Munich Personal RePEc Archive
Factor Endowment, the Choice of
Technology, and the Volume of Trade
Zhou, Haiwen
2007
Online at https://mpra.ub.uni-muenchen.de/76424/
MPRA Paper No. 76424, posted 27 Jan 2017 08:42 UTC
Factor Endowment, the Choice of Technology, and the Volume
of Trade
Haiwen Zhou
1
Abstract
This paper studies impacts of factor endowment on international trade in a general
equilibrium model in which firms choose their technologies endogenously. Though
countries only differ in factor endowment ex ante, countries may also differ in their chosen
technologies. If industries choose different capital-labor intensities in equilibrium, the
Heckscher-Ohlin theorem, factor price equalization theorem, the Rybczynski theorem, and
the Stolper-Samuelson theorem hold. If industries choose the same capital-labor intensity
in equilibrium, the volume of trade is zero. None of the four theorems applies.
Keywords: Choice of technology, factor endowment, factor price equalization, Heckscher-
Ohlin model, volume of trade
JEL Classification Numbers: F10, O33
1. Introduction
The Heckscher-Ohlin (HO) paradigm was originated by Heckscher (1919) and
elaborated by his student Ohlin (1933), an eminent scholar and politician. A formal
presentation of the two-factor, two-goods model is provided by Samuelson (1948, 1949)
and the multiple-factor and multiple-goods version of the model (the HOV model) is
studied by Vanek (1968). The HO theorem argues that a country will export the product
that uses its relatively abundant factor more intensively. Starting with Leontief (1953), this
hypothesis has been subjected to extensive empirical testing. Overall, empirical
performance of the model is unsatisfactory. Staiger (1988, p. 129) views that the bulk of
the empirical evidence suggests that factor content of trade as a linear function of national
and world endowment is not an empirically reliable description of the pattern of
international trade. Similar opinions have been expressed by Maskus (1985), Bowen et al.
(1987), and Trefler (1995). In Trefler (1995), it is also found that the volume of trade is
much lower than the level predicted by the HO theorem.
The HO paradigm has some charming features. First, the HO model is intuitively
appealing. For example, Kuwait exports oil mainly because it is well endowed with oil.
1
I thank Constantine Angyridis, Ingrid Bryan, Michael Jolly, Sunwoong Kim, Leo Michelis, Deborah
Minehart, Amy Peng, Robert Schwab, and Daniel Vincent for their helpful comments. I also thank two
anonymous referees for helpful suggestions. The usual disclaimer applies.
1
Hong Kong SAR imports apples because it is not endowed with the type of climate to
produce apples. Second, the HO paradigm is versatile. In the Ricardian model, since labor
is the only factor of production, income distribution effects of trade are absent. As stressed
by Heckscher (1919), the HO framework is built to address the income distribution effects
of trade. The four main theorems of the HO paradigm: the HO theorem (Heckscher 1919,
Ohlin 1933), the factor price equalization theorem (Heckscher 1919, Samuelson 1948,
1949), the Stolper-Samuelson theorem (Stolper and Samuelson 1941), and the Rybczynski
theorem (Rybczynski 1955) address various issues, such as the impact of tariffs on factor
returns. The HO model is also rich in policy implications. As the HO model is a very
important vehicle for studies in international trade, the inconsistency between theoretical
studies and empirical evidence thus poses a theoretically significant and policy relevant
question: can the HO framework be reformulated to be consistent with empirical evidence?
One key assumption in the HO model is that countries employ the same production
technologies. This assumption is controversial as scholars are concerned with the empirical
validity of this assumption. While Heckscher (1919) is more willing to assume that
countries have the same technologies, Ohlin (1933) stresses differences in technologies
among countries as a cause of international trade.
2
Samuelson (1948, p. 181, 1949, p. 195)
is cautious about this assumption even though he makes this assumption explicitly.
3
Samuelson (1951-1952, p. 121) even views this assumption may have the impact of
“explaining nothing and possibly obscuring a great deal.” Empirical studies such as Bowen
et al. (1987), Trefler (1993, 1995), Davis and Weinstein (2001), and Schott (2003) have
consistently revealed that by allowing differences in countries’ technologies, the
performance of the HO model is improved.
