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An Inframarginal Analysis of the Heckscher-Ohlin Model with Transaction Costs and Technological Comparative Advantage* Wenli Cheng
Abstract: In the paper we introduce technological comparative advantage and transaction costs into the Heckscher-Ohlin (HO) model and refine the HO theorem, the Stolper-Samuelson theorem, the Rybczynski theorem, and factor price equalization theorem. The refined core theorems can be used to accommodate recent empirical evidence that is at odds with the core theorems.
This paper introduces technological comparative
advantage and transaction costs into the Heckscher-Ohlin model and
refines the four core theorems in trade theory, namely, the Heckscher-Ohlin
(HO) theorem, Stolper-Samuelson (SS) theorem, factor price equalization
(FPE) theorem, and Rybczynski (RY) theorem . In the standard HO model, it is assumed that
trading countries share identical technologies. This assumption is
obviously inconsistent with empirical observation, and it has contributed
to the poor empirical performance of the HO theorem. According to
Trefler (1995), the HO theorem is consistent with empirical findings
only 50% of the time. Despite the unsatisfactory performance, the
HO theorem has retained its dominance in international economics simply
because economists have not found anything that performs better (Bowen
et. al., 1987). There are several lines of research that might
accommodate the new empirical evidences. Leontief (1953) suggested
to introduce technological differences between countries into the
HO model to accommodate observations. Trefler (1995) demonstrated
empirically that a modification is desirable that allows for consumption
bias and technology difference between countries. Bhagwati and Dehejia
(1994, pp.39, 42) indicate that the assumptions of the SS and FPE
theorems remain so extraordinarily demanding that they cannot be taken
seriously as the major theoretical construct justifying fears in industrial
countries that trade with developing countries will undermine the
wages of unskilled labor. They note that considerable analytical work
was devoted to showing why FPE seemed to be frustrated in reality.
They suggest three ways to invalidate the SS theorem and FPE theorem.
One is to consider the equilibrium that occurs outside of the diversification
cone and discontinuous jumps of equilibrium between different patterns
of specialization. Another is to consider the CES production function.
In the face of a sufficiently large shift in relative factor prices,
goods could switch over from being intensive in one factor to being
intensive in the other (factor reversal). Finally, scale economies
could be another reason for de facto differences in technology and,
in particular, could invalidate the SS theorem, causing both factors
real wages to rise (p. 44) as scale efficiencies from trade swamp
adverse effects on the scarce factor. Leamer (1999) and the current paper substantiate
Leontief's suggestion and the first method suggested by Bhagwati and
Dehejia. Both papers introduce technology differences between countries
to the traditional HO model. However, Leamer assumes the Leontief
production functions with zero elasticity of substitution between
capital and labor, while we assume the Cobb-Douglas production functions.
We shall show that if the trading countries differ in both productivity
and factor endowments or transaction costs are considered, the equilibrium
trade pattern may be opposite to what the traditional HO theorem or
the SS theorem predicts; and we shall propose a refined HO theorem.
Recently reviving interests in the effects
of international trade on domestic income distribution (see, for instance,
Krugman, 1995, Sachs, 1996, Feenstra, 1998, and Williamson, 1998,
Cline, 1997) motivate our refinement of the SS theorem in an extended
HO model. The SS theorem shows that tariffs can be used as an instrument
to improve domestic income distribution (Samuelson, 1953). However,
our extended model shows that within a certain parameter subspace,
the common sense might be closer to reality than the SS theorem. The
common sense indicates that tariff and associated transaction costs
may marginally improve domestic income distribution, but it may inframarginally
cause the general equilibrium to jump from a trade structure with
high trade dependence and high productivity to a structure in which
productivity is low and home residents receive little gains from trade.
The net effect of the transaction cost depends on whether the marginal
effect dominates inframarginal effect. The four core theorems are derived from the
traditional 2 2 2 HO model. The model has some standard neoclassical
assumptions (such as perfect competition and constant return to scale)
and several somewhat restrictive assumptions (which will be discussed
later). Given the assumptions, the theorems do not require specific
functional forms; yet, they are able to identify several regularities
in general equilibrium comparative statics. But our extended model explicitly specifies
the Cobb-Douglas utility and production functions. There are two reasons
for assuming specific functional forms. First, the trade off between
tractability, generality of functional forms, and generality of other
aspects of the model implies that introduction of technological comparative
advantage and transaction costs must be at the cost of generality
of functional form. Second, a well-known theorem in general equilibrium
theory states that in the absence of explicit model specifications,
we can say nothing about the properties of the equilibrium comparative
statics except that Walras' law holds, and that the excess demand
function is homogenous of degree zero (See Sonnenschein, 1973, Mantel,
1974, and Debreu, 1974). We will use the HO model with Cobb-Douglas
utility and production functions to show that some of the core theorems
may not hold even in the original HO model with no technological comparative
advantage and transaction costs. This confirms Sonnenschein, Mantel,
and Debreu's "everything possible theorem." When some economists prove the SS and RY theorems,
they assume that the equilibrium prices of goods can be treated as
exogenous. Sometimes the equilibrium prices of factors are treated
as exogenous when the HO theorem is proved (Dixit and Norman, 1980
and Jones, 1965). Since exogenous product or factor prices exclude
from the analysis the interactions between prices and other parameters
(such as endowment), the general equilibrium comparative statics become
less unambiguous. However, it is unjustified to assume exogenous prices
of goods or factors in a general equilibrium model for the same reason
that perfect competition (price taking behavior) cannot be used to
justify exogenous equilibrium prices in a general equilibrium model.
