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Mirela Keuschnigg
Comparative Advantage
in International Trade
Theory and Evidence
With 21 Tables
Physica-Verlag
A Springer-Verlag Company
Editorial Board
Winfried Pohlmeier, University of Konstanz, Germany
Baldev Raj, Wilfrid Laurier University, Waterloo, Canada
Andreas Worgotter, Institute for Advanced Studies, Vienna, Austria
Author
Mirela Keuschnigg
Steinhiibel 39
D-66123 Saarbriicken
Germany
ISBN 978-3-642-50214-9
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Comparative advantage in international trade: with 21 tableslMirela Keuschnigg. - Heidelberg; New York: Physica-Verl., 1999
(Studies in empirical economics)
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Acknowledgments
I wrote this thesis at the European University Institute in Florence and the
Institute for Advanced Studies in Vienna. Now the time has come to thank
a number of persons for the help they have given to me, either directly or
indirectly in completing the thesis.
Special thanks go to Stephen Martin, my thesis supervisor, for reading several
versions of the manuscript, for valuable suggestions and helpful discussions.
His door was always open to me. He also helped obtaining many data used in
the empirical work. Others helped as well. Louis Phlips, John Micklewright,
and Andreas Worgotter commented on various portions of the manuscript in
various stages of its development. I was able to discuss a number of issues
with Grayham Mizon, Josef Zweimiiller and Robert Kunst. Edward Leamer
was the first to read parts of the manuscript, encouraged me to continue
with it, and made many helpful suggestions. So did Wilhelm Kohler. I am
especially grateful for his extensive and helpful comments on drafts of some of
the chapters. Harald Sonnberger gave valuable computer assistance. Michael
Begg and Albert Hart corrected very carefully the English. I am also grateful
to the Economics Department secretaries. Jessica and Jacqueline provided
irreplaceable help and moral support.
I would like to mention the people with whom I shared these years. My
best friends, whose confidence in my work helped or kept me from giving up.
Cathy, Isabela, Merce, Jarko, Helmut, Bernhard, thank you all. Also, I wish
to thank my parents and all other relatives and friends, who have in some
way or another assisted and encouraged me during these years.
Finally, the ideas of this work have originated and been enriched by many
conversations with my greatest friend, Christian. His advice was really stimUlating. He deserves special thanks for offering more than one could ask in
intellectual and emotional support.
Contents
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
1
Theory
5
1 Introduction
7
I
2
The Basic HOV Theory
13
2.1
13
The Quantity Version
2.2 The Value Version
3
4
..
18
Generalizations of HOV Theory
21
3.1
21
Non-Neutral Technological Differences
3.2 Internal Increasing Returns
23
3.3 External Increasing Returns .
28
3.4 Internationally Mobile Capital
30
3.5 Armington Preferences . . . . .
32
Theory-Based EmpirIcal Implementation
35
4.1
Direct Tests .
35
4.2 Indirect Tests
36
4.2.1
Ranking Propositions
36
4.2.2
Simple Correlations
42
4.2.3
Multiple Correlations
44
Appendix
5 Conclusions
...........
50
53
CONTENTS
viii
II
Evidence
55
6 Introduction
57
7
Literature Overview
61
7.1
Factor Content Studies .
62
7.2
Overview of Cross-Industry Studies .
67
7.2.1
Problems in the Cross-Industry Empirical Studies
68
7.2.2
Cross-Industry Studies . . .
71
Overview of Cross-Country Studies
77
7.3
8
Empirical Analysis
81
8.1
Introduction . . .
81
8.2
Description of the Data and Variables
86
8.3
9
8.2.1
Data . . .
86
8.2.2
Variables
93
Empirical Results .
96
8.3.1
Simple Correlations
97
8.3.2
Ranking Proposition 1
114
8.3.3
Technology Parameters: How Similar is 8?
118
8.3.4
Similarities in the Trade Patterns .
119
8.3.5
Multiple Correlations
120
Conclusions
139
Appendix A .
143
Appendix B .
145
List of Symbols
149
List of Abbreviations .
153
Bibliography
155
Index
163
....
Introduction
Traditional trade theory explains trade only by differences between countries,
notably differences in their relative endowments of factors of production. It
suggests an inverse relationship between the similarity of countries and the
volume of trade between them. The Heckscher-Ohlin (HO) factor proportions theory derives the determinants of comparative advantage in a world
of "two-ness" (two goods, two factors, two countries). It predicts that each
country will export that good which uses the country's abundant factor relatively most intensively. The literature on trade offers an impressive number
of studies based on the HO theory. The main methodological problems encountered in the literature are: first, the appropriate formulation of the HO
theorem in a multi-factor, multi-good and multi-country framework; second,
proper tests of the HO theory and proper links of the theory to empirical
analysis.
The relevance of the HO theory began to be questioned when important facts
of modern international trade proved to be inconsistent with its theoretical
framework. Leontief (1953) tested the factor proportions theory, using the
US data for 1947, and found that the US had more labor-intensive exports
than imports, which is opposed to both perceptions and estimations of factor
endowments. The Leontief Pamdoxcreated doubt as to whether or not actual
trade patterns and factor endowments are related as predicted by theory, and
caused many controversial discussions with regard to the proper empirical
implementation of the factor proportions theory. Leamer (1980) showed that
Leontief's comparison does not reveal the relative abundance of capital and
labor in a multi-factor world and that, therefore, no paradox arises if the
computations are conceptually correct. Vanek (1968) was the first to offer a
restatement of the HO theorem in the multi-factor, multi-good case.
Very little empirical support is available for an exact linear relationship between trade flows and factor supplies as predicted by the HO theory. However,
the consensus seems to be that factor endowments exert a positive and linear
influence on the factor content of trade flows, but that they hardly constitute
the only important explanation of commodity trade patterns. Recent debates
cast suspicion over the usefulness of the regression interpretation of the HO
theory.
2
INTRODUCTION
The relevance of the HO theory is also questioned by the growing trade
between developed countries with similar factor endowments. Actual trade
patterns seem to include considerable two-way trade in goods of similar factor
intensity, which is difficult to explain from the point of view of a traditional
analysis. Essential contributions by Krugman (1979), Dixit and Norman
(1980), Ethier (1979, 1982), as well as Helpman and Krugman (1985) offer theoretical models that refine the HO model by allowing for economies
of scale, product differentiation, and departures from perfect competition.
The outcome is a more generalized HO theorem that preserves the factorendowment basis for inter-industry trade, while extending the theory to allow
for and explain intra-industry trade.
This study is inspired from previous work by Vanek and Leamer. It addresses
the empirical validity of the factor proportions theory on a new methodological as well as a new data basis. A first part presents theoretical models
based on the HO theory for explaining a country pattern of net trade. By
way of contrast to other studies, the models are derived in a multi-country,
multi-factor and multi-good framework, and they allow factor productivities
and factor prices to differ across countries.
The presence of scale economies and product differentiation makes the assumptions of the models slightly more realistic, while the standard model
is more general. Such generalization is required for a meaningful empirical
investigation of these models. Finally, a model with international capital
mobility is developed. The choice of these specific extensions, from the many
that could be tried, is determined by the fact that, in the existing empirical
work, foreign direct investment, economies of scale, or product differentiation
appear on the list of the regressors without any reference to a theoretical
model. Moreover, we hope that allowing for these extensions will help us to
better understand the shortcomings of the concept of comparative advantage.
Given these theoretical models, we turn to the issue of theory-based empirical estimation equations in the context of the factor proportions approach
to comparative advantage. A set of cross-industry regression equations is
proposed to be used for explaining the countries' patterns of comparative
advantage. A whole series of rank order propositions derived from the HOV
(Heckscher-Ohlin-Vanek) equations are reformulated. A significant feature
of this part is the emphasis on the difference between considering value and
quantity formulations. This is in contrast with the previous literature, which
is usually less careful in this respect as it repeatedly assumes factor price
equalization. Since we allow for internationally non-equalized factor prices,
the difference between quantity and value formulations of various propositions becomes very important.
Based on the models developed in the theory part, a second part reports the
results of an empirical study of the patterns of international trade for a big
sample of developed and developing countries in a cross-industry framework.
Introduction
3
The results of this empirical study show some support for the value version
of the HOV model, especially in the case of developing countries. First,
simple and multiple correlations between net exports and factor intensities
indicate that, as expected, developing countries have their trade negatively
(positively) correlated with high-skilled (low-skilled) labor, while the pattern
observed for the developed countries is the opposite. A second important
result is that, when defining factor intensities as factor cost shares, there is
no factor intensity reversal across countries. In contrast, previous studies
have reported the existence of factor intensity reversal when defining factor
intensities by unit factor requirements. Third, we find that the results are
sensitive to the way we define and compute some of the variables. Fourth,
using a ranking proposition we realize that the developing countries are revealed both by their trade and by their factor endowments to be relatively
better endowed with low-skilled than with high-skilled labor, while the opposite is true for the developed countries. All the countries for which this
proposition holds turn out to be better endowed with labor, either high- or
low-skilled, than with capital. Fifth, we find that we cannot reject the HOV
model, developed in a perfect competition framework, in favor of a model allowing for economies of scale and product differentiation. More detailed data
on production and input factors by industry and country are necessary to
make more precise statements about the role of scale economies and product
differentiation.
Part I
Theory
Chapter 1
Introduction
"Theories are neither true nor false. Theories are sometimes
useful and sometimes not so useful" (Edward Leamer, 1995)
The HO theory explains international trade only by differences in the countries' relative factor endowments. It is based on a number of very strong
assumptions. On the production side, it assumes identical technology across
countries. On the consumption side, it assumes identical and homothetic preferences. In addition, it assumes perfect competition in the goods and factor
markets, perfectly mobile production factors across sectors within countries,
but completely immobile factors across countries.
Leontief's (1953) unexpected results triggered many controversial discussions
with regard to the proper empirical implementation of the HO theory. He
compared the capital-per-man embodied in $1 million worth of imports with
the capital-per-man embodied in $1 million worth of exports and found that
the US was, in 1947, a net exporter of labor services. One response to the
Leontief Pamdox suggests that the US trade may be better explained in
terms of factors other than labor and capital. The Leontief Pamdox [Leontief (1953)] is based on the proposition that, if the ratio of capital to labor
embodied in exports is lower than the ratio of capital to labor embodied in
imports, the country is relatively better endowed with labor. But, as Leamer
(1980) shows, this is true only if the net exports of labor services have a sign
opposite to that of the net exports of capital services. When both are positive, as in Leontief's data, the correct comparison is between the capital-labor
ratio of net exports and that of consumption. According to this comparison,
Leontief's data for 1947 confirm that the US is relatively well endowed with
capital. Since Leontief's findings, a significant amount of research has been
devoted to establishing the general validity of the HO theorem. In general,
the effort has been unsuccessful.
8
CHAPTER 1. INTRODUCTION
The reconsideration of the Leontief Paradox rests on the HOV theorem due to
Vanek (1968), which is a generalization of the HO theory. In the multi-factor,
multi-good case there is no unique ordering of goods according to relative
factor intensities, hence, one cannot state it with respect to the commodity
structure of trade. Vanek, however, writes a factor content-of-trade version
of the HO theorem, irrespective of the number of input factors. Instead of
trying to rank many goods with respect to inputs of many factors, the Vanek
version orders factors with respect to a single criterion: their factor content
in net-trade flows.
There is little empirical support for an exact linear relationship between trade
flows and factor endowments as predicted by the HO theory. Maskus (1985),
Bowen, Leamer and Sveikauskas (1987), as well as Brecher and Choudhri
(1988) performed tests, based on Vanek's generalization, of the factor content version of the HO theory, using independent measures of trade, factor
intensities, and factor endowments. They all found that, empirically, the HO
theorem performs rather badly, which is not surprising given the extraordinary assumptions of the model. Maskus (1991) notices that little can be said
in a rigorous way about the empirical determinants of the patterns of trade.
The relevance of the HO theory also started to be questioned due to the
growing trade in goods of similar factor intensity between developed countries with similar factor endowments. An increased tendency, not towards
inter-industry specialization but rather to intra-industry trade, is noticed
in the context of European economic integration. Intra-industry trade can
be defined as the simultaneous import and export of products that are close
substitutes. The usual explanations of intra-industry trade are product heterogeneity within aggregates as well as border and seasonal trade. In addition, starting with Grubel and Lloyd (1975), a large amount of evidence,
supportive of intra-industry trade, has been provided, suggesting that product differentiation and economies of scale are a more appropriate explanation
of two-way trade. Meanwhile, Krugman (1979), Dixit and Norman (1980),
Ethier (1979,1982), and Helpman and Krugman (1985) offer theoretical models that amend the HO model by allowing for economies of scale, product
differentiation and departures from perfect competition.
This part presents theoretical models based on the HO theory that were
designed to explain a country's pattern of net trade in a multi-factor, multigood, multi-country setting. In contrast to previous studies, these models
allow for cross-country factor requirement and factor price differences. They
also allow for intermediate goods production, but preserve most of the strong
assumptions of the HO theory, such as internationally immobile factors, identical and homothetic preferences in consumption, free trade, no transportation costs, and factor market and world commodity market clearing.
Given the strong assumptions of the HOV theory, this study tries to formulate
two models that allow for departures from the original factor proportions
CHAPTER 1. INTRODUCTION
9
theory, and are thus based on more realistic assumptions. The first model
allows for increasing returns to scale, modelled by the existence of a fixed
cost at the level of the firm; the second allows for increasing returns to scale,
external to the firm but internal to the industry. All factor markets are
competitive and, in the competitive industries, constant returns are assumed,
so price must equal unit cost. Of the generalizations not yet attempted
would be one that combines increasing returns with product differentiation
and home bias in consumption. The model with internal scale economies and
product differentiation allows us to write separate equations for exports and
imports of the differentiated products. Finally, a model with international
capital mobility is developed.
Next we turn to the issue of theory-based empirical estimation of the HOV
equations. A set of regression equations is proposed to be used for explaining
the countries' patterns of comparative advantage in a cross-industry framework. The rank hypotheses that allow for tests of the HOV theory are reformulated.
The quantity version of the HOV equation is based on the assumption of
internationally identical technologies, which implies factor price equalization
across countries if endowments are not too dissimilar. These assumptions are
difficult to reconcile with the real world. A value version of the HOV model is,
therefore, derived without considering factor price equalization across countries. The value version uses factor cost shares rather than factor input
coefficients. Under a Cobb-Douglas (CD) technology, the input coefficients
are independent of factor prices and, therefore, are parametric. The value
version of the HOV equation for a particular country is:
eTt v
= Wv -
S
LWivi
(1.1)
i
or, for a particular factor h:
(}hT tV = Whv h -
S
L Whi v hi
i
e
where tV is the country's vector of net exports in value terms, T is the matrix
of total (direct plus indirect) factor cost shares, W is a diagonal matrix of
factor returns, v is the vector of factor endowments, s is the ratio between
the country's domestic absorption and world income, and j denotes countries.
Equation (1.1) predicts that the total factor content of trade in value terms
(e T tV) is a linear function of national (Wv) and world factor endowments
(2: Wiv i ), defined in value terms. Equation (1.1) will be derived rigorously
i
and in detail below in Section 2.
Given the partial 1 nature of the factor proportions theory, the ideal situation
1 "Partial" refers to the fact that there may be elements other than the relative factor
endowments that determine the countries' trade patterns.
CHAPTER 1. INTRODUCTION
10
would be to have a complete regression model that combines, in a rigorous
way, the factor proportions theory with other determinants of trade, such as
increasing returns to scale and product differentiation. Then, the empirical
analysis might suggest, for example, that the more complete model nests the
model based on the factor proportions theory as a special case.
The thesis develops theoretical models and, following Bowden (1983), theorybased estimation equations for the cross-industry regression analysis are derived. For example, a theory-based estimating equation based on the HOV
equation in its value version would be:
tr A = ao
+L
h
ahOfT(whiJh -
y~
L whjiJh j ) + ILi
(1.2)
j
where trA represents net exports in industry i, in value terms and adjusted for
the country's trade imbalance (hence the superscript vA), iJh and w h are the
country's endowment and income, respectively, for the input factor h, OfT is
the total cost share of factor h per dollar value of commodity i, y and yW are
the country and world income, IL is an error term, and a h are the regression
coefficients. By running cross-industry regressions, using data on net exports
(as the dependent variable) and factor cost shares (as independent variables),
the relationship between the commodity trade pattern and factor-intensities
is predicted for each country. Next, in a second stage, the estimation coefficients obtained in the first estimation step can be externally validated by
actual observations on factor endowments. The interactions implied by equation (1.2) should be understood in the following way: if a factor h is used
relatively intensively in the production of good i, OfT is relatively large, and
if the country is relatively well endowed with factor h, (whiJh - -..1!;- L whjiJh j )
Y
.
J
is large, and this combination favors the production and export of good i.
Such a regression equation may also be specified on a cross-country basis,
observing factor endowments and inferring the factor intensities from the
regression estimates. There are a few reasons for which we prefer a crossindustry specification. First, data on factor endowment earnings, which are
different across countries, are less reliable than data on factor intensities,
which are taken to be internationally identical. Second, by running crossindustry regressions, we observe the relationship between commodity trade
and factor intensities for each country, which further allows for inter-country
comparisons in this respect. In contrast, when running cross-country regressions, we obtain the relationship between net exports and countries' relative
factor abundance for each particular commodity, which is of less interest for
the present study.
Based on the above equation and the models developed in the thesis, theorybased estimation equations will be derived in the case of imperfect competition, increasing returns to scale, and product differentiation. The result of
CHAPTER 1. INTRODUCTION
11
extending the model is that one has to employ a factor shares matrix which
is adjusted for the new elements considered when computing the factor content of trade. Hence, the variables related to economies of scale and product
differentiation enter the explanatory part of the regression in an interactive
term together with factor cost shares, and not as a separate independent variable. When allowing for capital to be internationally mobile, this requires a
correction of the other side of the HOV equation, that is the factor endowment side. Usually, existing empirical studies have added increasing returns
to scale, product differentiation and foreign direct investment in the list of
explanatory variables, but without providing any theoretical justification.
Having said this, let us now proceed with our study. The theory part is
organized as follows. Sections 2.1 and 2.2 provide a theoretical framework
for deriving the factor content equations based on HOV, the quantity and
the value versions, in the presence of perfect competition and intermediate
production. Section 3 deals with generalizations of the HOV theory. A modification of the model that takes into account non-neutral differences in the
technological parameters across countries is proposed in Section 3.1. Sections 3.2 and 3.3 derive the theory-based net trade equations in the presence
of increasing returns to scale, either internal or external to the firms. It is
shown that the resulting equations are identical to equation (1.1), except
for the expression of T . In the case of intra-industry trade, separate factor content equations are derived for exports and imports of differentiated
products. Section 3.4 develops a model that relaxes the assumption of internationally immobile capital. Section 3.5 proposes a modification of the
consumption side of the HOV model that allows for home bias in consumption. Section 4, in an attempt to build a link between theory and empirical
implementation, shows how the developed models may be empirically implemented. The results in Sections 2 and 3 readily lead to direct tests which
might be used to evaluate the applicability of the HOV equations. Sections
4.2.1 and 4.2.2 formulate indirect tests based on the HOV equation, necessary
to explain countries' trade patterns. In Section 4.2.3, a possible derivation of
theory-based estimation equations for the cross-industry regression analysis
is discussed. We start with the basic HOV equation in its value version and
translate it into a theory-based estimation equation to be further used in a
cross-industry regression framework. Then, we turn to the equations for the
increasing returns to scale and product differentiation models derived in Section 3. The estimation equations are modified in order to allow for checking
whether countries' patterns of trade are better explained when we allow for
these qualifications. Section 5 concludes the theory part.
e
Chapter 2
The Basic HOV Theory
In a two-country, two-factor, two-commodity trade model, the HO factor
proportions theory provides an unambiguous explanation of the international
trade pattern: each country will export the good that uses its most abundant
factor most intensively in production. In the multi-factor, multi-commodity,
multi-country case, when the number of goods exceeds that of factors, the
precise commodity pattern of production and trade is indeterminate. However, the factor content of trade is still determinate. One can redefine trade
as an implicit flow of factors embodied in commodities. Vanek (1968) was
the first to obtain a mapping from commodity space to factor space under
special assumptions, among them factor-price equalization. A weaker version
of the HO theorem that explains the factor content of trade rather than its
commodity composition can, therefore, be proved. However, even though
this is more general than the HO theorem, it is not less restrictive in terms
of the assumptions needed for its proof.
2.1
The Quantity Version
Vanek (1968) derives a proposition based on the standard assumptions of the
HO theory, according to which a country's net exports of factor services reflect
the country's relative ranking in terms of factor endowments. The following
equation (which is derived in detail below) relates a country's factor content
of net trade to the difference between the country's factor endowment and
that of the world:
(2.1)
where RT is an m * n matrix (m factors and n industries) of total (direct and
indirect) factor input coefficients for the country, with its elements indicating
the total amount of each input factor required to produce one unit value of
CHAPTER 2. THE BASIC HOV THEORY
14
final demand in each industry, tV is the country's n * 1 vector of net exports
of commodities, in value terms, iJ is the country's m * 1 vector of factor
endowments, iJw is an m * 1 vector of world factor endowments, s is the ratio
between the country's domestic absorption and world income; s = (y_b)/yW,
wherey is GNP and b the trade balance of the country, and yW is world GN P.
The trade balance b is the inner product of the row vector p' and t, b = p't,
where p is the commodity price vector and t is the vector of net exports.
Equation (2.1) is based on many restrictive assumptions and is obtained in
the following way. In input-output formalism, gross output and final demand
are related through the following equation:
where the superscript v is a value index, I is the n * n identity matrix,
AV is an n * n matrix with elements indicating the value of the output a
particular industry must buy from each other industry to produce one dollar
of its own product, XV is an n * 1 vector of gross output produced by each
industry, in value terms, and xv! is an n* 1 vector of final demand for industry
output. The input-output accounts compactly show the relationship between
all industries in the economy and all the commodities they produce and use.
Estimates for commodities are typically shown at producers' prices. The
input-output tables show (I - AV)-l. Entries in each column of this matrix
show the value of the total output required by an industry from each other
industry to produce one dollar of final demand of its own product.
The vector of final demand for a particular countrY! consists of net exports
and final consumption, therefore the vector of net exports t equals the difference between net output and consumption2 :
t
or
t
x! - c
(I - A)x - c
(2.2)
where an element in the n * n matrix A shows the quantity used from each
industry to produce one unit of gross output in each other industry. An
element of matrix AV is defined as ail = Plail/Pi, where ail represents the
amount of output industry i is buying from industry l, and P denotes prices.
Thus, the relationship between A and AV is given by: AV = PAP-I, where
P is an n * n diagonal matrix of commodity prices. Hence, we may rewrite
equation (2.2) as:
t = (I - p- 1 A V P)x - c
(2.3)
lThe HOV equation is derived for a particular country even though no superscript or
subscript is used to denote it.
2This is a generally valid definition of net exports, irrespective of any technology assumption and regardless whether intermediates or final goods, or both, are traded. It may
be stated either in quantity or value terms.
2.1. THE QUANTITY VERSION
15
Consumption Side
The assumption of identical and homothetic tastes results in the neutralization of the consumption side of the model and implies that each country consumes input factors in proportion to world factor endowments. This means
that, in the absence of barriers to trade, all consumers face identical commodity prices, and have identical and homothetic tastes. Hence, all consumers
choose the same composition of the demand bundle (the assumption of identical tastes across countries), while the level of consumption is proportional to
income (the assumption of homotheticity). Thus, any country's consumption
vector is a scaled-down version of the world consumption vector, where the
scaling factor s is equal to the ratio of domestic absorption to world income
(see equation (2.6)):
(2.4)
where CW is the n * 1 vector of world final consumption. The consumption
share, s, is determined by pre-multiplying equation (2.2) by the row vector
of prices pi and using (2.4):
I
b = P t = p x - sp
I
I
I
(2.5)
CW
The left-hand side of equation (2.5) represents the country's trade balance b,
the first term on the right-hand side is the country's GNP (y = p' xl), and
yW = p' CW is world GNP. It follows that:
y-b
s = yW
--
(2.6)
Assuming identical matrices AV for all countries, and using xlw
L(I _p- 1 AV P)xj
=L
xlj
j
and the world commodity market clearing condition
CW
=
=
j
xlw, equation (2.3) becomes:
t=(J-P-1AVP)(x-sLxj) or
j
p-l(J - AV)-ltv
=x -
s Lxi
j
where tV is the vector of net exports, in value terms.
(2.7)
16
CHAPTER 2. THE BASIC HOV THEORY
Production Side
Assume that firms are engaged in perfect competition3 and that the production function in industry i, Fi = Fi(Vi, Xqi), is homogeneous of degree one in
factor inputs Vi and input-output requirements Xqi, and quasiconcave, with
Vi and Xqi being m * 1 and n * 1 vectors, respectively. Therefore, we may
write:
v· x .
1 = Fi(-.2,--..!1!.) = F(ri,ai)
Xi Xi
where Fi(ri,ai) is a unit isoquant for industry i, with ri and ai being the
column i vectors of matrices R and A, respectively. R is an m * n matrix of
the country's direct factor input coefficients, with its elements showing the
amount of each direct factor input used to produce one unit of output within
each industry4. In other words, the reciprocal of the elements r of matrix R
represent a measure of direct factor productivity.
The competitive firm chooses the direct unit factor requirements r and the
input-output coefficients a so as to minimize unit production costs:
¢>(w,p)
= min(A'p
+ R'w
r,a
s.t. F(r, a)
~
1)
where w is an m * 1 vector of factor prices. Using the first-order conditions
and the zero-profit condition 5 in the presence of free trade: p = ¢>(w,p) =
A'p + R'w, hence:
(2.8)
we get the unit factor inputs R(w,p) and the input-output requirements
A(w,p). It follows from our assumptions that firms located in different countries choose identical input-output requirements. Given the Constant Returns to Scale CRS assumption, the cost-minimizing input mix only depends
on the relative factor returns and is independent of the level of output.
Factor Markets
In the aggregate, production is subject to resource constraints. Assuming full
employment of factors, the factor market equilibrium conditions are given by:
Rx=v
where
(2.9)
v is the m * 1 factor supply vector.
Given the assumption of factor price equalization and internationally identical technologies, Rk (w k ,p) = Rj (wi, p) = R for any two countries k and j.
3Later, this assumption is relaxed, allowing for monopolistic competition.
As is shown below, matrix R is related to RT in equation (2.1) through RT = RP-l (I-
4
AtJ)-I.
5Later, under monopolistic competition, price is not driven to marginal cost, but only
to average cost.
2.1. THE QUANTITY VERSION
17
Equation (2.7) is mapped into the factor space by matrix R. Pre-multiplying
equation (2.7) by R and using (2.9), we obtain:
RP-l(1 - AV)-ltv = v -
S
Lvi
(2.10)
j
The combination between the elements of any row h of matrix RP-l and the
elements of any column i of matrix (1 - Av)-l gives the total factor input
requirements of factor h in industry i (that is, the total, direct plus indirect,
factor input h required for producing one unit value of the final demand in
industry i). The m *n matrix of total factor input requirements is given by
RT:
RT = RP-l(1 _ Av)-l
(2.11)
Using (2.11) in (2.10), we get equation (2.1):
RTtv = v - sv w
The factor content of trade RTtV is a linear function of national and world
factor endowments. The last equation represents the quantity version of
the factor content of trade according to the HOV model in the presence
of factor price equalization, free trade, identical and homothetic consumer
tastes, perfect competition, and internationally identical DRS technologies.
If matrix R were invertible, as in the case of n = m, one would determine
net trade by:
tV
= (1 -
AV)PR-1(v - SVW)
Without factor price equalization, there are country-specific factor input coefficients, necessitating thus the use of a different matrix R(w) for each country.
Trefler (1993) noticed that the net trade equation should be changed to allow for international differences in factor productivities. Trefler modified the
quantity version of the HOV model in order to allow for factor augmenting
international productivity differences. He defined a parameter 7r 1 such that,
if vi is the endowment of factor l for a country, then v*1 = 7r I VI is the corresponding factor endowment measured in productivity-equivalent units. It
follows that w*1 = wi /7r1 is the price per unit of v*l. Now, the HOV equation
(2.10) (without intermediate production) becomes:
R*(w*)P-1tv = IIv -
S
LIIivi
(2.12)
i
or:
R*(w*)P-1tv
= v* -
S
L v*i
i
where R*(W*)P-l is the country's technology matrix when its factors are
measured in productivity equivalent units and computed using the US technology data, and II is an m * m diagonal matrix with elements 7r 6. Trefler
6Trefler (1993) dropped the term (1 - Av)-l, because he did not include intermediates
(see his equations (1), (2), (4), and (5)).
18
CHAPTER 2. THE BASIC HOV THEORY
found that this modification of the H OV model based. on the assumption of
equal technology with respect to productivity equivalent units explains much
of the factor content of trade and the cross-country variation in factor prices.
Hence, following Trefler's qualification, to implement correctly the modified
quantity version of the HOV equation empirically, one has first to estimate
the parameters 7r.
2.2
The Value Version
The factor price equalization implicitly assumed by the HOV model in its
quantity version is in conflict with the large variation in factor prices across
countries observed in the real world. Hence, a different version of the HOV
model, not relying on factor price equalization, would be more useful. Under CD production functions, the assumption of factor price equalization can
be relaxed. A value version uses factor cost shares (instead of input factor
coefficients) which are parametric, hence independent of factor prices under
CD technology. Therefore, a value version of the HOV equation holds independently of factor price equalization, as long as we consider free trade.
However, as it is explained below, a modified version of factor price equalization is actually assumed. In addition, the value form of the HOV equation
does not need any further modification as proposed by Trefler (1993). Therefore, in order to implement it empirically, one would not need to compute
the parameters 7r.
The consumption side of the model is identical to that described in the previous section, so that equations (2.4), (2.5), (2.6) also apply here. On the
production side, we assume a CD production function. As before, R is defined so as to minimize the unit production cost 4>( w, p). Using the first-order
and zero-profit conditions, we obtain:
WR=8P
(2.13)
where 8 = W RP-l is an m * n matrix of direct factor cost shares (the CD
parameters), that is, each element of matrix 8 represents the value of each
factor per dollar value of gross output of each industry. W is an m*m diagonal
matrix of factor prices and P is an n*n diagonal matrix of commodity prices.
The assumption of full employment of input factors yields:
Rx = fJ
(2.14)
Pre-multiplying equation (2.14) by the matrix of factor prices W, we obtain:
WRx
= WfJ
(2.15)
2.2. THE VALUE VERSION
19
Pre-multiplying the net trade equation (2.7) by W R and using equations
(2.13) and (2.15), we obtain:
8(1 - AV)-ltv
= Wv -
S
LWRxi
(2.16)
i
U nder CD technology, Wi Ri = 8 P for any country j, which is constant,
hence EWRxi
E8Pxi = EWiRixi = EWiv i . Hence, equation
i i i
(2.16) becomes:
8(1 - AV)-ltv
i
= Wv -
S
L Wiv i
(2.17)
i
Equation (2.17) represents the factor content HOV equation in its value version.
Using the notation: 8(1 - AV)-l = 8 T , an m * n matrix of a country's total
(direct plus indirect) factor cost shares, equation (2.17) becomes:
8 T tv
= Wv -
S
LWivi
(2.18)
i
where 8 T t v = Wtf, and tf is the vector of factor content of trade or the
embodied trade in factor services. The factor content of trade in value
terms 8 T t v is a linear function of national and world factor endowment earnings. A prediction of the signs of the HOV equation coefficients
may be derived from equation (2.18). If the left-hand term for a factor h,
the factor content of trade (}hT tV, is positive, then, according to equation
(2.18), the right-hand term, the endowment income for factor h, should be
positive. In the case where the number of commodities is not equal to that
of input factors, matrix 8 (and matrix 8 T ) is not invertible. In this case,
the pattern of production and trade cannot be predicted, but the value of
the factor content of trade is determined.
Even though the factor prices differ across countries as, consequently, do the
unit factor requirements, according to equation (2.13) the product (Wi Ri) is
the same across countries. A remark is in order here. We assume that factor
prices differ across countries in such a way that they exactly reflect factor
productivity differences. We may define a parameter 7r hi for each factor h
and each country j such that:
where rfi is the unit requirement (reciprocal of factor productivity) of factor
h in industry i and country j. Thus, r~i 7r hi would denote the factor productivity when measured in productivity-equivalent units. Following 'frefler
(1993), the parameter 7r hi may have several interpretations. First, workers
CHAPTER 2. THE BASIC HOV THEORY
20
in different countries may not work equally hard. Second, international differences in productivity may be the result of different access to technology.
Third, countries belong to different cones of diversification, hence they use
different techniques in order to produce different mixes of products 7 .
We may find
7r hj
and
7r hk
such as:
for any countries j and k. Without loss of generality, 7r for the US is taken to
be 1 for all factors. Hence, we may define rhj as the productivity of factor h
in country j relative to the productivity in the US. Similarly, w hj is defined
as the income of factor h in country j relative to the factor h income in
the US. Productivity advantages are offset by higher factor costs, and factor
price equalization, stated in a modified way, holds. It follows that unit costs
are the same internationally, and comparative advantage is driven only by
differences in factor endowments.
