P ojec Con ingen Repudia ion Risk
in he Model o No h-Sou h Lending.
Cons an in T. Gu dgie
Depa men o Economics
T ini y College, Dublin
Depa men o Economics,
Na ional Uni e si y o I eland, Maynoo h
Open Republic Ins i u e, Dublin.
[email p o ec ed]
1s D a : Ap il 2002.
2nd D a : Augus 2002
Abs ac .
P esen esea ch p oposes he ex ension o he Ge le -Rogo -Lane model o
in e na ional lending unde he isk o epudia ion wi h mo al haza d o encompass he
possibili y o he p ojec con ingency in he epudia ion isk i sel . By linking he le el o
epudia ion isk o he size o he p ojec we show ha in es men p ojec s unde aken
can be biased in a di ec ion a ou ing la ge p ojec s. Al e na i ely, we show ha smalle
in es o s a e equi ed in he ma ke place, unde ce ain condi ions, o p o ide g ea e
gua an ees o highe colla e al in o de o ob ain unds needed o in es men .
In oduc ion.
In ecen yea s, he ole o isk and in pa icula epudia ion isk as a de e minan o
in es men decisions and capi al lows has been highligh ed by a ple ho a o models. A
he same ime, adi ional models o epudia ion isk ha e in a iably a oided
endogenising he isk-p ojec ela ionship ou side he gene al amewo k o he mo al
haza d and agency p oblems. Ye , wi h de elopmen o democ a ic ins i u ions and he
opening o na ional bounda ies o ade and capi al lows, in o ma ion lows ha e come
o he o e on o he eal in es men p ojec s assessmen wi h espec o bo h he
inhe en isk in ol ed and he ole ha he na u e o he p ojec plays wi hin he
cons ain s o such ins i u ions on he le el o o e all isk.
While he o me aspec o he epudia ion isk is co e ed ex ensi ely in he exis ing
li e a u e, he la e emains la gely unexplo ed. Ye as he esul o hese di e en ace s
o he same phenomena, bo h he inhe en isk o he in es men s and he epudia ion isk
in pa icula a e o en endogenous o he en i onmen o he p ojec . Ano he aspec
wo h conside ing is he ela ionship be ween he p ojec cha ac e is ics, such as size, and
he o e all a ailabili y o in o ma ion. In he socie ies wi h de eloped democ a ic
ins i u ions, such as cou s, media and poli ical campaigning, la ge p ojec s enjoy g ea e
public isibili y and elec o al sc u iny. Thus such p ojec s may be na u ally associa ed
wi h he lowe epudia ion isk. On he o he hand, in he socie ies wi h se e e deg ees o
ma ke dis o ions and co up ion, la ge p ojec s may be associa ed wi h go e nmen
in ol emen and hus may be linked o a highe deg ee o epudia ion isk. In wha
ollows, we e m hese e ec s p ojec -con ingen na u e o epudia ion isk and o he
sake o b e i y deal wi h he i s ype o ela ionship be ween he na u e o he p ojec
and he inhe en le el o isk in ol ed.
The majo i y o epudia ion isk li e a u e ocuses on he open economy side o he
mac oeconomic models, while he la ge sha e o mo al haza d models is conce ned wi h
he closed economies. Fo example, he seminal pape by Ge le and Rogo de elops a
2
model o in es men unde unce ain y in he p esence o mo al haza d ha igno es he
possibili y o epudia ion isk. As such, his model, acco ding o au ho s’ admission,
canno be used o dis inguish in es men lows be ween wo s a es wi hin he US and he
wo so e eign coun ies. Lane (1998, 1999) ex ension in oducing epudia ion isk mo es
his model in o he open economy mac oeconomics, while lea ing he conside a ion o
p ojec -speci ici y o isk no add essed. Simila ly, an impo an pape by Holms om and
Ti ole (1998) ocuses on he closed economy aspec o agency isk wi hou p o iding an
analysis o he epudia ion isk, o he link be ween he na u e o he p ojec and he
epudia ion isk.
Fu he mo e, adi ional li e a u e on epudia ion isk and in es men lending a ely deals
wi h he implica ions o he p ojec na u e o size linkages o he o e all iskiness o he
p ojec . In so a as epudia ion isk is ela ed o he limi ed liabili y and bank up cy
liquida ion laws, his implies ha mos heo e ical models o lending unde mo al haza d
lead o a conclusion ha cos s o such isk a e ei he e enly bo n by all en ep eneu s, o
bene i small in es o s in excess o he la ge ones. Howe e , as shown by many s udies,
see o example G oop e al (1996) and Be kowi z and Whi e (2002), empi ically such
cos s ac o edis ibu e c edi away om small en ep eneu s in a ou o he la ge
p ojec s. This empi ical con adic ion o heo e ical models o lending unde mo al haza d
isk appea s o be un esol ed in he mode n li e a u e.
Cu en s udy is designed o ill hese gaps by ex ending he Ge le -Rogo -Lane
amewo k o include conside a ion o he p ojec con ingen epudia ion isk. In he
ollowing we assume ha he impo ance o epudia ion isk in in es men decisions es s
in pa on he di e ences amongs a ious p ojec s. Fo simplici y, we assume ha his
endogenei y o epudia ion isk is linked o a speci ic cha ac e is ic o he p ojec , namely
i s size. Howe e , he model p esen ed below can be easily ex ended o co e many
con ingencies wi hin he ealm o he p ojec en i onmen ’s desc ip ion.
3
Pa 1. Model.
The e a e wo ypes o isk-neu al agen s, each li ing wo pe iods and +1:
en ep eneu s and lende s. Lende s a e in e es ed in maximising he expec ed a e o
epaymen on he p ojec , while en ep eneu s maximise hei expec ed u ili y o e he
choices o consump ion and in es men (assumed o be p opo ional o he capi al ou lay
o he p ojec ), subjec o budge cons ain . Li e- ime u ili y is gi en by:
E UC
,C 1,klog C 

