Quality of Foreign Direct Investments
under country risk with incomplete
markets
/Preliminary version/
Kinga Z. Elo*
Abstract
Empirical research shows that FDI is not necessarily an indication of good
health of an economy; on the contrary riskier countries with less developed
financial markets and weak institutions tend to attract less capital, but more in
the form of FDI. As incomplete capital markets impose a liquidity constraint on
firms from these economies, less constrained foreign investors tend to have an
advantage over domestic firms in acquiring financial resources. Thus increasing
foreign ownership under incomplete debt markets can add a virtual value to
the domestic firm not exploitable by domestic investors. Foreign ownership
however does not mean that firms become more efficient in their operations. To
achieve this, foreign investors must acquire some minimum level of knowledge
about the operation of the domestic firm. As the market for knowledge is
also incomplete one cannot assume that control of residual rights indicates also
control of the necessary intangible assets of operation. I therefore extend the
pure liquidity analysis with the effects of non-contractible intangibles, opening
up a new dimension in the analysis of the motives behind FDI and enabling
the assessment of its quality. Using a continuous time stochastic setting that
incorporates country risk, differentiated knowledge base, borrowing constraints
and bankruptcy costs for foreign and domestic investors, it is possible to show
that foreign residual control depends on the transparency of the target economy
as well as the knowledge base of its investors. This approach also enables us
to examine the differences between portfolio and classical FDI decisions, by
assuming that portfolio type investments involve less specific intangibles. In
accordance with the empirical evidence the model predicts riskier economies
to attract FDI which is not welfare improving thus showing the properties of
simple portfolio investments. These can also explain why in some countries
although foreign investments appear in high magnitudes, the safe form of FDI
is not present. Finally, this framework explains why the top FDI receivers
predominantly consist of ‘safe’ economies.
May 2003
*PhD student at Melbourne Institute of Applied Economic and Social Research, The
University of Melbourne This work is part of my doctoral studies at The University of Melbourne, Department MIAESR. I am grateful to Paul Kofman and Peter Summers for their
support and helpful comments. Please address correspondence to Kinga Elo, Department
MIAESR, The University of Melbourne, Parkville, 3010, Vic, Australia, phone: +61-3-
8344-8883, fax:+61-8344-5630, or email: k.elo@pgrad.unimelb.edu.au. All mistakes are my
own.
2
1
Introduction
Empirical research shows that Foreign Direct Investment (FDI) is not necessarily an indication of good health of an economy; on the contrary riskier countries with
less developed financial markets and weak institutions tend to attract less capital,
but relatively more in the form of FDI (Hausmann and Fernandez-Arias [8]). The
idea behind the superiority of FDI over other types of capital, particularly portfolio
investments, lies in the implicit assumption that FDI is less exposed to capital reversals and contagion that affect other types of resources as it is ’bolted down’ thus
almost impossible to move it on short notice. The superior quality of FDI is severely
challenged in recent literature, as with the development of financial markets it became more easy to withdraw capital investments, even if the original investment was
made solely in tangible assets( Hausmann and Fernandez-Arias [8], Razin[16]).Indeed
Claessens, Dooley and Warner [5] showed that under certain circumstances FDI can
behave much like portfolio investments.
Another interesting feature of FDIs, linked to their definition, provides also support for the above views. FDI is often falsely identified with multinational firms’
foreign mergers and acquisitions and greenfield investments resulting in full or majority ownership stakes. Nevertheless, according to the IMF, FDI is an investment
involving lasting interest and control comprising an ownership share above 10% in a
foreign enterprise. This definition of FDI allows for embracing a much broader spectrum of investors from sole investors through hedge funds finally to multinational
companies (MNC). As there is a wide variety of investors with different motivations,
the classical view of FDI as a long term resource of financing, as was the case for
MNCs, may not be valid anymore. Moreover as Blomstrom, Kokko and Zejan [3]
argue, even the traditional ways of MNC investments have changed from the creation and acquisition of foreign affiliations to more complex business arrangements,
in which the total costs and benefits are shared between the foreign and domestic
investors by creating less than fully owned joint ventures.
Therefore, we might wonder if the investments grouped under the labeling FDI
possess indeed special qualities that differentiate them from the ‘inferior’, below 10%
ones and what is the role, if any, of ownership/control. To extend the analysis we
might want to go further and ask what is the main difference between FDI and
simple portfolio equity investments, or what is the amount of sufficient transfer of
control. That is, loosely speaking, why one would expose himself to the risk to
invest in one particular type of asset instead of choosing a diversified portfolio in the
target economy or industry. Is there any relationship between ownership/control and
investment quality?
The theory of industrial organization provides a clear-cut answer to the question of why control is needed for foreign operation. Hymer [9] argues that portfolio
investments seek gains from international interest differences, capital appreciation
and diversification of market risk, whereas FDI is motivated by the need to maintain control over business operations abroad, as FDI is a strategic response to the
presence of market imperfections. This is in line with Buckley and Casson’s[4] internalization theory of MNCs foreign operation. They argue that different business
activities are linked by flows of intermediate products comprising not only semiprocessed materials, but knowledge and information. As external markets are often
inefficient, particularly with respect to intermediate products, imposing agency and
moral hazard problems, there are incentives for MNCs to develop their own internal organizational structure. This idea can be extended from MNCs to any other
types of investments involving intangible, knowledge capital investments or superior
3
information. This idea is also developed by Nakamura and Xie [15], who contend
that ownership is essential to reduce the loss of intellectual property rights as well
as agency costs. Nevertheless, they argue that although through full ownership the
investors can avoid losses due to unauthorized use of their intangible assets, their
unfamiliarity with the host country’s local environment may impose another cost on
them in terms of managing and monitoring their investments. Furthermore, control
is useful to reduce the costs of agency problems arising from the non-contractability
of the output of the target enterprise in the sense that not all future income resulting from transferred intangibles (knowledge assets) can be specified in a contract.
Thus if there are any types of non-contractible knowledge assets in the possession
of the potential investors, control is always a means for securing their investments if
markets are incomplete.
Under these terms ownership is an incentive mechanism to induce the supply of
intangible assets. If all inputs and outputs were observable and there were sufficient
amount of transparency in the economy, there would be no need for excessive foreign
control, as all aspects of the transactions between foreign investors and domestic firms
could be contracted. Under these circumstances the assets of the target firm would
be worth the same under domestic control as under foreign. The above theories are
also underlined by the empirical research done by Hausmann and Fernandez-Arias[8]
who found that the more market inefficiencies one can find in an economy the more
incentives are present for FDI as it can be a substitute for missing or inefficient
markets.
Although these theories are appealing in terms of explaining how FDIs emerge,
they lack the power to explain why the majority of FDI flows to ’safe’ economies with
less severe market imperfections and also why FDI is unevenly distributed among
countries. Lehmann [13]showed that the bulk of foreign direct investments flow to
the developed economies, and even among the developing countries we can observe
differences in their incoming FDIs. He argues that the core factor behind these
differences can be captured by the dissimilarities among the countries in terms of
their country risks. Thus country risk itself can cause differential need for control
without the presence of any market imperfection. This is in line with the findings of
the transaction cost literature stating that increasing control entails commitment of
resources which increases the firm’s exposure to the possibility of losses due to the
currency changes caused by the changing macroeconomic environment (Anderson
and Gatignon [2], Vernon [19]). Nevertheless, according Hymer’s classification of
FDI and portfolio investments only the latter should be affected by the changing
macroeconomic environment as the prevailing market imperfections are not altered
by country risk( or if they are market inefficiencies are increased).It seems then that
all investment decisions comprise a combination of the pure ‘portfolio’ and ‘FDI’
motivations accepted in the literature. Under these terms the old classification’s
terminology (Hymer,[9]) can be treated as the two extreme cases of the investment
decisions. Indeed, with the growing complexity of investments it can not provide a
satisfactory explanation for the majority of investments as most of them lie in the
‘gray’ zone. This idea is also in accordance with the recent literature, challenging
the resilience of FDI to country risk and financial crises. I claim therefore, that the
motivations behind direct investments comprise classical portfolio equity investment
motivations as well and as such country risk will have an effect on their behavior.
To incorporate these ideas we need to merge financial theory with the theory of
corporate decision making. As the former is used to evaluate portfolio investments
while the latter enables the assessment of direct investment decisions the combination
of them would provide a good basis for analyzing direct investment decisions. To do
4
this we need a modelling framework which suits both theories. Dynamic programming
is a general tool for corporate investment decision analysis as it handles uncertainty
with ease and reduces complex problems to just two components: the immediate
decision and a value function. There is, however, a more striking feature of this tool,
namely, its close relationship with the contingent claim analysis developed to assess
financial assets (see Dixit and Pindyck[6] for further reference). As Dixit and Pindyck
(among others) show both tools can provide the same answer to investment decisions
and contingent claim analysis can be viewed as a special version of the investment
decision analysis. The use dynamic programming setting then allows us to introduce
all the required features into the investigation providing a suitable framework for the
analysis of the issues of quality and control.