Applying Trefler's (1993) qualifications to equation (2.18), and ignoring intermediate production, this leaves the value version unchanged. Equation
(2.18), after applying Trefler's qualifications, becomes:
W*v* - s 2: W*v*j or
j
W*v* - s 2: W*v*j
j
which is equivalent to:
Wv - s 2: wjv j or
j
Wv - s 2: wjv j
j
Trefler (1993) had to assume that the HOV equation in its modified quantitative version holds, in order to compute the parameters 7r. When using
the value version of the HOV model, it is not necessary to compute the parameters 7r, because the way we incorporate factor price equalization already
takes into account the differences in factor prices and factor productivities
across countries. Hence, we may use the technology parameters e, computed
using the US data, for any other country than the US 8 .
7Leamer (1995) defines a diversification cone as the set of capital-labor factor supply
ratios compatible with the production of both goods in the interval,between the capitallabor ratios in the two sectors, if full employment of factors is assumed in a two-factor,
two-good and two-country framework.
8Notice the analogy between e for the value version and R* for the quantity version,
both being computed using data for a reference country, e.g. the US.
Chapter 3
Generalizations of HOV
Theory
3.1
Non-Neutral Technological Differences
The model derived in this section is based on the one developed previously.
It allows for non-neutral technological differences in the parameters e, the
direct factor cost shares, across countries. The technological differences are
non-neutral, as the adjustment of the direct factor cost shares within each
country is allowed to be different across factors. The model hinges on the
observation that, even after considering the differences in factor prices, w,
and unit factor requirements, R, the available data show, for some countries,
important departures from computed for a reference country, typically the
US. This would be, for example, the consequence of different access of countries to technologies. The previous model can be quite easily transformed if
we assume that the matrix 8 is modified in a non-neutral way and differently across countries. In Section 2.2 we had equation (2.13) for a particular
country:
e
WR=8F
where 8 was invariant across countries. Now, we assume that 8 is a countryspecific matrix of effective direct factor cost shares, following the adjustment
for non-neutral technological differences in the parameters. Remember that
in Section 2.2 we defined the factor price equalization in the presence of
different factor productivities and different factor prices in such a way that
the latter exactly reflected the differences in the former across countries.
Now, we redefine the factor price equalization so that differences in factor
prices do not reflect the differences in factor productivities exactly, hence:
(3.1)
22
CHAPTER 3. GENERALIZATIONS OF HOV THEORY
for any two countries j and k, with n being an m
a particular factor h, identity (3.1) becomes:
*m
diagonal matrix. For
.
w hj w hj rhj = whkwhkrhk
,
n
where w hj is an element of matrix j . Hence, the differences in factor productivities are not exactly compensated by the differences in factor prices
across countries. We may define parameters 7["hj, 7["hk, ¢hj and ¢hk, such that
whj = ;:~ and whk = ;:~, and ¢ '17[". It follows that:
h"
hk
(;h; )(r7j7rhj ) = (;hk )(rfk7["hk)
We use the normalization nus = J, where J is an m * m identity matrix.
Using the identity (3.1), for the US and country j, together with equation
(2.13), the matrix of direct factor shares for any country j is related to that
of the US through:
(3.2)
The net trade equation is given, as before, by equation (2.7). Pre-multiplying
that equation by W R, we get, for a particular country:
WRP-l(I - AV)-ltv
= WRx -
S
LWRxj
j
and, given equation (3.1), W R = n-1njwj Rj. Hence:
WRP-l(I - AV)-ltv = WRx -
S
n-1njwj Rjx j
L
(3.3)
j
Using the factor market condition (given, as before, by equation (2.14), Rx
n, we obtain:
v) and pre-multiplying equation (3.3) by
nWRP-l(J - N)-lt v
= nwv -
S
Lnjwjvj
=
(3.4)
j
Furthermore, from equations (2.13) and (3.2), it follows that
Finally, we obtain:
eUS(I - AV)-ltv = nwv -
S
L
njwjv j
nwR = eUs p.
(3.5)
j
where eUS(J - Av)-l is the US matrix of total (direct plus indirect) factor
cost shares. Equation (3.5) reveals that, when using the US technology parameters, the factor content of trade (in value terms), for any country other
than the US, equals the vector of relative factor endowment earnings adjusted for differences in technology parameters. The factor content of trade
is determined by differences in national factor endowments and differences in
technologies (as reflected in different and, implicitly, in different parameters
e across countries).
n
3.2. INTERNAL INCREASING RETURNS
3.2
23
Internal Increasing Returns
Recently, the new theories of international trade have added other determinants of the patterns of trade, such as increasing returns to scale and product differentiation, to comparative advantage. Thus, they introduce intraindustry trade. Ethier (1979) argues that economies of scale, resulting from
an increased division of labor rather than an increased plant size, are international in scope rather than depending upon the size of the national market,
as is assumed in the traditional theory. Scale economies provide the basis for a theory of intra-industry trade in intermediate goods between similar
economies. The main argument of Ethier's paper is that in the modern world
economy decreasing average costs imply intra-industry trade in intermediate
manufactures rather than arbitrary patterns of industry specialization 1 . The
more similar two countries are, the larger is the volume of their bilateral
trade in intermediate goods.
Ethier (1982) shows that, in the framework of international scale economies,
the factor proportions theory is consistent with those statements. He builds
a two-good, two-factor model that explores the relationship between national
and international returns to scale and the factor endowments theory of trade.
His results indicate that international returns to scale depend in an important
way on the interaction between the two types of scale economies, national
and international. Ethier assumes that final output in an industry is a function of components which are assembled to produce final goods. He models
national economies of scale by assuming the existence of a fixed cost at the
level of firms that produce components for final products. The international
economies of scale depend upon the size of the market for finished manufactures, as an increase in the size of the market increases the equilibrium
number of components. In the framework of such a model, Ethier shows that
the HO theorem and other basic propositions derived from it continue to
hold. In international equilibrium, each country necessarily exports the good
which is intensive in its most abundant factor. He shows that intra-industry
trade, like inter-industry trade, has a factor-endowment basis, and that trade
is basically complementary to international factor mobility. Although the existence of product differentiation and internal economies of scale are essential
to the theory, the size of scale economies does not need to be a key determinant of the degree of intra-industry trade. Helpman and Krugman (1985)
show that inter-industry trade is still explained by relative factor endowments, when allowing for economies of scale internal to the firm and product
differentiation.
The derivation of our model is based on the two-sector model developed by
Helpman and Krugman (1985). The production side allows for the coexis1 Arbitrariness refers to the fact that, in the presence of economies of scale, world production would be more efficient if concentrated in one country, but without any indication
of which particular country should be the location.
24
CHAPTER 3. GENERALIZATIONS OF HOV THEORY
tence of n1 Constant Returns to Scale (CRS) and n2 Increasing Returns to
Scale (IRS) industries, with the economies of scale modelled by assuming the
existence of a fixed cost at the level of the firm. Increasing returns at the
level of the firm make the industry imperfectly competitive.
CRS industries supply homogeneous products, while IRS industries produce
differentiated goods. Consumers demand both types of goods, and they appreciate the variety of goods. Following Helpman and Krugman, we assume
that preferences are represented by a two-level utility function:
(3.6)
where Ui(') is a subutility function specifying preference for type i products
and U is the upper tier utility function, assumed to be homothetic in its
arguments.
We assume identical and homothetic preferences in consumption and a subutility function that rewards variety. Let Ui (dil' di2, ... ) be the subutility from
consuming differentiated products, with d iw representing the amount of variety w of the differentiated product i that is being consumed. Ui is assumed
to be a symmetrical, constant-elasticity-of-substitution (CES) function, given
by:
U 1.·(d·1.1, d·12, ... ) - (~df3i)l/f3i
L..t iw
, 0< f3i < 1
w
where f3 i = (1 - ;i)' and ai > 1 is the constant elasticity of substitution
between pairs of varieties of the differentiated product of industry i. The
symmetry assumption implies that consumers allocate the same expenditure
eiw = edNi to any variety w. The subutility level Ui(.) is increasing in the
number of varieties Ni 2 :
f3 ,ld'l.W
U 1..( • ) -- N(l/
i
The consumer's problem of maximizing utility from consumption may be
solved in two stages, given the weak separability of preferences imposed by
the form of the utility function in (3.6). First, for a given allocation of
expenditures (e1' e2, ... ), consumers maximize Ui(') subject to ei. Secondly,
they choose the expenditure allocation in order to maximize overall welfare
subject to the overall budget constraint.
The first-stage maximization gives the demand diw for each variety w of the
product i:
ei
-O'i
d·•w = '"'" l-O"i p..w
uPiw
w
2This result is based on the assumption of identical production functions for varieties of
a differentiated product, which, in turn, implies equal variety prices and, hence, identical
quantities diw. Also, to be rigorous we should treat N as an integer, but the discrete
number problem is ignored.
3.2. INTERNAL INCREASING RETURNS
25
from which we may derive the world demand for variety w of the product i.
In each industry producing differentiated products, firms face a demand curve
with an elasticity a i perceived by the firms 3 . The firm chooses a variety to
produce as well as its price such as to maximize its profits, taking as given
the prices of other firms within the industry and competing on equal terms
with any other firm. Assuming that each firm can differentiate its products
costlessly, no variety will be produced by more than one firm, because no
firm would like to share the market with other producers. Firms producing
different varieties of the same product use the same production functions.
The economies of scale, internal to the firm, are modelled by the assumption
of a fixed cost ¢iw(w,P)Xi, where it is implicitly assumed that the technology
to produce fixed-overhead output Xi is the same as for variable output Xi'
Thus, these two activities are subject to the same factor requirements and
the same unit cost function ¢. Total cost is given by (~ + l)¢iw(w,p)xiw,
where ¢iw(W,P) is the minimum unit variable cost for producing each variety
w of product i, w is a vector of factor prices, and P is a vector of intermediate
input prices. Hence, the producer's problem is:
max(piwXiw - (Xiw
Piw
+ Xiw)¢iw(W,P)]
where (~+ l)¢iw(w,p) represents the firm's average cost which is declining
with output Xiw'
The firm's maximization problem results in marking up price over marginal
cost:
Piw =
¢iw(W,P)
i3 i
Assuming that all the firms in the differentiated-product industries use the
same technology, they compute the same unit cost ¢iw(W,P) = ¢i(W,P), and
all the firms producing different varieties of the same product have the same
price for their varieties:
Piw = Pi
=
¢i(W,P)
i3 i
Free entry and exit of firms implies a zero-profit condition in equilibrium.
This further implies that the price of differentiated products equals average
cost, (~+ l)¢i(w,p), and determines output with zero profits:
(3.7)
F.,
where Xiw =
and Xiw is the same for all the firms in industry i, given
the symmetry assumption. Therefore, firms in the IRS industries produce
3Given the assumption of a large number of firms, the elasticity faced by an individual
producer may be approximated by the elasticity of substitution between any two varieties
ai, and it determines the optimal mark-up for firms.
26
CHAPTER 3. GENERALIZATIONS OF HOV THEORY
different varieties in the same quantities and equally priced. Notice that the
output per firm was determined independently of factor endowments and
trade.
In the CRB industries, there are no fixed costs. Firms produce homogeneous
products and the industries are perfectly competitive. Hence, price is equal
to average cost which, in turn, is equal to marginal cost. We assume that
all firms, both competitive and monopolistically competitive, use internationally identical CD production functions and choose unit factor inputs and
input-output requirements in order to minimize unit production costs. Given
price-taking behavior and perfect competition in factor markets, unit factor
requirements are given by:
WR= 8{3P
(3.8)
where 8 is the matrix of direct factor cost shares, with its elements being
the CD parameters, and {3 being an n * n diagonal matrix, with the first nl
diagonal elements equal to 1 and the last n2 equal to {3i. As before, by using
the factor market equilibrium condition and assuming internationally identical production functions, we obtain the net trade equation for a particular
country. The factor market equilibrium condition is, in this case:
R(x+x)=v
(3.9)
where by x and x we denote the vectors of industry output, with Xi = Nixwi
and Xi = NiXwi for any IRS industry i. From equation (3.7), we get x+x =
jr1x and, substituting this expression in equation (3.9), the factor market
equilibrium condition becomes:
(3.10)
Identical preferences imply that (3i is the same across countries. Identical
technologies imply the same fixed overhead output Xiw per firm across countries. Pre-multiplying the net trade equation (2.7) by W R{3-1, and using
equations (3.8) and (3.10), the net trade equation for a particular country
becomes:
8(1 - AV)-ltV = Wv - s
wjv j
(3.11)
z=
j
or
8 T t V = Wv - s Z=Wjv j
(3.12)
j
where 8 T = 8(1 - AV)-l, and (1 - Av)-l represents the total (direct and
indirect) requirements matrix reported in the input-output tables. Equation
(3.12) is identical to equation (2.18), except that now 8 = W R{3-1 P-t,
while in the perfect competition case, 8 = W RP-l .
Every country produces some varieties of the differentiated products, but all
countries consume all the varieties. Hence, there is two-way trade, or intraindustry trade, in differentiated products. As in the Helpman and Krugman
3.2. INTERNAL INCREASING RETURNS
27
(1985) or Dixit and Norman (1980) models, there are both inter-industry
trade based on comparative advantage and intra-industry trade based on
scale economies. Thus, for the n2 industries that produce differentiated products, we may now write separate equations for exports and imports. Each
country will produce a certain number of varieties of each differentiated product and will consume a proportion of each of its own varieties, equal to the
ratio between its domestic absorption and world income, s. The difference
between total production and consumption of home-produced varieties will
be exported. In addition to its own domestically produced varieties, a country consumes a fraction s of the varieties produced elsewhere in the world.
Therefore, exports z and imports m for the differentiated products are given
by:
z = (1- s)xl
(3.13)
and
m =
s(Lxjl - xl)
(3.14)
j
where z is an n2 * 1 vector of exports of the differentiated products, m is
an n2 * 1 vector of imports of the differentiated products, xl is an n2 * 1
vector of output for final demand of the differentiated products, and j denotes
countries.
Now we follow an approach similar to the one used so far. In order to get
a feasible equation describing the factor content of exports and imports,
respectively, we need to assume that all industries produce differentiated
goods, hence all industries are characterized by monopolistic competition
and n2 = n. This assumption is necessary because of the presence of intermediates in the model, which impairs not only the derivation of the factor
content equations, but also their interpretation. Pre-multiplying equations
(3.13) and (3.14) by WR,8-1, and using the factor market condition (3.10)
and equation (3.8), the equations that define the value of the factor content
of exports and imports for a particular country are:
(3.15)
and
8(I - AV)-lmV
= 8 T mV = s(Lwjvj -
Wv)
(3.16)
j
where v is a value index, and z and m are the vectors of exports and imports
of the differentiated products, respectively. The left-hand sides of equations
(3.15) and (3.16) are identical to that of equation (3.11), except that equation
(3.11) is written for net exports, while equations (3.15) and (3.16) are written
for exports and imports, respectively. There are many situations when it is
of interest to explain the pattern of exports, rather than of net exports.
An important advantage of the model with monopolistic competition and
product differentiation is that it allows us to explain the countries' patterns
28
CHAPTER 3. GENERALIZATIONS OF HOV THEORY
of exports and imports separately. Notice that, to describe the pattern of
exports for a particular country, we need factor endowment data only for that
country while, for the net exports, data for all the countries are required.
The intra-industry trade i is defined as the difference between total (exports
and imports) and net exports:
i
= (z + m) - It I
Using equations (3.11), (3.15), and (3.16), we may write an equation for the
intra-industry trade i V of the industries producing differentiated products:
8(1 - AV)-liV = 28(2:: wjv j - Wv)
(3.17)
j
for the industries where the country is a net exporter of differentiated products, and:
(3.18)
for the net importer industries. This model predicts neither the pattern
nor the extent of intra-industry trade, but just its factor content. Equation
(3.17) shows that, when a country is a net exporter of differentiated products,
the factor content of intra-industry trade is still explained by the country's
relative factor abundance.
Equations (3.12), (3.15) and (3.16) enable us to formulate theory-based regression equations and to estimate the model with economies of scale and
product differentiation.
3.3
External Increasing Returns
The production side of the model allows for the coexistence of nl industries
that produce homogeneous products using Constant Returns to Scale (CRS)
technologies, and n2 industries with Increasing Returns to Scale technologies
(IRS), external to the firms but internal to the industry. We assume that
the economies of scale are the same world-wide for a particular industry. The
firms are small enough not to perceive themselves as influencing the industrywide economies of scale. Hence, returns to scale are perceived to be constant
at the level of the firm, this being consistent with perfect competition. This
type of external economies might be explained by the spread of production
knowledge among firms belonging to an industry.
We assume that scale economies are present at the industry level in a multiplicative way, e.g.:
3.3. EXTERNAL INCREASING RETURNS
29
where Xik represents the gross output of firm k in industry i that depends
parametrically on the gross industry output Xi, due to external economies
of scale of degree Ei. Fi(Vik) is the CRB production function, identical for
all the firms within industry i, and Vik is a vector of factor inputs employed
by a particular firm k. The first term on the right-hand side refers to the
productivity effect from external scale economies, while the second refers to
an index of factor inputs. Total output in industry i is given by:
where Ni is the number of firms in industry i and Vi is the vector of total factor
inputs employed in the industry 4. As before, firms choose the unit factor
inputs and input-output requirements in order to minimize unit production
costs. With increasing returns, unit factor requirements not only depend on
factor returns, but also on the level of industry output. We assume that
there are no cross-industry externalities and that technology is homothetic.
Therefore we may write:
R(w,p,x) = R(w,p)X-O
(3.19)
where R is the matrix of unit factor requirements, and X-o is an n * n
diagonal matrix, whose entries are xi oi • Ci is zero for the first nl industries
and close to, but larger than, zero for the last n2 industries. Since the firm
considers the external effect to be independent of its own actions, and since
Fi (Vik) is linearly homogeneous in Vik, the firm minimizes its unit marginal
cost, which is output-independent. The zero-profit condition is:
p = X-o(R'w
+ A'p)
Pre-multiplying this by Xc and rearranging terms we obtain:
(3.20)
Equation (3.20), together with the first-order conditions, implies that:
WR=8PXO
(3.21 )
We recall that, in the perfect competition model, the corresponding equation
is different (see equation (2.13), WR = SP).
Using equation (3.19), the factor market clearing condition is:
4With a CD production function and only two input factors, namely capital K and
OL'
Ok'
E'
OL'
Ok,
E'
OL'
Ok,
labor L, Fi(Vik) = Lik • K ik ' and Xi = Ni x i ' Lik • K ik ' = xi' Li • Ki ., where subscripts
k and i denote the firm and the industry, respectively.
CHAPTER 3. GENERALIZATIONS OF HOV THEORY
30
Using the results from Section 2.2, in the presence of free trade, internationally identical technologies, and identical and homothetic consumer tastes, the
HOV equation for a particular country becomes 5 :
8(1 - AV)-ltv
= Wv - S L wjv j
j
or
8 T tV
= Wv - S LWjvj
(3.22)
j
Equation (3.22) is identical to equation (2.18), except that now 8 = W RP-l X-e:,
whereas, in the perfect competition case, 8 = WRP-l. The factor content
of trade is still a linear combination of domestic and world factor endowment
earnings.
This model allows us to formulate a theory-based regression equation, with
economies of scale entering the explanatory part of the regression in an interactive term together with factor cost shares, rather than as a separate
independent variable.
When we consider the economies of scale to be international, we get:
where the superscript w denotes the world. The HOV equation is the same
as in the case with national external scale economies, except that now e =
WRP-l(xw)-c.
3.4
Internationally Mobile Capital
In a world where capital becomes more and more mobile internationally, caution is necessary in interpreting data on the capital content of trade. Usually,
a country is exporting capital both directly (through foreign direct investment) and indirectly (through the capital content of traded goods). Theory
in general focuses entirely on the indirect capital exports, hence a modification of the HOV model is required to take the observed direct international
capital flows into account.
Wood (1994a) noticed that capital, given the fact that it is internationally
mobile, cannot influence the pattern of trade of goods, which is determined
by the endowments of immobile factors only. The exclusion of capital from
the input factors explaining the pattern of net trade may improve the results
of the tests based on the HO theory. Wood proposed a model in which the
5The net trade equation (2.7) is pre-multiplied by WRX-< and, given equation (3.21)
and the above factor market equilibrium condition, we get equation (3.22).
3.4. INTERNATIONALLY MOBILE CAPITAL
31
production factors are skilled and unskilled labor, and suggested that capital
be defined as finance, not as capital goods. Ethier and Svensson (1986)
examined the theorems of international trade with factor mobility and found
explicitly that comparative advantage could be applied to factor trade as well
as to commodity trade.
The consumption and production sides of the HOV model are preserved when
allowing for capital to be mobile across countries. For input factors other than
capital, the factor market conditions are, as before, given by equation (2.14):
Rx=v
The capital market condition is now given by:
where the superscript k denotes capital, rk is the k row vector in the matrix
of unit factor requirements R, R is the domestic capital endowment, and t k
the country's direct net export of capital (the difference between the domestic
capital deployed abroad and the foreign capital deployed at home).
As before, the net-trade equation is given by equation (2.7) and, following
the same procedure as in Section 2.2, we obtain the HOV equation (2.18):
eTtv=wV-SLWiVi
j
or, written for a factor h,
()hTtv = whv h - S L whiv hj
(3.23)
j
The left-hand term of equation (3.23), which represents the factor content
of trade for factor h, is preserved for any factor other than capital. For
capital, the model is adjusted to allow for the international mobility of capital.
Using the new capital market condition and observing that, given the CD
technology, wkrk = w ki rki for any country j, equation (3.23) written for
capital is:
t1 = wk(R - t k ) - S L wki(Rj - t ki )
j
or
t1 +wkt k = wkR - S Lwki(Ri _t ki )
(3.24)
i
where w k is the rental price of capital, t1 = ()kT tV is the value of the country's
indirect capital content of net trade (capital services embodied in net exports
of goods), and wktk is the direct capital content. The rental price of capital
32
CHAPTER 3. GENERALIZATIONS OF HOV THEORY
is determined either by the market, or by the government in some countries.
Hence, the rental price of capital may differ from one country to another.
Therefore, when allowing capital to be internationally mobile, the measured
capital endowments should be adjusted for inflows and outflows of capital via
foreign direct investment. Gaisford (1995) proposes a similar modification:
tj
+ wktk = wkk -
:w Lwkjkj
(3.25)
J
However, when applying equation (3.25) to a set of data, we should keep in
mind that the 'world' refers to a limited number of countries, hence we should
adjust the capital endowments for all the countries, as in equation (3.24)6.
This model may be estimated either in the perfect competition framework
(see Section 2.2) or in the presence of scale economies and product differentiation (see Section 3.2 and 3.3).
3.5
Armington Preferences
Consumers show a bias towards domestically produced goods. This may be
explained by the existence of transportation costs, trade barriers or product
differentiation. Lancaster (1980) notices that domestically produced varieties
are probably closer to the ideal variety of domestic consumers.
When assuming Armington (1969) preferences, the consumption side of the
HOV model is modified. Equation (2.4) c = seW = sx fw becomes:
c = s[axf
+ a(x fw
- xf)]
(3.26)
where parameters a and a denote a preference bias towards domestic- and
foreign-produced goods, respectively. With this modification, the net trade
equation (2.7) becomes:
t
= xf -
s[ax f
+ a(x fw -
xf)]
(3.27)
and, following the approach used in Section 2.2, we obtain the value version
of the HOV equation, with Armington homothetic preferences:
eTtv = (1- sa
+ sa)Wv -
sa LWjvj
(3.28)
j
Therefore, the Armington assumption about preferences modifies only the
right-hand term of the HOV equation. Equation (3.28) nests the HOV equation (2.18) for a = a = 1.
6This is because
L
i
wkitki
i= 0
for a sample limited to a certain number of countries.
3.5. ARMINGTON PREFERENCES
33
Pre-multiplying equation (3.27) by the row vector of prices pi, and using the
definition of s, s = ~, we get a relationship between the parameters a and
a:
aJL
+ a(l - JL)
= 1
yW
yW
Estimates of a (or a) would allow us to estimate a model based on equation
(3.28). We may also incorporate this modification into the models which allow
for monopolistic competition and product differentiation, and internationally
mobile capital. Then, one may check empirically whether the HOV equation
is rejected in favor of one of the possible extensions of the original model.
Chapter 4
Theory-Based Empirical
Implementation
The main purpose of this study is to develop, in the framework of the factor
proportions theory, empirical models, to be further used to explain the trade
patterns for particular countries. One may either formulate tests based directly or indirectly on the HOV equation and its generalizations derived in
Sections 2 and 3 (e.g. simple correlations and ranking propositions) or try to
get theory-based regression equations. Whilst, to apply the first approach,
we only have to assume that HOV holds, to use a regression approach one
has also to rely on an approximation. Remember that the HOV equation for
a particular country j is:
eTt jv
=
wjv j -
si L W j v j
j
(see equation (2.18)). For a particular factor h, equation (2.18) becomes:
()hT t jv
=
whjv hj -
si L
whjv hj
j
4.1
Direct Tests
Before proceeding with determining the countries' trade patterns, it might
be interesting to check empirically the applicability of the HOV equation and
its generalizations. Based on the HOV equation, we may first derive direct
tests. One may check whether the left-hand term (the factor content of
trade ()hT t jV ) and the right-hand term (the relative factor abundance income
w hj v hj - sj I: w hj v hj ) of the HOV equation are identical for any factor h in
j
36
CHAPTER 4. THEORY-BASED EMPIRICAL IMPLEMENTATION
country j if the HOV equation holds. This test may be undertaken either for
the original perfect competition model, or for generalizations of itl.
However, given the strong assumptions on which the HOV theory relies, this
test may be too strong. A weaker test would be to check for the equality of
the signs of the two terms of the HOV equation (sign test):
sign(()hTtjV) = sign(whjiJh j -
s1 LwhjiJhj)
(4.1)
j
For both tests, the percentage of matches between the terms of the HOV
equation or their signs is taken to be a measure of the performance of the
HOV model.
4.2
Indirect Tests
Based on the HOV equation, one may also formulate indirect tests. Basically,
there are two types of indirect tests: ranking propositions and tests based
on the interaction between computed simple correlations among trade and
factor intensity on the one hand, and factor endowments on the other hand.
4.2.1
Ranking Propositions
The ranking propositions refer either to the ranking of any two factors in
terms of their relative abundance in a particular country (Proposition 1),
or the ranking of any two countries in terms of their relative abundance of
a specific factor (Proposition 2). One may want to check how well these
propositions perform by examining the percentage of matches between the
ranking of factors, as predicted by their abundance, and the ranking of factors, as revealed by the factor content of trade. The test may be undertaken
for each pair of factors for a particUlar country (Proposition 1) or for any
pair of countries for a specific factor (Proposition 2).
The derivation of the propositions follows Leamer (1980). He uses the factor
content version of the HOV equation in its quantity form, for a two-factor
(namely capital and labor) case:
Kx - Km
Lx - Lm
=
=
K - sK w
L - sL w
(4.2)
lThe assumption of increasing returns and product differentiation changes the left-hand
term of the HOV equation, while the assumption of internationally mobile capital alters
the right-hand term.
4.2. INDIRECT TESTS
37
where K x , Lx, Km and Lm denote capital and labor incorporated in exports
and imports, respectively. He uses the above equations to prove that a country is revealed to be relatively well endowed with capital (compared to labor)
iff one of the following conditions holds:
(4.3)
Kx - Km
> 0, Lx - Lm > 0, (Kx - Km)/(Lx - Lm) > Kc/Lc
(4.4)
Kx - Km
< 0, Lx - Lm < 0, (Kx - Km)/(Lx - Lm) < Kc/Lc
(4.5)
where Kc and Lc denote, respectively, capital and labor incorporated in consumption, with Kc = K -Kx+Km and Lc = L-Lx+Lm. The Leontief Paradox [Leontief (1953)] is based on the proposition that if (K/L)x < (K/L)m'
the country is relatively better endowed with labor. But this is true only
if the net exports of labor services have a sign opposite to that of the net
exports of capital services. When both are positive, as in Leontief's data,
the correct comparison is between (K / L ) t and (K / L ) c, where t denotes net
exports (see condition (4.4) above). It can be shown that Leontief's data for
1947 satisfy the second condition, therefore the US is proved to be relatively
well endowed with capital2 • Leamer gives five corollaries, which outline necessary and sufficient conditions for trade to reveal the abundance of capital
(as compared to labor), in a two-factor model of international trade.
Leamer's corollaries are, however, based on the quantity version of the HOV
model, which assumes factor price equalization across countries. Kohler
(1991) examines the arbitrariness of empirical tests of rank- order and sign
propositions, derived from the HOV model of the factor content of trade. He
shows that, when using different rank and sign propositions derived from the
HOV model, there are certain conditions under which a given data set will
support one hypothesis, while rejecting another. Based on the data set used
by Bowen, Leamer and Sveikauskas (1987), he checks the empirical relevance
of this fact and shows that the results of such rank and sign tests are not
robust. However, his tests are based on the quantity version of the HOV
model, which assumes that factor price equalization across countries holds.
This section proposes necessary and sufficient conditions for trade to reveal
the relative abundance of a particular factor, when compared to any other
factor for a particular country, or the relative abundance in a country, in
comparison with another country, of a particular factor. These propositions
are derived using a value version of the HOV model in a multi-factor, multigood, multi-country setting which allows for different factor returns and unit
factor requirements across countries.
The derivation of the ranking propositions follows Leamer (1980). Two important rank hypotheses may be derived from the value version of the HOV
2 However,
as Maskus (1985) shows, this result does not hold for 1958 and 1972.
38
CHAPTER 4. THEORY-BASED EMPIRICAL IMPLEMENTATION
model. Remember that the HOV equation in the value version written for a
particular country is:
Wtf
=
or
Wv-sEWivi
i
(4.6)
Wt fA
where tf = w-1eTt v is the factor content of trade. The factor content of
trade adjusted for trade imbalance is given by t1 = tf-(b/yW) EW-1Wivi.
i
For a particular input factor h, equations( 4.6) become:
(4.7)
Equations (4.7) may be written:
(4.8)
for any country and any input factor h.
Further, we use:
E w hj Vhi
=
i
whwfjhw, with whw and vhw denoting the world weighted average for the
return on factor h (with the weights being the national factor endowments
relative to the world factor endowments) and the world endowment of factor
h, respectively. Equations (4.8) become:
(
whth )
whWv'w
( whthA )
whW;s;w
/s
=
/(?) =
( whwvhw
whv h ) / s-l
( whwVhw
WhV h
)/(.JL)
1Iw-1
(4.9)
The first proposition refers to the ranking of any two input factors for a
particular country and may be formulated either in quantity or in value
terms. The second proposition refers to the ranking of any two countries for
a particular input factor, again stated either in quantity or in value terms.
Based on equations (4.9), there are four possibilities for deriving and stating
each proposition.
Rewriting equations (4.9), for a particular country and two different input
factors, hand l, we get the first proposition:
4.2. INDIRECT TESTS
39
Proposition Ia
If:
then:
An alternative quantity version of Proposition la may be written as:
Proposition Ib
If:
then:
Using equations (4.9), Proposition 1 may also be written as:
Proposition Ie
If:
then:
where t fhA = t fh
_
...1L '"
yW ~
J
whiiJhi
wh
and t flA = t fl _...1L
'" wliiJli represent the
yW ~ wi
J
content of trade, for factor hand l, if trade is balanced, and b is the country's
trade balance.
A quantity version of Proposition 1 c may be formulated as:
Proposition Id
If:
then:
Given Proposition 1 in its quantity version (b or d), if the input factors for a
particular country are ranked according to their endowment ratios relative to
the world, this would be reflected in the same ranking of the factor content
(adjusted factor content) of net exports of the factors relative to the world
40
CHAPTER 4. THEORY-BASED EMPIRICAL IMPLEMENTATION
endowment thereof, adjusted for differences from the world (weighted average) factor returns and the country's size. If factors were ranked according
to the value of their endowment ratios relative to the world (Proposition Ia
or Ie), this would be reflected in the same ranking of the values of the factor
content (adjusted factor content) of net exports, relative to the value of the
world endowment. In this case, no adjustment would be necessary for the
country size.
The second proposition refers to the ranking of any two countries with regard
to a particular input factor. Its derivation is based on equations (4.9particular
input factor l. There are four ways to state Proposition 2. The first is:
Proposition 2a
If:
then:
This may be written also in quantity terms:
Proposition 2b
If:
then:
t lk
I/k
w
Iw
<
t li
I / si
~I S + - I k >~I
VW
w
VW
Using equations (4.9), we may also obtain:
Proposition 2c
If:
then:
A last quantity version of Proposition 2 is:
Proposition 2d
If:
wlw
+-1-'
w'
4.2. INDIRECT TESTS
41
then:
t lkA
f
-lw
v
Y YW)
/( k/
lw
< t liA
W
+ -u;
>
W
f
-lw
v
/(
y i/YW)
lw
W
+ --z:i
W
Given Proposition 2 in its quantity version (b or d), if, for a particular input
factor, countries are ranked according to their endowment ratios relative to
the world, after adjusting for countries' sizes, then this will be reflected in
the same ranking of countries according to their factor content (adjusted
factor content) of trade relative to the world endowment, adjusted for world
differences in factor return and countries' sizes. If the countries are ranked
according to the value of their endowment ratios, relative to the world after
adjusting for the countries' size (Proposition 2a or 2c), this will be reflected in
the same ranking of the values of the factor content (adjusted factor content)
of net exports, relative to the value of the world endowment and adjusted
for differences in the countries' sizes.
