Thông tin tài liệu
ENTREPRENEURIAL NETWORKING,
INTERNATIONAL OUTSOURCING AND WAGE
INEQUALITY
KOH PHUAY LENG
(B.Soc. Sci.(Hons.), NUS)
A THESIS SUBMITTED
FOR THE DEGREE OF MASTER OF SOCIAL SCIENCE
DEPARTMENT OF ECONOMICS
NATIONAL UNIVERSITY OF SINGAPORE
2006
i
ACKNOWLEDGEMENTS
First and foremost, I will like to express my heartfelt gratitude and thanks to Dr
Ho Kong Weng, for his great patience and guidance in the development of the paper. In
particular, his valuable insightful comments, directions and explanations have enabled me
to smoothly complete this thesis. I will also like to thank Dr Chang Youngho for his
supervision and comments on the dissertation.
Secondly, I will like to thank my family members and Mr. Yan Cheok Kin for
their constant support and encouragement throughout the entire process. I am especially
thankful to my younger brother, Mr. Koh Chee Hui for proof reading my thesis. Special
thanks to Miss Tan Teck Kiah for her valuable help and patience in the use of MATLAB.
I will also like to grab the opportunity to thank Mr. Lin Zhiming and Mr. Kelvin Foo for
their comments and help respectively. In addition, here’s a big thanks to all other good
friends who have given me their great support and help in one way or another.
Koh Phuay Leng
August 2006
ii
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS
i
TABLE OF CONTENTS
ii
SUMMARY
iv
LIST OF TABLES
vi
LIST OF FIGURES
vii
LIST OF SYMBOLS
xii
1.
1
2.
INTRODUCTION
THE MODEL
2.1
2.2
2.3
2.4
2.5
3.
A Simple Static Model
The production process
2.2.1 Firms Choosing To Adopt Vertical Integration
2.2.2 Firms Choosing To Engage In Outsourcing Activities
Profit Functions
Optimization Behavior Across The Economy
2.4.1 Firms Engaging In Vertical Integration
2.4.2 Firms Engaging In Outsourcing Activities
Equilibrium
2.5.1 Threshold Level of Managerial Ability
2.5.2 Labor Market Equilibrium
7
7
8
8
9
10
11
11
13
15
15
17
DYNAMIC MODEL
20
3.1
3.2
3.3
3.4
3.5
3.6
20
21
23
25
26
27
30
34
The Model
Baseline Steady-state System
Parameterization
Simulation Results
Welfare Of The Domestic Country
Comparative Statics Analysis
3.6.1 Cost Before Quality Adjustment, ρ
3.6.2 Changes In Parameters Affecting Networking Of Both Types Of
Entrepreneurs
3.6.2.1 A Decrease In Inverse Of Networking Efficiency In
Outsourcing Mode, k1
3.6.2.2 A Decrease In Inverse Of Networking Efficiency In
Vertically Integrated Mode, k 2
3.6.3 Changes In Parameters Affecting Both Local And Foreign Labor
Markets
3.6.3.1 An Increase In Human Capital In The Local Labor
Market, H
3.6.3.2 An Increase In Human Capital In The Foreign Labor
Market, h
3.6.4 Change In Parameters Related To Efficiency Of Training
34
39
44
44
47
51
iii
3.6.4.1 A Decrease In Entrepreneurial Overload In Training
Unskilled Labor, α
3.6.4.2 A Decrease In Entrepreneurial Overload In Training
Skilled Labor, γ
3.7
4.
3.6.5 A Change In Parameter Relating To Matching Ability, b
Comparison With Previous Literature Results
GENERAL DISCUSSION
51
54
57
61
68
5.
CONCLUSION
69
6.
BIBLIOGRAPHY
72
7.
APPENDIX A
74
iv
Summary
The recent phenomenon of international outsourcing has taken place over the past
few years. Based on OECD data, it is observed that the United States and the United
Kingdom have experienced an upward trend on wage inequality over the years. Previous
studies have linked the reason behind such a trend to the evolution of technology either
due to international outsourcing or skilled-biased technical change. In this paper, we
investigate the impact of international outsourcing on both wage inequality and
entrepreneurs’ decision to outsource or perform in-house production. In addition, we
postulate that technology evolves over time due to spillover effects by networks formed
among firms undertaking integrated and outsourcing modes of production. Such an
evolution of technology will affect the wage inequality between skilled and unskilled
workers and the welfare of entrepreneurs versus domestic workers.
We construct a simple dynamic model for a small, developed and open economy
whereby the equilibrium organization of firms changes due to the formation of networks
among domestic firms that undertake vertical integration and those that are engaged in
outsourcing activities. The growth of integrated productivity and network knowledge
stocks over time contributes to the growth of a common aggregate stock, which has
spillover effects on the domestic economy in the next period. There exists a unique
threshold level of entrepreneurial ability below (above) which firms elect to do vertical
integration (international outsourcing). We show that in the long run, slightly more than
half of the entrepreneurs will choose to do vertically integrated production.
Although a static model without the evolution of the various stocks is inadequate
in explaining the impact of networking on the domestic economy, it is able to explain the
impact of other exogenous parameters adequately. We show that a reduction in the cost of
manual components, an increase in foreign human capital and efficiency of matching
firms with overseas supplier will increase the fraction of firms choosing to do outsourcing
v
and subsequently affect wage inequality.
In addition, we investigate the impact of
networking on GDP over time and find that an increase in outsourcing activities will
benefit the welfare of entrepreneurs while decreasing the welfare of domestic workers.
Furthermore, one of our striking results is that an increase in outsourcing activities is not
necessary beneficial to the domestic economy throughout all cases. An increase in the
ability of the entrepreneurs to match domestic firms to overseas supplier will result in a
lower GDP in the long run.
vi
LIST OF TABLES
1
Parameter Values Used for Baseline Static Model
2
Parameter Values Used for Baseline Simulation
3
Baseline Steady State Values
4
Baseline Values for Various Components of GDP
5
Summary of Comparative Statics Results for Baseline Static Model
6
Summary of Comparative Statics Results for Dynamic Model
7
Summary of Outcomes of Comparative Statics Exercise for an Increase in
Selected Parameters
8
Summary of GDP Outcomes of Comparative Statics Exercise for an Increase
in Selected Parameters
9
Comparison with Previous Literature Results (1)
10
Comparison with Previous Literature Results (2)
vii
LIST OF FIGURES
1-1
Percentage Ratio of Volume of Exports and Imports Between U.S Parent
Companies and Their Foreign Affiliates and Total Volume of U.S Exports
and Imports
2-1
Profits of Integration and Outsourcing Firms
3-1
Evolution Of Threshold Level of Entrepreneurial Ability mt* for 1%
Decrease in ρ
3-2
wts
Evolution of Wage Gap u for 1% Decrease in ρ
wt
3-3
Evolution of GDP for 1% Decrease in ρ
3-4
Evolution of Total Profits of All Firms Undertaking Integrated Mode of
Production for 1% Decrease in ρ
3-5
Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of
Production for 1% Decrease in ρ
3-6
Evolution of Total Unskilled Labor Income for 1% Decrease in ρ
3-7
Evolution of Total Skilled Labor Income for 1% Decrease in ρ
3-8
Evolution of Ratio of Total Skilled Labor Income to Total Unskilled
Labor Income for 1% Decrease in ρ
3-9
Evolution Of Threshold Level Of Entrepreneurial Ability mt* for 1%
Decrease in k1
3-10
Evolution of Common Aggregate Stock Tt for 1% Decrease in k1
3-11
Evolution of Network Knowledge Stock K t for 1% Decrease in k1
3-12
Evolution of Integrated Productivity stock At for 1% Decrease In k1 for 1%
Decrease in k1
viii
3-13
wts
Evolution of Wage Gap u for 1% Decrease in k1
wt
3-14
Evolution of GDP for 1% Decrease in k1
3-15
Evolution of Total Profits of All Firms Undertaking Integrated Mode of
Production for 1% Decrease in k1
3-16
Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of
Production for 1% Decrease in k1
3-17
Evolution of Total Unskilled Labor Income for 1% Decrease in k1
3-18
Evolution of Total Skilled Labor Income for 1% Decrease in k1
3-19
Evolution of Ratio of Total Skilled Labor Income to Total Unskilled
Labor Income for 1% Decrease in k1
3-20
Evolution of Common Aggregate Stock Tt for 1% Decrease in k 2
3-21
Evolution of Ratio of Network Knowledge Stock to Aggregate Stock
Kt
for
Tt
1% Decrease in k 2
3-22
Evolution Of Ratio of Integrated Productivity Stock to Aggregate Stock
At
Tt
for 1% Decrease in k 2
3-23
Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Decrease
in k 2
wts
for 1% Increase in k 2
wtu
3-24
Evolution of Wage Gap
3-25
Evolution of GDP for 1% Decrease in k 2
3-26
Evolution of Total Profits of All Firms Undertaking Integrated Mode of
Production for 1% Decrease in k 2
ix
3-27
Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of
Production for 1% Decrease in k 2
3-28
Evolution of Total Unskilled Labor Income for 1% Decrease in k 2
3-29
Evolution of Total Skilled Labor Income for 1% Decrease in k 2
3-30
Evolution of Ratio of Total Skilled Labor Income to Total Unskilled
Labor Income for 1% Decrease in k 2
3-31
Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Increase
in H
3-32
wts
Evolution of Wage Gap u for 1% Increase in H
wt
3-33
Evolution of GDP for 1% Increase in H
3-34
Evolution of Total Profits of All Firms Undertaking Integrated Mode of
Production for 1% Increase in H
3-35
Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of
Production for 1% Increase in H
3-36
Evolution of Total Unskilled Labor Income for 1% Increase in H
3-37
Evolution of Total Skilled Labor Income for Increase in H
3-38
Evolution of Ratio of Total Skilled Labor Income to Total Unskilled
Labor Income for 1% Increase in H
3-39
Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Increase
in h
wts
for 1% Increase in h
wtu
3-40
Evolution of Wage Gap
3-41
Evolution of GDP for 1% Increase in h
3-42
Evolution of Total Profits of All Firms Undertaking Integrated Mode of
Production for 1% Increase in h
x
3-43
Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of
Production for 1% Increase in h
3-44
Evolution of Total Unskilled Labor Income for 1% Increase in h
3-45
Evolution of Total Skilled Labor Income for Increase in h
3-46
Evolution of Ratio of Total Skilled Labor Income to Total Unskilled
Labor Income for 1% Increase in h
3-47
Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Decrease
in α
wts
for 1% Decrease in α
wtu
3-48
Evolution of Wage Gap
3-49
Evolution of GDP for 1% Decrease in α
3-50
Evolution of Total Profits of All Firms Undertaking Integrated Mode of
Production for 1% Decrease in α
3-51
Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of
Production for 1% Decrease in α
3-52
Evolution of Total Unskilled Labor Income for 1% Decrease in α
3-53
Evolution of Total Skilled Labor Income for 1% Decrease in α
3-54
Evolution of Ratio of Total Skilled Labor Income to Total Unskilled
Labor Income for 1% Decrease in α
3-55
Evolution of Threshold Level of Entrepreneurial Ability mt* for 1% Decrease
in γ
wts
for 1% Decrease in γ
wtu
3-56
Evolution of Wage Gap
3-57
Evolution of GDP for 1% Decrease in γ
3-58
Evolution of Total Profits of All Firms Undertaking Integrated Mode of
Production for 1% Decrease in γ
xi
3-59
Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of
Production for 1% Decrease in γ
3-60
Evolution of Total Unskilled Labor Income for 1% Decrease in γ
3-61
Evolution of Total Skilled Labor Income for 1% Decrease in γ
3-62
Evolution of Ratio of Total Skilled Labor Income to Total Unskilled
Labor Income for 1% Decrease in γ
3-63
Evolution of Threshold Level of Entrepreneurial Ability mt* for 1%
Decrease in b
3-64
wts
Evolution of Wage Gap u for 1% Decrease in b
wt
3-65
Evolution of GDP for 1% Decrease in b
3-66
Evolution of Total Profits of All Firms Undertaking Integrated Mode of
Production for 1% Decrease in b
3-67
Evolution of Total Profits of All Firms Undertaking Outsourcing Mode of
Production for 1% Decrease in b
3-68
Evolution of Total Unskilled Labor Income for 1% Decrease in b
3-69
Evolution of Total Skilled Labor Income for 1% Decrease in b
3-70
Evolution of Ratio of Total Skilled Labor Income to Total Unskilled
Labor Income for 1% Decrease in b
xii
LIST OF SYMBOLS
α
β
γ
δ
ρ
χ
a
b
d
h
v
Entrepreneurial overload in training unskilled labor
Diminishing rate of unskilled workers
Entrepreneurial overload in training skilled labor
Diminishing rate of effective labor hired in integrated production
Cost before quality adjustment
Diminishing rate of manual component
Inefficiency of network knowledge contributing to present period output
Inverse of matching between domestic firms and overseas supplier
Diminishing rate of effective labor hired in outsourcing
Human capital in foreign labor market
Decrease in efficiency of foreign labor producing low-skilled intensive
components
HLSO
t
Effective workers
LUt
Unskilled workers
S
L
U
L
H
n1
n2
C1
C2
k1
k2
ε1
ε2
Vf
Skilled labor supply
Unskilled labor supply
Human capital in local labor market
Inefficiency of last period aggregate stock contributing to current network
knowledge
Inefficiency of last period aggregate stock contributing to current network
knowledge
Aggregate productivity in evolution of network knowledge stock
Aggregate productivity in evolution of integrated productivity stock
Rate at which previous network knowledge depreciates.
Rate at which previous integrated productivity stock depreciates.
Rate at which previous network knowledge depreciates.
Rate at which previous integrated productivity stock depreciates.
Manual component
1
1.
Introduction
By splitting up the production process into various components, international
outsourcing has transformed the behavior of firms such that they no longer have to
constrain production within the domestic country as they can now take advantage of the
lower costs overseas. This is especially so when the host country for fragmented
production components is a developing country. At the same time, the role of
entrepreneurship has become increasingly important to not only utilize the cost
advantage but also to manage production (Acemoglu et al., 2002b).
In this paper, a simple dynamic model for a small, open and developed
economy is constructed to examine the impact of the formation of network knowledge
due to international outsourcing on the three key types of players in the domestic
economy, which are namely the entrepreneurs, skilled and unskilled workers. We seek
to investigate 1) the welfare between entrepreneurs and domestic workers and 2) the
wage inequality between skilled and unskilled workers. The model is able to trace the
evolution of GDP, profits, and wage incomes over time given various shocks to the
economy.