The modeling framework chosen, there remains only to specify the costs and benefits of the different investments based on their ownership structure. First we have
to specify the main factors that are responsible for varying need for control. Taking
a close look at the theories presented above we can separate two types of factors
affecting the need for control: financial market inefficiencies and the possession of
specific knowledge type assets, with incomplete markets. These are the determinants
of benefits coming from control. The costs of control come from the unfamiliarity of
operations in the market and from the reduced risk sharing among owners. Increasing
control namely, is not for free. As Vernon [19] indicates, control also entails commitment of resources, including overhead. Hence with increasing ownership there is an
additional cost imposed on the investor as managerial costs induced by the increased
responsibility in decision making in an uncertain environment. Country risk plays
an important role in shaping both the costs and benefits of control as it is a primary factor determining uncertainty. Therefore we can determine three core factors
affecting ownership and stability: knowledge differentials, country risk and financial
market inefficiencies.
This paper is devoted to the analysis of these core determinants of the connection between ownership and investment quality where quality describes the ability of
the investments to provide stable resources to finance the Current Account deficits
and/or to improve the economic environment of the host economy. I use a continuous time stochastic dynamic programming model, which comprises some of the
main features of the financial and decision theories. In line with the reasoning of
Hausmann and Fernandez-Arias[8, p.14] I assume that the investment in the firm is
not bolted down. Foreign investors‘ stake is measured by their share in the whole
firm’s value. This consists of all accounts: equity, domestic and foreign assets and
debts. Notwithstanding that they might not be able to sell their equity on short
notice, they still can change their ownership share in the total firm value by acquiring other types assets e.g. debt instruments. It is also assumed that financial
markets are inefficient in a way that country risk, which is external to the abilities
of the domestic firms, restricts the abilities of firms in these countries to borrow. It
is assumed that foreign investors tend to have an advantage over domestic firms in
acquiring financial resources as they do not rely on the inefficient domestic market.
Thus increasing foreign ownership under incomplete debt markets can add a value to
the domestic firm not exploitable by domestic investors. Foreign ownership however
does not mean that firms become more efficient in their operations. It is assumed
that to operate the domestic firm efficiently, the foreign investors need at least the
same level of knowledge about the operation as the domestic firm owner investors. It
is assumed that the market for knowledge is incomplete, thus investors are not able
to write complete contracts for their invested intangible knowledge. The inefficiencies
in the financial markets with country risk and the incomplete knowledge market are
5
assumed to impose costs on the foreign investors.
The paper is organized as follows. In section 2 the investment model is introduced
and the main assumptions are stated. In section 3 a numerical analysis of the problem
is provided by imposing special assumptions on the functions involved. Section 4
provides a comparative analysis of the main determining factor’s effects on foreign
ownership and stability: country risk, knowledge differentials and financial market
inefficiencies, while section 5 concludes.
2
The foreign investor’s problem
The investment problem that I consider can be described as follows. An investor
(foreign investor) is given the option to invest in a firm (domestic firm) in a specific country abroad (domestic country), by acquiring some part of the firm’s assets
through buying its liabilities. It is assumed that firms similar to the domestic firm
offer the same gains all over the world outside the domestic country. I will assume
that domestic firm owners have no bargaining power1 to impede foreign investors
overtaking actions, thus hostile takeovers are allowed. The acquired ownership in the
firm can take any form of financial assets from short term debt to equity ownership.
This assumption eliminates the problem that equity investments are ’bolted down’.
For example as Hausmann and Fernandez-Arias[8] argue that foreign investors can
decrease their net ownership (or their interest) in a firm through acquiring debt by
using the firm’s assets as collateral. In this case FDI is reduced by the acquired
debt amount , which is counted as an outflow in the current account. The approach
followed by assessing the firm’s assets instead of its liabilities side helps to analyze
the effects of country risk on the net investment values of foreign investors, thus the
stability questions can be better understood.
It is assumed that obtaining a specific share in the assets of the domestic firm
involves some costs arising from agency problems and non-contractability as discussed
above. The foreign investor’s objective is assumed to be the maximization of the long
term growth of the firm during his investment period. Foreign investors have a finite
planning horizon T ,after which they liquidate their investment at the then prevailing
price. The end of the planning horizon represents the end of extractable benefits from
foreign ownership. After this time competition eliminates the extractable rents. The
foreign investor can terminate its ownership at any time before T . It is assumed that
selling the ownership in the firm is involves no cost. Incorporating transaction costs
is an easy extension of the model and its exclusion does not change the results by
much.2 .The problem of foreign investors is to specify their ownership share in the
domestic firm’s assets and their optimal entry and exit time to maximize the growth
rate of their investments. Another useful assumption to make is to presume that in
case two assets offer similar gains home and abroad investors will choose the one in
their home country. In the model’s setting this will induce foreign Investors not to
enter the domestic country.
In accordance with the financial literature the domestic firm’s assets value, denoted by V is assumed to evolve according to a geometric Brownian motion. Assuming that the (Ω, F, P ) tuple is a complete probability space with a filtration (Ft )
satisfying the conditions of right continuity and augmentation by P - negligible sets
V 0 is the solution of the following stochastic differential equation:
dV = µ(kD )V dt + σV dz
1 This
(1)
is a fairly restrictive asssumption, which is worth for further investigation
course if transaction costs are very high they will cause firms to stay, yet I would like to
show the effects of other factors on the ownership share obtained by foreign investors.
2 Of
6
where µ(kD ) is the growth rate of the firm using sole domestic knowledge capital,
kD . Knowledge includes not only technical knowledge (research and development,
design, process engineering), but also knowledge of organization, management and
inter-firm and international relationships. In accordance with the financial literature
µ(kD ) can also be treated as the required rate of return for the domestic firm’s
operations. The variability of firm specific shocks is denoted by σ and it is assumed
to be a constant and z is a standard one-dimensional Ft − measurable Brownian
motion.
2.1
The effect of knowledge differentials on the value of the
firm
In concordance with industrial organization theory I will assume that foreign firms
are able to extract extra returns by either exploiting scale economies through superior management of the organization or superior knowledge yet these ’techniques’
are, however, non-marketable thus their exploitation needs intensive presence of the
owners.
The effect of a knowledge transfer on the operation of the firm is represented by
an efficiency function denoted by Φ (kF , kD ). The efficiency parameter is assumed to
affect the firm’s potential growth rate, µ(kD ),in a simple multiplicative way. Hence
the new rate of maximum extractable return under foreign ownership is assumed to
be Φ (kF , kD ) µ(kD ), where Φ (kF , kD ) ≥ 1 holds if kF ≥ kD and Φ (kF , kD ) < 1 if
kF < kD . As foreign presence is heavily needed for the extraction of extra rents I will
assume that the efficiency gains decrease if the owners of the intangible asset reduce
their ownership. Denoting the share foreign ownership by β F where 0 ≤ β F ≤ 1 we
can write the growth rate of the firm’s assets as a linear combination of µ(kD ) and
Φ (kF , kD ) µ(kD ) in the following form:
µF (β F , kF ) = µ(kD )Φ (kF , kD ) · β F + µ(kD ) · (1 − β F )
(2)
Assuming symmetry in the effect of both domestic and foreign knowledge on the
growth
´ Φ (kF , kD ) becomes linearly homogenous in kF and kD , thus we can write
³ rate
kF
F ,kD )
kD Φ kD . Holding kD fixed the following relationships must hold: ∂Φ(k
> 0.
∂kF
The positivity of the partial derivative implies that an increasing knowledge difference
between the home and foreign investors increases the exploitable potential growth
rate.
2.2
Gains extracted from financial market inefficiencies
As we could see by Krugman[12] and Hausmann and Fernandez-Arias[8] inefficient
domestic financial markets can limit the access to international financial markets
even if the company seeking it has sound background. Under these circumstances
local owners will miss some profitable opportunities because of the lack of financial
resources available. Thus in this case there is an additional value to be extracted
to those who are less limited in their financial resources. The problem of missing
debt markets is also present in case of small companies for whom to find financial
resources is much harder than for larger companies. These disadvantages though, are
independent from the capabilities of the managers..
To incorporate the effect of constrained resources I will assume that new positive
net present value investment opportunities appear in the industry, which follow a
Poisson process, dq.
¯
½
1 with probability
λ1 dt ¯¯
dq1 =
(3)
0 with probability
1 − λ1 dt ¯
7
where q1 represents the appearance of new opportunities. To implement the new
projects which are assumed to produce a Present Value flow of (1 + k)αV, firms
are required to pay kαV up-front cost, where k is the stochastic cost of capital and
α is the return on the investment. The Net Present Value of the project, which
will be added to the firm’s asset value is thus αV . Firms are assumed to behave
competitively in the world market thus they are forced to implement these advances
to remain in competition. Yet there is a constraint on this activity: the amount
of available free cash flow. It is assumed that some of the arriving projects need
external financing. The pecking-order theory of finances tells that firms use up their
own resources first and if they need external resources they prefer debt. Using this,
we can assume that the firm will always want to finance its projects from borrowings.
If the value of the project, however, amounts to a top of D they have to forego the
opportunity and the firm’s value does not change or could even decrease. In this
setting then there is an upper constraint on the achievable installation cost of the
project as k ≤ VDα has to hold for a project to be implemented.. This reflects the
inefficiencies in the debt market as D has nothing to do with the capabilities of the
firm as it is the result of the company’s external situation. It is assumed that the
D
probability of a new project’s cost being smaller than αV
is λ2 thus we can write the
arrival rate of achievable projects in the following form:
¯
½
1 with probability
λ1 λ2 dt = λdt ¯¯
(4)
dq =
0 with probability
1 − λ1 λ2 dt = 1 − λdt ¯
, where λ = λ1 λ2 is the arrival rate of the achievable projects. It would not change
the main findings of the model if we assumed that the arrival rate of achievable
projects without foreign ownership is zero, as we are only interested in the additional
value a foreign owner can add to the firm. In this setting economies with perfect
debt markets will cause the value of λ to be zero to foreigners.