The present formulation of these two ranking propositions differs from that
by Leamer (1980) or Bowen, Leamer and Sveikauskas (1987). These authors' derivation is based on the quantity version of the HOV equation, hence
it does not allow for differing factor productivities and factor prices across
countries. By contrast, the present setting has the advantage of permitting
world differences in factor prices, hence allowing for differences in the factor
productivities and factor returns across countries. Previous empirical studies
(e.g., Brecher and Choudhri (1982b), Maskus (1985), Bowen, Leamer and
Sveikauskas (1987)) use the quantity version of the HOV equation, which
does not allow the unit factor requirements to differ across countries, this
being possibly a source of error in their results. The aothors conclude that
HOV propositions to the effect that trade reveals factor abundance are not
supported by data. The data favor the hypothesis of neutral technological
differences and suggest measurement errors in both trade and national factor
endowments. Generally, data on the unit factor requirements for the US have
been used and, given the important differences in factor productivities across
countries, the results are inaccurate.
We have formulated propositions according to which the ranking of the adjusted net exports of factor services (in value or quantity terms, adjusted for
world differences in factor returns) should conform to the ranking of factors
by their abundance. Propositions 1 and 2 may be modified to allow for
increasing returns to scale, product differentiation and internationally mobile capital. When the assumption of perfect competition for the commodity
market is relaxed, Propositions 1 and 2 are perfectly preserved, except for
the expression of the factor content of trade, which is now computed based
on a different matrix of direct factor cost shares. An appendix to Section
4 gives the ranking propositions for the model with internationally mobile
capital (presented in Section 3.4).
42
CHAPTER 4. THEORY-BASED EMPIRICAL IMPLEMENTATION
4.2.2
Simple Correlations
An indirect test, based on the HOV equation, uses simple correlations between net exports and total (direct plus indirect) factor cost shares, for each
country j and factor h, across industries. As Deardorff (1982) noticed, the
trade vector t jv must contain both positive and negative elements, hence the
inner product ()hT t jv is at least suggestive of a correlation. The computations may be done for the perfect competition model or for any generalization
based on the original model.
The results of the tests based on simple correlations are identical to those
of the direct tests. However, in terms of predicting a country's pattern of
trade, correlations appear to be more sensible. The left-hand term of the
HOV equation, written for factor h, is ()hT t jv = L ()?T t{v. This is related to
the simple correlation between
()hT
•
and t jv through:
(4.10)
where n is the number of industries, ()hT is for factor h the row vector of
the matrix of total unit factor requirements T , t jv is country j's vector of
net exports, expressed in value terms, b is the country's trade balance, and
o denotes standard deviation. If the HOV equation were exact, then:
e
OehTOtivCorr(()hT, t jV )
+ bi7J hT = whjv hj
-
si L
whjv hj
(4.11)
j
The correlations are the stronger, the larger the factor endowment income
relative to that of the world and the less different the factor cost shares across
industries.
In a weaker sense, we expect that the sign of the left-hand term of equality
(4.11) will reproduce that of the relative factor endowment income:
sign [O"ehTO"tiVcorr(()hT, t jV ) +bi 7JhT]
= sign(whjv hj - si L
whjv hj )
(4.12)
j
If we denote by g~j the right-hand term of the HOV equation for country j
and factor h, and by {3hj the simple correlation between the net trade vector
t jv and the total factor cost share ()hT, we may rewrite equality (4.12) as:
(4.13)
Condition (4.13) is identical to the sign test (directly based on the HOV equation and defined in Section 4.1) and it has to hold for each factor h and each
4.2. INDIRECT TESTS
43
country j. As a consequence, the sign of the computed simple correlations
between trade and factor intensities, adjusted for the trade imbalance, would
have to replicate the sign of the actual relative factor endowment income for
each factor if the HOV equation were exact.
If we pre-multiply the HOV equation by the row vector g~ , we get a condition
that has to hold for each country j:
L g~j (}7T t{V = g~ gf, ~ 0
(4.14)
hi
or:
'"'" gbh'J h'
L.J
((3 JaghTatjO
'-hT
+ lY()
)
(4.15)
~ 0
h
Condition (4.15) imposes a restriction on the interactions between factor
endowments and factor content of trade, to the effect that they should be
positive on average across all factors. To my knowledge, up to now a condition such as that implied by (4.15) has neither been stated nor checked
empirically. This condition, which poses a contraint across all factors, is less
restrictive than (4.13), which has to hold for each factor.
The right-hand term of the HOV equation represents the relative factor endowment income. It is important to know how the computed simple correlations between trade and factor intensities are related to the true relative
factor abundance. We may define a measure of the true relative factor abundance of factor h in country j by true hj = :.h~j / sj - 13 . However, remember
~ Vh
3
that in Section 2.2 we defined the factor price equalization such that the factor endowments are computed in productivity equivalent units. Accordingly,
the true relative factor abundance may be given by: true hj = E::~j sj - l.
/
By definition, iJ,hj
= 7r hj iJhj
1). It follows that: true
h.
J
i'
related through:
true
= ':;':: =
w hUS (7r hUS is taken to be
-hj hj
.
hj
h'
vh'1w hj / sJ - 1. Hence, gb and true J are
and w'hj
=
j
h·
J
=
I:j
hj
gb
J'
/s
iJhjw hj
.
(
. (true h j ) -_ szgn
szgn
~
~j
hj
gbh' h' /
V Jw J
(4.16)
S
j)
(4.17)
and:
(4.18)
3The factor content of trade, divided by the world factor endowment and adjusted for
the country size is taken as an indirect measure of the relative factor abundance.
44
CHAPTER 4. THEORY-BASED EMPIRICAL IMPLEMENTATION
Following Leamer (1974) and Balassa (1979), conditions (4.13) and (4.15)
may be called "external validation" conditions. According to the first condition, in a post-trade equilibrium, the sign of the simple correlation between
trade and factor intensity has to be validated by actual observations of the
relative factor endowment income for each factor within a particular country. The second condition constitutes a restriction that should hold in a
post-trade equilibrium across all factors for a particular country.
4.2.3
Multiple Correlations
We are interested in explaining countries' trade patterns in the framework
of the factor proportions theory, using a cross-industry regression analysis.
This empirical approach uses measures of trade and factor intensities and
from these infers the factor abundance vectors, in a cross-industry framework. If the estimation of a factor coefficient in the cross-industry regression4
is positive, the country is supposed to be rich in that resource. Generally, the
results of these types of study are controversial, as different authors have obtained completely different results. This might be explained, to some extent,
by a lack of theoretical foundations. There is no general agreement upon the
precise form of the estimation equation, the definition of variables (dependent and independent) or the estimation procedure (OLB or GLS, applied to
bilateral or multilateral trade), etc.
Deardorff (1984) formulates a theory with a parametrized representation of
both the production and the consumption side of the model, in order to
justify its use as a framework for regression analysis. He assumes both the
production functions and the preferences to be CD, internationally identical,
and finds a relationship between autarchy and free trade commodity prices,
and factor endowments. By assuming CD preferences and CD technology,
the autarky factor and goods' prices can be expressed in terms of observable
factor cost shares and factor endowments, and therefore Deardorff's results
can be used in empirical analysis.
Harkness (1978, 1981) is among the few trade economists who tried to find
a theoretical justification for using cross-commodity regressions to explain a
country's trade pattern. He tries to characterize the link betw~n commodity
trade and factor-service trade, hence between commodity trade and factorabundance, in a form that preseves the spirit of the HO theorem for a twofactor world. He proposes a relationship between commodity net exports and
factor intensities:
tdXi = L~he?
+ iii
h
4Net exports are regressed on factor intensities in a cross-industry framework.
(4.19)
4.2. INDIRECT TESTS
45
()f
where ti and Xi are net exports and output in industry i,
is the cost share
of factor h in the production of good i, j3 is an OLB-computed partial regression coefficient, determined from the multiple regression of til Xi on all factor
cost shares, in a cross-industry framework, and jl is an OLB-computed error
term. The relationship described in equation (4.19) is a descriptive and not
a structural one. It characterizes the relationship between commodity net
exports and factor intensities, which, on average, occurs in general equilibrium. Hence, j3 is an OLB-computed descriptive statistic, summarizing the
average partial relationship between net exports and factor-intensity. It is
not a structural parameter invariant across commodities. The computed
OLS coefficient is, in fact, a proxy for the hypothetical direct coefficient
that would be defined if factor intensities were mutually uncorrelated across
commodities. Harkness's formulation of the HO theorem is as follows:
"Given that factor complementarities can be controlled through
multiple regression analysis, the sign and rank order of {ih will
duplicate those of the net indirect exports as a proportion of total
domestic supply, and thereby, according to Vanek, those of the
corresponding relative factor abundance. "
The very good fit he obtained suggests that omitted variables, should they exist, are highly collinear with factor intensities, their influence being captured
by j3.
An important contribution to explaining the link between the factor proportions theory and the regression analysis is provided by Bowden (1983).
Following Bowden (1983) and Kohler (1988) we show how, based on the
theoretical models developed in Section 2, one may derive the theory-based
estimation equations to be further used in a cross-industry empirical study.
We found in Section 2.2 that a value version of the HOV equation written
for a particular country j within the perfect competition framework is given
by:
(4.20)
where t jvA is the vector of adjusted net exports, in value terms. There
should be no debate about trade being treated as the dependent variable in
a regression study, while factor endowments and factor intensities are taken
as exogenous. Whenever the regression analysis is strictly derived from the
factor proportions theory, it is widely agreed that the correct choice of the
trade variable is net exports, rather than exports or imports, as used in many
empirical studies. If in (4.20), we denote the right-hand side by an m* 1 vector
46
CHAPTER 4. THEORY-BASED EMPIRICAL IMPLEMENTATION
gi of relative factor endowment income5 , then:
(4.21)
Pre-multiplying equation (4.21) by the row vector gli, we get:
(glieT)tivA
= g'i gi 20
(4.22)
We may write inequality (4.22) as:
2:){vA L:>hiOfT 2 0
h
or
(4.23)
i,h
Or
where index i denotes industries, h represents factors, and
represents
the row h vector in matrix eT. Inequality (4.23) is a restriction across
commodities and factors that must hold in a post-trade equilibrium for each
country j. It states that net commodity exports, t{vA, must be higher, in
some sense on average across all commodities, the higher the inner product
(gIOn. We may write inequality (4.23)6 as:
2)t{VA - [ivA)(ghj - gj)(OfT - OhT) 20
(4.24)
i,h
Inequality (4.24) shows that the goods that are exported (t{vA > 0) must
use, on average, relatively intensively (OfT> OhT) those factors in relative
abundance (ghi > gi), and non-intensively (OfT < OhT) those factors in
relative scarcity (ghj < gl). As Deardorff (1982) observes, an inequality such
as (4.24) gives mathematical content to the HOV theory as an explanation
of the pattern of commodity trade in an average sense.
If we denote the inner product
L ghi OfT by at, the inequality (4.23) becomes:
h
(4.25)
Hence, there would be a positive relationship, on average across industries,
between net commodity exports t{vA and
where i is the industry index
and a represent interactions between factor endowment income and factor
intensity. However, trade theory does not allow any specification of this
ai,
5Notice that ghi
= whifihi
-
~L
1J
i
whifihi differs from
g~i = whifihi
-
si L
i
whifihi.
6This result is based on the observation that t ivA has zero mean (across industries) and
= 1.
L: 8fT
h
4.2. INDIREOT TESTS
47
relationship for each commodity. Hence, the next step must necessarily be
an intuitive one and it involves an approximation. We may want to write
trA = f(a{), or, in a cross-industry regression:
with a j
> 0,
or, given the definition of
t{vA =
La
ai:
hj ()~T ghj
+ J1{
(4.26)
h
As Kohler (1988) remarked, a zero expectation of the error term implies an
unspecified cross-commodity restriction on the parameters 7 . If we consider
the existence of country-specific non-HO determinants, this may be modelled
through intercepts in equation (4.26). Harkness (1978) notices that "the constant may be interpreted as the implied regression coefficient on a composite
factor intensity defined as the value share of all omitted variables". Moreover,
the constant term captures the joint effect of all variables from competing
theories of comparative advantage, and it is country specific. As Bowen and
Sveikauskas (1992) have shown, the inclusion of a constant term implies a specific trade imbalance correction. The dependent variable in equation (4.26) is
already corrected for trade imbalance. It follows that the net trade equation
to estimate is:
(4.27)
where xwJv is a vector of world total production for final demand of good
within each industry, in value terms, and ao is a constant term measuring
the level of net exports when domestic production is zero. The left-hand
. A
.
. x wfv
.
term is t;V = t~V - bJ ~, with bJ being country j's trade balance. The
interactions implied by equation (4.27) should be understood in the following
way: if a factor h is used relatively intensively in the production of good i,
and hence ()~T is relatively large, and if the country is relatively well endowed
with factor h, hence (w hj v hj - -.JL,;
~ whjv hj ) is large, then this combination
Y
.
J
favors the production and export of good i.
A low R2 has always been a characteristic of this type of cross-section study.
We know besides, that there are determinants of trade which are not captured by the equation. Therefore, our expectations regarding the statistical
performance of the equation should be quite modest to start with. As for
the test of the factor-proportions model, neither the significance of individual
7 As for the variance of the error term, in a cross-commodity regression, one should
consider the problem of heteroskedasticity and hence, use GLB estimators.
48
CHAPTER 4. THEORY-BASED EMPIRICAL IMPLEMENTATION
coefficients nor the equation as a whole tells us a great deal. The test would
come with the "external validation". In a second stage, we should check
whether the coefficients obtained at the first estimation stage have the same
signs as the relative factor endowments.
The term
..If;Y
(whjfjhj -
Lwhjfjhj)
.
= g{,
is constant across industries in a
3
cross-industry regression. Hence, in a first-stage estimation, one may regress
on ()?T in a cross-industry framework. Then in a second stage, the
first-stage estimated coefficients may be externally validated by actual observations of factor endowments. Now we turn to the issue of the second-stage
t{vA
"external validation".
External Validation
In the first step we may estimate the following equation:
t jvA
t
=
830.
+ "L...J 8hj ()hT + vi
t
(4.28)
t
h
where the m
given by:
* 1 vector
of the estimated partial regression coefficient 8j is
11 = (eTMeT,)-1eTtjvA
or, given the HOV equation:
(4.29)
where M is a n*n idempotent matrix, M = I -1(1'1)-1 1" with 1 being an
* 1 vector of ones. Denote by ()hT' and ()kT the 1 * n row vector of matrix
e T and the n * 1 column vector of matrix T " respectively, where hand k
are two factors. Then, based on equation (4.29), we obtain for factor h:
n
e
m
"hT,-kT~kj
L..t()
()
8
h·
=g3
(4.30)
k=1
where
OkT
= ()kT _
OkT.
If we multiply (4.30) by
ghj
L
()hT'71 T tJk j ;:::
0
ghj,
we obtain:
(4.31)
k
We sum up condition (4.31) across all factors h using the notation ii j
f
=
«()hTI ghi)
m
' where ii j is a 1 * n row vector of weighted averages of factor
intensities for each industry i, across all factors h within country j, with the
weights being the relative income of the factors, ghj. Finally, we get:
h-l
(4.32)
4.2. INDIRECT TESTS
49
where m is the number of factors.
We have got now a theory-based second-stage condition that one may call an
"external validation" condition. Condition (4.32) is a restriction across all
factors k and industries for a particular country, that should hold in a posttrade equilibrium. According to condition (4.32), the first-stage estimated
coefficients
8{ should be "externally validated" by actual observations of ghj8.
Using equation (4.30) and summing it up across all countries, we may get a
second restriction that should hold across all factors and countries 9 :
L e hT'7/T '6 kj
L
k,j
ehT1{jkT
Lt
k
o
or
(4.33)
o
j
j
Condition (4.33) is a restriction across all factors and countries that should
hold in a post-trade equilibrium. When checked empirically, it might be more
restrictive than condition (4.32). As there is a limited number of countries
in the sample, it may happen that condition
L ,}-i =
0 does not hold.
j
Balassa (1979, 1986) and Balassa and Bauwens (1988) propose an "external validation" step, by regressing the coefficients obtained in the first crossindustry OLS estimation on the relative abundance factors, in a cross-country
framework, using a GLS estimation method. Therefore, the estimated coefficients obtained in the first cross-industry estimation step for each country
are externally validated by actual observations on factor endowments in a
cross-country framework. Notice that the theory does not predict a relationship between the first-stage estimation coefficients and the relative factor
endowments in an inter-country framework, as proposed by them. However,
given equation (4.29), we may write:
m
,hj
8
' " hk k'
= ~b
g
J
(4.34)
k=l
where bhk is an element of the m*m matrix (eTMeT1)-1. Hence, in a
h'
second-step estimation, each first-step OLS partial estimation coefficient '6 J
may be explained by a combination of all factor endowment earnings gkj in a
cross-country framework. In contrast, Balassa (1979, 1986) and Balassa and
Bauwens (1988) explained each first-step OLS partial estimation coefficient
,~
8
by each factor's endowment iJ
h
J
in a cross-country framework.
is captured by the term a j .
9The result is based on the observation that
8 g hj
L ghj = 0,
j
50
CHAPTER 4. THEORY-BASED EMPIRICAL IMPLEMENTATION
The ideal situation would be to have a complete regression model that combines, in a rigorous way, the factor proportions theory with other determinants of trade, such as scale economies and product differentiation. Then,
the empirical analysis might suggest, for example, that the more complete
model does nest the one suggested by the factor proportions theory, as a special case. Based on equation (4.28) and the results in Section 3, one might
give an explanation of the countries' patterns of trade, when allowing for
increasing returns to scale and product differentiation. AB was already discussed in Section 3.2, the independent variables, hence the factor cost shares,
are modified according to equations (3.8) and (3.21). Therefore, there are
no additional explanatory variables, but rather new, interactive ones. In the
case where the increasing returns to scale are internal to the firms, separate equations for the exports and imports of differentiated products may be
estimated.
Appendix
The possibility of internationally mobile capital can now be included in the
ranking propositions. This appendix states the rank Propositions 1 and 2
for the model with internationally mobile capital. Equations (4.7) and (4.8)
written for capital become:
tj = wk(k - t k ) - s I)w ki ki - wkitkij
i
and:
tj
_
wk(k _ t k )
l]wki Ki _ wkitki/ s - l]wki Ki _ wkitkij / s - 1
i
i
Propositions 1 and 2 are modified in the following way. Proposition 1, stated
in value terms, becomes:
Proposition 1
If:
wk(k - t k )
< Wl.iJl
l]wkiKi - wkitki/s > 'Lw1jvl)S
j
then:
j
tk
<
'L[wkj K/- wkitkij / S >
i
where I is an input factor other than capital.
The second proposition becomes:
tl
'L Jivlj / S
j
51
4.2. INDIRECT TESTS
Proposition 2
If:
wkg(kg-tkg)
g<
wkiki_tki
i
L:[wkj Kj - wkitkjj Is> L:[wkj Kj _ wkitkjj Is
j
then:
t kg
,
Isg
L:[w kj Kj - wkitkjj
j
for any two countries i and g.
j
<
>
tk,i
lsi
kj
L:[w Kj - wkitkjj
j
Chapter 5
Conclusions
Based on the HOV model in its value version, the first part of this study
developed theoretical models for explaining a country's pattern of trade in a
multi-factor, multi-good, multi-country framework. Contrasting with previous studies, these models allow for cross-country differences in technology and
factor prices, and for departures from some of the assumptions of the original
HO theory, such as increasing returns and product differentiation or internationally mobile capital. They also allow for intermediate production, while
preserving most of the strong assumptions of the HO theory, such as internationally immobile input factors (other than capital), identical and homothetic
preferences in consumption, free trade, no transportation costs, and factormarket and world-commodity clearing. The presence of economies of scale
and product differentiation, and internationally mobile capital renders the
assumptions of the models slightly more realistic, while the standard model
is more general. The presence of product differentiation and economies of
scale internal to the firm allows us to write separate factor content equations
for exports and imports of the differentiated products.
Based on these theoretical models, we addressed the issue of properly linking the theory to empirical analysis. The hypotheses which allow for direct
and indirect tests of the HOV theory were reformulated. We also proposed a
theory-based cross-industry regression estimation equation of the HOV equations, which may be modified to allow for imperfectly competitive commodity
markets. We showed that the economies of scale and product differentiation
variables enter the explanatory part of the regression in an interactive term
together with factor cost shares, rather than as additional explanatory variables. A second "external validation" step, theory-based, is suggested.
Part II
Evidence
Chapter 6
Introduction
"Don't treat the theory too casually ( ... J. Work hard to make a
clear and close link between the theory and data" (Edward Leamer
and James Levinsohn, 1995)
Based on the theoretical models developed in Sections 2 and 3, and the tests
and estimation approach proposed in Section 4, this part reports the results
of an empirical study of the patterns of international trade for a sample of
46 developed and developing countries in 1978 and 1989, in a cross-industry
framework 1 .
In carrying out the empirical analysis, one should pay attention to the assumptions of the theoretical model on which it is based. When using the
quantity version of the HOV model, a crucial assumption is that the countries in the sample have factor endowments which are not too dissimilar. The
likeness of factor endowments is necessary for achieving the implicit assumption of factor price equalization. This assumption implies that technologies
(unit factor requirements) are similar across countries. Many empirical studies use US data as a basis for computing unit factor requirements, then taken
to be identical for all the countries in the sample. When using a value version of the HOV model, as described in Section 2.2, both factor prices and
unit factor requirements differ across countries. Hence, the sample does not
have to be restricted to countries similar in factor prices and technologies.
However, the price paid for conforming to the underlying assumptions of the
lThe choice of the countries was dictated by the availability of trade data. These
countries actually account for more than 90% of world manufactures exports in 1989. The
countries used in the study are listed in Appendix A. The choice of the years 1978 and 1989
is determined by the availability of published trade data at the three-digit of the Standard
International Trade Classification (SITC) Revision 2, for both years. 1978 is the earliest
year for which trade data are reported according to Revision 2 of the SITC, while data for
the years before 1978 are reported according to SITC Revised.
58
CHAPTER 6. INTRODUCTION
theory is a restricted list of input factors, for which data on both endowments
and prices are available. Empirical implementations of the HOV equation call
for independent measures of both the right-hand (that is, trade and factor
intensities) and left-hand (factor endowment earnings) terms ofthe equation.
By contrast, when using a quantity version of the HOV model, data on the
factor incomes are not required, hence the analysis is not restricted in terms
of the number of factors.
The results of this empirical study provide some support for the value version of the HOV model, especially in the case of developing countries. First,
simple and mUltiple correlations between net exports and factor intensities
show that developing countries have their trade negatively (positively) correlated with high-skilled (low-skilled) labor, while the pattern observed for
the developed countries is the opposite. The correlations are usually stronger
for the developing countries. A second important result is that there is no
factor intensity reversal across countries, when defining factor intensities as
factor cost shares. In contrast, previous studies have reported the existence
of factor intensity reversal, when defining factor intensities by unit factor
requirements. Third, we find that the results are sensitive to the way we
define and compute some of the variables. Fourth, when checking a ranking proposition, correctly derived from the value version of the HOV model,
we find that the developing countries are revealed (both by their trade and
by their factor endowments) to be relatively better endowed with low-skilled
than with high-skilled labor, while the opposite is true for the developed
countries. All the countries for which the proposition holds are revealed to
be better endowed with either high- or low-skilled labor than capital. Fifth,
we find that we cannot reject the HOV model, developed in a perfect competition framework, in favor of a model allowing for economies of scale and
product differentiation.
This part is organized as follows. Section 7 offers an extensive discussion of
previous empirical studies based on the HO theory, with special importance
attached to the various procedures adopted. Section 8 proceeds with the
empirical analysis. Turning back to the theoretical considerations of earlier
sections we set the stage for the empirical investigation which includes sign
and rank order propositions, as well as simple correlations and multiple regressions. The estimation equations based on different specifications of the
theoretical models as well as the empirical methods used and the tests undertaken are described. Section 8.2.1 presents the data and variables used in
the empirical analysis. The problems associated with the quality of the data
are discussed. The data set does not cover as many factors as the famous
study by Leamer (1980), but it is much more detailed in terms of commodity
coverage. Moreover, it contributes additional types of information to the picture: factor price differences, scale of economies, industry markups. Section
8.3 discusses the empirical results. First, we examine some results based on
direct and indirect tests of the HOV equation (simple correlations and rank-
CHAPTER 6. INTRODUCTION
59
ing propositions). Second, we turn to the issue of theory-based regression
analysis. A two-step procedure is employed. In a first step, we report the
results of estimating a net export performance equation for each country in
the sample in 1989 and 1978 based on a cross-industry framework. This gives
rise to estimates of the countries' relative factor endowments income. If the
model is correct, these estimates should be validated by actual observations
on factor endowments, and this is subject to a second step of the regression
analysis.
The assumption of scale economies and product differentiation allows the
equations for exports and imports to be estimated separately. Section 9
contains concluding remarks.
Chapter 7
Literature Overview
This section reviews some of the typical studies based on the HO theory.
Some of the most important theoretical contributions are mentioned and the
results of several empirical studies are discussed, with emphasis on the crossindustry studies.
Maskus (1985), Bowen, Leamer and Sveikauskas (1987), and Brecher and
Choudhri (1988) tested the factor content version of the HO theory, using
independent measures of trade, factor-intensities, and factor endowments.
They found that the HO theorem departs significantly from its exact quantitative predictions. There is little empirical support for an exact linear
relationship between trade flows and factor supplies. One explanation may
be found in the fact that the empirical studies are usually based on the quantity version of the HOV theory, hence on the unrealistic assumption of factor
price equalization across countries. However, it seems to be uncontroversial
that factor endowments exert a positive and linear influence on the factor
content of trade flows, even though they are certainly not the only important
explanation of commodity trade patterns.
There are two important groups of empirical studies: factor content and
commodity studies. The first group tests propositions derived from the HOV
model. The second group focuses on the commodity composition of trade,
hence trying to explain the pattern of trade either for a particular country
(country studies) or for a specific industry (commodity studies). The studies
belonging to the first class perform cross-commodity regressions for a particular country, by regressing the industry trade balances on factor input
intensities, and the country's abundant factors are implicitly deduced. The
studies in the second class perform cross-country regressions, by regressing
trade balances for a particular industry on countries' factor endowments, and
the industry's factor intensities are implicitly deduced. Usually, these studies use only two, instead of three, elements of trade implied by the theory
62
CHAPTER 7. LITERATURE OVERVIEW
(net export flows, factor input intensities and factor endowments). Prior to
Bowen, Leamer and Sveikauskas (1987), only data on trade and endowments
were used in the commodity studies, factor intensities being implicitly deduced. Balassa and Bauwens (1988) were among the first to use the triad.
Recently, the cross-industry approach of determining the countries' abundant
factors was heavily criticized as not being properly linked to theory. Bowen
and Leamer (1981) and Anderson (1981) prove that the results of such studies are correct only in the case of two input factors or when the factors are
specific to each industry. Bowen and Sveikauskas (1992) examine the importance of these qualifications by comparing regression-derived estimates of
factor abundance with both revealed (by the factor content of trade) and
actual factor abundance (relative factor endowments) for 35 countries and
12 resources. They offer a theoretical explanation of the importance of trade
imbalances to the reliability of the regression estimates and propose and implement a theoretically consistent trade imbalance correction. Their results
show that, despite the validity of theoretical criticism, the interaction between net trade and factor intensities in cross-commodity studies is useful
for inferring the factor abundance.
7.1
Factor Content Studies
Most empirical studies use data on the US for different years, with different
specifications of variables. The most famous factor content study is by Leontief (1953) 1. He compared the capital per man embodied in $1 million worth
of imports with the capital per man embodied in $1 million worth of exports
and concluded that the US was in 1947 a net exporter of labor services. His
results doubts about the adequacy of the HO theorem and provoked many
controversial discussions with regard to the proper empirical implementation
of the factor proportions theory. In response, it was suggested that the US
trade be better explained in terms of factors other than labor and capital.
Leamer (1980) demonstrated that Leontief's comparison does not reveal the
relative abundance of capital and labor in a world with more than two factors,
and that there would be no paradox if the computations were conceptually
correct.
Kohler (1991) studies the arbitrariness of empirical tests of rank order and
sign propositions derived from the HOV model, in its factor content version.
He shows that, when using different rank and sign propositions derived from
the HO model, there are conditions under which a data set will support one
hypothesis, while rejecting another. Based on the data set used by Bowen,
Leamer and Sveikauskas (1987), he shows that the results of such rank and
sign tests are not robust.
1 His study cannot be considered as a test of the HO theorem, as he does not use data
on factor endowments.
7.1. FACTOR CONTENT STUDIES
63
Brecher and Choudhri (1982a) prove that the factor content approach derived
from the HO theorem is valid in the absence of factor price equalization, in
the framework of a two-country, two-factor, and multi-commodity world. The
factor content version of the HO theorem, in the presence of internationally
equal factor prices, predicts that the bundle of goods exported by the capitalabundant country uses more capital and less labor than that one exported
by the labor-intensive country. Without factor price equalization, every commodity exported by the capital-abundant country has a larger capital-labor
ratio than any good exported by the labor-abundant country. The factor
content version remains valid in the presence of trade impediments, intermediate goods or additional countries, unless trade impediments are combined
with either of the other two.
For a two-factor (labor and capital) model, Leamer (1980) shows that if a
capital-abundant country has both the labor and capital content of its net
exports positive, it does not need to have its exports more capital-intensive
than its imports. It follows that a necessary and sufficient condition for
proving the capital abundance of such a country, relative to labor, is:
where Kt. K c, L t , and Lc refer to the net exports and consumption of capital and labor, respectively 2. Leamer finds this explanation in accord with
Leontief's data on the US for 1947. Based on Leamer (1980), Brecher and
Choudhri (1982b) provide another testable condition:
Lt
> 0 iff L,/:/Lw > Lc/L
They conclude that the Leontief Paradox is present in the data for the US,
hence the US is labor abundant, when compared to an average of all resources. However, two critiques of their approach may be formulated: first,
they consider labor as a homogeneous factor, and this may provide an explanation for their findings; second, they develop a testable proposition based
on the quantity version of the HOV model which does not allow factor prices
to differ internationally. Section 4.2.1 of this study proposes testable propositions based on a value version of the HOV model, which are derived in the
absence of factor price equalization, and which may easily be modified to
allow for the presence of economies of scale and product differentiation, and
internationally mobile capital.
Maskus (1985) provides an empirical test of the HOV theorem, using US
data for 1958 and 1972 on trade, factor intensities and factor endowments.
2To derive the condition, we must first write the quantity version of the HOV equation
for capital and labor: Kt = K - sKw and Lt = L - sLw, where K and L are the
country's endowments of capital and labor, the superscript w denotes the world, and sis
the country's ratio of domestic absorption to world income. Using the definition for the
country's capital-abundance, K/K w > L/L w , and using Kc = K - Kt and Lc = L - Lt,
we obtain the above result.
CHAPTER 7. LITERATURE OVERVIEW
64
He performs his tests based on the HOV equation in its quantity version
written as:
(7.1)
where Fx and Fm are the total (direct plus indirect) factor contents of exports
and imports, F and F W are the factor endowments of the US and the world,
respectively, and C and CW are aggregate consumption in the US and the
world, respectively, hence their ratio is the US share in world consumption.
Maskus computes the rankings by the factor abundance according to the
criteria developed by Leamer (1980). The factors considered are the number
of engineers and scientists, production labor, other labor, physical and human
capital. In both years, engineers and scientists are revealed to be the most
abundant. He then tests three hypotheses, namely a weak HOV hypothesis,
a rank hypothesis, and a strong prediction. The first prediction refers to the
test proposed by Brecher and Choudhri (1982b), based on equation (7.1):
Fx - Fm
> 0 iff C / F < C W / F W
The second prediction states that, if the HOV model holds, the revealed endowment rankings must reproduce the actual endowment rankings computed
from independent data. This is stronger than the first prediction, because
it calls for an ordering across factors. The third prediction, derived from
equation (7.1), is:
CW / FW
= C/F/[(l- (Fx -
Fm)/F]
according to which, positive (negative) US net exports of a factor imply a
larger (smaller) world expenditure per unit of factor endowment. Based on
the empirical tests derived from the above hypotheses, Maskus shows that
US data diverge from their values, as predicted by the HOV theory, and he
concludes that the HOV theorem is inconsistent with available data on factor
endowments, factor intensities and trade, at least for the US.
Clague (1991) applies a different approach for predicting differences in the relative costs for producing different manufactured goods, using data on factor
prices (wages of skilled and less-skilled workers, and the prices of machinery
and buildings) in five developing countries from Asia and seven developed
countries. Then, using the predicted relative costs to explain the trade pattern between the two country groups, he obtains an R2 of 51%, better than
many other studies. After allowing for economies of scale and for differences
in the relative efficiency of different manufacturing sectors (such as R&D intensity, total factor productivity in the developed countries, factory size, and
some input-output measures of the degree to which the industry interacts
with the rest of the economy), R2 becomes even larger.
