Contract Frictions, Export and FDI: Training and The Inalienability of
Human Capital
Qing Liu
The University of Hong Kong
Email: qlecon@hku.hk
March 2009.
Abstract
One prominent feature of the world FDI is that most FDI goes into developed countries
from developed countries, which is a challenge to the current horizontal FDI theories. To account for the phenomenon, by noting another well-documented fact that most FDI happens
in skilled-labor-intensive industries, this paper develops a model embedding incomplete contracts between the rm and the skilled workers due to the inalienability of human capital in
the proximity-concentration framework with heterogeneous rms. In the bargaining between
the rm and the skilled workers, the higher the host country's development level, the higher
the rm's outside option thus the higher the FDI pro ts (the hold-up e ect), but at the
same time the higher the unskilled-labor costs of production which decrease the FDI pro ts
(the labor cost e ect). This paper then further identi es that the former e ect dominates
the later in skilled-labor-intensive industries, but be dominated in unskilled-labor-intensive
industries. With the contract friction, this model thus predicts industry-speci c correlations
between FDI and the host country development level. Speci cally, in skilled-labor-intensive
industries, the prevalence of FDI from developed countries is increasing in the host country's
development level, while in unskilled-labor-intensive industries, the relation is reversed. In
both kinds of industries, the prevalence of FDI is decreasing in the industrial skilled-laborintensity; the industrial skilled-labor-intensity and the host country development level are
complementary in attracting FDI. Those least developed countries may attract no FDI in
skilled-labor-intensive industries however productive the foreign rms are. These speci c
predictions gain supports from the empirical literature.
Keywords: Contract frictions; Heterogeneous rms; Skilled-labor-intensity; Host country development level; Export and FDI.
JEL: D23, F12, F16, F23, L23
I am very grateful to Larry D. Qiu for guidance and Xiaoguang Chen, Xinyu Hua, Yi Lu, Wing Suen,
Zhigang Tao for comments or discussions. All remaining errors are my own.
1
Introduction
The centerpieces of the theory of foreign direct investment (FDI) are the proximity-concentration
theory of horizontal FDI (see, Markusen 1984, Brainard 1997, and Helpman, Melitz and Yeaple
2004) and the comparative advantage theory of vertical FDI (see, Helpman 1984).1 The basic
idea of the former is that, to serve a foreign market with similar products in the home market,
rms will export (concentration of production) when plant-level economies of scale are high, and
do FDI (proximity to consumers) when transport costs and/or rm-level economies of scale are
high. The latter says that rms could fragment the production process into stages with di erent
factor intensities, and locate di erent stages in di erent countries according to their relative
factor endowments. Empirical evidence suggests that the bulk of world FDI is horizontal and
the proximity-concentration trade-o
is far more important than the comparative advantage
story in explaining the world FDI (for example, Brainard 1997, Carr, Markusen and Maskus
2001).2
However, the current proximity-concentration theory is challenged by the well-established
fact about the e ect of the host country development level on FDI. The traditional model predicts
that, after controlling for the proximity-concentration factors, FDI should be more prevalent in
less developed countries becuase of the low production costs there. Contrary to this model,
the bulk of FDI is from developed countries to those host countries with similar per capita
incomes (Markusen 1995, 2002), and the ratio of U.S. rms' foreign a liate sales to export sales
is decreasing in the di erence in GDP per capita between U.S. and the host country concerned
after controlling for the proximity-concentration factors (Brainard 1997).
Markusen and Venables (2000) build a Helpman-Krugman style relative factor endowmens
model of multinational enterprises (MNEs) to account for this challenge. However (see detailed
discussion in the literature review), it is a nice theory of MNEs but in essence not a theory of FDI.
What's more, there is little evidence that FDI is related to di erences in capital endowments
1
The knowledge-capital model integrates these two strands (see Markusen 1997).
A notable exception, Yeaple (2003), is regarded as evidence for the role of the comparative advantage
in FDI. However, this paper is more likely to be supportive of the current work (see this later). Also,
see excellent surveys about the empirical evidences on FDI in Markusen and Maskus (2001) and Yeaple
(2003).
2
1
or in the general return to capital across countries (Markusen 1995, 2002), which questions the
power of relative factor endowmens in explaining FDI.
The current paper responds to the challenge by rstly noting the following industrial feature
of the world FDI pattern. It is well-documented that MNEs concentrate in industries with
higher skilled-labor-intensities (Markusen 1995, 2002).3 Helpman, Melitz and Yeaple (2004)
also nd in their TABLE 2 that the U.S. outward FDI is more signi cant in industries with
higher productivity dispersion which, at the same time, is discovered to be highly, positively
correlated with the number of skilled-workers per establishment in that industry.
The above two country-level and industry-level patterns and their co-existence are robust.
Then, is the co-existence an incidence or is there any underlying relation between the e ects
of the country and the industry level heterogeneities? To explain anyone of them, should we
take into account the other one jointly? Anyway, to a great extent, the horizontal FDI decision
(export vs. FDI) is a production location choice. Except the traditional proximity-concentration
factors (such as xed costs, transport costs, market sizes), the host country's development level,
as well as the industry technology (speci cally, the input intensity in production) should both
play crucial roles in the choice. But they are missing in the traditional horizontal FDI theory.
This paper extends the proximity-concentration theory and explores a developed country's
rms' choices between export and FDI in serving a relatively less developed foreign country4 and
the resulted FDI pattern. In particular, by noting the special role of skilled-labor in a ecting
FDI and the signi cant role of contract frictions in a ecting rms' behavior in the international
economy,5 I look at FDI from the perspective of contract frictions between rms and skilled
workers. Speci cally, I examine one of the main channels of contract incompleteness suggested
explicitly by Hart and Moore (1994), that is, the inalienability of human capital. Because the
human capital owners are prevented from selling themselves into bondage by laws or from using
bonds to bind themselves by credit constraints, the nature of human capital is distincted from
3
In Markusen (1995, 2002), it is called nonproduction-work-intensity, which Yeaple (2003) refers to as
skilled-labor-intensity (the share of nonproduciton workers in value added). This paper follows Yeaple
(2003) in denoting the production- and nonproduction-work as unskilled- ans skilled-work, respectively.
4
There are other modes of serving a foreign country, such as licensing, etc. This paper focuses on the
choice between export and FDI. See the discussion about concerns in licensing in Markusen (1995).
5
See, for theory, Antras 2003, Antras and Helpman 2004, and for evidence, Nunn 2007.
2
that of physical capital: the human capital owners are unable to commit not to renegotiate
with the rm if there is surplus ex post. Due to this inalienability of human capital, the rm
could not contract ex ante with the skilled-labor owners upon their services ex post, that is, the
contract between the rm and the skilled workers is incomplete ex ante, which will distort the
rm's investment.
I embed this incomplete contract model in Helpman, Melitz and Yeaple (2004) and incorporate all the rm, industry, and country level heterogeneities. Production uses both skilledand unskilled-labor. Firms di er in their productivity levels as in Melitz (2003), industries differ in their skilled-labor-intensities, and host countries di er in their development levels (costs
as well as skill level of its workers). The degree of contract friction is determined jointly by
the industry and the host country characteristics. So in this paper, I particularly focus on the
technology (skilled-labor-intensity) and the development level as the industry and the country
heterogeneity, respectively, but not the traditional proximity-concentration factors.
In this way, this model identi es two e ects (or the dual e ect) of the host country's development level on FDI and the di erent dominance relations between these two e ects in di erent
kinds of industries. A little more speci cally, an increase in the host country development levle
will mitigate the hold-up problem (distortion in rm investments) in the relation between the
rm and the skilled workers, thus increase FDI pro ts (hold-up e ect), but at the same time will
aggravate the burden of unskilled worker costs thus decrease FDI pro ts (labor cost e ect). In
skilled-labor-intensive industries, the former will dominate the latter, while in unskilled-laborintensive industries, the latter dominates the former.
Due to the trade-o between the hold-up e ect and the labor cost e ect, this paper predicts
that, at the aggregate level the correlation between FDI in ows and the host country development level, and at the rm level the correlation between the cuto FDI productivity and the host
country development level, are industry-speci c (this industry-speci city is missed in both the
theoretical and the empirical literature previously). If we ignore the industry heterogeneities,
the estimations of the above correlations will be biased.
Speci cally, at the aggregate level, in skilled-labor-intensive industries, the prevalence of
3
FDI6 is increasing in the host country's development level, which explains the concentration of
FDI in developed countries and at the same time in skilled-labor-intensive industries. However,
this paper shows that this is only one part of the whole picture. In unskilled-labor-intensive
industries, the above relation is reversed. Furthermore, in all kinds of industries, the prevalence
of FDI is decreasing in the skilled-labor-intensity in production; the industrial skilled-laborintensity and the host country development level are complementary in attracting FDI, that is,
the interaction term of them has a positive e ect on the prevalence of FDI. All these aggregate
level predictions gain exact support from the available empirical evidence (see Yeaple 2003).