2.3
The effect of country risk on the firm’s value
Empirical research shows that FDI is unevenly distributed among countries. The
bulk of foreign direct investments flows to the developed economies, and even among
the developing countries we can observe differences in their incoming FDIs([13],[8]).
Lehmann [13] argues that these differences can be captured by the dissimilarities
in terms of country risks. Although as a sole explanation, differences in country
risks provide a weak explanation of direct investments, the inclusion of the effect of
country risk is vital to understand better their behavior.
In concordance with the Financial literature ([21],[14]) we can model the effect of
a financial crisis as a death process by introducing a Poisson variable CR:
¯
½
1
pdt ¯¯
dCR =
(5)
0
1 − pdt ¯
where pdt reflects the arrival probability of financial distress. When a crisis accrues investors suffer losses in terms of the value of their assets. This will be represented by assuming that in case of a crash V is decreased an amount of (1 − η)V,
where η represents the distress factor. Lower values of η refer then to more severe distress. It is assumed that besides its negative impact on the value of the firm, country
risk also has an effect on the credit ratings of the domestic firms. I will assume that
the credit rating is external to the individual firms depending on aggregate macroeconomic and political factors. To incorporate this, I assume that the crash arrival
parameter, p, alters the credit constraint the firms are facing, thus D = f (β F , p)
8
With increasing country risk the available financial resources decline thus the partial
derivative of D, with respect to p has to be negative.
To relate the specification of D to the variations of λ recall that λ = λ1 λ2 is the
arrival rate of achievable projects. Hence if D decreases it would cause the arrival
rate of affordable projects under foreign ownership to increase, causing ∂λ
∂p > 0.
2
∂ λ
This effect depends though on the amount of foreign ownership, causing ∂p∂β
>0
F
and the risk adjusted arrival rate will be λ0 = λ(p, t). It is assumed that with the
recovery from the crisis the opportunities coming from the increased risk disappear
thus these provide only a short term exploitable value, which means in the models
0
terms that: ∂λ
∂t < 0.
Based on the above we can write the firm’s value under domestic and foreign
investment as a jump-diffusion process of the following form:
Full domestic ownership: dV = µ(kD ) · V dt + σV dz − V (1 − η)dCR
(6)
Foreign ownership:dV = µF (β F , kF )V dt + σV dz + αV dq − V (1 − η)dCR
(7)
Using the above we are able to specify the foreign investors’ decision problem to
invest in the domestic firm. Let the value of the investment (the amount of financial
assets invested) be denoted by W such that:
W (t) = β F · V (t)
As it is assumed that investors can only change their ownership when selling the
whole firm the change in W can be written as:
dW = β F · dV
2.4
(8)
Costs of foreign operation
Foreign investment gaining control over the operations has costs attached to it. Attaching costs to control is in concordance with the prevailing theory of international investments. The transaction costs explanation of organizational choice determines several factors which affect organizational choices and the choice of control
(Williamson [20],Teece [18].) Based on these we can separate two major types of
costs falling into the category of general managerial costs and asset specific spillover
costs.
2.4.1
Managerial costs (CM )
Vernon [19] argues that increasing control is costly as it also entails commitment of
resources, including overhead. Hence with increasing ownership there is an additional
cost imposed on the investor as managerial costs induced by the increased responsibility in decision making in an uncertain environment. Anderson and Gatignon [2]
contend that control also increases exposure to risk resulting in High-control modes
with high returns and risks, and Low-control modes (e.g. licences and other contractual agreements) with low risk and returns. Therefore foreign investment can
be viewed as a trade-off between control and cost of resource commitment. It is
also assumed that the costs of the investment and the growth opportunity are influenced by the country risk factor, imposing additional costs on the investors in the
form of reduced liquidity and also increasing the overhead costs through increased
uncertainty.
9
To incorporate these into the analysis let us represent with CM the maximum
managerial and agency costs associated with full ownership. From transaction costs
theory we can see that both β F and country risk have an impact on the general
management costs hence CM takes the following form: CM = CM (β F , p).To satisfy
∂CM
M
transaction cost theory we need have: ∂C
> 0.
∂p > 0, and ∂β
F
2.4.2
Spillover costs (Cs , Cλ )
Another important group of costs are connected to the specific ‘assets’- both tangible
and intangible- provided by the foreign investors. Teece [18] claims that intangible
assets seem to be a crucial determinant of the amount of control obtained by foreign investors, since these enable firms to operate efficiently in a foreign environment
where domestic firms have various advantages. He argues that the more intangible
assets are provided by the foreign investors to the operation of the domestic firm, the
more reluctant the investor becomes to share information and the more he insists on
full control or majority-ownership in order to limit the spillover of the proprietary
knowledge. According to Nakamura and Xie [15] it is important to stress that if
contracts can be established to protect the intangible asset provider (i.e. complete
contracting is possible), ownership structure may not matter even if there is information asymmetry between the domestic firm owners and the foreign investor. If all
inputs were observable along with their quantities and resulting outputs produced
and well-specified contracting mechanisms were in place there is no need to exert
control over the operation of the target firm. As Nakamura and Xie argue that
in practice the quantities of inputs and the corresponding output is not verifiable.
Moreover, contractual relationships incorporate agency costs because of the lack of
effective incentive mechanisms to eliminate these costs. This validates the use of
spillover costs arising from the incapacity of parties to write contracts that avoid
agency problems.
To integrate these findings in the analysis, I will assume that depending on the
knowledge differential foreign investors incur a maximum cost of CS (Φ) technology spillover, with CS (Φ) < 0 if the foreign investor’s knowledge base is less than
that of the target company’ managers. I will also assume that intangibles are noncontractible thus neither licensing nor royalties nor meaningful side-payments can
be specified to eliminate the problem of unwanted knowledge spillover. With the
increase of ownership the knowledge spillover effects can be mitigated. The simplest way to express this connection is to assume that the costs depend linearly on
ownership, thus CS (Φ, β F ) = (1 − β F )CS (Φ).
The non-verifyability of inputs and corresponding outputs imposes also costs in
the case when only financial resources are provided to the domestic firm and foreign
investors are not more competent in running the business than domestic firm-owner
investors. As the monitoring of the use of these resources is costly without having
efficient control, foreign investors are willing to take over an increasing part of the
firm’s assets to avoid resource spillover to the domestic investors instead of using
these funds to finance value increasing projects. This shows that agency problems
can also be present in terms of tangible assets, provided that complete contracting
is not possible. I will therefore impose a monitoring cost on the investors arising
from the provision of extra financing resources. These costs then depend on λ. It is
assumed that increasing extra financial resources will increase the cost of monitoring,
which can be reduced by obtaining more control. Assuming that the maximum cost
of spillover is Cλ , we can write the spillover cost in the following form: Cλ (λ, β F ) =
(1 − β F )Cλ (λ)
We can write the costs function associated with the foreign investment in the
10
following form:
C(β F , λ, p, Φc) = (1 − β F ) [Cλ (λ) + CS (Φ)] + CM (β F , p)
(9)
In line with the previous reasoning, it is assumed that foreign investors‘ capital
gains decrease by C(β F , λ, p, Φ) each period. This allows us to write the change in
the foreign investor’s assets‘ value as follows:
dW = β F · dV − C(β F , λ, p, Φ) · dt
(10)
Applying the definitions of W and dV and using Ito’s lemma we obtain the
following relationship for dW , the change in the value of the investor’s ownership
share:
dW = β F µF (β F , kF )V dt + σV dz + αβ F V dq − β F (1 − η)V dCR − C(β F , λ, p, Φ)dt =
(11)
= [µF (β F , kF )W − C(β F , λ, p, Φ)] dt + σW dz − W dCR + αW dq =
= µC (β F , kF , W )dt + σW dz − W (1 − η)dCR + αW dq
2.5
Foreign investor’s decision problem
The decision to invest in the foreign firm is made at a stopping time τ F
I ∈ T , at
which time the foreign investor obtains a β F V ( τ F
I ) share of the firm’s asset value at
that time.3 The decision to sell the investment is made at a stopping time τ F
o , with
F
T = τF
o ∈ T = τ I . I assume that T is the end of the planning horizon of the foreign
investor, where he liquidates the investment at the then prevailing value of his stake.
After period T the excess returns disappear and the excess return on the investment
is assumed to become zero. To simplify the analysis assume that once the decision
of ownership share is made the firm will not alter its stake in the firm until he finally
sells it. The model is somewhat restrictive over in terms of buying additional stakes
through the time. The problem is overcome by assuming no transaction costs of
buying and selling. After selling the project the investor reverts back to the option
to enter and can return immediately to the market at the same price. Under these
terms obtaining higher ownership is indeed guaranteed throughout the life of the
opportunity.
I assume that foreign investors want to maximize the long term value of their
asset investments. Hence the problem of foreign investors can be formulated as the
following dynamic optimization problem:
h
i
F
F
F
0 F
−ρτ F
I + E(W (τ F ) · e−(µ(kD )τ o +ρτ I ) )
J(V 0 , τ F
,
β
,
τ
)
=
max
E
−W
(τ
)
·
e
I
o
I
o
F
βF
(12)
with an end condition
J(T, β F , T ) = 0
(13)
The end condition implies that the growth opportunities obtained by the acquisition of the firm disappear over time, thus it can be assumed that T is the last time
when the investment produces unusual returns. Duckworth and Zervos [7] state that
3 Note that the structure of the model does not require that the firm has publicly available shares
on a stock exchange.