Brecher and Choudhri (1993) propose feasible empirical tests of the supplyside assumptions of the HOV model with factor price differences across countries, in a multi-factor, multi-good and multi-country framework. They check
7.1. FACTOR CONTENT STUDIES
65
whether or not the HOV assumptions referring to the production side (i. internationally identical production functions, linearly homogeneous and quasiconcave, ii. firms minimizing costs, iii. perfectly competitive markets, and iv.
freely mobile factors within each country) are an adequate picture of the real
world. The basic testable implication is that unit costs would not be lower
if foreign instead of home factor requirements were used to produce a good
at home prices, given unequal factor prices across countries. Based on this
hypothesis, Brecher and Choudhri develop revised tests easily implemented
empirically, for different situations (such as measurement errors in factor and
good prices, imperfect competition, or immobile factors between industries
in the short run). They apply these tests to data for the US and Canada,
using a sample of 33 industries and 9 primary factors, excluding natural resources. The empirical evidence supports the HOV production-side model,
after modifications which allow for factor-price differences across industries,
and are robust, especially in the case where the differences occur in response
to imperfect factor mobility.
Maskus and Ramazani (1993) carry out a test of the HOV multi-factor content theorem of international trade for Korea, for 1970 and 1980, by comparing the relative factor endowment rankings with endowment rankings revealed
by trade and factor intensities. Their results suggest that the revealed factor
abundance deviates significantly from the actual factor supply.
Maskus, Sveikauskas and Webster (1994) investigate the total (direct plus
indirect) factor intensity of the US and UK net exports for a large number of
input factors, among them labor either at a disaggregated level, including 74
occupational categories, or at an aggregated level, including 7 occupational
categories. Their paper is focused on an examination of the hypothesis that
specialization in trade according to differentiated labor has two dimensions:
first there is specialization according to broad skill levels, and secondly there
is specialization within a broad category of labor as well as between a certain
category and other types of labor. In this context they compute the skill
content of both the US and UK trade with different partners, as well as
for their bilateral net exports. Following Bowen and Leamer (1981), their
empirical analysis is based on the test:
for proving the relative abundance of factor 1 in comparison with factor 2.
F x , Fm and Fc are the factor requirements of exports, imports, and consumption, respectively. The results are reported, both in terms of computed values
of net export requirements relative to consumption, and in the form of rankings. Maskus, Sveikauskas and Webster show that the US and the UK have a
similar pattern of net exports according to factors: both are strongly intensive in physical capital in trade with developing countries and specialized in
higher skill levels in trade with other partners. While the US has a pattern
of trade consistent both with factor and detailed occupation across different
66
CHAPTER 7. LITERATURE OVERVIEW
partners, the UK's pattern differs for trade with the Ee on the one hand, and
the US and less developed countries, on the other hand. The results suggest
that, in addition to the specialization of net exports according to broad skill
levels, there is a second layer of specialization in different skills at the same
level of education or training. Therefore, not only the endowment of skilled
labor is important in shaping the trade pattern of the UK and the US, but
also its composition. The computations are based on data for 1989 on each
country's input-output tables, factor-input coefficients, and consumption and
net exports for each commodity. The rank correlation between the estimates
of the factor content of their bilateral trade is negative and statistically significant at the 5% level of confidence, hence they conclude that international
differences in technologies can affect factor content calculations, but not necessarily invalidate them. Their conclusion is not surprising, given the very
high probability that the US and the UK lie in the same diversification cone,
thus having similar technologies and product mixes.
An important issue raised in the literature is the question of whether or
not trade affects the distribution of income and inequality. Evidence in this
respect is provided by Leamer (1992b) and Wood (1994b, 1995), among others. Leamer shows that, in a free trade agreement with the US, Mexico has
an incentive to concentrate production in the sectors most protected from
third-country competition in the US, and to export those goods to the US.
Hence, the US is confronted with the problem of the continued worsening
of the situation of its low-skilled workers. Wood remarks that the reduction
of trade barriers over the last decades has shifted the developed countries
from "manufacturing autarky", where they produced both skill- and laborintensive goods, to specialization in production of skill-intensive products, in
the presence of increasing labor-intensive imports from developing countries.
He provides evidence that, in the countries where import penetration was
prevalent, the unskilled workers did worse.
Wood (1995) provides evidence suggesting that trade is the main cause of the
deteriorating situation of the unskilled workers in the developed countries,
and that these problems are mainly caused by technology. He shows that
the methods used in empirical studies underestimate the effect of trade on
labor markets and proposes a modified approach that implies a considerably
stronger impact. He finds a negative cross-country relationship between the
increase in import penetration and the change in manufacturing employment
share in the OECD countries. By computing the factor content of trade, one
may estimate the effects of trade on labor markets. The difference between
the factor (e.g., unskilled labor or skilled labor) content of exports and imports is considered in measuring the effect of trade on the demand for that
particular factor. As noticed by Wood (1995), the imports from developing countries are "non-competing" with domestic products, hence the usual
factor content approach underestimates their unskilled labor content 3 . In
3The underestimation is caused by the implicit assumption of homogeneous goods
7.2. OVERVIEW OF CROSS-INDUSTRY STUDIES
67
addition, he mentions, among other sources of understatement, the contribution of trade to technical progress, labeled "defensive innovation", which
finds empirical support in the faster total factor productivity growth in lowskill, relative to high-skill, manufacturing industries. The evidence also shows
that the ratio of skilled to unskilled workers increased within most sectors,
despite the rise in their relative wage, suggesting that technical progress may
be biased against unskilled workers. In contrast, Leamer (1994, 1995) argues that technical progress is sectorally rather than factorally biased. The
main conclusions of Wood's (1995) paper are: first, unskilled workers in
developed countries are not and will not be hurt by trade with developing
countries abundant in low-skilled labor, as these countries produce goods that
are no longer manufactured in the developed countries. Second, all workers
from developed countries benefit from lower world prices for these products.
Third, international competition in middle-skill-intensive products gets more
intense, as new developing countries change their labor endowment mixture
in favor of higher-skilled workers, and as Eastern European countries participate in international competition. The Economist (November, 1995) states
that many debates about unemployment and trade are based on economic
fallacies. It is argued that trade with low-wage countries will change the
job mix, to the disadvantage of low-skilled workers in the developed countries. But, as trade expands, so does the demand for skilled-intensive goods
produced in developed countries, hence creating new jobs.
7.2
Overview of Cross-Industry Studies
The studies in this class apply measures of trade and factor intensities in a
cross-industry framework, and infer the factor abundance vectors from these.
If the estimated coefficient of a factor is positive, the country is implied to be
abundant in that resource. Anderson (1981) and Bowen and Leamer (1981)
show that this approach is not correct in a multi-factor world. This section
reports some of the most important contributions to cross-industry studies.
Generally, different authors obtained controversial results. This might be
explained, to some extent, by their lack of theoretical foundations. Empirical problems related to this type of study are also mentioned. There is no
agreement on the precise form of the estimation equation, the definition of
variables (dependent and independent), the estimation procedure (aLB or
GLB, applied to bilateral or multilateral trade), etc.
(goods in the same statistical category produced in different countries are of the same
type, hence of the same skill-intensity), and results from using domestic labor coefficients
which refer to the production of different and more skill-intensive goods in developed countries.
68
7.2.1
CHAPTER 7. LITERATURE OVERVIEW
Problems in the Cross-Industry Empirical Studies
Scaling
Given that industries differ in their importance in the world markets, the
dependent variable in a cross-industry regression study should be scaled in
order to account for the world market size. The question is whether one
should seale the whole equation, or the dependent variable only. The answer
depends on the choice of explanatory variables: when factor intensities are
measured in absolute terms, then it is appropriate to scale the entire equation;
when factor intensities are defined as factor shares or factor cost shares,
then scaling the dependent variable is the proper modification. Deardorff
(1984) proposes a measure of the size of the world market for scaling the
dependent variable, other than industry shipment, which was commonly used
before. He notices that, when scaling net exports by the industry shipments
of the exporting country, this reduces the apparent trade flow exactly in the
industries with an important comparative advantage.
Bowen (1986) discusses the issue of scaling the net trade variable in order
to allow for differences in the importance of countries and commodities in
the world markets in the framework of international comparisons. He provides a list of variables for scaling net exports, according to the assumptions
about preferences in consumption and the type of analysis (cross-country or
cross-industry). He shows that, in the presence of homothetic and identical preferences in consumption, for cross-commodity regression studies, the
proper scaling variable would be total world production by industry.
H eteroskedasticity
The scaling problem is related to the issue of heteroskedasticity. In crossindustry regression studies the presence of heteroskedasticity is related to
differences in the industries' sizes, the variance of the error term being likely
related to industry size. If, after adjusting for trade imbalance (see Bowen and
Sveikauskas (1992) for the reasoning in favor of a trade imbalance correction)
heteroskedasticity is still detected to be present, it has to be corrected. One
has to decide about the choice of the scaling variable.
Branson and Monoyios (1977) follow Johnston (1972). They scale the data
by the square root of the variable to which the variance of the error term is
proportional, which is equivalent to using a GLS estimation method. Their
approach to correcting for heteroskedasticity has two steps. First, they detect
the existence of heteroskedasticity using a procedure developed by Goldfeld
and Quandt. Then, following an approach suggested by Glejser and outlined
in Johnston (1972), they determine the proper scaling variable. This is done
by regressing the residuals from the unsealed regression equation on Si' Sf,
and VSi, where Si represents the country's shipments in industry i, and by
choosing the specification that produces the best fit. Applying this procedure,
7.2. OVERVIEW OF CROSS-INDUSTRY STUDIES
69
they divide their regression equation by the square root of industry shipments.
However, as Deardorff (1984) remarks, in dividing the dependent variable by
the industry shipments, the apparent trade flow is reduced exactly in the
industries with an important comparative advantage.
Maskus and Stern (1981) and Niroomand (1991) also use the square root of
shipments by industry to scale the whole equation. Branson (1971) scales
the dependent variable (net exports) by total exports, Balassa (1986) uses
exports plus imports to scale the dependent variable only. Baldwin (1971)
does not scale either the dependent variable or the whole equation. Harkness
(1978) scales his dependent variable, industry net exports, by the final output
in industry. Lee (1986) and Tan (1992) scale the dependent variable (exports)
only.
Estimation Methods
OLB, GLB and binary estimation methods are commonly used. Balassa
(1979) propuses and implements a two-stage OLB estimation procedure. The
estimated coefficients obtained in the first cross-industry estimation step for
each country are then externally validated by being regressed on factor endowments in a cross-country framework.
When data on the independent variables (technology parameters or factor
productivities) are different across countries, Zellner's (1962) BURE (Seemingly Unrelated Regressions Estimation) estimator for simultaneous estimation of equation (1.2) across all the countries in the sample should be used
instead of an OLB approach. However, when the regressors are identical
across countries, Zellner's estimator simplifies to the OLB estimator.
Adding Intercepts
Kohler (1988) notices that, in cross-industry regressions, the country-specific
non-HO determinants may be modelled through intercepts; if commodityspecific non-HO determinants are also considered, in order to avoid heteroskedasticity, GLB estimators should be applied. The non-HO determinants of trade may also be captured in the stochastic part of the equations
by using an error components model.
Bowen and Sveikauskas (1992) prove the theoretical importance of trade imbalances for the reliability of the cross-industry regression estimates and suggest a theoretically consistent trade imbalance correction. They show that
the inclusion of a constant term in a cross-industry estimation equation implies a certain trade imbalance adjustment, and this correction ensures that
the signs of the regression coefficients correspond to the factor abundance.
Hence, in a cross-industry regression, an imbalance correction should be applied to the trade variable, which is the dependent variable.
70
CHAPTER 7. LITERATURE OVERVIEW
Dependent Variable
The correct dependent variable to use, as the appropriate measure of comparative advantage, is net exports. Exports, imports, and the Revealed Comparative Advantage Index (RCAI, as defined by Balassa (1965)) have been
used by different authors.
However, when allowing for scale economies and product differentiation, separate equations may be estimated for exports and imports. Hence, only in
this case, are exports or imports properly used as dependent variables.
Independent Variables
The input factors usually employed in empirical studies are capital (physical
and human) and labor (total or differentiated by skills, occupational category,
or education). The factors enter either with their absolute quantities (e.g.,
number of workers within each industry), or ratios (e.g., capital per worker),
or shares (e.g., factor shares or factor cost shares). The use of factor cost
shares is proposed by Jones (1979) as a solution for the indeterminacy in the
ranking of the factor intensities when more than two factors are considered.
Harkness (1978) and Choudhri (1979) use factor cost shares as regressors in
their empirical studies. Branson and Monoyios (1977), Maskus and Stern
(1981), and Maskus (1985) use absolute factor inputs, scaled to correct for
heteroskedasticity. Balassa (1979, 1986), Baldwin (1971, 1979) and Branson
(1971) use absolute factors per worker.
Labor intensity may be defined by an industry's employment or the share of
labor cost per unit value of gross output. Skill intensity may be measured
either by the average wage or by the number of workers in different skill categories. Wood (1994a) remarks that the measure of factor intensity should be
in agreement with the theoretically postulated relationship between relative
factor prices and relative goods prices. He proposes as a measure of skill
intensity the ratio of the number of high and low-skilled workers within each
industry, because ''the natural way to compare the skill intensity of two goods
is in terms of the skill composition of employment needed for their production
(... J. This is the natural measure for an HO framework, because it ensures
that a greater scarcity of skilled relative to unskilled labor - reflected in a
higher ratio of skilled to unskilled wages - would increase the price of more
skill-intensive goods relative to less skill-intensive goods". In a cross-industry
study this would be equivalent to the average wage per worker. Physical
capital intensity may be measured either by the capital-labor ratio or the
non-wage value added per worker or the non-wage value added per unit value
of gross output. Human capital, as used by Branson and Monoyos (1977) or
Niroomand (1991), is defined by discounting the excess ofthe average wage
in each industry over the median wage earned by a male with 8 years of
education in the US, and mUltiplied by the industry's employment.
Ballance and Forstner (1990), using averages of data for 43 countries in 19701977 and 1978-1985, find that there is a complementarity between skill in-
7.2. OVERVIEW OF CROSS-INDUSTRY STUDIES
71
tensity and capital intensity. They measure skill intensity by the industry
average wage and capital intensity by the non-wage value added per worker.
Wood (1994 a,b) reports similar results. However, when measuring the skill
intensity by the ratio of the high- to low-skilled labor cost shares, the correlation is much weaker. When the correct calculations are done using total
(direct plus indirect) factor intensities, the complementarity is larger than
for the direct skill intensity 4. Wood (1994 a,b) argues that, as capital is in
reality internationally mobile, it can not influence a country's comparative
advantage. He proposes the exclusion of capital from the empirical explanations of trade. We also proposed a modification of the HOV model, which
takes into account the international mobility of capital (see Section 3.4).
7.2.2
Cross-Industry Studies
Balassa (1965) introduces the concept of revealed comparative advantage
(RCA), which refers to the relative trade performance of individual countries
in particular products. This concept was the basis for several subsequent papers. He assumes that the commodity pattern of trade indicates differences
in relative costs and in non-price factors between countries. He considers two
measures of RCA, the first one based on the export performance, and the
second one based on the export-import ratio, and proposes a normalization
by dividing a country's share of exports of a given commodity by its share
in total world exports 5 . The first measure is one of those most often used
to reveal comparative advantages. Balassa considers data on relative export
performance to be more appropriate, as the data on imports are influenced
by tariffs or other protective measures, which vary from one country to another. He suggests that the degree of specialization and diversification could
be measured by the standard deviation of the RCA indices (the smaller the
standard deviation, the higher the diversification). Hence, one would expect that large countries have a large degree of diversification, as a result of
economies of scale. His study refers to the trade pattern in manufacturing
for the years 1953-1955 and 1960-1962 in 10 industrial countries, for which
he computes the RCA indices and the corresponding ranks.
Baldwin (1971) runs cross-industry regressions of US trade for 1962 on different determinants of comparative advantage (capital-labor ratio and different
labor skill categories) 6 • In all the cases he finds that physical capital-labor
ratio is related negatively and significantly to US net exports, confirming the
Leontief Pamdox, using a different methodology and more recent data than
4Using the data set described in Section 8.2.1, the correlations are 0.15 and 0.24, respectively.
5 "World" refers to a group of countries to which the analysis is restricted.
6His dependent variable is defined as the difference between exports in $1 million total
exports and imports in $1 million total imports.
72
CHAPTER 7. LITERATURE OVERVIEW
Leontief's. He does not focus directly on human capital, but he finds that
skill and education variables explain net exports well. He also adds unionization, concentration, and scale economies to the explanatory variables for the
US. However, he does not provide any theoretical justification for the choice
of the (additional) regressors.
Branson (1971) tries to explain the US' pattern of trade in 1964. He scales the
dependent variable, net exports, by total exports and regresses it on physical
and human capital per worker, a measure of scale economies, the share of
R&D expenditures in value added, and the shares of professional, scientific
and technical workers in total employment. He finds that US' net exports
are intensive in human capital, rather than in physical capital.
Balassa (1977) computes the values of RCA for 11 industrial countries, for
research-intensive products, and for different years (1953, 1962, and 1971).
He also computes the changes in relative comparative advantage in these
industries over the period. The study provides data on the relative ranking
of research-intensive products in each country and the evolution over time of
these rankings (showing the direction of change in the comparative advantage
in this group of products) 7. He found that the US had increased its relative
advantage in these goods between 1953 and 1971 while losing out on goods
with low research intensity. His results may be at least partially explained
by the existence of multinational companies, and the extent of intra-industry
specialization.
Branson and Monoyios (1977) regress net exports on industry levels of physical capital, human capital and labor. They scale the equation to correct for
heteroskedasticity and find that US net exports for 1963 are best explained by
human capital intensity. The negative and statistically significant coefficient
for capital confirms the Leontief Paradox. However, Branson and Monoyios
exclusively focus on direct instead of total (i.e., direct plus indirect) factor
requirements.
Harkness (1978) was the first to use factor input shares as a measure of factor
intensity. He tried to motivate theoretically the use of a multi-factor crossindustry regression analysis. His study uses 16 input factors for explaining
the net exports (scaled by final output) of the US in 1958. In contrast
with Branson and Monoyios (1977), he obtains positive and highly significant
coefficients for the total (direct plus indirect) physical capital share. However,
as Anderson (1981) and Bowen and Leamer (1981) have shown, for his tests to
be valid, the matrix of factor iriput shares should satisfy some very restrictive
conditions. Their discussion produced doubts as to the usefulness and the
properness of the regression analysis of the HOV theory. Briefly, they show
7Research intensity is defined as the share of research and development (R&D) expenditures in total sales, or the ratio of R&D scientists and engineers to all employees. The
industries where these shares are both larger than 3.5% are taken to be research-intensive.
7.2. OVERVIEW OF CROSS-INDUSTRY STUDIES
that when
regn~sing
73
net trade t on the input factor requirements R, as in:
the elements of a* (the estimates of a) are assumed to have the same sign
as the corresponding elements of the vector of factor content, Rt, hence the
same sign as the elements of the relative factor supply vector, which is not a
rigorous implication of the HOV model 8 . However, Bowen and Sveikauskas
(1992) study the empirical importance of factor complementarities, making a
comparison between the sign of the regression coefficients and the sign of the
revealed factor abundance (as given by the factor content of trade, adjusted
for trade imbalances) and the true factor abundance (as given by the relative
factor supply). The proportion of correct sign matches is used as a measure
of conformity between the signs of estimated coefficients, the revealed and
the true factor abundance. They conclude that, despite valid theoretical
objections, the estimates are generally reliable indicators of revealed factor
abundance.
Balassa (1979) studies the changes in the pattern of comparative advantage
in manufactured goods, as a result of economic development, due to the
accumulation of physical and human capital. The study considers 36 developed and developing countries. For each country, regression equations are
estimated relating their RCA in 184 manufactured product groups to the
relative capital intensity (capital-labor ratio) of each industry, and then the
regression coefficients are correlated with the particular country characteristics in an inter-country framework. He uses the export performance ratio
as a measure of the RCA, this measure being preferred to the export-import
ratio because, especially in the developing countries' case, there are high
import barriers, differing from product to product. After estimating these
equations, the author tests the hypothesis that inter-country differences in
the coefficients can be explained by differences in country characteristics. Estimated coefficients for each country are regressed on variables representing
their physical and human capital endowments in an inter-country setting.
Explanatory variables, representing the level of development, are also used
in the experiment. Balassa concludes that the inter-country differences in
the structure of exports are largely explained by differences in physical and
human capital endowments, and the structure of exports tends to change
with the process of accumulation of capital. In a later paper, Balassa (1986)
simultaneously introduces trade flows, factor intensities, and factor endowments in the framework of a multi-country and multi-product model. By
using a three-factor model (physical and human capital, and labor), with
labor as the numeraire, he shows that the regression coefficients, statistically
8 0 ,0 = (RR,)-l (v-SV W ) for balanced trade. Aw (1983) proves that a sufficient condition
for vector a* to have the same sign as the vector of revealed factor abundance, Rt, is that
(RR')-l be diagonal with strictly positive elements, and this condition holds only if each
industry uses only one input factor.
74
CHAPTER 7. LITERATURE OVERVIEW
significant at the 1% level of confidence, have the expected signs, and that
the trade pattern is affected by foreign direct investment, the concentration
of the export structure, and the extent of trade orientation.
However, in all his papers, Balassa relies on the HO equation in its quantitative version, hence he considers technologies to be internationally identical,
in that factor productivities are identical across countries. He computes the
unit factor requirements (factor productivities) using either US or Japan
data, which may have biased his results. He introduces in his analysis other
possible non-HO determinants of trade patterns, but without offering any
theoretical basis.
Hilton (1981) uses factor input shares as explanatory variables, applying a
binary estimation technique to US manufacturing data for 1972. His dependent variable is the sign of net exports, while the independent variables are
factor shares. He finds that trade, though negatively and insignificantly related to physical capital, is significantly and positively (negatively) related
to human capital
Maskus and Stern (1981) undertake a cross-industry regression analysis over
the period 1958-1976 for the US and find that the negative coefficient on labor
increased both in size and significance over time. They use total (direct plus
indirect) absolute factor inputs, scaled, together with the dependent variable,
by the square root of the industry's shipments. They obtain a negative
coefficient for capital, confirming the Leontief Paradox.
Harkness (1983) provides tests of the factor proportions model on trade patterns among Canada, the US and the rest of the world in 1961. He finds that
the model corresponds to the facts, in that significant fractions of the variance in proportionate net factor-service (commodity) exports are explained
by relative factor endowments (intensities).
Lee (1986) studies changes in the patterns of exports for Korea, Japan and
Taiwan. For each country, he tries to explain the RCAl (as defined by Balassa (1965)) by human and physical capital, and energy intensity. He scales
only the dependent variable, uses human and physical capital-labor ratios,
and exports rather than net exports. He finds that there were important dynamic changes in the comparative advantage of export commodities in these
countries between 1963 and 1987.
Noland (1987) remarks that "middle" countries 9 may exhibit non-monotonic
net export functions across industry factor intensity, thus having different
patterns of comparative advantage across industries of different factor intensities. He uses a model that integrates information on trade, industry factor
intensity and country factor endowments for Taiwan. The estimation function is specified so as to allow net exports to take a non-monotonic form. By
g e .g .,
Nrc
countries.
7.2. OVERVIEW OF CROSS-INDUSTRY STUDIES
75
pooling data for 1965-1980, he finds that Taiwan is scarce in physical capital,
with a comparative disadvantage in capital-intensive goods and in the upper
end of the human capital-intensive product spectrum for the mid-sample year
1973. His results display a non-monotonic form, with Taiwan's comparative
advantage lying in the middle range of products. He suggests, therefore, that
it is unlikely that the NICs will quickly specialize in products of high physical
and human capital intensity. Rather, a more gradual pattern of improvment
is likely to emerge.
Niroomand (1991) employs a multi-factor proportions model to analyze the
bilateral pattern of US trade with different partners and the structural changes
in this respect between 1963 and 1980. To explain the US net exports in
manufacturing industries in a cross-industry regression framework, he uses
as explanatory variables human and physical capital (defined as in Branson
and Monoyios (1977)), labor and scale economies. Scale economies, s, are
estimated according to:
V=aN!
where V is the ratio between value-added per employee in a plant of particular size and the average value-added per worker for all the establishments
in that industry, Ni is the number of employees in establishment i, and a is
a constant. This procedure is developed by Niroomand and Sawyer (1989)
and is based on Hufbauer (1970). He corrects for heteroskedasticity following Branson and Monoyios (1977). All variables have their expected signs
based on previous studies: human capital is an important determinant of the
US comparative advantage, while the scale economies variable is positively
significant in shaping the trade pattern in 1963 only. Niroomand's results
confirm the Leontief Paradox in most of the cases, especially for earlier years.
He finds structural changes between 1963 and 1980 in the US global and bilateral trade with Japan, Canada and the NICs. However, he does not offer
any theoretical explanation for the choice of his regression equation.
Maskus' (1991) study is particularly "data-intensive", being focused on the
practical data problems in the area of models of production and trade, based
on the factor proportions theory. He reports simple correlation results between net exports, scaled by a measure of the world market size 10 , and direct
factor shares (unskilled labor, human capital, physical capital, and materials
and intermediate inputs) for each country. He uses a sample of 28 countries with observations from 1984 for 28 manufacturing industries defined at
the 3-digit level of the ISIC. These simple correlations are mainly taken to
be descriptive indicators of the input basis of international competitiveness,
and are in general weak, except for a few countries. Some countries have a
trade pattern uncorrelated with any factor share, and a few show positive
correlation for unskilled-labor (Korea, the Philippines, Portugal and Spain)
lOFollowing Deardorff (1984), the sum of gross output for 27 countries in the sample is
taken as an approximation of the world market size.
76
CHAPTER 7. LITERATURE OVERVIEW
or human capital (Germany, Japan, Sweden and the US). The countries in
the last group have very similar trade patterns with respect to all the factors. Among the developed countries in the sample, Italy is an exception in
that it has a strong positive correlation with the unskilled-labor and a strong
negative correlation with the human capital. It is important to point out
here the way in which Maskus defines the direct factor shares. The minimum average wage across all industries is taken to be the compensation of
the unskilled workers. The unskilled labor cost share within each industry is
thus defined as the minimum wage times the employment as a proportion in
the value of gross output. The human capital share is defined as the deviation of industry's average wage from the minimum wage across the economy,
times employment and divided by the value of gross output. The share of
capital cost is defined as the proportion of the non-wage value added in the
value of gross output. He implicitly assumes that value added comprises only
payments to labor and capital. Hence, the unskilled-labor and the human
capital cost shares are given by:
where W U is the minimum wage within the economy, and Wi, Li, and xi are
the average wage, employment and the value of gross output in industry i,
respectively. Notice that, when used in a cross-industry analysis (as Maskus
does), as W U is invariant across industries, ()'t captures the differences in the
total labor rather than unskilled-labor requirements in $1 value of output.
However, Maskus' his definition of the human capital share is a good approximation for the real direct high-skilled labor cost share when used in a
cross-industry analysis. Section 8.2.2 of this thesis proposes an improvement
in the definitions of the unskilled- and skilled-labor cost shares to be used in
a cross-industry study.
Lundberg (1992) provides an explanation of the structure and long-run development of Swedish international trade and specialization. He combines
the nro-factor and nro-technology approaches to R&D in order to explain
the patterns of specialization. An index of international competitiveness in
an industry is defined as the ratio of production and consumption in that
industry. Lundberg finds that there are complementary models explaining
specialization and trade patterns. Differences in factor endowments seem to
contribute to the explanation of the trade pattern and specialization according to the principle of comparative advantage. However, Lundberg notices
that a large part of trade is intra-industry trade, for which a preference for
variety in demand, combined with economies of scale, may be important. He
finds that intra-industry trade as a share of gross trade depends both on the
degree of product differentiation within the product group and on relative
costs as determined by relative factor endowments.
7.3. OVERVIEW OF CROSS-COUNTRY STUDIES
77
Tan (1992) uses all three elements of the HO theory (trade, factor endowments and factor intensities) to study Singapore's dynamic comparative advantage in manufacturing in terms of year-to-year change. He uses an interactive model with both factor endowments and factor intensities as explanatory
variables, with the interactive terms capturing the interactions between factor intensities and endowments. In order to study the dynamic comparative
advantage, he uses panel data from cross-section and time series data, while
previous studies merely used comparisons over two different years. However,
a few remarks are in order. First, he uses data on direct factor input requirements only, instead of correct total factor requirements for explaining
net exports, as suggested by Hamilton and Svensson (1983). Second, he uses
economies of scale and technology-gap explanatory variables in his regression equation, but without mentioning any link to theory. However, he finds
these variables to be insignificant in determining the dynamic comparative
advantage.
7.3
Overview of Cross-Country Studies
Even though the focus of the present analysis is on cross-industry rather
than on cross-country studies, a few notable examples of the latter are to
be mentioned. Cross-country regression studies use data on trade and factor
endowments and implicitly infer factor intensities. The most important ones
will be addressed in what follows.
Leamer (1984) provides an extensive empirical study. He offers a broad description of the patterns of trade and factor endowments for 59 countries in
1958 and 1975, as well as a brief critical literature review of earlier attempts
to test the HO theorem.
The following paragraph, a citation from Leamer (1984), is a very good description of the conceptual and practical difficulties related to the empirical
tests of the HO theorem:
"The general proposition that trade depends on resource endowments is not testable. At best it demonstrates that the data
can be organized so that there appears to be a relation between
trade and some function of a set of measured resources. If the list
of resources is "brief" and "sensible", if the functional form is
"plausible", and if the relation is "close", an empirical study will
surprise and amuse. "
Regressing net exports of commodities on resource endowments in a crosscountry framework, he shows that trade is properly represented by a linear
78
CHAPTER 7. LITERATURE OVERVIEW
function of factor endowments. He uses the HOV model:
to regress net exports on relative factor supplies. R is the matrix of input
factor requirements. He considers trade in primary products as well as manufactures. Given that the number of commodities is too large by far to allow
a separate analysis of each of them, in order to get an invertible matrix R, he
aggregates commodities into ten bundles and uses data on eleven resources
(capital, three types of labor, four types of land, coal, minerals, and oil).
Leamer shows that comparative advantage in manufactures is related to the
supply of moderately skilled workers and capital, and is negatively related
to the supply of land. His results indicate that the roles of knowledge l l
and physical capital as sources of comparative advantage in manufacturing
industries are reversed from 1958 to 1975: in 1958 the most skilled-labor
contributed to comparative advantage in all 4 manufactured aggregates, but
in 1975 it contributed only in chemicals, the most skill-intensive aggregate;
physical capital was, in 1978, a source of comparative advantage only in chemicals, and in 1975 it contributed to all 4 manufactured aggregates. Leamer
provides trade dependence profiles (the composition of net exports of the 10
aggregates relative to GNP) and resource abundance profiles (relative abundance of 11 factors, hypothesized to be sources of comparative advantage)
for many countries both for 1958 and for 1975.
Balassa and Bauwens (1988) examine the change in the pattern of trade in
manufacturing industries for a sample of 38 developed and developing countries in 1979. They test the HO theory in a cross-country framework by using
a "stages approach", according to which, a country's trade pattern changes
in a predictable way as it accumulates physical and human capital. They
use a two-stage estimation procedure proposed by Balassa (1979). In the
first estimation step, trade performance is regressed on relative factor intensities, in a cross-industry framework. The estimation coefficients obtained
for each country are then regressed, in a second estimation step, on relative
factor endowments in an inter-country framework. The dependent variable
is net exports, scaled by total trade by industry, and the regressors are total
(physical and human) capital per worker. The results show that differences
in the structure of manufacturing net exports are largely explained by international differences in physical and human capital endowments. Balassa and
Bauwens explained the first-stage estimation residuals in a second estimation
stage by additional explanatory variables for trade policy, the extent of trade
orientation, foreign direct investment, and the concentration of the export
structure. They found that export orientation and foreign direct investment
are statistically significant. Interpreted in a time-series framework, the crosssection results indicate that the accumulation of physical and human capital
11 Leamer
defines knowledge capital as the number of professional and technical workers.
7.3. OVERVIEW OF CROSS-COUNTRY STUDIES
79
determines shifts in the pattern of manufacturing trade, from labor-intensive
to capital-intensive products.
Ballance and Forstner (1990) provide a comprehensive empirical study of
trade and specialization, within the framework of the HO theory. They analyze the changes in the global pattern of production and trade in manufacturing industries over the last two decades, exploring both inter- and
intra-industry trade. As for the pattern of inter-industry trade, they try to
explain the variations in trade patterns among countries by the variations
in factor endowments. They also use a two-stage method. First, for each
industry they regress trade flows on factor endowments across countries and
secondly, they regress the estimated coefficients on factor intensities across
industries. In addition to the traditional explanatory variables, capital and
labor, they examine the importance of economies of scale and market structure in shaping trade patterns. However, they consider a measure of vertical
product differentiation without a clear link to the theory, and their results
are ambiguous, requiring further explanation.
