Debt vs Foreign Direct Investment: The Impact of
International Capital Flows on Investment in
Environmentally Sound Technologies
J. O. Anyangah
Abstract
This paper employs the methods of mechanism design under informational asymmetry to examine the relationship between …nancing arrangements and optimal investment in environmentally sound technology (EST).
In a model incorporating both adverse selection and moral hazard, it is
shown that the …nancial structure has implication for agency costs and the
optimal provisions of incentives. Relative to debt …nance, Foreign Direct
Investment (FDI) is characterized by less intense adverse selection, but a
more pronounced moral hazard problem. Thus, when the scope of adverse
selection consequences are su¢ ciently signi…cant vis-à-vis the moral hazard
e¤ects, FDI outperforms debt …nance in terms of the level of technological
investment that is optimally induced.
1
Introduction
International transfer of environmentally sound technologies (ESTs) has received
much attention recently as a means to ameliorate leading environmental problems. Many researchers recognize, for example, that the transfer of energy ef…cient technologies from developed countries to developing countries can not
only lead to local development, but also help the developed countries meet their
commitment to reduce greenhouse gases in a cost e¤ective manner ( Fischer
et al., 1998). However, for the process of technology transfer and its uptake
to be successful, it is crucially important that adequate …nancing be in place.
Consider debt and foreign direct investment as alternative media through which
Department of Economics,
joshua.anyangah@uleth.ca
University
1
of
Lethbridge.
E-mail
address:
the requisite …nancing can be obtained. While debt typically precludes the foreign investor from any role in project implementation, foreign direct investment
(FDI) may allow the investor to gain in‡uence over the domestic …rm’s broad
strategic objectives and organizational direction potentially reducing the severity of any informational asymmetry. A simple and spontaneous argument may
then lead to the conclusion that the agency problem could be largely mitigated
under FDI than debt. But is this intuition correct? More generally, how can
…nancial structure a¤ect optimal incentives for investment in technology? The
literature that has attempted to answer this question is scant.1
This paper employs the methods of mechanism design under informational
asymmetry to examine the relationship between …nancing arrangements and
the optimal investment in environmentally sound technology. In the model, a
resource-constrained domestic agent must secure core capital from a risk neutral
foreign investor (principal) in order to undertake a project. The project involves
large-scale modernization (“greening”) of the production process at a …rm owned
by the agent. Two forms of …nancing - Foreign Direct Investment (FDI) and
debt …nance - are considered. The central conclusion is that …nancial structure
has implication for the nature of investment decisions. More precisely, relative
to debt …nance, FDI diminishes the severity of the adverse selection problem,
but exacerbates the moral hazard problem. Hence, whether or not agency costs
are higher under FDI depends upon the signi…cance of the adverse selection
consequences vis-à-vis the moral hazard e¤ects.
To discern the logic behind this result, one must understand the distinguishing characteristics of the two funding mechanisms and the concomitant informational structures. The basic di¤erence between debt and FDI revolves around the
degree of control that can be exercised by the foreign investor over the project.
Under debt …nance, the two parties are presumed to interact strictly at arms
length and any role played by the investor does not extend beyond providing
liquidity. Here, the success or failure of the project depends upon the domestic
…rm’s absorptive capacity, which is private information to the agent, and unobservable level of technological investment that is undertaken by the agent. By
contrast, FDI enables the investor to intervene in the operations of the …rm by
providing managerial and organizational expertise. Thus, when examining FDI,
it is argued that the success or failure of the project depends not only upon the
1
Although a number of studies have examined the implication of …nancial policy, most have
focused on the relationship between capital struture and the value of the …rm in a domestic
environment. These include work by Lewis and Sappington (1995) and Myers and Majluf
(1984), Jensen and Meckling (1976) and Ross (1977).
2
domestic …rm’s absorptive capacity and the unobservable level of technological
investment, but also on the amount of expertise supplied by the investor.
The foregoing implies the following. Under debt …nance, the foreign investor
confronts a one-sided moral hazard problem and an adverse selection problem.
To limit the agent’s information rent, the level of investment is distorted away
from its full information value. When FDI is the …nancing channel, however,
the optimal contract must not only take care of the moral hazard and adverse
selection problems on the part of the domestic agent. It must additionally deal
with a moral hazard incentive on the part of the investor because the value of
the investor’s expertise cannot be ascertained and therefore contracted upon.
Consequently, the cost of inducing any given level of investment must include
an incentive loss on the part of the investor since enhancing incentives for the
agent implies a diminution of the investor’s incentives. Another result is that the
associated information rent is less pronounced. This arises because reducing the
agent’s incentive in a rational attempt to capture some of the information rents
brings forth an o¤setting incentive gain on the part of the investor. In sum,
the cost of extracting informational rent is lower under FDI. Hence, whether
FDI leads to more investment as compared to debt …nance depends upon the
magnitude of the bilateral moral hazard e¤ect relative to the adverse selection
one. Only in the special case where the adverse selection e¤ect is su¢ ciently
large vis-a-vis the moral hazard e¤ect will the agent invest more under FDI than
under debt …nance.
This paper is in the same spirit as previous studies that have examined the
problem of international technology transfer. Recent work in this realm include
Choi (2001) and Tao and Wang (1998). Choi uses an incomplete contract model
of the licensing relationship to explain the prevalence of royalty contracts. Tao
and Wang focus on contractual joint ventures between multinationals and local
…rms in an environment characterized by weak enforcement of binding contracts.
Although both studies employ the principal-agent framework, they assume away
the crucially important role played by the absorptive capacity of the technology
recipient in ensuring successful technology transfer. In these studies, imperfect
information result from hidden action (moral hazard) only. By contrast, this
paper is cast in an environment in which the foundation of imperfection information can be found in both moral hazard and hidden information (adverse
selection).
Among the earliest papers on international technology transfer are Gallini
and Wright (1990). They focus on licensing contracts for newly patented inno-
3
vations when the licensor has private information about the economic value of
the patent. One di¤erence with this paper is that …nancial structure does not
a¤ect agency problems between the contracting parties. The second di¤erence
relates to the structure of information asymmetry. While our model assumes
that the agent (technology recipient) is the one with a relevant private information, theirs is one of signalling by a privately informed principal in the spirit of
Maskin and Tirole (1992) and Beaudry (1994).
Also closely related to this paper are studies that have compared debt and
foreign direct investment as forms of international investment under di¤erent
institutional arrangements. Among the earliest papers in this realm is Razin et.
al. (1996) who examine sources of market failure in the context of international
capital ‡ows. Their focus is on providing guidelines for e¢ cient tax structure in
the presence of market imperfection. Schnitzer (2002) considers the impact of
sovereign risk on the structure of international capital ‡ows. Neumann (2003)
is perhaps closest to this paper. She compares FDI with debt …nance when
monitoring is costly and …nds that FDI …nancing is preferred to debt …nance
because costly monitoring increases investment, output and consumption for
the domestic …rm. There is no private information in Neuman’s model and the
moral hazard problem is one-sided.