11
general problems involving a sequential choice of a finite number of intervention times
can be decomposed into a sequence of optimal stopping problems, which are then
solved backwards in time. In the next sections I closely follow the analysis of optimal
stopping problems presented by Knudsen et. al.[11] and Duckworth and Zervos[7]
Using the value function defined in equation (12), we can write the problem of the
firm in the following form:
¡ ¢
v V0 =
sup
(τ I ,τ o ,β F )
F
J(V 0 , τ F
I , τ o , βF )
n
¡
¢o
¡ ¢
−ρτ F
I + v
b W 0, τ F
v V 0 = sup E −W 0 (τ F
I )·e
I , βF
(14a)
(14b)
(τ I ,β F )
¢
¡
vb V 0 , τ , β F =
n
o
¡
¢
−µ(kD )τ F
o
, where vb V 0 , T, β F = W (T )
sup E W (τ F
o)·e
0<τ o <T
(14c)
With reference to standard theory of optimal stopping we expect that under
usual conditions v, vb have solutions w and w
b which satisfy the following variational
inequalities:
max max
βF
max
µ
µ
£ ¡
¢
¤
1 2 02
σ V wV V + µ(kD )V 0 wV + p w ηV 0 − w
2
¢
b − W0 − w = 0
+wt − ρw, w
£ ¡
¢
¤
1 2 02
bW W + µC (β F , kF , W 0 )w
bW + λ0 w
b (1 + α) W 0 − w
b
σ W w
2
¢
¢
¤
£ ¡
b =0
b − ρw
b+w
bt , W 0 − w
+p w
b ηW 0 − w
bW W , wt are the first and second derivatives of the functions with
where w
bW ,w
respect to W. and t
The above Hamilton-Jacobi-Bellman (HJB) equations do not admit a unique
solution even within the space of infinitely differentiable functions. I do not want
to analyze the existence and unicity of these solutions yet refer the interested reader
to the articles of Knudsen et. al. [11] and Duckworth and Zervos [7]. The simple
structure of the parameters (e.g. they are constants) ensure that we will have a
unique solution.
According to the optimal stopping literature(see for example Brock, Rotschild
and Stiglitz [1], Karlin [10]) the value function of the problem with a solution of the
HJB equations incorporates the smooth pasting conditions requiring that
©
ª
w
b0 − 1 = w0 ∀W 0 ⊆ S := W 0 ∈]0∞[: w(V 0 ) = w(W
b 0) − W 0
©
ª
b 0) = W 0
w
b0 = 1∀W 0 ⊆ Sb := W 0 ∈]0∞[: w(W
(15)
Thus first taking the second stage problem, based on a fixed amount of ownership
share we determine the optimal stopping region and the value of the investment
opportunity for all initial values. This region will determine the value at which
the foreign investors will move out of the country and sell their investments in the
firm. This time is reached whenever vb(W ∗ ) = W ∗ . If vb(W ∗ ) > W ∗ the increment in
12
the value of the investment exceeds the market value of the assets thus holding the
investment produces additional gains.
The first stage problem involves moving backwards to the entry decision of the
firm. By knowing the value of the investment for different ownership structures, we
have to specify the rule which ensures when to optimally invest in the firm. We have
to determine the value of the option to invest for different levels of ownership and
initial values. Then we have to select the maximum of these option values for each
V 0 to specify the optimal ownership β ∗F for the different initial values.
The first stage problem is equivalent to a contingent claim on investing into the
foreign market. Its value depends on the opportunity cost of delaying the investment
that can be expressed by δ = |µ(kD ) −ρ| (see Dixit and Pindyck, [6, p.149]). If δ were
zero there would be no opportunity cost of delay thus there would be never optimal
to invest. If, however, δ is very large the value of the option to postpone entry would
be very small because the opportunity cost of waiting in that case becomes very large.
Thus as δ → ∞ the investment choice becomes a now and never investment, which
means that the entry and exit decisions will overlap and the investment decisions will
reduce to the analysis of the second stage optimal stopping problem.
The separability of investment problems allows for the analysis for both now and
never and delayed investments, which will be heavily used in the analysis. To obtain
a meaningful entry time we need that µ(kD ) < ρ as there is a cost associated with
waiting. As we can see in equation 12 the discount rate in the second stage is the required rate of return of the project,µ(kD ), instead of ρ. This means that if the growth
rate after merger is the same as before the mergers and there are no financial market
inefficiencies, the Present Value (PV) of the foreign investment ex investment costs
is the same as the paid price, W 0 . I will assume that µ(kD ) expresses the required
rate of return of all the firms similar to the target independently of their location 4 .
Under these circumstances foreign investors will not enter the domestic country as
the overhead costs incurred from the unfamiliarity of the domestic environment will
decrease their assets’ long term capital gains below world average, thus the value of
their investment opportunity becomes negative.
3
The solution of the foreign investor’s problem
I will assume that wt = 0, thus the opportunity to enter the foreign market is always
present. The first stage problem then reduces to an ODE that has a solution of the
following general form:
w(V 0 ) = A(V 0 )δ1 + B(V 0 )δ2
(16)
A,B are some constants and δ 1 and δ 2 are the roots of the following non-linear
polynomial (Dixit and Pindyck,1994,[6] ):
1 2
(17)
σ δ(δ − 1) + µ(kD )δ + pη δ − p − ρ = 0
2
To rule out bubble solutions we have to assume that the B the constant corresponding to the negative root δ 2 is zero. Therefore we have that:
w(V 0 , β F ) = AV 0δ1
(18)
The value of A can be determined by the smooth-pasting conditions in equation(
15).
4 This means that the required rate of return reflecets the firm‘s qualities instead of the whole
range of uncertainties in his environment.
13
The second stage problem’s partial differential equation does not have a closed
form solution. We then have to use numerical techniques to obtain the value of the
investment. Using the method of Finite-Differences we can rewrite the partial differential equations in the HJB equations above in a discretized version. To overcome
the restrictions on the asset steps implied by the simple structure of the explicit
method I will use upwind differencing instead of the central differences, commonly
used in numerical solutions involving derivatives. The use of upwind differencing is
underscored by the fact that µC can take both negative and positive values( [21]).
As the underlying process is a jump-diffusion we have to incorporate the jumps
also into the analysis. In case of jumps, the defined grid may not match the after jump
values of the underlying asset so we have to use some approximation for the values
of the option. According to Tavella[17] this can be done by a simple extrapolation
technique. In the numerical model presented below I have used a simple two-point
intrapolation between the gridpoints to obtain the after jump values of the option
and a 4 point extrapolation beyond the gridpoints in case of positive jumps. The
accuracy of the underlying method is of the order O(dW 2 , dt).
To handle the problem of exit we have to incorporate the smooth-pasting and
value matching conditions defined in equation (15) into the numerical method. In
the second step it is an easy extension of the numerical model. As the second stage
problem resembles very much an American type call option we can use the solution
method for these. Willmott[21]showed that imposing the following constraint will
result in a continuous solution which satisfies equation (15) without affecting the
accuracy of the method.
w
bik+1 = max(w
bik+1 , Wi )
(19)
where w
bik = w(iδW,
b
kδt). δW and δt are the asset and time steps respectively,
defining the finite difference grid.
The entry decisions smooth pasting problem is somewhat more complicated. I
use the method developed by Dixit and Pindyck[6] to obtain a free-boundary for the
numerical solution.
Using the fact that at the entry point
w(V ∗ ) = w(W
b ∗ , t) − W ∗
0
∗
w (V ) = w
b0 (W ∗ , t) − 1
and equation (18) must hold we can rewrite the condition into the following form:
w(W
b ∗ , t) =
w
b0 (W ∗ , t)W ∗ + (δ 1 − 1)W ∗
δ1
(20)
After discretizing equation (20) we get the free-boundary condition necessary to
obtain the switch points between stage 1 and stage 2. The solution proceeds backwards from the terminal boundary:w(W,
b
T ) = WT . Each time a value is calculated
for w
b we have to check whether equation (19) holds. If we allow for switching between entry and exit states we have to incorporate the free boundary conditions in
the solution for the single w
bik values checking each time step whether the boundary
value has been reached. If we do not allow for switching, the solution mechanism
changes in the way that we have to specify all the second step option values after
which we check whether the boundary has been reached. In practice these provide
very similar result. As we are not interested in the exact value of the assets, as just
the general behavior of the investment decisions are of interest we can use either of
14
these to solve the problem. After defining the option values for all investment levels
assuming a grid of β F values we can determine the maximum value of these,β ∗F , for
all W 0 .
To produce numerical solutions we have to define the underlying functions. In
order to keep the set of decisive parameters small I have introduced the simplest
functions which express the required attributes of the model.:
CM = β 2F (1 + p)2 V0 µ(kD )
Cλ = λV0 α
Φ (kF , kD ) =
kF
kD
CS = [(Φ − 1)µ(kD )]2 V 0 ;
, kD = 1
Thus the underlying cost function takes the following form:
"
CF oreign (β F ) = (1−β F )V0 λα +
µµ
¶
¶2 #
kF
− 1 µ(kD )
+β 2F (1+p)2 V0 µ(kD ) (21)
kD
The shape of the cost function is convex, which assumption is in line with cost
theory. The arbitrary choice of functions has an important effect on the model
outcome, yet the general direction of acquisitions as well as the quality implications
F
remain the same. In our setting Φ (kF , kD ) = kkD
, where kD = 1 thus Φ represents the
foreign knowledge base in home knowledge units. To express the effects of country
risk we can write the risk adjusted arrival rate in the following form:
λ0 = (λ + p + λp)
λ0 = λ
if t ≤ 1
if 1 < t ≤ T
(22)
(23)
Equation 22 shows that either increasing market inefficiencies(λ) or country risk
(p) can impose a liquidity constraint on domestic firms. The t ≤ 1 constraint represents the fact that the accessible value through the unlimited financing is short term
in case there are no additional financial market inefficiencies.