Greiner, Rubart and Semmler (2004) have observed that wage inequality had
been increasing in the United States (U.S) and the United Kingdom (U.K) from early
1960s to late 1990s1. However, the pattern of wage inequality for West Germany is
unclear. Using OECD data, they observed that wage inequality in West Germany has
been decreasing over time from 1984 to 1996. In contrast, using disaggregated data
from the Federal Office of Statistics, they observed that there is an upward trend in
wage inequality. Most studies have attributed the upward trend due to the evolution of
technology. Some of the most commonly cited reasons for the evolution of technology
over time are skilled-biased technological change (Galor and Moav, 2000) and the
1
For the U.S, U.K and West Germany, cross-country data of wage differentials are taken from OECD
Employment Outlook (1993,1996) whereby wage inequality is measured using the ratios of the 10th and
50th percentile to the 90th percentile wage earners.
2
development of skill-complementary technology due to the rapid increase in the supply
of skilled labor (Acemoglu et al., 2002a). DeGroot (2001) also proposed that an
increase in the efficiency of R&D labor via the accumulation of own past knowledge
can achieve technical progress. Moreover, under the assumption that capital and
unskilled labor are complements, Greiner, Rubart and Semmler (2004) postulated that
technical progress is embodied within new capital goods since the amount of new
capital goods affects the efficiency of both skilled and unskilled labor. According to
Gao (2005)’s paper, he also postulated that the world’s growth rate increases when
more resources are concentrated on R&D in the North2, given a reduction in trade costs
due to globalization. Egger and Grossmann (2005) further postulated that the provision
of firm-specific on-the-job training by high-skilled, non-production labor leads to
accumulation of human capital.
We break away from these usual conventions by postulating that the change in
wage inequality over time is mainly due to the interaction effects of network stocks
formed by entrepreneurs involved in integrated and outsourcing modes of production.
One major motivation for the incorporation of network knowledge is that international
outsourcing can be hindered by informal trade barriers, such as weak enforcement of
international contracts (Anderson and Marcouiller, 2002) and inadequate information
about international trading opportunities (Portes and Rey, 1999). Thus, we adopt Rauch
(2001)’s approach whereby the development of business and social networks operating
across national borders not only alleviate these problems, but also help in facilitating the
transfer of technology to the recipient country. These networks also enable foreign agents
to be connected to domestic networks via intermediaries.
This is consistent with the increasing role of intra trade between parent firms and
their affiliates as observed in reality. In Figure 1-1, although there are some fluctuations
2
A North-South endogenous growth model is used, whereby the North is abundant in skilled-labor. It
is also assumed to be the only innovator in the world. In the model, there is relocation of production of
unskilled components to the South.
3
in the ratio of volume of imports and exports between U.S parent companies and their
foreign affiliates to the total volume of U.S imports and exports from 1982 to 1988, there
is an upward trend in the percentage ratio from 1989 to 1994. Hence, over the period of
12 years, intra trade between U.S parent companies and their foreign affiliates has been
steadily increasing from 18.8% in 1982 to 21.6% in 1994.
FIGURE 1-1: PERCENTAGE RATIO OF VOLUME OF EXPORTS AND IMPORTS
BETWEEN U.S PARENT COMPANIES AND THEIR FOREIGN AFFILIATES TO
TOTAL VOLUME OF U.S EXPORTS AND IMPORTS
22.0%
21.5%
21.0%
20.5%
20.0%
19.5%
19.0%
18.5%
18.0%
17.5%
17.0%
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Source: Our computations are based on U.S data from the Bureau of Economic Analysis3
In addition, using input-output data from six OECD countries and German timeseries data, Kleinert (2003) has also found strong empirical evidence of growing trade in
intermediate goods due to the increasing importance of Multinational Enterprises (MNE)
networks.
The development and enhancement of such networks can lead to the accumulation
of knowledge due to learning activities from abroad through the overseas intermediaries.
As a result, technical progress takes place. For instance, through establishing
intermediaries in Singapore, Multinational Corporations (MNCs) have gained knowledge
such as better labor and capital management, and more efficient management of
3
We obtain the ratio by dividing the volume of exports and imports in terms of millions of US dollars
between U.S parent companies and their foreign affiliates by the total volume of U.S exports and
imports in terms of millions of US dollars. This is in turn multiplied by 100% in order to obtain the
percentage ratio.
4
processing activities. They can therefore apply the knowledge gained to their parent
companies, hence increasing their efficiency and output over time. We therefore adopt a
simple framework that captures the evolution of technology due to the formation of
networks.
Using a simple dynamic model, we assume that there are two organizational
forms of production in the domestic economy producing similar final products, namely
vertically integrated production and outsourcing. We further assume that firms in the
developed country are homogeneous and unconstrained by contracts. Firms adopting the
vertically integrated mode of production are defined to produce both manual and skilled
components, thereafter combining them to form a final product. In contrast, firms
engaged in the outsourcing mode concentrate on producing skilled components and
purchase manual components from an overseas supplier in a foreign, developing country,
which is abundant in unskilled labor. The final product is produced through assembling
them by the domestic firms. We hence investigate the impact of domestic firms forming
networks within the two modes of production respectively, on the domestic economy. To
introduce dynamics to the model in a simple manner, we let both types of networking
affect the growth of integrated productivity stock and entrepreneurial network stock over
time, which will in turn affect the aggregate stock of knowledge in the economy. The
aggregate stock of knowledge will also influence the accumulation of the stocks of
integrated productivity and entrepreneurial network in the next period. In this manner, we
examine the dynamic linkage between the three stock variables – integrated productivity
stock, entrepreneurial network stock, and aggregate stock of knowledge in the economy.
We examine the above model via the incorporation of entrepreneurial ability to
determine the threshold level above which international outsourcing will occur, which is
often neglected by previous literature. This is crucial since entrepreneurs are required to
train workers and coordinate outsourcing activities. In the outsourcing mode of
5
production, entrepreneurial ability is required to find the appropriate suppliers in the
foreign, developing country. At the same time, entrepreneurs are required to train skilled
labor to produce skilled components. Hence, the higher the ability to match firms to
supplier, the higher the profit earned by the domestic firms. In the other mode of
production, there is no need for entrepreneurial ability in matching since the integrated
form of production is done in-house. However, entrepreneurial time is required to train
both skilled and unskilled labor to produce skilled and unskilled components respectively.
Another key assumption to note is that both home and foreign countries are assumed to
have totally different production structures. Thus, human capital is assumed to be
exogenous and different across the two countries.
This idea is similar to the manager in Acemoglu et al. (2000b)’s model who have
to spend time on both production and innovation activities, where skills are more
important for the latter. However, in their paper, there exists only corner solution in the
economy which is namely imitation-based or innovation-based equilibrium. This is
mainly due to their assumption that the skill level of the manager takes on only two
values to indicate that he is either high or low-skilled. We differ from their paper by
assuming that the ability is uniformly distributed among entrepreneurs so as to allow for a
mixed equilibrium, which is more consistent with reality. This implies that the higher the
threshold level of entrepreneurial ability, the lower the fraction of firms outsourcing the
manual part of the production activities.
The idea of the threshold level of entrepreneurial ability is reminiscent of
managerial incentives in Grossman and Helpman (2003). Using a threshold level of
revenue that acts as the main determinant in choosing the organizational form and the
location of their subsidiaries or suppliers, managerial incentives of heterogeneous firms in
an industry were examined in the short run. This is under the assumption that the
principals of a firm are constrained in the nature of contracts with suppliers and
6
employees. These principals can elect to outsource the production of components by
choosing a supplier either in the North or in the South. Input costs and skills required to
head a production unit are assumed to be lower in the South. They mainly investigated
how firms with different productivity levels are sorted into different organizational forms.
They suggested that the least and most productive firms will choose to obtain components
from external suppliers from the South and the North respectively. Moreover, firms that
operate foreign subsidiaries will be less productive than those that manufacture their own
components in a plant nearer to their headquarters. Even though we adopt a different
approach from theirs, our model in this paper however provides a richer picture since we
investigate the transition of the threshold level of entrepreneurial ability over time.
Our results reveal that there exists a mixed equilibrium in the long run whereby at
a unique threshold level of entrepreneurial ability, slightly more than half of the firms in
the economy will prefer vertical integration to international outsourcing. This is
consistent with the trend in Figure 1 whereby the share of intra trade between U.S parent
companies and foreign affiliates accounted for less than 50% of U.S total trade in the time
period between 1982 and 1994. We also show that although the static model (without the
evolution of the stock variables) is inadequate in explaining the impact of networking on
the domestic economy, it is able to explain the impact of other exogenous parameters. We
find that a reduction in the inefficiency of matching domestic firms to overseas supplier
and a decline in the cost of manual components obtained from the overseas supplier will
result in a lower threshold level of managerial ability. At the same time, wage inequality
falls. Going one step further, we also compare our findings with previous literature’s
results and find that most studies have only examined the impact on wage inequality or
the decision to outsource, but not both at the same time. Hence, we are able to provide a
richer model on the interdependence between entrepreneurs, skilled and unskilled workers.
7
Our model also reveals that as outsourcing activities increase, the welfare of
workers decreases, while entrepreneurs’ welfare increases. Hence there is a trade off
between the welfare of workers and entrepreneurs. Ethier (2005) has postulated that given
the degree of complementarity between skilled labor and equipment, an increase in
fragmentation will worsen the policy trade off of limiting the skill premium while
maximizing employment. Our model is richer than Ethier’s as he has failed to take into
account the role of entrepreneurs, hence neglecting to compare welfare between
entrepreneurs and domestic workers.
The remainder of our paper is organized as follows. Section 2 presents the static
model and static optimization. Section 3 outlines the dynamic model and its steady state
outcome, followed by a detailed discussion on the comparative statics for both static and
dynamic models. A general discussion on the implications of the results is provided in
Section 4. Section 5 concludes this paper.
2.
The Model
In this section, we first examine a simple static model set up before looking at the
dynamic model in the latter section, whereby the evolution of network knowledge and
integrated productivity stocks is introduced.
2.1
A Simple Static model
In our model setup, we adopt some features similar to Acemoglu et al. (2002b).
The economy consists of a continuum of non-overlapping generations of one-period lived
agents. In each generation, there constitutes a mass 1 of entrepreneurs, which are the
owners of the intermediate firms in the economy. They are profit maximizers and have
the option to either engage in vertical integration within the economy, or to outsource the
manual aspect of the production process to a foreign, developing country with abundant
8
unskilled labor, depending on the level of their entrepreneurial ability. Thus, there are two
organizational forms of production in the economy. Firms produce according to an
aggregate production function, which varies according to the form chosen. Hence, firms
undertaking either mode of production produce a single, all-encompassing final good of
unitary price, and operate within a perfectly competitive environment.
2.2
The Production Process
Firms require either a combination of technology, unskilled labor and human
capital augmented skilled labor or previous period network knowledge and human capital
augmented skilled labor, depending on the organizational form of production chosen. All
firms adhere to an aggregate Cobb-Douglas production function which satisfies the usual
Inada conditions. We further assume that all firms experience decreasing returns to scale.
To simplify the analysis, we assume that there is a fixed exogenous supply of high-skilled
and low-skilled labor in the economy. Hence, we assume that skilled labor is mobile
between firms undertaking the two different forms of production:
L S = LSI + LSO
(1)
and total labor supply in the economy is equivalent to:
L = LU + L S
2.2.1
(2)
Firms Choosing To Adopt Vertical Integration
The Cobb-Douglas production function is:
B I = f (t tu , Lt )g (t ts , HLSIt ) = t tu Lut At t ts ( HLSIt ) δ
α
β
γ
(3)
where α , β , γ , δ ∈ (0,1) . Firms hire unskilled labor Lut and human capital augmented
skilled labor or effective labor HLSIt , and therefore incur wage costs from hiring skilled
and unskilled labor, which are denoted by wtu and wts respectively. In addition,
9
entrepreneurs are required to split their time in training unskilled labor, t tu and skilled
labor, t ts , such that:
t tu + t ts = 1
(4)
According to Acemoglu et al. (2002b), managerial overload is modeled by
introducing a convex cost of effort into the cost function, whereby the higher the
managerial effort, the higher the marginal cost of such effort. Since our model does not
have a cost function for the coordination of activities for firms involved in integrated
production, we model entrepreneurial overload in the training of unskilled and skilled
labor through the parameters α and γ respectively, as t tu and t ts lies between zero and
one. Similarly, as Lut and LSI
t are less than one, β and δ imply that unskilled workers
and effective workers increase at a diminishing rate respectively.
2.2.2
Firms Choosing To Engage In Outsourcing Activities
Firms follow an aggregate production structure similar to that adopted in the
vertical integration mode of production for easy comparison:
c
d
B O = V fχ [ K t −1 mt t tSO ( HLSO
t ) ]
a
b
(5)
where a, b, c, d ∈ (0,1) . The firm outsources the manual component to the foreign,
developing country and purchases the manual component V f from the supplier at a unit
cost of
ρ
hν
, where ρ andν ∈ (0,1) . It can also be interpreted as the effective cost incurred
after adjusting for the productivity of the supplier. ρ is seen as an indexing parameter
and represents the cost before quality or productivity adjustment i.e. service link costs
such as telecommunication, transport and coordination costs. A higher ρ would indicate
that cost has increased, leading to an increase in the effective cost of purchasing the
manual component.
10
The cost decreases with an increase in the foreign economy’s human
capital h , h ∈ (0,1) . We assume that better-trained foreign workers are more efficient in
producing the labor-intensive product but such efficiency diminishes with additional
increase in human capital via the parameterν . In addition, it is assumed that the foreign
UN
economy follows a production structure such that V f = λLUN
denotes the total
t where Lt
number of unskilled labor in the developing country and λ is an indexation productivity
parameter for overall production in the foreign country. Since the two countries have
different production structures, V f is assumed to be exogenous and experiences
diminishing returns such that χ ∈ (0,1) . To simplify, V f can be also known as the
marginal product of manual component.
mt denotes entrepreneurial ability and is uniformly distributed between zero and
one. Thus, the parameter b is the inverse of the matching of domestic firms with the
overseas supplier. Since mt p 1 , the ability of a successful match decreases with an
increase in b . It is to be noted that b is exogenous and may be influenced by government
policies that facilitate success matching. K t −1 refers to previous period network
knowledge and lies between zero and one in the static model. Thus, a refers to the
inefficiency of network knowledge contributing to present period output.
