to an old one,
because the old one has
alreadybeen
screened n thepast and because
the bank also
has, we
may presume, some first-hand
experience in
dealing with the customer,
which can be used to substitute or other resources n screening (see also [12]). To
capturethis difference
between old
and new customers we assume
that the total
administrative ost of lending to
n
old
customers and
nl new customers is
c(ohn
+ nl), where c is a
cost function
with positive and increasing
marginal cost
(c ' > O, c > O), and O
< cx< 1. In
other words we assume that old
and new cus-
tomers are
perfectly
substitutableas far as
administrative osts are
concerned, but
that
lending to an old
customercosts only the fraction
cxas much as to a new one.
Inkeepingwith the
literature n
contracts or laborwe shall suppose
hatone side of
the markets systematicallymore riskaversethantheother. Inparticular uppose hat
the
customersareriskaversebut the bank
s risk-neutral.
n the former iterature uch
an
asymmetrical
assumption s often justified by the
naturalselection
that tends to
make
entrepreneurs ystematically
more willing to
bear risk than are workers.
Likewise, in the present
case, the asymmetrycan be
justified by
reference to the
traditionally ited role of banks as
financial
ntermediaries hatspecialize in bearing
financial
risks that neither
ts creditorsnor its debtors
could bear as
efficiently in the
absenceof
suchintermediaries.7 n any
event it should
be noted that nwhat follows,
while an
extremeassumptionof
risk-neutral anks s
crucialfor theparticular ormof
many of the results, such as the fixed loan-rate heorem, it is quiteinessentialto the
primary
purposeof rationalizing he
phenomenonof
credit rationing,which would
still existundera very
large varietyof
alternativeassumptions.8Thus
the chief merit
of ourextreme
assumption s the
analytical simplicity that it permits.
Again, in the interest
of simplicity,
assume that each customer
wishes to borrow
one unitof
money, and
that he bankmustgrant his loan
either n full or
not at all. Let
nk(i) denote the number
of class kcustomers(k = O,l )
to whom the
bank will lend
in state i.
Let rk(i) be the
correspondingreal rate of
interest chargedon the loan.
Then the
bank will seek
to maximize its expected
profits
r I
A
iel k=O
J
6Large ompanies hathave
been rated
nationally may entail no screeningcosts to the
individualbank.
While we do
not make such gradations, an
implication would be
that ceteris paribus,nationally rated
corporations
will be treatedmore
ike old customers han ike new
customers n termsof
nonprice ationing.
7An
alternativeway of justifying this
assumption s to say that a given variabilityof
i imposes lower
perceived eal
costs on a bank han t would on a firm
f the firmwere to
handle ts financingby borrowing n
the securities
market.This could
be because the transactions osts to
the firm borrowing
n the securities
market varies positively with i whereas, because of deposit pooling and economies of scale, these
transactionsosts are state
invariant or banks. A
second alternative s to supposethat
familiaritywith the
financial
market tself decreasestheperceived
iskiness of operating
n it so that the subjectiveriskiness
of fluctuating
is less to banks
than to firms.
8For
xample, see the closely relatedanalysison
labor-market
ontractsby Markusen 14], in which both
sides areassumed o be risk
averse. It is an obvious
consequenceof continuity hat f the
loan rate s constant
and credit
rationingmay occurwhen the bank is
risk neutral
theorems1 and 2 below], then the loan rate
will be almost
constantandcreditrationingmay
still occur if the bank s almost risk
neutral.This in itself
shows that
risk neutrality s
inessential for our main objective.
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
6/18
JOEL
FRIED
AND
PETER
HOWITT :
475
Customers
f
differentclasses
differffom
each
otheronly
with
respectto
adminis-
trativecosts.
Thus
each
customer is
assumedto
have a
utility
function uf ),
with
u ' >
O, u
< O,
which
depends
upon
therandom
real
returnx,
to a
project
hat he
wishesto financebymeansof a loan.If he getstheloan ata rater hisexpectedutility s
w(r)-Exu(x-r). If
he is
rationed
we
assume
that his
utility is
equal to
K.9Note
that
w',
w O; Xk >
O, Vk
(6)
i
mk - nk
(i) > 0, >
k (i)
> ; ti,
k,
(7)
with at least
one
equality in each
complementary
pair of conditions
in
(4)-(7), and
where
cx = cx,cxl =
1, andthe Xk's
and Fk(i)'s
areLagrangian
multipliers.
Note that if
8 is an
equilibriumwith
respect to (m,
ml), then
Xk
> O
if mk > O; k
= O, 1 .
(8)
For
suppose
that mk > Oand
Xk
>
O.