Throughout the analysis I will use the following values for the parameters:
α = 0.3
σ = 0.4
1 − η = 0.5
µ(kD ) = 0.1
T =2
ρ = 0.6
The parameters are taken arbitrary, yet these are choices, which can be calibrated
to empirical data. There are only two restrictions, namely:α < 1 − η and µ(kD ) < ρ.
The first condition indicates that the effect of a possible financial crisis has to be
larger than the possible achievable gain on the financial market thus the crash must
be severe enough. In accordance with the previous analysis on the opportunity cost
of delaying investment decisions, the required rate of return from the domestic firm
must be less than the discount rate ρ. 5
Consistent with the model’s setting, if λ and Φ are zero, thus the growth rate after
investing is the same as the domestic firm’s required rate of return, µ(kD ), foreign
investors will not enter the market. To show this I have calculated the investment
values for ten different ownership levels, without imposing the stopping condition.
As we can see from Figure 1 the Net Present value of Foreign Investment is
invariably negative as there are costs associated with it. Notwithstanding that foreign
5 Note that the large difference between the two values is only a convenience matter to get results
for the numerical analysis with relatively few grid points (41) on the firm‘s value V.
15
Figure 1: Net Present Values of foreign investment with and without Stopping
Investment value with entry option, Φ= 1, λ= 0, p= 0
0
←β
=0.1
←β F =0
←β F =0.2
F
←β =0.3
F
Inve stme nt`s value
-1
←β =0.4
F
←β =0.5
-2
F
Step2
Step1
NPV of investment
without ex it option
←β =0.6
F
-3
←β =0.7
F
-4
←β =0.8
F
-5
←β =0.9
-6
F
-7
←β =1
F
-8
0
10
20
30
40
V
50
60
70
80
0. 7
0.8
0
Cost func tion and the value of µ and λ
F
4
cost
3.5
µF
λ0
3
cost, Φ
2.5
2
1.5
1
0.5
0
0
0.1
0.2
0.3
0.4
0. 5
0.6
0. 9
1
βF
investors‘ option to exit renders present values to become zero as negative values can
be averted by exit, there will be no investments made as home investments offer the
same gains thus there is no need to go abroad.
To induce foreign investors to enter the domestic country, domestic firms must
provide exploitable sources to produce extra gains. These sources depend on three
core parameters Φ, describing the knowledge differential of foreign and domestic
firms, λ, achievable project arrival rate, which describes the amount of financial market inefficiencies (e.g. decreasing λ implies fewer opportunities through the available
inefficiencies), p, the country risk parameter. In what follows I will describe the
effect of these parameters on the desired foreign ownership share in the domestic
firm and their effects on the quality of these investments. Quality is defined from
the domestic country’s welfare point of view. There are two ways how foreign investments can contribute to the welfare of the host economy. First, foreign capital
investments provide resources to finance the Current Account deficit. Secondly, direct investments can improve the economic environment of their host by introducing
superior knowledge and by eliminating obstacles coming from inefficient or missing
markets. Consequently, to qualify as a desirable capital inflow, investments should
provide stable financial resources and/or improve the economic environment of the
host country. As the aim of the paper is to provide an answer to the question whether
FDI can be treated as a more secure form of financing than portfolio investments, I
will restrict the investigation to stability issues.
The optimal stopping framework presented above provides a convenient basis to
address the problem of commitment. Under the model’s setting, stability can be
measured by the optimal exit and entry values at given levels of desired ownership
16
stakes. A lower exit value means that the foreign investor is committed to hold his
investment position for a larger decline in the value in his investment. This means
that the variability of these investments will be smaller than that of the investments
with higher exit values. The ability to improve the economic environment in the
domestic country can be measured by the foreign investors relative knowledge base,Φ,
and the quality of business environment in domestic economy represented by λ. The
larger the difference between the domestic and foreign knowledge base, the more
beneficial the foreign investment is assumed to be. By the same token, if there
are financial market inefficiencies or missing markets in the domestic economies,
foreign direct investor can circumvent them by acquiring control (see Hausmann and
Fernandez-Arias [8, pp. 16-18]). Under these terms the more financial inefficiencies
there are in the host economy the more beneficial effects FDI investments may deliver.
The basic tools provided we are now able to discuss the effects of the core parameters on the decisions of the foreign investors.
4
4.1
Comparative Analysis
Knowledge differentials, ownership and stability
To start with the impact of knowledge differentials, we have to solve the optimal
stopping problem for different values of the efficiency parameter Φ assuming no additional financial market inefficiencies or country risk. Using the numerical solutions
to the partial differential equations in the second and first stage, we can generate the
present values of the investments with different ownership levels varying from zero
percent to full ownership for all possible initial firm values V0 and a large range of Φ.
After obtaining these values and using a simple maximization process we can specify
the ownership shares at a particular level of V0 and Φ which maximize the foreign
investor’s net gains for the two stages of the optimal stopping problems. The results
are presented in figure 2 that shows the effect of knowledge differentials on desired
ownership.
The lower panel describes the effects of knowledge differentials on the desired foreign ownership share in case of the possibility of delayed entry thus representing the
solutions to our stage 1 problem in equation (14b). The panel’s contours represent
the desired levels of ownership ensuring the highest capital gain on the investment
if investors have an option to delay acquisitions. As we know from the previous
sections if ρ goes to infinity the option to delay becomes worthless and the entry
and exit decisions overlap. Stage 2 solutions then also represent Stage1 optimal decisions. The first panel of the figure represents these ideas, depicting the optimal levels
of ownership for now-and never investment opportunities, with infinite opportunity
costs of delay (ρ → ∞). Using this setting enables us to also investigate the effect
of an option to delay on the quality and the ownership structure of foreign direct
investments.
As the contour lines in Figure 2 indicate, increasing knowledge differentials induces foreign investors to acquire more control in the domestic firm as agency costs
incurred from the non-contractability of their intangible knowledge investments can
be mitigated through ownership. For smaller knowledge differentials, however, we
can see that investors are willing to accept domestic participation as the managerial
costs of operating in a foreign environment outweigh the effects of agency problems.
As the costs of foreign ownership were assumed to be fixed in terms of the domestic
firm’s asset value, V0 , there are values for which foreign investors will stay inactive.
Nevertheless, these values reduce with increasing efficiency. By the same token, the
lower panel of the figure indicates that for very small Φ foreign investors will never
17
Figure 2: Desired levels of ownership for different levels of Φ and V 0
Optimal β F levels for different Φ and V 0 values without option to delay investments
*
βF
λ= 0, p= 0
0. 9
0.9
0.8
0.3
70
0.7
0.5
80
0.7
60
0
V
0.6
0. 2
50
0.5
40
0.2
30
0.9
0.4
0.3
0.
0. 1
3
20
0.2
10
0
0 .5
0.7
Inaction
1
0.1
1.5
2
2.5
3
3.5
4
Φ
*
βF
Optimal βF levels for different Φ and V 0 values with option to delay investments λ=0, p=0
5
0.
0
In action
0.6
0.3
V
0.8
0.7
0 .1
50
0.9
0.9
60
0.7
70
0.5
0 .3
80
40
0.7
0.9
0.5
0.4
30
0.3
Wait
20
0.2
10
0
0.1
1
1.5
2
2.5
3
3.5
4
Φ
enter the economy even if they have the choice to wait. Comparing now and never
investments and investments with delaying options we can find in concordance with
the option theory, that less immediate foreign investments are made if there is a possibility to defer entering the market. For example, let us take the parameter values
Φ = 2 and V0 = 30. The upper panel of Figure 2 indicates that the desired level of
ownership foreign investors are willing to acquire is 50 percent if they have no option
to defer their investments. Comparing this with the case of option to wait, we can
see that foreign investors will choose to wait until the value of the firm reaches at
least the value of 40. At this point however, their desired level of ownership is 70
percent. This shows that uncertainty about the prospects of the domestic firm will
decrease foreign investors’ willingness to enter directly and increases their required
amount of control over the operations. If the foreign firms have an ’option’ to delay
investments then, for a fairly range of values, they use their option to wait to exploit
the best opportunities. Even if there is no option to delay, investors try to minimize
their exposure to the uncertain business by acquiring smaller ownership shares.
These outcomes of the model are consistent with the empirical findings of Nakamura and Xie[15] and Blomstrom and Kokko [3]. They showed based on Japanese
and Swedish data respectively that the more technologically oriented firms are less
willing to share information with domestic firm owner investors, thus relying more
on full ownership. Indeed, Blomstrom and Kokko found that in the non-electrical
machinery industry, where the comparative advantage of the industry is strongly related to continuous R&D by the parent companies and firm-specific advantages are
18
closely connected to the overall management of the firm, the share of joint ventures
from overall manufacturing associates was only 19% in 1978[3, pp. 22-23]. Nakamura and Xie found that based on Japanese data consisting of 231 foreign affiliated
manufacturing firm in the technology oriented electric equipment, general machinery, precision and pharmaceutical industries, there is a positive correlation between
foreign ownership and the foreign investor’s intangible assets.