At the rm level, besides the results in Helpman, Melitz and Yeaple (2004) that rms with
productivity higher than a cuto level choosing FDI, lower than the cuto choosing export, this
paper also predicts that, after controlling for the proximity-concentration factors, in di erent
kinds of industries, rms investing in di erent host countries have di erent comparison relations.
Speci cally, in unskilled-labor-intensive industries, in a cross-country sample, we should observe
that rms investing in a more developed country be more productive than those investing in
a relatively less developed country; while in skilled-labor-intensive industries, this relation is
reversed. In a cross-industry sample, rms doing FDI in a more skilled-labor-intensive industry should be overall more productive than those in a more unskilled-labor-intensive industry.
In a country-industry panel sample, the cuto
productivity level should be decreasing in the
interaction of the industrial skilled-labor-intensity and the host country development level.
The industry-speci city of the relations between FDI in ows and the host country development level, and between the cuto productivity and the host country development level, reminds
us that ignoring this industry-speci city will lead to a biased estimation.
Also, this paper characterizes that, not surprisingly, those country with low development
level will attract no FDI in ow in skilled-labor-intensive industries, given a low transport cost.
This sheds some light on why the 49 least developed countries attract only 0.3 percent of world
FDI ows (World Investment Report 2001).
6
Following Helpman, Melitz and Yeaple (2004), the prevalence is de ned as the fraction of active rms
that choose FDI to serve the foreign country.
4
1.1
Main Idea and Implications
The idea is as follows. There are two countries, one developed home country, the other relatively
less developed host country. Firms compete monopolistically in the host market. Production
consists of two kinds of tasks, skilled-task and unskilled-task. The unskilled-task could be
done by anyone skilled or unskilled without di erence, but the skilled-task could only be done
e ciently by skilled-labor, otherwise, the output will be discounted. Suppose the unskilled
worker cost in the developed country is higher than that in a less developed country, and the
skilled workers in the developed country are endowed with enough skills but in the less developed
country the skill level of skilled workers is lower.
Consider the problem of a rm of the developed country to serve the relatively less developed
foreign country. If the rm produces at home and then export with xed export costs and iceberg
transport costs, it involves high unskilled worker costs but without problem of contract friction:
because in the developed country all skilled workers are of high quality and the rm could always
replace the current workers costlessly if they renege on the contract, therefore there is no ex post
surplus in the relationship between the rm and the skilled workers, i.e., no hold-up problem in
export.
If it chooses FDI, there is no transport cost but the xed investment costs are high, and the
contract between the rm and the skilled workers will be incomplete. Because workers in less
developed countries are not endowed with enough skills (i.e., skilled workers there are of low
quality), the rm need to pay to train them after hiring them. The rm could produce with
untrained workers, but then the output will be discounted. Therefore after training the rm
could not replace the trained workers costlessly if these workers renege. Following the standard
literature in labor economics (e.g., Becker 1993), assume such training is rm-speci c and is
useless elsewhere. Therefore there is surplus between the rm and the trained workers after
training and the hold-up problem arises. The trained workers have incentive to bargain with
the rm over the surplus. In the bargaining, the higher the host country's development level, the
higher the outside skilled workers' quality, thus the better the rm's outside option and the less
harmful the hold-up problem. This force tends to increase the FDI pro t (the hold-up e ect). On
5
the other side, the unskilled worker costs will be high in FDI when the host country development
level is high. This force tends to decrease the FDI pro t (the labor cost e ect). Thus, for a rm
in a given industry, when it evaluates a production location of FDI, it needs to consider the
trade-o between the labor cost e ect and the hold-up e ect. Further, as in standard incomplete
contract theory (Grossman and Hart 1986, Hart and Moore 1990), the higher the skilled-laborintensity in production, the more the
the hold-up e ect. The trade-o
rm relies on skilled workers and the more signi cant
between the labor cost e ect and the hold-up e ect is thus
determined jointly by both the host country development level and the skilled-labor-intensity,
which in turn will a ect the nal pro ts from FDI.
The
rm compares pro ts from export and FDI to decide the mode of serving a foreign
market. The total trade-o in the export vs. FDI decision is still proximity-concentration, but
it is encroached on by the trade-o in FDI between the labor cost e ect and the hold-up e ect.
The crucial deviation of this paper from Helpman, Melitz and Yeaple (2004) is that, this
paper looks at FDI from an incomplete contract view such that rms need to consider both the
labor cost e ect and the hold-up e ect in FDI. Though it is possible to extend the traditional
horizontal FDI models to include the labor cost e ect, this extension could not explain the rst
fact (The prediction is contrast to it. See details later). This demonstrates the essential role of
the contract friction here.
While con rming all results in Brainard (1997) and Helpman, Melitz and Yeaple (2004), this
model shows that the host country's development level as well as the industrial skilled-laborintensity, and their interaction, have important and clear implications for the export vs. FDI
decision, thus for the prevalence of FDI. First, in unskilled-labor-intensive industries, the cuto
productivity level between export and FDI (the prevalence of FDI) is increasing (decreasing) in
the host country's development level. This implies that, in such industries, in a cross-country
sample, we should observe that rms investing in a more developed country be more productive
than those investing in a relatively less developed country, and FDI be more popular in the
latter. The intuition is that in these industries, the labor cost e ect dominates the hold-up
e ect. The lower the host country's development level, the lower the labor costs, the higher the
6
pro ts from FDI, thus the more likely that FDI is advantageous to export, and vice versa.
Second, things are di erent in skilled-labor-intensive industries: the cuto productivity level
between export and FDI (the prevalence of FDI) is decreasing (increasing) in the host country's
development level. This means that, in such industries, in a cross-country sample, we should
observe that, rms investing in a relatively less developed country be more productive than those
investing in a more developed country, thus FDI be more popular in a more developed country.
This is exactly the world FDI pattern the Introduction reveales, i.e., the concentration of FDI
in developed countries and at the same time in skilled-labor-intensive industries. The intuition
is that in these industries, the hold-up e ect dominates the labor cost e ect. The higher the
development level of the destination country, the less investment distortion from the hold-up
problem, thus the more pro table the FDI.
This result is new relative to previous export vs. FDI models (Brainard 1997; Helpman,
Melitz and Yeaple 2004) without contract friction. In those models, keeping other proximityconcentration factors unchanged, the higher the host country's wage level, the less likely will it
be FDI destination because of its high labor costs, whichever industry the rm is in.
The above two results together also imply that if we put all industries together, in a crosscountry sample, the correlation between the cuto productivity and the host country's development level, or between the prevalence of FDI (MNEs) and that development level, will be biased.
This emphasizes that we should go into more details, i.e., incorporating industrial technology
carefully, when we investigate export and MNEs.
Third, in both kinds of industries, the cuto
productivity level (the prevalence of FDI)
is increasing (decreasing) in the skilled-labor-intensity; and the industrial skilled-labor-intensity
and the host country development level are complementary in attracting FDI, that is, the higher
the interaction term of these two factors, the higher the FDI in ows. The former part is because
in more skilled-labor-intensive industries, in FDI the hold-up problem is more serious, at the same
time the cost saving from unskilled workers is less since less of them are needed in production.
The latter part is because, an increase in the skilled-labor-intensity will always weaken the
negative labor cost e ect but reinforce the positive hold-up e ect.
7
Last but not least, this paper identi es that in those least developed countries there will be
no FDI in ow in those skilled-labor-intensive industries, because there the worker-cost saving
motivation is weak but the hold-up problem is signi cant. As for the counterpart, i.e., unskilledlabor-intensive industries in relatively developed countries, there will still be FDI in ows.7 Because there the hold-up problem is trivial, and relative to export, the rm could still save worker
costs and transport costs from FDI.
1.2
Literature Review
The model is related to three strands of literature. One is on heterogeneous rms' export vs.
FDI decision. The second is the incomplete contract view of MNEs, though till now this strand
is mainly on rms' vertical sourcing strategies. The third is the factor endowments comparative
advantage story of MNEs.
Firstly, Markusen (1984) and Brainard (1997) show the proximity-concentration trade-o
in export vs. FDI decision. However, in this model rms are identical, thus in each industry,
rms pervasively export or pervasively invest abroad, with the mixed equilibrium existent only
in a knife-edge case. Therefore it can not account for the fact that the extent and the ways of
di erent rms engaging in international economic activities vary (see Bernard, Eaton, Jenson
and Kortum 2003, Bernard, Jenson and Schott 2005, among many others).