Based on Leamer (1984), Maskus (1991) provides estimations for the relationship between net exports in each industry and endowments across 38
countries, using both an OLS and a WLS estimation procedure. His analysis
suggests that the model explaining trade by factor endowments is sensitive
to the existence of heteroskedasticity and measurement errors. Heteroskedasticity may be induced by differences in countries' sizes, while the presence
of measurement errors in computing factor endowments may be explained
by the existence of different definitions of factors across countries and by
variability in skills across countries even at the same level of education.
Chapter 8
Empirical Analysis
8.1
Introduction
In Section 2.2, we derived the value version of the HOV model, which allows
for different factor productivities and factor returns across countries, while
the technology parameters (}~, the cost shares of factor h in industry i, are
taken to be identical across countries. The HOV equation for a particular
country j is (according to (2.18)):
e T t jv =
wjv j -
si I: wjv j
j
e
where tV is the vector of net exports in value terms, T is the matrix of total
(direct plus indirect) factor cost shares, W is a diagonal matrix of factor
returns, v is the vector of factor endowments, and a superscript j denotes
countries. The above equation predicts that the total factor content of trade
in value terms (eTt jv ) is a linear function of national (Wjv j ) and world
factor endowment income (2:: wj v j ).
j
Given the strong assumptions of the theory, one would not expect the HOV
equation to hold exactly. Hence, one would not expect to observe equality
between the two terms of the HOV equation. Instead, a weaker test of the
HOV equation would require equality for the signs of the right- and lefthand terms of the equation. We follow Bowen, Leamer and Sveikauskas
(1987) in considering a measure of the "exactness" of the HOV equation,
by checking the proportion of matches between the signs of the two terms
for each factor across countries. When allowing for economies of scale and
product differentiation, the left-hand term is changed, according to the results
in Section 3.2. When the assumption of immobile capital across countries is
CHAPTER 8. EMPIRICAL ANALYSIS
82
dropped, the right-hand term of the HOV equation is modified, according to
the results in Section 3.4.
For each country j and factor h, simple correlations between net exports
and the total (direct plus indirect) factor cost shares are computed. A positive correlation for a factor implies that, on average, the country exports
goods that are produced using that factor relatively intensively. A negative
correlation for a factor implies that, on average, the country imports goods
which are produced using that factor relatively intensively. In Section 4.2.2,
an "external validation" step was proposed, where the simple correlations
(3hj are "validated" by actual observations on factor endowment earnings
g~j. According to condition (4.13), for each country and factor, it is checked
h·
·-hT
hj
whether sign((3 Ja(jhTatjV +bJO ) = sign(gb ). The results are reported as
the percentage of matches for each factor.
In Section 4.2.2, we also propose a condition which must hold for each country across all factors if the HOV equation holds. According to condition
~
h·
·-hT
(4.15), 'Lgb ((3 Ja(jhTatjV + bJO )? 0 for each country j. The percentage
h
of countries for which the condition holds is reported.
Another test refers to the ranking propositions formulated in Section 4.2.1.
For each possible pair of factors, the percentage of cases where Proposition
1 holds is reported. In addition, the results are shown in the form of a
ranking of factors within each country for which Proposition 1 holds, both
as predicted by the relative factor endowments and as revealed by the factor
content of trade.
In Section 4.2.3 we try to find a rationale which would allow us to formulate
estimation equations with a direct link to the theoretical models previously
developed. This attempt is motivated both by the huge number of previous
regression studies that lack any theoretical foundation and by the controversial results reported by them. Based on Bowden (1983) and Kohler (1988),
we proposed to translate equation (2.18) into the following cross-industry
regression equation:
t tjv = ~
8hj OhT
+ ,....,,,,
"j
(8.1)
~
t
h
where ti represents net exports in industry i in value terms, h is an input
factor, O?T is the cost share of factor h in one dollar of output in industry i,
and J..l is an error term. Running cross-industry regressions using data on net
exports (as the dependent variable) and factor cost shares (as independent
variables), the relationship between the commodity trade pattern and factor
intensities is estimated for each country.
As Kohler (1988) remarks, a zero expectation of the error term implies an
unspecified cross-commodity restriction on the parameters. If we consider
the existence of country-specific non-HO determinants, this may be modelled
8.1. INTRODUCTION
83
through an intercept in equation (8.1). However, as Bowen and Sveikauskas
(1992) have shown, the inclusion of a constant term implies a specific trade
imbalance correction. Following them and using the results from Section 2.2,
the following first-stage trade estimation equation is proposed:
(8.2)
where xwfv is a vector of world total production for final demand, in value
terms, and
is a constant term which measures the level of net exports when
domestic production is zero. Estimates of xffv /yW can be obtained from
data on the expenditure shares of only one country, given the assumption
of identical and homothetic preferences in consumption. US data on final
demand will be used to measure expenditure shares 1 . The left-hand term,
t jv - bi x;~v = t jvA , is the vector of net exports in value terms, adjusted for
trade imbalance.
8i
Running cross-commodity regressions for each country, we can obtain estimates of 8hj for each country j and factor h. In order to satisfy the fundamental requirement for the empirical tests of the factor proportions theory, equation (8.2) should include each of the three notions of the theory:
net export flows, factor endowments and factor shares (intensities). Balassa
(1979, 1986), and Balassa and Bauwens (1988) propose a second stage regression, where the estimated coefficients are then "externally validated" by
the observed factors endowments in a cross-country regression. In the second estimation stage, following Balassa and Bauwens (1988) and Amemiya
(1978), one would apply a WLS estimation method, in order to give higher
weights to the first-stage estimated coefficients with low standard errors, and
to correct for unequal variance of the disturbances in the second-stage estimation. However, as it is argued in Section 4, a direct sign test may be
applied for each country separately across all factors. We also show that
each first-step estimated coefficient may be explained by combinations of all
factor endowment earnings in a cross-country framework. In contrast, Balassa (1979, 1986), and Balassa and Bauwens (1988) explain each first-step
estimated coefficient by each factor's endowment.
However, once we scale the dependent variable for correcting the heteroskedasticity, we can no longer check the "external validation" condition. This follows from the observation that the HOV equation does not hold when we
use scaled net exports instead of net exports. Therefore, we restrict our
second-step theory-based validation to the case of simple correlations.
Equation (8.2) remains the same when we estimate the countries' trade patterns based on the IRS model developed in Section 3.2. However, e T differs.
In the case of the model with economies of scale and product differentiation,
lThe expenditure shares are normalized to add up to 1.
84
CHAPTER 8. EMPIRICAL ANALYSIS
if we assume that in all industries there is monopolistic competition, we may
write regression equations for both exports and imports:
(8.3)
and
where zi and my represent exports and imports in industry i, in value terms,
and zT and m T are total exports and imports, respectively.
Based on equations (8.2), (8.3) and (8.4), multiple correlations across industries are computed using an OLS estimation method, in order to observe the
net trade, export and import pattern for each country. When the regression analysis is properly linked to the factor proportions theory, the correct
choice of the dependent variable is net trade flow, rather than exports or
imports, which were extensively used in previous empirical studies. However,
when economies of scale and product differentiation are allowed for, separate
equations may be estimated for exports and imports. In this case, the proper
dependent variable is either the net exports, or the flow of exports or imports.
The explanatory variables are either the total factor cost shares (capital, lowand high-skilled labor, or skill intensity 2), or interactions between total factor cost shares and a product differentiation variable (as in the model with
economies of scale internal to the firm and product differentiation). The regression equations are adjusted for the trade imbalance (following Bowen and
Sveikauskas (1992)), tested, and corrected for heteroskedasticity. Following
Branson and Manoyios (1977), the dependent variable (adjusted net exports)
is scaled by world total exports3 . However, there are a few countries in the
sample for which heteroskedasticity is detected (using a White (1980) test)
even after scaling the dependent variable, and it depends on the regressors.
For these countries, an EGLS estimation procedure is used.
There are two specifications of the estimation equation in the case of the
perfect competition model. For the first one, the regressors are the factor cost
shares: low-skilled labor, high-skilled labor, and capital cost shares. For the
second specification, the independent variables are the skill intensity, defined
as the ratio of the high- to low-skilled labor cost shares, and the capital cost
share. The results of an encompassing test are reported in order to check
whether either specification encompasses the other. Pc Give provides an
2 As will be shown in Section 8.2.2, the industry's skill intensity is proportional to the
number of high- to low-skilled workers within the industry or the average industry wage.
3We denote by total world's exports the sum of exports for the countries in the sample.
8.1. INTRODUCTION
85
encompassing test based on Cox (1961). The Cox non-nested hypothesis test
is calculated and a test of either model encompassing the other is reported4 •
We use Pc Give Version 7 and SPSS estimation packages for the regression
analysis. Pc Give provides the results of the OLS estimation (the size of the
estimated coefficients, their standard errors, the t-statistics). In addition, it
provides a test for heteroskedasticity based on White (1980), which involves
an auxiliary regression of the estimated residuals from the OLS estimation on
the original regressors and their squares. The null hypothesis is homoskedasticity, while the alternative is that the variance of the error term depends on
the independent variables and their squares.
After estimating the net trade equations for each country in the sample, a
test for checking the parameter constancy across countries is undertaken.
Based on Hsiao (1986), an analysis of covariance to test for the homogeneity
of cross-industry parameters (coefficients and intercepts) across countries is
carried out. First, we test for overall homogeneity, and the null hypothesis
is that both the intercepts and the coefficients are equal across countries. In
the unrestricted model a separate cross-industry regression for each country
is postulated, while the restricted version is the pooled model (one estimation
equation for all countries). An F-test is set up, based on the residual sum of
squares for the unrestricted and restricted versions, and the null hypothesis is
rejected if the computed F exceeds a critical value. When the null hypothesis
is rejected, we may further test whether non-homogeneity can be attributed to
heterogeneous slopes or heterogeneous intercepts. We test the null hypothesis
of heterogeneous intercepts but homogeneous slopes. Again, an F-test is set
up and the null hypothesis is rejected if the computed F exceeds a critical
value. The test for parameter constancy is done for both specifications of the
perfect competition model.
If data on technology parameters e T were different across countries, Zellner's
(1962) SURE (Seemingly Unrelated Regressions Estimation) estimator for
simultaneous estimation of equation (8.2) for all the countries in the sample
should be used instead of an OLS approach. Given the identical independent
variables across countries in the present analysis, Zellner's estimator simplifies
to the OLS estimator, therefore there is no gain from using it.
An encompassing test for the two rival models, the perfect competition model
and the increasing returns to scale and product differentiation model, is undertaken.
4This tests whether the adjusted likelihoods of two rival models are compatible, and it
is equivalent to checking variance encompassing.
86
CHAPTER 8. EMPIRICAL ANALYSIS
8.2
Description of the Data and Variables
8.2.1
Data
To implement an estimation equation as described by equation (8.2), one
needs data on international trade, national production and factor endowments for many countries. The difficulties encountered cover the availability
of data, the correct methods for constructing the missing data, and the definition of variables, as well as matching the data reported in different classification systems. As always in empirical investigations, we tend to put the
blame on the data for the failure (at least partial) of the model to give a
better explanation of the trade patterns.
The fundamental data referring to trade flows and production for manufacturing industries, as well as for factor endowments in 1978 and 1989, are presented below. There are 3 factors, 46 countries, and 108 (116) manufacturing
industries in 1978 (1989). This new database offers a detailed description of
the construction of variables, including the sources and highlighting the differences to previous ones. To my knowledge, this is the most comprehensive
existing database, since Leamer's (1984).
Physical Capital Endowment
The endowment of physical capital is defined as the net stock of capital at
current market prices, assuming 15 years for the average life of assets, applying a depreciation rate of 13.33%. The data referring to gross domestic
investment, both in real and nominal terms, in domestic currency, are available from the World Tables of Economic and Social Indicators, the World
Bank, different issues. Following Leamer (1984), the capital stock, in current
US dollars, is calculated according to:
k~
= kZp~et,
k~
=[ L
where:
t
j=t-14
(1 - 8)t- j (Ij/pJ)
1is the real capital stock at the end of year t
in terms of year b domestic currency,
et is the exchange rate in time period t, in US dollars per units of domestic
currency,
8 is the rate of depreciation,
Ij is the gross domestic investment CD I in year j expressed in domestic
currency, and
pJ is the implicit CDI deflator at time j, with base year b.
The implicit CDI deflator, pJ, is derived from the United Nations, Yearbook
of National Accounts Statistics data on nominal gross domestic investment
8.2. DESCRIPTION OF THE DATA AND VARIABLES
87
and estimated real gross domestic investment from the World Tables of Economic and Social Indicators, the World Bank, different issues.
The average annual exchange rate data are also taken from the World Tables
of Economic and Social Indicators, the World Bank, different issues. An
alternative computation is based on the investment-based P P P adjustment
for the exchange rates, as reported by Heston and Summers (1991).
Data on gross domestic investment are taken from the United Nations, Yearbook of National Accounts Statistics and from the World Bank, the World
Tables of Economic and Social Indicators.
The real capital stock at the end of 1978 and 1989 is computed for each country in the sample. There are a few countries for which, given the availability
of the data, the real capital stock is computed for years different from 1978
and 1989. This is the case for Kuwait (1988 instead of 1989) and Guatemala,
Kuwait, Malaysia, the Netherlands and New Zealand (1979 instead of 1978).
For 1964, data on gross domestic investment are not available. Instead, data
on the total gross capital formation from the United Nations, Yearbook of
National Accounts Statistics, different issues, were used. For Brazil, Egypt,
Guatemala, Hong Kong, Indonesia, the Ivory Coast, Kenya, Morocco, Pakistan, Peru, Portugal, Tunisia, and the UK only data on the gross fixed
capital formation for 1964 were available. For Yugoslavia, data on the net
fixed capital formation were used.
Labor Endowment
Data on the total labor endowment, defined as the employment in manufacturing industries in the occupational categories 0/1, 2, 3, 4, 5, and 7/8/9, in
1978 and 1988, are taken from the International Labor Office (ILO), Labor
Force Projections, Yearbook of Labor Statistics, and the World Bank. However, instead of data for 1988, data for the following countries are available for
other years: Luxembourg (1987), Colombia (1989), Egypt (1989), Germany
(1987), India (1991), Italy (1989), Morocco (1989), New Zealand (1991), Peru
(1991), Portugal (1987), Singapore (1985), Sweden (1989), Tunisia (1989),
and the UK (1987).
Low- and High-Skilled Labor Endowment
The definition of white-collar (high-skilled) workers refers to the professional,
technical and related workers (divisions 0/1), administrative and managerial
workers (division 2), clerical and related workers (division 3), sales workers
(division 4), and service workers (division 5 of the ISCO). The definition of
blue-collar (low-skilled) workers refers to production and related workers, and
transport equipment operators and laborers (divisions 7/8/9 of the ISCO).
Data for 1988 are taken from the ILO Yearbook of labor Statistics (1989-1994
issues) for 1988, except for a few countries for which data are available for
88
CHAPTER 8. EMPIRICAL ANALYSIS
other years (for details see the discussion below). For 1978, data are taken
from the !LO Yearbook of Labor Statistics (1979-1987 issues).
Data are available for 1985 for Kuwait, for 1987 for Pakistan (1987-1988),
Peru and Portugal, for 1989 for Colombia, Egypt, Germany and Sweden,
for 1990 for Indonesia, and for 1991 for New Zealand. For Israel, data refer
to total employment in the mining, quarrying, and manufacturing activities.
Data for Sweden refer to major divisions 2-4. Data are available for 1984
for Austria, for 1983 for Denmark, for 1979 for Egypt and the Netherlands,
for 1980 for Malaysia, Mexico, Pakistan and Turkey, for 1975 for Tunisia, for
1981 for Australia, Belgium, Greece, Italy, the Philippines, Spain, the UK
and Yugoslavia.
There are a few countries for which, even though data are not available
from ILO, there are data available at the three-digit of the ISIC (International Standard Industrial Classification) for 1988 and 1978, published by
the United Nations, the Industrial Statistics Yearbook. This is the case for
India (1987), Italy (1987), the UK and Yugoslavia (1988), Australia, Brazil,
India and Italy (1978).
For the countries for which neither data from YLO nor from ISIC were available, their high- to low-skilled labor ratio is approximated by the ratio in
the country with the closest minimum wage5 . Hence, for 1988, data for the
Philippines are used for Argentina, data for Austria are used for France, data
for Pakistan are used for Kenya, data for Australia are used for Switzerland,
and data for Peru are used for Thailand. For 1978, data for Belgium are
used for France and data for the Netherlands are used for Switzerland. Thus,
using data on total labor endowments and the proxied ratios of high- to lowskilled labor endowments, we may estimate the low- and high-skilled labor
endowments for these countries.
For Belgium and the UK, there are data available from the OECD, The
Employment Outlook (1994) for the ratio of white- to blue-collar workers
for the whole economy in 1990, while for Brazil similar data are taken from
YLO. Using additional data on the ratio of manufacturing employment to
total employment from the YLO (available for 1988 for Belgium and for 1987
for the UK), an approximation of the ratio of high- to low-skilled workers in
manufacturing activities is obtained. Available ISIC data for Belgium allow
us to check how accurate this approximation is. The ratio computed with
ISIC data is 0.44, as compared to the 0.45 obtained in the first place.
There are no available data on either employment or wages for the Ivory
Coast, Morocco or Tunisia in 1989, nor for Argentina, the Ivory Coast or
5Both the Pearson and Spearman rank correlation coefficients between the minimum
wage and the ratio of high- to low-skilled workers are positive and strongly statistically
significant, when computed for a sub-sample of 37 countries for which data are available in
1988. The Pearson correlation coefficient is 0.716, while the Spearman ranking correlation
coefficient is 0.724, both being statistically significant at least at the 1 % confidence level.
8.2. DESCRIPTION OF THE DATA AND VARIABLES
89
Kenya in 1978.
Human Capital (Skill) Endowment
There are several measures of human capital endowment used in the existing
literature:
a. One measure uses data on educational attainment. Balassa (1979) uses
the Harbison-Myers index, a flow measure of school enrollment, defined as
the secondary school enrollment rate plus five times the university enrollment in the representative age cohorts. Inconvenience is created by the fact
that it only measures the educational attainment of the population currently
enrolled in school, not the stock of education embodied in the whole labor
force.
b. A second measure uses total educational expenditures, embodied in the
working population. Psacharopoulos index of per capita educational capital
is defined as:
PIND
= Y1A1C1 + Y2A2C2 + Y3A3C3,
where:
Y; is the number of years spent in primary (i=l), secondary (i=2), and higher
education (i=3), respectively,
Ai is : '"te nercentage of the work force for which the first (i=l), the second
(i=2), ana ~e third (i=3) level of education was the highest attained,
C i are the expenditure weights, defined as the average annual expenditure
ratios derived by Psacharopoulos (1973) from a heterogeneous 14 countrysample.
The inconvenience of this measure is rooted in the fact that it only measures
formal education, without capturing education from on-the-job training.
c. A third measure, used by Bowen and Leamer (1981), is based on the
0/1 division (professional, technical and related workers) of the International
Standard Classification of Occupations (ISCO); the inconvenience of this
measure derives from the fact that ISCO 0/1, the category that identifies
skilled workers, contains many occupations irrelevant to the production of
tradable goods, while there are other divisions, such as the administrative
and managerial workers (division 2), and clerical and related workers (division 3), which may contain occupations relevant to the production of tradable
goods.
d. A fourth measure, used in the present study, is based on the ratio of
low- and high-skilled, economically active workers (or blue- and white-collar
workers) in manufacturing activities.
90
CHAPT~8.
EMPllUC~AN~~m
International Wages
International wages are defined as earnings per hour (or per day, per week or
per month) in manufacturing activities, in 1978 and 1988, in domestic currency, as reported in the ILO Yearbook of Labor Statistics. However, there
are differences in the definition of earnings across countries. Wages per hour
are then converted into US dollars, using a consumption-based P P P adjustment for exchange rates taken from the Penn World Table as documented
in Summers and Heston (1991). Because the data in the Penn World Table
are mainly for 1988 (except for Brazil (1987), Kuwait (1986) and Singapore
(1985)), wages per hour are for 1988. Earnings per hour data are missing for
some of the countries in the sample and, following Trefier (1993, footnote 9),
we use data for other countries with similar per capita income. For 1988 there
are the cases of Colombia and Guatemala (data for Peru are used), Indonesia (data for the Philippines are used), the Ivory Coast and Morocco (data
for Egypt are used), Malaysia (data for Mexico are used), Italy and Kuwait
(data for Belgium are used), and Tunisia (data for Turkey are used). For
1978, data for Mexico are used for Argentina and Brazil, data for Korea for
Chile, Malaysia and Turkey, data for Egypt for India, Indonesia, Kenya, Morocco, Pakistan, the Philippines, and Thailand, data for Peru for Colombia
and the Ivory Coast, data for Singapore for Hong Kong, data for Switzerland for Kuwait, data for Guatemala for Tunisia, and data for Portugal for
Yugoslavia. The wages per hour are finally transformed into wages per year,
based on the number of working hours published in the YLO. The number of
working hours are reported either per day, or per week, or per month. In the
case of Brazil, the number of working hours per week for Mexico are used to
compute the earnings per hour.
International Minimum Wages
The minimum wage in manufacturing activities within an economy is defined
as the minimum wage across all manufacturing industries, as reported in
YLO or, as secondary sources, the Handbook of Industrial Statistics 1992
(an UNIDO pUblication) and the Industrial Statistics Yearbook (a United
Nations pUblication). The manufacturing industries are defined at the threedigit of the ISIC (as in YLO and the Industrial Statistics Yearbook) or at
the four-digit of the ISIC (as in the Handbook ofIndustrial Statistics 1992).
The same methodology as above is also applied here in order to compute the
minimum wage per year in US dollars.
Trade
Trade data at the three-, four-, and five-digit level of the SITC (Standard
International Trade Classification), for 1978 and 1989 are taken from the
United Nations, the International Trade Statistics Yearbook, vol. I (Trade
by Country) and II (Trade by Commodity), SITC Revision 2,1981 and 1991.
In order to match the US SIC (Standard Industrial Classification), as published by the Executive Office of the President (1987), and the SITC (1975)
8.2. DESCRIPTION OF THE DATA AND VARIABLES
91
(Standard International Trade Classification Revision 2 (1975)), a correspondence between the SIC and the SITC Revision 2 was necessary (see Appendix
B). Because the SIC has been revised during this period, different correspondence tables have been built for 1977 and 1987.
GNP
GNP data for 1978 and 1989 are computed using data on GNP per capita
at current market prices in US dollars and population data from the World
Bank, the World Tables of Economics and Social Indicators. A second set of
computations use data on GNP as reported by Heston and Summers (1991).
Direct Factor Input Requirements
The direct factor share costs are computed using data for the US. Data on
total compensation and employment for each industry are used to compute
the average wage in each industry. Data are taken from the US Department
of Commerce, the Survey of Current Business, different issues (printed data
and diskettes), and the Statistical Abstract of the US 1992. The estimates
from the 1977 and 1987 benchmark input-output US accounts, at the sixdigit, are used as an approximation of the data for 1978 and 1989. The
minimum average wage per worker across all industries is taken to be the
compensation of the low-skilled laborers. In a similar way, the maximum
average wage across industries is taken to be the compensation of the highskilled workers. Given the minimum (w") and maximum (W S ) wages within
the US, and the average wage (Wi) and total employment (Li) within each
industry, the high- and low-skilled employment within each industry, Li and
L't, respectively, are computed according to the following formulas:
U
L. (Wi-W
VI
L.
,
,
U
)
'(ws-w u )
CWS-Wi)
'(ws-w u )
The low-skilled labor cost share within each industry is defined as the minimum wage times the low-skilled employment as a proportion in the value of
gross output. The high-skilled labor cost share within each industry is defined as the maximum wage times the high-skilled employment and divided
by the value of gross output.
The share of capital cost within each industry is defined as the non-wage
value added as a proportion of the value of gross output, assuming that the
value added comprises only payments to labor and capital. The non-wage
value added by industry is from the Survey of Current Business.
Prod uct Differentiation
Data on product differentiation are proxied by the reciprocal of the ratio of
advertising expenditures to output within each industry for the US, as values
are reported in the Input-Output tables provided by the Survey of Current
Business.
92
CHAPTER 8. EMPIRICAL ANALYSIS
Mark-Up
Estimations of the mark-up for the US industries, at the two-digit level of
the SIC, are provided by Morrison (1990).
Input-Output
The input-output data are from different issues of the Survey of Current
Business (printed data and diskettes). The estimates from the 1977 and
1987 benchmark input-output US accounts, at the six-digit, are used as an
approximation of the data for 1978 and 1989. Data refer to the direct and
total requirements (industry-by-commodity) coefficients. The industry-bycommodity total requirements table shows the input requirement coefficients
for the output from each industry that is directly and indirectly required to
deliver a dollar of a commodity to final users.
Many of the 116 industries for 1987 (108 industries for 1977), which represent
the units of observation, are in fact a collection of several detailed sectors from
the 1987 480-order input-output table. In cases where an industry contains
several input-output sectors, overall industry input requirement coefficients
are calculated from the input requirements coefficients for each component
sector by weighting each sector's output for final demand by its proportion
in the industry's output.
Industrial Data
Value-added data, average per employee, share of value-added in output,
share of wages (average) in value added, and average wages per employee, in
US dollars, at the 4-digit of the ISIC, are taken from the Handbook ofIndustrial Statistics 1992, UNIDO. The data are available only for 28 countries in
the sample, in 1989 (1988 or 1987 for some countries), and for 23 countries,
in 1980. Data are available for 1988 for: Australia, Austria, Canada, Chile,
Colombia, Egypt, Finland, Germany, Guatemala, Hong Kong, India, Indonesia, Japan, Korea, Kuwait, Malaysia, the Netherlands, New Zealand, Norway,
Pakistan, Peru, the Philippines, Portugal, Singapore, Spain, Turkey, the UK,
and the US. For 1980, data are available for the same countries, except Chile,
Japan, New Zealand, Pakistan, and the US.
Foreign Direct Investment
Data on net foreign direct investment in current prices, in US dollars, for years
covering the period 1975-1989 are taken from the World Tables of Economic
and Social Indicators 1995, the World Bank, and they are transformed into
net stock data at 1989 current market prices, following a procedure similar
to that used to compute the physical capital endowments. There are no
data available for the whole 15 year period for Luxembourg, Hong Kong,
Switzerland, and Yugoslavia. For Argentina, the net stock of foreign direct
investment is computed for 1991 (given the availability of data for 1977-1991).
8.2. DESCRlPTION OF THE DATA AND VARlABLES
93
School Enrollment
Data on secondary school enrollment, computed as the percentage of enrolled
between the ages 12-17 (usually), are given in the World Tables of Economic
and Social Indicators 1995, by the World Bank. No data are available for
Yugoslavia.
Education Expenditures
Data on total education expenditures as percentages of GNP in 1989 are
published by UNESCO, the Statistical Yearbook.
8.2.2
Variables
The empirical analysis is limited to manufactures, excluding highly resourceintensive industries6 . An important issue is the choice of input factors. The
attention is restricted to three input factors: low- and high-skilled labor, and
capital. This selection is determined by the fact that, when using a value
version of the HOV model, not only data on technology parameters and
factor endowments are needed, but also data on factor returns. While the
technology parameters are considered to be identical across countries (and
we compute them based on US data), the factor returns are internationally
different. Hence, for each factor considered, we need data on its income for all
the countries in the sample. The analysis may be extended to any additional
factor.
One may call the labor input factors unskilled and skilled, but what is of
interest is the presence of differentiated labor. We denote by I; the country
endowment (employment) with high-skilled labor in manufacturing industries
and by Iu that with low-skilled labor. We assume that each low-skilled
worker is paid the minimum wage across manufacturing industries within
the economy, w U , while each high-skilled worker is paid the maximum wage
within the economy, w". We define an average wage for the whole economy7,
W, and an average wage within each industry i, Wi:
WS[;StwU[;U
wSL~+LwuLu
J
;
(8.5)
Li
where Land Li are total labor within the manufacturing industries and
industry i, respectively, and I = I" + Iu by definition. Different ratios
of low- and high-skilled labor endowments result in different average wages
across countries. Different industries require low and high-skilled workers in
different proportions, causing average wages to be different across industries.
Data on w" are not available for all the countries in the sample, hence we use
6This refers to groups 5-8 at the first-digit of the SITe Revision 2, except group 68.
7The average wage refers to the manufacturing industries only.
CHAPTER 8. EMPIRICAL ANALYSIS
94
equations (8.5) to compute it, based on the available data on
and w U , according to:
W
S
LU
= -=L8 ('Iii -
WU
)
Ls, £11., L, 'Iii,
+ 'Iii
The availability of W S data for a sub-sample of 41 countries in 1989 allows us
to check whether the computed W S is a good approximation for the maximum
wage within manufacturing industries. Both the Pearson and the Spearman
correlation coefficients between W S and the computed W S are positive and
statistically significant, at least at the 1% confidence level8 .
Denoting the direct factor cost shares for factor h in industry i by
define:
Otl,
,
=
o~
Of,
we
wULj
XV
wsi:
x~
Ol,
Wji;
Ok,
(nwva)i
xi
xi
07
where oy, Of, O~, and
are, respectively, the direct factor cost shares in 1
dollar of gross output within each industry for low- and high-skilled workers,
labor, and capital, nwva is the non-wage value added, and xi is the value of
gross output in industry i. Therefore, the low-skilled labor cost share within
each industry is defined as the minimum wage times low-skilled employment
as a proportion of the value of gross output. The high-skilled labor cost share
within each industry is defined as the maximum wage times high-skilled employment and divided by the value of gross output. The share of capital cost
within each industry is defined as the non-wage value-added as a proportion
of the value of gross output, assuming that the value added comprises only
payments to labor and capital.
These definitions differ from those previously used (e.g., Maskus (1991»:
oy
wULj
Of
(W:-WU)Li
x~
=
xf
Notice that, when using O~ as defined by Maskus in a cross-industry analysis,
the differences in total labor are captured, rather than in the low-skilled labor
requirements, in 1 dollar's value of output.
Following Wood (1994 a,b), the skill intensity is defined as the ratio between
the number of high- and low-skilled workers within each industrl. Hence,
8The Pearson correlation coefficient is 0.8941, while the Spearman correlation coefficient
is 0.895 for 41 observations.
9For details, see Section 7.2, the part referring to the definition of the independent
variables in cross-industry regression studies.
8.2. DESCRIPTION OF THE DATA AND VARIABLES
95
in a cross-industry study, direct skill intensity may be defined as the ratio
between factor cost shares for high- and low-skilled labor:
Of _
O'!t
w BLf _
w"L':'t
it _ WB(Wi L~
w")
w"(wB-w·)
1.
w"
WS
and this is proportional to both Wi and
more high-skilled composition of labor,
skill intensity
U- will be higher.
fb.
Therefore, if an industry has a
th~s a
higher
fb and a higher Wi, its
'
The direct factor cost shares are computed using US data. There are no
available data on Lf and Li for the US. However, based on equations (8.5)
and using data on w B , w", Wi, and Li for the US, we may first compute 0;
and the ratio
and then the low- and high-skilled labor cost shares and
the skill intensity within each industry:
fb,
Data on direct factor cost shares e are then combined with information from
the input-output tables in order to determine the total (direct plus indirect)
factor cost shares T = 8(1 _ AV)-l 10.
e
Similarly, a country will be relatively skill-abundant, the higher its total
high- to low-skilled labor ratio in comparison to that of the world. Bowen
and Sveikauskas (1992) call the left- and right-hand terms in the quantity version of the HOV equation Revealed and True factor abundance, respectively.
Their Revealed factor abundance is the factor content of trade (net exports)
adjusted for trade imbalance, while True would be the relative factor supply
vector, if the HOV equation were exact. One should notice that, in the case
of the value version of the HOV equation, the right-hand term indicates the
true abundance of factors only when defining the factor endowments in productivity equivalent units (following Trefter (1993)). According to Section 4,
the true relative factor endowment abundance for any factor h and country
j may be defined either as:
lOThe input-output tables report the matrix (I - Av)-l.
96
CHAPTER 8. EMPIRICAL ANALYSIS
or, after adjusting for international differences in factor productivities:
In particular, given the definition of the skill intensity, we may define the
true skill abundance of a country by:
trues kill
=
La
!-u _ 1
Law
Luw
(8.6)
where a superscript w denotes the world. Given that the lower the ratio
of low- to high-skilled workers, the higher w U , the income of the low-skilled
labor, we may define an alternative measure of trues kill :
Both the Pearson and Spearman rank correlation between these two alternative measures are computed, and the correlations turn out to be statistically
significant at the 1% confidence level. By definition, when a country is relatively abundant in high-skilled workers, it has relatively few low skilled
workers, and vice-versa. In this case, the analysis is therefore reduced to two
factors, relative skill and capital. However, based on the above definitions,
we cannot derive any relationship between the skill intensity, (r / (r, and
true skill .
We may also define the true skill abundance in productivity equivalent units
as:
(8.7)
A country is predicted to be relatively abundant (poor) in a factor h if true h
is positive (negative).
