The Heckscher-Ohlin model, or where mathematics fails to meet the real world [en]

24 ottobre -



David Ricardo: why countries trade


In 1817 David Ricardo explained us why countries should trade. Long story short, according to Ricardo’s theory of comparative advantage, a country should produce and export those goods and services for which it is relatively more productive than other countries, and should import those goods and services for which other countries are relatively more productive.

This theory incorporates the concept of opportunity cost, as in the value of what is given up in order to get a good. In a situation of comparative advantage, a trade-off of this kind always takes place.

But what is the role of trade? The historical context matters: both Smith and Ricardo wanted to counter the prevalent mercantilist mind-set. According to Adam Smith, mercantilism, by avoiding imports, forces a country to squander its resources on goods that it is not suited to produce. By focusing on what it is relatively better at producing, a country could minimize the costs of mercantilism. This is why countries should trade – simply because it makes them better off.


It is important to underline that there is a difference between Smith’s view and Ricardo’s. The former is an advocate of the absolute advantage, whereby a country should export those goods and services for which it is more productive and import those for which other countries are more productive. Ricardo believed that this theory was flawed: if a country holds more absolute advantages than the other, he says, trade would be unequal and, in extreme situations, even may not take place. However, the notion of opportunity costs also works in an absolute advantage setting. Let us make an example: suppose a physician is good at her job. She’s also good at cutting the grass. So good, that in fact, she’s better than her fifteen year-old neighbour. However, she still pays him to cut the grass because focusing on her job would produce greater advantages not just for both, but also for the whole community. In fact, if the physician wasted her time by cutting the grass, she would have less time to devote to her patients. Applied to trade, this means that even if a country has absolute advantage to all the goods it produces, trade should still occur, in that the cost of maintaining both is higher than the cost of (that is, the profit gained at) excelling in one.



Heckscher and Ohlin: what countries trade and how


What neither Smith nor Ricardo tell us, however, is how countries should trade. Saying that a country will produce and export those goods in which it has a comparative advantage is not telling the whole story. In the first half of the past century, Eli Heckscher and Bertil Ohlin developed a mathematical model that was meant to answer exactly this question. Central to their theory was the assumption that comparative advantages arise from differences in factor endowments: a country will have a comparative advantage in goods produced using a lot of their abundant factor. Therefore, according to the two economists, a country should export those goods that intensively use those factors of production that are relatively abundant in the country (and import those that use factors of productions that are relatively scarce).



The Heckscher-Ohlin model: assumptions


This model, however, rests on a series of assumptions that denude all the frailties and contradictions of the very same model. First of all, Heckscher and Ohlin decided to use a 2x2x2 model: two countries that use two factors of production to produce goods in two different sectors, which use the factors in different proportions. To be sure, little can be said against this decision, since models in their very essence are meant to be nothing more than ideal-types. However, the assumptions do not end here, and the following prerequisites make for a very rigid model, from which no real situation seems to be ascribable.

A second assumption, in fact, is that both countries have identical production technology. This means that no matter where a good is produced, it will always be produced at the same level. Of course this is a highly unrealistic assumptions, as it would entail that the trading countries are very similar in their industrial output, if not equal. This could work on a very small regional scale, but hardly on the global scenario.

Moreover, production output is assumed to exhibit constant returns to scale. Constant returns to scale imply that by doubling the input of both factors of production, the output will also double. Although not very realistic, it is useful to simplify things.

Underpinning this assumption is the need for constant returns to scale to differ between industries: if they didn’t, there would be no difference at all between factor endowments, and the gist of the theorem would be rendered moot.

Another thing to take into account is that the H-O model is a factoral one: factors of production in a sector can be shifted easily to another, if needed. That is, factors of production are highly mobile. Again, this is an unrealistic assumption, because what it basically says is that expertise in, say, woodworking can be easily employed in the computer industry with no cost losses, and vice versa. Obviously, this is not what happens in the real world. A woodworker cannot instantaneously become a computer expert, without undergoing any training process whatsoever.

A final assumption is that commodity prices are the same everywhere, that is, purchasing power parity (PPP) applies everywhere and having separate currencies does not affect trade at all.