Then from
(6),
Xk =
O.
Therefore,
from (3),
nk(i) = O ti e
I. Therefore,
from (6),
K- Ak> O,
contradicting
2).
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
8/18
JOELFRIED
AND
PETERHOWITT :
477
Our
firstresult
illustrates n
extreme form
the
possibilitythat
such
contractsmay
involve the
bank
insuring its
customers
againstrisks of
variations in
the rate
of
interest.
THEOREM.
In any optimalcontract,
k(i) =
rk(i')
for all i, i'
e
I suchthat
nk(i) + O
+ nk
(i').
Proof.
follows immediately
from
(1), (3), and
(8).
Thus
withineach
class
whenever a loan is
granted he same rate
will
be charged,
independentlyof
variations n
the
economy-wide
interestrate i.
It follows
from
theorem 1 that we
may
safely assume that
rk(i) s
constantlfor
all
i, [rk(i)
= rk > O
ti, k]since
neitherthe
bank nor
the class k
customercares
what
the loan rate is
if nk(i)
= O. Next,
note
that, from (3),
(4), and
theorem1,
q(i) [Z (rk) - i
- o2..kC'(
)]
0;
ti k
(9)
with at
least
one equality in
each
complementary
pair,
where
z(r)-r- [w'
(r)]-l [w(r)
-K] .
(10)
The
functionz ( ) is
importantor the
followinganalysis. It
may be
interpreted s
the
shadow-value o
thebankof an
additionaloan at the
rater
in statei; i.e.,
the
interest
revenueplus theaddition nexpectedprofits hat trealizesbecausethe
additionaloan
reduces
the probability
of
rationing n state
i by the
amount
/mk to each
of its mk
customers,each
of whom can
be
chargedaninterest
ratethat
s higher han
otherwise
by the amount
l/mk)
[wt
(r)]-
1 [w(r)
- K]with
no loss
in utility. Thus
(9)
asserts
that f O
< nk(i)
O Rli,
k.
( 13)
The
theorem
follows from ( 10),
( 12),
and ( 13).
These
necessaryconditions
are illustrated n
Figure 1, which
is constructed
as
follows. If no
rationing
s to occur, then
r and rl
can be calculated
rom (12).
Thus
the linesRR
andR 1R
can be constructed
by finding he tangent
o
w(i) at eachwk nd
shifting t in so as to pass throughEi. Now according o theorem2 if there s to be no
credit-rationing
hentherecan be
no valueif i in I
greater han
lma or imaX.
f course
thiscondition
will not
always holdon the
basis of
the assumptions
madeso far.Thus t
is possible
(but
not necessary)
for credit
rationing o occur
as part
of an equilibrium
contract.
n(i)+ nl(i)
m+ml
Xz(rl) -i -c'(am+nl(i))=
O
_
m --l---------- |
l\
:
I l\
I
l
|
\ z(r)-i
-ac'(an(i))= O
i
i a
\ i
jA
jB jC
jD
=z (rl) - c'(am+
ml)
= z (rl) = z (r)
= z ( r)
-c'(a m)
- ac'(a m) -ac'(O)
Fig.
1. Equilibrium
Contractswith
No Credit
Rationing
It
can be verified
directly
from Figure l that
the likelihood
of credit
rationing
occurring s larger the largeris: (l) the mean interestrateEi (becausean increase
in Ei
shifts the entire
distribution
o the right
but it thereby
makesRR
and RIRl
lower
and steeper, thus
reducing
maxk
-
Ei), (2)
the varianceof
interest
rates, (ri2,
(3) the marginal
cost
of loans, c' (
), (4) the ratio (ml/m)
for
a given value of
m
+ ml, (S)
the expected
utility derived
by rationed
customers,
K, or (6) the
inverse
of Ex, the expected
return from
the typical
customer's
project
(because
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
10/18
JOELFRIED
AND
PETER
HOWITT : 479
reducing Ex
shifts the
w(
) curve
down and
makes it
steeper,
thereby
doing
the
same to
RRo nd
R9R) .
The last
result
of the
present
section
shows that, as
long as
r 0,
withr O Vi.
That is,
whenevern(i) >
O,r' (i) =
r (i) = i + c' [n
(i)]. But,
given
perfectmobility
of customers,
r'(i) is
an equilibrium
rate only if
n(i) equals the
numberof customersper bank actuallydesiringa loan at the rate r'(i). Thus, an
equilibrium
s
a contractwith
[r(i), n(i)] =
[i + c'(m),
m] if w[i + c'(m)]
>
K, or
(w - 1(K),
max {O,s [w- 1
(K)- i]})
otherwise,
(15)
where
m is the
given number
of customers
per bank, and
sf ) is the
inverseof the
functionc'( ). It follows from(15) thattheorem1 no longerholds;that is the loan
ratenow fluctuates.