In this paper prices of goods and factors in the HO model are endogenously
determined. With endogenous prices, the core theorems of trade theory
may or may not hold; certainly they cannot be derived in the same
way as in the traditional way. As depicted in Figure 1, there are 8 possible
trade structures in the HO model. Only the first 2 structures involve
incomplete specialization for both countries. The last 6 structures
involve complete specialisation in at least one country. We can refer
to the first 2 structures as interior structures since the output
choices of each goods for both countries are strictly positive, ie,
they are based on interior solutions. And the last 6 structures can
be referred to as corner structures as at least one country chooses
zero value of output level of one good, ie, corner solutions are involved.
To find the general equilibrium of the model,
we need to know which of the 8 structures (or trade patterns) occurs
within which parameter subspace and also the prices and quantities
in that structure. Correspondingly, the comparative statics analysis
of general equilibrium should investigate not only marginal changes
of quantities and prices in response to parameter changes within each
structure, but also inframarginal changes (discontinuous jumps) of
trade patterns across structures as parameters reach some critical
values (or as parameter values shift between parameter subspaces that
demarcate the structures). The comparative statics that relate to
changes within a given structure are referred to as marginal comparative
statics and those related to changes between structures are referred
to as inframarginal comparative statics. For some purposes, inframarginal comparative
statics are more important than marginal comparative statics since
the latter involve only marginal changes in quantities and prices
within a trade structure, while the former involve discontinuous jumps
of all endogenous variables including prices and quantities as well
as changes of trade structure. For instance, marginal comparative
statics may indicate that a tariff benefits labor which is a scarce
factor in home country, but inframarginal comparative statics may
indicate that the tariff may cause inframarginal jump of trade structure,
so that the cost of the tariff to workers may outweigh its benefit. In some work, inframarginal changes of trade
structure (for instance, shifts of equilibrium from or to the diversification
cone) are explained by changes in prices. Since comparative statics
of general equilibrium explain changes of equilibrium values of all
endogenous variables including prices by changes in parameters, it
is not legitimate to explain inframarginal changes of trade structure
by changes in prices which themselves should be explained by parameter
changes. In this paper, we will explicitly solve for inframarginal
comparative statics of general equilibrium by partitioning parameter
space into subspaces. The parameter subspace within which an unambiguous
negative sign of the derivative of the equilibrium value of an endogenous
variable with respect to a parameter occurs may have no intersection
set with the parameter subspace within which the trade pattern concerned
occurs in general equilibrium. This implies that identifying the sign
of the derivative is not enough and the partition of the parameter
space is essential for working out the comparative statics of general
equilibrium. But the implications of the partition of the parameter
space did not receive deserved attention when the four core theorems
were proved. The main findings of this paper are: (1) the
HO theorem continues to hold when prices of goods and factors are
endogenized and inframargianl comparative statics of general equilibrium
are considered, though it needs to be refined when transaction costs
or differences in technology are introduced; (2) the SS theorem remains
valid within the diversification cone if the changes in prices are
due to a change in taste or endowment, but no longer holds if the
changes in prices are due to changes in production or transaction
cost parameters; (3) the part of the RY theorem which states that
an increase in a factor endowment leads to an expansion of the sector
that uses the factor intensively remains valid, but the other part
which states that such an increase leads to a contraction of the other
sector is no longer true; (4) the factor price equalization theorem
does not always hold within the diversification cone if transaction
costs and differences in technology are introduced. The rest of the paper is organized as
follows. Section 2 presents the HO model that incorporates technology
differences and transaction costs and checks the validity of the HO
theorem. Section 3 discusses the concept of the diversification cone
and analyzes the conditions for factor price equalization in the extended
model. Sections 4 and 5 check the Stolper-Samuelson theorem and the
Rybczynski theorem, respectively, in the extended model. Section 6
analyzes effects of the introduction of transaction costs on the core
theorems. Section 7 concludes the paper. Inframarginal Economics Society www.inframarginal.com
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