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OUTSOURCING TYPES, RELATIVE WAGES, AND THE DEMAND FOR
SKILLED WORKERS: NEW EVIDENCE FROM U.S. MANUFACTURING
AEKAPOL CHONGVILAIVAN, JUNG HUR and YOHANES E. RIYANTO*
Existing studies on the impact of outsourcing on relative wages and the demand for
skilled workers mainly focus on aggregate outsourcing, in which imported
intermediate inputs are used as a proxy. We depart from the existing studies by
focusing on various types of outsourcing based on the six-digit NAICS U.S.
manufacturing data. We show that downstream materials and service outsourcing
are skill biased, whereas upstream materials outsourcing is not. We also produce
other supplementary results pertaining to the impact of technology, different
capital inputs on relative wages, and the demand for skilled workers. (JEL C33,
F14, F15)
I. INTRODUCTION
The pivotal roles of international outsourc-
ing and skill-biased technology in explaining
the dramatic increase in relative wages of
skilled workers in industrialized economies
have been extensively documented and ana-
lyzed in the literature.
1
In this literature, the
notion of outsourcing is typically confined
mainly to the imported intermediate inputs.
For analytical purposes, using imported inter-
mediate inputs can be justified, given that
imports of intermediate inputs should be ex-
pected to affect the relative demand for
manufacturing workers and relative wages;
2
nevertheless, some important insights into the
role of different types of outsourcing cannot
be sufficiently emphasized.
In principle, firms differ in the extent of
their specialization in activities along the ver-
tical chain of production. Some firms may
engage in many activities along the chain, ex-
tending from upstream (intermediate inputs)
production to downstream (final goods) pro-
duction, while some other firms may specialize
in either upstream or downstream production.
The upstream production of intermediate
inputs may involve an intensity of skills differ-
ent from that of the downstream production
of final goods. For instance, General Motors
may outsource activities that deal with the
product design and the production of high-
tech components (upstream activities) and
may specialize in car production (downstream
activity), whereas Apple may outsource the
production of its iPod players (Apple’s down-
stream activity) and specialize in research and
development and product design (upstream
activity). Consequently, it seems unrealistic to
assume that upstream outsourcing should have
the same impact on the relative demand for
skilled workers as downstream outsourcing.
*We gratefully thank two anonymous referees for
helpful comments. The first author would also like to fur-
ther thank participants at the Asia Pacific Trade Seminars
2007 for thoughtful discussions.
Chongvilaivan: Research Fellow, Department of Eco-
nomics, National University of Singapore, AS2, 1 Arts
Link, Singapore 117570. Phone +65-6516-4524, Fax
+65-6775-2646, E-mail ecsac@nus.edu.sg
Hur: Associate Professor, Department of Economics,
Sogang University, Shinsu-dong, Mapogu, Seoul,
121-742, Republic of Korea. Phone +82-2-705-8179,
Fax +82-2-705-8180, E-mail ecsjhur@sogang.ac.kr
Riyanto: Assistant Professor, Department of Economics,
National University of Singapore, AS2, 1 Arts Link,
Singapore 117570. Phone +65-6516-6939, Fax +65-
6775-2646, E-mail ecsrye@nus.edu.sg
1. See, for instance, Feenstra and Hanson (1996, 1999)
for United States, Feenstra and Hanson (1997) for Mex-
ico, Anderton and Brenton (1999) for the United King-
dom, Geishecker (2002) for Germany, and Hsieh and
Woo (2005) for Hong Kong.
2. Note that it is generally accepted that changes in
labor supply fail to account for this phenomenon.
ABBREVIATIONS
ASM: Annual Survey of Manufactures
H-O: Heckscher-Ohlin
NAICS: North American Industry
Classification System
IV: Instrumental Variable
OLS: Ordinary Least Squares
Economic Inquiry doi:10.1111/j.1465-7295.2008.00131.x
(ISSN 0095-2583) Online Early publication April 17, 2008
Vol. 47, No. 1, January 2009, 18–33 Ó2008 Western Economic Association International
18
Outsourcing or contracting out some activ-
ities along the vertical chain of the production
process enables firms to specialize in other
activities along the vertical chain where they
have a comparative advantage. Firms that
specialize in downstream production may out-
source their upstream materials, while firms
that specialize in upstream production out-
source their downstream materials. Both types
of firm may also outsource their services, for
example, repair and maintenance services for
machinery, communication services, financial
services, and information technology services,
in order to focus on their core activities.
3
If
upstream production is more skill intensive,
outsourcing downstream production can re-
duce their dependency on unskilled workers
and hire more skilled workers to take advantage
of the increasing productivity of the upstream
activities driven by specialization. Given this
difference in skill intensity along the production
chain, the negative impacts on the relative
skilled labor demand would likewise be
expected if they outsource upstream produc-
tion. Obviously, types of outsourcing that are
different may have different impacts on both
the demand for skilled workers and the relative
wages. Therefore, focusing on the various types
of outsourcing activities should enable us to get
richer results. To the best of our knowledge,
these refined notions of outsourcing have
largely been unexplored in the literature.
4
A study by Amiti and Wei (2006) is perhaps
the closest to our paper. Their paper analyzes
the impacts of both materials and service out-
sourcing on overall labor productivity. They
argue that, by engaging in materials and ser-
vice outsourcing, firms can delegate parts of
the production process that are inefficient to
other more efficient firms. They can then focus
on those activities in which they have compar-
ative advantage and increased output. Conse-
quently, the average productivity of the
remaining workers should increase. It should
be noted, however, that Amiti and Wei (2006)
only look at aggregate workers; they do not
really examine the impact of outsourcing activ-
ities on the demand for skilled workers relative
to that for unskilled workers. Furthermore, in
contrast with this study, they do not really
decompose materials outsourcing any further.
Our approach, which separates materials out-
sourcing into upstream and downstream mate-
rials outsourcing, allows us to capture the
notion of the vertical specialization of firms
along different stages of the production pro-
cess and to examine the impacts of this vertical
specialization on the labor market.
Ourempirical estimations arebased on the dis-
aggregated six-digit North American Industry
Classification System (NAICS) U.S. data on
manufacturing industries (Sectors 31–33). To
investigate the more detailed impacts of out-
sourcing, we combine two data sets. The first is
the 2002 Annual Survey of Manufactures
(ASM), which contains six-digit NAICS data
on U.S. manufacturing, such as estimates for
employment, plant hours, payrolls, value added
by manufacturers, capital expenditures, and cost
of materials for most manufacturing industries.
The second data set is the 2002 Economic Census,
which contains detailed data on production
structuresandcostsandalsoondownstream
and upstream materials and service outsourcing.