Helpman, Melitz and Yeaple (2004) incorporate the Melitz (2003) type heterogeneous rms
in the proximity-concentration model. They con rm the proximity-concentration trade-o and
nd a neat sorting pattern of the modes of serving foreign markets according to rm productivity levels, that is, FDI (most productive rms), exporting (moderately productive rms) and
exiting (least productive
rms), and predict that the prevalence of FDI should be higher in
industries with higher productivity dispersion. Their ndings are extensively supported by empirical studies.8 In this model, however, there is no explicit role for the industry technology or
the host country development level, though they think that these factors are important and are
7
In this paper the rm could serve a foreign country through only export or FDI. If there are other
modes, e.g., export-platform, this may be not true.
8
See, for example, Head and Ries (2003), Girma, Kneller and Pisu (2005), Chen and Moore (2008),
and Helpman, Melitz and Yeaple (2004) themselves.
8
included in the empirical part. Thus this model does not account for one of rms' important investment decisions, i.e., the production location choice, not to mention this decision in di erent
kinds of industries. The current paper complements Helpman, Melitz and Yeaple (2004) by introducing and focusing on the industry and the country heterogeneities through their e ects on
the contract friction which is found to further a ect the export vs. FDI trade-o , and provides
predictions consistent with the stylized facts (i.e., FDI concentration in developed countries and
in skilled-labor industries). Without the e ect through the contract friction, these facts could
not be explained by the current proximity-concentration model.
Secondly, the contract friction has been proved important in a ecting rms' ways of doing
business. Antras (2003), Antras and Helpman (2004, 2008) develop an incomplete contract
view of MNEs and highlight the importance of contract friction in shaping rms global sourcing
strategies in the international economy. Nunn (2007), Nunn and Tre er (2008) empirically
shows that consideration of contract incompleteness explains more of the world trade pattern
than capital and skilled labor combined.
However, these papers all focus on rms' vertical sourcing strategies. Are contract frictions
also important for a rm's choice between export and FDI in serving a foreign market? This has
not been examined yet.9 Here I view from the incomplete contract perspective rms' horizontal
investment problems. Particularly I examine one of the main approaches of contract incompleteness, i.e., the inalienability of human capital. This approach has been emphasized and employed
on studying debt design by Hart and Moore (1994), and widely used on credit cycles (Kiyotaki
and Moore 1997), banking (Diamond and Rajan 2001), venture capital (Kaplan and Stromberg
2003), and industry clustering (Almazan, de Motta and Titman 2007), etc, but has not been
employed on examing FDI.
Finally, Markusen and Venables (2000) is a closely related paper, which extends an otherwise standard Helpman-Krugman model to include transport costs and endogenous MNEs.
9
The only exception is Ottaviano and Turrini (2007). They introduce contract incompleteness in
outsourcing to a foreign counntry and consider the e ect of trade barrier in intermediate inputs on the
export vs. FDI decision through its e ect on the nal good producer's outside option in the bargaining
with the foreign input supplier. In this paper, however, I consider the e ects of the industry technology
and the host country development level. Both the theme and the underlying mechanism are di erent.
9
This work shows that MNEs are more likely to exist when the relative factor price di erences
across countries are small, which requires countries to be similar in both relative and absolute
factor endowments. The intuition is that, if two countries di er greatly in their relative factor
endowments, the relative factor price di erences will be large, then the costs of production will
be much higher in one country than in the other, thus the rm should not set up plants in each
country. Large di erence in market size will also deter the emergence of MNEs. This is a quite
general model of factor endowments, and is also intended to explain the fact that most FDI
happens among countries with similar GDP per capita by interpreting these countries as with
similar relative factor endowments.
Though more detailed empirical tests are needed to discriminate between the factor endowments story and the current contract friction story, several points could be noted. First, this
is a comparative advantage theory of MNEs, but in essence not a theory of FDI. FDI does not
necessarily mean MNEs. One counter and important as well case is the rms in industry transfers. These rms move completely to the host countries as the industries transfer and consistute
important sources of world FDI, but they are not MNEs since they only produce in the host
countries. Second, there is little evidence that FDI is related to di erences in capital endowments or in the general return to capital across countries (Markusen 1995, 2002).10 Even if, to
compare the comparative advantage story with the current model, we interpret the GDP per
capita as the relative abundance of skilled-labor and argue that this relative factor abundance
is the driving force of horizontal FDI, then why the comparative advantage story works with
the skilled-labor abundance but not the capital abundance? No matter whether the comparative advantage story works or not on horizontal FDI, there must be something special for GDP
per capita in a ecting horizontal FDI through channels other than the comparative advantage.
The current paper demonstrates a potential mechanism through contract frictions (of which
the e ect on vertical FDI has gained supports extensively) and which is totally di erent from
the underlying mechanism of the comparative advantage story that large relative endowment
10
Even on trade issues, the factor endowments theory is hopelessly inadequate as an explanation for
historical or modern trade patterns unless we allow for technological di erences across countries (Feenstra
2004, P.1).
10
di erences generate large factor price di erences across countries.11
Third, it is not beyond question to assume that countries with similar GDP per capita are
with similar relative factor endowments. If this is true, then all these countries should have
similar industrial structure according to the comparative advantage theory, which is not the
case. Last, rms in Markusen and Venables (2000) are homogenous, thus there is no identity of
the rm. In the current paper, consistent with the recent empirical literature, rms are modeled
as heterogeneous and thus several new and testable rm-level predictions are generated.
The outline of the remainder is as follows. I describe the set-up of the model in section
2. Section 3 gives rms' optimization behaviors under export and FDI, respectively. Firms'
equilibrium choices and rm-level characterization are discussed in section 4, and the prevalence
of MNEs (aggregate level FDI pattern) and the empirical evidence are presented in section 5.
The last section concludes the paper.
2
Set-up
There are two countries, developed home country H and relatively less developed foreign country
F .12 Consider the export vs. FDI problem of rms of country H and thus the resulted FDI
out ows pattern. To serve the F market, a rm of country H could choose export, i.e., producing
the goods at home and then selling them to F , or FDI, i.e., producing and selling the goods
directly in F . There are N +1 industries in the economy. One industry produces a homogeneous
good z; which is taken as numeraire, while each of the other N industries, denoted by n = 1; :::; N;
produces a continuum of di erentiated products. We refer to these di erentiated productes as
varieties and denote a variety by v: Assume that the homogeneous good is freely traded and
produced by both countries with constant-returns-to-scale technology.13
11
This chain may break down for many possible imperfections of markets, such as politics of regulation,
di erent origins of labor laws, human capital externalities, etc. See Deardor (1979) for the case of
transport costs.
12
F is not necessarily the usually categorized \South" in the trade literature. It is only less developed
relatively to H and could be a developing or a developed country.
PN
13
This could be justi ed by assuming that n=1 n is small enough, and/or that the labor supply is
large enough in each country.
11
In each country, there are skilled and unskilled workers, though the skill levels of the skilled
workers are di erent across countries. In particular, one unit of skilled-labor in country i; i =
H; F; could produce wis units of z; which means that the market wage for skilled workers in
country i is wiu . Since more developed countries have better (formal or informal) education
systems, the skill level of a country's skilled wokers is positively determined by its development
level. Therefore, assume the home skilled workers are endowed with better skills but the foreign
s > w s . As for the unskilled workers, assume one
skilled workers are only limitedly skilled, i.e., wH
F
unit of unskilled-labor in country i could produce wiu units of z: This means that the unskilled
worker wage in country i is wiu . Similarly, since the unskilled-labor cost in a developed country
u > wu :
is higher than that in a less developed country, assume wH
F
In this paper, the only assumptions we need are that the skill level of the skilled workers is
higher in H than in F , and that the labor cost of unskilled workers is higher in H than in F ,
s > w s and w u > w u : Therefore, for simplicity but without loss of generality, with
that is, wH
F
H
F
s = wu = w
normalization, we assume wH
H
H
1; and wFs = wFu = wF 2 (w; 1); where w is a
small but positive lower bound of wF : This amounts to assume that workers in the developed
home are all of high skill and of high cost, while workers in F are of relatively low skill and of
low cost.
2.1
The Demand Side
Country F is inhabited by a unit measure of identical consumers. A representative consumer
will derive the following utility from consuming z units of the homogeneous good and xn (v)
units of varity v in industry n:
U = (1
N
X
n=1
n ) log z
+
N
X
n=1
Z
n log(
xn (v)
n
dv)
1
n
; 0<
n
< 1;
v2Vn
where Vn denotes the measure of available products in industry n, (1
PN
n=1
n)
and
n,
respectively, are the fractions of expenditure on the homogeneous good and on industry n goods.