The rest of this chapter is structured as follows: The next section presents
the basic elements of the model. Section 3 develops a benchmark solution.
Section 4 analyzes the equilibrium when asymmetric information prevails. Under
debt-…nancing, the investor’s interaction with the domestic agent does not go
beyond providing liquidity. As a result, the investor is only constrained by the
standard incentive compatibility and participation constraints. Under FDI, the
investor participates in the project by providing managerial and organizational
expertise. It is assumed that the investor’s intervention enhances the project’s
success probability, but the value of this contribution can not be contracted
upon. Thus, this version of the model imposes the additional constraint that
the investor’s participation be optimal given the contract. Section 5 concludes.
2
Basic Model
There are two players in the model: a domestic agent and a foreign investor.2
The agent owns a …rm that currently employs a technology that involves an in2
The agent can be thought of as the government of a developing country that currently
owns and operates a state entreprise such as an electric power utility.
4
e¢ ciently high rate of fossil fuel use and emissions of greenhouse gases that are
known to a¤ect the overall environmental quality in the region. By undertaking
investment in a clean technology, the …rm’s rate of energy use could be significantly reduced.3 The technological switch can be thought of as a large-scale
modernization of the …rm’s production process that requires major purchases
of EST. We assume that the agent’s initial endowment, which we normalize to
zero, is not su¢ cient to meet the investment requirement. It is also assumed
that the domestic capital markets can neither provide all the required capital
nor the clean technology. These assumptions are necessary to ensure the that
the agent will need core capital from the foreign capital market. The …rm is
otherwise assumed to be a large enterprise which can bene…t from the international capital markets. The foreign investor is meant to be a foreign entity with
deep pockets.
The agent seeks funds from the foreign investor in order to undertake the
technological switch. If the investor accepts to underwrite the cost of converting
to the clean technology, then he has the option of channelling his funds through
two media: Foreign Direct Investment (FDI) or a market loan (Debt).4 It is
assumed that FDI enables the foreign investor to control the …rm’s strategic
direction.5 With FDI, the investor e¤ectively obtains authority over the project
by acquiring an equity stake in the domestic …rm. Under a debt contract, however, the …rm secures the external resources but retains control and management
rights over the project.
Once …nancing has been secured, the execution of the project involves two
successive steps.
1. In the …rst stage, the agent embarks on plant modernization by buying
and installing an EST from a foreign supplier. The amount of expenditure on
the ETS is given by I 2 <+ .
2. During the second step, which corresponds to the main source of risk,
the agent uses the new technology to produce and deliver a composite good
to the market. The use of the EST generates a number of …nancial bene…ts:
Reduced cost of raw materials and resources, improved compliance and reduced
regulatory interference, reduced future liabilities and improved quality products
3
Throughout we use ‘owner,’‘…rm,’‘agent’and ‘manager’interchangeably.
Throughout we use the masculine term ”he” to refer to the investor and the femine term
”she” to refer to the domestic …rm/manager.
5
Control is de…ned as owning 10% or greater of the voting shares of an incorporated …rm,
having 10% or more of the voting power for an unincorporated …rm or development of a
green…eld investment. Thus, FDI can also be interpreted as a situation where the government
privatizes a state-owned enterprise.
4
5
and reduced defects.
The net …nancial bene…ts from the project are uncertain. In particular, if
the technological switch is successful, the investment yields a net cash ‡ow of
H.
If the technological switch is not successful, however, the corresponding net
cash ‡ow
L.
We assume that
=
H
L
> 0.
A fundamental di¤erence between the two funding mechanisms relates to the
degree of control exercised by the foreign investor over the project. If funding
takes the form of debt, then it is assumed that the two parties interact at arms
length. In this case, any role played by the investor does not extend beyond
funding the project. By contrast, FDI enables the investor to be involved in
the operations of the domestic …rm. This may stem from the fact that FDI, by
its nature, a¤ords the investor a greater degree of management control which is
conducive to eliminating perquisite consumption and other wasteful activities.
Also, FDI enables the investor to obtain better information because she is geographically closer to the …rm. By having a representative from headquarters
on the board of directors of the local establishment, the foreign direct investor
is better able to in‡uence the …rm’s overall investment decisions and closely
monitor the project than a lender. FDI may bring additional bene…ts such as
managerial expertise and technological skills.
Formally, we account for these di¤erences by assuming that the probability that the project is successful depends upon the level of investment in the
clean technology I, the …rm’s ability to absorb the clean technology (absorptive
capacity) , and the managerial and organizational expertise provided by the
investor E. We denote the probability function by p(I; E; ), where
is the intervention parameter. Under debt contract,
= f0; 1g
= 0 since the investor’s
involvement does not extend beyond providing liquidity. Under FDI, however,
the foreign investor provides cash, but in addition participates in the project so
= 1.
The function p(I; E; ) satis…es the following standard properties:
pI (:) > 0; pII (:) < 0, pE (:) > 0; pEE () < 0,
pIE (:) = pEI (:) = 0, p (:) > 0, pI (:) > 0, pE (:) > 0.
(1)
The …rst four conditions say that investment and expertise increase the likelihood
of success at a decreasing rate. The next assumption simply states that the
probability function is separable in investment and expertise. The last three
conditions say that …rm’s absorptive capacity enhances both the likelihood of
6
success and the productivity of both I and E. The assumption on pEI (:) has
been imposed for analytical simplicity, but most importantly, to underscore the
fact that the investor’s input supplements the manager’s investment I and is not
absolutely essential for project success. To give more structure to the probability
function and to obtain sharp results, we make the following assumption:
Assumption 1 p(I; E; ) = (q(I) + h( E)) =
I + E
(0; 1).6
where ; 2
Information: A crucial assumption is that the two parties have asymmetric information. The agent knows exactly the value of
investor’s knowledge of
from the outset; the
is limited. The investor only knows that parameter
belongs to some compact set
R+ . Without loss of generality we take
=
[ ; ]. In addition, I and E, cannot be contracted upon. However, it is publicly
known whether the project is a successful or not. Since the success probability
is a function of , E and I, the model is characterized by both bilateral moral
hazard and adverse selection.
