Jensen-Theoretical_FDI_Human Capital_Growth_5-12

Connecting Policy to the FDI Human Capital Threshold: A
Theoretical Framework
Joshua Jensen∗
Abstract
Many empirical studies over the last 15 years have found that FDI is positively correlated with
economic growth conditional on a minimum human capital threshold being met; if this condition is
not met effects of FDI on growth are found to be statistically insignificant from zero or even negative.
This paper builds off of Borensztein, De Greggario, and Lee’s (1998) theoretical model to incorporate
this threshold and evaluate basic policy actions. This paper theoretically demonstrates that when
an economy does not meet the FDI human capital threshold it can weakly increase economic growth
rates by placing a tax on foreign firms.
1 Introduction
A prevalent theme found in policies of governments, whether national or regional, is the attempt to
attract foreign direct investment (FDI) via multinational corporations (MNCs). This is especially seen
in developing countries. This is based on the basic idea that FDI can bring economic growth, primarily
through technology spillovers. Consider, world FDI growth rates over the last three decades have had
dramatic increases, peaking around 40 percent average annual growth rate by the late 1990s (Wang and
Wong 2011). Further, the literature has shown that human capital is a pivotal factor in determining the
impact of FDI.
FDI is often sought out at the policy level on the assumption that it will bring economic growth;
indeed many countries, especially developing, try to attract MNCs to induce inward FDI (Wang and Wong
2009). For example, Mastromarco (2008) observes that a developing country in early industrialization
may find it to be more effective to attract FDI to gain access to technology spillovers, than to just
develop the same technology locally. However, FDI may not always have positive effects or be more
beneficial than domestic investment. For instance, Figilio and Blonigen (2000) find in US states that
while foreign firms tend to pay higher wages, the established incentives to attract the firms usually result
in a decrease in public education expenditure. Similarly, Miyamoto (2003) observes that developing
countries governments face very limited budgetary resources and tend to underinvest in human capital.
Ironically, human capital is found to be a crucial determinant of attracting FDI as well as determining
FDI’s effectiveness. Indeed a wave of studies, which will be discussed at length later on, have found that
FDI is positively correlated with economic growth conditional on a minimum human capital threshold
being met; if this condition is not met effects of FDI on growth are found to be statistically insignificant
from zero or even negative (Borensztein, De Greggario, and Lee 1998, Xu 2000, Ford, Rork, and Elmslie
2008, Wang and Wong 2009 & 2011).
In a key study, Borensztein, De Greggario, and Lee (1998, henceforth BDL (1998)) establish a strong
theoretical framework and demonstrate a positive relationship between FDI and economic growth. Build-
ing off of their model, this paper incorporates the human capital threshold into a theoretic framework
and evaluates basic policy actions. This paper theoretically demonstrates that when an economy does
not meet the FDI human capital threshold it can weakly increase economic growth rates by placing a
∗Author is from the University of Hawai’i at Manoa. Thank you to Dr. James Roumasset for helpful comments. All
errors are my own.
1