Also,
the possibility
of credit
rationingnow disappears
because,
according o
(15), any
customerdesiring
a loan
is always granted
one. In fact, we
would
hardlysay that
this equilibrium
s one with
contracts
at all. For the customers
see
themselves
as alwaysable to
go to any
bankatall for a
loan at themarket
ate and
banks
see themselves
as able
to attract
any number of
customers
at that rate,
irrespective
f any understandings
The
price-quantityombinations
15) arenothing
other
than the
competitiveauction-market
ombinations.
What he aboveexample
representss
a breakdown
f contractsbecause
of
adverse
selection:If a bank commitsitself to lendat a given rateovera rangeof i, sometimes
takingshort-run
rofits
or short-runosses,
it will
find morefirmsborrowing
over the
loss
range hanwhen it
would obtain
short-run rofits.
In the
limit abankmaintaining
a fixed
loan rate would
have
no customers when
profits
were positive
and an
arbitrarily
argenumber
of customerswhen
profits
were negative.
Now, since
there
are
gains to both customers
and banks from insulating
firms from interest
rate
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
12/18
JOEL
FRIED
AND
PETER
HOWITT
:
481
fluctuations
t
may well
pay
the
borrower
and
lender
to
enterinto
explicit
contracts
that
mpose
switching
costs
to
customers
n exchange
for
insurance
against
luctuating
loan
rates.
If monitoring
osts
were
low
we would
expect
thesecontracts
o
arise
nthe
absenceof othercosts.
1
4.
DEFAULT
RISK
To incorporate
default
risk,
suppose,
as do
Modigliani
andJaffee
[ 10]and
others,
thatthe
bank's
expected
revenue
froma
loan
at any
rate
r is: e
(r)
= Er
min (x,
r),
and
that
the customer's
expected
utility
from
getting
a loan
at the
rate
r is:
g (r)
=
Eru(x
-
min(x,r)).
ltcanbeshownthate(r)
zO,O 0, mk
>
o, nk (i)
> 0,
ek,
i.
The fixed
rate theorem
(1)
andthe
preferredustomer heorem 3) go throughasbefore.Furthermore,heanalogue o
Figure
1 can
be drawn
withe
on the
horizontal
xisand
g =
r(e)-g
[r
(e)]
replacing
thefunction
w(r),
where
r (e)
is the
inverse
of the
function
e (r).
Thus
by
analogous
reasoning
credit
rationing
will
occur
unless
for
all
i e
I g (A)
+
[g' (rk)le'
(*)]
(i -
Ei)
K
where
rt =
r(Ei
+ otkct
(0tO
m
+
m')); k
= 0,1.
Thus
the
analysis
can
easily
be
extended
o
coverthe
case
of explicit
detault
risk,although
only
at the
cost
of extraneous
notational
complexity.
5. CHARACTERIZINGEQUILIBRIUMCONTRACTS
Letus return
o
the
model
analyzed
in
section
2.
We
showed
there
the
conditions
necessary
for
no
rationing
to
occur
in equilibrium.
The
present
section
further
characterizes
he
equilibrium
whenthe
possibility
of rationing
exists.
First,Figure
2
shows
how
thenumber
of successful
customers,
n
(i)
+ nl (i),
varies
in
equilibrium
as
a function
of i, under
he
assumption
hat
r < rl.
Along this
schedule
the
values
of r and
rl as
well
asthose
of
allexogenous
variables
areheld
constant.
The
meaning
of
the figure
s
self-explanatory,
ndits
exact
form
follows
directly
rom(7)
and(9).
In theinterest f simplicity uppose hat alwaysremainsnsidetheintervalO,
B)
in
Figure
2;
i.e., that
old customers
are
never rationed.
Suppose
also
that
the func-
tion c'
(
) is linear,
so that
s'
( ), the
inverse
of c (
),
is a constant,
s
> O.
One example
of such
voluntarily
mposed
switching
costs
on borrowers
s interest
rate
penalties
on
Canadian
mortgages.
It should
also
be noted
that,
in principle,
it is not
necessary
that
banks
mustbe
the
ones to
provide
insurance
nstead
of a third
party.
Underwriters
n the
bond
markets
may,
in fact,
be
providing
ust
such a
service to
firms
thatchoose
to borrow
in
the securities
market.
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
13/18
482 : MONEY,
CREDIT, AND BANKING
w
w(r)
_
oXt
______________
|
: | | i
c'(am+m)
w(i) R'
Fig. 2.