The investor has some a prior probability on
continuous density function f ( )
which is associated with a
dF ( )=d , where F ( ) is the distribution
function of . As is standard in the incentive literature, we assume the following
with respect to F ( ):7
Assumptionh2 The distribution
of types F ( ) satis…es the monotone hazard
i
@ 1 F( )
0.
rate property: @
f( )
The analysis covers a single period from point 0 when …nancing, investment
and production decisions are made to point 1, where returns are realized. Before
investment activities can be undertaken, the …rm and the investor must negotiate a contract specifying how the investor will be compensated for funding the
project. Such a contract must be based on variables that are veri…able by the
investor or a third party. Since investment, expertise and type
are unobserv-
able (except under full information), the only possible basis for the contract is
the realized cash ‡ows
i,
i = H; L.
One more point is worth noting here. The nature of the contractual arrangement between the investor and the …rm will depend on the bargaining capabilities of the two parties. In this paper, we will assume that the investor has all
the bargaining power when designing the contract. This may be a reasonable
6
A similar technology has been speci…ed by Lewis and Sappington (2000). All qualitative
results do not depend on this speci…cation.
7
See, for example, Fudenberg and Tirole, 1991, p. 267.
7
assumption in situations where there is intense competition for foreign …nancial
resources among between host countries. 8 Thus, during contract negotiation, it
can be appropriate to assume that the investor makes a take-it or leave-it o¤er
to the …rm.
To complete the model set up, we assume that the international rate of
interest is r so the opportunity cost of funds for both the investor and the …rm
is (1 + r) per unit.
3
E¢ ciency
Before proceeding to characterize the investor’s optimum under information
asymmetry, we consider, as a benchmark, a setting where no moral hazard or
adverse selection problem arises because the investor shares the …rm’s knowledge
of its absorptive capacity and is able to observe the level of investment; that is,
both
and I are observed by the investor. We also assume that E is observed
by the …rm and can therefore be contracted upon.
Consider a debt contract. When the …rm and the investor get together to
negotiate a contract in this setting, they have two decisions to make: First, they
must specify the loan amount b that the foreign investor will provide. Second,
they must agree on the repayment schedule specifying the transfer that the
…rm must make for each possible realization of cash ‡ows. We assume that the
optimal contract calls for the …rm to repay R when the project fails and and
R+
in the event that the project is a success. Here
is a loading factor
that can be heuristically interpreted as the incremental reward/punishment for
success. Thus, if
is negative in value, the …rm is e¤ectively punished for
success. On the other hand, if
is positive, the agent is rewarded in the event
of success.
The …rm’s expected utility is U = p(I; )[
+ ]+
L
R + (1 + r) [b
I]
while the investor’s expected payo¤ is V = p(I; )[R+ ]+[1 p(I; )]R (1+r)b.
The investor’s problem [L] reads:
max p(I; ) + R
(I;R; )
(1 + r)b
(2)
subject to
p(I; )[
]+
L
R + (1 + r) [b
I]
0,
(3)
8
There is evidence that host-countries do compete for foreign direct investment. See, for
example, Koray and Taylor (2000), and Hau‡er and Wooton (1999).
8
where the constraint is the usual ex ante participation constraint, which says
that the …rm’s manager payo¤ must be positive in order to guarantee his or
her participation. Solving this problems is straightforward. The participation
constraint of the …rm is binding.
Now consider FDI. Here, the investor acquires signi…cant ownership and
control rights over the project through an outright purchase of shares in the …rm
but retains the local manager to execute the investment project on its behalf.
Thus, when the …rm and investor get together to construct a contract, they must
specify a purchase price and how the investor will be compensated for supplying
the funds. Such a contract must be based on variables that are veri…able by the
investor or a third party. We assume that the investor implements the following
linear payment scheme:
s= ( )
i
h
i
2 ( ) , ( ) , i = H; L:
+ v( ) 8
(4)
In this formulation, v can be interpreted as the purchase price or lump sum
transfer of funds. We assume that v accrues directly to the agent and does
not therefore become part of the …nal cash ‡ows to be shared between the two
parties.
can be thought of as the manager’s stake in the project. In other
words, the investor acquires proportion (1
return pays
v.9
) of the …rm’s shareholding and in
The investor solves the following problem [D]:
max [p(I( ); E( ); )
+
(I;E; ;v)
L
+ v( )](1
( ))
v( )
(5)
0;
(6)
subject to
[p(I( ); E( ); )
+
L
] ( ) + (1 + r)[v( )
I( )]
where again the constraint gives the participation constraint of the agent.
The following result is immediate:
Proposition 1 Suppose that investment in technology can be funded either through
FDI or debt. Then under full information, the investment chosen will be the
same regardless of the funding mechanism.
Proof. The proof follows readily from problems [L] and [D] and the fact that
constraints (3) and (6) are binding. Making use of the binding participation
constraints, the …rst-best levels of investment under debt and FDI can be given
9
v can also be interpreted as a base salary or an up-front payment.
9
by the solution to maxp(I; )
I
L
(1 + r)I
U
+
L
+ (1 + r)I
U and maxp(I; E; )
E, respectively. These imply that pI
under debt and pI (I D ; E; )
I
(I L
; )
+
(1 + r) = 0
(1 + r) = 0 under FDI, where I L and I D
are the …rst-best level of investment. Given that pIE (:) = pEI (:) = 0 and from
the fact that p(:) is concave in I, it follows from the …rst-order conditions that
IL = ID .
Intuitively, the e¢ cient investment to undertake is the amount that maximizes the total expected surplus. In this …rst-best setting with no private
information and moral hazard, the agent earns no rents (U = 0) and the optimal investment is equates the marginal return to the opportunity cost of funds.
Since this cost is exogenously determined by the international capital markets
independently of the …nancial structure, the investor faces the same marginal
cost of investment regardless of the medium used to obtain the required …nancial
resources.
4
Combining moral hazard and adverse selection
When both moral hazard and adverse selection informational problems exist
in the same context, the contract design problem can be analyzed within a
mechanism design framework. By the revelation principle, there is no loss in
generality in focusing on a direct mechanism in which the investor provides the
…rm with incentives that induce truthful behavior (e.g., Fudenberg and Tirole,
1991 and La¤ont and Tirole, 1993). In a direct mechanism, the investor o¤ers
a standard screening contract C = fs(^) : ^ 2 g, prescribing a level of transfer
s(^) conditional upon the manager’s announcement ^. We assume that the
investor can credibly commit not to renegotiate the contract.
The investor selects s(^) to maximize her expected payo¤. In so doing, he
takes into account the response of the privately informed …rm. As in similar
models, the optimal actions of the privately informed …rm gives rise to two
kinds of constraints that the investor must take into account when designing the
mechanism. The …rst kind ensures that the …rm reports its type ^ truthfully
and undertakes the optimal level of investment. These constraints are called
the incentive compatibility constraints. The second kind of constraints are the
individual rationality constraints. They require that the …rm, whatever his type,
gets its reservation payo¤, the payo¤ that the …rm would get by not participating
in the project.