The Heckscher-Ohlin model: outcomes


The H-O model comes to three different, yet intertwined conclusions, each of which is expressed as a theorem.

The first one, which was also stated before, is the Heckscher-Ohlin theorem, according to which a country should produce and export those goods that intensively use that factor of production that is relatively abundant in the country itself. Therefore, if we assume again the 2x2x2 model we could make an easy example. Let us suppose that there are only two countries, the United States and China, and only two factors of production, labour and capital. The United States is a capital-abundant country, and thus should produce and exports those goods that intensively use capital, like computers, cars, or anything that is related to a capital-intensive sector like machinery. China is a labour-abundant country, and therefore should produce and export those goods that require an intensive use of labour, like apparel, fabrics, or anything that is related to a labour-intensive sector like textiles. This theorem is easy to put to test empirically, and this is exactly what Wassily Leontief did in 1954.

The second outcome is the Rybczynski theorem. At constant relative goods prices, a rise in the endowment of one factor will lead to a more than proportional expansion of the output in the sector which uses that factor intensively, and an absolute decline of the output of the other good. Let us suppose again that there are only two factors (capital K and labour L) and two sectors (a capital-intensive one, machinery, and a labour-intensive one, textiles). Let us also suppose that gK is that good that is produced through an intensive use of capital and gL the one that is produced through an intensive use of labour. Be SK the sector that uses capital intensively, then SL is the one that uses labour intensively. According to this theorem, what happens is simply that when the capital K of a country rises, the output of gK will rise more than proportionally, thus an expansion of SK occurs, while the output of gL declines, thus restricting SL. The opposite happens when labour L is the factor for which the country experiences an endowment.


Finally, the relationship in the prices of the two factors is described by the Stolper-Samuelson theorem. Following from the Rybczysnki theorem, the good that use a factor intensively will see a rise in its relative price, as well as a rise in the return to the factor. Said in other terms, trade raises the income of society’s abundant factor and reduces the income of society’s scarce factor. A corollary of this theorem is factor-price equalization, which entails a tendency for trade to cause factor prices to converge. This convergence, in turn, should signal a trend in declining wage inequality.



The Heckscher-Ohlin model: criticisms of the assumptions


Some of the critiques that underline the weaknesses of the H-O model can be found in the assumptions paragraph. Two of these assumptions should be developed further.

The first assumption that requires some delving is that regarding the two countries having identical production technology. As it has been stated, this is a highly unrealistic assumption, in that it would require both countries to have similar industrial output. But how exactly does this assumption translate in today’s world? Again, it has been said that this assumption can work on a small regional scale, but, once again, that is not telling the whole story. In more practical terms, it follows that there would be no income disparity at all in any country of the world. This is obviously an unrealistic approach, because income inequality does exist, and it is most remarkable between the Northern Hemisphere and the Southern one. The United States and Benin do not have identical production technology, nor will they ever. Developing countries are involved in an aimless catching-up process that, under no present conditions could come to an end. Even in Ohlin’s long-run vision, this does not account for the huge difference between infrastructure, education, and know-how. Herein lies the fallacy of the assumption: not its abstractness, but its hapless, hopeless conceit.

The second assumption that should be considered again is that on commodity prices based on PPP. In Ohlin’s mind this was meant to be a neutral simplification: there were no transaction costs and currency issues, since all the trade concerned commodities and the law of one price applied. However, econometric research (the Balassa-Samuelson hypothesis and the Penn effect, for instance) in the past sixty years has shown that this simply cannot hold true: prices in richer countries are systematically higher than prices in poorer countries, and productivity between countries necessarily varies. This is not to bash the model, which, it has to be repeated, is nothing short of an ideal-type. This latter critique has to be anchored to the former: inequalities do exist on the global scale, and this model cannot be applied to anything wider than regional co-operation between countries that have similar GDP, and industrial output and technology, or that can be provided with equally skilled labour. Nowhere in the world does such a regional arrangement exist. Even the EU, mainly because of its enlargement, presents steep inequalities among its Member States. MERCOSUR is a regional organization of Latin American countries, fairly similar in economic tendencies, technological advancement and industrial outcomes for the most part, yet dominated by a hegemonic power – Brazil. The ASEAN forum comprises countries with similar social – and even political in some cases – conditions, but with different economic strategies.