The Supply of Credit
Furthermore,uppose that the
initial set of
parameter alues for all the conceptual
experiments elow is such that the
partition: IA-{i
e 1:0 S i S iA}, IB-{ i e 1:
iA < iB } }
remainsunaffectedby
small enoughparameter hanges.Let z
(r, K) denote
the valueof z(r)
with the dependenceuponK made
explicit, andnote that
a zl AK< O.
We shallconsider he effects on
two endogenous
ariables: a) rl therateof interest
on loans to new
customers,and (b) (-1 - Es q(i)
l (i)/ml the
probability f any
given new customerbeing rationed,
of changes in the following four
parameters;i)
K theutilityof
not acquiring loan,(ii) Ex the
expected eturno a
customer's roject,
(iii) Ei the expectedeconomy-widerate of interest,and (iv) (n the varianceof i.
(a)Theeffectson rl canbe
calculated sing he
followingequilibriumondition,which
follows directly rom (11):
E q(i)ml
[rl - i-c' (cx
m + ml)]
idA
_
idB
The derivative f
this expression
with respect o rl is
Jr= # q (i)
ml + E
q
(i) *s * aZ *
[rl _ Z1]
IA
IB
(+)
(+)
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
14/18
JOEL
FRIEDAND PETER
HOWITT : 483
+ , q(i)
[s (zl -i) -otm] (l --) >
O .
IB
Ar
(17)
(+) (+)
Thus he firstresult s that
1
,. O bX
_ _ _
(
) ( )
( )
Tocalculatehe
effectsof Ex we
considerheeffectofa uniform
ightwardhift n the
distributionofx.Notethat
w(r)l8Ex-
-w'(r)>O,dw'(r)ldEx>O, anddz(r)/
dEx = 1 + [dw' (r)ldEx] [w(r) -K]l[w' (r)]2 > O.
ThusS
- =
-Jr I -
z q (i) [5
(rl _
Zl)
_ nl (i)] > O .
(18.ii)
dEx
dEx
I
( ) (+)
(
)
Similarly,we calculate he effects
of Ei as
_
dEi =Jr-l
E q(i)ml +(rl _
Zl)5 EF q(i) ,
(18.iii)
- IA
SB _
(+)
(+)
(-)
the signof which
s indeterminate.
uttheeffectof thevariancef can
be calculated
by defining
-Ei + ff (i' -Ei)
for a fixed set of i', and
differentiating ith
respect o C at i = it:
Ar'
_ _
J
-l , (i - Ei) q (i)
ml + (rl - Z ) s
E
(i
- Ei) q (i)
O.)
(b) To analyzeheeffectsof
parameterhanges n
(, theprobabilityf rationing
note hat orparameterhanges i)
and ii) theeffectsdepend ntirely
ponwhether
theoverall ffecton z(rl) is
positiveornegative. f it
is positive,,henFigure shows
that he irsttwo
inearpieces fthe
schedule hift ightward,mplying
hatn(i) never
decreases utmay increase.Thus,iromthedefinition f (,
sgn (atI8K)
= - sgn
(dzlldK) .
But from nspection f (17) and
(18.i)
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
15/18
484 : MONEY, CREDIT, AND
BANKING
(dzildK)= (8zl8k + (8zlAr)* (8rl/ak
= (8zl8K)Ei
q (i) ml + E q(i) (13z/13r)rl
_ z
IA IB
IB
-(8zlAr) E q (i) s(rl -zl) _ nl (i)]} Jr
IB
= (a-zl8K) E q(i)ml + E q (i)nl (i) Jr-l
< O .
_ IA IB _
(-) (+) (+) (19)
Therefore,
(,3g/,3K) O
(20.i)
Next,
note that, by inspection of
(18.i) and (18.ii),
(8rll8Ex) = (8rll8K) *
(8zs1
8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
16/18
JOEL
FRIED
AND PETER
HOWITT :
485
- E q (i)
nl (i)
[1 -(8zl/8r)]}
IB
J-1
[(8zl/8r)
- 1]
Eq(i)ml
+
Eq(i)n
(i)
8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
17/18
486 : MONEY,CREDIT,ANDBANKING
analysis but not
the analysis of Jaffee and Russell
[ 11 , since they explicitly
assume
that lenders cannot
distinguish
between honest anddishonest borrowers.
Two assumptionsused that
simplified our analysis were that
banks were risk
neutraland thatborrowerseitherhad their loan needsfulfilled completelyor did not
receive any loan
at all from the
bank The firstof these is necessaryfor
the fixed loan
rate theorem
but is not necessarily
crucial for the existence of rationing.