The sequence of events is as follows: In the …rst stage, nature draws a type
10
for the …rm from a set of feasible types
2
. Only the …rm learns the true
value of . In the second stage, the investor and the …rm agree on a menu of
contracts. The …rm reports its type and then chooses a level of investment in
the green technology given the sharing rule. Final project output is observed
and the transfers implied by the menu of contracts are implemented.
4.1
Debt Finance
Consider …rst the case where the required liquidity is delivered through a debt
contract. In this setting,
= 0 and the success probability collapses to p(I; ).
Recall from the previous section that the investor provides a loan in the amount
of b dollars to the …rm and that the optimal contract calls for the …rm to repay
R+
and R( ) when the realized cash ‡ows are
H
L,
respectively. Thus,
^
^
the revelation mechanism in this situation is s( ) = fR( ); (^); b(^)g!^ 2[! , !] .
A …rm type that reports that her type is ^ when the true parameter is has
a utility U (^; ):
U (^; ) = p(I(^); )[
+ (^)] +
and
h
R(^) + (1 + r) b(^)
L
i
I(^) .
(7)
i
I(^)
(8)
I( )] .
(9)
Hence, incentive compatibility requires that
2 arg max p(I(^); )[
^
+ (^)] +
L
h
R(^) + (1 + r) b(^)
Let U ( ) = U ( ; ) denote type ’s rent when reporting truthfully:
U ( ) = max p(I( ); )[
^
+ ( )] +
L
R( ) + (1 + r) [b( )
A …rst step in studying the mechanism design problem of the investor is to
characterize the set of functions corresponding to an incentive compatible mechanism. Lemma 1 below characterizes this set.
Lemma 1
only if
If
2
, a pair fU ( ),
dU ( )
= p (I( ); )[
d
U( )
(:)g is incentive compatible if and
+ ( )],
is convex on
(10)
(11)
and
( ) is non-decreasing.
11
(12)
In sum, the Lemma states that if the local incentive-compatible constraints
are satis…ed and
(:) is nonincreasing, then these necessary conditions are suf-
…cient. Hence the in…nite incentive constraints that the investor must take into
account during the process of contract design collapse to a di¤erential equation
and monotonicity constraint. A direct revealing mechanism is then characterized
by (10) - (12).
There are two standard approaches to studying the mechanism design problem of the investor. One alternative is to focus on the transfer schedule ( ( ); R( ); b( )).
The other option is to focus on the information rent U ( ). In the following, we
will adopt the latter technique. Using the de…nition of transfers as given in U ( ),
we can rewrite the investor’s …nal wealth in terms of U ( ) as V(U (:); (:); ) =
p(I; )
+
L
+ (1 + r)(I( )
U ( ). Since the investor does not know , his
expected payo¤ can be written as
Ve (U (:); (:); ) =
Z
p(I; )
+
L
+ (1 + r)I
U ( ) dF ( ).
(13)
Thus, the screening problem under a debt contract is as follows:
max
fU ( );R( ); ( )g
subject to (10), (11), (12),
U( )
0
Ve (U ( ); ( ); )
8 2
(14)
;
(15)
and
I 2 arg max p(I; )[
I
+ ( )] +
L
R( ) + (1 + r)(b( )
I( )).
(16)
Expression (14) states that the investor desires to maximize the expected
total surplus less the …rm’s expected rent. Notice that since the …rm’s rent
is costly, the investor has an incentive to optimally induce distortions away
from e¢ ciency in order to reduce the ability of the …rm to command the rent.
The participation constraint (15) for the …rm ensures that it receives nonnegative expected payo¤, regardless of its type and report. Equation (16) requires
that the manager select
o the level of investment optimally given contract
n
(R(^); (^); b(^)) : ^ 2 [ ; ] .
12
The participation constraint must be binding somewhere. If it was not, then
the investor could raise the …rm’s repayment commitment uniformly by a small
amount, and thus recoup larger revenues, while still inducing participation of
all types. It turns out that because U ( ) is nondecreasing from (10), we only
need to require the participation constraint to be satis…ed at the lower end point
= . Thus, the manager’s participation constraint can be replaced by
U( ) = 0
U ( ) free
( ; given).
(17)
The investor’s modi…ed problem, therefore denoted by (L’), can be written as
an optimal control problem:
max
fU ( );; ( )g
Ve (U ( ); ( ); )
(18)
subject to (10), (11), (12), (16) and (17).
4.1.1
Equilibrium contract and optimal investment
We adopt a standard strategy to solve problem (L’). First, we ignore the monotonicity conditions (11) and (12), and solve the so called relaxed problem (L”). We
then show that the solution derived in this way also satis…es the monotonicity
conditions and thus solves problem (L’). This will be true, for example, if the
distribution of
satis…es assumption 1. The following proposition summarizes
the solution to the investor’s problem (L’). The formal proof can be found in
the appendix.
Proposition 2 The solution to (L’), denoted { (^),U L ( ); R( ), I D ( )}, is
given by
[1
F ( )]
;
f ( ) + [1 F ( )])
Z 0
Z 0
p(I( ); )d +
( )d ;
( )=
U( ) = U( ) +
R( ) = p(I( ); )[
+ ]+
L
and
pI
= (1 + r) + p
I
p
U ( ) + (1 + r) [b
pII
pI
I( )] ;
(1 + r) [1 F ( )]
.
pI
f( )
(19)
(20)
(21)
(22)
The …rst expression gives the incremental reward for success. From the fact
that F ( )
1, it is evident that this term is negative for all host types below
13
the upper end point
< . This suggests that the most e¢ cient type will be
o¤ered a standard debt contract (with a non-contingent repayment schedule)
while those below the upper end point will be subjected to a payment structure
that includes a penalty in the event of success.
To discern this rather counterintuitive outcome, one must understand the
combination of agency problems in this situation. Under pure moral hazard,
but without adverse selection, by di¤erentiating the total surplus, p(I( ); )
+
L
(1 + r)I, the …rst-order-condition with respect to
[pI (I; )
where dI=d
=
(1 + r)]
pI (I; )=[pII (I; )(
+
is given by
dI
=0
d
(23)
)] is obtained from the incentive
compatibility condition on I:
pI (I; )[
+ ]
(1 + r) = 0.
(24)
Since the last two equations must in equilibrium hold simultaneously and given
the fact that dI=d
> 0, it follows straightforwardly that the optimal contract
in the absence of private information (but only moral hazard) will set
to zero
and commit the …rm to a …xed repayment schedule.