4.1.1
The effect of knowledge differentials on investment stability
Recall that the stability of the investments is defined as foreign investor’s willingness
to commit their resources independently of market movement that can be assessed by
analyzing the optimal exit and entry values for the desired levels of foreign ownership
stakes. The exit and entry values are by definition the solutions to the stage 1 and
stage 2 optimal stopping problems at the optimal levels of ownership, β ∗F . Using
these values we can create a figure similar to Figure 2.
Figure 3: Optimal entry and exit values for different V0 and Φ
V*
Optimal E xit* values for different Φ ,V and β * , wit h λ=0, p= 0
0
F
80
30
15
10
70
20
25
30
60
25
V
0
50
20
20
40
30
15
15
20
10
0
10
1
1.5
2
2.5
3
3.5
4
Φ
*Also Entry if ρ →∞
*
V*
Optimal V values for different Φ, V and β* values at step 1 λ=0, p=0
0
F
80
65
65
55
50
V
50
45
45
35
0
50
55
40
60
60
25
60
70
40
40
30
35
20
30
10
25
0
1
1.5
2
2.5
3
3.5
4
20
Φ
The upper panel in Figure 3 illustrates the exit values corresponding to the optimal levels of ownership at a particular Φ, V0 combination, while the lower panel shows
the entry values for these parameters. We can see that the lowest acceptable entry
and exit values decrease with increasing Φ. This indicates that increasing knowledge
differentials improve the stability of foreign investments as foreign investors are willing to keep to their assets even for fairly low market values. This result underlines
the prevailing industrial organization literature on the resilience of classical types of
FDI with large amounts of intangible asset investments. Yet Figure 3 also indicates
that to ensure stability, fairly large knowledge differentials are needed. Thus, the
19
naive assumption that any investments involving intangible knowledge capital being
stable per se, is refuted by the model. If we assume that all possible V 0 values represent existing investment opportunities to foreign investors, then the increasing area
of active investments indicates a larger capital inflow to the domestic economy.
Another interesting issue is that stability and ownership are not merely two sides
of the same coin. Taking a closer look at Figure 2 and Figure 3, we can see that
the same level of desired ownership does not induce similar optimal exit values the
different efficiency parameters. Hence the ownership structure of a firm, or the level
of FDI in the Current Account may not say much about the quality of investments
in practice. We can claim then that ownership can not be the sole determinant of
the quality of foreign direct investments.
4.2
Financial market inefficiencies, ownership and stability
Financial market inefficiencies also exert a significant impact on foreign investors‘
desired level of ownership. Obstacles of moral hazard, monitoring problems and nonobservability of outcomes can impose constraints on borrowing even in the case of safe
economies. For example, small enterprises with only a few years of experience find it
very hard to get access to financial resources for their operations even if their projects
are promising. Under these circumstances control eliminates the inefficiencies in the
financial market providing the necessary resources. Yet monitoring the provided
resources becomes difficult if the investor does not have any control on the operation
of the firm. Thus it is expected that exploiting the benefits of increased resources will
amplify the desire for more ownership. In this section I assume that foreign investors
are not more competent than domestic investors. Their advantage over the domestic
investors lies solely in their relatively unlimited access to financial resources whereas
domestic investors have constraints on their abilities to raise funds. In the model
financial market inefficiencies are depicted by the relative arrival rate of achievable
projects. It was assumed that the more financial market inefficiencies (the higher
is λ) in the domestic country, the more value can be extracted by investors who
are relatively better endowed with financial resources.Similarly to the analysis of the
effect of knowledge differentials, we can solve the model for different values of λ.
Figure 4 depicts the desired levels of foreign ownership for increasing levels of market
inefficiencies.
Figure 4 shows that increasing levels of λ, that is, higher levels of market inefficiencies, increases the desired amount of foreign ownership. This outcome is similar
to our findings on the effects of knowledge differentials, yet the motivation for the
acquisition of control is very different. In case of knowledge differentials intensive
control is needed to exploit gains from superior competence of foreign investors.
Benefits obtained from financial market inefficiencies, however, do not depend on the
amount of foreign control since foreign investors do not have special abilities to run
the business. Thus there is no need for their intensive presence in controlling the
domestic firm’s operation. Therefore, if foreign investors could exploit gains from
their unlimited financial resources freely, they would not obtain a significant level of
ownership in the domestic firm. The motivation behind acquisition of control lies in
the cost of monitoring the distribution of the provided capital. Increasing level of
control lessens the cost of monitoring resulting in an increment in desired ownership.
As Figure 4 shows this increment is more gradual than in the case of knowledge
differentials. As the lower panel of the figure indicates, more efficient markets with
a transparent financial system eliminate the sources of gains from unlimited access
to financial resources. Investors who only differ from their domestic counterparts in
their financial abilities will then not enter the market. The model does not indicate
20
Figure 4: Desired levels of ownership with financial market inefficiencies
0
0.8
60
0.7
50
0.6
40
0. 9
0.8
0 .7
0.6
0.5
20
0.5
0. 4
30
0.3
0 .2
V
*
βF
0. 9
0.8
0.6
0.5
0. 4
0.3
0 .2
70
0.7
Optimal β values for different λ and V values without option to delay investments , φ= 1,p= 0
F
0
80
0.4
Inaction
0.3
10
0
0.2
0
0.1
0.2
0. 3
0.4
0.5
0.6
0.7
0.8
0.9
1
λ
Optimal βF values for different λ and V 0 values with option to delay φ=1,p=0
*
βF
80
0
In actio n
0.7
0. 9
V
0.8
50
0.6
0.5
40
0.4
30
0.3
Wait
20
0.2
10
0
0.9
0.8
0 .7
60
0.6
0.5
0. 4
0.3
0 .2
0.1
70
0.1
0
0.1
0.2
0. 3
0.4
0.5
0.6
0.7
0.8
0.9
1
λ
though that all financial resources disappear. Indeed, if foreign investors presume
that the growth rate of their investment is higher than that of the market predicted
value, they will still enter the market. These investments fall into the category of
simple speculation. As the gains from speculation do not depend on the amount of
acquired control, managerial costs of increased ownership will ensure that investors
avoid exposing themselves to large investments. Indeed when calculating the model
for different levels of expected growth rates we obtain that the desired level of ownership does not change.
4.2.1
The effect of financial market imperfections on stability
Increasing market inefficiencies have the same impact on foreign investors‘ commitment to stick with their assets as do knowledge differentials. As we can see from
Figure 5, the more gains foreign investors can obtain from their increased access
to financial resources (the more market inefficiencies are present) the less they are
affected by large drops in their asset values.
In case of the exit decisions, depicted by the upper panel, the optimal value
inducing foreign investors to leave reduces by half for high levels of λ. The willingness
to enter the market also increases with a worsening financial environment as shown
by the decreasing optimal entry values in the lower panel.
21
Figure 5: Optimal entry and exit values with market inefficiencies
Optimal V * Exit * values for different λ,V0 and β*F values φ=1,p=0
V*
22
10
14
16
18
20
22
70
12
80
20
60
18
16
40
22
14
12
10
16
12
20
14
20
30
18
V
0
50
10
10
0
0
0.1
0.2
0. 3
0.4
0.5
0.6
0.7
0.8
0.9
*Al so Entry if ρ→∞
Optimal V * Entry values for different λ, V0 and β*F , Φ= 1,p= 0
50
50
45
40
40
35
30
40
35
0
50
45
50
V
V*
25
30
60
35
70
40
45
80
8
1
λ
25
30
30
20
25
10
0
0
0.1
0.2
0. 3
0.4
0.5
0.6
0.7
0.8
0.9
1
20
λ
4.3
4.3.1
Cross effects of country risk, knowledge differentials and
financial market inefficiencies
Country risk and knowledge differentials
The positive effect of efficiency differentials on foreign investments is clear as long
as we neglect the impact of country risks upon investment decisions. Accepting that
all investment decisions involve classical ’portfolio equity’ investment features it is
inevitable to also include the effects of country risk into the analysis. Introducing
the effect of a possible macroeconomic downturn implying losses in terms of the
asset values, we can show the effects of risks on investment decisions, even with
the assumption of risk neutral foreign investors. For this purpose I have solved the
previous numerical problem using two representative values of p, the country risk
parameter. To eliminate the effects of liquidity constraints arising from the increased
country risk, I assumed that p does not have an impact on λ0 .
Figure 6 shows the effects of the country risk parameter at p = 0.05 and p = 0.1
without the liquidity effects of country risk. As we can see from panels 1 and 3,
increasing country risk decreases the area of immediate entry. The range of low
value and low efficiency investments declines as the increase in country risk renders
their gain to become less than the costs involved with the investments. With p = 0.1,
highly efficient investments remain present. The lower panels in the figures show that
the range of inaction increases with p.
22
Figure 6: The joint effect of country risk and efficiency on ownership
*
βF
Optimal β levels for different Φ and V values with no option to delay λ=0, p=0.05
F
0
80
70
0.85
9
0.
60
0
40
0.75
0.6
V
0.8
8
0.