In addition to these two data sources, we use the
U.S. International Trade Statistics,providedby
the U.S. Census Bureau, for the data on imports.
Our empirical strategy is to estimate the rel-
ative demand for skilled workers derived from
a modified version of the translog cost func-
tion pioneered by Brown and Christensen
(1981). Our results show that upstream mate-
rials outsourcing is not skill biased,
5
whereas
downstream materials and service outsourcing
is skill biased. Our results thus partly contrast
with conventional findings, which assert that
outsourcing is always skill biased. It should
also be highlighted that, due to data availabil-
ity, our results rely on cross-sectional estima-
tions rather than panel data estimations that
are generally found in the outsourcing litera-
ture. For future research, when data availabil-
ity is no longer an issue, it would be interesting
to check for the robustness of our results
under panel data estimations.
3. The above decomposition of outsourcing into three
different types is consistent with the definition of out-
sourcing put forward by Grossman and Helpman
(2002, 2005). They basically define outsourcing as the
extent to which the production materials, parts, or service
activities are contracted out to outside partners.
4. The index of outsourcing in this paper is therefore
different from those of Feenstra and Hanson (1996) and
other mainstream outsourcing literatures in the sense that
ours is concerned with its typology, whereas theirs deals
with its location.
5. Throughout this paper, the skill-biased effect of
outsourcing refers to the extent to which outsourcing
has a positive effect on the demand for skilled labor rel-
ative to that of unskilled labor.
CHONGVILAIVAN, HUR & RIYANTO: OUTSOURCING TYPES 19
The intuitions behind our results can be
explained as follows. Downstream materials
and service outsourcing activities enable
skill-intensive firms to reallocate their resour-
ces to the upstream production activities,
which are skill intensive. The productivity
of skilled workers engaged in the upstream
production activities will then be enhanced.
Accordingly, these kinds of outsourcing activ-
ities should have a positive impact on the
relative wages of skilled workers. Upstream
materials outsourcing activities, on the other
hand, have an opposite impact. They enable
firms to specialize in those downstream pro-
duction activities that are not skill intensive,
thereby having a negative impact on the rela-
tive wages of skilled workers.
We also report two further interesting
results. First, we find that, when disaggregat-
ing capital into machinery and buildings, the
former is a substitute for and the latter a com-
plement of, skilled workers. This is partly in
contrast with the existing empirical evidence,
which shows capital stocks and skilled work-
ers as complements.
6
Second, we also show
that technological progress is skill biased.
This paper is organized as follows. Section
II briefly reviews the existing empirical results
on the impact of outsourcing activities on the
relative demand for skilled workers. Section
III discusses our empirical model and its der-
ivation together with our empirical strategy.
Section IV gives detailed descriptions of our
data and data measurement. Section V pres-
ents our empirical results, and Section VI
offers some conclusions.
II. OVERVIEW OF THE RELATED LITERATURE
Throughout the 1980s and 1990s, the U.S.
economy witnessed a widening gap between
skilled and unskilled wages. Various theoreti-
cal propositions have been put forward to
explain this phenomenon, such as Grossman
and Helpman (2002, 2005) and Gao (2007)
among others. Trade economists, for instance,
have argued that the gap can be attributed to
international trade in intermediate goods or
‘‘outsourcing’’ as it is often referred to in
the literature. Feenstra and Hanson (1996)
were the first to empirically verify this out-
sourcing-based theoretical proposition. They
show that around 15%–33% of the relative
increase in wages of skilled workers can indeed
be explained by international outsourcing.
Later, Feenstra and Hanson (1999), using im-
ported intermediate inputs, revealed that
skill-biased technological change can also sig-
nificantly explain the observation. Subsequent
to the publication of these two seminal papers,
many authors have replicated these results
using data from other industrialized countries,
such as the United Kingdom, Germany,
and Hong Kong, and have found supporting
evidence.
7
More recently, some papers have shed fur-
ther light on the issues of wage inequality.
Blum (2007), for instance, shows that a struc-
tural shift in the sectoral composition of the
economy could also explain the rising wages
of, and demand for, skilled workers. His argu-
ment is motivated by an observation that in
the United States, there have been some falls
in the level of employment and capital accu-
mulation in the manufacturing sector and,
at the same time, some increases in the level
of employment and capital accumulation in
the nonmanufacturing sector, for example,
in services and in the retail and wholesale trade
sectors. He further asserts that if capital is
complementary to skilled workers in the non-
manufacturing sector, the above sectoral shift
would have caused an increase in the wage
inequality between skilled and unskilled work-
ers in the economy. He empirically tested his
assertion using U.S. data and shows that the
sectoral reallocation from manufacturing to
services and retail and wholesale trade sec-
tors can indeed account for the increasing
wage gap.
In contrast to Blum’s (2007) model, in
which capital is immobile across countries,
Sachs and Shatz (1998) develop a model in
which capital is allowed to flow outside the
country. They show that such a capital out-
flow can raise the relative wages of skilled
workers in the nontraded goods sectors.
Despite the above essential difference, both
models do indeed highlight the important role
of capital inputs and structural change in
explaining the wage inequality between skilled
6. See Geishecker (2002), Anderton and Brenton
(1999), and Feenstra and Hanson (1997).
7. See Feenstra and Hanson (1997) for Mexico,
Anderton and Brenton (1999), Hijzen, Go
¨rg, and Hine
(2005), and Hijzen (2007) for the United Kingdom,
Geishecker (2002) for Germany, and Hsieh and Woo
(2005) for Hong Kong.
20 ECONOMIC INQUIRY
and unskilled workers. Our paper will also
investigate the role of capital inputs empiri-
cally. In particular, we will decompose capital
inputs into two categories. The first category is
machinery and equipment, and the second is
buildings and other structures. We show that
different capital inputs will have different
implications for relative wages and the de-
mand for skilled workers.
The study of Amiti and Wei (2006) is, in
content, perhaps the closest paper to ours.
They evaluate the impacts of international
outsourcing, or offshoring in their terminol-
ogy, on the productivity of the U.S. manu-
facturing sector. The starting point of their
paper is the twin stylized observations of in-
creasing trends in productivity and inter-
national outsourcing in the United States in
recent decades. In their framework, produc-
tion technology is determined by both materi-
als and service offshoring. They argue that if
firms are able to internationally fragment the
inefficient parts of their production process by
outsourcing, they can then specialize in other
parts of the production process where they
have a comparative advantage. Accordingly,
the average productivity of labor in the econ-
omy should increase. In addition to the spe-
cialization effect, the average productivity
will also increase due to a host of other effects
such as restructuring effects, learning external-
ities, and variety effects brought about by off-
shoring.
8
Their empirical results substantiate
their argument. They are able to show that
outsourcing does make a positive impact on
overall labor productivity. Unfortunately, few
conclusions can be drawn about the impact
of outsourcing on wage inequality.