The elasticity of substitution across varieties within an industry, say n; is "n =
1
1
n
> 1; while
the elasticity of substitution across varieties in di erent industries is unity, which means the
expenditure on each industry is a constant. Due to this speci cation, we could do the analysis
12
industry-by-industry and drop industry notation n when not causing confusion.
Suppose a consumer in country F maximizes her utility subject to some budget constraint,
then it is standard to derive the demand for each variety in a given industry as follows, with the
industry notation dropped:
x(v) = Ap(v)
"
;
where A is the industry's aggregate consumption index and is exogeneous to an individual rm.14
2.2
The Supply Side
Each of the di erentiated varieties is produced by a single rm and there is free entry into all
industries. To produce a variety v in an industry, the rm need to pay a xed entry cost, fE units
of numeraire, which may include expenditures on R&D; brand development, etc. As in Melitz
(2003), upon paying this xed cost, the rm draws a productivity level
from a cumulative
distribution G( ), then decides whether to exit or to stay in the market. If exits, then the game
is over for it. If chooses to stay in the market, it need to choose how to serve the market F:15
If produces at home and then exports, the rm pays an additional overhead cost of fX units of
numeraire (e.g., costs of setting up and operating a plant at home and a distribution network
abroad), and bears an iceberg transport cost
2 (0; 1) (only 1
units of good reach the
destination per unit shipped), while if it chooses FDI, it pays an additional overhead cost fI
(e.g., costs of setting up and operating a plant and a distribution network abroad). Thus fI
represents the extra costs of forming a plant in the foreign country. Assume fI
To produce goods,
fX
fX > 0:
rms employ workers to perform two kinds of tasks, skilled-task and
unskilled-task. The unskilled-task could be done by anyone skilled or unskilled without di erence, but the skilled-task could only be done e ciently by skilled-labor, otherwise, the output
will be discounted. If needed, a rm could train workers that are not skilled enough to obtain
the speci c production skills. Denote the skilled-labor service by m and the unskilled-labor
14
The demand function is derived in the Appendix. In a general equilibrium A is endogeneously
determined by the free entry condition. This paper presents a partial equilibrium analysis by ignoring
the host country rms.
15
To x idea, I ignore the domestic market here. Introducing the domestic market will not change the
analysis qualitatively.
13
service by l: The production technology gives the output of each variety as an industry-speci c
Cobb-Douglas function of the two kinds of service inputs as follows:
xn (v) = [
mn (v)
n
where
] n[
ln (v) 1
]
1
n
is the rm-speci c productivity level,
n
n
; 0<
n
< 1;
is industry-speci c and denotes skilled-labor-
intensity in production in industry n. Suppose each person could provide one unit of service.
People are immobile across countries (see Glaeser and Kohlhase 2004).
The timing of the events could be summarized as follows:
(1) A rm, upon paying an up-front cost, enters an industry and draws a productivity level.
After observing the draw, it chooses to exit or to stay in the game.
(2) If stays, it need to choose serving market F via export or FDI, then employ workers (and
train them if needed) to produce.
(3) The skilled-workers bargain with the rm if there is surplus ex post.
(4) The production and the revenue are realized.
3
Firm Behavior
Now consider the rm's optimization behavior. If it exports, it need to pay iceberg transport
costs and high production labor costs. The advantage is that the xed export cost is lower than
the xed FDI cost, and it is free from the contract friction. The reverse is true for FDI.
3.1
Export
If the rm chooses to produce goods at home and then export, then it employs domestic skilled
and unskilled workers, and because the domestic skilled workers are of high quality, it need
not to train them. In this case the rm is not subject to the contract friction problem caused
by the inalienability of human capital, because if the workers (skilled or not) threat to quit,
the
rm could always
nd outside workers costlessly to replace them. There is no surplus
between the rm and the workers, and quit is not a credible threat. Now the rm's optimization
14
problem is to allocate its inputs between skilled and unskilled tasks, and decide its product price
monopolistically in market F:
After producing x(v) units of product v at home and transport them abroad, it gets revenue
R(v) = A1
[(1
)x(v)]
) A1
= (1
[
m(v)
] [
l(v)
]
1
(1
)
:
Therefore, the rm's problem is to maximize its operating pro t
max
m(v);l(v)
X(
) A1
; ) = (1
[
m(v)
] [
l(v)
]
1
(1
)
m(v)
l(v)
fX :
Solving it we get the operating pro t from export:
X(
; ) = A(1
A
with
X(
)
(1
)1
1
(1
to the measure of productivity
3.2
)1
X(
)
1
1
(1
)
1
fX
fX ;
) > 0 as a component of the slope of
1
(1)
X(
; ) with regard
:
FDI
If the rm chooses FDI and produces goods in country F; then, because the skill level of local
workers are not good enough to e ciently perform the skilled task, the rm need to train them;
otherwise, there would be a discount in the output if the rm produces with untrained workers.
Following the labor economics literature, assume that such on-the-job training is rm-speci c
and is useless for other rms (see Becker 1993 and Mincer 1974, and Weiss 1986 and Parsons
1986 for surveys).16 Due to the inalienability of human capital, the rm and the trained workers
could not contract ex ante upon their future services and these workers could always withdraw
16
An alternative theory based on adverse selection argues that the training could be general. However,
due to the information asymmetricity on the employee's ability, if the employee quits the current rm he
will su er a discount in his earning because the new employer does not know his productivity, thus the
employee is also locked-in (see Acemoglu and Pischke 1998, 1999).
15
their human capital after training.17 Therefore, a surplus arises in the relationship between the
rm and the trained workers after training is completed, and these workers could credibly threat
to quit to bargain over the surplus with the rm.18 Suppose the trained workers act as a union
thus bargain with the rm a la Nash.
Here we can see clearly that training locks-in both the rm and the trained workers. The ex
post hold-up problem will distort the rm's ex ante investment in hiring and training.
The above idea is formalized as follows. If the negotiation fails, the
rm employs new
untrained workers at the market wage to ll in each position. Due to the discount, the new
untrained workers could only produce a fraction of
F
2 (0; 1) of the variety. The red trained
workers will earn market wage wF due to the rm-speci city of the training, and the rm's
training costs are sunk. Assume the per worker training cost is tF :
Now we investigate the investment and the payo
of the
rm in FDI. If the negotiation
between the rm and the trained workers fails, the payo (outside option) to the rm is
A1
=
(
FA
1
F x(v))
[
m(v)
wF m(v)
] [
l(v)
]
1
tF m(v)
(1
)
wF l(v)
wF m(v)
fI
tF m(v)
wF l(v)
fI :
The red workers' total payo (outside option) is wF m(v).
If they reach an agreement, the rm's and the trained workers' joint payo is
A1
[
m(v)
] [
l(v)
]
1
(1
)
tF m(v)
wF l(v)
fI :
So the surplus for the rm and these workers from the relationship is
(1
F )A
1
[
m(v)
] [
l(v)
]
1
(1
)
;
which is divided equally by the rm and the trained workers in the Nash bargaining.
17
Suppose they could not at the beginning contract upon the future output or revenue either. See Hart
and Moore (1999) and Segal (1999).
18
The unskilled-workers' quit threat is not credible, because they could be replaced costlessly.
16
Since there is a positive surplus, they will always reach an agreement ex post. Thus the
rm's pro t is
(
=
F
1
+ (1
2
1
(1 +
2
F )A
F ))A
1
[
1
[
m(v)
m(v)
] [
] [
l(v)
]
1
l(v)
]
1
(1
)
(1
)
wF m(v)
wF m(v)
tF m(v)
tF m(v)
wF l(v)
wF l(v)
fI
fI ;
and ex ante its problem is
max
m(v); l(v)
1
(1 +
2
F )A
1
[
m(v)
] [
l(v)
]
1
(1
)
wF m(v)
tF m(v)
wF l(v)
fI :
The F.O.C.s for m(v) and l(v) are, respectively:
m(v)
1
1 l(v)
(1 + F )A1
[
]
[
] (1
2
1
m(v)
l(v)
1
(1 + F )A1
[
] [
]
2
1
)
(1
wF
) 1
tF
= 0;
(2)
wF
= 0:
(3)
To focus on the central idea (the e ect of contract friction), without loss of generality,
assume tF = 1
wF : Three subtle tricks here are to be noted. With tF + wF = 1; rstly, the
expenditure on each skilled worker (the training cost plus the wage) is the same as that of export,
i.e., unity, thus, compared with export, in FDI there is no labor-cost e ect through the channel
of skilled workers: it is only through the unskilled workers. Secondly, across di erent kinds of
host countries, the expenditure on each skilled worker is the same, i.e., unity, therefore there
is no e ect of the magnitude of the training cost on the total pro ts of FDI in a speci c host
country F . Since there is no evidence that the volume of training costs is signi cant in a ecting
MNEs' decision, its e ect is in this way eliminated in the paper.19 Thirdly, from (2) and (3)
we know that the rm's investment decision on employment and training (i.e., the number of
workers to train) is not a ected by the magnitude of the training cost, but only by two factors,
the strategical consideration of future hold-up,
F,
and the unskilled-labor cost wF : Therefore,
the equilibrium investment (m (v); l (v)) of the system is only determined strategically by the
19
If the training cost is increasing and convex in 1
mechanism in the paper.