Since unskilled components have been outsourced to the foreign country,
entrepreneurs are no longer required to hire and train unskilled workers and can fully
concentrate on training skilled workers. Thus t tu = 0 and t tSO = 1 whereby ttSO denotes the
time spent on training skilled workers in the outsourcing mode of production. Therefore,
c denotes the share of time spent in training skilled labor. Similarly, as HLSO
t is less than
one, the total amount of effective workers increases at a diminishing rate through the
parameter d .
11
2.3
Profit Functions
Assuming that the price of the final product P takes on the unitary value of 1,
firms adopting vertical integration face the aggregate profit function, which is denoted
by π tI :
π tI = B I − wtu Lut − wts LSIt
(6)
On the other hand, the portion of the firms that engages in international outsourcing
activities faces the aggregate profit function, π tO , which is given by:
ρ
V
v f
h
π tO = B O − wts LSO
−
t
2.4
(7)
Optimization Behavior Across The Economy.
Firms maximize their profits subject to the time constraint:
α
Vertical integration: u max
s
u
t t , t t , L t , L SI
t
β
γ
π tI = t tu L ut A t t ts ( HL SIt ) δ − w tu L ut − w ts L SIt
(8)
subject to equation (4).
ρ
a
b SO c
χ
I
SO d
s SO
=
−
−
V
[
K
m
t
(
HL
)
]
w
L
π
Outsourcing: smax
t
f
t
−
1
t
t
t
t
t
hν
t t , LSO
t ,V f
V f
(9)
subject to t tSO = 1 , since t tu = 0 .
The Langrangian for each profit function can be written as follows:
α
β
γ
u
s
Vertical integration: l I = t tu Lut At t ts ( HLSIt ) δ − wtu Lut − wts LSI
t + λ1 (1 − t t − t t )
(10)
ρ
a
c
b
d
s SO
Outsourcing: l O = V fχ [ K t −1 mt t tSO ( HLSO
− ν
t ) ] − wt Lt
h
(11)
V f + λ 2 (1 − t tSO )
where λ1 and λ 2 are the co-state variables for l 1 and l 2 respectively.
2.4.1
Firms Engaging In Vertical Iintegration
The solutions obtained from the first order conditions are as follows:
12
α t tu
α −1
α
β
α
β −1
α
β
L ut
β
γ
A t t ts ( HL
γ t tu L ut A t t ts
β t tu Lut
γ −1
( HL
SI
t
)δ = λ1
(12)
)δ = λ1
SI
t
(13)
γ
A t t ts ( HL SIt ) δ = w tu
(14)
γ
δ t tu L ut A t t ts ( HL SIt ) δ −1 H = w ts
(15)
t tu + t ts = 1
(16)
Equation (12) is seen as the marginal benefit of training unskilled labor to its
marginal cost. Similarly, equation (13) is the marginal benefit of training skilled labor to
its marginal cost. The left hand sides of equations (14)-(15) show the marginal products
of the respective types of labor, whereas the right-hand sides are the marginal costs.
Solving equations (12) to (16), we obtain the following optimal solutions:
t ts =
t tu =
γ
(17)
α +γ
α
(18)
α +γ
Lut =
1
α
Atδ δ H
α + γ
L
SI
t
=
H δ β βδ
δ
α
δ
w ts
γ
α +γ
γ
δ
β + δ −1
1− δ
δ −1
β δ wtu δ
(19)
1
w ts
1− β
(1− β )
w tu
β
α
A t
α + γ
α
γ
α + γ
δ
β + δ −1
(20)
From equations (19) and (20), we observe that the demand functions for unskilled
and skilled labor supply are constrained by wage costs, integrated productivity and human
capital in the economy.
13
Proposition 1: Profit for integrated production is positive if and only if the condition
β + δ p 1 exists.
Proof: See Appendix A.
Hence, proposition 1 shows that both effective and unskilled labor must increase
at a diminishing rate such that profit for integrated production is positive. Otherwise,
firms will have to hire a large amount of effective and unskilled workers, resulting in
negative profit as wage costs increase.
Substituting equations (17) to (20) back into equation (6), we can re-express the
profit function for the intermediate firm that engages in vertical integration as:
δ
β
wts wtu
I
πt =
α
γ
δ α γ
At H α + γ α + γ
1
β +δ −1
1
δ δ β β
1
β +δ −1
1
− δ 1−δ
δ β
− − +
= π tI wts , wtu , At
1
β +δ −1
1
− 1−β β
δ β
1
β +δ −1
(21)
It can be seen that π tI has a positive relationship with integrated productivity whereas
skilled and unskilled wages are inversely related with it.
2.4.2
Firms Engaging in Outsourcing Activities
This time, the solutions under first order conditions are:
χ
a
χ
a
b
cV f K t −1 mt t ts
c −1
d
( HLSO
t ) = λ2
c
d −1
dV f K t −1 mt t ts ( HLSO
H = wts
t )
b
c
d
χV f χ −1 K t −1a mt b t ts ( HLSO
t ) =
t ts = 1
ρ
hν
(22)
(23)
(24)
(25)
14
Equation (22) shows that the marginal benefit of training skilled labor is equaled
to its marginal cost while equation (23) shows the marginal benefit of hiring skilled labor
equaled to its marginal cost. Equation (24) indicates the marginal benefit of manual
component to the marginal cost of acquiring it. Similarly, solving equations (22) to (25),
the optimal solutions are:
ρ
V f = ν
h χ
d −1
1−d − χ
K ad d m b H d
t
t −1
d
s
wt
1
1−d −χ
1
LSO
t
1−d − χ s 1+ dχ −1− dχ
ρ − χ
a
b
d
wt 1− d − χ d 1− d − χ
= ν K t −1 mt H
h χ
(26)
1
d −1
(27)
From equations (26) and (27), it can be seen that the marginal product of manual
component and demand for skilled labor are constrained by the cost of the manual
component, previous period network knowledge stock, entrepreneurial ability, human
capital and skilled wages.
Proposition 2: Profit for outsourcing mode of production is positive if and only if the
condition d + χ p 1 exists.
Proof: See Appendix A.
Thus, proposition 2 indicates that effective labor and marginal product of manual
component must be increasing at a diminishing rate in order for entrepreneurs engaging in
outsourcing activities to earn positive profits. If both increase at an increasing rate,
entrepreneurs will earn negative profit as they have to incur higher costs in hiring more
effective labor and purchasing manual components.
Similarly, substituting equations (26) and (27) back into equation (7):
15
π
O
t
a
b
K m Hd
= t −1 χt
ρ sd
ν wt
h
1
1− d − χ
χ d
χ d
(
)
1
1− d − χ
χ d −1( d+ −χ1−)dχ
−χ d
1
1− d − χ
− χ 1− d d d
(
− + +
= π tO wts , K t −1 , mt
)
1
1− d − χ
(28)
From equation (28), it can be seen that previous period network knowledge,
entrepreneurial ability and human capital are positively related to π tO while skilled wages
and marginal product of manual component are inversely related to it.
2.5
Equilibrium
In this section, we analyze firms’ decision to engage in international outsourcing
or integration, depending on entrepreneurial ability. Firms will only decide to adopt the
former when the profit from engaging in it is greater than that from vertical integration,
i.e. π tO > π tI .
2.5.1
Threshold Level of Managerial Ability
Setting π tI = π tO from equations (21) and (28) and rearranging the terms, we
obtain the critical threshold level of managerial ability:
w
*
mt =
H
s
t
where
δ (1− d − χ )+ d ( β +δ −1)
b ( β +δ −1)
χ
wu β
t
At
(1−d − χ ) ρ
( β +δ −1)b hν
K t −1a
1
b
1− d − χ
W
b
S
(29)
16
1
W =
α
α γ
α + γ α + γ
and S = χ χ d d
(
)
1
1− d − χ
γ
1
β +δ −1
1
δ δ β β
− χ χd
d −1 + χ − d χ
( d −1 )
1
β +δ −1
1
− δ 1−δ
δ β
1
β +δ −1
1
− 1− β β
δ β
)
1
1− d − χ
− χ 1− d d d
(
1
1− d − χ
1
β +δ −1
(30)
(31)
Proposition 3: Given the 3 conditions: 1) β + δ p 1 in Proposition 1, 2) d + χ p 1 in
Proposition 2 and
ρ
ν
s
u δ (1− χ )− d (1− β ) h
3) wt p wt
K t −1 a
χ
β ( χ + d −1)
−
b ( β +δ −1 )
b
W
S
b ( d + χ −1 )( β +δ −1)
b
H δ (1− d − χ )+ d (β +δ −1) At
(1− d − χ )
, an
interior solution exists for mt* .
Proof: See Appendix A.
Proposition 3 indicates that if skilled wages are too large, all entrepreneurs will
switch to vertically integrated production such that mt* = 1 as the cost of hiring skilled
labor is too high for firms involved in outsourcing activities to earn positive profit. Hence,
these three conditions must hold for 0 p mt* p 1 to exist.
From equation (29), several things can be noted. There exists a unique m*
whereby entrepreneurs with mt p m * will find it more profitable to undertake vertical
integration, whereas those with mt f m * will choose to outsource manual component of
the production process to the developing country. Secondly, we assumed that
entrepreneurial ability is uniformly distributed in the interval [0, 1], thus m* is
17
constrained by the value 1. When m* = 1 , this implies that all managers find it profitmaximizing to engage in vertical integration. On the contrary, all firms prefer to choose
the outsourcing mode of production when m* = 0 . Thus, a mixed equilibrium exists
when 0 p m * p 1 , whereby managers decide to undertake vertical integration or outsource,
depending on managerial ability.
2.5.2
Labor Market Equilibrium
From equations (19), (20) and (27), we can derive the demands for unskilled and
skilled workers in the domestic economy:
m*
Demand for unskilled labor=
∫ L dm
u
t
(
= m t*φ1 w ts , w tu , At
t
)
(32)
0
where φ1 wts , wtu , At =
1 α
At δ δH
α + γ
(
)
δ
wts
α
δ
γ
α +γ
γ
δ
β +δ −1
,
1−δ
δ −1
β δ wtu δ
(33)
whereas
m
demand for skilled labor=
*
∫
1
L
SI
t
dm
t
0
= m t*φ 2 ( w ts , w tu , A t ) +
∫
+
m
L SO
dm
t
t
*
(1 −
1+ b − d − χ
d − χ)
φ 3 ( m t* , w ts , K t −1 ) 1 − m * 1 − d − χ
1+ b − d − χ
s
u
where φ 2 ( w t , w t , A t ) =
H δ β βδ
(34)
1
w ts
1− β
(1− β )
w tu
β
α
A t
α + γ
1
α
γ
α + γ
1− d − χ s 1+ dχ −1− dχ
ρ − χ
a
s
d
wt 1− d − χ d 1− d − χ
and φ3 ( wt , K t −1 ) = ν K t −1 H
χ
h
δ
β + δ −1
(35)
1
d −1
(36)
18
Since the supply of unskilled and skilled labor, which are denoted by L
U
and
S
L respectively, are assumed to be exogenous, we can solve for equilibrium wages in the
U
S
labor market by equating equation (32) to L and equation (34) to L . After rearranging
the terms, we obtain:
LU
s
wt = *
mt
β + δ −1
δ
α
Atδ δH
α + γ
1
α
δ γ
α + γ
γ
δ
β
1−δ
δ
wtu
δ −1
δ
(37)
δ −1 1 − d − χ + d χ
δ (1 − d − χ )( d −1 )
1
w tu δ φ 4 ( m t* , A t ) + φ 5 ( m t* , K t −1 )φ 6 ( m t* , At ) w tu
U 1− β
β + δ −1
L
m t*
1
*
whereby φ 4 ( m t , At ) =
α
H
α γ
β At α + γ α + γ
φ5 (mt* , K t −1 ) =
(1 − d − χ )
1 − m
1 + b − d − χ
U
L
*
and φ6 (mt , At ) = *
mt
β +δ −1
δ
S
(38)
1
( )
1+ b − d − χ
* 1− d − χ
t
=L
γ
δ
,
1 ρ
ν
H h χ
−χ
(39)
a
K t −1
1
1−d − χ
−1−1−ddχ− χ
d
1
d −1
(40)
1− d − χ + dχ
α
At δ
α + γ
1
δ
α
δ
γ
α + γ
γ
δ
(1− d − χ )( d −1)
1−δ
β δ
(41)
It can be seen from the two labor equations that the terms are too complicated to be
solved simply. Together with equation (29), assuming that the two state variables At
and K t −1 are exogenous, there are three endogenous variables in this system of equations,
namely mt* , wts and wtu . Therefore, we shall use numerical simulation to solve for the
three equations (29), (37) and (38) and study the properties of the system.
Since the two labor equations are functions of mt* , we vary mt* to solve for the
equilibrium values of wts and wtu . Thereafter, we substitute all the equilibrium values
back into the two profit functions to obtain Figure 2-1. Hence, the figure shows the two
19
profit functions corresponding to the two different modes of production, which are
denoted by π tI and π tO respectively, with respect to the level of entrepreneurial ability m .
π tI shows a downward sloping convex curve, whereas π tO is an upward sloping concave
curve. The intersection of the two curves will give a unique m* . From the figure, it is
obvious that entrepreneurs with entrepreneurial ability less than m* will opt to undertake
vertical integration in order to maximize profit. On the contrary, those with
entrepreneurial ability greater than m* will choose to outsource the manual aspect of the
production process to the foreign country. This is because profit earned from outsourcing
activities is higher than that from vertical integration. Besides indicating firms’ decision
to outsource or do vertical integration, the unique threshold level shows the share of firms
that undertakes vertical integration as m* . In contrast, 1 − m* indicates the amount of
firms engaging in outsourcing activities.
Hence m* have two properties: 1) the ability of entrepreneurs to match firms to
foreign supplier and 2) a measure of the fraction of firms choosing to adopt vertical
integration.
FIGURE 2-1: PROFITS OF INTEGRATION AND OUTSOURCING FIRMS
π
πO
0.25
0.2
0.15
πI
0.1
0.05
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
m
20
3.
Dynamic Model
In this section, we introduce simple evolution mechanism of the entrepreneurial
network stock and integrated productivity stock and proceed to investigate how the
evolutions of the two stock variables, At and K t , may affect the organizational form of
production and factor prices over time.