This is to say that, while it would be absurd and completely far-fetched to ascribe real life solutions from theoretical models, the letter have to provide for a substantial basis for empirical evidence. Whenever this is lacking, the model – and the theory underpinning it – needs to change.



The Heckscher-Ohlin model: criticism of the outcomes


In 1954 a Russian-born American economist, Wassily Leontief, tried to test the H-O model empirically by analysing the trading activities of the United States. His findings were staggering at the time, and can be summarized in this simple preposition, thereafter known as the Leontief Paradox: the United States, the most capital-abundant country in the world, exported labour-intensive commodities and imported capital-intensive ones. This was in obvious and near-exact contradiction with the H-O model.

Further testing on the model bore contradicting views on the paradox. Some claimed that Leontief failed to account for the importance of highly skilled labour (which is even more abundant than capital in the US). This was the view held by the Ricardian model, which put more emphasis on the technological differences that determine comparative advantages (thus, also undermining the assumption of countries having identical production technology).

Others upheld Leontief’s findings. In particular, the Linder hypothesis claimed that demand played a far bigger role than comparative advantage as a determinant to trade. Linder thus stated that countries are more likely to trade with those that share similar demands. This hypothesis is not bereft of meaning: it would be very hard for the US to sell Apple appliances or Tesla cars in a Sub-Saharan state, since the two do not share similar demands – nor have the necessary infrastructure, in some cases. Conversely, products of this kind may fare far better on the European market.


The Stolper-Samuelson outcome, too, was subject to heavy criticism, particularly in its factor-price equalization corollary. For instance, following trade liberalization in Latin American countries, wage inequality did not decline, as the S-S theorem predicted, under the assumption that these countries were more labour-abundant – on the contrary, it rose. Nonetheless, it has to be pointed out that this was a weak claim: not only has wage inequality in the longer run redressed, but also the S-S theorem is not exactly about wage inequality, as much as it is about the relationship between output prices and relative wages. Most empirical evidences confirm the theorem, to a degree.





The H-O model is just one example of a swath of mathematical models employed in economics that have very little connections with the real world.

What needs to be pointed out, however, is not the theoretical frailty of the model’s framework. It’s the necessity for the academia to tell the whole story. More often than not, models or theorems like Heckscher and Ohlin’s are presented to students as economic certainties, even when empirical evidence has disproven them.


Of course, very few would deny the importance of the basis provided by models like this one, but at the same time, a problem can arise when the structural, inherent weaknesses jeopardise the validity of these very same foundations.

To rethink economics does not simply mean to come up with alternative models, but to fix the existing ones when necessary, too – even if the fixing process can prove difficult to carry out when there is a lack of willingness from the academia. Yet, fixing the models is just one part of a two-step process: what academia really should understand is that improving the theories is also a way to improve the world – theirs, and ours alike.





Griffin, Ricky W., and Michael W. Pustay. International business: A managerial perspective. Pearson Prentice Hall, 2005.


Heckscher, Eli Filip, and Bertil Gotthard Ohlin. Heckscher-Ohlin trade theory. The MIT Press, 1991.


Leontief, Wassily. Domestic production and foreign trade: The American capital position re-examined. 1954.


Oatley, Thomas H. International political economy. Boston: Longman, 2012.


Ricardo, David. Principles of political economy and taxation. G. Bell and sons, 1891.


Rybczynski, Tadeusz M. “Factor endowment and relative commodity prices.” Economica (1955): 336-341.


Stolper, Wolfgang F., and Paul A. Samuelson. “Protection and real wages.” The Review of Economic Studies 9.1 (1941): 58-73.

  • lnkjb

    Marco, great to read your analysis of the assumptions of HO. Maybe to “tell the whole story”, as you say, it might be instructive to look at trade theory from a perspective that is seemingly even further removed: philosophy! Such an external perspective might help to see that economists are philosophers – especially when they argue in favor of certain policies over others, and particularly in the case of trade! For example:

    • Marco Schito

      Thanks for your comment. I have to confess I actually never took the philosophical perspective into account, while writing.
      Thank you also for the paper. I’ll make sure to read it as soon as I’ve got some time.