The Heckscher-Ohlin-Samuelson Theory of Trade

It is somewhat ironic that, following Heckscher’s lead and despite Ohlin’s objection to the term comparative advantage, Ohlin ultimately provided the first book-length analysis of the causes of comparative advantage based on international factor endow­ment differences and differential factor intensities across commodities.

The very general nature of Ohlin’s formal trade model presented Samuelson (1948 and 1949, preceded by the Stolper and Samuelson paper of 1941) with a golden oppor­tunity to create a scaled-down version capable of throwing greater light on the factor endowments theory. This was a two-by-two-by-two (or 2 ? 2 ? 2) model featuring two countries, two commodities and two factors of production. Looking back on these contributions 50 years later, Samuelson interpreted his simplification of Ohlin’s model as “bringing it out of the realm of n + m equations and n + m unknowns to the beauti­fully simple diagrams of land and labour, cloth and corn.

when differential factor endowments are the main explanation of trade flows. However, on the theoretical side the H-O-S model is built on the following restrictive assumptions that are taken to be valid for both trading countries, and most of which would have been rejected by both Heckscher and Ohlin:

• its limited 2 ? 2 ? 2 structure, although extensions are possible with varying degrees of difficulty to more than two goods, factors or commodities;

• commodities and factors of production are qualitatively identical;

• production functions are identical and display constant returns to scale;

• commodities differ in their factor intensities so that one commodity uses inten­sively the same factor at all factor price ratios;

• there are zero transport costs, no trade impediments, and perfect competition in commodity and factor markets;

• factors of production are inelastically supplied, perfectly mobile among economic sectors, but internationally immobile;

• relative factor endowments (such as land-labour ratios) are unequal, so that one country is (say) relatively land-abundant while its trading partner is labour-abundant;

• demand functions are identical and homothetic, so that commodities are bought in the same proportions by all consumers at any given price ratio regardless of their income, in violation of Engel’s law.

While some of these assumptions can be relaxed, others are much harder to generalize. The Samuelsonian strong factor-intensity assumption implies that there are no factor­intensity reversals, so that a commodity cannot be labour intensive at one set of factor prices and land intensive at another set.

Given these assumptions, the H-O-S theory yields four main propositions in the form of theorems initially proved for the 2 ? 2 ? 2 case, although some can be generalized to higher dimensions. The Heckscher-Ohlin theorem states that the country abundant in a particular factor exports the commodity that intensively uses that factor and imports the other commodity. According to the Stolper-Samuelson theorem, an increase in the relative price of a good increases the real wage of the factor used intensively in produc­ing that good and lowers the real wage of the other factor. Provided that neither country specializes in its export commodity, the factor price equalization theorem states that trade equalizes both relative and real factor prices in the two countries. The Rybczynski theorem proves that if commodity prices are held constant and one factor expands, the output of the commodity that intensively uses that factor expands in a greater proportion, while the output of the other commodity actually declines.

These theorems constitute the four legs of the stool supporting the H-O model. Leontief (1954 [1968]) provided the first empirical test of the H-O theory using an input-output table of the US economy for 1947, and reached unexpected and discon­certing results. His test limited the factors of production to two, capital and labour, but extended to hundreds the number of export and import-competing commodities whose factor intensities he measured. Contrary to the general impression of economists and public opinion that the US immediately after World War II was the world’s most capital-abundant economy, Leontief discovered that on average it exported labour­intensive and imported capital-intensive commodities! His finding became known as the Leontief paradox, and unleashed a torrent of papers that either attempted to explain what appeared to be a flagrant violation of the first theorem of the H-O model, or claimed that Leontief’s test was invalid.

Recent tests of the factor endowment model followed Leontief’s suggestion and aban­doned the H-O-S assumption that factors are qualitatively identical in different coun­tries. The endowment of a given factor in a country is “corrected” by multiplying it by its estimated productivity so as to arrive at a stock labelled the country’s “effective factor endowment”. However, other serious concerns were voiced regarding the viability of even a modified H-O model as an explanation of most international trade flows. Despite the factor endowments of the industrialized countries being fairly similar, large and increasing amounts of trade were observed to occur among them rather than between industrialized and less developed countries with radically different relative factor endow­ments, as the H-O-S theory would predict. Economists began to search for alternative explanations of trade that incorporated features such as product differentiation and intra-industry trade. Their very existence could not be accommodated by the H-O-S theory, one of whose basic assumptions is that commodities and factors of production are homogeneous. The perceived inadequacies of a theory of trade crucially based on international factor endowment differences eventually gave birth to the new paradigms of trade explored next.