8.3
Empirical Results
The present formulation of the HOV model allows for differences in factor
productivities and factor prices across countries, while previous studies are
based. on the quantity version of the HOV model, which implicitly assumes
factor price equalization l l . However, the value version of the HOV model
11 Harkness (1978) is an exception, as he uses factor cost shares to predict the trade
pattern for the US.
8.3. EMPIRICAL RESULTS
97
used in this study assumes also factor price equalization, but in a modified
way. We assume that factor productivities differ across countries and the factor returns are such that they exactly compensate for these differences. The
superiority of the present formulation may be judged by the improvements
brought about by the empirical analysis. This refers to direct tests of the
HOV equation and the propositions derived from the HOV equation, as well
as multiple correlations.
8.3.1
Simple Correlations
As discussed in Section 4.2.2, simple correlations may be computed between
the vector of net exports and total factor cost shares for each country j and
factor h. There are three important issues. First, the sign and size of the
statistically significant simple correlations is of interest. Second, we check
the two "external validation" conditions derived in Section 4.2.2, which have
to hold either for each factor separately or for all the factors within each
country if the HOV equation holds. Third, we may want to check whether
the sign of the simple correlations matches that of the true relative factor
endowments, as defined in Section 8.2.2.
Sign and Size
Simple correlations between ()uT, ()sT, ()kT, ()sT I()UT (skill intensity) and net
exports for each country in 1989 are reported in Table 1. Usually, the signs
for the statistically significant correlations 12 are as expected, namely, positive
for developing and negative for developed countries for low-skilled labor, and
positive for developed and negative for developing countries for high-skilled
labor. The sign of the correlations is preserved when computing the simple
correlations between net exports, adjusted for trade imbalance and total factor cost shares. The best results, in terms of coverage of the countries with
statistically significant correlations, are obtained for the skill intensity (29
countries, 12 developed and 17 developing countries), the poorest for capital
(4 countries). Two-thirds of the countries have their net exports positively
correlated with low-skill intensity, while three quarters of them have their
trade negatively correlated with high-skill intensity 13. There are five times
more countries with significant negative than positive correlations for highskilled labor. Usually, developing countries belong to the first group, while
Japan and Germany are the only countries in the second group. More than
30% of the countries, mainly developed, have no statistically significant correlation for any factor (Australia, Austria, Belgium, Brazil, Canada, Denmark,
Finland, Israel, Kuwait, Mexico, New Zealand, Norway, Switzerland, and the
UK).
12 Statistical significance is given at the 1% confidence level, when using a two-tailed test.
13This refers to countries with statistically significance correlations.
98
CHAPTER 8. EMPIRICAL ANALYSIS
Table 1. Simple Correlations, Net Exports, 1989
87<T
Country
BuT
Similar trade pattern
8 sT
8 sT 1..8uT
Arg
-0.255
-0.219
-0.207
Pak
+
Aus
-0.224
Zea
+
Aua
Fra
Bel
Can
+
Bra
Ind, Tha, Tur
+
Can
Fin
+
-0.226
Chi
Ins
+0.220
+
Col
-0.595
Ind
+0.420
+
-0.187
Den
Mex
+
+
+
-0.422
Egy
Tur
+0.349
+
Swe, Can
Fin
-0.295
Fra
+0.251 Aua
+
-0.266
Ger
+0.180
+0.234 Swi
-0.283
Gre
Tun
+0.308
-0.430
Ken
Gua
+0.290
+
+
-0.210
Tha, Kor, Phi
HK
+0.340 -0.168
+
-0.367
Col, Pak, Tha
Ind
+0.413 -0.263
+
-0.266
-0.398
Mal, Chi
Ins
+0.301
+
Ire
+0.192 +0.195 Fra
Mor, Tun
Isr
+
+
Spa
-0.434
Ita
+0.536
Kuw
Ivo
+
+
-0.207
Jap
+0.192
+
-0.430
Col
Ken
+0.282
+
-0.224
-0.333
Tha, Tur
Kor
+0.452
+
Ivo
Kuw
+
+
-0.316
Ins
Mal
+0.288
+
Gre, Tun
Mex
+
+
Tun
Mor
-0.282
Net
+0.170 +0.4' . Kuw, UK,USA
-0.192
Arg, Aus
Zea
+
Gre
Nor
+
-0.335
Arg,Ind
Pak
+0.296 -0.180
-0.481
-0.180
Tha, Gua, Ind
Per
+0.371
-0.349
HK
Phi
+0.446
+
-0.296
Tha, Chi, Phi
Por
+0.552
+
Mal
Sin
+0.174
+
Spa
-0.352
Ita
+0.330
-0.226
Fin
Swe
+
+
Swi
+0.247 Ger
+
+
-0.397
Col, Ins, Kor
Tha
+0.442 -0.196
+
-0.314
Mor, Gre
Tun
+
Col, Egy, Pak
Tur
+0.368 -0.251
+
USA
UK
+
+
+
UK, Ger
-0.191
USA
+
+
+
-0.292
Yug
Tur, Por
+0.513
+
Note: bold-face numbers indicate statistical significance at the 5% level of confidence, when using a two-tailed test.
Source: International Trade Statistics Yearbook, Survey of Current Business, Statistical Abstract of the US 1992, and own computations.
8.3. EMPIRICAL RESULTS
99
Statistically significant correlations were obtained between both the US direct low- and high-skilled cost shares, on the one hand, and those for all
other countries for which data were available, on the other hand 14 • Therefore, we may consider the signs of the simple correlations between trade and
labor factor cost shares as reliable, at least for those which are statistically
significant.
As for the size of the significant correlations between trade and low-skill intensity, the largest positive values are observed for the developing countries
as well as Greece, Italy, Portugal, and Spain; the largest negative values are
obtained for some of the most developed countries (France, Germany, Japan,
the Netherlands, Sweden, and the US), but they are much smaller in absolute
value than the largest positive correlations. The size of the significant correlations between net exports and high-skill intensity is much smaller, and the
positive correlations are smaller than the negative ones in absolute value.
There might be an explanation for the differences in the respective size of the
correlations for low- and high-skilled labor. US data for computing the direct
factor cost shares e are used, and table 2 presents the correlations (Pearson
and Spearman) between Sus and e for any other country in a sub-sample of
28 countries for which data were available. Notice that, when comparing the
size of the correlations for the direct low- and high-skilled labor cost shares,
the first is larger than the second in most of the cases 15 . For capital, the size
of the correlations is much smaller than for the other two factors.
To summarize, the significant correlations are larger in absolute value for
the developing than for the developed countries. The significant correlations
between trade and low-skilled intensity are larger than those between trade
and high-skilled intensity, and this result may be partially explained by larger
observed correlations between the direct low-skill intensity for the US and
other countries, than for the high-skilled labor. The signs of the significant
correlations usually match our expectations.
14Exceptions are Guatemala and Pakistan for low-skilled labor, and Guatemala, Kuwait,
Peru, and the Philippines for high-skilled labor. Also, for skill intensity, all the rank
correlations, except for Hong Kong, are statistically significant. See Section 8.3.3 below
and Table 2 for details.
15The Pearson correlation computed for low-skilled labor is larger than that of highskilled labor in 71% of the cases, while the rank correlation is bigger in 79% of the cases.
CHAPTER 8. EMPIRICAL ANALYSIS
100
Table 2. Correlations With US Direct Factor Cost Shares, 1988
Country
OU
{P)
os
OBjOU
Ok
{P)
{S)
{S)
{P)
{S)
{P)
{S)
Aus
0.73 0.76 0.75 0.71 0.39 0.80 0.58
0.52
Aua
0.68 0.62 0.57 0.60
0.29
0.43
0.23
0.10
Can
0.76 0.72 0.81 0.79
0.03
0.74 0.56
0.60
0.24
0.33
Chi
0.65 0.66 0.66 0.65 0.50 0.78
0.67
0.23
Col
0.26
0.48 0.61 0.43 0.63
0.16
Egy
0.59 -0.16 -0.12
0.48 0.41 0.48 0.39
0.05
Fin
0.72 0.74 0.70 0.75
0.22
0.78
0.37
0.40
0.83 0.86 0.68
0.73
Ger
0.76 0.76 0.81 0.85
Gua
0.33 0.33
0.23
0.31
-0.02 0.57
0.19
0.18
0.37 0.36 0.39 0.31
0.20
0.14
0.09
-0.07
HK
0.51 0.61 0.50 0.50
0.16
0.62
0.24
0.37
Ind
0.13
0.16
0.66 -0.07 -0.07
Ins
0.55 0.77 0.30
0.72
Jap
0.84 0.81 0.68 0.67 0.55 0.78 0.70
0.32
0.06
Kor
0.71 0.74 0.52 0.57 0.68 0.75
0.09
0.34
0.77 -0.12
0.12
0.44 0.57 0.11
Kuw
0.32
0.45
0.83 0.82 0.61 0.47 0.76 0.72
Mal
0.01
0.35 -0.03 -0.04
Zea
0.29 0.34 0.53 0.56
0.27
0.90 0.45
0.36
0.83 0.81 0.73 0.78
Nor
0.59 0.41
0.45
0.18
0.44 0.47 0.42 0.31
Pak
0.29
0.23
0.62
0.21
0.27
Per
0.64 0.59 0.27
0.37
0.19 0.37
0.04
0.70 0.32
Phi
0.42 0.63
0.28
Por
0.76 0.81 0.57 0.70 0.29 0.86 0.30
0.48
0.62
0.51 0.54 0.47 0.47 0.69 0.72
Sin
Spa
0.44
0.87 0.88 0.75 0.74 0.80 0.88 0.38
Swe
0.20
0.79 0.63
0.57
0.72 0.76 0.51 0.52
0.15
0.74 0.32
0.38
'IUr
0.47 0.61 0.56 0.66
0.79
0.78 0.83 0.70 0.78 0.39 0.83 0.63
UK
Note: bold-face numbers denote statistical significance at the 1% level of
confidence. P and S denote Pearson and Spearman correlation, respectively.
Source: Handbook of Industrial Statistics 1992 and own computations.
When simple correlations are computed between net exports and factor intensities for 1978, the signs of the statistically significant correlations are
usually as expected (see Table 3).
8.3.
EMPIR1CALRESULTS
Table 3. Simple Correlations, Net Exports, 1978
(Ju'l'
(Js'l'
(J1iT
(JsT/(JuT
Country
-0.172
-0.169
Arg
+0.345
Aus
+
-0.174
Aua
+
+
+
Bel
+0.172
+
+
-0.213
-0.241
Bra
+
Can
+0.194
+
+
Chi
+
+
-0.183
Col
-0.230
+0.210
Den
+
Egy
-0.237
+0.212
Fin
Fra
+0.233
+
-0.240
Ger
+0.195
+0.290
+
Gre
+0.180
+
-0.168
Gua
+
-0.237
-0.209
-0.189
HK
+0.195
-0.240
-0.222
Ind
+0.315
-0.180
Ins
+
-0.175
Ire
+
+
-0.180
Isr
+
-0.277
-0.261
Ita
+0.314 -0.246
Ivo
+
+
Jap
+0.204
+
Ken
+
-0.235
-0.257
Kor
+0.349
Kuw
+
+
-0.235
Mal
+0.203
Mex
+
-0.221
-0.206
Mor
+
Net
+0.251
+
-0.197
-0.178
Zea
+
Nor
+
Pak
+0.202
Per
+0.183 -0.182
-0.201
-0.208
Phi
+0.201
-0.266
Por
+0.314 -0.178
Sin
+
Spa
+
+
-0.187
Swe
+
+
Swi
+
+
+
Tha
+0.175
-0.186
Tun
+
-0.176
Tur
+
UK
USA
+
+
+
Yug
-0.237
-0.203
+
Note: bold-face numbers indicate statistical significance
at the 5% confidence level, when using a two-tailed test.
Source: International Trade Statistics Yearbook, Survey
of Current Business, Statistical Abstract of the US 1992,
and own computations.
101
102
CHAPTER 8.
EMnmCMANMY~S
Again, the largest correlations are observed for developing countries, as well
as Germany and Italy as for low-skilled labor, and for the developing countries, France, Germany, Italy, Japan, and Portugal as for skill intensity. There
are fewer (more) countries with statistically significant correlations for lowskilled 16 (high-skilled) labor in 1978 than in 1989, and a lot fewer for skill
intensity 17. The positive statistically significant correlations for low-skilled
labor and the negative correlations for high-skilled labor are smaller in 1978
than in 1989. For more than 80% of the countries, the statistically significant
correlations are positive for low-skilled labor and negative for high-skilled
labor. The largest correlations are observed for low-skilled labor and the
smallest for high-skilled labor. For high-skilled labor there is only one country, Germany, with a positive statistically significant correlation. Like for
1989, for 30% of the countries in the sample there is no statistically significant correlation for any factor.
External Validation
It is expected that the sign of the correlations will be related to the sign of
the relative factor supply earnings through equality (4.13) (sign test):
We called this condition an "external validation" condition: the sign of the
simple correlations between trade and factor intensities has to be validated
by actual observations of the relative factor endowment earnings. Table 4
reports the countries for which condition (4.13) holds. The best results in
terms of the number of sign matches are obtained for the high-skilled labor
factor (33 countries, 77% of the totaI 18 ). The lowest number of matches is
observed for the low-skilled labor factor (24 countries, 56% of totaI 19 ). As for
capital, the results improve slightly when we adjust the capital endowments
for the foreign direct investment flows.
16There are twice as many developed countries with a statistically significant correlation
in 1989 than in 1978.
17There are twice as many developing countries with a statistically significant correlation
in 1989 than in 1978.
18The figure is 82% when we consider the significant correlations only.
19The figure is 62% when we consider the significant correlations only.
8.3. EMPIRICAL RESULTS
103
Table 4. External Validation Condition A, 1989
Country
Arg
Aus
Aua
Bel
Bra
Can
Chi
Col
Den
Egy
Fin
Fra
Ger
Gre
Gua
HK
Ind
Ins
Ire
Isr
Ita
Jap
Ken
Kor
Kuw
Mal
Mex
Net
Zea
Nor
Pak
Per
Phi
Por
Sin
Spa
Swe
Swi
Tha
Tur
UK
USA
~g
Note:
u
s
Case 1
+
+
+
+
+
+
+ +
+ +
+
+
Case 2
+
k
Case 3
Case 4
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
the external validation condition A is given by:
sign[j3hiIJOhTIJtiV + lJiehTj = sign(gZi). f3h i is the simple correlation between the net trade vector t iV and the total factor cost
share (}hT, for factor h and country j, IJ denotes standard deviation, and 9 is the relative factor endowment income. u, s, and k
denote the low- and high-skilled labor, and capital, respectively.
Cases 1 to 4 refer to four possible ways to compute capital endowments.
Source: International Trade Statistics Yearbook, Survey of Current Business, Yearbook of Labor Statistics, The World Bank
Tables of Social and Economic Indicators, Statistical Abstract of
the US 1992, and own computations.
104
CHAPTER 8. EMPIRICAL ANALYSIS
Several remarks are in order. First, the results of the "external validation"
check are sensitive to how we compute countries' eN P and capital endowments. The capital endowments may be computed in US dollars in three
different ways: first, we may use market exchange rates (case kl in Table
4); second, a PPP investment-based adjustment for the exchange rates (as
documented by Heston and Summers (1991)) is used for converting the capital endowments computed in domestic currency into US dollars (case k3);
third, in addition, the endowments of capital are adjusted in order to take
into account the net flows of foreign direct investment (cases ~ and k4) 20.
When using eN P data as published by the World Bank, there is an equal
number of developed and developing countries for which the condition holds
for low- and high-skilled labor, while for capital there are twice as many developing as developed countries. When computing the eN P using the set of
data provided by Heston and Summers (1991), there are more developed than
developing countries for which the condition holds for high-skilled labor and
for capital, when computing the capital endowments in US dollars, using a
P P P adjustment for the exchange rates. For low-skilled labor the condition
holds for an equal number of developed and developing countries.
Second, there are more cases where the condition holds with a negative sign
than with a positive sign. There are a few countries which seem to be either
poor in all factors (e.g., Colombia, Finland, Kuwait, the Netherlands, and
New Zealand when using the World Bank data for eN P; Chile, Colombia,
Egypt, France, Guatemala, Kenya, Kuwait, New Zealand, and Peru when
using Heston and Summers' data), or rich in all factors (e.g., Germany, Japan,
and Korea, or Germany and Korea, respectively).
The first "external validation" condition was also checked for 1978 (see Table
5). There are 15 countries (for low-skilled labor), 20 (for high-skilled labor),
and 16 (for capital) for which the validation condition holds both in 1978
and 1989. There are fewer countries in 1978 for which the condition holds
for high-skilled labor and capital. Like for 1989, there are more countries
for which the validation condition holds for high-skilled labor than for any
other factor. Also, there are many more countries for which the condition
holds with a negative sign than a with positive one. In 1978, there are
a few countries, apart from those in 1989, which seem to be scarce in all
factors (Colombia, Egypt, Hong Kong, Israel, Malaysia, Pakistan, Peru, the
Philippines, and Singapore). As in 1989, Germany and Japan are rich in all
factors.
20 Data
on foreign net direct investment were available only for 40 countries in the sample.
8.3. EMPIRICAL RESULTS
105
Table 5. External Validation Condition A, 1978
Country
Aus
Aua
Bel
Bra
Can
Chi
Col
Den
Egy
Fin
Fra
Ger
Gre
Gua
HK
u
s
k (Case 1)
+
+
+
+
+
+
+
+
Ind
Ins
Ire
Isr
Ita
Jap
+
+
+
Kor
Kuw
Mal
Mex
Mor
Net
Zea
Nor
Pak
Per
Phi
Por
Sin
Spa
Swe
Swi
Tha
Tun
+
+
+
Tur
UK
USA
Yug
Note: see Table 4.
Source: International Trade Statistics Yearbook,
Survey of Current Business, Yearbook of Labor
Statistics, The World Bank Tables of Social and
Economic Indicators, Statistical Abstract of the
US 1992, and own computations.
106
CHAPTER 8. EMPIRICAL ANALYSIS
In Section 4.2.2 we derived an additional "external validation" condition.
According to condition (4.15), 'L,g;i(J3hiaOhTat,iV + biO hT ) ~ 0 across all
h
factors h within each country j if the HOV equation holds. This condition
is checked for each country in the sample. The computations are done for
the perfect competition model, and then for the model allowing for scale
economies and product differentiation. Again, the results are sensitive to the
measure of GNP. In the case where GNP data form the World Bank are
used, the predicted result for 23 countries (53% of the total) is obtained,
for almost twice as many developed than developing countries (see Table
6). The condition holds for more than 80% of the developed countries. The
results are not changed when we adjust for the foreign direct investment flows.
When GNP data, as provided by Heston and Summers (1991), are used, the
condition holds in 29 countries (67% of the total), for almost twice as many
developing than developed countries. The condition holds for more than 80%
of the developing countries. When allowing for scale economies and product
differentiation, we get the same results as for the perfect competition model.
The results are likely to be affected by the choice of input factors. If we
analyze countries or industries for which there are factors other than those
considered, mOle relevant for their patterns of trade, then for these countries
this condition may not be satisfied. Also, remember that the poor quality of
some of the data may bias the results in an indeterminate direction.
When the second validation condition is checked for 1978, the results differ in
terms of the type of the country for which the condition holds: in 1978 there
are three times more developing than developed countries, while in 1989 there
are two times more developed than developing countries (see Table 7)21.
21The comparison is done for the case where GNP data are taken from the World Bank.
8.3. EMPIRICAL RESULTS
Table 6. External Validation Condition B, 1989
Country Case I Case 2 Case 3 Case 4
Arg
+
+
+
+
Aus
+
+
+
+
Aua
Bel
Bra
Can
Chi
+
+
+
+
Col
+
+
+
+
Den
+
+
Egy
+
+
+
+
Fin
Fra
+
+
+
+
Ger
+
+
+
+
Gre
+
+
+
+
Gua
+
+
+
+
HK
+
+
Ind
+
+
+
+
Ins
Ire
Isr
+
+
+
+
Ita
Jap
+
+
+
+
Ken
+
+
+
+
Kor
+
+
+
+
Kuw
+
+
+
+
Mal
+
+
+
+
Mex
+
+
+
+
Net
Zea
+
+
+
+
Nor
+
+
+
Pak
+
+
+
+
Per
+
+
+
+
Phi
+
+
+
+
Por
+
+
+
+
Sin
+
+
+
+
Spa
+
+
+
+
Swe
+
+
+
Swi
Tha
+
+
+
+
Tur
+
+
+
+
UK
USA
Yug
Note: the external validation condition B is given
h· h·
·-hT
by: Lhg/(f3 JCTOhTCTtiv +b10 );::: O. Cases 1 to
4 refer to the approach used to compute capital
endowments. Variables are defined as in Table 4.
Source: International Trade Statistics Yearbook,
Yearbook of Labor Statistics, The World Bank
Tables of Social and Economic Indicators, Survey
of Current Business, Statistical Abstract of the
US 1992, and own computations.
107
CHAPTER 8. EMPIRICAL ANALYSIS
108
Table 7. External Validation Condition B, 1978
Country Case 1
Country Case 1
Aus
Kuw
Aua
Mal
+
Bel
Mex
+
Bra
Mor
+
Can
Net
Chi
Zea
Col
Nor
+
Den
Pak
+
Egy
Per
+
+
Fin
Phi
+
Fra
Por
+
Ger
Sin
+
+
Spa
Gre
Gua
Swe
+
HK
Swi
+
Ind
Tha
+
+
Ins
'lUn
+
Ire
'lUr
+
Isr
UK
+
+
Ita
USA
+
Jap
Yug
Kor
+
Note: see Table 6.
Source: International Trade Statistics Yearbook,
Yearbook of Labor Statistics, The World Bank
Tables of Social and Economic Indicators, Survey
of Current Business, Statistical Abstract of the
US 1992, and own computations.
"True" Factor Endowment Abundance
A last issue of interest is to examine whether the respective sign of the simple
correlation reproduces that of the true relative factor endowment abundance.
As was discussed in Section 8.2.2, the vector of the true relative factor abundance for factor h is defined either as:
h'
true hj
= ~/s3
I:v hJ
1
j
or, when defined in productivity equivalent units, as:
true hj =
8.3. EMPIRICAL RESULTS
109
which is equivalent to22 :
true hj =
In both cases, the ratio of the country's absorption to world income s may be
computed using either GNP data, published by the World Bank, the World
Tables of Economics and Social Indicators, or data as documented by Heston
and Summers (1991). The ratio of GNP values as provided by the WB and
of those reported by Heston and Summers, is either much smaller than 1 (as
for developing countries) or much larger than 1 (as for developed countries),
taking values between 0.23 for Pakistan and 1.78 for Japan. In conclusion,
the true relative factor endowment abundance calculations are sensitive to
both the way we define it and the measure we choose for GNP.
Only the results obtained when GNP data from Heston and Summers were
used are reported below. Since PPP consumption- and investment-based
adjustments of the exchange rates are used when computing wages and capital
endowments in US dollars, as reported by Heston and Summers, it would be
more appropriate to use data from the same source for the countries' GNP.
In addition, the superiority of the results in one case or the other may be
decided in terms of the percentage of matches between the obtained signs
and prior expectations, and these are better when GNP data from Heston
and Summers are employed. Table 8 reports the signs of the true relative
factor endowment abundance, for both definitions.
When using the first definition, the signs of the low-skilled labor endowments
are usually as expected, namely positive for developing and negative for developed countries. As for high-skilled labor, the signs fail to coincide with
the expectations in many cases. When adjusting the factor endowments to
allow for cross-country differences in the quality of the factors (hence, when
defining the factor endowments in productivity equivalent units), there are
more developed and fewer developing countries which are low-skill abundant
than in the former case. As for high-skilled labor, the second set of calculations gives better results in terms of conformity with sign expectations.
That is, usually the sign is positive for developed and negative for developing
countries.
22For details of the derivation, see Section 4.2.2.
CHAPTER 8. EMPIRICAL ANALYSIS
110
Table 8. True Relative Factor Endowments (Sign), 1989
Definition 1
Definition 2
Country trueU trueS true skill trueU trueS true skill true k,
true k3
Arg
+
+
Aus
+
+
+
+
Aua
+
+
+
+
+
Bel
+
+
Bra
+
Can
+
+
+
+
+
Chi
+
+
Col
+
+
+
Den
+
+
+
+
Egy
+
+
Fin
+
+
+
+
Fra
+
Ger
+
+
+
+
+
+
+
Gre
+
+
Gua
+
+
+
HK
+
+
+
+
+
Ind
+
+
Ins
+
+
+
+
+
Ire
+
+
+
+
+
+
+
Isr
+
+
+
Ita
+
+
Jap
+
+
+
+
+
+
+
+
Ken
+
Kor
+
+
+
+
+
Kuw
+
+
Mal
+
+
+
Mex
+
+
+
Net
+
+
+
+
+
+
Zea
+
Nor
+
+
+
Pak
+
+
Per
+
+
Phi
+
+
Por
+
+
+
+
Sin
+
+
+
+
+
Spa
+
+
+
Swe
+
+
+
+
+
Swi
+
+
+
+
Tha
+
+
+
Tur
+
+
UK
+
+
+
+
USA
+
+
+
Yug
+
+
+
+
+
+
Note: definition 1 refers to the usual way of computing relative factor endowments:
true hj =
lsi - 1. According to Definition 2, the relative factor endowment
-r;:h:hj
is given by: true hj = -r;~";,t:hj lsi
Source: see Table 4.
-
1. Variables are defined as in Table 4.
B.3. EMPIRICAL RESULTS
111
The choice between the two measures of the true relative factor endowment
abundance is not only difficult, but it is also very important. It might be
useful to look at those cases where the signs do not meet our expectations.
For example, when employing the usual definition for the factor endowment
abundance, an unexpected sign for the high-skill endowments is found for
almost 50% of the countries. The sign is negative for some developed countries (Belgium, Canada, France, Switzerland, the UK, and the US), while
positive for some developing countries (Chile, Colombia, Egypt, Guatemala,
Hong Kong, Mexico, Thailand, and Turkey). When adjusting the factor
endowments for differences in factor productivities, an unexpected sign for
low-skilled labor occurs in almost 50% of the cases. One would expect countries like Argentina, Chile, Egypt, Guatemala, India, Peru, the Philippines,
Singapore, Thailand, and Turkey to be low-skill abundant, while Denmark,
the Netherlands, Sweden, Switzerland, and the UK scarce in low-skilled labor.
For all these countries, a sign opposite to expectations is reported.
One explanation of the controversial results may be found in the lack of data
on labor endowment and wages for some of the countries. For example, for
Argentina, France, Kenya, Switzerland, and Thailand data are missing on
low- and high-skilled labor endowments. For Brazil, Colombia, Guatemala,
Indonesia, Malaysia, Italy, and Kuwait there are no available data on wages.
For these countries, data from other countries were used as proxies for the
missing data23 . Another explanation may come from the limited number of
factors considered in the present study. This may be an important limitation
in the case of the countries which are heavily specialized in relatively resourceintensive sectors, where factors other than capital and labor may be more
important for explaining their trade patterns.
However, when considering the definition of the factor endowments in productivity equivalent units, the results seem to be in accord with Wood (1995) and
The Economist (November, 1995). Both suggest that the threat of competition by low-wage developing countries in low-skilled manufacturing exports is
exaggerated, as there are important differences in international factor productivities. Our results show that, when considering the international differences
in the quality of factors, the number of developing (developed) countries predicted by their relative factor abundance to be low-skill abundant is smaller
(larger) than in the case of usual computations.
To summarize, the usual definition overestimates (underestimates) the relative high-skill endowment for some developing (developed) countries. However, computed Pearson and Spearman rank correlations between the relative
high-skill endowments using both definitions are statistically significant both
in 1978 and 1989. As for the relative low-skill endowments, the definition
allowing for differences in the quality of the factors underestimates them for
many developing countries, while overestimating them for some developed
23For details on the construction of the missing data, see Section 8.2.1.
112
CHAPTER 8. EMPIRICAL ANALYSIS
countries. One may conclude that the high-skilled labor endowments should
only be adjusted for international differences in factor productivity.
Relative factor endowments are also computed for 1978 (see Table 9). All
the Pearson (except for high-skill labor) and Spearman rank correlations
between the relative factor endowments in 1978 and 1989, using any of the
two definitions, are statistically significant and positive.
We now turn to the matching between the signs of the simple correlations
between trade and total factor intensities, on the one hand, and the sign of
the true relative factor abundance, on the other hand. As the best measure of
the true relative factor abundance was difficult to decide upon, the discussion
below refers to both definitions for factor endowments.
As for the usual definition of the factor endowments, for low-skill the signs
match for 32 countries, of which 19 are developing and 13 developed. Among
these, only for Kuwait are both signs (of the simple correlation and of the
factor endowment abundance) opposed to expected signs. For the high-skilled
labor, there are 23 countries for which the signs match. As for capital, the
proportion of sign matches is less than 50% of the cases. However, the sign
of the correlation between trade and capital intensity may not be reliable, at
least in those countries for which the direct capital intensity is not correlated
with that ofthe US. This is the case for 13 countries, mainly developing (see
table 2). For eight of them, the sign of the correlation for capital does not
match that of the relative capital endowment.
When computing the factor endowments in productivity equivalent units,
sign matches are obtained for 20 countries (12 developed and 8 developing)
for low-skilled labor. For high-skilled labor, the signs match for 32 countries,
16 developed and 16 developing. However, there are 7 countries, mainly
developed, for which both signs, even though they match, are opposed to our
expectations24 .
24These are mainly countries for which factors other than those considered here may be
relatively more relevant for their trade pattern, e.g. Australia, Finland, New Zealand and
Norway.
8.3. EMPIRICAL RESULTS
113
Table 9. True Relative Factor Endowments (Sign), 1978
Definition 2
Definition 1
Country true U trueS trueskil! trueU trueS trueskil!
Aus
Aua
+
+
+
+
Bel
+
Bra
+
+
Can
+
+
+
+
Chi
+
+
Col
+
Den
+
+
+
Egy
+
+
Fin
+
+
+
+
Fra
+
Ger
+
+
+
+
+
Gre
+
+
Gua
+
HK
+
+
Ind
+
Ins
+
Ire
+
+
+
+
+
+
Isr
+
+
+
Ita
+
+
+
+
Jap
+
+
+
+
Kor
+
+
+
Kuw
Mal
+
Mex
+
Mor
+
+
+
+
Net
+
+
Zea
+
+
+
Nor
+
+
+
Pak
+
Per
+
Phi
+
Por
+
+
+
+
Sin
+
Spa
+
+
+
+
Swe
+
+
+
+
+
Swi
+
+
+
Tha
+
Tun
+
+
+
+
Tur
+
UK
+
+
+
USA
+
+
+
Yug
+
+
+
+
Note: see Table 8. Source: see Table 4.
true k1
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Depending on the employed definition for the factor endowments, there are
a few countries predicted by their relative factor endowments to be either
scarce or abundant in all factors. When using the usual definition, Belgium,
CHAPTER 8. EMPIRlCAL ANALYSIS
114
France, Italy, Kuwait, New Zealand, the UK, and the US are predicted to be
scarce in all factors. In contrast, Austria, Germany, Ireland, Japan, Korea,
Portugal, Singapore, and Yugoslavia seem to be relative abundant in all factors. Notice that almost all latter are developed countries. These results do
not confirm Trefler's (1995), who reports that developed countries tend to be
scarce in all factors and developing countries abundant in all factors25. When
adjusting the endowments for differences in factor productivities, mainly developing countries (Argentina, Chile, Colombia, Egypt, Guatemala, India,
Kenya, Kuwait, Peru, the Philippines, Thailand, and Turkey) and Belgium,
Italy and New Zealand, are predicted to be scarce in all factors. There are a
few countries which seem to be relatively abundant in all factors: Germany,
Indonesia, Ireland, Japan, and Korea.
In Section 8.2.2, we proposed two ways of defining true skill (see definitions
(8.6) and (8.7)). When using the first definition, there are 34 countries for
which the signs of the skill endowments and those of the simple correlations of
trade with skill intensity match 26. When using the second definition, hence
when adjusting the skill endowments for international differences in factor
productivities, there are 28 sign matches.
8.3.2
Ranking Proposition 1
In Section 4.2.1 we formulated ranking propositions derived from a value
version of the HOV equation. Proposition 1, in quantity terms is:
Proposition 1
If:
then:
t hA
v{w /(y/yW) +
:h
hw
< t lA
> v{w/(y/yW) +
:1
Iw
Given Proposition 1 in its quantitative version, if two input factors h and I for
a particular country are ranked according to their endowment ratios relative
to the world, this would be reflected in the same ranking of the adjusted
factor content of net exports of the factors, relative to the world endowment
of those factors, adjusted for differences from the world (weighted average)
factor returns and country's size.
Proposition 1 is checked for each country and pair of factors. Table 10 shows
the results. In the case of low- and high-skilled labor, the ranking hypothesis
25Trefl.er (1995) defines relative factor endowments using our first definition. The abundance of a country is judged upon the number of factors in which the country is predicted,
by its factor endowments, to be relatively abundant.