17
wL ; this training cost e ect will just reinforce the
hold-up problem and the labor cost, which are the focus of this paper. All possible e ects of the
host country development level through other channels are not existent in the model.
Solving the optimization problem, we get the equilibrium
m (v) =
A
1
1
l (v) = (1
21
1
1
1
)A
1
1
(1
1
wF
21
1
)
(1 +
wF
1
1
F)
(1 +
1
1
F)
;
1
1
:
Because ex ante the rm could specify a lump-sum transfer T from the workers, which would
make the workers break even and the rm grasp all the pro ts from the relationship, thus, the
rm's pro t from FDI is
I (wF ;
;
) = A1
F;
A
with
I (wF ;
;
F)
(2
)2 1
[
m (v)
I (wF ;
1
1
;
wF
] [
l (v)
]
1
(1
F)
1
fI ;
1
(1 +
F)
with regard to the measure of productivity
1
)
m (v)
wF l (v)
fI
as a component of the slope of
1
I
:
Before we go further, we rst note the following benchmark case. On one hand, every other
thing equal, we have
@
I (wF ;
@wF
;
F;
)
< 0; that is, FDI pro t is decreasing in the host country
development level. An especially interesting case here is when
contract friction problem in FDI, we must have
@
I (wF ;
@wF
;
F;
)
F
= 1; i.e., when there is no
< 0: This is the standard prediction
of the traditional proximity-concentration model, which contradicts the concentration of world
FDI in developed countries. However, the current paper shows that this is only one side of the
whole story. On the other side, here we have, ceteris paribus,
@
I (wF ;
@
F
;
F;
)
> 0; that is, the
higher the rm's outside option (or the lower the contract friction), the higher the FDI pro t.
The current paper shows that it is this second (but missed in the traditional theory) force that
helps to explain the gap between the traditional theory and the reality.
Though in any kind of F the contract between the rm and the trained workers is incomplete
and they need to bargain, the division of the surplus is sensitive to the characteristics of country
F . In particular, in the bargaining, the higher the development level of F , the higher the rm's
outside option. The logic is as follows. When the two parties fail to reach an agreement in the
negotiation, the rm could re the trained workers and employ new workers. Since the new
18
workers are not of high quality, the disagreement will cause a loss in output. Because the higher
the development level of F , the higher the quality of the outside workers, thus the lower the loss
to the rm from the disagreement.
This argument is analogous to the popular assumption in the literature (for example, Antras
and Helpman 2004) that such output discount is smaller in a developed country than in a
relatively less developed country. While the literature defends this assumption by less corruption and better legal protection in the more developed country, this paper provides additional
justi cation for this outside option argument and makes it natural in the current context.
To x the idea that the rm has higher outside option in a relatively more developed country
than in a less developed country, and for the sake of simplicity of the model, assume
F
= wF :20
This is the key idea to incorporate the e ect of the host country development level on FDI.
Therefore, we have FDI pro t
I (wF ;
with
I (wF ;
)
(2
)2 1
1
1
; )=A
wF
1
I (wF ;
)
(1 + wF ) 1
:
1
fI ;
(4)
Equilibrium Choice: Export vs. FDI
4
To derive a rm's equilibrium choice between export and FDI, we compare the two pro t functions,
X(
; ) and
I (wF ;
; ). It is straightforward to have the following properties of the
pro t functions in Lemma 1.
Lemma 1 Both pro t functions,
ductivity measure
1
; i.e.,
X(
X(
; ) and
) > 0;
I (wF ;
I (wF ;
; ); are linearly increasing in pro-
) > 0:
In words, more productive rms will earn higher pro ts no matter they export or invest
abroad to serve a foreign market. This implies, more productive rms are more likely to cover
any kinds of xed costs and survive. This result will drive the rms into the sorting pattern
across FDI, export and exiting.
0
20
The mechanism in the paper also holds for a general speci cation L = h(wL ); where h (wL ) > 0 but
0
not very large. The condition, i.e., h (wL ) > 0 but not very large, makes sense because one country's
education level increases in its development level, but not very fast.
19
To compare the rm's pro t from each choice, by checking the pro t functions (1) and (4),
with fI > fX and a common component A; we see that what matters is the comparison between
the slopes,
X(
) and
I (wF ;
): Other things given, an increase in the slope represents an
increase in the pro t:
The following proposition gives the e ects of the industry technology and the host country
development level on the FDI pro t, which provides the driving forces of the main results.
Proposition 1 For FDI pro t
I (wF ;
; ) of a rm of the developed country H:
(1) It is decreasing in the skilled-labor-intensity of production, ; i.e.,
@
I (wF ;
@
; )
< 0:
(2) In unskilled-labor-intensive industries, it is decreasing in the host country development
level wF ; In skilled-labor-intensive industries, it is increasing in wF . Speci cally, for
1
(0; 1+w
);
F
@
I (wF ;
@wF
; )
< 0; for
1
2 ( 1+w
; 1);
F
@
I (wF ;
@wF
; )
2
> 0:
(3) In all industries, the higher the ; the larger the increase (or the smaller the decrease) of
I (wF ;
; ) in an increase of wF : That is, in all industries, we have
@2
I (wF ; ; )
@wF @
> 0:
Proof. See Appendix.
About part (1), an increase in skilled-labor-intensity, ; means that the production relies
more on skilled-labor and less on unskilled-labor, which has three e ects: more serious hold-up
problems, more costs on skilled workers (because more of them are needed), and less cost-saving
from low-wage unskilled workers in F . Thus it is natural that
I (wF ;
; ) decreases in :
The second part is the central mechanism for our main results. Firstly, we look at the e ect of
the host country development level. When wF increases, the unskilled-labor costs will increase,
which tends to decrease FDI pro ts (the labor cost e ect, negative), while the hold-up problem
will be mitigated because of the higher quality of outside labor force, which tends to increase FDI
pro ts (the hold-up e ect, positive). Secondly, we look at the e ect of the industry technology.
In low
industries, the need for skilled-labor is not intensive and the hold-up problem is not that
severe, at the same time the quantity of unskilled worker input is large in production, thus the
labor cost e ect dominates the hold-up e ect. On the contrary, in high
industries, the hold-up
problem is serious and the use of unskilled worker is not that intensive, thus the labor cost e ect
will be dominated by the hold-up e ect. Therefore, in total, an increase in wF will decrease FDI
20
pro ts in unskilled-labor-intensive industries but increase FDI pro ts in skilled-labor-intensive
industries.
As for the cross derivative of
a complementary e ect between
I (wF ;
; ) over
and wF in part (3), the positive sign means
and wF on increasing FDI pro ts, that is, across industries,
in industries more intensive in skilled-labor, the pro ts of FDI will increase more (or decrease
less) in a given increase of the host country development level. Though the marginal e ect of
wF on FDI is di erent in di erent kinds of industries, the sign of the cross derivative is the same
in both kinds of industries, because an increase in
will always reinforce the hold-up e ect but
weaken the labor cost e ect. In unskilled-labor-intensive industries, the negative labor cost e ect
dominates. An increase in the intensity of skilled-labor will weaken the degree of the dominance
because less intensively the unskilled workers are employed, thus, with an increase in ; the
FDI pro ts will decrease less in an increase of wF and the cross partial derivative is positive.
For skilled-labor-intensive industries, the positive hold-up e ect dominates. An increase in the
intensity of skilled-labor will reinforce this dominance relation because skilled-labor matters
more in the production, thus, with an increase in ; the FDI pro ts will increase more in an
increase of wF and the cross partial derivative is positive.
Now we determine the rms' equilibrium choices between FDI and export. The productivity
level at which the operating pro ts of export is zero is
X(
The intersection productivity level of
)
(
X
(wF ; ) =
X)1
and
I;
=
fX
:
A X( )
if exists, is
fI fX
A[ I (wF ; )
X(
)]
:
Suppose fX is small enough relative to fI such that, for any reasonable ;
X(
)<
(wF ; )
always holds.21 This kind of assumption is popular in the literatue. It is to ensure that there
are always some low productivity, active rms choosing export rather than FDI. Otherwise it is
possible that all active rms choose FDI in the model, which is not interesting.