E logC 1

alog k (1)
whe e in gene alU, U U
C0 1
C0,
CC,U

1
CC

0

and U
k

0, U
k
k
0.
The income a ailable o en ep eneu s a ises om wo sou ces. O iginal, pe iod
endowmen o weal h, W , can be in es ed in isky p ojec wi h s a e con ingen payo s
desc ibed below, and he isk ee asse , , yielding he g oss a e o e u n, R. Risky
in es men echnology is gi en as ollows. A da e en ep eneu uses he own unds,
B
W
C
, oge he wi h he bo owed amoun o b o inance capi al o ma ion in he
amoun o k. This capi al is hen applied o he isky in es men p ojec and en ep eneu
chooses he le el o e o o be applied o he p ojec . The esidual unds a e
au oma ically deposi ed in o bond holdings.
The p ojec yields a da e +1 a e u n

G
wi h p obabili y

k

 co esponding o he
‘good’ s a e o na u e, o a e u n

B wi h p obabili y 1


k

 co esponding o he ‘bad’
s a e o na u e. We assume ha 0


B



G
. Le el o e o (capi al ou lay o he
p ojec ) unde he possibili y o in es ing he bo owed unds in he isk- ee asse is
p i a e in o ma ion a ailable o he en ep eneu bu no o an in es o . A da e upon
bo owing unds o in es men , en ep eneu commi s o epay s a e-con ingen a e o
e u n
Z
G

Z
B. Howe e , in es o aces an addi ional isk o de aul due o limi ed
liabili y ( epudia ion). A e ealisa ion o he p ojec , in es o s may exp op ia e only a
sha e o inal ou pu . This sha e is p ojec -size-con ingen , so ha

k

iZi iG,B (2)
4
We shall conside only one case:

'k

0 , co esponding o he si ua ions in which
epudia ion isk is dec easing (so ha epaymen sha e is inc easing) in he size o a
p ojec . In a democ a ic socie y wi h de eloped media and socio-poli ical checks and
balances on co po a e and public bu eauc acy, high p o ile (la ge k) in es men p ojec s
a e associa ed wi h highe deg ee o isibili y. The esul ing educ ion o in o ma ion
cos s makes la ge p ojec s cheape o moni o han smalle ones. In addi ion, wi h high
deg ee o public exposu e, such p ojec s a e less subjec o co up ion (media exposu e in
democ a ic se ing inc eases cos o co up ion) and he e o e a e associa ed wi h lowe
epudia ion isk han smalle , less isible ones. This si ua ion can wa an he
a o emen ioned link be ween he size o he p ojec and he epudia ion isk in ol ed. As
was men ioned in he in oduc ion, in case o se e e co up ion p oblems a he op o he
go e nmen appa a us, we can speci y he opposi e di ec ion o he ela ionship be ween
he p ojec size and epudia ion isk in ol ed. Such ex ension o he model would equi e
e e sing he sign o

'k o

'k



0.
Gi en he expec ed a e o e u n o he isky in es men p ojec , we speci y he in e -
empo al budge cons ain as:
C C 1
R

k
R



BB

RWbk (3)
Deno e by
Z

Z
G

Z
B and



G


B. To con ol o he p esence o mo al haza d
p oblem in e ms o in es men p ojec choice, we impose he s anda d incen i e
compa ibili y cons ain acco ding o which isky p ojec s mus yield a leas he same
a e o e u n as isk- ee bonds:

'k

ZR (4)
We u he assume ha nei he u u e income, no he expec ed epudia ion unds can be
le e aged in he deb ma ke s, so ha
W
bkB C 0 (5)
Fu he mo e, in es o s mus be gua an eed a epaymen le el a leas in he amoun o he
oppo uni y cos o isky in es men , i.e. R:

kZZBRb (6)
5

We a e now eady o pos ula e he p oblems aced by en ep eneu who chooses
consump ion o e wo pe iods, capi al in es men , deb le el, and he le el o he s a e-
con ingen epaymen o o e so as o:
max C ,C 1,k,b,ZG,ZB

E UC
,C 1,k

subjec o (1)-(6). Deno e by

i,

,

,

,

he mul iplie s on cons ain s (2)-(6)
espec i ely. Then he i s o de condi ions o he gene al p oblem a e gi en by:
U
CR

U 1
C

1
C
R

C 1
(7a)
R

U 1
C

R

C 1
0 (7b)
U
k


'
R

Z1


 



'Z

''

Z

'

G

G

B

B



a
k

'
R

Z1


 



'Z

''

Z

'

G

G

B

B


0
(7c)





R (7d)



R


 



'



G (7e)
1





R


 



'



B (7 )
F om (7a) i is clea ha we ha e wo cases o conside :
Case 1: R

C C 1U
C

R

U

1
C which implies ha


0 wi h (5) sa is ied a
inequali y. This is a case when bo owe s will hold non-ze o le el o
bonds and colla e al ese e, so ha mo al haza d applies.
As shown below he esul ing op imal le el o capi al alloca ion is below
he ull in o ma ion i s -bes solu ion in Ge le -Rogo -Lane.
Case 2: U
CR

U 1
C which implies ha

0 and (5) is sa is ied a equali y. This
is a case when bo owe s will hold no bonds and cola e al, so ha mo al
haza d does no cons ain he op imal le el o capi al a ailable o
bo owe s. Repudia ion isk alone ma e s.
As shown below he esul ing op imal capi al alloca ion is de e mined by
i s e ec on epudia ion isk.
6
Pa 2. Case-Speci ic Solu ions.
2.1. Case 1: Mo al Haza d in Absence o E ec i e Repudia ion Risk.
Conside Case 1. Since

0, hen he op imal solu ion o he p oblem is gi en by he
ollowing equa ions:

kZZBRb (8a)
MR cu e bC k 
W
B
B
0
IC cu e

'k

ZR (8c)
ZZ cu e

k



k

ii iG,B (8d)
Equilib ium le el U
kU
C
R

'k

R

(8e)
k1
*a
C
R

'


R
Compa ing in e cep IC wi h le el,
k1
*k1
*

k0
IC . The eason o his is ha unde he
assump ions o Case 1 mo al haza d applies and bo owe s ha e o se aside a ce ain
amoun o ese es in o m o bonds o supply colla e al o he loans. This limi s he
le el o capi al in es men ha can be unde aken. Howe e , since ne e u n o
bo owe s a e epaymen o he loan is highe han he isk- ee a e o e u n, IC
cons ain does no bind a he op imum. Hence k1
*˜
k
, whe e ˜
k
deno es he solu ion o
s anda d G-R-L p oblem wi hou epudia ion isk bu wi h mo al haza d. In p esence o
colla e al, bo owe s can gua an ee highe epaymen a e Z1
*˜
Z
han in case o G-R-L.
Thus, lende s a e compensa ed o he added isk by ob aining he expec ed e u ns in
excess o isk- ee a e o e u n. The epudia ion isk does no ma e in his case because
i is e ec i ely o se by he bond holdings, which can be epudia ed unde he
assump ions o (2), (3) and (5). Figu e 1 below shows hese esul s.
7
Figu e 1. Equilib ium Le els o Capi al In es men and Repaymen Pledge.
Benchma k Case o No Repudia ion Risk.
Z MR
Z1
*
˜
Z
isk-p emium o lende
IC
k
˜
k
k k1
*
0
IC
B>0
No e ha in his case wel a e analysis conduc ed in Ge le (1992) ully applies. Thus
inc ease in weal h endowmen o en ep eneu s will shi bo h IC and MR cu es
igh wa d he eby inc easing he c edi a ailabili y. Al e na i ely inc ease in pe sonal
weal h will educe he isk-p emium equi ed by he lende s.
2.2. Case 2: Mo al Haza d in P esence o Repudia ion Risk.
Nex we conside Case 2. In gene al, assump ions o his case imply ha