When the …rm has private information, however, a high type host, for whom
success is most likely, will have an incentive to intentionally misreport her type
as lower in order to earn information rent. And the incentive to misreport
will be particularly more pronounced those states of the world in which the
project is successful. To counter this incentive, the investor optimally lowers
the attractiveness of contracts designed for low
…rms when
L
is the realized
cash ‡ow. This is achieved by requiring the …rm to repay a higher amount in
the event of success than without success. The e¤ect of this is to di¤erentially
disadvantage high type …rms who attempt to mimic the low types.10
The second expression gives the amount of rent that is optimally ceded to
the host in order to induce truthtelling. As in many screening models of this
kind, this rent is positive for all types except the least e¢ cient. The third
expression gives the base repayment amount. It says that the …rm will repay
the investor an amount that is equal to the expected total surplus less the sum
of her rent and cost of investment. In essence, the investor appropriates all
10
This result parallels Lewis and Sappington’s (1997) argument that in a dynamic agency
setting, early success should be optimally purnished to limit the agent’s incentive to understate
his ability
14
the proceeds from the project and then not only compensates the …rm for her
expenditure on investment, but also a¤ords her rent. The last expression gives
the condition for optimal investment. Compared with equation (24), which gives
the corresponding investment equation in the absence of private information, we
can conclude that the second term on the RHS of (22) represents the e¤ect of the
…rm’s private information. This term is strictly positive for all host types below
the upper end point
< . Since intense investment increases the informational
rent of the host, the investor …nds it optimal to lower investment in order to
reduce this costly informational rent.
An important consideration is the role played by the opportunity cost of
investment, r, in determining the nature of distortion in investment. It is evident
that an increase in r has two e¤ects: On the one hand, the distortion term on
the right-hand-side of equation increases in signi…cance. In other words, the
informational rent that must be paid for any implementable level of investment
and the investor’s incentive to distort investment is increased following a rise
in r.
On the other hand, the second term on the left-hand-side of equation
(22), becomes more negative and therefore increases in signi…cance; that is, the
marginal cost of investment increases. It follows that pI (:) must rise when r
rises in order to maintain the equality in equation (22). Given the concavity of
p(I; ), I must decrease as would be the case under pure moral. In sum, the
e¤ect of a higher level of r on the size of the optimal investment incentives is
unambiguously negative. The adverse selection e¤ects reinforce the moral hazard
e¤ects to increase the distortion in investment. Thus, our model predicts that
an increase in the opportunity cost of funds will exacerbate the agency problem.
4.2
Foreign Direct Investment (FDI)
The previous section assumed away any direct contributions that the investor
might make toward enhancing the success of the technological transfer. In that
section the foreign investor was portrayed as a purely passive actor with no
role beyond providing liquidity. This assumption was a plausible one given that
standard debt contracts are often transacted at arms length.
We now consider a situation in which the foreign investor funds the project
and in return acquires an interest in the …rm through an equity purchase. To
make the problem interesting, we assume that the investor purchases su¢ cient
amount of stock or shares of the domestic …rm as to gain in‡uence over the …rm’s
broad strategic objectives and organizational direction. Thus, the investor’s
involvement does not end with the transfer of funds. Additionally, he exercises
15
control and makes decisions over the implementation of project. Since
= 1,
the success probability now becomes p(I; E; ).
Endogenizing the investor’s participation in the manner described above
modi…es the model by introducing a moral hazard incentive on the part of the
investor. Thus, unlike the previous section, the model here features bilateral
moral hazard and adverse selection. There is bilateral moral hazard because the
value of the investor’s expertise E cannot be ascertained and therefore contracted
upon.
11
In addition to eliciting information from the domestic agent and in-
ducing productive technological investment, the optimal contract must not only
compensate the investor for providing funds. It must also reward the investor
for the organizational and managerial skills that he brings to the project. The
foregoing implies that any contract has to take into account both the investor’s
own incentive provision as well as the manager’s incentive provision.12 One can
anticipate a tension in providing incentives to both parties, for providing the domestic agent with a¤ective incentive to undertake investment necessarily entails
an incentive loss on the part of the investor.
The assumption that the investor needs to be given adequate incentives to
deliver appropriate level of expertise may on the surface look uncommon, but
it is nevertheless a reasonable one. Since expertise is personally costly for the
investor to supply, an investor with interest in a portfolio of projects may have
an incentive to spend too little time on a particular project if his expected return
from that project is too low.
Let f (^); v(^)g!^ 2[! , !] be the revelation mechanism, where
plays the dual
role of motivating both the domestic agent and the investor whilst v elicits
information. The investor’s payo¤ is obtained as:
V ( ( ); v( ); ) = [p(I( ); E( ); )
+
L
+ v( )](1
( ))
v( ).
Ex ante, the investor does not know the manager’s productivity.
11
(25)
She sets
We believe that this is the …rst study that has endogenized the investor’s intervention in
this form. Choi (2001) is, perhaps, a notable exception in this regard. As we show below,
however, Choi does not incorporate adverse selection in the same context.
12
The framework we follow below is analogous to that employed in the literature on team
production. In this setting one player designs the compensation scheme as a Stackelberg leader,
and thereafter participates in the production as a team member (McAfee and McMillan, 1991).
16
f ( ); v( )g to maximize her expected payo¤:
E[V (U (:); ( ); )] =
Z
(1
( )) p(I( ); E( ); )
L
+
+ v( )
v( ) dF ( ).
(26)
The domestic agent’s payo¤ is comprised of the value of her equity stake less
the cost of undertaking investment and is given by
U ( ; ) = [p(I( ); E( ); )
L
+
] ( ) + (1 + r)[v
I( )]
(27)
Let U ( ) = U ( ; ). Then using equation (27), we can rewrite the investor’s
objective function in terms of U ( ) as
Ve (U (:); ( ); ) =
Z
p(I( ); E( ); )[
+
L
U (:)
(1 + r)I dF ( ).
(28)
Hence, the screening problem under FDI, [D’] is as follows:
max Ve (U (:); ( ); )
(29)
U( )
(30)
( )
subject to
0
8 2
dU ( )
= p (I( ); E( ); )
d
I 2 arg max p(I( ); E( ); )
,
( ) 8 2
,
(31)
( ) + (1 + r)[v
I]
(32)
and
E 2 arg max(1
( ))p(I( ); E( ); )
E
v,
(33)
where equation (30) is the participation constraint and equations (31) - (33)
are the incentive compatibility conditions.13 The main di¤erence between the
investor’s problem [D’] and problem [L’] in the preceding section is that the
former has the additional constraint (33), which states that the investor’s input
into the project E must be chosen optimally given any contract.
13
This is a standard way of setting up problems characterized by doubled sided moral hazard.
For more detailed overview of the double moral hazard literature, see, for example, Demski
and Sappington (1991), Bhattacharya and Lafontaine (1995) and Kim and Wang (1998).