3.1
The Model
We assume that interaction between firms involved in vertical integration and
outsourcing activities in the domestic economy has spillover effects on next period’s
common aggregate stock, Tt . This is modeled in the following equation:
Tt = mt*−1 At −1 + (1 − mt*−1 ) K t −1
(42)
Thus, present period’s common aggregate stock is influenced by spillover effects
from previous period’s entrepreneurial ability mt*−1 , integrated productivity stock At −1 and
network knowledge stock K t −1 . Such spillover effects will indirectly affect both the
evolutions of present period’s At and K t .
For the evolution of network knowledge stock, we use the following equation:
K t = C1Tt −1 1 (1 − mt*−1 ) k1 + (1 − ε 1 ) K t −1
n
(43)
where C1 , n1 , k1 , ε 1 ∈ (0,1) . Since Tt −1 is less than 1, n1 refers to the inefficiency of last
period’s common aggregate stock contributing to current network knowledge stock while
k1 refers to the inverse of networking efficiency among firms engaging in outsourcing
activities. C1 acts as an indexing parameter to the first term in the equation and can be
treated as aggregate productivity. In the second term of the equation, ε 1 refers to the rate
at which previous period’s network knowledge depreciates. Hence, the second term on
21
the right hand side of the equation indicates the portion of past period’s network
knowledge that contributes to future network knowledge stock.
The equation for the evolution of integrated productivity stock follows a similar
framework and is given as:
k
At = C 2Tt −1 2 mt*−1 2 + (1 − ε 2 ) At −1
n
(44)
where C 2 , n2 , k 2 , ε 2 ∈ (0,1) . Similarly, n2 indicates the inefficiency of last period’s
common aggregate stock contributing to integrated productivity stock while k 2 refers to
the inverse of networking inefficiency among firms choosing to undertake vertical
integration. Similarly, C 2 is treated as an aggregate productivity to At and ε 2 determines
the rate at which integrated productivity depreciates. Hence, we observe that the common
aggregate stock Tt is eventually made up of lagged effects of Tt and mt* since Tt is a
function of K t −1 and At −1 .
3.2
Baseline Steady- state System
Setting Tt = Tt −1 , mt* = mt*−1 , At = At −1 and K t = K t −1 , we can obtain:
Tt = mt* At + (1 − mt* )K t
(45)
C1Tt 1 (1 − mt* ) k1 − ε 1 K t = 0
(46)
n
k
C 2Tt 2 mt* 2 − ε 2 At = 0
n
(47)
1
χ b
(1−d − χ ) ρ
δ (1− d − χ )+ d ( β +δ −1)
1− d − χ
s
u β ( β +δ −1)b ν
b ( β +δ −1)
w
w
W
h
b
t
mt* = t
H
Ka S
At
t
where
(48)
22
W =
α
α + γ
S = χ χd d
(
LU
s
wt = *
mt
1
α
γ
α +γ
)
1
1− d − χ
β + δ −1
δ
γ
1
β +δ −1
− χ χd
1
δ δ β β
d −1 + χ − d χ
( d −1 )
1
− δ 1−δ
δ β
δ γ
α + γ
(
γ
δ
β
1−δ
δ
wtu
)
1
β +δ −1 1
− 1− β β
δ β
1
1− d − χ
− χ 1− d d d
α
α
Atδ δH
α + γ
1
1
β +δ −1
1
1− d − χ
(50)
δ −1
δ
(51)
δ − 1 1− d − χ + d χ
δ (1 − d − χ )( d −1 )
1
w tu δ φ 4 ( m t* , A t ) + φ 5 ( m t* , K t )φ 6 ( m t* , At ) w tu
U 1− β
β + δ −1
L
m t*
1
*
whereby φ 4 ( m t , At ) =
α
H
α γ
β At α + γ α + γ
=L
S
γ
δ
,
(53)
1
φ5 (mt* , K t ) =
(1 − d − χ )
1 − m
1 + b − d − χ
U
L
*
and φ6 (mt , At ) = *
mt
β +δ −1
δ
(52)
1
( )
1+ b − d − χ
* 1− d − χ
t
1
β +δ −1
(49)
−χ
1−d − χ −1− dχ
1 ρ
a
d 1− d − χ
ν K t
H h χ
1
d −1
(54)
1− d − χ + dχ
α
At δ
α + γ
1
δ
α
δ
γ
α + γ
γ
δ
(1− d − χ )( d −1)
1−δ
β δ
(55)
Substituting equations (43) and (44) into equations (46) and (47) respectively, we can
further obtain:
[
]
C mt* At + (1 − mt* )K t (1 − mt* ) k − ε 1 K t = 0
n
[
(
) ]
n
k
and C mt* At + 1 − mt* K t mt* − ε 2 At = 0
(56)
(57)
Using equations (48), (51), (52), (56) and (57) to solve for the baseline steady state values,
it can be seen that the equations are too complex to simply obtain an analytical solution
23
for the five endogenous variables mt* , K t , At , wts and wtu . Subsequently, we use numerical
simulation4 to obtain the baseline values and the corresponding comparative statics of the
system of equations.
3.3
Parameterization
The parameter values for the baseline simulation of both static and dynamic
models are presented in Table 1 and 2 respectively. We have adopted the same parameter
values for the numerical simulation of the dynamic model, so that we can easily analyze
the changes in the endogenous variables in both short and long runs.
The appropriate parameters are being set at values so as to satisfy Propositions 1,
2 and 3, which have held the guidelines 1) profits for both modes of production are
positive, 2) the wage gap
wts
is greater than one and 3) there exists an interior solution
wtu
for mt* . Since our focus is on a mixed equilibrium in the economy, corner solutions are
ignored.
The supply of skilled labor L S is also assumed to be 0.7, in order to reflect the
fact that the domestic developed country has a larger pool of skilled labor. The human
capital of foreign labor market h is set to be 0.2, which is lower than the domestic
country’s human capital of 0.3 so as to reflect the lower level of human capital in the
foreign, developing country. Moreover, we assume α 1 p α 2 because setting α 1 = α 2 and
α 1 f α 2 do not yield any interior solution in the dynamic model. We further assume that
ε 1 p ε 2 in the dynamic model, whereby integrated productivity stock depreciates faster
than network knowledge stock, otherwise no interior solution can be achieved as all firms
will move towards integrated production when ε 1 f ε 2 or ε 1 = ε 2 . Intuitively,
4
All numerical simulations are run using MATLAB 6.1.
24
entrepreneurs who are involved in international outsourcing are more capable than those
choosing to adopt vertical integration since they have higher entrepreneurial ability.
Therefore, the network knowledge stock created is more durable than integrated
productivity stock. This results in the former stock depreciating slower than the latter
stock.
Given these parameters, we are able to obtain a unique and stable steady state
solution for each of the endogenous variables, where no multiple equilibriums exist. To
check the stability of these steady state values, we have done some calibrations and
observe that any slight (1%) changes in the values will always evolve back to the original
steady state values. The existence of a unique and stable steady state for the threshold
level of entrepreneurial ability tallies with reality, whereby firms choose either to
outsource or undertake vertical integration.
TABLE 1: PARAMETER VALUES USED FOR BASELINE STATIC MODEL
Parameter
Entrepreneurial overload in training unskilled labor
Diminishing rate of unskilled workers
Entrepreneurial overload in training skilled labor
Diminishing rate of effective labor hired in integrated production
Cost before quality adjustment
Diminishing rate of manual component
Inefficiency of network knowledge contributing to present period
output
Inverse of matching between domestic firms and overseas supplier
Diminishing rate of effective labor hired in outsourcing
Human capital in foreign labor market
Decrease in efficiency of foreign labor producing low-skilled
intensive components
Skilled labor supply
Unskilled labor supply
Human capital in local labor market
Integrated productivity stock
Network knowledge stock
α
β
γ
δ
ρ
χ
Value
0.15
0.1
0.3
0.3
0.79
0.25
a
b
d
h
0.1
0.6
0.1
0.2
v
0.2
S
L
U
L
H
At
Kt
0.7
1
0.3
0.5457
0.6556
25
TABLE 2: PARAMETER VALUES USED FOR BASELINE SIMULATION
Parameter
Entrepreneurial overload in training unskilled labor
α
β
γ
δ
ρ
χ
Diminishing rate of unskilled workers
Entrepreneurial overload in training skilled labor
Diminishing rate of effective labor hired in integrated production
Cost before quality adjustment
Diminishing rate of manual component
Inefficiency of network knowledge contributing to present period
output
Inverse of matching between domestic firms and overseas supplier
Diminishing rate of effective labor hired in outsourcing
Human capital in foreign labor market
Decrease in efficiency of foreign labor producing low-skilled
intensive components
Unskilled labor supply
Human capital in local labor market
Inefficiency of last period aggregate stock contributing to current
network knowledge
Inefficiency of last period aggregate stock contributing to current
network knowledge
Aggregate productivity in evolution of network knowledge stock
Aggregate productivity in evolution of integrated productivity
stock
Inverse of networking efficiency in outsourcing mode
Inverse of networking efficiency in integrated production mode
Rate at which previous integrated productivity stock depreciates.
3.4.
0.1
0.6
0.1
0.2
v
0.2
L
U
L
H
0.7
n1
0.3
n2
C1
0.3
C2
k1
k2
0.3
ε1
ε2
Rate at which previous network knowledge depreciates.
0.15
0.1
0.3
0.3
0.79
0.25
a
b
d
h
S
Skilled labor supply
Value
1
0.3
0.3
0.3
0.3
0.3
0.4
Simulation Results
The baseline steady state values are presented in Table 3 below.
TABLE 3: BASELINE STEADY STATE VALUES
Threshold level of
* SS
entrepreneurial ability, m
Integrated productivity
stock, A SS
Network knowledge stock, K SS
SS
0.5860
Skilled wage, w s
0.5457
Unskilled wage, w u
0.6556
Common aggregate stock, T SS
0.0952
SS
0.0173
0.5912
Note: The above values are all corrected to 4 significant figures.
It can be seen from the above table that there exists a unique and stable mixed
equilibrium in the long run. Slightly more than half of the total number of entrepreneurs
in the economy will choose to adopt vertical integration whereas the remaining portion
will engage in outsourcing activities. The baseline wage gap is observed to be 5.5029.
26
Since the common aggregate stock T SS is a function of m *
SS
, A SS and K SS , it is
SS
sufficient to look at the changes in the five endogenous variables, which are namely m * ,
SS
SS
w s , w u , A SS and K SS . We also note that it is impossible to show a phase diagram for
these endogenous variables. Hence, in the following section, individual phase diagram
will be generated for each of them. We observe that K t and At will evolve smoothly to
the steady state values since they are state variables. They do not jump upon any changes
even though a 1% variation is made one at a time for each exogenous variable, and
therefore undergo a smooth transition to the new steady state values.
3.5
Welfare Of The Domestic country
Using the baseline steady state values, we can easily obtain the GDP of the
domestic country at each time period by summing up the total profits of all firms
undertaking vertical integration, total profits of all firms doing outsourcing activities,
skilled and unskilled labor income. This can be expressed in the following equation:
GDPt =
∫
m*
0
1
*
U
S
*
π tI dm + ∫ π tO dm +w tu L + w tS L
m
*
1
β +δ −1
1
1
1
sδ u β
β +δ −1
β +δ −1
β +δ −1
1
1
1
w
w
*
t
t
δ β
− δ 1−δ
− 1−β β
= mt
α
γ
δ
β
δ
β
δ
β
A H δ α γ
t
α + γ α +γ
1
1−d − χ
a d
b +1−d − χ
1 − d − χ
χ d
* 1−d − χ Kt −1 H
1 − mt
+
χ
χ d
ρ sd
b + 1 − d − χ
ν wt
h
(
* U
*
+ wtu L + wtS L
)
1
1−d − χ
1
1−d − χ
d −1+ χ −dχ
− χ χ d (d −1)
1
(58)
− χ1−d d d 1−d − χ
(
)
S
Thus, we can obtain the baseline values for the various components of GDP, which is
presented in Table 4 below:
27
TABLE 4: BASELINE VALUES FOR VARIOUS COMPONENTS OF GDP
0.2841 Labor income of skilled workers 0.0667
GDP
Profit of all firms undertaking
Labor income of unskilled
0.1036
0.0173
integrated mode of production
workers
Profit of all firms undertaking
0.0967
outsourcing mode of production
Note: The above values are all corrected to 4 significant figures.
Therefore, in the long run, it can be seen that the total profits of all firms
undertaking integrated mode of production is greater than that for all firms undertaking
outsourcing mode of production as more than half of the all entrepreneurs in the economy
will choose to engage in the integrated mode of production.
3.6
Comparative Statics Analysis
In this section, we examine the effects of various exogenous changes, one at a
time, on the five endogenous values. Before proceeding to do so, we first present a
summary of the comparative statics for the static model in Table 5. As K t and At are
chosen at steady state values in the static model, it thus shows the short run effects on the
economy. Thereafter, Table 6 shows a summary of the comparative statics for the
dynamic model. Thus, we analyze short run and long run changes based on these two
tables. Moreover, we analyze the transition of GDP and its various components over time.
A detailed discussion of the results is made in the following sub-sections.
28
TABLE 5: SUMMARY OF COMPARATIVE STATICS RESULTS FOR BASELINE
STATIC MODEL
A 1%
increase in
variable
α
β
γ
δ
ρ
χ
a
b
d
h
v
L
S
U
L
H
At
Kt
m*
%change in
entrepreneurial
ability, m*
ws
wu
ws/wu
% change in
wage gap,
ws/wu
0.58499
-0.17065
0.09504
0.01721
5.52287
0.11572
0.58547
0.58524
0.58167
0.58803
0.59157
0.58634
0.58854
0.58773
0.58559
0.58665
-0.08874
-0.12799
-0.73721
0.34813
0.95223
0.05973
0.43516
0.29693
-0.06826
0.11263
0.09524
0.09509
0.09580
0.09526
0.09541
0.09523
0.09532
0.09544
0.09521
0.09524
0.01743
0.01722
0.01709
0.01731
0.01739
0.01727
0.01732
0.01729
0.01725
0.01728
5.46292
5.52125
5.60666
5.50373
5.48766
5.51439
5.50398
5.52030
5.51890
5.51224
-0.97104
0.08751
1.63470
-0.23123
-0.52242
-0.03793
-0.22656
0.06926
0.04376
-0.07687
0.58701
0.17406
0.09458
0.01734
5.45544
-1.10650
0.58660
0.58701
0.10410
0.17406
0.09533
0.09553
0.01712
0.01734
5.56790
5.51001
0.93206
-0.11737
0.59212
1.04609
0.09631
0.01758
5.47858
-0.68703
0.58518
-0.13823
0.09520 0.01724 5.52158
0.09232
0.58599
0.09522 0.01726 5.51648
Baseline
Note: Since c has no impact on the static model, we do not investigate its effect. All values are
corrected to 5 significant figures in order to reflect changes accurately.