Interestingly, in an earlier work, Amiti and
Wei (2005), using a similar framework, found
that offshoring has either a small negative
effect on employment when a disaggregated
manufacturing sector is used or no effect at
all when a more aggregated manufacturing
sector is used. Thus, the effect of offshoring
on employment seems to be inconclusive.
Our paper departs from Amiti and Wei
(2005, 2006) by focusing specifically on the
impacts of outsourcing on the relative wages
of skilled to unskilled workers and on the
demand for skilled workers instead of on
the impacts of outsourcing on overall produc-
tivity and employment. The notion of out-
sourcing in our context follows that of
Abraham and Taylor (1996) in the sense that
outsourcing and in-house production are sub-
stitutes; therefore, they should affect the
demand for labor regardless of location. As
such, rather than merely focusing on the
trade-related aspects of outsourcing, we take
into consideration both domestic and interna-
tional outsourcing. Our paper also differs
from their papers in many other respects.
First, we categorize workers as skilled or
unskilled, while they view workers as one
whole group. Second, we further decompose
outsourcing activities into upstream and
downstream materials outsourcing and service
outsourcing, while they look at aggregate
materials and service outsourcing. Third, we
estimate a cost share of skilled workers using
a cross-industry analysis, while they estimate
a production function using a panel data anal-
ysis. Finally, our paper focuses on a more dis-
aggregated level of the manufacturing sector
than theirs does.
The main contributions of our paper are as
follows. To the best of our knowledge, our
paper is the first empirical paper that looks
at various types of outsourcing activities, that
is, upstream and downstream materials out-
sourcing and service outsourcing.
9
Next, our
paper produces a new empirical finding that
shows that outsourcing is not always skill
biased. Downstream materials outsourcing
and service outsourcing are skill biased, but
upstream materials outsourcing is not.
III. THE EMPIRICAL MODEL
Our empirical strategy is to estimate a rela-
tive demand for skilled workers. The most
essential structural variables in our analysis
are those that capture various types of out-
sourcing activities.
The production function for an industry iis
given by the following expression:
Yi5FiðLHi;LLi ;Ki;outs
i;outm
i;TiÞ:ð1Þ
8. A more detailed description of these effects can be
found in Amiti and Wei (2006).
9. It should also be noted that the present paper also
departs from Go
¨rg and Hanley (2005) in the sense that
they split sample industries into upstream and down-
stream industries, but we look at the impacts of outsourc-
ing upstream and downstream activities by manufacturing
industries.
CHONGVILAIVAN, HUR & RIYANTO: OUTSOURCING TYPES 21
The output for industry i,Y
i
, depends on
three primary factors, namely high-skilled
workers, L
Hi
, low-skilled workers, L
Li
,and
capital, K
i
. The service outsourcing, outs
i,
materials outsourcing, outm
i, and the level of
production technology, T
i
are assumed to
enter the production function via neutral
and nonneutral technological shifts. Note that
Amiti and Wei (2006) use a production func-
tion similar to that in Equation (1), but their
variables are confined to a neutral technolog-
ical shift fashion. Furthermore, we disaggre-
gate the labor input according to the skill
attribute in order to capture the impacts of
outsourcing on the relative demand for skilled
workers.
Subsequently, we derive a short-run cost
function, assuming that capital stockK
i
is quasi
fixed in order to take into account the extent to
which it may be different from its long-run
equilibrium. Accordingly, the short-run (vari-
able) cost function, where the levels of capital
and output are fixed, can be derived from the
following optimization problem:
ciðwHi;wLi ;Ki;Yi;outs
i;outm
i;TiÞ
5min
LHi;LLi
wHiLHi þwLi LLi
subject to ð1Þ:
ð2Þ
The next step is to choose a functional form
fitting the short-run unit cost function (2). Fol-
lowing Brown and Christensen (1981), the unit
cost function (2) can be approximated by a
general translog function with variable and
quasi-fixed input factors. For notational sim-
plicity, we temporarily drop the industry sub-
script i. Without loss of generality, we also
assume symmetry. Equation (2) can be further
written into:
ln c5aoþw
#aþz
#bþð1=2ÞH
#XH;ð3Þ
where w#
5ðln wHln wLÞ,a#
5ðaHaLÞ,z#
5
ðln Kln Yln outmln outsln TÞ,b
#
5ðbKbY
bMbSbTÞ,H#
5ðw#z#Þ, and Xis a 7 7
matrix of coefficients. We relegate the expan-
sion of Equation (3) and the restrictions on
parameters, ensuring the linear homogeneity
of Equation (3) to Appendix A1.
The crucial property of the translog function
can be derived by differentiating Equation (3)
with respect to ln wk;k5H;L.LetWS
k5ð@ln
c=@ln wkÞ5Lkwk=c;k5H;Ldenote the cost
share of skilled and unskilled workers in vari-
able costs. Since skilled and unskilled workers
are the only variable factors of production,
the share of both factors must add up to unity
and only one of them is linearly independent.
As such, we focus on the estimation of the
skilled workers’ cost share equation. By differ-
entiating Equation (3) with respect to ln w
Hi
and
invoking the symmetry assumption and linear
homogeneity restriction, we obtain
WSHi 5aHþclnðwHi=wLi Þþ/HK ln Ki
þ/HY ln Yiþ/HS ln outs
i
þ/HM ln outm
iþ/HT ln Ti:
ð4Þ
It is conventionally known that the cost
share is essentially an expression of the relative
demand for skilled workers, which in turn
reflects not only the relative employment but
also the relative factor prices. However, we
are going to modify the above specification
for the following reasons.
First, it is questionable whether the rela-
tive-wage term in Equation (4) should be
incorporated in the estimation. This is because
the dependent variable is a composite measure
of not only the relative demand for skilled
workers but also the relative wages. Hence,
the relative-wage term should be excluded
from the estimation of Equation (4) since rel-
ative wages are unlikely to be exogenous and
there is a problem of a definitional relationship
between the share of skilled workers’ wage bills
and the wage terms. Furthermore, as noted by
Berman, Bound, and Griliches (1994), the
cross-industry variation in wages provides lit-
tle information because the wage differential
across industries is mainly explained by the dif-
ference in the skill content of workers, so we do
not expect high-wage industries to economize
on the high-skilled workers. As such, an esti-
mation of Equation (4), with the relative-wage
term included, would yield biased coefficients.
Accordingly, we drop the relative-wage term
from Equation (4).
Second, the empirical model analogous to
Equation (4) has been prevalently employed
to explore the impacts of materials outsourc-
ing on the relative demands for skilled workers
in various economies by many studies, such
as Hanson and Harrison (1999), Anderton
and Brenton (1999), Dell’mour et al. (2000),
Geishecker (2002), and Hsieh and Woo (2005).
