FRIED & HOWITT, Credit Rationing and Implicit Contract Theory

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.

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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)

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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.



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.



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.



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).



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



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



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.



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

(+)

(+)



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)



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


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)


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.



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.

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