29
TABLE 6: SUMMARY OF COMPARATIVE STATICS RESULTS FOR
DYNAMIC MODEL
A 1% increase in parameter
%change
in
entrepreneurial
ability, m*
%change
in A
%change
in K*
ws/wu
%change
in wage
gap,
ws/wu
Entrepreneurial overload in
training unskilled labor
Diminishing rate of
unskilled workers
Entrepreneurial overload in
training skilled labor
Diminishing rate of effective
labor hired in integrated
production
Cost before quality
adjustment
Diminishing rate of manual
component
Inefficiency of network
knowledge contributing to
present period output
Inverse of matching between
domestic firms and overseas
supplier
Diminishing rate of effective
labor hired in outsourcing
Human capital in foreign
labor market
Decrease in efficiency of
foreign labor producing lowskilled intensive components
α
-0.2526
-0.0531
0.1266
5.5233
0.1191
β
-0.1331
-0.0348
0.0656
5.4713
-0.8233
γ
-0.1843
-0.0531
0.0961
5.5233
0.1191
δ
-0.9523
-0.2364
0.4622
5.6000
1.5102
ρ
0.5154
0.1301
-0.2395
5.4828
-0.6150
χ
1.4028
0.3317
-0.6818
5.4743
-0.7686
a
0.0887
0.0202
-0.0412
5.5087
-0.1453
b
0.6348
0.1484
-0.3005
5.4885
-0.5108
d
0.4300
0.1118
-0.2090
5.5260
0.1690
h
-0.0990
-0.0165
0.0503
5.5349
0.3299
v
0.1741
0.0385
-0.0717
5.5087
-0.1453
Skilled labor supply
L
0.2594
0.0568
-0.1175
5.4368
-1.4484
0.1570
0.0385
-0.0717
5.5789
1.1286
H
0.2594
0.0568
-0.1175
5.4943
-0.4066
n1
-0.0137
-0.0348
-0.1785
5.5029
-0.2501
n2
-0.2867
-0.2547
0.1114
5.5174
0.0137
C1
1.9147
1.8894
0.4927
5.4358
-1.4670
C2
1.8635
1.6878
-0.6666
5.4551
-1.1172
Unskilled labor supply
Human capital in local labor
market
Inefficiency of last period
aggregate stock contributing
to current network
knowledge
Inefficiency of last period
aggregate stock contributing
to current network
knowledge
Aggregate productivity in
evolution of network
knowledge stock
Aggregate productivity in
evolution of integrated
productivity stock
baseline ws/wu
L
S
U
5.5167
30
A 1% increase in parameter
%change in
entrepreneurial
ability, m*
%change
in A
%change
in K*
ws/wu
%change
in wage
gap,
ws/wu
Inverse of networking
-0.0137
-0.0531
-0.3005
5.5192
0.0449
efficiency in outsourcing
k1
mode
Inverse of networking
efficiency in integrated
-0.3038
-0.2730
0.1114
5.5174
0.0137
k2
production mode
Rate at which previous
-0.0478
-0.1997
-1.1547
5.5233
0.1191
network knowledge
ε1
depreciates.
Rate at which previous
-1.8055
-1.6475
0.6452
5.5928
1.3800
integrated productivity stock
ε2
depreciates.
baseline ws/wu
5.5167
Note: Since c has no impact on the static model, we do not investigate its effect. The values are
corrected to 4 significant figures
3.6.1 Cost Before Quality Adjustment, ρ
We now consider how the economy evolves to its new steady state when there is a
decrease in ρ , which is the cost before quality or productivity adjustment. As mentioned
earlier, such cost can also be seen as service link cost which is related to transportation,
communication and coordination cost and the degree of openness of the developing
country. In the short run, the portion of firms involved in vertical integration decreases.
Intuitively, as the service link cost decreases, the cost of purchasing low quality final
components subsequently decreases. Thus, firms are encouraged to purchase more
manual components instead of producing them in-house. This is consistent with
Grossman and Helpman (2003) whereby a decrease in trading costs will encourage
*
outsourcing. Similarly, m SS evolves to a lower steady state in the long run.
31
FIGURE 3-1: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL ABILITY
mt* FOR 1% DECREASE IN ρ
0.586
0.5855
0.585
m*
0.5845
0.584
0.5835
0.583
0.5825
0
20
40
60
80
t
100
120
140
160
In both short and long runs, a decrease in ρ causes wage inequality to increase.
This is because firms demand more skilled labor as the demand for outsourcing mode
rises. Subsequently, the wage gap increases and converges to a higher new steady state as
seen in Figure 3-2. It is to be noted that we have presented the figures with time periods
till 160 so as to provide a clear picture that each endogenous variables will converge to a
new steady state in the long run. In contrast, the figures for GDP and its various
components are presented with time periods till 40 for the benefit of readers to clearly
observe the changes that occur within the first few time periods.
FIGURE 3-2: EVOLUTION OF WAGE GAP
wts
FOR 1% DECREASE IN ρ
wtu
5 .5 36
5 .5 34
5 .5 32
5 .53
ws/wu
5 .5 28
5 .5 26
5 .5 24
5 .5 22
5 .52
5 .5 18
5 .5 16
0
20
40
60
80
t
100
120
140
160
32
It can be seen from Figure 3-3 that GDP will initially overshoot in the short run as
the total profits for all firms in outsourcing increase more than the fall in labor income.
However, it will eventually diminish as the fall in both skilled and unskilled labor income
outweighs the increase in total profits even though the labor income gap has increased.
Hence, it can be seen that the welfare of entrepreneurs increases although that for both
types of labor declines over time. We also observe that the pattern of labor income
inequality is similar to that of wage inequality, mainly because the supply stocks of
skilled and unskilled labor are constant over time.
FIGURE 3-3: EVOLUTION OF GDP FOR 1% DECREASE IN ρ
0.2845
GDP
0.2844
0.2843
0.2842
0.2841
0
5
10
15
20
t
25
30
35
40
FIGURE 3-4: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN ρ
0.1037
0.1036
totalpieI
0.1035
0.1034
0.1033
0.1032
0.1031
0.103
0
5
10
15
20
t
25
30
35
40
33
FIGURE 3-5: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN ρ
0.098
0.0978
totalpieO
0.0976
0.0974
0.0972
0.097
0.0968
0.0966
0
5
10
15
20
t
25
30
35
40
FIGURE 3-6: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1%
DECREASE IN ρ
0.0173
0.0173
total wu income
0.0172
0.0172
0.0172
0.0172
0.0172
0
5
10
15
20
t
25
30
35
40
FIGURE 3-7: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1%
DECREASE IN ρ
0.0667
0.0667
total ws income
0.0666
0.0666
0.0666
0.0666
0.0666
0.0665
0.0665
0
5
10
15
20
t
25
30
35
40
34
FIGURE 3-8: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO
TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN ρ
3.876
3.874
ws income/wu income
3.872
3.87
3.868
3.866
3.864
3.862
3.86
0
5
10
15
20
t
25
30
35
40
3.6.2 Changes In Parameters Affecting Networking Of Both Types Of Entrepreneurs
3.6.2.1 A Decrease In Inverse Of Networking Efficiency In Outsourcing Mode, k1
To examine the impact of networking in outsourcing or integrated activities by
entrepreneurs on the mode of production chosen, we first isolate the change in parameters
to that in k1 . In the short run, it is observed that a decrease in inverse of networking
efficiency in outsourcing initially causes mt* to jump up in the first period. The reason
behind the jump is unknown to us. However, in the next period, the decline in mt* is
intuitive as entrepreneurs prefer to do more outsourcing due to the increase in networking
efficiency in outsourcing. However, in the long run, as Tt −1 increases further with no
further decrease in k1 , both At and K t increase, causing profits for both integrated and
outsourcing mode to increase. Differentiating profit equations (21) and (28) with respect
to the two different types of stocks, we obtain the following equations:
∂ ln π tI
1
=
∂At
β + δ −1
(59)
∂ ln π tO
a
=
∂K t −1
1− d − χ
(60)
35
Substituting the parameter values from Table 3 into the above equations, we can obtain
the magnitude for each of the elasticity of the two profit equations to be
∂ ln π tI
∂ ln π tO
= 1.66667 and
= 0.230769 respectively. Since the elasticity of integrated
∂At
∂K t −1
profit is greater than that of outsourcing, the positive impact on integrated profit is larger
when the percentage increase in At is similar to that in K t , holding other things constant.
However, it can be seen that other factors do not remain constant. Hence in the short run,
the direct effect of a fall in k1 dominates whereas integrated productivity stock dominates
in the long run due to the elasticity effect.
Correspondingly, wage gap initially decreases and then increases in the short run.
In the long run, wage inequality converges to a lower steady state as the integrated mode
of production gains dominance in the economy.
FIGURE 3-9: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL
ABILITY mt* FOR 1% DECREASE IN k1
0.5861
0.5861
0.586
0.586
m*
0.586
0.586
0.586
0.5859
0.5859
0.5859
0.5859
0
20
40
60
80
t
100
120
140
160
36
FIGURE 3-10: EVOLUTION OF COMMON AGGREGATE STOCK Tt FOR 1%
DECREASE IN k1
0.5922
0.592
T
0.5918
0.5916
0.5914
0.5912
0.591
0
20
40
60
80
t
100
120
140
160
FIGURE 3-11: EVOLUTION OF NETWORK KNOWLEDGE STOCK K t FOR 1%
DECREASE IN k1
0.658
0.6575
K
0.657
0.6565
0.656
0.6555
0
20
40
60
80
t
100
120
140
160
FIGURE 3-12: EVOLUTION OF INTEGRATED PRODUCTIVITY STOCK At
FOR 1% DECREASE IN k1
0.546
0.5459
0.5459
A
0.5458
0.5458
0.5457
0.5457
0.5456
0
20
40
60
80
t
100
120
140
160
37
wts
FIGURE 3-13: EVOLUTION OF WAGE GAP u FOR 1% DECREASE IN k1
wt
5.5174
5.5172
5.517
ws/wu
5.5168
5.5166
5.5164
5.5162
5.516
5.5158
0
20
40
60
80
t
100
120
140
160
We further observe that an increase in networking efficiency among firms
engaging in outsourcing activities will increase GDP over time as seen in Figure 3-14
below. The majority of the increase in GDP is contributed by the increase in total profits
of all firms undertaking the integrated mode of production. Both skilled and unskilled
workers gain too as the integrated mode of production dominates in the long run. At the
same time, income inequality falls. In this case, the overall welfare of entrepreneurs has
decreased.
FIGURE 3-14: EVOLUTION OF GDP FOR 1% DECREASE IN k1
0.2843
0.2843
0.2843
0.2843
GDP
0.2842
0.2842
0.2842
0.2842
0.2842
0.2841
0.2841
0
5
10
15
20
t
25
30
35
40
38
FIGURE 3-15: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN k1
0.1036
totalpieI
0.1036
0.1036
0.1036
0.1036
0
5
10
15
20
t
25
30
35
40
FIGURE 3-16: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN k1
0.0967
0.0967
totalpieO
0.0967
0.0967
0.0967
0.0967
0.0967
0.0967
0
5
10
15
20
t
25
30
35
40
FIGURE 3-17: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1%
DECREASE IN k1
0.0173
0.0173
total wu income
0.0173
0.0173
0.0173
0.0173
0.0173
0.0173
0.0173
0
5
10
15
20
t
25
30
35
40
39
FIGURE 3-18: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1%
DECREASE IN k1
0.0667
0.0667
0.0667
total ws income
0.0667
0.0667
0.0667
0.0667
0.0667
0.0667
0.0667
0.0667
0
5
10
15
20
t
25
30
35
40
FIGURE 3-19: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO
TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN k1
3.8621
3.862
ws income/wu income
3.8619
3.8618
3.8617
3.8616
3.8615
3.8614
3.8613
3.8612
3.8611
0
5
10
15
20
t
25
30
35
40
3.6.2.2 A Decrease In Inverse Of Networking Efficiency In Vertically Integrated Mode,
k2
Next, isolating the change to that in k 2 , a decrease in the inverse of networking
efficiency in networking among firms undertaking vertical integration implies that the
demand for outsourcing activities falls. Hence, there is an increase in demand for
integrated production, as shown by a decrease in mt* . The increase in the accumulation of
integrated productivity stocks over time causes
At
to rise over time. In contrast, the
Tt
decline in network knowledge stocks due to the fall in demand for outsourcing activities
40
Kt
over time. Hence, integrated production dominates in both short
Tt
leads to a decline in
and long runs. Subsequently, this results in a narrowing of wage gap.
Similarly, an increase in the networking efficiency among firms undertaking
integrated mode of production will cause GDP to increase over time as seen in Figure 325. This increase is due to the dominance of the increase in total profits of all firms
undertaking the integrated mode of production and labor income over the decrease in total
profits of all firms undertaking outsourcing mode of production. Hence, workers in the
domestic economy gain from the increase in k 2 .