21
In the current setup, technically this need a positive lower bound on wL : With a reasonable lower
bound w, because 0 < < 1; there must exist such small fX that X ( ) < I (wL ; ):
21
As in Helpman, Melitz and Yeaple (2004), there is a neat sorting pattern of rms across
FDI, exporting and exiting, which is shown in Figure 1 and taken as the benchmark sorting
pattern. The most productive rms with productivity levels
less productive rms with
<
X(
2(
X(
>
(wF ; ) choose FDI, the
); (wF ; )) export, while the least productive rms with
) exit. One special case is that the cuto productivity level between FDI and export,
(wF ; ); may not exist (or say, is in nity) in some industries in some kinds of host countries. In
this case no rm will choose FDI in these country-industry pairs whatever its productivity is: the
most productive rms with
>
X(
) will choose export and the rest rms with
<
X(
)
will exit.
[Figure 1]
At this moment we rstly investigate individual rm's choice between export and FDI, and
later we will look at the aggregate level prevalance of export and FDI. Proposition 2 characterizes
the sorting pattern and the cuto productivity level for rms' choices.
Proposition 2 To serve country F; rms of country H with
while rms with
paribus,
2(
X(
>
(wF ; ) will choose FDI
); (wF ; )) will choose export, with the rest rms exiting. Ceteris
(wF ; ) has following properties:
(1) It is increasing in the industrial skilled-labor-intensity, i.e.,
@ (wF ; )
@
> 0;
(2) In unskilled-labor-intensive industries, it is increasing in the host country development
level wF ( @
(@
(wF ; )
@wF
(wF ; )
@wF
> 0), however, in skilled-labor-intensive industries, it is decreasing in wF
< 0);
(3) In all industries, the higher the , the smaller the increase (or the larger the decrease)
of
(wF ; ) in an increase of wF . That is, in all industries, we have
(4) Especially, when the transport cost is low,
FDI) if wF is low and
@ 2 (wF ; )
@wF @
< 0:
(wF ; ) will be in nity (i.e., no rm choosing
is high.
Proof. See Appendix.
To understand the proof, it is easy to see Figure 2. The productivity variable is measured
along the horizontal axis and the operating pro ts are measured along the vertical axis. When
22
I (wF ;
; ) is steeper than
X(
; ); these two pro t lines will always intersect thus
exists (not in nity). In this case rms with
FDI, those with
s.t.
X(
)<
<
>
(wF ; )
(wF ; ) will attain the highest pro ts through
(wF ; ) will attain the highest pro ts through exporting,
whereas the least productive rms with
<
X(
) will exit the market. That is, rms will
sort into FDI-Export-Exit pattern according to their productivity levels. The intuition of this
pattern is the same as in Helpman, Melitz and Yeaple (2004): given the transport costs, the
more productive the rm is, the more pro ts it will earn in any choice thus the more likely for
it to cover the (higher) xed cost.
[Figure 2]
Relative to Helpman, Melitz and Yeaple (2004), the rest predictions are new. The slope of
the export pro ts,
X(
); is decreasing in transport cost
from Proposition 1, the slope of FDI pro ts,
I (wF ;
but not a ected by
or wF ; and
); is decreasing in ; decreasing in wF in
unskilled-labor-intensive industries (Figure 2.1) but increasing in wF in skilled-labor-intensive
industries (Figure 2.2). Then all the following predictions are natural and the intuitions follow
from Proposition 1. Part (1) predicts that, ceteris paribus, it would be more stringent (i.e., with
higher cuto productivity
(wF ; )) for rms to make more pro ts from FDI than from export
in more skilled-labor-intensive industries. As part (2) says, ceteris paribus, in unskilled-laborintensive industries,
rms investing in a relatively more developed country should be overall
more productive (i.e., with higher
(wF ; )) than rms investing in a less developed country; on
the contrary, in skilled-labor-intensive industries, rms investing in a relatively less developed
country should be overall more productive than rms investing in a more developed country.
As far as part (3) is concerned, the negative sign of the cross partial derivative term means
that an increase in skilled-labor-intensity will make the increase of
unskilled-labor-intensive industries, or make the decrease of
(wF ; ) in wF smaller in
(wF ; ) in wF larger in skilled-
labor-intensive industries. The reason is the same as the part (3) of Proposition 1. An increase
of wF tends to, on one hand, increase the pro tability of FDI due to the hold-up e ect, on the
other hand, decrease the pro tability of FDI due to the labor cost e ect. An increase in
will
enhance that hold-up e ect but weaken that labor cost e ect, thus the interaction of wF and
23
has positive e ect on the pro tability of FDI and negative e ect on the cuto productivity level
between export and FDI.
As one of the deviations from Helpman, Melitz and Yeaple (2004), it is not guaranteed
that
I (wF ;
; ) is always steeper than
X(
; ) in this model, therefore there may be no rm
investing in some kinds of industries in some kinds of host countries, no matter how productive
the rms are. In part (4) this paper identi es that, given proper transport costs, there is a
discrete change of
the more likely
(wF ; ) such that: ceteris paribus, the lower the wF and the higher the ;
(wF ; ) be in nity thus no rm choosing FDI there. This is intuitive (and not
surprising) because for low wF and high
country-industry pairs the incentive of labor cost
saving is very weak and at the same time the problem of hold-up is very serious in FDI. Thus
when the transport cost is not high, rms will be more likely to choose export rather than FDI.
These rm-level predictions with regard to the industrial skilled-labor-intensity and the host
country development level are new in the theory, and they also remind us of the importance
of di erences across industries when investigating FDI or MNEs. Especially important is that,
as part (2) reveals, it would be biased for the estimation of the correlation between MNEs'
productivity and the host country devleopment level if we don't take into account industrial
heterogeneities. Partly because of the limited availability of such rm-level data, the rm-level
empirical work on comparing the productivity levels between exporters and MNEs appeared only
in recent years (for example, Head and Ries 2003, Girma, Kneller and Pisu 2005, Tomiura 2007,
Chen and Moore 2008), and all of these papers consider the traditional proximity-concentration
factors, but not the factor of contract frictions in this paper. Detailed empirical analyses taking
into consideration of contract frictions, industrial technology and the host country development
level are needed.
5
Prevalence of MNEs (FDI Pattern)
This model has implications for variations of channels of serving a foreign country by
rms
from developed countries. The previous section mainly examines characteristics of individual
24
rms choosing export or FDI. Now we turn to the industry and country level patterns, i.e., the
variations of the prevalance of MNEs (i.e.,
rms performing FDI) across industries and host
countries.
Following Antras and Helpman (2004), Helpman, Melitz and Yeaple (2004), assume each
rm's productivity is drawn from a Pareto distribution with shape parameter k > 0 and lower
bound d; that is,
G( ) = 1
where
1
k
d
( )k ; f or
d > 0;
is positively correlated with the productivity dispersion (or the degree of heterogeneity)
within an industry and is assumed small to ensure a nite variance of the distribution of rm
size in that industry. With this productivity distribution, the sales distribution is also Pareto,
which is consistent with the evidence (Axtell 2001; Helpman, Melitz and Yeaple 2004). I employ
the fraction of MNEs of all active rms as the measure of the prevalence of MNEs (FDI). Using
the market share of MNEs as the measure will result in similar conclusions.
Denote by sI the fraction of active rms that choose FDI to serve country F in an industry.
Then in the case of
(wF ; ) being in nity, we have sI = 0 and sX = 1: For the benchmark case
of rms sorting into FDI-Exporting-Exiting, we have
1
G ( (wF ; ))
sI =
1
G (
X(
))
1
1
= [(
I (wF ;
X(
)
)
with the fraction of active rms that choose export sX = 1
1)
fX
]k(1
fI fX
)=
sI : Because 0 <
;
X( )
(wF ; )
< 1; we
have 0 < sI < 1: At this aggregate level, from Propositon 2, we have the following central result
for the prevalence of MNEs (FDI) in country F from the developed country H.
Proposition 3 For the prevalence of MNEs (FDI) from country H; sI ; ceteris paribus:
(1) It is decreasing in the FDI xed cost fI ; increasing in the export xed cost fX ; transport
cost ; and the industrial productivity dispersion
1
k;
I
(2) It is decreasing in the industrial skilled-labor-intensity, ( @s
@ < 0);
(3) It is decreasing in the host country development level wF in unskilled-labor-intensive
@sI
@sI
< 0), but increasing in wF in skilled-labor-intensive industries ( @w
> 0);
industries ( @w
F
F
25
(4) In all industries, the higher the , the larger the increase (or the smaller the decrease)
of FDI in an increase of wF . That is, in all industries,
@ 2 sI
@wF @
> 0;
(5) Especially, when the transport cost is low, there will be no FDI in ow (sI = 0) if wF is
low and
is high.
Part (1) is the familiar proximity-concentration results in Helpman, Melitz and Yeaple (2004).