26More than 80% of the correlations between trade and skill intensity have the expected
sign.
8.3. EMPIRICAL RESULTS
Table 10. Ranking Proposition 1, 1989
Country
Arg
Aus
Aua
Bel
Bra
Can
Chi
Col
Den
Egy
Fin
(u, s)
+
+
+
Fra
Ger
Gre
Gua
+
+
Ind
Ins
+
+
HK
Ire
Isr
Ita
Jap
Ken
Kor
Kuw
Mal
Mex
Net
Zea
Nor
Pak
Per
Phi
Por
Sin
Spa
Swe
Swi
Tha
Tur
+
+
+
+
+
+
+
+
+
+
+
+
UK
USA
Yug
Note: the variables are as defined in Table 4. A positive (negative) sign indicates that a country is revealed
both by its factor-content of trade and relative factor endowment to be relatively abundant (scarce) in the factor
which is listed first in the pair.
Source: as in Table 4.
115
116
CHAPTER 8. EMPIRICAL ANALYSIS
holds for 72% of the countries, with an equal proportion of developing an
developed countries. For the developing countries and Greece, Portugal and
Spain, for which the proposition holds, both their factor endowments and the
factor content of tradeof low-skilled labor as compared to high-skilled labor.
As expected, the developed countries are revealed to be relatively abundant
in high-skilled labor in comparison with low-skilled labor.
When the comparison is undertaken for capital and each of the two types of
labor, the results are poorer in terms of coverage of countries, and are better
for the developing than for the developed countries. When the comparison is
made for low-skilled labor and capital, the condition holds for almost all the
developing countries, and for Greece, Portugal and Spain. With no exception,
all these countries are predicted by their factor endowments to be relatively
better endowed with low-skilled labor than with capital, and their factor content of trade reveals the same ordering. When high-skilled labor and capital
are compared, again the condition holds for more developing than developed
countries. Except for Norway, all these countries are revealed by both their
factor endowments and factor content of trade to be relatively more abundant in high-skilled labor than capital. This outcome is preserved regardless
of the way we compute the endowments of capital. However, there are more
countries for which Proposition 1 holds for both pairs of factors (capital and
low-skilled labor, and capital and high-skilled labor, respectively), when we
use both a P P P investment-based adjustment for the exchange rates and
adjust for the foreign direct investment flows.
To sum up, Proposition 1 holds for more developing than developed countries.
As expected, the developing countries are revealed, both by their trade and
factor endowments, to be relatively better endowed with low- than highskilled labor, while the opposite is true for the developed countries. All the
countries for which Proposition 1 holds are revealed to be better endowed
with high- or low-skilled labor than with capital. Greece, Portugal and Spain
behave in this respect like developing, rather than developed, countries.
Similar results are obtained for 1978. The developing countries are revealed
both by their trade and factor endowments to be relatively better endowed
with low- than high-skilled labor, while the opposite is true for the developed
countries (see Table 11).
All the countries for which Proposition 1 holds are revealed to be better
endowed with high- or low-skilled labor than with capital. There are more
developing than developed countries for which the condition holds in 1978
for the pair low- and high-skilled labor, while in 1989 the condition holds for
an equal number of developing and developed countries.
B.3. EMPIRICAL RESULTS
117
Table 11. Ranking Proposition 1, 1978
Country
Aus
Aua
Bel
Bra
Can
Chi
Col
Den
Egy
Fin
Fra
Ger
Gre
Gua
HK
Ind
Ins
Ire
Isr
Ita
(u, s)
(k,s)
(k,u)
+
+
+
+
+
+
+
Jap
Kor
+
Kuw
Mal
+
Mex
Mor
+
Net
Zea
Nor
Pak
+
Per
+
Phi
+
Por
+
Sin
+
Spa
+
Swe
Swi
Tha
+
Tun
+
Tur
+
UK
USA
+
Yug
Note: variables are defined as in Table 4. A positive (negative) sign indicates that a country is
revealed both by its factor-content of trade and
relative factor endowment to be relatively abundant (scarce) in the factor listed first in the pair.
Source: as in Table 4.
118
8.3.3
CHAPTER 8. EMPIRICAL ANALYSIS
Technology Parameters: How Similar is 8?
The empirical results depend in an important way on the assumption that
total (direct plus indirect) factor cost shares are identical across countries.
In a weaker sense, one might like to check whether the countries' direct
factor cost shares e, the parameters for a CD technology, are correlated
with those for the US, as used in our computations. We expect the results
to be biased if there are important differences in the underlying variables
across countries. Important differences in this respect may result in a factor
intensity reversal27 . Thus, it is of interest to check the extent of inter-country
variations in factor intensities. Pearson and Spearman rank correlations are
computed between skill intensity, high-skilled labor and capital cost share
for each country, on the one hand, and those for the US, on the other hand.
When the correlations are statistically significant, we may conclude that the
assumption of non-reversal factor intensity across countries is not violated.
Detailed input-output data are published for the US only. Available data at
the 4-digit of the ISle allow us to compute the direct factor cost shares (lowand high-skilled labor and capital cost shares, and skill intensity) for a subsample of 28 countries 28. Data are available for developing and developed
countries, which belong to different diversification cones.
Table 2 shows these correlations for 1989. In the case of skill intensity, for
most countries, the Pearson correlation is not statistically significant29 . However, the Spearman correlation yields much better results: except for Hong
Kong, all other countries have significant rank correlations, while the Pearson
correlation is significant for 12 countries only. The best results, in terms of the
number of countries with statistically significant correlations, are obtained
for the low-skill cost share: except for Pakistan (the Pearson correlation)
and Guatemala (the rank correlation), all the correlations are statistically
significant. There are a few developing countries for which the high-skill cost
share is not significantly correlated with that for the US. This is the case
for Guatemala, Indonesia, Kuwait 30 , Peru, and the Philippines, all of them
developing countries. The smallest number of countries with statistically
significant correlations was found for the capital cost share, most of them
developed countries.
The correlations for low-skilled labor are usually larger than those for highskilled labor and capital. The Pearson correlation is larger for low- than for
27When factor prices differ across countries, the order of factor intensities may be reversed between industries. The absence of factor intensity reversal ensures that the ranking
of industries by factor intensities is the same everywhere.
28Data availability differs across countries, the number of 4-digit manufacturing industries ranging from 21 and 52. The countries for which data are available are listed in
Section 8.2.1.
29Statisticalsignificance is given at the 1% confidence level, when using a two-tailed test.
30Data are available only for 20 industries for Kuwait, hence the results may not be
reliable.
8.3. EMPIRlCAL RESULTS
119
high-skilled labor in 71% of the cases, while the Spearman rank correlation
is bigger in 79% of the cases. For capital, the correlations are much smaller
than for any type of labor.
The discussion above suggests that one should have a differentiated attitude
towards the results reported by the empirical study. On the one hand, there
seems to be no skill (intensity) reversal across countries, at least for 27 out of
the 28 countries previously referred to. As these countries belong to different
diversification cones, this conclusion might be extended to all the countries in
the sample. This is good news, as previous empirical studies report the presence of factor intensity reversal, when defining factor intensity by unit factor
requirements. On the other hand, even though statistically significant, the
computed correlations are quite far from 1. There are important differences
especially in the capital cost shares across countries, hence the sign and the
significance of this variable in the present analysis, at least for the countries
with reported differences in this respect, should be treated cautiously.
8.3.4
Similarities in the Trade Patterns
An important issue is which countries have the most similar net trade patterns in manufacturing industries. In order to answer this question, simple
correlations are computed between net exports, scaled by world total exports,
for each possible pair of countries. The last column in Table 1 reports the
country with the most similar trade pattern (defined by the largest positive
statistically significant correlation) with each other country. In general, developed countries have trade patterns similar to those of countries within their
group, and developing countries to those within theirs. The NICs (Newly
Industrialized Countries) have their most similar country within their group,
and there are some countries which have a similar trade pattern with neighboring countries (such as Finland and Sweden, Morocco and Tunisia, Spain
and Portugal, Australia and New Zealand, India and Pakistan).
We also computed the correlation between net exports in 1989 and 1978
for each country in the sample. Except for Norway, all the correlations are
positive and statistically significant. The largest correlations are observed
for developed countries and Hong Kong (the second largest), the smallest
for developing countries (and Israel, France, Ireland, and the UK). The last
result indicates that, while the developed countries preserved to a large extent
their trade structure patterns during 1978-1989, the developing countries
experienced important changes in this respect.
CHAPTER 8. EMPIRICAL ANALYSIS
120
8.3.5
Multiple Correlations
Perfect Competition
A cross-industry, multiple regression equation is estimated for each of the
46 countries in the sample, using an OLS or, for a few countries, a GLS
estimation method. For the perfect competition model, two different sets
of equations are estimated. In the first case, the independent variables are
the total (direct plus indirect) low- and high-skilled labor and capital cost
shares while, in the second case, they are the capital cost share and the skill
intensity. The dependent variable is net exports in value terms, adjusted for
trade imbalance, and scaled to correct for heteroskedasticity. We now turn
to the issue of detecting and correcting the heteroskedasticity.
H eteroskedasticity
By applying the Goldfeld-Quandt test, as described in Johnston (1972), the
presence of heteroskedasticity is detected for each country's estimation equation, for both specifications. In the cross-industry regression studies, the
presence of heteroskedasticity is supported to be related to differences in the
industries' size, the variance of the error term being probably related to the
size of the industry. Following Bowen (1986), the net exports should have
been scaled by the world total production by industry, but data at the necessary level of aggregation were not available31 . Instead, the world total
exports by industry were chosen.
Regressing the absolute values of the residuals from the unsealed regression
equation either on the world total exports or their squares or their square
root, we get the best fit in the first case. Hence, we scale the dependent
variable by the world total exports. As the independent variables are factor
cost shares, it is not necessary to scale the whole regression equation, but
rather the dependent variable only.
After scaling the trade variable, using a White (1980) test, heteroskedasticity was still detected for a few countries. Heteroskedasticity was thus
related to some of the independent variables or their squares. This was the
case for Argentina, Brazil, Colombia, France, Guatemala, Hong Kong, India,
Kenya, Morocco, Pakistan, Thailand, Tunisia, and Yugoslavia for the first
specification of the regression equation, and France, Guatemala, Hong Kong,
31 Using the assumption of identical and homothetic tastes in consumption, one may
use the data on consumption expenditure shares for one country, say the US, in order
to build a proxy for the world production. Given identical and homothetic consumption
tastes cUs = suscw = (yUS -bUS)xwl hence xwl =
cUSyw
and XW = Bxwl =
,
yW'
(yUS _bUS)
us W
B (y::'s _~US)' where c is the consumption vector, B the input-output requirement matrix,
B =
(I - AtI)-l, f denotes final demand and w the world. Given that
(yUS"::'b US ) is
constant across industries, we may use as a scaling variable BiCUS in a cross-industry
study, where i is an index for industry and Bi denotes row i in matrix B.
8.3. EMPIRICAL RESULTS
121
Morocco, and Thailand for the second specification. For these countries, an
EGLS estimation method was then used. The estimated coefficients, when
using an EGLS method, have the same sign as those obtained from an OLS
estimation, but their magnitude and significance are lower. We may now
proceed with the main estimation step.
Estimation Results
In what follows, we briefly discuss the results of the first-stage OLS estimation, for both specifications of the independent variables. Table 12 shows
the results for the first set of regressions, where adjusted net exports were
regressed on low- and high-skilled labor and capital cost shares in a crossindustry framework. The sign for the statistically significant coefficients for
u and
s are as expected, except for Belgium, Italy and Spain (positive
sign for u and negative for S ). There are relatively fewer countries with
a significant coefficient for the capital cost share, as compared to the highand low-skilled cost shares. For four of them, their capital cost shares are
not significantly correlated with those for the US (as discussed in Section
8.3.3). A constant, which was supposed to capture the country specific nonHO determinant of net exports, was included in each regression equation.
The constant term was statistically significant for 9 countries only and, when
significant, it had a sign opposite to the capital intensity variable. For almost
one third of the countries in the sample, usually developed countries, the estimated coefficients were not jointly significant. Among the latter, there were
a few countries for which it might be reasonable to assume that the present
model, which considers only these three input factors, does not allow for a
proper explanation of their trade pattern. This may be the case for Australia,
Canada, Finland, Kuwait, and Norway. In general, better results in terms
of the significance of the estimated coefficients and R2 were obtained for the
developing countries and Germany, Italy and Japan. Both the low- and highskilled labor cost shares were statistically significant for almost twice as many
developing as developed countries.
e
e
e
e
122
CHAPTER 8. EMPIRICAL ANALYSIS
Table 12. Multiple Correlations, Specification 1, 1989
87<'1'
8"'1'
Country 8u '1'
R2 {%}
{t}
{t}
{t}
Arg
-3.606
-3.082
11.2
+
Aus
2.9
+
+
Aua
-2.735
5.8
-2.723
-2.522
Bel
7.2
Bra
7.2
+ +3.057
Can
0.4
Chi
-2.561
9.6
+ +2.519
-2.389
Col
16.2
+ +3.331
+
-0.3
Den
+
+
+
Egy
11.7
+ +2.523
+ +3.205
-1.1
Fin
+
-2.512
Fra
5.5
+
+
-3.550
Ger
-2.123
22.2
+ +3.236
-2.163
Gre
2.3
+
+
Gua
4.3
+
+ +2.491
HK
5.1
+ +2.878
+
-3.874
Ind
23.6
+ +4.277
+
-3.905
Ins
12.8
+
+
-1.7
Ire
+
+
-1.5
Isr
Ita
-2.245
-3.383
16.2
+ +3.199
Ivo
1.8
+
+
Jap
13.8
+ +3.177
Ken
4.7
+ +1.975
+
-2.391
Kor
14.9
+ +3.896
+
Kuw
1.0
+
+
+
Mal
-2.896
9.6
+
+
-1.5
Mex
+
Mor
-3.239
10.8
+
+
Net
6.3
+
+ +2.613
Zea
-0.4
Nor
2.6
+
Pak
-3.119
10.9
+ +2.491
Per
-2.478
9.9
+ +2.702
+
Phi
13.1
+ +3.733
+
Por
20.8
+ +5.527
+
Sin
2.7
+
+ +2.166
Spa
-2.415
11.9
+ +3.032
+
Swe
5.8
+
Swi
-2.479
14.3
+ +3.359 +
Tha
-4.197
29.8
+ +5.115
+
-3.301
Tun
6.7
-2.877
Tur
14.2
+
8.3
UK
+
+ +2.981
-2.669
USA
11.5
+ +2.229 + +2.721
Yug
1.6
+ +2.155
+
Note: bold-face numbers denote statistical significance at the 5% level of
confidence, when using a two-tailed test.
Source: International Trade Statistics Yearbook, Survey of Current Business, Statistical Abstract of the US 1992, and own computations.
8.3. EMPIRICAL RESULTS
123
For the second set of equations, where the adjusted net exports were regressed
on the skill intensity and the capital cost share, usually the signs of the
significant coefficients for the skill intensity variable were as expected, namely
positive for relatively skill abundant (except Italy and Spain) and negative
for skill scarce countries (see Table 13). Notice that in the case of Austria,
Belgium, Canada, Israel, the Ivory Coast, Kuwait, and Norway, the skill
intensity variable had the expected sign (significant or not) while, for the
first specification, both the high- and the low-skilled variable had the same
sign. As for the capital variable, it was significant in twice as many cases
as the first specification, and it was positive for all the developing countries.
Again, the sign of the significant constant term seems to be opposite to that
of the capital intensity variable. There were more developing countries with
a statistically significant skill intensity variable, while the capital cost share
was significant for as many developed as developing countries. Better results
in terms of the significance of explanatory variables and R2 were obtained
for the developing countries and Germany. There were more countries with
the estimated coefficients not jointly significant, usually developed countries,
when compared to the first specification.
The previous discussion, referring to the differences between the technology
parameters between the US and other countries, also applies here. One would
expect the results to be biased if there were important differences in the
explanatory variables across countries, hence the results for some countries
should be treated cautiously, especially those referring to capital intensity.
Balassa (1979) proposes an "external validation" step, by regressing the coefficients obtained in the first OLB stage on the relative abundance of factors in
a cross-country regression, using a GLB estimation method. However, there
are several problems with this approach. First, as already discussed, the correlations between the direct factor cost shares for the US and other countries,
even though many were statistically significant, are far from being 1. Given
the high correlations observed, we may consider the signs of the first-step estimation coefficients as reliable (though not the values), at least for the lowand high-skilled labor factors. However, when regressing these coefficients on
factor endowments in an inter-country framework, the imperfections in the
values of the first-step estimated coefficients become more important.
124
CHAPTER 8. EMPIRICAL ANALYSIS
Table 13. Multiple Correlations, Specification 2, 1989
(}B7.'L(}uT
R2 (%}
Country (}7C7.'
{t}
{t}
Arg
3.7
4.3
Aus
+ +2.549
-3.020
6.0
Aua
+
2.5
Bel
+2.224
+
0.5
Bra
2.1
Can
+2.071
+
-3.085
10.8
Chi
+ +3.203
-4.954
20.7
Col
+ +3.856
0.4
Den
-3.659
Egy
17.2
+ +4.302
-{).O
Fin
+
3.2
Fra
+
+
-3.886
14.6
+3.436
Ger
+
-{).4
Gre
+
-3.510
13.9
Gua
+3.632
+
-2.283
3.3
HK
+
-5.132
18.9
Ind
+ +2.075
-2.006
3.7
Ins
+ +1.986
-1.0
Ire
+
+
2.0
Isr
+
-2.097
-2.897
11.3
Ita
2.3
Ivo
Jap
-3.156
7.7
+2.018
+
-4.179
14.4
Ken
+ +2.917
-2.532
4.3
Kor
+
-1.7
Kuw
+
-2.754
7.2
Mal
+ +2.436
-1.6
Mex
+
+
0.3
Mor
+
8.3
Net
+2.071
+
+ +2.257
0.2
Zea
1.9
Nor
+
+
-4.477
13.6
Pak
+
-4.975
17.3
Per
+ +2.276
-3.659
11.5
Phi
+ +2.713
-2.663
4.4
Por
+
Sin
3.7
+ +2.536
Spa
-2.792
6.6
+ +2.139
Swe
-2.201
3.7
+
6.3
Swi
+3.112
+
-5.670
23.1
Tha
+ +3.386
0.2
Tun
+
+
-3.283
10.6
Tur
+ +2.926
5.2
UK
+
+ +2.136
4.3
USA
+
+
-1.5
Yug
+
Note: bold-face numbers denote statistical significance at the
5% level of confidence, when using a two-tailed test.
Source: International Trade Statistics Yearbook, Survey of
Current Business, Statistical Abstract of the US 1992, and
own computations.
8.3. EMPIRICAL RESULTS
125
Second, the only theory-based prediction which may be checked in an intercountry framework refers either to a relationship between the first-stage estimated coefficients only, for each factor separately, or between each of the firststep estimated coefficients and all factor endowments (see identities (4.33)
and (4.34) in Section 4). However, none of these theory-based conditions
could be checked, as scaled net exports were used as the dependent variable
in the first-stage OLS estimation. The theory does not predict any relationship between the first-stage estimation coefficients and the relative factor
endowment earnings in an inter-country framework, when scaled net exports,
rather than net exports, are used. Nevertheless, we may check whether the
sign of the first-step estimation coefficients replicates that of the relative factor endowment abundance.
The number of sign matches for both definitions of the true relative factor
abundance and both specifications of the regression equation are reported.
For the first specification and the usual definition of the endowments, there
are 31 matches between the signs for low-skilled labor, 24 for high-skilled labor, and 18 for capital32 . Only for high-skilled labor there are more developed
than developing countries for which the signs match. When the endowments
are adjusted for differences in the quality of the factors, there are 22 matches
for low-skilled labor and 36 for high-skilled labor. Here, for low-skilled labor there are almost twice as many developed as developing countries for
which the signs match. Once again, the results are sensitive to the way the
variables are defined. As it was the case in checking the external validation
for the simple correlations, the best results, in terms of sign matches, were
observed for low-skilled labor when defining the endowments as usual, and
for high-skilled labor when adjusting the factors for differences in quality.
For the second specification of the regression equation, the biggest number of
sign matches were obtained for the usual definition of the factor endowments
(32, as compared to 24 for the second definition).
Which Specification Is Better?
In order to check which specification yields better results, first the adjusted
R2, namely fl2, obtained for each country, was compared for both specifications. The first specification is better for 23 countries (the US included),
while the second is better in 8 cases only33. These 8 countries are all, except for the Netherlands, developing countries and, for 5 of them, the capital
intensity variable is not significantly correlated with that for the US.
Second, the results of an encompassing test is reported in order to check
whether either specification encompasses the other. There are more countries
for which the first specification encompasses the second (the US included).
32Here, only the results when capital endowments are computed in US dollars, using a
PPP adjustment for the exchange rates, are reported.
33The countries whose the estimated coefficients are not jointly significant at least for
one specification are excluded from the comparison.
126
CHAPrnR8.
EMnmCMANM~ffl
The countries for which the second specification encompasses the first one
are usually developing countries, except Australia. For those countries the
capital intensity variable is not significantly correlated with that for the US
(e.g., Chile, Colombia, Egypt, Guatemala, and Peru).
We may conclude that the first specification is better than the second.
Parameter Constancy
After estimating a net trade equation for each country in the sample, we check
whether the estimated coefficients are significantly different across countries.
Based on Hsiao (1986), an analysis of covariance to test for the homogeneity
of cross-industry parameters (coefficients and intercepts) across countries was
undertaken. First, overall homogeneity was tested for, and the null hypothesis was that both the intercepts and the coefficients are equal across countries.
In the unrestricted model a separate cross-industry regression for each country was postulated, while the restricted version was the pooled model (one
estimation equation for all countries). An F-test was built, based on the
residual sum of squares for the unrestricted and restricted versions, and the
null hypothesis was rejected at the 1% level of confidence, as the computed
F, 6.15 for the first specification and 4.84 for the second, was higher than
the critical value in both cases.
Furthermore, it was tested whether non-homogeneity could be attributed to
heterogeneous slopes or heterogeneous intercepts. The null hypothesis was
that of heterogeneous intercepts and homogeneous slopes. An F-test was
built and the null hypothesis was rejected at the 1% level of confidence, as
the computed F was 7.127 for the first specification and 5.75 for the second,
which was higher than the critical value in both cases.
Therefore, for both specifications of the regression equation, we may reject at
the 1% level of confidence both the hypothesis of equal intercepts and slopes,
and that of heterogeneous intercepts and equal slopes.
Scale Economies and Product Differentiation
The regression analysis was repeated for the model that allows for Increasing
Returns to Scale (IRS), internal to the firm. In Section 3.2 it was shown that
the matrix of total factor cost shares is modified according to:
aTIRS -- aT j3-1
where j3 is a diagonal matrix, with its elements indicating the mark-up price
within each industry, and aT is the matrix of total factor cost shares, computed for the perfect competition model. Estimations of the mark-up prices
for the US industries, at the 2-digit level of the SIC, are taken from Morrison (1990). Given the availability of the mark-up data at the 2-digit of the
SIC only, the results may not be very reliable. Hence, the level of advert is-
8.3. EMPIRICAL RESULTS
127
ing expenditures in total sales is additionally used as an instrument for the
reciprocal of the mark-up variable34 •
Estimation Results
The results of the multiple regressions, using the first specification of the
regressors, are shown in Table 14. There are no important changes in the
sign and the significance of the variables.
Table 15 shows the multiple correlations for the second specification. The skill
intensity variable has the same sign as in the perfect competition model for
all countries, whether it is statistically significant or not, and for 3 countries
(Argentina, Belgium and Indonesia) it becomes insignificant. Perhaps more
importantly, there are 6 fewer countries with statistically significant capital
cost share, therefore when allowing for an imperfect competitive framework,
capital becomes even less important in shaping the pattern of trade, especially
for developed countries35 . As for the constant term, the sign remains the
same, and for some countries it becomes statistically significant, while for
others it becomes insignificant.
34 Advertising expenditures are reported in the input-output tables for the US at the
same aggregation level as the input-output requirements. Hence, they are available at a
much lower aggregation level than the mark-up data from Morrison (1990).
35For the perfect competition model, there is an almost equal number of developing and
developed countries with a statistically significant multiple correlation coefficient while, for
the IRS model, the ratio is 2 to 1.
128
CHAPTER 8. EMPIRICAL ANALYSIS
Table 14. Multiple Correlations, IRS (1), 1989
07<'1'
0 8 '1'
Country ou'1'
R2 {%~
{t}
{t}
{t}
Arg
-2.579
+2.143
5.9
+
Aus
-2.023
2.6
+
+
-2.291
Aua
4.4
+
Bel
3.7
+
-2.010
Bra
8.8
+ +3.643
Can
0.3
+
-2.964
8.1
Chi
+
+ +2.068
-4.063
17.1
Col
+
+ +3.639
---0.4
Den
+
Egy
-2.213
5.4
+
+
-1.0
Fin
+
-2.935
6.2
Fra
+
+ +2.315
-3.565
-2.176
22.3
Ger
+ +5.108
-2.937
4.7
Gre
+
+
4.7
Gua
+ +2.046
+
3.4
HK
+
+ +2.349
-4.705
25.1
Ind
+
+ +5.166
-4.157
12.6
Ins
+ +1.958
+
-1.7
Ire
+
+
-1.9
Isr
+
+
-2.657
-2.146
13.4
Ita
+ +4.158
1.1
Ivo
+
+
-2.698
15.8
Jap
+ +4.500
-2.088
4.2
Ken
+
+ +1.968
18.1
-3.455
Kor
+
+ +4.774
---0.8
Kuw
+
-4.114
11.9
Mal
+2.005
+
+
---0.6
Mex
+
+
10.1
-3.352
Mor
+
+ +2.092
6.8
-2.586
Net
+
+ +2.927
---0.3
Zea
+
2.1
Nor
+ +2.146
9.1
-2.848
Pak
+ +3.281
11.5
-2.938
Per
+
+ +3.125
24.3
Phi
+ +3.354
+ +3.530
-3.558
19.3
Por
+ +5.142
0.8
Sin
+
15.7
Spa
-4.556
+
+ +3.148
6.5
Swe
+ +2.496
-3.731
14.9
Swi
+ +4.069 +
-5.598
31.6
Tha
+
+ +5.760
-3.052
15.4
Tun
+
+
-4.303
14.7
Tur
+
+ +2.797
6.7
-3.062
UK
+
+ +2.298
10.5
-4.029
USA
+
+
1.3
Yug
+
Note: bold-face numbers denote statistical significance at the 5% level of
confidence, when using a two-tailed test.
Source: International Trade Statistics Yearbook, Survey of Current Business, Statistical Abstract of the US 1992, Morrison (1990), and own computations.
8.3. EMPIRICAL RESULTS
Table 15. Multiple Correlations, IRS (2), 1989
(Js7.'L(Ju'l'
R2 (%)
Country (J'TC'l'
{t}
{t}
Arg
2.3
0.4
Aus
+
-2.855
5.2
Aua
+
2.8
Bel
+2.267
+
-0.3
Bra
1.8
Can
+2.005
+
-2.543
6.0
Chi
+ +2.140
-4.397
15.7
Col
+ +2.804
Den
1.2
Egy
-2.795
8.1
+ +2.548
-0.4
Fin
+
1.9
Fra
+
+
-2.667
8.0
Ger
+2.677
+
-1.3
Gre
+
-3.178
10.4
Gua
+ +2.840
-3.129
3.3
HK
+
-4.737
Ind
17.7
+ +2.892
2.3
Ins
+
-1.1
Ire
+
+
0.4
Isr
+
-2.959
7.5
Ita
0.8
Ivo
Jap
-2.161
3.1
+
-3.865
11.5
Ken
+ +2.101
-2.292
3.7
Kor
+
-1.8
Kuw
+
-2.362
3.8
Mal
+
-1.8
Mex
+
1.0
Mor
+
+
7.1
Net
+2.536
+
+
0.3
Zea
0.9
Nor
+
+
-4.292
12.7
Pak
+
-4.847
18.4
Per
+ +2.952
-4.263
28.2
Phi
+ +6.067
-2.256
2.6
Por
+
-0.4
Sin
+
-2.266
Spa
3.0
+
-2.016
2.6
Swe
+
4.7
Swi
+2.768
+
-5.148
21.1
Tha
+ +3.429
0.2
Tun
+
+
-2.654
5.6
Tur
+
1.8
UK
+
+
1.7
USA
+
+
-1.6
Yug
+
Note: bold-face numbers denote statistical significance at the
5% level of confidence, when using a tW<rtailed test.
Source: International Trade Statistics Yearbook, Survey of
Current Business, Statistical Abstract of the US 1992, and
own computations.
129
130
CHAPTER 8. EMPIRICAL ANALYSIS
We will discuss briefly the results obtained when using an instrumental variable estimation. The results are reported in Tables 16 and 17. In comparison
to the outcome of the OLS estimation (based on the mark-up data), for the
first specification there are few changes in the signs of the coefficients, and
all of these occur for the coefficients which are not statistically significant.
The R2 is usually lower, there are fewer developed countries with statistically
significant correlations for high-skilled labor and capital, while many fewer
developing countries have significant correlations for low-skilled labor. As for
the second specification, usually the R2 is larger for the instrumental variable
estimation, and there are fewer significant coefficients for capital.
Encompassing Test
An encompassing test was done in order to check whether either the perfect
competition or the scale economies model encompasses the other. The encompassing test was done for both specifications of the independent variables,
using both estimations of the mark-ups and the instrumental variable. To
facilitate the following discussion, let us call the perfect competition model
Ml and the scale economies model M2.
When using the mark-up estimations as reported by Morrison (1990), there
is no clear pattern for the first specification of the estimation equation. First,
for half of the countries, neither model encompasses the other one. Usually
this refers to countries for which either there is no statistically significant
estimated coefficient or the coefficients are not jointly-significant. Second, for
about 25% of the countries, both developed and developing, Ml encompasses
M2. Third, for roughly 20% of the countries, belonging to both country
groups, M2 encompasses MI' For the second specification of the regressors,
there is a clear pattern: Ml encompasses M2 for all but one country.
When the ratio of advertising expenditures to sales was used as an instrumental variable for the reciprocal of the mark-ups, for both specifications Ml
encompasses M2 except for three and two countries, respectively.
If we take into account that the instrumental variable estimation yields more
reliable results, we may conclude that, as for the net exports, the presence of
economies of scale does not explain anything which is left unexplained by the
perfect competition model. Hence, the HOV model is not rejected in favor
of a model with economies of scale and product differentiation, at least not
the one based on the assumption of CES in consumption.
B.3. EMPIRICAL RESULTS
Table 16. Multiple Correlations, IRS (1), IV Estimation, 1989
OB7.'
01i'1'
Count!1 ou7.'
(t}
(t}
(t}
R2 t%~
Arg
.4
+
Aus
0.09
+
Aua
2.56
+
Bel
0.50
+
Bra
2.46
+ +2.349
Can
-3.074
6.36
+
+
Chi
-3.076
5.74
+
+
Col
-3.495
9.44
+ +2.017
+
Den
0.50
+
+
Egy
-2.968
5.64
+
+ +2.126
-1.55
Fin
+
-3.563
Fra
9.64
+
+ +2.708
-2.532
Ger
14.88
+ +4.737
-D.42
Gre
+
+
Gua
6.77
+
+ +2.794
2.25
HK
+ +2.000
+
-3.672
10.05
Ind
+ +2.761
+
-3.582
8.41
Ins
+
+
-2.68
Ire
+
+
-2.27
Isr
+
-2.921
11.29
Ita
+ +3.542
-D.63
Ivo
+
+
-2.164
8.51
Jap
+ +3.582
-2.258
3.89
Ken
+
+
-3.034
9.75
Kor
+
+ +3.298
-1.96
Kuw
+
+
-3.655
8.31
Mal
+
+
0.20
Mex
+
+
-2.632
4.41
Mor
+
+
-2.275
4.41
Net
+ +2.508
-1.55
Zea
+
-D.63
Nor
+
-2.548
5.02
Pak
+ +2.390
+
-2.056
4.61
Per
+ +2.027
+
-3.133
20.42
Phi
+ +3.351
+ +2.576
-3.406
15.60
Por
+ +4.527
0.61
Sin
+
+
-3.541
8.41
Spa
+ +2.254
+
3.79
Swe
+
-3.273
10.77
Swi
+ +3.497 +
-5.350
21.14
Tha
+ +4.092
+
-2.460
2.87
Tun
+
+
-3.379
8.00
Tur
+ +1.992
+
-2.810
5.74
UK
+
+ +2.486
-3.713
9.13
USA
+ +1.984 +
-D.32
Yug
+
Note: bold-face numbers denote statistical significance at the 5% level of
confidence, when using a two-tailed test. IV denotes instrumental variable
estimation.
Source: International Trade Statistics Yearbook, Survey of Current Business, Statistical Abstract of the US 1992, Morrison (1990), and own computations.
