We show that the principal result of Aghion and Bolton (1992) related to the optimality properties of contingent control allocations under incomplete contracting environment holds only if an additional condition is satisfied.

Jukka Vauhkonen

English

Research Papers in Economics

An incomplete contracts approach to financial contracting: a
comment 
Jukka Vauhkonen
Bank of Finland
Abstract
We show that the principal result of Aghion and Bolton (1992) related to the optimality
properties of contingent control allocations under incomplete contracting environment holds
only if an additional condition is satisfied.
I thank Juha−Pekka Niinimäki and Tuomas Takalo for perceptive comments.
Citation: Vauhkonen, Jukka, (2002) "An incomplete contracts approach to financial contracting: a comment." Economics
Bulletin, Vol. 7, No. 1 pp. 1−3
Submitted: April 22, 2002.  Accepted: May 28, 2002.
URL: http://www.economicsbulletin.com/2002/volume7/EB−02G30001A.pdfIn their seminal paper, Aghion and Bolton (1992) (hereafter AB) examine a long-term
financial contracting problem between a wealth-constrained entrepreneur and a
wealthy investor in an incomplete contracting environment. At date 0, the entrepre-
neur, who has no funds, seeks funding from the investor to cover the set-up cost K of
an investment project. At date 2, the project yields monetary returns and unobservable
and unverifiable private benefits for the entrepreneur. The sizes of the monetary re-
turns and private benefits depend on the date 1 realization of the state of the world and
the action taken at date 3/2. As the agents have potentially conflicting interests, they
may prefer different actions. The potential conflict over the choice of action cannot
always be solved by ex-ante contracts since, by assumption, contracts can be contin-
gent only on publicly verifiable signals but not on the true state of the world or the
action. Then, the right to decide what action to choose (control) becomes important.
In this framework, AB show that different control allocations are efficient for differ-
ent values of monetary returns and private benefits.
In Proposition 5(iii) of their paper, AB argue that for some sufficiently high values of
the set-up cost K , a contingent control allocation where control is allocated to the in-
vestor when the signal realization  0 = s  and to the entrepreneur when  1 = s  dominates
unilateral control allocations (entrepreneur control and investor control). The purpose
of this comment is to show that the contingent control allocation stated in their Propo-
sition 5 dominates investor control only if the values of the monetary returns satisfy
an additional condition. Furthermore, we show that this additional condition is not
satisfied in their numerical example.
The model and notation are described in section II of AB. For further usage, we write
out AB´s expression for the investor´s expected return under contingent control (AB´s
equation 6) and their Proposition 4. The investor´s expected return  c p  under contin-
gent control allocation  ( ) 1 ; 0 1 0 = = a a  with a transfer schedule  ( ) 0 , = r s t  for all s
and r is:
( ) [ ] ( ) ( ) [ ]
b
b
b b
g
b g
b
g g
g
g
c y y q y y q b b b b p - + - + - + = 1 1 1 . (1)
Their Proposition 4 reads as follows:
Proposition 1.  When monetary benefits are not comonotonic with total returns, a
necessary and sufficient condition for the first-best action plan to be feasible under
investor control is  ( ) ( ) K y y y q qy
g
b
g
g
b
b
g
b ‡ - + ” / 1 4 p .
It is important to note that one assumption underlying the definition of  4 p  is that the
entrepreneur´s share of the final monetary returns, determined in the initial contract, is
set as a constant 
g
b
g
g y y t / 1- = .
AB state that contingent control dominates investor control when the investor´s ex-
pected returns under contingent control and investor control are determined by equa-
tion (1) and Proposition 1, respectively. More specifically, AB claim that if the set-up
cost  K  belongs to the non-empty interval  ( ) ( ]
b
b
g
g y q qy - + 1 , 4 p , a contingent control
allocation  ( ) 1 , 0 1 0 = = a a  strictly dominates investor control when  ( ) ( ) 0 , 1 , ﬁ
b g b b .1
Their reasoning goes as follows (see their p. 485). By Proposition 4, the first-best ac-
tion plan is not implemented under investor control when  4 p > K , since investor con-
trol implements the inefficient action  b a  in state  g q . As a result, the aggregate pay-
offs under investor control are bounded away from the first-best aggregate payoffs.
On the other hand, the aggregate payoffs under contingent control converge to the
first-best aggregate payoffs as  ( ) ( ) 0 , 1 , ﬁ
b g b b . This argumentation leads them to
conclude that contingent control allocation strictly dominates investor control under
the conditions stated in their Proposition 5.
However, their reasoning is not valid. To see this, consider an alternative investor
control contract with a signal-contingent transfer schedule  ( ) t t t = = 1 0 , 0 , that is, a
contract giving the investor the right to choose the action and stipulating that the en-
trepreneur´s share of the monetary returns  0 0 = t  when the signal realization  0 = s ,
and 
g
b
g
g y y t t / 1 1 - = =  when the signal realization  1 = s . Correspondingly, the  in-
vestor´s share of the monetary returns is 1 when  0 = s  and 
g
b
g
g y y /  when  1 = s . Given
this contract, the investor´s expected (post-renegotiation) return under investor control
is
( ) [ ] ( ) ( ) ( ) [ ]
b
b
b g
b
g
g
b
b
b g
b
g g
g
g y y y y q y y q b b b b p - + - + - + = ¢ 1 / 1 1 4 . (2)
Now, AB´s reasoning is not valid, since  4 p¢  also converges to the first-best when
( ) ( ) 0 , 1 , ﬁ
b g b b . Therefore, to show that contingent control dominates investor con-
trol we must show that  0 4 > ¢ -p pc  for some values of  K . The difference  4 p p ¢ - c  is
positive only if the monetary returns satisfy the following condition:
( ) 0 / > - = F
g
b
g
g
b
b
b
g y y y y . (3)
Thus, AB´s Proposition 5(iii) is correct if and only if the condition  0 > F  is satisfied.
This condition is not necessarily satisfied in AB. For example, in their numerical ex-
ample  25 - = F , which implies that there are no values of  K  in their numerical ex-
ample such that contingent control strictly dominates investor control.
REFERENCE
Aghion, P., and P. Bolton (1992) "An incomplete contracts approach to financial
contracting" Review of Economic Studies 59, 473-494.

An incomplete contracts approach to financial contracting&quot;

An incomplete contracts approach to financial contracting: a comment

http://www.accessecon.com/pubs/EB/2002/Volume7/EB-02G30001A.pdf

An incomplete contracts approach to financial contracting: a comment

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