50
Inaction
30
0.8
0.6
20
0.9
0.7
0.65
10
0
1
1.5
2
2.5
3
3.5
0.6
4
Φ
*
βF
Optimal β levels for different Φ and V values wit h opt ion to delay λ= 0, p= 0.05
F
0
80
0.9
0.9
70
60
0.8
0.7
Inaction
0.6
V
0
50
0.5
0.9
40
0.4
Wait
30
0.3
0.9
20
0.2
10
0
0.1
1
1.5
2
2.5
3
3.5
4
Φ
*
βF
Optimal β levels for different Φ and V values wiyhout opyion to delay λ=0, p=0. 1
F
0
80
70
0.95
60
4
0.9
V
0
50
0.9
0.9
2
40
30
0.9 2
Inaction
20
0.9 6
0.85
10
0
1
1.5
2
2.5
3
3.5
0.8
4
Φ
*
βF
Optimal β levels for different Φ and V values with option t o delay λ= 0, p=0.1
F
0
0.9
70
0.8
0.9
80
0.7
60
0
V
0.6
Inaction
50
0.5
40
0.9
Wait
30
0.4
0.3
20
0.2
10
0.1
0
1
1.5
2
2.5
3
Φ
23
3.5
4
If we introduce the liquidity effects of country risk by allowing λ0 to increase with
p we get similar results, with the exception that the same value of country risk has
less impact.
Figure 7: The impact of country risk on investments if liquidity effects are introduced
*
βF
Optimal β levels for different Φ and V values without option to delay λ=0, p=0.05
F
0
0.7
0.6
70
0.9
0.9
80
0.8
60
0.4
V
40
0.7
0.
0
50
4
0 .6
30
0.7
0.6
0.9
Inaction
20
0.5
10
0
1
1.5
2
2.5
3
3.5
0.4
4
Φ
*
βF
Optimal β levels for different Φ and V values wit h opt ion to delay λ= 0, p=0.05
F
0
0. 5
70
0.9
0.9
80
0.8
0.7
60
0.6
Inaction
V
0
50
40
30
0.5
Wait
0.4
0. 9
0.3
0.9
20
0.2
10
0
0.1
1
1.5
2
2.5
3
3.5
4
Φ
Indeed comparing Figure 7 with Figure 6 shows that the active area is much
smaller if country risk has no effect. Evidently as country risk causes domestic
firms. access to financial resources to decline, foreign investors have two potential
sources of gains: their unlimited financial resources and their superior knowledge base.
Nevertheless, the general pattern of a declining amount of investments concentrating
on the high ownership and efficiency range remains valid, even in this case.
The outcomes of the model, particularly foreign investors willingness to retain
investments with more control if the probability of financial distress increases, are in
line with the empirical findings of Hausmann and Fernandez-Arias [8, p. 6.]. They
demonstrated that total capital flows decrease with decreasing level of development
(increasing level of country risk). However, the share of those flows that take the
form of FDI tends to increase. They showed that the accumulated stock of FDI is
the highest in Latin America (7%) while the industrial countries in East Asia had
only 1.2% of these flows on average.
4.3.2
Effect of country risk and knowledge differentials on stability
In line with the previous section we can solve for the exit and entry values in the
optimal stopping problem for different levels of p. Figure 8 presents these values for
24
country risk parameter values 0.05 and 0.1 respectively.
Comparing Figure 8 with Figure 3, can see that the optimal entry and exit values
increase for given levels of efficiency suggesting foreign investors’ declining commitment to hold on to their assets under increasing uncertainty. Increasing country risk
therefore induces less capital inflows, but with higher shares of ownership and decreasing levels of stability. The model presented above clearly shows the decreasing
willingness to keep risky projects going even if there are large knowledge differentials. This outcome again shows that ownership is a misleading indicator for quality
of investments, which again contradicts the theory about the superiority of FDI in
general.
The difference between ownership and stability is more apparent if we present the
desired levels of ownership and the optimal values of entry and exit for a particular
level of Φ with varying p. Comparing Figures 8 and 6 we can see that even if the
desired level of ownership is 100 percent for all values of Φ, the optimal exit values
are intensively varying.The same issue can be highlighted by taking a representative
value of Φ to show the effect of increasing arrival probability of financial distress.
As we can see from Figure 9 the level of commitment reduces along with the
desire to share control with domestic investors.
4.4
Country risk and financial market inefficiencies
In the model, country risk and financial market inefficiencies have opposite effects on
the firm’s value. While the former lowers it by (1−η)V with probability pdt the latter
adds to it a positive value, αV, with probability λdt at each period. In addition to this
primary effect, country risk also has an impact on the arrival rate of projects that are
above the debt limit of the domestic firm. As overall economic uncertainty increases,
it is assumed that the general opinion about the credit-worthiness of domestic firms
worsens. Thus their debt limit tightens allowing foreign investors to gain extra value
on the domestic firm’s assets. This effect is stronger the more financial market
inefficiencies are present. Nevertheless, increasing country risk by itself does not
induce investment inflows according to the model’s settings, as from (1 − η) > α it
follows that the achievable benefits coming from the increased funds are outweighed
by the possible losses in case of a crisis. This indicates that some level of market
inefficiencies must be present to trigger foreign investment inflows. The idea behind
this is that if there were no moral hazard or agency problems connected to the issuing
of debt and full contracts could be written,6 country risk would not alter the ability
of the domestic firm to borrow as its debt constraint would only depend on the firm’s
qualities and not on the prevailing macroeconomic environment. Another impact of
increasing country risk, similar to the case of the knowledge efficiency problem, is the
extra costs incurred in terms of general overheads and other expenses coming from
the increased uncertainty of foreign operation.
The above effects have an interesting resultant impact on the desired levels of
ownership.
As we can see from Figure 10, in contrast with findings from the knowledge
differential case, country risk causes the desired level of ownership to decrease at a
particular level of λ. This reduction is fairly slow with small changes over a large range
of p values. As the cost of uncertainty increases it outweighs the gains from increased
liquidity, rendering ownership to decrease. Thus, these capital flows resemble the
behavior of portfolio flows, where increased country risk reduces the willingness to
6 Note that this is a really unrealistic assumption as it is impossible to cover all risks in a contract
in practice. Therefore some form of financial market ineffieciencies are also peresent in the so-called
’safe’ economies also.
25
Figure 8: The joint effect of country risk and efficiency on stability
Opt imal V* Exit* values for different Φ ,V0 and β*F values λ= 0, p= 0.05
V*
35
10
15
20
25
70
30
35
80
30
40
25
25
20
20
V
0
50
30
35
60
20
15
10
15
30
10
0
10
1
1.5
2
2.5
3
3.5
4
Φ
*Entry if ρ→ ∞
Opt imal V* Entry values for different Φ, V 0 and β *F values λ= 0, p=0.05
30
60
V*
70
40
70
70
50
80
65
60
60
50
55
40
45
30
V
50
40
0
50
30
40
20
35
10
30
0
25
1
1.5
2
2.5
3
3.5
4
Φ
Optimal V* Exit* values for different Φ ,V0 and β *F values λ=0, p=0.1
40
15
30
40
50
40
30
25
25
0
40
35
60
V
V*
15
25
30
35
70
20
80
20
15
20
30
20
10
0
15
1
1.5
2
2.5
3
3.5
4
Φ
*Entry if ρ→ ∞
Optimal V * Entry values for different Φ , V0 and β *F values λ=0, p=0.1
70
65
45
60
70
30
40
50
70
V*
35
80
60
60
0
55
50
30
V
40
40
35
45
50
45
30
40
20
35
10
0
30
1
1.5
2
2.5
3
Φ
26
3.5
4
Figure 9: The joint effect of country risk and knowledge differentials
Optimal β values for different p and V 0 values without option to delay at lambda= 0and
F
Φ= 2
*
βF
80
70
60
0.8
50
0.8
V
0
0.7
40
0.5
20
0.4
0.7
0.7
0.6
30
0.8
0.9
0.9
0.6
0. 6
0.5
0.5
Inaction
10
0
0.4
0
0.01
0.02
0.03
0. 04
0.05
p
0.06
0.07
0.08
0.09
0.1
Optimal β values for different p and V 0 values with option t o delay at lambda=0and Φ=2
F
*
βF
80
0
0.
9
0 .9
70
V
0.9
60
0.9
50
0.8
0.85
0.8
7
0.
40
Inaction
0.75
Wait
30
0.7
20
0.65
10
0
0
0.01
0.02
0.03
0. 04
0.05
p
0.06
0.07
0.08
0.09
V*
Optimal V* Exit* values for different p, V0 and β *F values, lambda=0and Φ =2
35
30
35
40
30
40
25
50
0
50
45
60
40
35
20
V
55
50
70
45
40
25
30
80
0.6
0.1
30
20
30
25
15
20
20
10
0
15
0
0.01
0.02
0.03
0. 04
0.05
p
0.06
0.07
0.08
0.09
0.1
*Entry if ρ→∞
V*
Optimal V* Entry values for different p, V0 and β *F values, lambda=0and Φ =2
0
55
45
V
75
70
60
60
50
75
65
70
70
65
60
80
65
50
60
45
40
55
30
50
20
45
10
0
40
0
0.01
0.02
0.03
0. 04
0.05
p
0.06
27
0.07
0.08
0.09
0.1
Figure 10: Desired levels of ownership with different levels of p at λ = 0.2
Optimal β values for different p and V 0 values with no option to delay at lamb da=0.2and
F
0.2
0 .3
70
*
βF
Φ= 1
0.28
0. 22
0.24
80
0.27
60
0.26
0.24
40
0.25
0.24
0. 28
V
0
50
30
0.23
Inaction
20
0.22
10
0.21
0
0
0.05
0.1
0.15
p
0.2
0.25
Opt imal β values for different p and V 0 values wit h option to delay at lambda=0.2and
F
Φ=1
*
βF
0. 25
80
70
Inaction
50
0
0.25
0.2
60
V
0.2
0.3
0.15
Wait
40
0.1
30
20
0.05
10
0
0
0.05
0.1
0.15
p
0.2
0.25
0.3
0
acquire large ownership stakes. The amount of capital inflow also follows this pattern.