0, so ha
ou side he bond holdings colla e al ese es a e ze o and cons ain (5) holds a equali y.
I is s aigh o wa d o show ha equali ies in cons ain s (3) and (6) will ollow as well.
Finally, simpli ying (7c) we can summa ise he main equa ions o he model as ollows:
8
MR cu e

kZZBRb (9a)
bC k 
W
IC cu e

'k

ZR (9b)
ZZ cu e

k



k

ii iG,B (9c)
E-le el
U
k

'k

U 1
C

ZU
C
RZ







''

ZU
C

'k

G

G

B

B

(9d)
As in G-R-L we can conside wo cases o applica ion o epudia ion isk.
Case 2.A.: epudia ion isk does no bind in ‘good’ s a e, i.e.

G

0
Case 2.B.: epudia ion isk does bind in ‘good’ s a e, i.e.

G
0
2.2.1. Case 2.1: Repudia ion Risk in ‘Bad’ S a e Alone
Fi s suppose epudia ion isk cons ain does no bind in case o ‘good’ s a e ealisa ion.
This implies ha

k

G

G
and he e o e,

B0 unambiguously. The go e ning
equa ions a e:
MR cu e

kZ

k

BRk

C

W

 (10a)
IC cu e

'k

ZR (10b)
ZZ cu e

k

 (10c)
E-le el
a
ki
*AZ

'


''

'

Z

'

B


 

1
C



'

C 1
A1
RC


C 1
(10d)
As be o e, MR cu e slopes up in k,Z

 space, howe e , equa ion (10a) gi es a la e
slope han co esponding equa ion in Case 1, since now epudia ion cons ain does no
bind in ‘good’ s a e. In addi ion, MR has non-ze o in e cep a k0
M
R.
9
puzzle a ises in so a as adi ional heo e ical models o lending in p esence o mo al
haza d imply he e e se e ec s o limi ed liabili y on he abili y o he en ep eneu s o
aise c edi ela i e o he size o he p ojec s. In ou model la ge p ojec s a e a ou ed by
in es o s due o he link be ween he size o he p ojec and he le el o he epudia ion
isk. The smalle (less weal hy) en ep eneu s and p ojec s a e less likely o bene i om
he epudia ion isk linkage. This implies ha in so a as limi ed liabili y and bank up cy
liquida ion clauses ha e he same e ec on lowe ing he expec ed abili y o en ep eneu s
o epay he lende s in case o bad ou come, i is he la ge in es o s who ha e g ea e
access o he c edi ma ke s. Thus ou model con i ms he empi ical egula i ies obse ed
in he li e a u e.
In so a as he p esen s udy o e s a way o endogenising he epudia ion isk by linking
he le el o isk wi h he cha ac e is ic o he p ojec i sel , he model p esen ed abo e
o e s an in e es ing case o he u u e empi ical analysis.
Fi s ly, i con i ms he gene al hypo hesis ha democ a ic ins i u ions o checks and
balances can ac in asymme ic ashion on he deg ee o epudia ion isk. Wi h la ge
in es men p ojec being subjec o he g ea e sc u iny in local and in e na ional media,
cos s o moni o ing he p ojec de elopmen and he h ea o po en ial public exposu e o
he loan aiding en ep eneu s ac o amelio a e he epudia ion isk and lowe he
equi emen s on epaymen pledge and colla e al.
Secondly, he s udy de elops an explici ela ionship be ween he es able hypo heses
conce ning he obse able en i onmen and he ex an e analysis o he po en ial
in es men p ojec s.
Thi dly, we show ha he model can be easily in e p e ed in he con ex o he o ce
majeu epudia ion isk (bad s a e only case) and he gene al epudia ion isk. Bo h ypes
can be sepa a ed wi hin he cons ain s o he model and he e ec s o hei di e ences
can be aced back o he abili y o he en ep eneu s o aise unds. O e en g ea e
impo ance is he ac ha he size o he p ojec unde he assump ions o he democ a ic
16

17
ma ke -d i en ins i u ions, can be in insically linked o hese di e ences as well. While
o ce majeu causes may apply o he epudia ion aid whe eby in he bad s a e o na u e,
especially when such bad s a e is mac oeconomic (down cycle, coun y-wide shock, e c)
e en in democ a ic ma ke -o ien ed socie ies, he gene al epudia ion isk mos ce ainly
mee s no app o al om he gene al elec o a e. Thus he ex e nal en i onmen di e ences
be ween hese wo o ms o epudia ion isk mus be kep clea ly dis inguished in any
model o in es men unde unce ain y wi h he possibili y o capi al unds exp op ia ion.
Ou model sa is ies his c i e ion.
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