17
The optimal levels of investment and expertise given f (^); v(^)g, are de…ned
by equations (32) and (33). The two parties will undertake activity such that
given f (^); v(^)g, the marginal bene…t from the activity just equals the marginal
bene…t from undertaking the activity. In view of the inherent friction between
motivating the domestic agent on the one hand, and inducing appropriate level
of participation by the investor on the other, an interesting question is how the
choice of I and E will change in response to changes in the sharing parameter ;
that is, what are the signs of dI/ d and dE/ d ? From the total di¤erentiation
of the …rst order conditions associated with (32) and (33) we obtain
dI
=
d
pI (I( ); E( ); )
> 0,
pII (I( ); E( ); ) ( )
(34)
and
dE
pE (I( ); E( ); )dF ( )
=
< 0.
d
(1
( ))pEE (I( ); E( ); )
(35)
Equation (34) says that an increase in the manager’s stake in the project will
induce an increase in the level of investment. This makes intuitive sense: An
increase in
will increase the manager’s share of the expected project’s proceeds,
thereby increasing the rate of return on investment. Equation (35) says that the
amount of attention devoted to the project by the investor decreases with
equilibrium. Again the intuition for this is obvious. A higher level of
in
reduces
the investor’s share of the project’s cash ‡ow, thereby decreasing the investor’s
return from labouring diligently for …rm.
Proposition 3 below characterizes the optimal level of investment in this
setting. The construction of the proof follows along the lines of proposition 2.
The appendix contains the derivations of the optimal investment rule.
Proposition 3 Suppose that assumptions 1 and 2 hold. Then the condition
necessary for optimal level of investment under FDI will be given by
pI
where
1(
) and
2(
= (1 + r) +
1(
)+
2(
)
[1
F ( )]
f( )
(36)
) are de…ned as
1(
) = [pE
1]
18
pII [pE ]2
(1 + r)
pEE [pI ]2
(37)
and
2(
"
)= p
I
pII
pI
p
p
pII
pEE
E
pE
pI
#
2
(1 + r)
(1 + r)
pI
(38)
respectively.
Expression (36) says that the optimal level of investment is determined by
equating the marginal bene…ts (the left-hand-side) with the marginal costs (the
sum of the terms on the right-hand-side). To better understand the implication
of this condition, it is necessary to recall that the …rst-best level of investment
required the maximization of the total surplus which gave the marginal condition
pI
(1 + r) = 0 for all . Under bilateral moral hazard but without adverse
selection, by maximizing the expected total surplus subject to the incentive
contracts of I and E, the optimal investment rule is given by
pI
Thus, the …rst term
(1 + r) = [pE
1(
1]
pII [pE ]2
(1 + r).
pEE [pI ]2
(39)
) gives the distortion in investment that derives from
bilateral moral hazard. The second term
2(
)[1 F ]=f represents the distortion
that arises from the …rm’s private information. Since both
1(
) and
2(
)[1
F ]=f (see the appendix) are all positive, equation (36) leads to the conclusion
that two-sided moral hazard and adverse selection reinforce each other as to
increase the marginal cost of inducing investment.
In this second-best outcome, the optimal level of investment is obtained by
replacing the agent whose marginal cost is (1 + r) with a virtual type whose
marginal cost is (1 + r) +
1(
1(
)+
2(
)[1
F ]=f . It is important to note that
) is always positive regardless of the type. Because of the tension between
providing incentives to the agent on the one hand and motivating the investor
to provide adequate expertise, on the other, the moral hazard problem is never
resolved in this model. The magnitude of
on type. In particular,
boundary
2(
)[1
2(
)[1
F ]=f is, however, dependent
F ]=f is equal to zero for all types at the upper
but is strictly positive for all types over the interval [ , ). This
result follows easily from the fact that F ( ) = 1 and is consistent with the main
lesson of standard principal-agent models: to limit the informational rent paid
to the agent, the principal optimally induces distortion in activity over some
interval. In the context of our model, the level of investment is set below its full
information value.
This result relies on the agent’s utility function satisfying the Spence-Mirlees
19
single-crossing property assumption:
dU=d
dU=dv
@
d
d^
=
dE
+p
d
dI
+ pE (I; )
d
pI (I; )
It can be shown that
2(
)=
@
dU=d
dU=dv
1 d
0.
(1 + r) d^
(40)
dI
.
d
(41)
Since dI=d > 0,
sign
Hence, if pI (I; )
@
dU=d
dU=dv
[dI=d ] + pE (I; )
= sign
2(
).
[dE=d ] + p
(42)
0, then
is
nonincreasing. In other words, as the agent’s reported type increases, she is
awarded a reduced stake in the project. This result can be understood by …rst
considering the special case in which there is only moral hazard and no private
information. In this case, the optimal sharing parameter for any given levels of
I and E is given by =(1
@=@ [ =(1
)=pE =pI (1 + r) = pE + rpE =pI , which implies that
)] = pE > 0 and
is increasing in type.
Intuitively, when no adverse selection considerations are present,
is used
strictly to limit the moral hazard incentive. If this sharing schedule is o¤ered in
a setting characterized by private information, however, the agent with higher
absorptive capacity (for whom success is most likely) will have an incentive to
pass herself o¤ a lower type since doing so would enable her to earn informational
rents. To dampen the agent’s incentive to understate her type, the investor
lowers the attractiveness of contracts designed for the low type agents. This
is done by raising
(increasing the agent’s equity stake). Higher equity stake
for the agent is costly, from her perspective, because it lowers the investor’s
incentive to provide expertise. Hence, an agent who misreport her type must
now undertake more costly investment to make up for the diluted incentives on
the part of the investor.
4.3
Comparison of investment incentives under alternative funding mechanisms
We now compare and contrast the level of investment that is optimally induced
under the two funding mechanisms. In undertaking this exercise, we wish to
uncover any qualitative di¤erences in the nature of optimal incentive provision
when the project is …nanced through a debt contract than when it is …nanced
through the issue of equity to the investor.
20
The following proposition summarizes the key conclusion. The proof is relegated to the appendix.
Proposition 4 Suppose that assumption 1 and 2 holds. Then at the optimum
FDI will yield a higher level of investment only when the adverse selection consequence of FDI exceeds the moral hazard e¤ ects. .