FIGURE 3-20: EVOLUTION OF COMMON AGGREGATE STOCK Tt FOR 1%
DECREASE IN k 2
0.5916
0.5916
0.5915
0.5915
T
0.5914
0.5914
0.5913
0.5913
0.5912
0.5912
0.5911
0
20
40
60
80
t
100
120
140
160
FIGURE 3-21: EVOLUTION OF RATIO OF NETWORK KNOWLEDGE STOCK TO
COMMON AGGREGATE STOCK
Kt
FOR 1% DECREASE IN k 2
Tt
1.1095
1.109
K/T
1.1085
1.108
1.1075
1.107
0
20
40
60
80
t
100
120
140
160
41
FIGURE 3-22: EVOLUTION OF RATIO OF INTEGRATED PRODUCTIVITY
STOCK TO AGGREGATE STOCK
At
FOR 1% DECREASE IN k 2
Tt
0.9255
0.925
A/T
0.9245
0.924
0.9235
0.923
0
20
40
60
80
t
100
120
140
160
FIGURE 3-23: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL
ABILITY mt* FOR 1% DECREASE IN k 2
0.588
0.5875
m*
0.587
0.5865
0.586
0.5855
0
20
40
60
80
t
100
FIGURE 3-24: EVOLUTION OF WAGE GAP
120
140
160
wts
FOR 1% DECREASE IN k 2
wtu
5.52
5.518
5.516
ws/wu
5.514
5.512
5.51
5.508
5.506
5.504
0
20
40
60
80
t
100
120
140
160
42
FIGURE 3-25: EVOLUTION OF GDP FOR 1% DECREASE IN k 2
0.2846
0.2845
GDP
0.2844
0.2843
0.2842
0.2841
0.284
0
5
10
15
20
t
25
30
35
40
FIGURE 3-26: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN k 2
0.1042
0.1041
totalpieI
0.104
0.1039
0.1038
0.1037
0.1036
0.1035
0
5
10
15
20
t
25
30
35
40
FIGURE 3-27: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN k 2
0.0967
totalpieO
0.0966
0.0965
0.0964
0.0963
0
5
10
15
20
t
25
30
35
40
43
FIGURE 3-28: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1%
DECREASE IN k 2
0.0173
0.0173
0.0173
total wu income
0.0173
0.0173
0.0173
0.0173
0.0173
0.0173
0.0173
0
5
10
15
20
t
25
30
35
40
FIGURE 3-29: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1%
DECREASE IN k 2
0.0669
0.0669
total ws income
0.0668
0.0668
0.0668
0.0667
0.0667
0
5
10
15
20
t
25
30
35
40
FIGURE 3-30: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO
TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN k 2
3.863
3.862
ws income/wu income
3.861
3.86
3.859
3.858
3.857
3.856
3.855
3.854
0
5
10
15
20
t
25
30
35
40
44
3.6.3 Changes In Parameters Affecting Both Local And Foreign Labor Markets
3.6.3.1 An Increase In Human Capital In The Local Labor Market, H
As the skill profile of the domestic economy is enhanced through an exogenous
increase in human capital H , vertical integration mode gains a greater share in the
economy in the short run. This is because the supply of skilled labor has increased, hence
raising the profit for integrated production more than that for outsourcing. This is mainly
due to the parameter values whereby δ > d such that the increase in human capital given
a fixed value of δ in firms adopting vertical integration will contribute to a higher
increase in profit than that for firms engaged in international outsourcing, while holding
d fixed. In the long run, entrepreneurial ability similarly converges to a higher steady
state.
FIGURE 3-31: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL
ABILITY mt* FOR 1% INCREASE IN H
0.5875
m*
0.587
0.5865
0.586
0
20
40
60
80
t
100
120
140
160
Hence, wage inequality decreases in both short and long runs since the fall in
demand for outsourcing will lead to an overall decline in demand for all skilled labor.
Conversely, demand for unskilled labor increases, thus increasing wages for such workers.
Figure 3-32 shows the transition of wage gap over time.
45
wts
FIGURE 3-32: EVOLUTION OF WAGE GAP u FOR 1% INCREASE IN H
wt
5.517
5.516
5.515
5.514
ws/wu
5.513
5.512
5.511
5.51
5.509
5.508
5.507
0
20
40
60
80
t
100
120
140
160
An increase in the human capital of the local labor market will also result in an
increasing GDP over time. The increase in total profits of all entrepreneurs undertaking
the integrated mode of production and total labor income has not only offset the fall in
total profits of all entrepreneurs engaging in outsourcing activities, but also dominates it.
FIGURE 3-33: EVOLUTION OF GDP FOR 1% INCREASE IN H
0.285
0.2849
0.2848
GDP
0.2847
0.2846
0.2845
0.2844
0.2843
0.2842
0.2841
0
5
10
15
20
t
25
30
35
40
46
FIGURE 3-34: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
INTEGRATED MODE OF PRODUCTION FOR 1% INCREASE IN H
0.1043
0.1042
0.1041
totalpieI
0.104
0.1039
0.1038
0.1037
0.1036
0.1035
0
5
10
15
20
t
25
30
35
40
FIGURE 3-35: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
OUTSOURCING MODE OF PRODUCTION FOR 1% INCREASE IN H
0.0967
0.0967
totalpieO
0.0966
0.0966
0.0965
0.0965
0.0964
0
5
10
15
20
t
25
30
35
40
FIGURE 3-36: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1%
INCREASE IN H
0.0174
0.0173
0.0173
total wu income
0.0173
0.0173
0.0173
0.0173
0.0173
0.0173
0.0173
0.0173
0
5
10
15
20
t
25
30
35
40
47
FIGURE 3-37: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1%
INCREASE IN H
0.0669
0.0669
total ws income
0.0668
0.0668
0.0668
0.0667
0.0667
0
5
10
15
20
t
25
30
35
40
FIGURE 3-38: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO
TOTAL UNSKILLED LABOR INCOME FOR 1% INCREASE IN H
3.863
3.862
ws income/wu income
3.861
3.86
3.859
3.858
3.857
3.856
3.855
0
5
10
15
20
t
25
30
35
40
3.6.3.2 An Increase In Human Capital In The Foreign Labor Market, h
Turning our attention to the foreign economy, a one percent increase in the human
capital in the foreign labor market h leads to an increase in outsourcing activities in both
short and long term periods. Entrepreneurs in the domestic economy will want to take
advantage of the higher foreign human capital since the quality of outsourced manual
components have improved, resulting in a lower effective cost. Hence, domestic firms
prefer to purchase more manual components from the overseas supplier. This results in
outsourcing gaining a greater share. Wage inequality therefore increases as the demand
for skilled workers increases. In the long run, based on the same explanations,
48
mt* converges to a lower, new steady state while wage gap converges to a higher, new
steady state.
FIGURE 3-39: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL
ABILITY mt* FOR 1% INCREASE IN h
0.5861
0.586
0.5859
m*
0.5858
0.5857
0.5856
0.5855
0.5854
0.5853
0
20
40
60
80
t
100
FIGURE 3-40: EVOLUTION OF WAGE GAP
120
140
160
wts
FOR 1% INCREASE IN h
wtu
5.5205
5.52
5.5195
ws/wu
5.519
5.5185
5.518
5.5175
5.517
5.5165
0
20
40
60
80
t
100
120
140
160
An increase in foreign human capital will benefit entrepreneurs engaging in
outsourcing activities and foreign labor, as seen from the increase in total profits of all
firms undertaking outsourcing mode of production and the decrease in skilled and
unskilled labor income. Hence, although GDP initially overshoots in the short run, it is
dampened by the combined fall in total profits of all firms involved in integrated
production and labor income in the long run.
49
FIGURE 3-41: EVOLUTION OF GDP FOR 1% INCREASE IN h
0.2842
0.2842
0.2842
0.2842
GDP
0.2842
0.2842
0.2842
0.2842
0.2841
0.2841
0
5
10
15
20
t
25
30
35
40
FIGURE 3-42: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
INTEGRATED MODE OF PRODUCTION FOR 1% INCREASE IN h
0.1036
0.1036
totalpieI
0.1035
0.1035
0.1035
0.1035
0.1035
0.1034
0
5
10
15
20
t
25
30
35
40
FIGURE 3-43: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
OUTSOURCING MODE OF PRODUCTION FOR 1% INCREASE IN h
0.0969
0.0968
totalpieO
0.0968
0.0967
0.0967
0.0966
0
5
10
15
20
t
25
30
35
40
50
FIGURE 3-44: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1%
INCREASE IN h
0.0173
total wu income
0.0173
0.0173
0.0172
0.0172
0.0172
0
5
10
15
20
t
25
30
35
40
FIGURE 3-45: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1%
INCREASE IN h
0.0667
0.0667
total ws income
0.0666
0.0666
0.0666
0.0666
0.0666
0.0666
0
5
10
15
20
t
25
30
35
40
FIGURE 3-46: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO
TOTAL UNSKILLED LABOR INCOME FOR 1% INCREASE IN h
3.865
3.8645
ws income/wu income
3.864
3.8635
3.863
3.8625
3.862
3.8615
0
5
10
15
20
t
25
30
35
40
51
3.6.4 Change In Parameters Related To Efficiency Of Training
3.6.4.1 A Decrease In Entrepreneurial Overload In Training Unskilled Labor, α
In the integrated mode of production, a decrease in entrepreneurial overload in
training unskilled labor α , will lead to an increase in the efficiency of training such
workers, hence reducing the training cost. As a result, profit for integrated production
increases and firms prefer to do production in-house in both short and long runs.
FIGURE 3-47: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL
ABILITY mt* FOR 1% DECREASE IN α
0.5875
m*
0.587
0.5865
0.586
0
20
40
60
80
t
100
120
140
160
Therefore, entrepreneurs demand more unskilled workers relative to skilled
workers, hence depressing the wage gap. Figure 3-48 shows the transition of wage gap
over time. It can be seen that wage gap decreases in both short and long runs.
FIGURE 3-48: EVOLUTION OF WAGE GAP
wts
FOR 1% DECREASE IN α
wtu
5.517
5.516
5.515
5.514
ws/wu
5.513
5.512
5.511
5.51
5.509
5.508
5.507
0
20
40
60
80
t
100
120
140
160
52
Similar to previous cases, the decrease in entrepreneurial overload in training
unskilled workers results in the dominance of increase in total profits of all entrepreneurs
involved in integrated mode of production and labor income over decrease in total profits
of all entrepreneurs involved in outsourcing mode of production. Hence, GDP increases
over time.
FIGURE 3-49: EVOLUTION OF GDP FOR 1% DECREASE IN α
0.2845
GDP
0.2844
0.2843
0.2842
0.2841
0
5
10
15
20
t
25
30
35
40
FIGURE 3-50: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN α
0.1041
0.104
totalpieI
0.1039
0.1038
0.1037
0.1036
0.1035
0
5
10
15
20
t
25
30
35
40
FIGURE 3-51: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN α
0.0967
0.0967
0.0966
totalpieO
0.0965
0.0965
0.0964
0.0964
0.0963
0.0963
0
5
10
15
20
t
25
30
35
40
53
FIGURE 3-52: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1%
DECREASE IN α
0.0173
0.0173
0.0173
total wu income
0.0173
0.0173
0.0173
0.0173
0.0173
0.0173
0.0173
0
5
10
15
20
t
25
30
35
40
FIGURE 3-53: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1%
DECREASE IN α
0.0668
total ws income
0.0668
0.0667
0.0667
0.0666
0.0666
0
5
10
15
20
t
25
30
35
40
FIGURE 3-54: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO
TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN α
3.863
3.862
ws income/wu income
3.861
3.86
3.859
3.858
3.857
3.856
3.855
0
5
10
15
20
t
25
30
35
40
54
3.6.4.2 A Decrease In Entrepreneurial Overload In Training Skilled Labor, γ
In the short run, as the entrepreneurial overload in training skilled labor γ
decreases, the training of skilled labor becomes more efficient such that the cost of
training them is now lower. This leads to an increase in profit for integration and
entrepreneurs prefer not to outsource manual components. Hence in both short and long
term periods, outsourcing gains a lower share. Firms demand less skilled workers and
instead demand more unskilled workers as more firms switch to integrated production
mode. Subsequently, the wage gap decreases. In the long run, the wage gap continues to
fall and converges to a lower steady state. Figures 3-55 and 3-56 show the transition of
mt* and wage gap over time. In addition, the impact on GDP is similar to the impact due
to a decrease in entrepreneurial overload in training unskilled labor.
FIGURE 3-55: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL
ABILITY mt* FOR 1% DECREASE IN γ
0.5872
0.587
0.5868
m*
0.5866
0.5864
0.5862
0.586
0.5858
0
20
40
60
80
t
100
120
140
160
wts
FIGURE 3-56: EVOLUTION OF WAGE GAP u FOR 1% DECREASE IN γ
wt
5.518
5.517
5.516
ws/wu
5.515
5.514
5.513
5.512
5.511
5.51
5.509
0
20
40
60
80
t
100
120
140
160
55
FIGURE 3-57: EVOLUTION OF GDP FOR 1% DECREASE IN γ
0.2845
0.2844
0.2844
GDP
0.2843
0.2843
0.2842
0.2842
0.2841
0.2841
0
5
10
15
20
t
25
30
35
40
FIGURE 3-58: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN γ
0.1039
0.1039
0.1038
totalpieI
0.1038
0.1037
0.1037
0.1036
0.1036
0.1035
0
5
10
15
20
t
25
30
35
40
FIGURE 3-59: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN γ
0.0967
0.0966
totalpieO
0.0966
0.0965
0.0965
0.0964
0.0964
0
5
10
15
20
t
25
30
35
40
56
FIGURE 3-60: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1%
DECREASE IN γ
0.0173
0.0173
total wu income
0.0173
0.0173
0.0173
0.0173
0.0173
0.0173
0
5
10
15
20
t
25
30
35
40
FIGURE 3-61: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1%
DECREASE IN γ
0.0668
total ws income
0.0668
0.0667
0.0667
0
5
10
15
20
t
25
30
35
40
FIGURE 3-62: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR
INCOME TO TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN γ
3.862
ws income/wu income
3.861
3.86
3.859
3.858
3.857
3.856
0
5
10
15
20
t
25
30
35
40
57
3.6.5
A Change In Parameter Relating To Matching Ability, b
It is interesting to observe how a decrease in the inverse of matching between
domestic firms and overseas supplier b will affect the mode of production and wage
inequality. Allowing a 1% decrease in b results in a higher entrepreneurial ability to find
a suitable match. Subsequently, outsourcing profit rises, hence increasing outsourcing
activities in both short and long runs. Similarly, as more entrepreneurs switch to
outsourcing mode of production, they demand more skilled labor relative to unskilled
labor, resulting in an upward pressure on wage inequality. Thus, the wage gap increases
in the short run and converges to a higher steady state in the long run as shown by Figure
3-64 below.
FIGURE 3-63: EVOLUTION OF THRESHOLD LEVEL OF ENTREPRENURIAL
ABILITY mt* FOR 1% DECREASE IN b
0.5865
0.586
0.5855
0.585
m*
0.5845
0.584
0.5835
0.583
0.5825
0.582
0
20
40
60
80
t
100
FIGURE 3-64: EVOLUTION OF WAGE GAP
120
140
160
wts
FOR 1% DECREASE IN b
wtu
5.545
5.54
ws/wu
5.535
5.53
5.525
5.52
5.515
0
20
40
60
80
t
100
120
140
160
58
It is striking to observe that an increase in matching ability will initially result in a
sharp increase in GDP, followed by a decline in GDP over time. The increase in profits of
total entrepreneurs engaged in outsourcing activities has contributed to the initial increase
in GDP. However, in the long run, the fall in total integrated profits and labor income
overwhelms the increase in outsourcing profit, causing GDP to be lower than the baseline
value in the long run. This shows that an increase in outsourcing activities is not
necessary beneficial to the welfare of the economy all the time. In this case, GDP has
worsened in the long run.