None of them, to the best of our knowledge,
22 ECONOMIC INQUIRY
has actually investigated the possibility that
various types of sourced materials that are
used in different stages of production have dif-
ferent effects on the relative demand for skilled
workers.
Therefore, we believe that it is worthwhile
to further investigate the role of various types
of outsourcing such as upstream and down-
stream materials outsourcing and also service
outsourcing. Accordingly, outm
iin Equation
(4) will be further broken down into upstream
materials outsourcing (outmu
i) and down-
stream materials outsourcing (outmd
i).
Last, the vector of three-digit NAICS
manufacturing industry dummies (D
i
) is also
introduced to control for industry-fixed ef-
fects. By adding a stochastic error term u
i
with
E(u
i
)50 and VarðuiÞ5r2, the estimated
econometric model can be specified as follows:
WSHi 5aHþ/HK ln Kiþ/HY ln Yi
þ/HS ln outs
iþ/HMuln outmu
i
þ/HMdln outmd
iþ/HT ln Ti
þ/HDDiþui:
ð5Þ
In addition to the wage share equation,
we also estimate the following employment
share equation to control for interindustry
differences in the relative wages of skilled
workers:
ESHi 5aHþclnðwHi=wLi Þþ/HK ln Ki
þ/HY ln Yiþ/HS ln outs
i
þ/HMuln outmu
iþ/HMdln outmd
i
þ/HT ln Tiþ/HDDiþui;
ð6Þ
where ES
Hi
is the share of skilled worker
employment in the total employment and
w
Hi
/w
Li
is the relative wages of skilled to
unskilled workers. Admittedly, as is also noted
in Anderton and Brenton (1999), the ad hoc
specification of Equation (6) is less satisfac-
tory from a theoretical point of view. Never-
theless, it should give us some interesting
insights into the impact of various types of
outsourcing on the employment of skilled
workers. It should also enable us to compare
our results with those obtained in previous
studies that also estimate such an employment
equation, such as, for example, Machin, Ryan,
and van Reenen (1996).
Two econometric problems may arise when
estimating Specifications (5) and (6), and they
need to be corrected. First, due to the varia-
tion in the size of the industries in our sample,
the stochastic error term u
i
is likely to be het-
eroskedastic, thereby producing a biased esti-
mator of r
2
in the standard ordinary least
squares (OLS) method. To tackle this problem,
we employ White’s (1980) heteroskedastic-
robust standard error procedure in the estima-
tion of Equations (5) and (6).
Second, there may be an endogeneity bias
problem in the estimation of Equations (5)
and (6). That is, the industry-specific level of
technology (T
i
), which is measured by high-
technology capital stocks such as computers
and data processing equipment, may be corre-
lated with an unobserved variable in the error
term. In order to verify whether there is indeed
such a problem, we run an instrumental vari-
able (IV) regression and apply a Hausman test
to the results. We use the rate of capacity uti-
lization and value added per establishment as
our instruments and express them as a loga-
rithm. Both are proxies for the industry-
specific production performance. Intuitively,
an industry that possesses high production
performance, as measured by its capacity uti-
lization and value added per establishment,
should be more likely to rely heavily on
high-technology capital stocks in order to
maintain a higher production efficiency and
lower production costs.
IV. DATA
A. Data Sources
Our data are retrieved from the following
data sources provided by the U.S. Bureau of
Census: the 2002 ASM, the 2002 Economic
Census, and the U.S. International Trade Sta-
tistics. The 2002 ASM provides six-digit
NAICS statistics for the manufacturing indus-
try. The manufacturing sector (Sectors 31–33)
in this survey is defined as comprising estab-
lishments that engage in the mechanical, phys-
ical, or chemical transformation of materials,
substances, or components into new products.
From this survey, we obtain data on the wages
and employment of skilled and unskilled
workers across the manufacturing sector.
Although this survey also provides data on
materials used in the production, unfortu-
nately it does not provide sufficiently detailed
CHONGVILAIVAN, HUR & RIYANTO: OUTSOURCING TYPES 23
statistics on materials and service outsourcing
or on proxies for technology capital. As noted
by Feenstra and Hanson (1999), we do not
normally think of, say, the purchase of steel
by a U.S. automobile producer as outsourc-
ing. But it is more common to consider the
purchase of automobile parts by such a com-
pany as outsourcing. Moreover, unlike the
existing empirical studies on the impacts of
outsourcing on the relative demand for labor,
there is no reason to confine the extent of out-
sourcing merely to sourcing of materials.
10
We
therefore supplement the above data with the
2002 Economic Census.
From the 2002 Economic Census, we obtain
detailed information on the cost and produc-
tion structure of manufacturing firms and
also on their use of technological capital
(e.g., computers, data processing equipment,
etc.), their purchase of intermediate materials
(e.g., components, containers, packaging,
etc.), and services (e.g., communication serv-
ices; accounting, auditing, and bookkeeping
services; computer services, etc.). We focus
specifically on the six-digit NAICS manu-
facturing sector data (Sectors 31–33).
Our combined data from the 2002 ASM
and the 2002 Economic Census yield 474 six-
digit NAICS manufacturing industries.
B. Dependent Variables
Using both data sets, we can express the
wage share of skilled workers in industry i
(WSHi) in Equation (5) as the ratio of the total
wage bills of nonproduction workers to the
total annual payrolls. The employment share
of skilled workers in industry i(ESHi ) in Equa-
tion (6) is measured by the ratio of the total
number of nonproduction workers to that
of workers.
C. Outsourcing
Upstream materials outsourcing (outmu
i)is
measured by the share of the total production
costs taken up by the costs of intermediate
parts and materials employed in the upstream
production stage. The downstream materials
outsourcing (outmd
i) is measured by the share
of the costs of contracting out activities, such
as reprocessing, repackaging, and blending, in
the total production costs. The scatter plots of
WSHi against ln outmu
iand ln outmd
iare repre-
sented in Figures 1 and 2, respectively. As
expected, the former shows a negative rela-
tionship between ln outmu
iand WSHi, while
the latter shows a positive correlation between
ln outmd
iand WSHi. Thus, different types of
materials outsourcing, that is, upstream or
downstream materials outsourcing, should
have different impacts on the relative demand
for skilled workers.