One possible way to save the HO model is to drop the assumption of identical
production technologies. However, scholars may have reservations about using differences
in technologies together with differences in factor endowments to explain the pattern of
2
Heckscher (1919, p. 280) is aware that a tacitly made assumption in his paper is that “the same technique
is used to produce a given commodity in different countries”. For Ohlin (1933, p. 101), he writes “many
important articles are produced in various countries by means of widely different technical processes.”
3
With the assumption of identical technologies between countries, Heckscher (1919) and Samuelson (1948,
1949) find that international trade leads to equalization of factor returns. As Ohlin (1933) views that different
technologies are relevant, his opinion is that trade will lead to partial rather than full equalization of factor
returns.
2
trade. By assuming that countries have the same production technologies, the HO model
tries to isolate the impact of different factor endowments on the pattern of international
trade. Assuming differences in both factor endowments and technologies to explain the
pattern of international trade deviates from this spirit.
This paper studies the impact of factor endowment on international trade in a two-sector
general equilibrium model in which firms choose their production technologies
endogenously. In this paper, similar to the HO model, the only difference between the two
countries is their endowments of factors of production. It is assumed that different countries
have access to the same set of technologies. In each country, given the prices of factors of
production, firms choose their technologies. These technologies reflect the possibility that
there is some degree of substitution between capital and labor. A firm’s choice of
technology is affected by the prices of factors of production, which reflect the endowments
of factors.
The optimal choice of technologies leads to two possibilities. In the first case, the two
sectors have the same capital-labor ratio in equilibrium. None of the four theorems of the
HO model applies. In this case, though countries differ in their factor endowments, the
volume of trade of final goods is zero as the price ratio of final goods is the same in both
countries. Thus, one contribution of this paper is that it provides an explanation to Trefler’s
(1995) observation of “missing trade.” The intuition behind this case is that different factor
endowments between countries are totally absorbed by different technologies, rather than
by different price ratios of final goods. In the second case that the two industries choose
different factor intensities in equilibrium, it is shown that the four theorems of the HO
model are valid. Though countries only differ in factor endowment ex ante, countries will
also differ in their production technologies as countries choose different technologies in
equilibrium, regardless of whether industries choose the same factor intensity or not. Thus,
another contribution of this paper is that it shows technology is a channel through which
endowment differences affect the pattern of trade. With this indirect channel, the factor
content of trade may not be a linear function of national and world factor endowment.
Whether the two sectors choose the same factor intensity in equilibrium depends on the
specification of production technologies of the two sectors. The two sectors are more likely
3
to have the same factor intensity if they have similar degrees of substitution between capital
and labor. The degree of substitution of an industry can be measured by empirical studies.
Following Zhou (2004), the key assumption in this paper is that there are many different
technologies to produce the same product. Casual observation supports the empirical
validity of this assumption. An example is the technology for the production of agricultural
goods. In a developing country such as China, labor is used intensively in the production
of agricultural goods. In a developed country such as Canada, the production of agricultural
goods relies more on capital inputs, such as harvest machines. Though China and Canada
have access to the same set of production technologies, they choose different technologies
in equilibrium. Given China’s large surplus of workers and low wage rate, though harvest
machines are available in China, they are not adopted as it is more profitable to use labor
more intensively. Similarly, given the large amount of accumulated capital and high wage
rates, though agricultural goods in Canada could be produced by mainly employing labor,
it is more profitable to use capital more intensively.
In this paper, compared to a country with a lower capital-labor intensity, a country with
a higher capital-labor intensity substitutes labor by capital in production. The discussion of
the substitution between capital and labor on international trade goes back at least to
Heckscher (1919). Arrow et al. (1961) argue that this type of substitution is very important
in various fields of economics. Minhas (1962) formally explores the implications of this
type of substitution in international trade. Impact of the choice of technology is also studied
at Zhou (2007a, b). The innovation of this paper is that it connects the substitution between
capital and labor to the fundamental endowment of factors. Thus, by employing a simple
general equilibrium model, a third contribution of this paper is that it introduces a firm’s
endogenous choice of technology to the study of the impacts of factor endowments on
international trade.
The rest of the paper is organized as follows. This paper allows the production function
to be either of the constant returns to scale type or the increasing returns to scale type. The
basic model assumes perfect competition as Sections 2-4 study the case that the production
functions have constant returns to scale. Section 2 sets up the basic framework. In Section
3, as industries choose the same factor intensity in equilibrium, the four theorems of the
HO model do not apply. In Section 4, industries choose different factor intensities in