High xed export cost and transport cost will encourage FDI, while high extra xed cost of FDI
will discourage it. A larger productivity dispersion means, given the lower bound of productivity,
a fatter right tail of the distribution, i.e., a larger fraction of high productivity rms, thus more
rms become MNEs.
The remaining parts are new relative to the previous horizontal FDI literature, but they are
quite intuitive with the contract friction taken into account. Other things equal, an increase in
will aggravate the hold-up problem and decrease labor cost saving incentive for FDI, thus, as
part (2) says, decrease the prevalence of FDI/MNEs overall.
Part (3) means that, ceteris paribus, in unskilled-labor-intensive industries, there will be
more FDI/MNEs in a less developed country than in a relatively more developed country, while
in skilled-labor-intensive industries, there will be more FDI/MNEs in a more developed country
than in a relatively less developed country, of which the underlying mechanism is the di erent
dominance relation between the labor cost e ect and the hold-up e ect in the two kinds of
industries. The second part of this result exactly explains the co-existence of the two facts in
the introduction, that is, most FDI goes to countries with relatively high GDP per capita and
at the same time happens in skilled-labor-intensive industries. This paper identi es as (one of)
the underlying driving force(s) of this pattern the contract friction determined by the industrial
technology and the host country development level, in particular, the trade-o
between the
labor-cost e ect and the hold-up e ect in FDI location decision.
Part (4) says the interaction e ect of wF and
on the prevalence of MNEs. The underlying
reason is familiar now: as mentioned in Proprosition 1, the skilled-labor-intensity of production
and the development level are complementary in attracting FDI. Part (5), which could be looked
at as an extreme case of the prevalence of FDI, predicts the division of the country-industry
26
space by a threshold into with-FDI-in ows area and without-FDI-in ow area. In particular, it
is quite likely that those least developed countries will attract no FDI in skilled-labor-intensive
industries. This is not surprising, because the hold-up problem is severe and the labor cost
saving incentive is weak there. Though the World Investment Report (2001) has documented
that the 49 least developed countries attracting only 0.3 percent of world FDI ows, it is only
an overall description and more detailed empirical work is needed to characterize those no-FDI
industries and countries, which is meaningful not only by itself but also because FDI is thought
of as an important factor in promoting economic development.
The big picture of the FDI ows could be summarized in Figure 3 for a given, low level
transport cost, where the horizontal axis is the host country development level and the vertical
axis is the skilled-labor-intensity. In the shadowed area with low wF and high ; there will be no
FDI in ow. This no-FDI area shringks with regard to the transport cost. In the south-west area
for unskilled-labor-intensive industries, the prevalence of MNEs increases along the decreases of
wF and . In the north-east area for skilled-labor-intensive industries, the prevalence of MNEs
increases along the increase of wF and the decrease of .
[Figure 3]
These aggregate level predictions receive almost exact support from the limited empirical
literature. A well-known paper by Yeaple (2003) shows that U.S. industry level outward FDI is
positively correlated with the interaction of the host country skilled-labor abundance and the
industry skilled-labor intensities, which is seen as suppotive of the vertical FDI theory.
However, if we go into more details of the paper, we could nd that that paper and the
results in section IV.D provide exact supports for the predictions of the current contract friction
horizontal FDI story. Firstly, to test for the vertical FDI theory (comparative advantage),
it should be a relative measure of skilled- to unskilled-labor that matters. However, in the
regressions the measures of country skilled-labor abundance are somewhat absolute measures,
the average schooling years per worker and the GDP per worker,22 which are exactly what matter
22
Though these two variables are also used in the related literature to proxy factor endowment proportions, this proximation is not beyond question: with the same value of the absolute measure, di erent
countries could have very di erent relative abundance of skilled-labor. In fact, there are other \relative"
27
for the current contract friction model, that is, the absolute measure of the quality of \outside
skilled-labor". Thus, to some extent, Yeaple (2003) could be looked at as a test for the current
contract friction model.
Secondly, the results of the estimation give support to all critical predictions of Proposition
3. In Yeaple (2003) Table 3 presents direct test for the trade-o between export and FDI as
follows:23
sXij =
1 HumanCapitalj + 2 HumanCapitalj
0
SkillIntensityi + 3 SkillIntensityi +P Cij
+"ij ;
where i indexes industries and j indexes host countries, the dependent variable is the ratio of
exports from U.S. to the host country divided by the sum of these exports plus U.S. multinational a liate sales to host country customers, which is qualitatively equal to 1
sI in this
paper. HumanCapital is the average schooling years per worker or the GDP per worker, and
the industrial skilled-labor-intensity SkillIntensity is calculated as the share of nonproduction
workers in value added by industry. P C is the vector including all the proximity-concentration
factors, such as freignt costs, tari rates, plant and rm economies of scale, market sizes, host
countries' corporate tax rates and policies towards FDI, and an intercept.
In the current paper's notations, from the regression results of the above full speci cation in
column (1) of Table 3 and the summary statistics in the Appendix, with sI = 1
@ 2 sI
@wF @
= 1:31 > 0;
@sI
@
=
3:93+1:31wF 2 [ 2: 279 4; 0:615 7]; and
@sI
@wF
=
sX ; we have
6:32+1:31 2 [ 1:
590 9; 0:374 1]; that is,
@sI
@
@sI
@wF
< 0;
@ 2 sI
> 0;
@wF @
< 0 when
and
is low, otherwise
@sI
> 0:
@wF
The results are similar if we use the coe cients in column (3) (which does not include the
proximity-concentration controls). These empirical results are broadly consistent with the contract friction predictions.
measures of skilled-labor abundance in the literature, e.g., Carr, Markusen and Maskus (2001) use the
ratio of skilled labor to total labor force in a country.
23
The dependent variable there is the ratio of exports from U.S. to the host country divided by the sum
of these exports plus U.S. multinational a liate sales to host country customers, which is qualitatively
equal to sX .
28
6
Conclusions
This paper extends the proximity-concentration model with heterogeneous rms through embedding an incomplete contract view of FDI in it to account for rms' export and FDI location
decisions in di erent kinds of industries. The degree of the contract friction, which is determined jointly by the industry technology and the host country development level, will a ect
pro ts from FDI: because the higher the development level of F , the higher the rm's outside
option in the bargaining between the rm and the skilled workers, an increase in host country
development level will mitigate the hold-up problem (the hold-up e ect) though at the same time
increase the unskilled-labor costs (the labor cost e ect), and it turns out that the former e ect
dominates the latter in skilled-labor-intensive industries while the latter dominates the former
in unskilled-labor-intensive industries. In this way, this paper provides an explanation for the
world FDI patterns (i.e., concentration in developed countries and at the same in skilled-laborintensive industries), and furthermore, several new testable predictions about FDI/MNEs and
the no-FDI in ow case. These results call for more detailed and more careful empirical work on
analysing export and FDI, that is, taking into account the contract friction factors, as well as
the proximity-concentration factors, and paying attention to the di erences of the roles of these
factors in di erent kinds of industries. Without considering the industrial heterogeneities in the
technology, the estimation of the relation between FDI and the host country development level
may be biased.
As for future work, it is also quite tractable to consider in this model the export vs. FDI
problem of rms of relatively less developed countries to serve more developed countries. To
my knowledge this was not discussed by previous MNEs literature but is emerging as a more
and more important economic phenomenon. The incomplete contract view of horizontal FDI
could also be employed to explore other related questions, such as the composition of FDI (for
example, joint ventures vs. wholly-owned enterprises, merger vs. green eld investment).
29
Appendix.
Calculation of the demand function for variety v.
Suppose a consumer in country L maximizes her utility subject to the budget constraint
z+
N Z
X
pn (v)xn (v)dv
E;
n=1 v2Vn
where E is the total expenditure of country L; which is exogenous in my partial equilibrium
analysis. It is well-known that
problem is
Z
max (
xn (v)
nE
will be expended on goods in industry n, thus the consumer's
n
xn (v)
dv)
1
n
s:t:
v2Vn
R
The F.O.C. is ( v2Vn xn (v)
n
Z
pn (v)xn (v)dv
n E:
v2Vn
dv)
1
n
n
xn (v)
n
1
= pn (v); thus
Z
pn (v)
(
xn (v)
Zv2Vn
n
1 p (v) n 1 (
xn (v)
n
1
n 1
xn (v) =
1
n
pn (v)xn (v) =
1
n 1
n
dv)
1
n
;
n
dv)
1
n
:
v2Vn
With
Z
Z
Z
1
1
n
pn (v)xn (v)dv = n 1 (
xn (v) n dv) n
pn (v) n 1 dv
v2Vn
v2Vn
v2Vn
Z
Z
1
n
pn (v)1 "n dv;
= pn (v) n 1 xn (v)
pn (v) n 1 dv = pn (v)"n xn (v)
nE =
v2Vn
v2Vn
droping the industry notation, we have the demand for each variety in a given industry as
follows:
x(v) = R
v2V
E
p(v)1
" dv
p(v)
"
Ap(v)
"
:
Proof of Proposition 1.