Service outsourcing (outs
i) is measured by
the share of services purchased in the total
production costs of industry i. Examples of
FIGURE 1
The scattered plot between ln out
mu
i
and WS
Hi
skilled wage share
-.6 -.4 -.2 0
logarithm of ratio of upstream material outsourcing
to total production cost
0.2.4.6.8
FIGURE 2
The scattered plot between ln out
md
i
and WS
Hi
.2 .4 .6 .8
skilled wage share
-8 -6 -4 -2 0
logarithm of ratio of downstream material outsourcing
to total production cost
10. For example, in Feenstra and Hanson (1999) and
Amiti and Wei (2006), the (imported) materials are used
as proxies of ‘‘broad measures’’ of materials outsourcing.
One can argue that these measures may be imprecise as the
use of raw materials should not by definition be considered
as the result of outsourcing decisions of firms.
24 ECONOMIC INQUIRY
services that are outsourced are repair and
maintenance services of machinery and equip-
ment; communication services; accounting,
auditing, and bookkeeping services; and com-
puter and hardware services. Figure 3 depicts
a positive relationship between ln outs
iand
WSHi.
D. Control and IVs
Capital Inputs. Similar to Geishecker (2002),
we use the value of buildings and other struc-
tures (KBLD
i) and also machinery and equip-
ment (KMCH
i) in industry ias proxies for the
total amount of capital inputs employed in
industry i(K
i
). The expected sign of the
coefficient of ln K
i
could be either negative
or positive depending on whether or not
capital inputs and high-skilled workers are
substitutes.
Figure 4 depicts a positive relationship
between the ratio of the total value of build-
ings and other structures to the total value
of the assets and the wage share of skilled
workers. Figure 5 depicts a negative relation-
ship between the ratio of the total value of
machinery and equipment to the total value
of the assets and the wage share of skilled
workers. The relationship portrayed in Fig-
ure 5 is the exact opposite of the one portrayed
in Figure 4. It appears that machinery and
equipment and skilled workers are substitutes.
Where firms are machinery and equipment
intensive, their workers tend to have a lower
wage share. By contrast, buildings and other
structures and skilled workers are comple-
ments. The skilled workers of firms that are
more buildings and other structures intensive
tend to have a higher wage share. We should
thus expect that these two types of capital
input will affect the demand for skilled workers
differently.
Industrial Production. We also control for
industry size using the logarithm of the total
amount of sales (ln Y
i
) as a proxy. A larger size
industry would be expected to have a larger
demand for skilled workers. This implies that
the coefficient of ln Y
i
should be positive.
Industry-Specific Technology. The level of
technology of an industry i(T
i
) is measured
by the ratio of high-technology capital to the
total value of assets of industry i.AsinAmiti
and Wei (2006), we proxy high-technology
FIGURE 3
The scattered plot between ln out
s
i
and WS
Hi
.2 .4 .6 .8
skilled wage share
-8 -6 -4 -2
logarithm of ratio of service outsourcing
to total production cost
FIGURE 4
The scattered plot between ln K
BLD
i
and WS
Hi
0.2.4.6.8
skilled wage share
-7 -6 -5 -4 -3 -2
logarithm of ratio of building to total asset
FIGURE 5
The scattered plot between ln K
MCH
i
and WS
Hi
0.2.4.6.8
skilled wage share
-.5 -.4 -.3 -.2 -.1 0
logarithm of ratio of machinery and
equipment to total asset
CHONGVILAIVAN, HUR & RIYANTO: OUTSOURCING TYPES 25
capital using the value of computers and data
processing equipment used in industry i.WS
Hi
and ln T
i
, as shown in Figure 6, are positively
related. This implies that high-
technology capital and skilled workers are
complements, and thus, we should expect that
the regression coefficient for high-technology
capital has a positive sign.
Import Shares. In the analysis, we also control
for the impact of imports on workers’ wages
and employment. We know from the standard
Heckscher-Ohlin (H-O) theory that when
domestic production is supplanted by imports,
a substitution of this kind should negatively
affect wages and employment. We thus in-
corporate the industrial import share (IM
i
)
variable in our regressions. This variable is
proxied by the ratio of the imports of industry
i’s product (six-digit NAICS) to its total
domestic consumption. The data are retrieved
from the U.S. International Trade Statistics,
U.S. Bureau of Census.
Instrumental Variables. As mentioned previ-
ously, we run IV regressions with a heteroske-
dasticity-robust variance estimator using
capacity utilization and value added per estab-
lishment as our instruments for the level of
technology (T
i
). We use the ratio of electricity
and fuel consumption used in production to
the total capital expenditure as a proxy for
capacity utilization, and we use the ratio of
the total industry value added to the total
number of establishments as a measure of
the value added per establishment.
Table 1 provides the details of three-digit
NAICS codes of manufacturing industries.
Statistics summarizing all the variables elabo-
rated above and the matrix of correlations
among these variables are presented in Appen-
dices A2 and A3.
V. EMPIRICAL RESULTS
Tables 2–5 present our regression results.
Column (1) in all tables shows the results we
obtained using a regression specification that
uses aggregated capital inputs and materials
outsourcing. Column (2) gives the results we
obtained when the control variable imports
are excluded from the regression. Column (3)
presents our results when capital inputs were
further disaggregated into buildings and other
structures (ln KBLD
i) and machinery and equip-
ment (ln KMCH
i). Finally, Column (4) presents
the results we obtained when materials out-
sourcing was further decomposed into up-
stream materials outsourcing, ln outmu
i,and
downstream materials outsourcing, ln outmd
i.
11
A. The Wage Share of Skilled Workers
According to the standard H-O paradigm,
imports and domestic production are substi-
tutes, and hence, imports should affect relative
wages and the demand for skilled workers.
Therefore, to take into consideration this
import effect, we also run a regression with
import share (ln IMi) as an explanatory vari-
able. The result of this regression is presented
in Column (1). Consistent with Leamer (1998),
we find that the import share is not significant,
which suggests that international trade has no
influence on the wage gap between skilled and
unskilled workers.
As revealed in Table 2, the coefficients of
all structural variables for all specifications
are statistically significant at the 5% signifi-
cance level.
12
The aggregate proxy for capital
inputs, see Columns (1) and (2), is statistically
significant and has negative sign, implying
that capitals and skilled workers are substi-
tutes. Our results are thus consistent with
FIGURE 6
The scattered plot between ln T
i
and WS
Hi
0 .2.4.6.8
skilled wage share
-4 -3.5 -3 -2.5 -2 -1.5
logarithm of ratio of computer and
data processing equipment to total asset
11. Since values of materials outsourcing are missing
for some industries, the number of observations in the
actual estimation is slightly reduced to 465 and 452
observations.
12. These results are also consistent with Ftests. As
reported in Table 2, the results, based on Fstatistics,
assert that all coefficients are jointly statistically significant
at the 95% level of confidence.
26 ECONOMIC INQUIRY
Geishecker’s (2002) result that shows a nega-
tive relationship between capitals and the rel-
ative demand for skilled workers.