tax on foreign firms. As well, this paper illustrates a subsidy on human capital formation would strictly
increase economic growth in all cases, which is what one would predict by BDL (1998).
The paper proceeds as follows: section 2 provides a literature review, section 3 develops the papers
theoretical framework, section 4 analyses two policy actions, and section 5 concludes.
2 Literature Review
FDI has long been a popular topic in Economics, in which there have traditionally been mixed results
on FDI and technology spillovers. In the view of Ford, Rork, and Elmslie (2008, henceforth FRE(2008))
although many studies’ results are mixed on FDI and technology spillovers, those that control for the
capacity of local firms to absorb the technology do find correlation between the two. Thus it is clear that
the host’s absorption capacity plays a crucial role. In that vein, several studies have identified human
capital as an important determinant of FDI. Noorbakhsh, Paloni, and Youssef (2001) find that human
capital has a statistically significant relationship with FDI inflow and is one of the most important
determinants of FDI inflow. Additionally they observe that countries that rely on low-cost, low-skill
labor, or natural resources find it difficult to induce FDI for high-value industries. Further, Miyamoto
(2003) finds that human capital is a key factor in attracting FDI. Thus, we see that human capital plays
a crucial role in determining FDI.
In their seminal study, BDL (1998) establish a robust positive relationship between FDI and economic
growth provided a minimum threshold of human capital is met; given this condition they further find
evidence that FDI contributes to economic growth by being an important vehicle for technology transfer
and stimulating technological progress in the host country. BDL (1998) use gross FDI inflow panel data
from the IMF along with Barro and Lee’s (1993) measures of average years of male secondary schooling
as a proxy for human capital stock; the data is across 69 developing countries from 1970 to 1989.
Using mainly seemingly unrelated regressions (SUR) techniques, their main regression shows that FDI
has a positive overall effect on economic growth with the magnitude depending on the stock of human
capital. However, when only considering countries with low human capital the direct effect of FDI is
observed to be negative. The authors calculate thresholds of secondary school attainments for various
specifications, in which each country that satisfies the human capital threshold benefits positively from
FDI in terms of economic growth. Further, the authors infer that the benefits of FDI come through a
channel of technological spillover resulting in higher efficiency rather than that of capital accumulation.
BDL (1998) also develop a HK model to motivate the study, which this paper builds off of. Their
theoretical model is important as it establishes a basis for understanding the relationship between FDI
and economic growth, which is shown to be strictly positive. However, the model does not account for
the human capital threshold. In all, BDL’s (1998) most robust empirical finding is the positive effect of
FDI on economic growth is dependent on the level of human capital of the host country. Their finding
of the FDI and human capital threshold has since been much extended upon.
Moreover, Wang and Wong (2009) provide a meaningful extension of both BDL (1998) and Alfaro,
et al. (2004). In short, Alfaro, et al. (2004) find that FDI has a positive correlation with economic
growth given that a well-developed financial system is in place. Wang and Wong (2009) in bringing
these studies together find evidence that FDI has two main catalysts for economic growth each of which
creates growth through different channels: 1. once a host country reaches the human capital threshold
FDI is positively correlated with only productivity growth, and 2. that at certain level of development
in the countrys financial system FDI is positively correlated with only capital growth. The authors show
this using the same data as in BDL (1998) and similar SUR techniques. Wang and Wong’s (2009) main
contribution is studying and providing evidence on the channels of economic growth of FDI under noted
correlated conditions.
Furthermore, Xu (2000) investigates the impact of FDI on technology transfers and spillovers based
on US MNCs contributions across 40 countries from 1966 to 1994. Xu observes that FDI coming from a
US MNC positively contributes to growth when a minimum human capital threshold is met in the host
economy. As well, Wang and Wong (2011) revisit BDL (1998) but take quality of education into account
as well as quantity. They use education quality measures from Lee and Barro (2001), to construct two
2