As
ln
I (wF ;
I (wF ;
)
2
2
) = ln(2
21
1
)
(1 + wF ) 1
1
1
ln 2 +
wF
(1
1
ln
1
30
)
; we have
+
1
ln(1 + wF )
(1
1
)
ln wF :
(1) For skilled-labor-intensity of production,
@ ln
I (wF ;
)
@
=
:
ln wF < 0
1
because wF < 1:
(2) For F 0 s development level, wF :
@ ln
I (wF ;
)
@wF
If 0 <
<
1
1+wF
; then
@ ln
I (wF ; )
@wF
< 0; if
=
(1 + wF ) 1
:
wF (1 + wF )
1
1
1+wF
<
< 1; then
@ ln
I (wF ; )
@wF
> 0:
(3) For the cross partial derivative:
@ 2 ln I (wF ; )
=
@wF @
1
1
> 0:
wF
To prove Proposition 2, we need to identify di erent comparative possibilities between export
and FDI pro ts, to do which we rst compare some extrem cases of
I (wF ;
) with
X(
) in
Lemma 2.
Lemma 2 (1) For industries with
1
1+wF
(2) For industries with
>
(3) For inf
I (w; 1);
X(
I (wF ;
); and when 0 <
)=
< e;
Proof of Lemma 2.
extrem wF = 1 and
=
<
; sup
1
1+wF
; sup
I (wF ;
)=
there is a cuto
I (w; 1)
<
X(
):
I (wF ;
)=
1
I (1; 2 )
>
I (w; 0)
X(
>
X(
);
);
e such that when 1 >
> e;
I (w; 1)
>
Following the proof of Proposition 1, we have the critical point in
1
1+wF
=
1
2
from
@ ln
I (wF ;
@
)
= 0 and
@ ln
I (wF ; )
@wF
= 0: Furthermore, we
have
@ 2 ln
I (wF ;
@ 2
)
= 0;
@ 2 ln I (wF ; )
> 0;
@wF @
and
therefore,
@ 2 ln
I (wF ;
@ 2
) @ 2 ln
I (wF ;
@wF2
)
@ 2 ln I (wF ; )
< 0;
@wF @
that is, the extrem case (wF ; ) = (1; 12 ) is neither a maximum nor a minimum, but a saddle
point.
31
(1) Firstly we consider industries with
<
1
1+wF
: Because the function ln
tinuous, consider the optimization problem on f(wF ; )jw
wF
optimization problem is max ln
I (wF ;
wF ;
1
1+wF
1; 0
is compact and so there must be maximum and minimum for ln
I (wF ;
) s.t. (wF ; ) 2 f(wF ; )jw
I (wF ;
) is con-
g: This set
). The constrained
wF
1; 0
1
1+wF
g;
with the solution (wF ; ) = (1; 12 ) and
ln
I (1;
1
) = ln(2
2
)
ln 2 +
ln :
1
Three possible corner solutions are, with w being very small,
ln
I (w; 0)
= ln(2
)
ln
I (w; 1)
ln(2
)
I (1; 0)
= ln(2
)
ln
It is clear that ln
With ln
I (w; 0)
ln
1
ln 2 +
1
ln 2 +
I (wF ;
) = ln
I (w; 0);
I (wF ;
ln(1 + w)
1
I (1; 0)
ln
I (wF ;
)=
X (0)
1
ln w
+1;
I (w; 1);
I (wF ;
) = ln
therefore for (wF ; ) 2
I (w; 1):
> 0, we have
I (w; 0)
1
1+wF
>
> ln
and inf ln
I (w; 0)
(2) Now consider industries with
wF ;
= ln
g; we have
) > ln
+
ln ; and
1
1
1+wF
sup
problem max ln
ln
1
ln :
1
1
I (1; 2 )
> ln
<
X(
ln 2 +
1
I (w; 0)
f(wF ; )jw < wF < 1; 0 <
sup ln
1
>
X(
):
: Similarly, for the constrained optimization
) s.t. (wF ; ) 2 f(wF ; )jw
1
1; 1+w
F
wF
1g; the solution is
(wF ; ) = (1; 12 ) and
ln
I (1;
1
) = ln(2
2
)
ln 2 +
ln :
1
Two possible corner solutions are, with w being very small,
ln
ln
It is clear that ln
1
1; 1+w
<
F
I (w; 1)
ln(2
)
I (1; 1)
= ln(2
)
1
I (1; 2 )
= ln
I (1; 1)
> ln
1
1
ln 2 +
I (w; 1);
ln 2 +
1
1
ln ; and
ln :
therefore for (wF ; ) 2 f(wF ; )jw < wF <
< 1g; we have
sup ln
I (wF ;
) = ln
I (1;
1
); and inf ln
2
32
I (wF ;
) = ln
I (w; 1):
1
I (1; 2 )
With ln
ln
X(
sup
I (wF ;
(3) On the other hand, for inf
1
ln 2
1
0 <
ln(1
)
< 1; ln
have
X (1)
<
I (w; 1)
I (w; 1)
< 1;
I (w; 1)
ln
<
X (0)
X (0):
X (e)
>
X(
I (w; 1)
= ln 2(11
1
)>
2
I (w; 1);
X(
ln
)+
I (w; 1)
(2
)(1 ln 2) 1
(1
)2 (2
)
=0
= 0: Together with
X(
ln 2 > 0, we have
):
=
j
With
X (0)
I (1;
)=
@
@
<
ln
)=
I (wF ;
; we have
a cuto e de ned by
e<
1
I (1; 2 )
) > ln
=
ln
X (0)
0:306 85(2
) 1
(1
)2 (2
)
I (w; 1)
= ln(2
)
< 0; thus, with
>
X (1)
= 0; we
) being continuous, decreasing in ; we must have
< e;
such that when 0 <
):
I (w; 1)
<
X(
); and when
Proof of Proposition 2.
(wF ; ) and
From the de nition of
fI fX
A[ I (wF ; )
(wF ; )
it is clear that if
<
0>
(wF ; ),
X(
>
X(
; )>
(wF ; );
; )>
I (wF ;
X(
I (wF ;
);
X(
)]
I (wF ;
; ) >
; ) and
X(
> 0 and
X(
X(
fX
;
A X( )
)
; ) > 0; rms choose FDI; if
X(
; ) > 0; rms choose export; when
<
) <
X(
);
; ); rms will exit.
(1), (2), (3) follows from Proposition 1.
is,
(4) From Lemma 2, we know that when e <
I (wF ;
; ) is steeper than
X(
< 1; we always have
I (wF ;
)>
X(
); that
; ): With fI > fX , we must have a nite cuto productivity
(wF ; ):
When
have sup
is low, i.e., 0 <
I (wF ;
)=
< e; we have
I (w; 0)
>
X(
)>
I (w; 1)
<
I (w; 1):
Due to the continuity of
Similarly, in industries
fF
I (w
0
; e0 ) =
must have
@ e0
0
@w
f
F
X(
>
1
1+wF
@ ln
I (wF ;
@
)
): In industries
1
(0; 1+w
) such that
F
and ; then we must have a threshold (w
fF ; e) 2 (w; 1)
Because in this kind of industries,
X(
< 0 and
@ ln
I (wF ; )
@wF
<
1
1+wF
; we thus
I (wF ;
) in wF
fF ; e)
I (w
=
< 0; we must have
X(
@e
@w
f
F
):
< 0:
1
; we must have a threshold (w
fF 0 ; e0 ) 2 (w; 1) ( 1+w
; 1) such that
): Because in this kind of industries,
> 0: For (wF ; ) 2 (w; w
fF 0 )
(e; 1);
@ ln
I (wF ;
I (wF ;
@
)<
)
< 0 and
X(
@ ln
I (wF ; )
@wF
); that is, for those host
country-industry pairs with very low development level and high skilled-labor-intensity,
33
> 0; we
X(
; )
is steeper than
I (wF ;
; ): With fI > fX , rms will always earn more from exporting than
from FDI. This means, no active rm will choose FDI (or, in another way,
if wF is low and
is high.
34
(wF ; ) be in nite)
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38
exit
export
FDI
Figure 11. Firms ’ sorting pattern: FDI-Export-Exit
Figure 2.1. Export vs. FDI in unskilled-labor-intensive industries:
when wF increases and/or η increases.
Figure 2.2. Export vs. FDI in skilled-labor-intensive industries:
when wF decreases and/or η increases.
wF
Figure 3. The prevalence of MNEs (FDI inflows) across
country-industry
t i d t pairs
i when
h transport
t
t costt is
i low.
l