To see this more clearly, the capital stock is
separated out into two components, buildings
and other structures (ln KBLD
i) and machinery
and equipment (ln KMCH
i) in Columns (3) and
(4). We found that ln KBLD
ihas a positive
effect, whereas ln KMCH
ihas a negative effect.
Our results suggest that buildings and other
structures are complementary to skilled work-
ers, while machinery and equipment are not.
In line with Amiti and Wei (2006), the coef-
ficients of ln Yiare positive and statistically
significant at the 1% level of significance in
all regression specifications. This suggests that
larger industries are more likely to be charac-
terized by a higher wage share of skilled work-
ers. Employing skilled workers is relatively
more expensive than employing unskilled
workers, and larger firms would be more able
to afford it as they can tap the benefit of the
economies of scale.
The estimated coefficients of materials out-
sourcing (ln outm
i) in Columns (1), (2), and (3)
are all negative and statistically significant at
the 5% level of significance. This result is in
contrast to those of Feenstra and Hanson
(1996, 1999), Anderton and Brenton (1999),
and Geishecker (2002), who all find a positive
relationship. In these papers, materials out-
sourcing is proxied by imported intermediate
materials. The negative relationship between
materials outsourcing and the wage share of
skilled workers as depicted in Columns (1),
(2), and (3) may be consistent with the results
of studies done by Siegel and Griliches (1991)
and Egger and Egger (2006). These show that
materials outsourcing leads to a short-run
deterioration in the overall productivity of
labor and therefore in the efficiency of produc-
tion. If indeed there is a negative short-run
effect of materials outsourcing, then we should
expect a negative relationship between materi-
als outsourcing and relative wages of skilled
workers.
We further break down materials outsourc-
ing into upstream (ln outmu
i) and downstream
(ln outmd
i) materials outsourcing. From the
results presented in Column (4), we can see
that upstream materials outsourcing nega-
tively affects the wage share of skilled workers,
while downstream materials outsourcing pos-
itively affects the wage share of skilled work-
ers. As elaborated previously, materials used
in upstream production stages include inter-
mediate parts and materials, and activities
involved in downstream production stages
include reprocessing and repackaging activi-
ties. The former is often more skill intensive
than the latter. Consequently, in contrast with
performing these skill-intensive activities in-
house, outsourcing them from the market is
unlikely to yield a rise in the wages paid to
skilled workers in downstream industries,
and thus, a negative relationship of this kind
may indeed prevail. On the other hand, con-
tracting out downstream materials allows
firms to specialize in the production of up-
stream materials, therefore resulting in higher
productivity and thus higher wage shares
for skilled workers. Accordingly, a positive
TABLE 1
Three-Digit NAICS Manufacturing Industry
Code (Sectors 31–33)
2002 NAICS
Code Report Title
311 Food Manufacturing
312 Beverage and Tobacco Product
Manufacturing
313 Textile Mills
314 Textile Product Mills
315 Apparel Manufacturing
316 Leather and Allied Product
Manufacturing
321 Wood Product Manufacturing
322 Paper Manufacturing
323 Printing and Related Support Activities
324 Petroleum and Coal Products
Manufacturing
325 Chemical Manufacturing
326 Plastics and Rubber Products
Manufacturing
327 Nonmetallic Mineral Product
Manufacturing
331 Primary Metal Manufacturing
332 Fabricated Metal Product
Manufacturing
333 Machinery Manufacturing
334 Computer and Electronic Product
Manufacturing
335 Electrical Equipment, Appliance,
and Component Manufacturing
336 Transportation Equipment
Manufacturing
337 Furniture and Related Product
Manufacturing
339 Miscellaneous Manufacturing
CHONGVILAIVAN, HUR & RIYANTO: OUTSOURCING TYPES 27
relationship between downstream materials
outsourcing and the wages of skilled workers
relative to those of unskilled workers does
prevail.
We also show that service outsourcing has
a positive impact on relative wages. Service
outsourcing in our context includes purchases
of communication, accounting, auditing, book-
keeping, and computer services. This result is
consistent with Amiti and Wei (2006).
The coefficients of the level of technology
(ln T
i
) are positive and statistically significant
TABLE 2
OLS Estimation with Heteroskedasticity-Robust Variance Estimators for the Nonproduction
Wage Share
Variable (1) (2) (3) (4)
ln Ki.070485 (.0126)*** .0691555 (.0121)*** ——
ln KBLD
i— — .0279638 (.0081)*** .0222022 (.0078)***
ln KMCH
i——.0954548 (.0117)*** .0984122 (.0117)***
ln Yi.0741474 (.0143)*** .0722082 (.0133)*** .0680672 (.0137)*** .0763347 (.0133)***
ln outm
i.1026495 (.0480)** .1033926 (.0483)** .1264937 (.0491)*** —
ln outmu
i———.1162443 (.0495)**
ln outmd
i— — — .0111673 (.0046)**
ln outs
i.0446323 (.0070)*** .0446084 (.0069)*** .0430307 (.0067)*** .0352395 (.0075)***
ln Ti.0621345 (.0162)** .0611889 (.0156)*** .0619721 (.0154)*** .0713033 (.0151)***
ln IMi.002676 (.0039) — — —
Constant .1740138 (.1231) .1817248 (.1172) .2442866 (.1234)*.2034584 (.1214)*
R
2
0.5490 0.5485 0.5778 0.5948
Fstatistic 24.36*** 25.30*** 27.93*** 26.84***
No. of observations 465 465 465 452
Note: Robust standard errors in parentheses.
*Statistically significant at 10%; **statistically significant at 5%; ***statistically significant at 1%.
TABLE 3
IV Estimation with Heteroskedasticity-Robust Variance Estimators for the Nonproduction
Wage Share
Variable (1) (2) (3) (4)
ln Ki.0966811 (.0162)*** .09423 (.0152)*** ——
ln KBLD
i— — .0243746 (.0083)*** .0180049 (.0082)**
ln KMCH
i——.1101216 (.0138)*** .1126119 (.0131)***
ln Yi.0974795 (.0177)*** .093969 (.0162)*** .0843162 (.0164)*** .0926931 (.0157)***
ln outm
i.1420326 (.0529)*** .14318 (.0533)*** .1536721 (.0533)*** —
ln outmu
i———.132627 (.0496)***
ln outmd
i— — — .0122447 (.0047)**
ln outs
i.0379679 (.0083)*** .037954 (.0082)*** .0387463 (.0076)*** .0305174 (.0085)***
ln Ti.1349419 (.0302)*** .1329736 (.0293)*** .1107754 (.0274)*** .1187505 (.0257)***
ln IMi.0047177 (.0043) — — —
Constant .0490066 (.1655) 0.03451 (.1566) .0810549 (.1616) .045763 (.157)
R
2
0.5189 0.5190 0.5641 0.5823
Fstatistic 22.48*** 23.19*** 26.01*** 25.39***
Hausman test statistic (pvalue) 2.32 (1.00) 16.12 (.9111) 0.97 (1.00) 3.01 (1.00)
No. of observations 465 465 465 452
Notes: Robust standard errors in parentheses. Hausman specification test is distributed as chi-squared distribution
with degrees of freedom equal to the number of instruments under the null hypothesis that ln T
i
is uncorrelated with
the error term.