FIGURE 3-65: EVOLUTION OF GDP FOR 1% DECREASE IN b
0.2843
0.2843
GDP
0.2842
0.2842
0.2841
0.2841
0
5
10
15
20
t
25
30
35
40
FIGURE 3-66: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
INTEGRATED MODE OF PRODUCTION FOR 1% DECREASE IN b
0.1036
0.1035
0.1034
totalpieI
0.1033
0.1032
0.1031
0.103
0.1029
0.1028
0
5
10
15
20
t
25
30
35
40
59
FIGURE 3-67: EVOLUTION OF TOTAL PROFITS OF ALL FIRMS UNDERTAKING
OUTSOURCING MODE OF PRODUCTION FOR 1% DECREASE IN b
0.098
0.0978
totalpieO
0.0976
0.0974
0.0972
0.097
0.0968
0.0966
0
5
10
15
20
t
25
30
35
40
FIGURE 3-68: EVOLUTION OF TOTAL UNSKILLED LABOR INCOME FOR 1%
DECREASE IN b
0.0173
0.0173
total wu income
0.0172
0.0172
0.0172
0.0172
0.0172
0.0171
0
5
10
15
20
t
25
30
35
40
FIGURE 3-69: EVOLUTION OF TOTAL SKILLED LABOR INCOME FOR 1%
DECREASE IN b
0.0667
0.0667
total ws income
0.0666
0.0666
0.0665
0.0665
0.0664
0
5
10
15
20
t
25
30
35
40
60
FIGURE 3-70: EVOLUTION OF RATIO OF TOTAL SKILLED LABOR INCOME TO
TOTAL UNSKILLED LABOR INCOME FOR 1% DECREASE IN b
3.878
3.876
ws income/wu income
3.874
3.872
3.87
3.868
3.866
3.864
3.862
3.86
0
5
10
15
20
t
25
30
35
40
Table 7 thus summarizes the relations between a 1% increase in each of the selected
exogenous parameters and the five endogenous variables. The outcomes in the table
below are different from what we have discussed in the main text above. For easy
interpretation and comparison, we have assumed an increase in all the selected exogenous
parameters. In contrast, in the main text, we have considered increases in domestic and
foreign human capital whereas other exogenous parameters each experience a decrease so
as to be consistent with world developments.
TABLE 7: SUMMARY OF OUTCOMES OF COMPARATIVE STATICS EXERCISE FOR
AN INCREASE IN EACH SELECTED PARAMETERS
Parameter
Cost before quality adjustment
Inverse of networking efficiency in
outsourcing mode
Inverse of networking efficiency in
integrated production mode
Human capital in local labor market
Human capital in foreign labor market
Entrepreneurial overload in training
unskilled labor
Entrepreneurial overload in training
skilled labor
Inverse of matching between domestic
firms and overseas supplier
Threshold
entrepreneurial
ability
ρ
k1
mt*
Wage gap
wts
wtu
At
Kt
+
-
+
+
-
-
k2
-
+
-
+
H
h
α
+
-
+
+
+
-
+
+
γ
-
+
-
+
b
+
-
+
-
Similarly, Table 8 shows all the relationships between the 1% increase in each exogenous
parameters and the welfare of the three major types of players in the economy: 1)
61
entrepreneurs, 2) skilled workers and 3) unskilled workers. From the table, we observe
that there exists a trade off between the welfare of domestic workers and entrepreneurs.
TABLE 8: SUMMARY OF GDP OUTCOMES OF COMPARATIVE STATICS EXERCISE
FOR AN INCREASE IN SELECTED PARAMETERS
Parameter
Cost before quality
adjustment
Inverse of networking
efficiency in outsourcing
mode
Inverse of networking
efficiency in integrated
production mode
Human capital in local labor
market
Human capital in foreign
labor market
Entrepreneurial overload in
training unskilled labor
Entrepreneurial overload in
training skilled labor
Inverse of matching between
domestic firms and overseas
supplier
3.7
GDP
ρ
+
Profit of
entrepreneurs
involved in
integrated
production
+
k1
-
-
+
-
-
k2
-
-
+
-
-
H
+
+
-
+
+
h
+
-
+
-
-
α
-
-
+
-
-
γ
-
-
+
-
-
b
+
+
-
+
+
Profit of
entrepreneurs
involved in
outsourcing
activities
-
Skilled
labor
income
Unskilled
labor
income
+
+
Comparison With Previous Literature Results
We compare our results with previous literature and present the summaries of the
differences in Tables 9 and 10. We find that Egger and Grossmann (2005) only examined
the effects of outsourcing on wage inequality in the short and long runs, whereas Grenier,
Rubart, Semmler (2004) and DeGroot (2001) have only examined the decision to
outsource or adopt integrated production in the long run. Hence our model provides a
richer model by exploring the interdependence between entrepreneurs, skilled and
unskilled workers. Moreover, previous literature has failed to take into account other
factors affecting outsourcing and integrated production, such as entrepreneurial overload
in training unskilled and skilled labor.
62
In our results, a change in skilled (unskilled) labor supply will lead to a decrease
(increase) in wage inequality respectively. In contrast, Egger and Grossmann (2005)
postulated that wage inequality remains constant regardless of an increase in high-skilled
or low-skilled workers. This is because in their model setup the reduction in relative
wages is offset by the increase in relative wages. For instance, an increase in high-skilled
labor leads to a decrease in wage gap due to an increase in the skill intensity of
production labor. However, supporting low-skilled labor becomes more attractive since
the marginal cost of supporting low-skilled labor is now lower relative to non-supported
low skilled labor. Thus, as more high-skilled labor is allocated towards non-production
activities, the skill-intensity of production labor decreases. This results in a narrowing of
wage gap.
From Table 9, it can be seen that the decision to adopt integrated production is
inversely related with unskilled labor supply in DeGroot (2001)’s results. According to
his paper, he postulated that an increase in the scale of economy, whereby labor supply is
the sum of skilled and unskilled labor supply, will result in an increase in outsourcing.
This is mainly because the fixed cost of superior technology can now easily be distributed
over a larger output (the size of the market will restrict the degree of specialization). In
contrast, in our model, the decision to do integrated production is positively related to
unskilled labor supply.
In Table 10, Grenier, Rubart, Semmler (2004) postulated that an increase in the
number of skilled workers will lead to an increase in the profitability of technology which
are complementary to skilled labor. Hence, skilled wages increase, resulting in an
increase in wage inequality. However, our model shows that wage inequality should fall.
Comparing our model with a model that performs foreign direct investment (FDI)
instead of international outsourcing, Davies (2005) has developed a static model of FDI
whereby the skilled workers of different countries are imperfect substitutes for one
63
another. In addition, the production of HQ services by skilled labor takes place in both
countries. Thereafter a Multinational Enterprise (MNE) combines the services using
unskilled labor. Hence, FDI can occur without trade costs or factor-price differences.
Davies postulated that the increase in the hiring of host country’s skilled labor increases
home country’s unskilled wages. At the same time, there is an ambiguous effect on home
country’s skilled wages. Furthermore, an increase in the host production of the
multinational’s good will result in an increase in wage inequality in the home country.
However, depending on the degree of imperfect substitution of skilled labor, FDI
will lead to additional wage effects. For instance, if the skilled labor of both home and
host country are perfect substitutes, home skilled wage will fall as the role of FDI
increases. In contrast, as the degree of substitutability falls, wage inequality in the home
country increases as domestic skilled wages increase. In contrast, we show that an
increase in network knowledge stock in the static model will lead to an unambiguous
increase in wage inequality. Since Davies has only examined these changes in the short
run, our model is more realistic as we examine the transition of wage inequality over time.
According to Grossman and Helpman (2003), they postulated that heterogeneous
firms in an industry will choose their mode of organization and location of their
subsidiaries or suppliers, depending on their level of productivity. A fall in trade cost will
lead to firms with low level of productivity to increase outsourcing to the South. Firms
with intermediate level of productivity will prefer to perform more FDI while the fraction
of components in the market produced by vertically integrated firms in the North declines.
Although we have adopted a different approach from their paper, our model is richer as
we have examined the endogenous relationship between entrepreneurs’ decisions to
outsource and wage inequality.
To summarize, most literature has focused the impact of international outsourcing
on wage inequality and failed to endogenize the influential role of entrepreneurship
64
together with wage inequality. Furthermore, they have neglected to compare the welfare
of entrepreneurs versus domestic workers over time. In contrast, we have not only
examined the transition of GDP over time, but also compare the welfare of the three
major types of players in the domestic economy.
65
TABLE 9: COMPARISON WITH PREVIOUS LITERATURE RESULTS (1)
DeGroot
(2001)
Model
Parameters
SR
Entrepreneurial overload in
training unskilled labor
Diminishing rate of unskilled
workers
Entrepreneurial overload in
training skilled labor
Diminishing rate of effective
labor hired in integrated
production
Cost before quality adjustment
Diminishing rate of manual
component
Inefficiency of network
knowledge contributing to
present period output
Inverse of matching between
domestic firms and overseas
supplier
Diminishing rate of effective
labor hired in outsourcing
Human capital in foreign labor
market
Decrease in efficiency of foreign
labor producing low-skilled
intensive components
Skilled labor supply
Unskilled labor supply
Human capital in local labor
market
Integrated productivity stock
Network knowledge stock
Inefficiency of last period
aggregate stock contributing to
current network knowledge
Inefficiency of last period
aggregate stock contributing to
current network knowledge
Aggregate productivity in
evolution of network knowledge
stock
Aggregate productivity in
evolution of integrated
productivity stock
Inverse of networking efficiency
in outsourcing mode
wts
wtu
LR
LR
mt*
wts
wtu
mt*
+
-
+
-
-
-
-
-
+
-
+
-
+
-
+
-
-
+
+
-
+
+
-
+
-
+
-
+
-
+
+
+
+
+
+
-
+
-
-
+
-
+
+
-
+
+
+
+
-
+
+
+
+
+
-
-
+
-
-
+
-
-
+
-
wts
wtu
mt*
Grossman
and
Helpman
(2003)
SR
wts
wtu
mt*
Egger and
Grossmann (2005)
SR
wts
wtu
LR
mt*
wts
wtu
+
+
+
+
-
0
0
0
0
-
-
-
+
*
+
mt*
66
DeGroot
(2001)
Model
Parameters
SR
LR
LR
s
t
u
t
s
t
u
t
s
t
u
t
w
w
Inverse of networking efficiency
in integrated production mode
Rate at which previous network
knowledge depreciates.
Rate at which previous
integrated productivity stock
depreciates.
Note: * stands for ambiguous
mt*
w
w
mt*
+
-
+
-
+
-
w
w
mt*
Grossman
and
Helpman
(2003)
SR
s
t
u
t
w
w
mt*
Egger and
Grossmann (2005)
SR
s
t
u
t
w
w
LR
mt*
wts
wtu
mt*
67
TABLE 10: COMPARISON WITH PREVIOUS LITERATURE RESULTS (2)
Grenier,
Rubart,
Semmler
(2004)
LR
Model
Parameters
SR
Entrepreneurial overload in training
unskilled labor
Diminishing rate of unskilled
workers
Entrepreneurial overload in training
skilled labor
Diminishing rate of effective labor
hired in integrated production
Cost before quality adjustment
Diminishing rate of manual
component
Inefficiency of network knowledge
contributing to present period output
Inverse of matching between
domestic firms and overseas supplier
Diminishing rate of effective labor
hired in outsourcing
Human capital in foreign labor
market
Decrease in efficiency of foreign
labor producing low-skilled intensive
components
Skilled labor supply
Unskilled labor supply
Human capital in local labor market
Integrated productivity stock
Network knowledge stock
Inefficiency of last period aggregate
stock contributing to current network
knowledge
Inefficiency of last period aggregate
stock contributing to current network
knowledge
Aggregate productivity in evolution
of network knowledge stock
Aggregate productivity in evolution
of integrated productivity stock
Inverse of networking efficiency in
outsourcing mode
Inverse of networking efficiency in
integrated production mode
Rate at which previous network
knowledge depreciates.
Rate at which previous integrated
productivity stock depreciates.
FDI
Note: * stands for ambiguous
LR
w
w
mt*
-
+
-
-
-
-
-
+
-
+
-
+
-
+
-
-
+
+
-
+
+
-
+
-
+
-
+
-
+
+
+
+
+
+
-
+
-
-
+
-
+
+
+
+
+
+
+
-
+
-
+
+
+
-
-
+
-
-
+
-
-
+
-
+
-
+
-
+
not considered
-
s
t
u
t
w
w
m
+
*
t
s
t
u
t
s
t
u
t
w
w
mt*
Davies
(2005)
SR
s
t
u
t
w
w
+
+
+
-
*
mt*
68
4.
General Discussion
After obtaining interesting relationships from the comparative statics analysis, we
hereby attempt to provide a general discussion on the implications of the selected
relationships, which tally with world developments, on the domestic economy with
respect to entrepreneurs’ decision to perform outsourcing and factor prices.
In the model, we found that the reduction in the cost before quality adjustment of
the manual components can lead to an increase in the prevalence of outsourcing activities.
With the advancement of technology over time, service link costs have been rapidly
reduced. Such advances have included the advancement in management, human resource,
information
and
engineering
technology.
These
technological
changes
have
unambiguously led to higher wage inequality which is consistent with Egger and
Grossmann (2005). Although the welfare of entrepreneurs has been raised, the welfare of
domestic workers has fallen.
A reduction in the inverse of matching between domestic firms and overseas
supplier can lead to an increase in outsourcing activities. This is reinforced by the
implementation of policies which include the liberalization of the telecommunication
sector in developing countries such as China and India and the formulation of Free Trade
Agreements (FTAs) between nations, which can encourage more outsourcing activities.
However, the prevalence of outsourcing activities will lead to a fall in GDP as the fall in
welfare of domestic workers dominates the overall increase in that of entrepreneurs.
Thirdly, entrepreneurs undertaking the integrated mode of production have been
enhancing their efficiency in training skilled and unskilled workers. Such an increase in
efficiency will lead to the dominance of integrated production over time. In addition, the
welfare of the economy is raised, as skilled and unskilled labor earn higher income. Since
there is a trade off between the welfare of domestic workers and entrepreneurs, the overall
welfare of entrepreneurs decline.