The logic of this result can be understood by …rst supposing that funding
is obtained through the medium of FDI, but the investor is precluded from
providing any expertise. In this case, the optimal level of investment is given by
pI
= (1 + r) +
where
0
2(
)= p
I
p
0
2(
)
[1
pII
pI
F ( )]
f( )
(43)
(1 + r)
.
pI
(44)
Comparing equation (43) with equation (22), it is straightforward that investment incentives under FDI and debt …nance would coincide if there were no
moral hazard incentives on the part of the investor. Thus, the distortion term
1(
) and the last element of
2(
) (which is given by p
E
pII
pEE
pE
pI
2
(1 + r))
on the right-hand side of equation (36) represent the e¤ect of FDI (or allowing
the investor to exercise operational control over the project). We will call
1(
)
the bilateral “moral hazard e¤ect”of FDI because it captures the incentive loss
that occurs on the part of investor whenever the agent is induced to increase
investment a little bit. Since this term is strictly positive, equation (36) leads to
the conclusion that the investor’s intervention beyond providing liquidity may
actually increase the cost of achieving any given level of investment, thereby
worsening the agency problem.
This “moral hazard e¤ect”is, however, tempered by p
E
pII
pEE
pE
pI
2
(1+r),
which we will call the “adverse selection e¤ect .” Because this term is strictly
positive for any positive I and E, equation (36) appears to suggests that the
investor’s intervention in the project will reduce the marginal cost of undertaking
investment that occurs in term of informational rent that must be ceded to the
agent. To see this, suppose …rst that E=0. In this case, in order to limit the rents
earned by the agent, the investor induces distortion in investment by o¤ering
low powered incentives. Accordingly, the informational cost of implementing
any given level of investment includes the rents that must be paid to all types
higher than . Now suppose that E > 0 so the investor must also be motivated
21
to pay attention to the project. In this case, reducing the agent’s incentive in
a rational attempt to limit information rents will entail an o¤setting incentive
gain on the part of the investor. Consequently, the extraction of informational
rents becomes less costly.
In sum, whether FDI leads to more investment relative to debt …nance depends upon the relative magnitude of the bilateral “moral hazard e¤ect” and
“adverse selection e¤ect.” Only in the special case where the adverse selection
e¤ect is su¢ ciently large vis-a-vis the moral hazard e¤ect will the agent invest
more under FDI than under debt …nance.
5
Conclusion
This paper developed a framework to illustrate simply the interaction between
…nancing arrangements and the optimal investment in clean technology. The
main point of the analysis is that the media through which …nancing is obtained
has implications for agency costs and the nature of investment decisions.
Relative to debt …nance, FDI entails less intense adverse selection but an
elevated level of moral hazard problem. Adverse selection is less pronounced
here because reducing the agent’s incentive in a rational attempt to capture
some of the information rents induces an o¤setting incentive gain on the part of
the investor. The moral hazard problem is greater because providing incentives
to the agent must necessarily come at the expense of a diminution of the investor’s incentives. Hence, if the adverse selection consequences are su¢ ciently
signi…cant vis-à-vis the moral hazard e¤ects, FDI will outperform debt …nance
in terms of the level of technological investment that is optimally induced.
These results are obtained through a number of simplifying assumptions,
which could be extended in a variety of ways. The model assumes that both
the investor and the …rm are risk neutral. Risk neutrality for the agent is
questionable in this context, however, because agents are unlikely to possess a
portfolio of similar projects spread across the developing world. Thus, a deeper
exploration of the impact of …nancing mechanism might involve an examination
of the e¤ects of risk preferences. A second possible objection to this model is that
it assumes that debt contract precludes the investor from exercising control over
the …rm. In reality, an investor may intervene even under a debt arrangement
by way of a commitment to terminate funding if the …rm’s performance is not
satisfactory. These lines of thought are beyond the scope of this study and are
left for further research.
22
6
Appendix
6.1
Proof of Lemma 1
Equation (7) implies that for any pair of values
p(I( ); )[
p(I( 0 ); )[
L
+ ( )] +
L
+ ( 0 )] +
0
and
in
R( ) + (1 + r)(b( )
,
I( ))
R( 0 ) + (1 + r)(w + b( 0 )
I( 0 ))
(45)
and
p(I( 0 ); 0 )[
+ ( 0 )] +
p(I( ); 0 )[
+ ( )] +
L
L
R( 0 ) + (1 + r)(w + b( 0 )
I( 0 ))
R( ) + (1 + r)(w + b( )
I( )).
(46)
Adding up (45) and (46) yields
[ ( )
Therefore, if
0
>
,
( )
( 0 )][p(I; )
p(I; 0 )]
0:
(47)
( 0 ) or equivalently
0
( )
0.
Thus, incentive compatibility requires that
(48a)
(:) be a nondecreasing function.
This implies that
(:) is di¤erentiable a.e.
If a …rm type reports type ^ to the …nancier, she will get the expected
utility as described in (7). If ^ = is the optimal response for type …rm, then
the following …rst-order condition will be satis…ed;
p(I( ); ) 0 ( ) + p (I( ); )I 0 ( )[
R0 ( ) + (1 + r)[b0 ( )
+ ( )]
I 0 ( )] = 0
(49)
together with the second-order condition
p (I( ); ) 0 ( )I 0 ( ) + p(I( ); )
+p (I( ); )[I 0 ( )]2 [
+ ( )]
00
( ) + p (I( ); )I 0 ( ) 0 ( )
R00 ( ) + (1 + r)[b00 ( )
I 00 ( )]
0
(50)
Using the fact that (49) holds identically and taking its second derivative yields
p (I( ); ) 0 ( ) + p (I( ); )I 0 ( )[
23
+ ( )]
+p (I( ); ) 0 ( )I 0 ( ) + p(I( ); )
+p (I( ); )[I 0 ( )]2 [
+ ( )]
00
( ) + p (I( ); )I 0 ( ) 0 ( )
R00 ( ) + (1 + r)[b00 ( )
I 00 ( )] = 0.
(51)
Substituting this relation in (50) yields
p (I( ); ) 0 ( ) + p (I( ); )I 0 ( )[
+ ( )]
0.
(52)
Let U ( ) = U ( ; ) denote type ’s rent when reporting truthfully:
U ( ) = U ( ; ) = p(I( ); )[
+ ( )] +
L
R( ) + (1 + r) [b( )
I( )] . (53)
Then the envelope theorem applied to the maximization of (7) with respect to
^ yields
dU ( )
= p (I( ); )[
+ ( )]
(54)
d
which is condition (10) in the text. Condition (54) combined with (52) ensures that U ( ) is convex on
and di¤erentiable almost everywhere. Condition
(54) and the monotonicity condition on
( ) constitute the local incentive con-
straints, which ensure that the …rm will truthfully reveal her type locally. It is
possible to check that these conditions are su¢ cient for incentive compatibility.