**Statistically significant at 5%; ***statistically significant at 1%.
28 ECONOMIC INQUIRY
at the 1% level of significance. This suggests
that technology is skill biased. This result
confirms the findings of previous studies such
as those of Anderton and Brenton (1999),
Geishecker (2002), and Amiti and Wei
(2006): technology and skilled workers are
TABLE 4
OLS Estimation with Heteroskedasticity-Robust Variance Estimators for the Nonproduction
Employment Share
Variable (1) (2) (3) (4)
lnðwH=wLÞ.156266 (.0289)*** .1549583 (.0287)*** .1730969 (.0291)*** .1871572 (.0312)***
ln Ki.0559354 (.0123)*** .05504275 (.0116)*** ——
ln KBLD
i— — .02547996 (.0076)*** .02084408 (.0074)***
ln KMCH
i——.08107041 (.0113)*** .0858007 (.0114)***
ln Yi.061330 (.0135)*** .06013335 (.0125)*** .05792525 (.0128)*** .06658104 (.0125)***
ln outm
i.0849718 (.04347)*.08544506 (.0436)*.1051191 (.0447)** —
ln outmu
i—— —.1018513 (.0491)**
ln outmd
i— — — .009487451 (.0043)**
ln outs
i.03914103 (.0066)*** .03909266 (.0066)*** .0381617 (.0064)*** .03228012 (.0073)***
ln Ti.05020533 (.0157)*** .04954298 (.0151)*** .05199395 (.0149)*** .06196547 (.0148)***
ln IMi.001504368 (.0037) — — —
Constant .1708056 (.1139) .1745268 (.1092) .2409251 (.1160)** .2106188 (.1174)*
R
2
0.5523 0.5521 0.5790 0.5969
Fstatistic 23.02*** 23.90*** 24.80*** 23.50***
No. of observations 465 465 465 452
Note: Robust standard errors in parentheses.
*Statistically significant at 10%; **statistically significant at 5%; ***statistically significant at 1%.
TABLE 5
IV Estimation with Heteroskedasticity-Robust Variance Estimators for the Nonproduction
Employment Share
Variable (1) (2) (3) (4)
lnðwH=wLÞ.1859667 (.0319)*** .1826022 (.0310)*** .1913028 (.0303)*** .2042324 (.0324)***
ln Ki.0798355 (.0160)*** .07749905 (.0148)*** ——
ln KBLD
i— — .02306583 (.0077)*** .01784023 (.0076)**
ln KMCH
i——.0941091 (.0134)*** .09835439 (.0128)***
ln Yi.08223176 (.0172)*** .07922251 (.0154)*** .07134585 (.0153)*** .08008163 (.0147)***
ln outm
i.1142604 (.0478)** .1150295 (.0481)** .1246902 (.0485)** —
ln outmu
i———.1131556 (.0494)**
ln outmd
i— — — .01044543 (.0044)**
ln outs
i.03474913 (.0076)*** .03468615 (.0076)*** .03547988 (.0072)*** .02917135 (.0081)***
ln Ti.1100077 (.0296)*** .1078033 (.0283)*** .08974336 (.0262)*** .09902341 (.0249)***
ln IMi.003509386 (.0041) — — —
Constant .009901217 (.1504) .02032706 (.1424) .1295635 (.1473) .1028038 (.1460)
R
2
0.5295 0.5301 0.5700 0.5884
Fstatistic 21.79*** 22.54*** 24.02*** 22.66***
Hausman specification
test statistic (pvalue)
0.09 (1.00) 2.88 (1.00) 1.39 (1.00) 0.6 (1.00)
No. of observations 465 465 465 452
Notes: Robust standard errors in parentheses. Hausman specification test is distributed as chi-squared distribution
with degrees of freedom equal to the number of instruments under the null hypothesis that ln T
i
is uncorrelated with
the error term.
**Statistically significant at 5%; ***statistically significant at 1%.
CHONGVILAIVAN, HUR & RIYANTO: OUTSOURCING TYPES 29
complementary. So as we show here, higher
technology results in a larger wage share for
skilled workers.
In our regressions, we also include dummies
for industries. As expected, chemical, machin-
ery, computer, and electronic products are
relatively skill intensive, while textile mills,
clothing, leather and allied products, and
wood product manufacturing are not.
13
Finally, as noted by Feenstra and Hanson
(1997), the estimation of the wage share
equations might be subject to not only a poten-
tial heteroskedasticity problem but also an
endogeneity problem, thereby resulting in in-
efficient and biased estimators. More specifi-
cally, it is possible that ln T
i
is correlated
with an unobserved variable in the error term
(u
i
). To verify this, we run IV regressions and
apply the Hausman test for the endogeneity
problem to the results. Our null hypothesis
posits that ln T
i
is not correlated with u
i
.
The result of the Hausman test shows that
the null hypothesis cannot be rejected, sug-
gesting that there is no endogeneity problem.
As pointed out by Hausman (1978), when ln T
i
is indeed uncorrelated with the unobserved
variable in u
i
, the OLS and IV estimators
would essentially produce the same qualitative
results.
14
Indeed, when we compare the results
from the OLS regressions presented in Table 2
and the results from IV regressions presented
in Table 3, we observe that the explanatory
variables that are significant in the OLS re-
gressions are also significant in IV regressions
and they all have the same predicted signs.
B. The Employment Share of Skilled Workers
In this subsection, we discuss the results of
our OLS and IV estimations of the employment
shareequation (6). They are reportedin Tables 4
and 5, respectively. The result of the Hausman
test for the endogeneity problem is reported in
Table 5. It shows that the null hypothesis of
no correlation between ln T
i
and u
i
cannot be
rejected for all specifications, thus suggesting
that there is no endogeneity problem.
15
We also include the relative-wage variable,
lnðwH=wLÞ, in the estimations and find that the
coefficients of lnðwH=wLÞhave a negative sign
and are statistically significant at the 1% level
of significance. This implies that an increase in
lnðwH=wLÞtriggers a replacement of skilled
workers by unskilled workers.
