In a piece for Bloomberg, Noah Smith wrote:

No. 9. The Heckscher-Ohlin theorem

This is a theory about trade. It says that countries with more capital — industrialized countries such as the U.S. or Japan — will tend to make things that are more capital-intensive. And countries with more labor — such as India — will tend to make things that are more labor-intensive. That’s why the U.S. makes a lot of semiconductors (which require huge fabrication plants), and India makes a lot of clothes.

Tyler Cowen says Noah Smith oversimplified/misrepresented the theorem. He raises four objections, concluding with:

I continue to believe most economists don’t have such a clear sense of the Hechscker-Ohlin theorem. There are so many tricks to HOT I wouldn’t be surprised if I slipped up somewhere myself in this post.

Indeed, I do think Tyler slipped up a bit. He’s right that identifying “effective units” of capital and labor is the relevant exercise and also very difficult (objection #2), and of course the Heckscher-Ohlin theorem is all about ratios, not absolute quantities (objection #3).¹

But I want to defend Noah a bit from Tyler’s first complaint, which was:

The HOT proposition is about exports being relatively capital- or labor-intensive, not about production per se. Even for a popular audience, I think that substitution should have been easy enough.

Is that so? Here’s how Ron Jones and Peter Neary stated the theorem in question in their 1984 Handbook chapter, which surely was not aimed at a popular audience:

Heckscher-Ohlin theorem. A country has a production bias towards, and hence tends to export, the commodity which uses intensively the factor with which it is relatively well endowed.

Why does production composition determine net export composition in this model? Well, the factor-abundance theory is a story about economies’ endowments determining the pattern of trade. To talk only about endowments (and thus only about supply-side elements), we have to neuter demand by assuming identical, homothetic preferences.² Given commodity-price equalization and homothetic preferences, each country has a consumption vector that is proportionate to its share of world income. With no differences in the composition of consumption, differences in the composition of production translate into differences in the composition of net exports, which are simply production minus consumption.

Thus, the prediction about the pattern of trade simply falls out of the prediction about the pattern of production. Here’s how Jones and Neary explained it:

The final core proposition is the Heckscher-Ohlin theorem itself, but this in fact is closely related to the Rybczynski theorem. Consider two countries with different relative factor endowments and the same technology for producing both goods. If both countries face the same commodity prices then, by the Rybczynski theorem, the country with the greater relative endowment of capital will produce relatively more of the capital-intensive good… Provided this production bias is not offset by a demand bias, the relatively capital-abundant country will export the relatively capital-intensive good. When it is expressed in terms of a physical definition of factor abundance, the Heckscher-Ohlin theorem is thus a simple corollary of the Rybczynski theorem…

In terms of the canonical theorem, I think that Noah got that part right. And in a meta sense, Tyler was right as well.

1. When he cites the Leontief paradox, he’s getting into more complicated territory, see Leamer (JPE 1980).
2. In reality, of course, I think that the composition of demand matters!