separate quality indices. Wang and Wong (2011) find that the BDL (1998) established relationship
between FDI and economic growth with a given human capital threshold still holds when controlling for
education quality, although the human capital threshold is significantly lower. 1
Additionally, FRE (2008) show that US states with high foreign presence grow faster relative to states
with a low presence given a minimum threshold of human capital. A major improvement in this study
is how it deals with the potential issues of using FDI flow data, an issue which is acknowledged by BDL
(1998). 2
As labor conditions are clearly different in the US than developing countries, FRE (2008) use
percent of population with at least a college degree as a more case appropriate proxy for human capital
than secondary educational attainment. FRE (2008) find that within US states a well educated workforce
is important in realizing potential growth effects of FDI and find evidence of a necessary human capital
threshold to experience a greater impact on per capita output growth than domestic investment.
To conclude, the key finding of positive effects of FDI on economic growth given a met threshold of
host human capital has been supported in many studies and in both developing and developed countries.
This is a strong finding that has many potential economic and policy implications that have yet to be
explored. Hence, this is a rich topic that requires further investigation and has been sparse in theoretical
study. This paper attempts to present a theoretical framework that incorporates the human capital
threshold and investigates two basic policy instruments.
3 Model Framework
This paper’s model is based on and building off of the BDL (1998) theoretical model, which has roots
in the Romer (1990) endogenous technological change model. Based on the history of strong empirical
findings regarding it, this paper incorporates the FDI human capital threshold and its relationship to
FDI and growth into the model.
3.1 Derivation
We begin by defining the key variables:3
Y ≡ final good
A ≡ state of the environment
K ≡ physical capital
H ≡ human capital
H ≡ human capital threshold
x(j) ≡ capital good j in continuum of varieties
m(j) ≡ capital good j rental rate
N ≡ total varieties of capital goods in economy
N∗
≡ total world varieties of capital goods
n ≡ capital good varieties produced by domestic firms
n∗
≡ capital good varieties produced by foreign firms
F(•) ≡ fixed setup cost of technology adaptation
r ≡ interest rate
C ≡ consumption
σ ≡ risk aversion
ρ ≡ time discounter
1This emphasizes the importance of quality in education as higher quality reduces the required quantity.
2FDI flow data may be suspect as it represents present investment, thus it assumes that related effects take place in
the same period. Hence it is unlikely that flow data reflects effects of spillovers to domestic firms. In this case sign and
significance both hold, but it is the magnitude that is suspect. To get around this problem FRE (2008) measure FDI
through the average share of nonbank employment.
3This paper begins by following closely the derivation method of its framework from BDL (1998)
3

We define an economy with a single consumption good following a constant returns to scale Cobb-
Douglas HK production:
Yt = AHα
t K1−α
t (1)
H0 & K0 given
The economy has an aggregate of N accumulating varieties of capital goods that comprises physical
capital. Thus physical capital expands through increasing N. So at each time period:
K =
N
0
x(j)1−α
dj
1
1−α
(2)
Furthermore, in the economy there are two types of firms which produce capital goods: domestic and
foreign. All firms directly invest in the economy. Hence,
N = n + n∗
(3)
As well, equations 1 and 2 imply that the marginal productivity of an individual capital good is:
∂Y
∂x(j)
= A(1 − α)Hα
x(j)−α
Firms are assumed to rent produced capital goods to final goods producers. Thus, the optimality
condition would imply the good’s rental rate would equal the good’s marginal productivity,
m(j) = A(1 − α)Hα
x(j)−α
(4)
Certain technologies must be adapted in order for an increase in the amount of capital varieties.
Technology adaptation is assumed to be costly, with fixed setup costs (F). Foreign firms are assumed
to bring advanced ‘knowledge’ on new capital goods that may be available in other countries, thereby
potentially making it easier to adopt the technology. Thus technology adaptation costs have a negative
relationship to the ratio of foreign firms to total number of firms (n∗
N ). Based on the strong empirical
findings over the last two decades regarding the human capital threshold on FDI as previously discussed,
we make the assumption that if the human capital threshold is not met foreign firms are not able to
adequately capture gains from an advance in ‘knowledge’. Thus technology adaptation costs incurred in
this case may be no different than domestic firms or perhaps even greater. Also there is assumed to be a
‘catch-up’ effect, where it is cheaper to imitate certain products over others,typically products that have
been around longer. This is achieved by imposing a positive relationship between technology adaptation
costs and the ratio of varieties in an economies to the varieties in the world ( N
N∗ ). Thus,
F
n∗
N
,
N
N∗
, H (5)
where:



∂F
∂(
n∗
N
)
< 0, if H ≥ H
∂F
∂(
n∗
N
)
≥ 0, otherwise
and
∂F
∂(
N
N∗
)
> 0
4

We then assume capital goods fully depreciate in each time period and steady state where interest
rate (r) is constant. So capital firms profits for new variety of capital j are:
Π(j)t =
∞
t
[m(j)x(j) − x(j)]e−r(s−t)
ds − F
n∗
N
,
N
N∗
, H (6)
Maximizing equation 6 subject to 4 yields:
x(j) = A
1
α (1 − α)
2
α H (7)
Further, equation 7 back into 4 finds rental rate:
m(j) = (1 − α)−1
(8)
Assuming free entry into market we can conclude equilibrium profits will be zero. Thus with zero
profits condition we can solve for interest rate:
r = A
1
α φF
n∗
N
,
N
N∗
, H
−1
H (9)
where, φ = α(1 − α)
2−α
α
Consumers maximize a CRRA utility function:
Ut =
∞
t
C1−σ
s
1 − σ
e−ρ(s−t)
ds (10)
Thus optimal consumption path with rate of return equal to interest rate,
˙Ct
Ct
=
1
σ
(r − ρ) (11)
So in steady state equilibrium consumption growth is equal to output growth:
g =
1
σ
(r − ρ) (12)
Hence by substituting equation 9 into 12 we derive the economy growth rate:
g =
1
σ
A
1
α φF
n∗
N
,
N
N∗
, H
−1
H − ρ (13)
3.2 Extending Model with Tax and Subsidy
Suppose now there is a tax, τ, imposed on foreign firms. Assume that:
n∗
(τ), such that
∂n∗
∂τ
< 0 (14)
Also suppose a subsidy for human capital formation activities, ξ. Assume that:
H(ξ), such that
∂H
∂ξ
> 0 (15)
Thus one can restate equation 13 incorporating these definitions:
g(τ) =
1
σ
A
1
α φF
n∗
(τ)
N
,
N
N∗
, H(ξ)
−1
H(ξ) − ρ (16)
Note that the definitions from 14 and 15 imply the following relations:
n∗
(τ) < n∗
(0)
H(ξ) > H(0)
5

4 Results
Generally, we find that equation 13 implies:
∂g
∂(n∗
N )
= −
1
σ

A
1
α φ
F n∗
N , N
N∗ , H
F n∗
N , N
N∗ , H
2 H + ρ

 (17)
hence,
∂g
∂(n∗
N )
=
> 0, if H ≥ H
≤ 0, otherwise
This is congruent with previous empirical results, that FDI (n∗
N ) affects economic growth positively when
the human capital threshold is met but has either no effect or a negative effect when not met.
In the following subsections this paper analyses the effect on economic growth from implementing
the two basic policies, a tax on foreign firms and a subsidy to human capital formation. Analysis is done
by comparing an economy with the enacted policy to a baseline economy with no such policies.
4.1 With Tax Alone
Consider a policy of a simple tax specifically on foreign firms as denoted earlier. We compare the growth
of an economy that has the policy of a tax on foreign firms, g(τ), and an economy that has no such
policy, g(0). We can assume for the analysis that the tax revenue is destroyed.
In analysing a policy of placing a tax on foreign firms, we find two distinct cases of whether or not
the human capital threshold is met.
Case 1: H ≥ H
This case is when the human capital threshold is met. Begin with comparing technology adaptation
fixed costs,
F
n∗
(τ)
N
,
N
N∗
, H > F
n∗
(0)
N
,
N
N∗
, H
due to
∂F
∂ n∗
N
< 0 and n∗
(τ) < n∗
(0). Hence,
F(τ, •)−1
< F(0, •)−1
F(τ, •)−1
H < F(0, •)−1
H
So equation 16 implies4
that,
g(τ) < g(0) (18)
Under the case where the human capital threshold is met, a policy of a tax on foreign firms yields a
lower economic growth rate than the baseline. Therefore, as one would expect placing a special tax on
foreign firms would reduce the growth of an economy.
4Equation normalized with ξ = 0 in this subsection.
6