69
The recent trend of an increase in the human capital of developing countries such
as China and India has resulted in more outsourcing activities. This is consistent with
reality as developed countries such as Japan and the U.S have increasingly outsourced
manual components to these developing countries. Furthermore, to raise the welfare of
domestic workers, the developed country should seek to actively raise the skill level of
the economically active through providing skills upgrading courses and providing higher
education opportunities for the population.
5.
Conclusion
This paper takes a fresh approach in developing a simple dynamic model for a
small, developed and open economy, which captures the transition of the two state
variables, namely integrated productivity and entrepreneurial network knowledge stocks.
Our motivation arises from the fact that firms are increasingly outsourcing manual
components to foreign, developing countries, thus establishing networks with affiliates in
the process. Through the evolution of the two stock variables, previous periods’ stocks
have contributed to a common aggregate stock which has spillover effects on all firms in
the domestic economy in the present period. Moreover, we have endogenized the
entrepreneurial ability threshold together with skilled and unskilled wages. This paper has
thus examined the impact of evolution of networking on 1) wage inequality between
skilled and unskilled labor 2) the decision to outsource by entrepreneurs and 3) the
welfare of entrepreneurs versus domestic workers.
In the long run, both wage inequality and the threshold level of entrepreneurial
ability undergo a gradual transition to a unique and stable mixed equilibrium, which
differs from Acemoglu et al. (2002b) whereby only corner solutions exist. This is more
consistent with the observation made in the real world. In addition, through examining the
70
transition of the threshold level of entrepreneurial ability and wage inequality over time,
the short-run and long-run impacts on endogenous variables are different in magnitude.
In comparing the comparative statics for both static and dynamic models, we find
that the static model is inadequate in explaining the impact of networking on the economy
since it fails to take into account the transition of the state variables over time. However,
it is adequate in explaining other exogenous parameters such as human capital in local
and foreign labor markets and service link cost. We find that the decrease in service link
cost and increase in human capital of foreign country will increase outsourcing activities
while increasing wage inequality. In particular, the increase in human capital of the
domestic economy and decrease in entrepreneurial overload in training both types of
labor reduce wage inequality, which differ from conventional results. Interestingly, an
increase in networking efficiency in the outsourcing mode leads to different impacts on
the endogenous variables in the short and long runs: outsourcing activities will dominate
in the short run whereas integrated production dominates in the long run.
Given the exogenous changes in all the parameters, we also observe that there
exists a positive correlation between outsourcing activities (which is defined in terms of
threshold level of entrepreneurial ability) and wage inequality. Thus, they co-move in the
same direction.
In addition, we examine the impact of the exogenous parameters on the GDP of
the domestic economy, as well as the welfare of the three major types of players in the
economy. Interestingly, we observe that there exists a trade off between the welfare of
domestic workers and entrepreneurs. This implies that an increase in outsourcing
activities will reduce the welfare of domestic workers while increasing the overall welfare
of entrepreneurs. The converse is true when entrepreneurs prefer to undertake integrated
production. Another striking result is that an increase in outsourcing activities is not
necessary beneficial to the overall welfare of the domestic economy. An increase in
71
outsourcing activities due to an increase in matching ability of the entrepreneurs actually
worsens GDP. This is mainly due to the dominance of the decrease in total integrated
profits and labor income over the increase in total outsourcing profits.
From these interesting findings, we are able to shed light on world developments,
which are namely the reduction in transaction and telecommunication costs, increase in
training efficiency and increase in human capital of developing countries. Finally, we also
compare our model’s results with previous studies’ and find that most papers have
focused on wage inequality. Our model is thus richer as we explore the endogenous
relationships between entrepreneurs, skilled and unskilled workers in both short and long
runs.
Hence, the above results add a challenge to many of the prevailing views on wage
inequality and the structure of the economy. Future research could incorporate FDI and
endogenous human capital accumulation of skilled workers and the subsequent impact on
wage inequality, GDP, welfare of entrepreneurs and domestic workers and hence growth
of the economy. It also remains to test the hypothesis empirically, whether the formation
of the two different types of networking stocks truly affects wage inequality and the
decision to outsource.
72
Bibliography
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Journal of Economic Literature, Vol.40, no.1, p.7-72
2. Acemoglu, Daron, Aghion, Philippe and Zilibotti, Fabrizio (2002b). “Vertical
Integration and Distance to Frontier.” National Bureau of Economic Research
Working Paper 9191.
3. Anderson, James E. and Marcouiller, Douglas (2002). “Insecurity and the Pattern
of Trade: An Empirical Investigation.” Review of Economics and Statistics,
Vol.84, no.2, p.342-52
4. BEA, 1997. Survey of Current Business, the United States.
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North American Journal of Economics and Finance, Vol.16, p.61-79
6. DeGroot, Henri L.F De (2001). “Macroeconomic Consequences of Outsourcing:
An Analysis of Growth, Welfare, and Product Variety”, De Economist, Vol.149,
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Labor, New Technologies and Wage Inequality.” Metroeconomica, Vol.56, no.1,
p.37-57
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inequality, and economic growth.” Quarterly Journal of Economics, Vol.115,
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Integration.” Journal of International Economics, Vol.67, issue 1, p.157-74
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11. Greiner, Alfred, Rubart, Jens and Willi, Semmler. (2004). “Economic growth,
skilled-biased technical change and wage inequality: A model and estimations for
the US and Europe.” Journal of Macroeconomics, Vol.26, p.597-621.
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the international organization of production.” Journal of International Economics,
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Global Sourcing, or Increasing Importance of MNE Networks?” Review of
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74
APPENDIX A
i)
Proof of Proposition 1
We substitute equations (17) to (20) into equation (6), and re-express the profit
function for the intermediate firm that engages in vertical integration as:
δ
β
s
u
w
w
t
t
πtI =
α
γ
α
γ
δ
At H α +γ α +γ
1
β +δ −1
1
1
1
β
+
δ
−
1
β
+
δ
−
1
β
+
δ −1
1
1
1
− δ 1−δ
− 1−β β
δ δ β β
(A1)
δ β
δ β
For the above profit function to be positive, we set π tI f 0 . It can be seen that the first
term in equation (A1) is positive regardless of positive or negative values for β and δ .
Hence, we will be focusing on the second term in the equation:
1
1
δ β
δ β
β +δ −1
1
− δ 1−δ
δ β
1
δ β
δ β
β +δ −1 1
f δ 1−δ
δ β
1
1
Dividing δ β
δ β
1
β +δ −1
1
1
1
− 1−β β
δ β
β +δ −1 1
+ 1− β β
δ β
β +δ −1
f0
(A2)
1
β +δ −1
(A3)
1
β +δ −1
throughout equation (A3) and rearranging the terms, we
obtain β + δ p 1, hence proving the sufficient condition for Lemma 1. It can easily be seen
that the necessary condition is satisfied too.
ii)
Proof of Proposition 2
Similarly, we substitute equations (26) and (27) back into equation (7):
π tO
a
b
K t −1 mt H d
=
ρ χ sd
ν wt
h
1
1− d − χ
d −1+ χ − dχ
χ d 1−d1− χ χ
(
χ d )
− χ d ( d −1)
1
1
1− d − χ
1
−
d
d
− (χ d )1− d − χ
(A4)
75
For outsourcing profit to be positive, we set π tO f 0 . It can be seen too that the first term
in equation (A1) is positive regardless of positive or negative values for d and χ . Hence,
focusing on the second term in the equation:
(χ
χ
d
−χ χd
)
1
d 1− d − χ
d −1+ χ − dχ
( d −1)
1
1− d − χ
(
)
1
1− d − χ
− χ 1− d d d
f0
(A5)
1
(χ
χ
d
)
1
d 1−d − χ
Dividing
χ d −1(d+−χ1−)dχ 1−d −χ
f χ d
+ χ 1−d d d
(χ
(
χ
dd
)
1
1−d − χ
)
1
1−d − χ
(A6)
throughout equation (A6) and rearranging the terms, we
obtain d +χp1, thus proving the sufficient condition for Proposition 2. Similarly, it can
easily be seen that the necessary condition is satisfied too.
iii)
Proof of Proposition 3
To prove that the conditions must be given so that an interior solution 0 p mt* p 1 exists,
we use equation (29):
ws
*
mt = t
H
t
At
χ
1
b
1− d − χ
W
h
b
K t −1a S
(1−d − χ ) ρ
δ (1− d − χ )+ d ( β +δ −1)
β ( β +δ −1)b ν
u
b
1
β
+
δ
−
(
)
w
(A7)
where
W =
α
α + γ
S = χ χd d
(
1
1
)
α
γ
α + γ
1
1− d − χ
γ
β +δ −1
1
δ δ β β
− χ χd
d −1 + χ − d χ
( d −1 )
1
β +δ −1
1
− δ 1−δ
δ β
1
1− d − χ
− χ 1− d d d
(
)
1
β +δ −1 1
− 1− β β
δ β
1
1− d − χ
1
β +δ −1
(A8)
(A9)
76
Assumptions in Proposition 1 and Proposition 2 prove that m t* f 0 . This is mainly
because under both the assumptions whereby β + δ p 1 and d +χp1 , W and S are
ensured to be positive and greater than zero. In addition, since wts , w tu , H , At , K t −1 and
ρ
ν are between zero and one, it can be easily seen that the right hand side of
h
equation (A7) is greater than zero, hence proving m t* f 0 .
To prove that condition 3 must be given so that m t* p 1 :
χ
(1− d − χ ) ρ
δ (1− d − χ )+ d ( β + δ −1)
b ( β + δ −1 )
w u β (β +δ −1)b hν
wts
t
H
At
K t −1 a
δ (1− d − χ )+ d ( β + δ −1 )
s
b ( β + δ −1)
wt
β (1− d − χ )
u ( β + δ −1)b
wt
ρ χ
ν
h
p a
K t −1
−
1
b
1− d − χ
W
b p1
S
(A10)
1
b
W
S
d + χ −1
b
H
δ (1− d − χ )+ d ( β + δ −1)
b ( β + δ −1)
(1− d − χ )
At (β +δ −1)b (A11)
Rearranging the terms, we can rewrite equation (A11) as:
ρ
ν
s
u δ (1− χ )− d (1− β ) h
wt p wt
K t −1 a
χ
β ( χ + d −1)
−
b ( β + δ −1 )
b
W
S
b ( d + χ −1 )( β + δ −1 )
b
H δ (1− d − χ )+ d ( β +δ −1) At
(1− d − χ )
(A12)
At this point, given that wages are not yet endogenized, it can be seen that equation (A12)
must hold in order for m t* p 1 . To illustrate this, if wtu increases, wts must increase too.
However, the magnitude of increase in wts cannot be too large until it exceeds the left
hand side of equation (A12), hence violating the third condition. Intuitively, when
equation (A12) is violated, no entrepreneurs will choose to undertake outsourcing mode
77
of production when wts is too large, which implies that skilled workers are too expansive
to be hired.
[...]... evolution of GDP, profits, and wage incomes over time given various shocks to the economy Greiner, Rubart and Semmler (2004) have observed that wage inequality had been increasing in the United States (U.S) and the United Kingdom (U.K) from early 1960s to late 1990s1 However, the pattern of wage inequality for West Germany is unclear Using OECD data, they observed that wage inequality in West Germany... in wage inequality over time is mainly due to the interaction effects of network stocks formed by entrepreneurs involved in integrated and outsourcing modes of production One major motivation for the incorporation of network knowledge is that international outsourcing can be hindered by informal trade barriers, such as weak enforcement of international contracts (Anderson and Marcouiller, 2002) and. .. small, open and developed economy is constructed to examine the impact of the formation of network knowledge due to international outsourcing on the three key types of players in the domestic economy, which are namely the entrepreneurs, skilled and unskilled workers We seek to investigate 1) the welfare between entrepreneurs and domestic workers and 2) the wage inequality between skilled and unskilled... integrated production, we model entrepreneurial overload in the training of unskilled and skilled labor through the parameters α and γ respectively, as t tu and t ts lies between zero and one Similarly, as Lut and LSI t are less than one, β and δ imply that unskilled workers and effective workers increase at a diminishing rate respectively 2.2.2 Firms Choosing To Engage In Outsourcing Activities Firms... and aggregate stock of knowledge in the economy We examine the above model via the incorporation of entrepreneurial ability to determine the threshold level above which international outsourcing will occur, which is often neglected by previous literature This is crucial since entrepreneurs are required to train workers and coordinate outsourcing activities In the outsourcing mode of 5 production, entrepreneurial. .. trend in wage inequality Most studies have attributed the upward trend due to the evolution of technology Some of the most commonly cited reasons for the evolution of technology over time are skilled-biased technological change (Galor and Moav, 2000) and the 1 For the U.S, U.K and West Germany, cross-country data of wage differentials are taken from OECD Employment Outlook (1993,1996) whereby wage inequality. .. 1 d −1 (27) From equations (26) and (27), it can be seen that the marginal product of manual component and demand for skilled labor are constrained by the cost of the manual component, previous period network knowledge stock, entrepreneurial ability, human capital and skilled wages Proposition 2: Profit for outsourcing mode of production is positive if and only if the condition d + χ p 1 exists... (20) From equations (19) and (20), we observe that the demand functions for unskilled and skilled labor supply are constrained by wage costs, integrated productivity and human capital in the economy 13 Proposition 1: Profit for integrated production is positive if and only if the condition β + δ p 1 exists Proof: See Appendix A Hence, proposition 1 shows that both effective and unskilled labor must... it can be seen that previous period network knowledge, entrepreneurial ability and human capital are positively related to π tO while skilled wages and marginal product of manual component are inversely related to it 2.5 Equilibrium In this section, we analyze firms’ decision to engage in international outsourcing or integration, depending on entrepreneurial ability Firms will only decide to adopt... introduce simple evolution mechanism of the entrepreneurial network stock and integrated productivity stock and proceed to investigate how the evolutions of the two stock variables, At and K t , may affect the organizational form of production and factor prices over time 3.1 The Model We assume that interaction between firms involved in vertical integration and outsourcing activities in the domestic economy ... technology either due to international outsourcing or skilled-biased technical change In this paper, we investigate the impact of international outsourcing on both wage inequality and entrepreneurs’... that international outsourcing can be hindered by informal trade barriers, such as weak enforcement of international contracts (Anderson and Marcouiller, 2002) and inadequate information about international. .. both short and long runs, a decrease in ρ causes wage inequality to increase This is because firms demand more skilled labor as the demand for outsourcing mode rises Subsequently, the wage gap
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