We show that the independent variable,
ln IMi, is not significant, see Column (1). This
suggests that the conventional H-O frame-
work cannot really explain the change in the
employment share of skilled workers. We also
show that capital inputs have a negative
impact on the employment share of skilled
workers, see Column (2). When we break
down capital inputs into buildings and other
structures and machinery and equipment, we
find that the former are skill biased, while
the latter are not, see Columns (3) and (4).
Next, we also show that industry size has a pos-
itive impact on the employment share.
As with our previous results, we find that
aggregate materials outsourcing has a negative
impact on the relative demand for skilled
workers. When we separate materials out-
sourcing into upstream and downstream
materials outsourcing, we find that the latter
has a positive impact on the relative demand
for skilled workers, whereas the former has
a negative impact. We also show that service
outsourcing has a positive impact on the rela-
tive demand for skilled workers.
The coefficients of ln T
i
are positive. This
suggests that technology is skill biased. This
is consistent with our earlier results from the
estimation of the wage share equation. Last,
we find that chemical, fabricated metal,
machinery, computers, and electronic prod-
ucts are skill intensive, while textile, clothing,
leather, and wood products are not.
VI. CONCLUDING REMARKS
In this paper, we estimate the impacts of
outsourcing on relative wages and the demand
for skilled workers using six-digit NAICS U.S.
manufacturing sector data. We break down
outsourcing into three categories, namely
upstream and downstream materials out-
sourcing and service outsourcing. Our results
show that downstream materials and service
outsourcing have a positive impact on the
wages of skilled workers relative to those of
unskilled workers and the relative demand
13. The results are not shown in Table 2. They are
available upon request.
14. That is, the estimators from OLS and IV estima-
tion should differ only by the sampling errors.
15. The coefficients of instruments in the first-stage
regression are statistically significant at the 1% level of sig-
nificance for all specifications with the adjusted R
2
ranging
from .5766 to .6172.
30 ECONOMIC INQUIRY
for skilled workers, while upstream materials
outsourcing has the opposite impact.
The positive impact of downstream materi-
als and service outsourcing on relative wages
and the demand for skilled workers can be
explained by the idea that these types of out-
sourcing allow firms to specialize in the
upstream production activities, which usually
employ a greater number of skilled workers.
Therefore, an increased attention to upstream
production activities will naturally induce
firms to hire more skilled workers. In contrast,
downstream production activities and services
tend to be less skill intensive than upstream
production activities; hence, firms that focus
more on the former do not really require
numerous skilled workers. Accordingly, their
demand for skilled workers will fall.
Our empirical results also shed further light
on the different roles played by different types
of capital inputs. We discover that the nature
of the relationship between capital inputs and
skilled workers depends on the types of capital
input employed in the production process. We
find that machinery and equipment are substi-
tutes for skilled workers, while buildings and
other structures are complementary to skilled
workers. To the best of our knowledge, there
has been no theoretical discussion on the rela-
tionship between the capital inputs typology
and wage inequality. With regard to the role
of technology, we find a positive relationship
between technology and the demand for
skilled workers. It can thus be concluded that
technology is skill biased.
It may be interesting in future research to
rigorously investigate the roles of domestic
and international outsourcing as explanatory
factors for wage inequalities. Furthermore,
a natural extension to our empirical analysis
would be to conduct a dynamic panel data
analysis rather than a cross-sectional analysis
like the one carried out in this paper. Such an
analysis should enable us to obtain richer
results. Unfortunately, more recent detailed
six-digit NAICS manufacturing sector data
are not available at the time of writing. We
therefore leave this to our future research.
APPENDIX A1
Given assumption of symmetry, the translog cost func-
tion (3) can be expressed as:
ln c5a0þaHln wHþaLln wLþcLH ln wLln wH
þð1=2ÞcHH ðln wHÞ2þð1=2ÞcLL ðln wLÞ2
þbKln Kþ/HK ln wHln Kþ/LK ln wLln K
þð1=2ÞdKK ðln KÞ2þbYln Yþ/HY ln wHln Y
þ/LK ln wLln YþdKY ln Kln Yþð1=2ÞdYY ðln YÞ2
þbSln outsþ/HS ln wHln outsþ/LS ln wLln outs
þð1=2ÞdSS ðln outsÞ2þdSK ln outSln K
þdSY ln outsln YþbMln outm
þ/HM ln wHln outmþ/LM ln wLln outm
þð1=2ÞdMM ðln outmÞ2þdMK ln outmln K
þdMY ln outmln YþdMS ln outmln outs
þbTln Tþ/HT ln wHln Tþ/LT ln wLln T
þð1=2ÞdTT ðln TÞ2þdTK ln Tln KþdTY ln Tln Y
þdTS ln Tln outsþdTM ln Tln outm:
In addition, since the linear homogeneity property of
the translog function must be satisfied, the following
parameter restrictions are inevitably required:
aHþaL51and cHL þcHH
5cLH þcLL 5/Hj þ/Lj 50;
where j5K,Y,M,S, and T.
CHONGVILAIVAN, HUR & RIYANTO: OUTSOURCING TYPES 31
APPENDIX A2
APPENDIX A3
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Summary Statistics
Variable Observation Mean Standard Deviation Minimum Maximum
WSHi 473 0.398688 0.128719 0.107686 0.809284
ESHi 473 0.2920663 0.1181443 0.0871373 0.7155634
ln Ki473 11.57682 1.402426 6.760415 15.81277
ln KBLD
i468 9.626691 1.539867 4.844187 15.01045
ln KMCH
i473 0.398688 0.128719 0.107686 0.809284
ln Yi473 15.19392 1.195375 11.69909 19.08729
ln outm
i473 0.15894 0.213304 3.21235 0.034746
ln outmu
i471 0.18833 0.137927 1.00866 0.030587
ln outmd
i459 4.11236 1.273217 10.4188 0.47696
ln outs
i469 5.08162 0.90867 8.68661 2.20799
ln Ti468 1.856451 0.391024 0.584914 3.035576
ln IMi473 2.01712 1.328415 13.5 0.0104
Correlation Matrix of Independent Variables
ln KBLD
iln KMCH
iln Yiln outmu
iln outmd
iln outm
iln Tiln IMi
ln KBLD
i1
ln KMCH
i0.6512 1
ln Yi0.4203 0.6426 1
ln outmu
i0.0965 0.1141 0.255 1
ln outmd
i0.0688 0.0561 0.1412 0.4494 1
ln outs
i0.0794 0.0871 0.1838 0.2705 0.5024 1
ln Ti0.077 0.1202 0.1629 0.0549 0.0792 0.2957 1
ln IMi0.0699 0.1279 0.3968 0.2546 0.2164 0.0963 0.0292 1
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CHONGVILAIVAN, HUR & RIYANTO: OUTSOURCING TYPES 33