Had we
required hatbankswere relatively
ess risk averse
thanborrowers heloan ratewould
generallyvarywith i but gains
would still be obtained
rom an explicit contract hat
had an inelastic
response of r to i and permitted ome
rationing n some
states. The
second assumption
meant that this form of the
model cannot describe
the partial
rationing of
borrowersthat concernedJaffee and
Russell [11]. The
model can be
expanded to
permit partialrationingbut greater
technical detail associatedwith K
and the bankcost function would have to be specified.
While it is not necessary that
a bank will sometimes
rationcustomers,it is shown
that he likelihoodof rationingcontracts
ncreases
with increases n themean and the
varianceof the
cost of funds to banks with increases
n the marginal
cost of making
loans (including
hatcaused by
decreases n the ratioof old to new customers,
andby
decreases in
the expected gain
to borrowersfrom obtaining a loan
relative to not
getting one.
We also show if rationingcontracts
are optimal
and r S rl thenthe amountof
rationing s lower
and the loan rate
s higherthe greater s the expected
return o firms
from obtaininga loan or the lower is the utility to borrowers n not obtainingone.
Also, the greater s the expected
cost of funds to banks
(Ei), the greater he expected
level of rationing
but the loan ratemay go up or
down. The greater
s the variance
of i, the lower
will be the loan ratebutthe change n
expectedrationing
s ambiguous.
It should be
stressed, however, that the contracts
discussed in this
paper only deal
with one dimensionof the risks
to borrowersand
lenders in the real world, namely
that associated
with the cost of
obtaining funds by banks. Nothing
precludes the
existence of additional
mplicitcontracts hat nsure
one participant
r the otherfrom
risks arisingfrom
other sources.
Before any predictionson the macroeconomic
evel
can be confidently
stated, these
other possible contractsshould be
explored.
LITERATURECITED
1. Azariadis,Costas. Implicit
Contracts and Underemployment
Equilibria. Journalof
Political
Economy, 3 (December 1975), 1183-1202.
2. . On
he Incidenceof Unemployment. Review
fEconomic tudies,
3 (February
1976), 115-25.
3. Bailey, Martin
N. On the Theoryof Layoffs and
Unemployment.
Econometrica,5
(July 1977), 1043-63.
4. . Wages and Employment
Under UncertainDemand.
Reviewof Economic
Studies, 1
(January1974), 37-50.
5. Baltensperger,
Ernst. CreditRationing: ssues and
Questions. Journal
f MoneyCredit
andBanking,
0 (May 1978), 170-83.
This content downloaded from 200.128.60.106 on Wed, 19 Nov 2014 17:36:55 PMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp8/10/2019 FRIED & HOWITT, Credit Rationing and Implicit Contract Theory
18/18
JOEL
FRIED AND PETER HOWITT : 487
6. Barro,RobertJ. Long-TermContracting,StickyPrices, and MonetaryPolicy. Journal
of MonetaryEconomics, 3 (July 1977), 305-16.
7. Gordon, Donald F. A Neoclassical Theory
of Keynesian Unemployment. Economic
Inquiry, 12 (December 1974), 341-59.
8. Hodgman, Donald R. CommercialBank Loan and InvestmentPolicy. Champaign,Ill.:
Bureauof Business and Economic Research,
University of Illinois, 1963.
9. . CreditRisk and CreditRationing.
QuarterlyJournal of Economics, 74 (May
1960), 258-78.
10. Jaffee, Dwight M., and Franco Modigliani. A Theory and Test of Credit Rationing.
AmericanEconomicReview, 59 (December 1969), 850-72.
11. Jaffee, Dwight M., and ThomasRussell. Imperfect
nformation,Uncertainty nd Credit
Rationing. Quarterly ournal of Economics, 90
(November 1976), 651-66.
12. Kane, Edward, and BurtonG. Malkiel. Bank
Portfolio Allocation, Deposit Variability
and the Availability Doctrine. QuarterlyJournal of Economics, 79 (February1965),
113-34.
13. Koskela, Errki. A Study of Bank Behavior and Credit Rationing. Helsinki: Academia
ScientiarumFennica, 1976.
14. Markusen,James. Personaland Job Characteristics
s Determinantsof Employee-Firm
ContractStructure. QuarterlyJournal of Economics, 93 (May 1979), 255-79.
15. Phelps, Edmund S., and Sidney G. Winter. OptimalPrice Policy Under Atomistic
Competition. In Microeconomic Foundations
of Employmentand Inflation Theory,
edited by Edmund S. Phelps, pp. 309-37. New
York.: Norton, 1970.