6.2
Proof of proposition 1
The solution to the relaxed problem (L”) can be obtained using control theoretic
techniques with being treated in the same manner as a time index in an optimal
control program. We take U as the state variable with trajectory determined by
(54), and
as the control variable (See Chiang, 1992). The Hamiltonian can be
written as
H( ; I; U; ; ) = p(I; )
+ ( )p (I; )[
+
L
+ ] + [pI (I; )[
Assuming an interior solution for
U
(1 + r)I f
+ ( )]
(1 + r)]
(55)
( ), the maximum-principle conditions in-
clude:
@H
= ( )p (I; ) + pI (I; ) = 0
@ ( )
24
[maximizing the Hamiltonian]
(56)
@H
= pI (I; )
@I( )
(1 + r) + ( )p I (I; )[
+ pII (I; )[
d
=
d
dU
= p(I( ))[
d
+ ]
+ ( )] = 0 [maximizing the Hamiltonian]
@H
@U
[equation of motion for ]
+ ( )] =
@H
@
(57)
[equation of motion for U ]
(58)
and
( ) = 0.
[transversality condition]
(59)
Since the reservation payo¤ is independent of type and U ( ) increases with
type (U 0 ( ) > 0), the participation constraint will bind only at the lower bound:
U ( ) = 0. Hence, the co-state variable, ( ), will be zero at the upper end point,
. The solution for the control variable
[pI (I; )[
(1 + r)] +
where
dI
=
d
f
( ) is
pI (I; )[
+ ]
dI
+ p(I; ) = 0
d
f
(60)
pI (I; )
.
pII (I; )[
+ ]
(61)
Making use of the latter most equation and the fact that
p(I( ); )
pII (I( ); )
= pI (I( ); )
pI (I( ); )
(62)
from assumption 1, the …rst-order condition (60) can be rewritten as
[pI (I( ); )[
(1 + r)] +
+ pI (I( ); )[
f
Since (60) expresses
f
+ ]
pI (I( ); )[
1
+ ]
=0
(63)
in terms of ( ), we must look for a solution for ( ). We
resort to the equation of motion for the co-state variable. Equation
d
d
=
@H
@U
is a di¤erential equation which can be solved by separating the variables. Now
write
d
=
d
@H
= f ( ) =) d ( ) = f ( )d .
@U
25
(64)
Integrating both sides of the latter most equation and using transversality condition ( ) = 0 yields the following value for the co-state variable, ( ):
( )=
[1
F ( )] < 0.
Substituting back into the …rst order condition on
- p (I; )
1
(65)
( ) yields
F( )
+ pI (I; ) = 0
f( )
which implies that the multiplier
= [p (I; )(1
(66)
F ( ))]=f ( )pI (I; ) > 0.
Hence, the moral hazard constraint must be binding. Substituting for
and
( ) in equation, we obtain
pI (I; )
(1 + r)
p I (I; )[
+
1
+ ]
F( )
f( )
p (I; )
pII (I; )[
pI (I; )
+ ( )]
1
F( )
=0
f( )
Recall that the incentive compatibility for investment is
pI (I; )
(1 + r) =
pI (I; )
(67)
Manipulation of the last two equations provides
( )=
+ (1
)
1
f( )
F( )
+ 1 F( )
(68)
and
pI (I; )
(1 + r) = p I (I; )
(1 + r) [1 F ( )]
p (I; )
pII (I; )
, (69)
pI (I; )
pI (I; ) f ( )
which are equations (19) and (22) of proposition 2. From (10) , we can write
dU ( ) = [p(I( ))[
(1
) + ( )]]d . Integrating both sides of this equation,
we obtain
U( ) = U( ) +
Z
0
p(I( ); )d +
Z
0
( )d
(70)
which is (20) of proposition 2. Substituting back into (53) yields equation (21)
of proposition 2. We now check that
0(
26
)
0 and U 00 ( ) > 0. From (68) we
obtain
2
d ( )
=
d
Hence,
d ( )
d
p (I( ))
6.3
(1
6
4
+
> 0 since by assumption
00 (
0 and
)
h
(1 F ( ))
f( )
2
[1 F ( )]
f( )
) dd
d
d
0.
h
(1 F ( ))
f( )
3
i
i
7
5
(71)
0.U 00 ( )
0 so long as
Proposition 2
Let L be the Lagrangian function associated with problem [D’]. Then
L=
where ;
1
Z
p[
+
1 [pI
and
2
+
L
( )
E
U
(1 + r)I f d + ( )p
(1 + r)] +
2 [(1
( ))pE
1] ,
(72)
are the Lagrangian multipliers of the incentive compatibility
constraints. The corresponding Hamiltonian is
H =
p
+
L
+ ( )p
E
+
U
(1 + r)I +
1 [pI
( )
2 (1
( ))pE
f
(73)
(1 + r)]
2
+
1 pII
( )=0
(74)
2 pEE
(1
( ))f = 0
(75)
The …rst-order conditions include:
[ pI
(1 + r)]f + ( )p
[pE
1]f + ( )p
I
+
E
( )=
[1
F ( )]
(76)
and
( )p
Let
= [1
and
2
+
1 pI
2 pE
f = 0.
F ]/ f . Then, from these conditions, we obtain
= - [pE
1
p
E
]/ pEE
(1
(77)
1
=
[pI
(1 + r)
). These multipliers are all
nonzero, implying that the incentive conditions (32) and (33) must be binding.
Substituting for
1
and
2
in equation (77) and after some manipulation, we
27
p
I
]/ pII
obtain the following expression for the optimal level of investment:
pI
= (1 + r)
+ p
I
(78)
p
+ [pE
pII
pI
1]
pII [pE
(1 + r) [1 F ( )]
(1 + r)
2
pEE [pI ]
pI
f( )
2
[pE ]
(1 + r)
[pI ]2
p
pII
pEE
]2
E
This is equation (36) in the text.
6.4
Proof of proposition 3
Note that equations (22) and (36) give the optimal level of investment under
debt …nance and FDI, respectively. Thus, evaluating (36) using (22), we obtain
pI
(1 + r)
"
=
p
p
I
(
[pE
[pE
pII
pI
1]
p
E
pII [pE ]2
(1 + r)
pEE [pI ]2
pII
pEE
pII [pE ]2
(1 + r)
1]
pEE [pI ]2
pE
pI
p
E
2
#
(1 + r)
pII
pEE
(1 + r) [1 F ( )]
pI
f( )
pE
pI
2
(1 + r)2 [1 F ( )]
pI
f( )
)
=
=?
Given the concavity of p in I, a necessary and su¢ cient condition for I D > I L
is that
(
=
[pE
pII [pE ]2
1]
(1 + r)
pEE [pI ]2
p
E
pII
pEE
pE
pI
2
(1 + r)2 [1 F ( )]
pI
f( )
)
< 0.
The last inequality will be satis…ed in settings where the adverse selection e¤ect
of FDI dominates the moral hazard e¤ect.
28
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