Similar to the case of knowledge differentials, the incoming capital flows decrease with
higher levels of country risk, p.
Another interesting feature of the effect of country risk can be noticed, when
analyzing the whole range of market inefficiencies for different levels of p.Comparing
the lower panels of Figure 11 and Figure 4 we see that increasing the level of country
risk changes the range of inaction. As we see in case of p = 0.05, the no entry area
is smaller than under no country risk, while it grows and even exceeds the base case
when p = 0.2. Growing macroeconomic uncertainty can result in growing capital
inflows up until a level of country risk. This is in line with the empirical findings
depicted by Krugman [12] showing that both in the case of the Asian crisis in 1998 and
the Mexican crisis in 1995 inward direct investment flows could be observed although
short-term capital and portfolio equity holdings were withdrawn. This effect can also
0
be shown if we use the definition of λ0 . As ∂λ
∂p > 0 the new value of λ is higher than
that of the p = 0 case. Therefore the correct level of investment can be found at that
higher rate. As we can see from the figures, the amount of investment level increases
with λ. Therefore the direction of liquidity induced capital flows is a result of two
effects: the negative effect of the increased crash probability and the positive effect of
liquidity constraints allowing for inward capital flows under increased country risk.
28
Figure 11: Effect of country risk and financial market inefficiencies on ownership
*
0.9
0.3
0.7
0.8
60
0.7
50
0.6
0.5
0.9
0. 8
0.7
0. 5
30
0.6
40
0.4
0 .3
0
βF
0.2
V
0. 8
0.6
0.4
0.2
70
0.5
Optimal β values for different λ and V values without option to delay, φ=1,p=0.05
F
0
80
0.4
Inaction
20
0.3
10
0
0.2
0
0.1
0.2
0. 3
0.4
0.5
0.6
0.7
0.8
0.9
1
λ
*
βF
0.9
0.7
0.9
0.8
0. 5
70
0. 8
2
0.4
0.
80
0.6
Optimal β values for different λ and V values with option t o delay φ= 1,p= 0.05
F
0
0.7
60
Inaction
0
V
0.5
0. 8
0.4
0 .9
30
0.6
0.7
40
0.6
0.5
50
0.3
20
0.2
10
0.1
0
0
0.1
0.2
0. 3
0.4
0.5
0.6
0.7
0.8
0.9
1
λ
*
βF
0.9
0.7
0.5
0 .8
0 .6
0.3
0.2
70
0.4
Optimal β values for different λ and V values without option to delay, φ=1, p=0.2
F
0
80
0.8
60
0.7
0.
0
0.6
0 .9
0 .8
0. 7
Inaction
20
0.5
0 .6
30
0.5
40
0.4
0.3
V
2
50
0.4
0.3
10
0
0
0.1
0.2
0. 3
0.4
0.5
0.6
0.7
0.8
0.9
0.2
1
λ
Optimal β values for different λ and V values with option t o delay, φ=1,p= 0.2
F
0
0
Inac tion
0.5
0 .9
0 .8
30
0. 7
40
0.6
0 .6
50
0.7
0.5
60
0.9
0.8
0.4
70
V
*
βF
0.3
80
0.4
Wait
0.3
20
0.2
10
0.1
0
0
0.1
0.2
0. 3
0.4
0.5
0.6
λ
29
0.7
0.8
0.9
1
4.4.1
The effect of country risk and financial market inefficiencies on
stability
The cross effect of country risk and market inefficiencies on stability is more straightforward. Using the same levels of country risk, p to illustrate the optimal exit and
entry values we obtain that increasing level of country risk results in larger exit values
at all levels of λ. Taking a look at the channels through which country risk impinges
on stability we find that both the increment in λ0 and p have negative effects on
stability.
Indeed we can see from Figure 12 that increasing λ parameter values are connected
with larger optimal exit values. By the same token comparing panel 1 with panel 3
in the figure we can see that increasing country risk increases the optimal exit points
at the same level of λ. The model predicts therefore that even if there might be a
surge of foreign direct investments under country risk the quality of these investments
reduces.
5
Conclusion
This paper presents a stochastic dynamic programming model to analyze the quality
of foreign direct investments. The main question was to investigate whether there
is any relationship between ownership/control and investment quality. Quality is
defined in terms of foreign investments’ ability to provide stable financial resources to
the domestic country, where stability of investments is measured by the optimal exit
and entry firm values at given levels of desired ownership stakes. In accordance with
the prevailing FDI literature three types of factors are investigated that determine the
desired level of foreign control and the stability of foreign investments corresponding
to this specific level of ownership : financial market inefficiencies, the possession of
specific knowledge type assets and overall macroeconomic uncertainty.
The results of the model indicate that the largest foreign investment flows are
among ’safe’ economies and the level of investment flows to poor(riskier) economies
reduces along with foreign investors’ desire to share information with the domestic
firms. Increasing country risk therefore induces less capital inflows with higher shares
of ownership and decreasing levels of stability. We also see that the major source
of willingness to increase control lies in the presence of market imperfections which
allow extraction of additional benefits from operation but also impose costs on the
investors.
It was shown that uncertainty about the prospects of the domestic firm decreases
foreign investors’ willingness to immediate entry and increases their required amount
of control. If the foreign firms have an ’option’ to delay investments then, for a fairly
large amount of values, they use this option to wait to exploit the best opportunities.
The model also reveales that ownership can not be the sole determinant of the
quality of foreign direct investments. Even in safe economies the same ownership
structure implied varying levels of foreign financial resource commitment. I also
show that the naive assumption that any investments involving intangible knowledge
capital being stable per se can be refuted as for resilience a fairly large degree of
knowledge differentials is needed.
The direction and stability of capital flows induced by financial market inefficiencies is found to be a result of two effects: the negative effect of the increased crash
probability and the positive effect of liquidity constraints allowing foreign investors
to exploit excess gains from their unlimited access to financial resources. We see that
growing macroeconomic uncertainty can induce growing capital inflows under financial market inefficiencies even with increasing country risks. Yet independently of
30
Figure 12: The effect of country risk and financial market inefficiencies on stability
Optimal V * Exit* values for different λ,V0 and β*F values φ= 1,p= 0.05
V*
35
15
20
25
30
35
70
25
20
20
40
25
30
50
0
30
35
60
V
10
80
30
10
15
20
15
10
0
10
0
0.1
0.2
0. 3
0.4
0.5
0.6
0.7
0.8
0.9
1
λ
Entry if ρ→∞
V*
Opt imal V * Entry values for different λ, V0 and β*F values Φ =1,p= 0.05
60
30
70
70
40
50
80
70
60
50
60
40
40
30
0
V
50
40
50
30
20
30
10
0
0
0.1
0.2
0. 3
0.4
0.5
0.6
0.7
0.8
0.9
20
1
λ
Optimal V* Exit* values for different λ,V0 and β*F values, φ=1,p= 0.2
V*
45
45
80
40
30
15
0
50
V
35
20
25
60
40
30
40
70
30
25
20
20
10
0
15
0
0.1
0.2
0. 3
0.4
0.5
0.6
0.7
0.8
0.9
1
λ
*Entry if ρ→ ∞
Optimal V* Entry values for different λ, V0 and β *F values Φ =1,p=0.2
V*
70
60
80
65
60
60
30
40
50
70
55
V
0
50
50
40
45
30
40
20
35
10
30
0
25
0
0.1
0.2
0. 3
0.4
0.5
0.6
λ
31
0.7
0.8
0.9
1
its effect on the direction of capital flows it was shown that country risk destabilizes
investments.
The outcomes of the model support recent empirical research on the behavior of
FDI. There is, however, scope for further analysis. The model should be calibrated
to real data to get meaningful results, which would allow its use in real decision making. The most delicate issue is to define the cost functions involved in the analysis.
Nevertheless, if we are only interested in relative measures it is sufficient to specify
the relative importance of the different factors of the cost function. Further research
should also be devoted to the investigation of interactions between investors and
governments in terms of the assessment of the efficiency of different policies toward
foreign investments. Another interesting issue would be to demonstrate how domestic
investors’ increased bargaining power might alter the results of the model.
In conclusion, the merger of portfolio equity theory with the classical FDI literature proves to be a powerful tool to explain the very complexity of investment
decisions. It allows us to put a model behind the controversial empirical research in
the area of the stability of foreign direct investments. Having demonstrated that foreign direct investments may very much differ in their quality, ranging from unstable
classical ‘portfolio type’ to resilient classical ‘FDI type’ investments, and also that
quality can not be identified with ownership, we argue that the welfare implications
of capital inflows cannot be determined only by taking a short look at their labelling.
We can therefore refute the naive notion that considers FDI as a superior source of
financing over other types of investments.
32
References
[1] Brock W. A., Rotschild M., and Stiglitz J. E. Stochastic capital theory. NBER
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