Case 2: H > H
In this case the economy does not satisfy the human capital threshold. So fixed setup costs of
technology adaptation compared are:
F
n∗
(τ)
N
,
N
N∗
, H ≤ F
n∗
(0)
N
,
N
N∗
, H
due to
∂F
∂ n∗
N
≥ 0.5
Hence,
F(τ, •)−1
H ≥ F(0, •)−1
H
Hence, equation 16 implies that,
g(τ) ≥ g(0) (19)
So interestingly, placing a tax on foreign firms when the human capital threshold is not met weakly in-
creases economic growth rates. Note too that under this same framework if τ2 > τ1, then g(τ2) ≥ g(τ1);
which implies that the greater restriction there is on foreign firms the higher growth will be.
Therefore, we find that placing a tax on foreign firms when an economy falls below the human capital
threshold results in a weakly higher growth rate than the case in which there is no such restrictions on
foreign firms. However, if an economy is in a state above the human capital threshold then a tax has the
expected result of constricting the affected firms and lowering economic growth.
4.2 With Subsidy Alone
Consider the policy of a simple subsidy that increases human capital as denoted earlier. Adopting a
policy of subsidizing human capital formation one finds expected results as predicted by the BDL (1998)
theoretical model. We find three distinct cases:
Case 1: H > H(ξ) > H(0)
In the case where both levels of human capital fall below the threshold, comparing technology adap-
tation costs yields,
F
n∗
N
,
N
N∗
, H(ξ) = F
n∗
N
,
N
N∗
, H(0)
as human capital does not directly affect the technology adaptation costs but instead the partial derivative
of FDI. Then of course follows:
F(ξ, •)−1
= F(0, •)−1
F(ξ, •)−1
H(ξ) > F(0, •)−1
H(0)
Hence a modified equation 16,6
g(ξ) > g(0) (20)
5Also n∗(τ) < n∗(0)
6Equation normalized with τ = 0 and denoted as g(ξ) in this subsection.
7

Case 2: H(ξ) ≥ H > H(0) In this case the economy with the subsidy meets human capital
threshold, but the baseline does not. It follows,
F
n∗
N
,
N
N∗
, H(ξ) < F
n∗
N
,
N
N∗
, H(0)
due to
∂F(ξ, •)
∂
n∗
N
< 0 and
∂F(0, •)
∂
n∗
N
≥ 0. So in extension,
F(ξ, •)−1
> F(0, •)−1
F(ξ, •)−1
H(ξ) > F(0, •)−1
H(0)
Again equation 16 then implies,
g(ξ) > g(0) (21)
Case 3: H(ξ) > H(0) ≥ H
Lastly when both levels of human capital satisfy the threshold,
F
n∗
N
,
N
N∗
, H(ξ) = F
n∗
N
,
N
N∗
, H(0)
again because human capital does not directly affect the technology adaptation costs, as in Case 1.
It follows,
F(ξ, •)−1
= F(0, •)−1
F(ξ, •)−1
H(ξ) > F(0, •)−1
H(0)
So finally equation 16 infers,
g(ξ) > g(0) (22)
Therefore, we find that in all three cases the economic growth rate is strictly higher with the subsidy
than in the baseline. This is what we would expect, as one of the original results from the BDL (1998)
theoretical model is a positive correlation between human capital and economic growth. Note that
uniquely in the case where the economy with the subsidy meets human capital threshold but the baseline
economy does not, technology adaptation costs F are strictly lower. This policy runs into obvious issues
in terms of funding and may not outweigh opportunity costs for funding other programs.
5 Conclusion
Literature shows strong evidence of the existence of a necessary human capital threshold. Virtually all
related studies, in both developing and developed countries, have found that FDI is positively correlated
with economic growth conditional on the condition that a minimum human capital threshold is met; if
this condition is not met effects are found to be statistically insignificant from zero or even negative.
There appears to be no prior existing theoretical model that incorporates this finding. This paper builds
off of BDL’s (1998) theoretical model to incorporate this human capital threshold and evaluate basic
policy actions.
This paper theoretically evaluates the policy actions of a tax placed on foreign firms and a subsidy to
human capital formation. It is demonstrated that when an economy does not meet the FDI human capital
threshold it can weakly increase economic growth rates by placing a tax on foreign firms. However if the
8

human capital threshold is met, placing a tax on foreign firms would strictly decrease the economic growth
of an economy. Furthermore, this paper illustrates a subsidy on human capital formation would strictly
increase economic growth in all cases. These are obviously potentially important policy implications and
require further rigorous investigation.
References
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[19] Xu, Bin. “Multinational enterprises, technology diﬀusion, and host country productivity growth.”
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