131
CHAPTER 8. EMPIRICAL ANALYSIS
132
Table 17. Multiple Correlations, IRS (2), IV Estimation, 1989
Country
Arg
Aus
Aua
Bel
Bra
Can
Chi
Col
Den
Egy
F~
Fra
Ger
Gre
Gua
HK
Ind
Ins
Ire
~
Ita
OkT
+
(t)
-2.289
+
+
+
+
+
+
+
+
+
os1';0..1'
+
+
+
+
+
+3.079
-2.363
(t)
-2.230
-3.450
-2.211
+2.578
+2.306
-1.953
-2.127
-3.120
+
+
-3.444
R2
J%J
.5
-1.36
2.71
1.59
-1.06
-0.24
2.91
9.53
0.88
2.81
~~
5.76
2.91
-1.16
9.22
2.20
6.58
1.08
-1.36
~n
11.56
Ivo
+
1.38
Jap
+
0.06
Ken
+
-3.495
9.63
Kor
+
-2.388
3.83
Kuw
-1.77
Mal
-2.134
2.20
Mex
-1.16
Mor
+
-0.85
Net
+
+
+2.820
5.66
Zea
0.06
Nor
+
+
-0.14
Pak
+
-3.835
10.24
Per
+
-3.760
11.56
Phi
+ +4.019
-3.158
17.77
Por
-2.730
4.95
Sin
-1.77
Spa
-2.079
2.10
Swe
+
2.50
Swi
+
+
+3.390
8.00
Tha
+
-4.541
14.41
Tun
+
-1.16
Tur
+
-2.018
2.61
UK
+
+
+2.331
4.03
USA
+
+
+2.345
3.32
Yug
+
-1.77
Note: bold-face numbers denote statistical significance at the 5%
level of confidence, when using a two-tailed test. IV denotes instrumental variable estimation.
Source: International Trade Statistics Yearbook, Survey of Current Business, Statistical Abstract of the US 1992, and own computations.
8.3. EMPIRICAL RESULTS
133
Export and Import Patterns
Simple correlations between factor cost shares (modified as to allow for scale
economies) and exports, and between factor cost shares and imports were
computed. For exports, the statistically significant correlations for low-skilled
labor were positive for the developing countries (except Kenya) and negative
for developed countries (except Portugal) (see Table 18). There were three
times more developed than developing countries for which the correlations
were statistically significant, and almost all the correlations were negative.
As for high-skilled labor, all the statistically significant correlations were
observed for the developing countries (and Greece and Portugal) and all are
negative.
For imports, statistically significant correlations for low-skilled labor were obtained, mainly for developing countries, and all were negative (see Table 19).
There were only 3 and 1 countries with statistically significant correlations
for high-skilled labor and capital, respectively. The best results in terms of
the number of countries with statistically significant correlations were observed for imports, for skill intensity (39 countries). Larger correlations were
obtained for the developing countries. The correlations for skill intensity are
considerably larger than for low- or high-skilled labor, for both exports and
imports.
134
CHAPTERS. EMPIRICAL ANALYSIS
Table 18. Simple Correlations, IRS Exports, 1989
ou'l'
osT
07CT
os'l'LOu'l'
Country
Arg
-0.209
+0.240
Aus
-0.244
+0.314
Aua
+0.184
Bel
+0.285
Bra
+
Can
+0.182
Chi
+0.444
+
Col
-0.293
+
+
Den
+0.197
Egy
+
Fin
+
Fra
-0.204
+0.408
-0.181
Ger
+0.298
-0.270
Gre
Gua
+0.319 +0.341
HK
-0.226
+
+
-0.236
Ind
+
-0.236
Ins
+
Ire
+0.322
+
Isr
+0.428
+
+
Ita
+
+
Ivo
+
Jap
+
+
Ken
-0.168 -0.230
+0.275
+
Kor
+0.181 -0.201
Kuw
-0.190
+0.501
+
Mal
+
Mex
+0.256
Mor
-0.231
+0.184
+
Net
-0.240
+0.612
+
Zea
+0.216
Nor
-0.200
+0.369
Pak
-0.178
+
Per
+
+
Phi
+
Por
+0.256 -0.190
Sin
+
Spa
+0.208
Swe
-0.192
+0.204
Swi
+0.516
+
+
Tha
+0.213 -0.196
+
Tun
-0.239
+
+
Tur
-0.267
+
UK
-0.237
+0.472
+
USA
-0.214
+0.381
+
Yug
+
+
Note: bold-face numbers denote statistical significance
at the 5% confidence level, using a two-tailed test.
Source: International Trade Statistics Yearbook, Survey of Current Business, Statistical Abstract of the US
1992, and own computations.
8.3. EMPIRICAL RESULTS
Table 19. Simple Correlations, IRS, Imports, 1989
ou'1'
osT
01CT
osT louT
Country
Arg
-0.231
+0.668
+
Aus
-0.169
+0.252
Aua
+0.195
Bel
+0.417
-0.235
Bra
+0.631
+
+
Can
+0.180
+
-0.224
Chi
+0.358
-0.246
Col
+0.619
+
Den
+0.319
Egy
-0.263
+0.462
Fin
+0.288
Fra
+0.327
Ger
+0.265
Gre
+0.237
-0.277
Gua
+0.608
+
HK
-0.216
+
+
+
-0.233
Ind
+0.477
-0.224
Ins
+0.537
+
Ire
+0.307
+
-0.219
Isr
+0.423
+
-0.178
Ita
+0.363
Ivo
+0.208 +0.283
Jap
-0.196
+0.290
+
+
Ken
-0.249
+0.447
Kor
-0.181
+0.383
+
-0.168
Kuw
+
+
Mal
+
+
-0.205
Mex
+0.464
-0.201
Mor
+0.323
Net
+0.389
-0.170
Zea
+0.269
+
Nor
+
+
-0.249
Pak
+0.577
+
-0.289
Per
+0.640
+
'+
-0.177
Phi
+0.281
-0.172
Por
+0.271
Sin
+
+
-0.216
Spa
+0.379
Swe
+0.249
Swi
+0.266
+
-0.222
Tha
+0.356
Tun
+
-0.230
Tur
+0.499
UK
+0.280
USA
+
Yug
-0.209
+0.499
Note: bold-face numbers denote statistical significance at
the 5% level of confidence, when using a two-tailed test.
Source: International Trade Statistics Yearbook, Survey
of Current Business, Statistical Abstract of the US 1992,
and own computations.
135
136
CHAPTER 8. EMPIRICAL ANALYSIS
Separate equations for exports and imports were estimated for the model
with increasing returns to scale and product differentiation. Briefly, the results may be summarized as follows. For exports, usually the sign for the
low-skilled labor was as expected, namely positive for developing (and Italy
and Portugal) and negative for developed countries (and Guatemala) (see
Table 20). The sign for high-skilled labor was positive for developed (and
Singapore) and negative for developing countries. Low- and high-skilled labor were less important in explaining the export pattern than in explaining
net exports. There were twice as many developing countries with statistically
significant correlation for the labor factors and three times more developed
countries for low-skilled labor for net exports than for exports. The picture of
the sign matches between the correlations of exports with factor intensities,
on the one hand, and the factor endowments, on the other hand, is similar to
that observed for the net exports. Capital is relatively more important in explaining the pattern of imports than exports or net exports, while low-skilled
labor is less important. There were twice as many developing countries with
statistically significant correlation for capital for imports as there were for
exports and net exports. High-skilled labor is less important in explaining
the pattern of imports than in explaining net exports (see Table 21).
8.3. EMPIRICAL RESULTS
Table 20. Multiple Correlations, IRS Model, Exports, 1989
(}1i'1'
(}sT
R2 {%}
Country (}u'l'
{t}
{t}
{t}
Arg
1.8
+
Aus
4.9
+
-2.975
Aua
8.3
+
Bel
3.1
+
-2.368
5.5
Bra
+
+
-2.471
Can
10.1
+ +2.345
Chi
3.6
+
-3.299
Col
11.1
+ +2.597
+
-2.359
Den
5.4
+
Egy
1.6
+
+
Fin
6.6
+ +2.000
Fra
3.3
+
-2.171
Ger
10.3
+ +2.886
-2.212
Gre
5.6
+
-3.046
Gua
19
+ +4.757
4.1
HK
+ +2.129
-2.080
11.3
Ind
+ +3.622
Ins
3.3
+
Isr
4.1
+ +2.005
2.2
Ire
+
+
-2.563
7.8
Ita
+ +2.440
Ivo
1.7
+
-2.263
Jap
12.7
+ +3.659
Ken
1.7
+
7.4
Kor
+ +2.943
Kuw
2.6
+
Mal
2.8
+
+
2.8
Mex
+
Mor
1.8
+
+
Net
3.5
+
Zea
1.4
+
Nor
4.7
+
Pak
2
+
Per
1
+
+
+
Phi
15.3
+ +2.202 +
+ +2.023
-2.685
Por
15.3
+ +4.218
Sin
6.4
+ +2.174
Spa
-2.022
3.6
+
+
Swe
-2.698
12.9
+ +3.054
Swi
9.9
+ +3.412
Tha
-2.758
14.9
+ +4.172
Tun
-2.003
3.8
+
Tur
2.8
+
UK
-2.038
8.7
+ +2.819
USA
11.8
+ +3.318
Yug
3.1
+
Note: bold-face numbers denote statistical significance at the 5% level of
confidence, when using a two-tailed test.
Source: International Trade Statistics Yearbook, Survey of Current Business, Statistical Abstract of the US 1992, Morrison (1990), and own computations.
137
138
CHAPTER 8. EMPIRICAL ANALYSIS
Table 21. Multiple Correlations, IRS Model, Imports, 1989
(}s'!'
(}"kT
R'l {%}
Country (}u'1'
{t}
{t}
{t}
Arg
5.2
+ +2.123
Aus
4.9
+
-2.169
Aua
4.2
+
+
3.1
Bel
+
6.4
Bra
+
-2.126
9.6
Can
+ +2.413
Chi
7.7
+ +2.223
Col
6
+
2.5
Den
+
Egy
5.2
+
-2.494
7.7
Fin
+
2.8
Fra
+
+
-2.112
4.1
Ger
+
+
2.2
Gre
+
-2.461
5.3
Gua
+
+
2
HK
+
-2.389
10.3
Ind
+ +2.442
-2.941
Ins
11.9
+ +2.845
2
Ire
+
2.5
Isr
+
2.9
Ita
+
Ivo
3.7
+
1.8
Jap
+
5.1
Ken
+
-2.892
12
Kor
+ +2.910
Kuw
2.3
+
+
-2.430
10.1
Mal
+ +2.821
-2.512
10.7
Mex
+ +2.904
6.2
Mor
+
2.7
Net
+
1.6
Zea
+
-2.140
5
Nor
+
+
5.9
Pak
+
8.5
-2.323
Per
+ +2.498
4.9
Phi
+
3.9
Por
+
-2.256
7.6
Sin
+ +2.243
-2.182
Spa
7.9
+ +2.310
-2.518
7.1
Swe
+
2.5
Swi
+
+
7.8
Tha
+ +2.280
3.9
Tun
+
7.4
Tur
+
4.3
UK
+
-2.252
5.3
USA
+
+
-2.119
Yug
5.7
+
Note: bold-face numbers denote statistical significance at the 5% level of
confidence, when using a two-tailed test.
Source: International Trade Statistics Yearbook, Survey of Current Business, Statistical Abstract of the US 1992, Morrison (1990), and own computations.
Chapter 9
Conclusions
The results of a comprehensive empirical study were reported for 1989 (1978),
covering 46 developing and developed countries, 116 (108) manufacturing industries, and 3 factors. The analysis provides a reasonably good explanation
of trade data in terms of a very short list of production factors. The results for
individual countries, mainly developing, show that international trade, factor intensities, and factor endowments are related as predicted by the HOV
theory. Briefly, here are the most important results of this part.
Simple correlations between trade and total factor intensities were computed.
Usually, the signs of the correlations conformed to prior expectations, namely
positive (negative) ones for the developing (developed) countries for lowskilled labor and the opposite for high-skilled labor. Better results, in terms
of the number of countries with statistically significant correlations, were
observed for skill intensity and low-skilled labor, while the poorest results
were obtained for capital. Better results were found for developing countries
for all the factors. Larger correlations were observed for low-skilled labor
for developing countries and Greece, Italy, Portugal, and Spain; the largest
correlations for high-skilled labor were also found for developing countries.
Larger observed correlations between trade and low-skilled intensity may be
explained by larger correlations between countries' direct low-skilled labor
cost shares and those of the US, as used in our computations.
Two "external validation" conditions were checked, validating the signs of
the correlations between trade and factor intensities by actual observations
of factor endowments if the HOV equation holds. For the first validation
condition, which has to hold for each factor within a particular country,
better results, in terms of matches of the signs, were obtained for high-skilled
labor. However, the results were sensitive to the method of computation of
capital endowments and the measure used for the countries' GNP. As for
the second validation condition, which had to hold across all the factors for
140
CHAPTER 9. CONCLUSIONS
each particular country, the results were again sensitive to the way GNP was
computed. When GNP data as provided by the World Bank were used, the
condition held for 53% of the countries, the ratio of developed to developing
countries being 2 to 1. When data as reported by Heston and Summers
(1991) were used, the ratio was 1 to 2, and the condition held for 67% of
the countries. The results were preserved when using the model with scale
economies and product differentiation. There were very few changes in this
respect when the endowments of capital were adjusted for the foreign direct
investment flows. The choice of the factors may also have affected the results
of checking the second validation condition.
The countries' true relative factor abundance depended on the definition
used. When it was defined in productivity equivalent units, many developing
countries were predicted to be scarce in low-skilled labor. This result is in
line with Wood's (1995) and that of The Economist (November, 1995). Nevertheless, it is difficult to decide upon the proper definition of the true factor
endowment abundance, even though taking the international differences in
factor productivities into account seems more appealing. Most matches between the signs of the correlations of trade with factor intensities, on the
one hand, and true factor endowments, on the other hand, are obtained for
low-skilled labor when using the normal definition, and for high-skilled labor
when using the alternative one. Regardless of how true factor abundance was
defined, there are countries which seemed to be either scarce in all factors
(e.g., Belgium, Kuwait, New Zealand) or rich in all factors (e.g., Germany,
Ireland, Japan). Trefler (1995) uses the first definition to compute factor
endowments and measures abundance by the number of factors for which the
true factor abundance is positive. He finds that rich countries tend to be
scarce in all factors, while poor countries tend to be abundant in all factors.
Our results are different and they do not contain the addressed "anomaly".
An important contribution of this study was to verify one of the ranking
propositions based on the value version of the HOV model. Proposition
1 holds for more developing than developed countries. As expected, the
developing countries are revealed both by their trade and factor endowments
to be relatively better endowed with low- than with high-skilled labor, while
the opposite is true for the developed countries. All the countries for which
Proposition 1 holds are revealed to be better endowed with high- or lowskilled labor than with capital. Greece, Portugal and Spain behave in this
respect like developing, rather than developed countries.
When defining factor intensity as the factor cost share per unit value of gross
output, it was found that there is no factor intensity (skill, low- and highskilled labor) reversal across countries, at least for a sub-sample of countries.
As these countries belong to different diversification cones, this conclusion
might be extended to all the countries in the sample. This is an important
result, as previous empirical studies report the presence of factor intensity reversal, when defining factor intensities by unit factor requirements. However,
CHAPTER 9. CONCLUSIONS
141
even though statistically significant, the computed correlations are rather far
from being 1. There are important differences especially in the capital cost
shares across countries, and therefore the sign and the significance of this
variable in the present analysis, at least for the countries with reported differences in this respect, should be treated cautiously. A model allowing for
non-neutral technological differences, as developed in Section 3.1, would be
more useful. Unfortunately, the required data were not easily available.
Multiple correlations do not seem to bring a lot of notable new facts into the
analysis. Cross-country regressions were performed for each country in the
sample, for two specifications of the independent variables. The dependent
variable, net exports, was adjusted for trade imbalance and scaled to correct
for heteroskedasticity. Usually the signs of the estimated coefficients were
as expected. Better results in terms of R2 and the significance of the variables were observed for developing countries and Germany. The ratio of the
statistically significant estimated coefficients for both low- and skilled-labor
is 2 to 1 in favor of the developing countries (as for the first specification).
For the second specification, there were more countries for which capital was
significant and positively correlated with net exports for all the developing
countries. For almost one third of the countries, mainly developed, the coefficients were not jointly statistically significant.
We found that not only is capital less important in determining the countries
trade patterns, but also is its role ambiguous. This last result may provide
an explanation for the inconsistency found in repeated empirical studies with
regard to this factor (e.g., Leontief Paradox). Also, adjusting capital for
taking into account the existence of foreign direct investment flows does not
qualitatively change the results.
Balassa (1979) proposes an "external validation" step, namely regressing the
coefficients obtained in the first OLB stage on the relative abundance of
factors in a cross-country regression. There are several problems with this
approach. First, the correlations between the direct factor cost shares for
the US and other countries, even though many are statistically significant,
are far from being perfect. Given the high correlations observed, we may
consider the signs of the first-step estimation coefficients as reliable (though
not the values), at least for low- and high-skilled labor. When regressing
these coefficients on factor endowments in an inter-country framework, the
imperfections in the values of the first-step estimated coefficients become
more important.
Second, the only theory-based prediction which may be checked in an intercountry framework refers to a relationship either between the first-stage estimated coefficients only, for each factor separately, or between the first-step
estimated coefficients and all factor endowments. However, the theory does
not predict any relationship between the first-stage estimation coefficients
and the relative factor endowment earnings, when scaled rather than net ex-
142
CHAPTER 9. CONCLUSIONS
ports are used. Hence, none of these conditions can be verified, as scaled net
exports were used in the analysis. Instead, it was checked whether the signs
of the first-step estimation coefficients replicate those of the relative factor
endowments. Once again, the results are sensitive to the way in which we
define the factor abundance. As in the case of the simple correlations, the
best results in terms of sign matches are observed for the low-skilled labor
when defining the endowments as usual. The dominant role of this particular factor may partly depend on its low degree of international mobility,
which is an important assumption of the standard HOV model. However,
when factor endowments are adjusted for international differences in factor
productivities, better results are obtained for high-skilled labor
It was also checked whether the estimated coefficients are significantly different across countries. Based on Hsiao (1986), an analysis of covariance to test
the homogeneity of cross-industry parameters (coefficients and intercepts)
across countries was undertaken. For both specifications of the regression
equation, we may reject at the 1% level of confidence both the hypothesis of
equal intercepts and slopes, and that of heterogeneous intercepts and equal
slopes.
The same estimation exercise was repeated for the model that allows for the
presence of economies of scale and product differentiation. There were no
important changes in the signs and the significance of the variables, except
that for the second specification capital became even less important in determining the countries' trade patterns and was relatively more important
for developing countries. When using an instrumental variable estimation,
we noticed few changes in the signs, primarily in the signs of the statistically
insignificant coefficients. In comparison with the results of the OLB estimation, R2 was usually lower (higher) for the first (second) specification. There
were quite fewer developing countries with a statistically significant coefficient for low-skilled labor, and fewer developed countries with a significant
coefficient for high-skilled labor and capital. As for the pattern of exports,
the signs were usually those reported for net exports, while being the opposite
for imports.
An encompassing test was undertaken to check whether either the perfect
competition or the scale economies models encompassed the other. This encompassing test was done for both specifications of the independent variables,
using both estimations of the mark-ups or the instrumental variable. If we
consider that the instrumental variable estimation yields more reliable results,
then we may conclude that, as for net exports, the presence of economies of
scale does not explain anything which is left unexplained by the perfect competition model. Hence, an alternative model which performs better than the
original HOV, developed in a perfect competition framework, was not found.
Put together, these results suggest that more detailed production and factor input data by industry and country are required to make more precise
statements about the role of scale economies and imperfect competition.
Appendix A: The Sample
of Countries
Developed countries (abbreviations) in the sample:
Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany,
Greece, Ireland, Israel, Italy, Japan, the Netherlands, New Zealand, Norway,
Portugal, Spain, Sweden, Switzerland, UK, US.
Developing countries in the sample:
Argentina, Brazil, Chile, Colombia, Egypt, Guatemala, Hong Kong, India,
Indonesia, the Ivory Coast, Kenya, Korea, Kuwait, Malaysia, Mexico, Morocco, Pakistan, Peru, Philippines, Singapore, Thailand, Tunisia, Turkey,
Yugoslavia.
Appendix B: Concordance
Between the US Standard
Industrial Classification
(SIC) and the Standard
International Trade
Classification (SITC
Revised 2)
APPENDIX B
146
SIC 1987
281 exc. 2819, 2865, 2869, 2895
285, 2893
3952
283
2861, 2891, 2892, 2899
2844
2841, 2842, 2843
2873, 2874, 2875
2821, 2822, 2823, 2824
2879
311
313, 319
301
2421, 2426, 2429, 2431, 2435, 2436,
2439, 2491, 2493
2441, 2448, 2449, 2451, 2452, 2499,
2517
262, 263, 2671, 2672, 2679, 2796
2673, 2674, 265
2675, 2676, 2677, 2678, 276, 2782, 3955
221-4, 2257-8, 2261-2, 2269, 227, 2281,
2282,2284,2295,2297-9,2391-7,2399,
3996
2296
3274, 3292
324
328,3295
3255
3251, 3253, 3259, 3261
3271-3, 3275, 3291, 3296-7, 3299
321, 3229, 323
3221
3262-3, 3269
3312-3,3315-7,3398,3497
3491-2, 3494, 3498
332,3462
3441-2, 3444, 3448-9
3411-2, 3443
3451-2, 3495-6
3423, 3425, 3465, 3542, 3544-5, 3953
3421
3431-3, 3631
3429, 3446, 3466, 3469, 3471, 3479, 3493,
3499,3965
3511
3724, 3764
3621
3523-4
3531-3
SITC Rev.2
511, 512, 513, 514, 515,
516, 522, 523, 524, 531, 532
533.(1,2,4)
533.5
541 exc.541.9
551, 572, 592.2, 598.(1,2,3,9)
553
554,592.1
562
582, 583, 584, 585
591
611
612
625
634
633,635
641
642,1
642 exc. 642.1
651, 652, 654,
655, 656, 657, 658,
659
653
661.(1,8), 663.8
661,2
661.3
662,3
662.4, 812.2
663 exc. 663.8
664
665
666
671, 672, 673, 674,
675, 676, 677, 678 exc. 678.5
678.5
679, 737.1
691
692,718.7
693,694
695, 736 exc. 736.1
696
697,812.1
699
711, 712, 714, 718.8
713
716
721,722
723
APPENDIX B
(cont.)
SIC 1987
3553
3552, 3582
3559
3554
3555
3556
3541
3548-9
3585, 3589
3567, 3569, 3821
3561, 3563, 3586
3564
3537
3534-6
3547, 3565, 3581, 3593-4, 3596
3592
3562, 3566, 3568
3053, 3543, 3599
3579
3578
3571
3572, 3575, 3577
3651
3661
3612
3629, 3672, 3675-9
3613, 3625, 3643-4
3845
3844
3633
3632
3634-5, 3639
3671, 3674
3691-2
3641
3694
3264, 3663, 3669, 3699
3624
3546
3711
3714
375,3799
3713, 3715, 3716, 3792
374
3721, 3728, 3769
3731-2
3645-8
2511
2515, 2521-2
147
SITC Rev.2
724,3
724 exc. 724.3
728
725
726
727
736.1
737.3
741.(3,4)
741 exc. 741.(3,4),743.(3,5,9)
742,743.(1,2)
743.(4,6)
744.1
744.(2,9)
737.2, 745.2
749.2
749.(1,3)
745.1,749.9
751.1
751.2
752
759
761,762,763.1,764.2
764,1
771,1
771.2, 772.(2,3), 778.84
772.1, 773
774.1
774.2
775.1
775.2
775 exc. 775.(1,2)
776
778.1
778.2
778.31
764.(3,8,9), 778.32, 778.8
exc. 778.(84,87)
778.87
778.4
781, 782, 783
784
785
786
791
792
793
812.4
821.1
821.2
APPENDIXB
148
(cont.)
SIC 1987
2512, 2519, 253, 2541, 2591, 2599
316,3171-2
2514,2542
2251-4, 2259, 231-8, 315, 3999
302
3142-4, 3149
3826-7
3841-3
381, 3822-5, 3829
386
385
387
2731-2, 274, 2789
271-2
275,277
2591, 3052, 306, 308
3942, 3944, 3949
3951
2791
3911, 3914-5, 3961
393
3652,3695
3991
SITC Rev.2
821.9 exc. 821.(91,99)
831
821.(91,99)
842, 843, 844, 845, 846,
847, 848
851.01
851 exc. 851.01
871,884.1
541.9, 872, 899.6
873,874
751.82, 763.8, 881, 882, 883
884.2
885
892.1
892.2
892.(4,8)
621,628,893
894
895.2
895 exc. 895.2
897
898.(1,2,9)
898.3
899.7
List of Symbols
a) Superscripts:
• i, j, 9 countries,
• w world,
• f
final demand,
• h, l input factors,
• v value term,
• A adjusted,
•
I
transpose of a matrix,
• l labor,
• u low-skilled labor,
• s high skilled-labor,
• k capital,
• T total.
b) Subscripts:
• k firm,
• i industry,
• w variety of a differentiated product,
• f
factor content,
• q intermediate.
150
LIST OF SYMBOLS
c) Matrices:
• I n
• AV
* n identity matrix,
n * n input-output matrix,
with elements indicating the value of
output a particular industry must buy from each other industry to
produce one dollar of final demand of its own product,
• R m * n matrix of direct factor requirements, with elements r showing
the quantity of each direct factor input required to produce a unit of
gross output in a particular industry,
* n matrix of the total (direct and indirect) input factor requirements, with elements showing the total requirement of each factor input
per unit value of final demand in each industry,
• RT m
• e m *n
matrix of direct factor cost shares (the CD parameters), with
elements () representing the value of each factor in a dollar value of
gross output of each industry,
• W m
*m
diagonal matrix of factor prices,
* n diagonal matrix of commodity prices,
• (3 n * n diagonal matrix of mark-up prices,
• n m * m diagonal matrix, with entries showing the non-neutral adjust-
• P n
ment on direct factor cost shares.
d) Vectors:
* 1 vector of gross output produced,
• c n * 1 vector of final consumption,
• t n * 1 vector of net trade,
• z n2 * 1 vector of exports of the differentiated products,
• m n2 * 1 vector of imports of the differentiated products,
• i n2 * 1 vector of intra-industry trade in the differentiated products,
• v m * 1 vector of factor endowments,
• v m * 1 vector of factor demand,
• ¢>(w,p) n * 1 vector of unit production costs,
• w m * 1 vector of factor prices,
• x n
LIST OF SYMBOLS
• X n2
151
* 1 vector of fixed costs in the IRS industries,
* 1 vector of expenditures,
N n2 * 1 vector of the number of varieties of the differentiated product,
p n * 1 vector of commodity prices,
a 8 n * 1 vectors of regression coefficients,
j.L, nu n * 1 vectors of error terms.
• en
•
•
•
•
e) Other symbols:
• s ratio between a country's domestic absorption and world income,
• y GNP,
• b trade balance of a country,
• K capital endowment of a country,
• t k net exports of capital of a country,
• F( v) production function,
•
Ui (.)
subutility function derived from the consumption of product i,
• U upper tier utility function,
• a constant elasticity of substitution between pairs of varieties of the
same differentiated product,
•
E
external economies of scale in the IRS industries,
• m number of input factors,
• n number of industries,
• N number of firms,
• c number of countries.
List of Abbreviations
Arg Argentina
Aus Australia
Aua Austria
Bel Belgium
Bra Brazil
Can Canada
Chi Chile
Col Colombia
Den Denmark
Egy Egypt
Fin Finland
Fra France
Ger Germany
Gre Greece
Gua Guatemala
HK Hong Kong
Ind India
Ins Indonesia
Ire Ireland
Isr Israel
Ita Italy
Ivo the Ivory Coast
154
Jap Japan
Ken Kenya
Kar Korea
Kuw Kuwait
Mal Malaysia
Mex Mexico
Mor Morocco
Net the Netherlands
Zea New Zealand
Nor Norway
Pak Pakistan
Per Peru
Phi the Philippines
Par Portugal
Sin Singapore
Spa Spain
Swe Sweden
Swi Switzerland
Tha Thailand
Tun Tunisia
Tur Turkey
UK the UK
USA the US
Y ug Yugoslavia
LIST OF ABBREVIATIONS
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Weltwirtschaftliches Archiv, Band 130 (1), 20-49
Ohlin
a
Chance!
[88] Wood, A. (1994b): North-South Trade, Employment and Inequality.
Changing Fortunes in a Skill-Driven World. Clarendon Press, Oxford
[89] Wood, A. (1995): How Trade Hurt Unskilled Workers. Journal of Economic Perspectives 9, no. 3, 57-80
[90] World Bank: World Tables of Economic and Social Indicators. Washington, different issues
[91] Zellner, A. (1962): An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias. Journal of the American Statistical Association 57, 348-368
Index
capital
cost share, 76,84,91,94,118123, 128, 141
humall, 64, 70--76, 78, 88
cost shares, 76
international mobility, 2, 9, 11,
30--33, 41, 50, 53, 63, 71
stock, 86, 87
Cobb-Douglas, 9
parameters, 18, 26
preferences, 44
production functions, 18, 26
technology, 9, 18, 19, 31, 44,
118
comparative advantage, 1,2,9,20,
23, 27, 31, 47, 68-78
constant elasticity of substitution,
24, 150
economies of scale, 2, 3, 8, 9, 11,
23, 24, 27, 28, 30, 32, 49,
53, 58, 59, 63, 64, 70--72,
75-77,79,81,83,84,106,
126, 132, 140, 142, 143
external, 29, 30, 150
internal, 23, 25, 53, 84
international, 23, 30
national, 23
external validation, 44, 47-49, 53,
82, 83, 97, 102, 105, 106,
123, 125, 139, 141
factor content, 8, 13, 19, 28, 36,
39-41,61-63,66,72,114,
148
adjusted, 39-41, 73
equation, 11, 27, 53
quantity version, 11, 17
value version, 11
of exports, 27, 64
of imports, 27, 64
of intra-industry trade, 28
of trade, 1,8,9, 11, 13, 17-19,
22, 30, 31, 35-38, 41, 43,
61,62,66,81,82,95,114
studies, 62
theorem, 65
factor intensity reversal, 3, 58, 118,
119, 141
factor price equalization, 2, 9, 1618, 20, 21, 37, 43, 57, 61,
63, 96
factor proportions, 2, 74, 75
theory, 1, 2, 9, 10, 13, 23, 35,
44, 45, 49, 50, 62, 75, 83,
84
foreign direct investment, 2, 11,30,
32, 73, 78, 92, 102, 106,
114, 140, 141
Heckscher-Ohlin (HO), 1
-Vanek,13
theory
generalization, 8
HOV
generalization, 11, 21, 35, 36,
42
quantity version, 9,13,17,18,
37, 41, 57, 58, 61, 63, 64,
95,96
value version, 3, 9-11, 18-20,
32, 37, 38, 45, 53, 57, 58,
164
INDEX
63, 81, 93, 95, 96, 114,
140
imperfect competition, 10, 65, 143
increasing returns, 9-11, 23, 24,
29, 41, 50, 53, 85, 135
external, 28
internal, 50, 126
labor, 148
high-skilled, 3, 58, 88, 93, 95,
97,99,102,103,105,106,
111-116, 118, 119, 123,
125, 132, 134, 136, 139142
cost shares, 71, 76, 84, 91,
94, 95, 98, 99, 118, 120,
121
endowment, 87, 88, 93, 109,
111
low-skilled, 3, 58, 67, 88, 9397,99,101-103,105,109,
110, 113, 114, 116, 118,
123, 125, 132, 133, 136,
139-142, 148
cost shares, 71, 84, 91, 94,
95, 98, 99, 118, 120, 121,
139
endowment, 87, 88, 93,109,
111
Leontief Paradox, 1, 7, 8, 37, 63,
71, 72, 74, 75, 141
monopolistic competition, 27, 33,
83
perfect competition, 2, 3, 7, 8, 11,
16, 17,26,28-30,32,36,
41,42,45,58,84,85,106,
120, 126, 127, 132, 142
preferences, 24, 68
Armington, 32
Cobb-Douglas, 44
homothetic, 7, 8, 24, 53, 68,
83
identical, 7, 8, 24, 26, 53, 68,
83
weak separability, 24
product differentiation, 2, 3, 8-11,
23, 27, 28, 32, 33, 41, 49,
50, 53, 58, 59, 63, 70, 79,
81, 83-85, 91, 106, 126,
132, 135, 140, 142
degree of, 76
ranking proposition, 2, 3, 35-41,
50, 58, 82, 96, 114-116,
140
quantity version, 39-41
regression analysis, 44, 45, 72, 84,
85, 126
cross-industry, 10, 11, 44, 72,
74
multiple, 45
second step, 59
theory-based, 58
simple correlations, 35, 36, 42, 43,
58,75,81-83,96,97,100,
119, 132, 139
sign, 44, 96, 97, 99, 102, 108,
111-113, 125, 142
size, 97
technology, 18, 19, 25, 53, 66
-gap, 77
-neo,76
Cobb-Douglas, 9, 18, 19, 31,
44,118
homothetic, 29
identical, 7
matrix, 17
parameters, 20, 22, 69, 81, 85,
93, 118, 123
US, 17,22