# Heckscher–Ohlin model

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Basic situation: Two identical countries (A and B) have different initial factor endowments. Autarky equilibrium (${\displaystyle A^{A},A^{B}}$): no trade, individual production equals consumption. Trade equilibrium: both countries consume the same (${\displaystyle C^{A}=C^{B}}$), especially beyond their own Production–possibility frontier; production and consumption points are divergent.

The Heckscher–Ohlin model (H–O model) is a general equilibrium mathematical model of international trade, developed by Eli Heckscher and Bertil Ohlin at the Stockholm School of Economics. It builds on David Ricardo's theory of comparative advantage by predicting patterns of commerce and production based on the factor endowments of a trading region. The model essentially says that countries will export products that use their abundant and cheap factor(s) of production and import products that use the countries' scarce factor(s).[1]

## Features of the model

Relative endowments of the factors of production (land, labor, and capital) determine a country's comparative advantage. Countries have comparative advantages in those goods for which the required factors of production are relatively abundant locally. This is because the profitability of goods is determined by input costs. Goods that require inputs that are locally abundant will be cheaper to produce than those goods that require inputs that are locally scarce.

For example, a country where capital and land are abundant but labor is scarce will have comparative advantage in goods that require lots of capital and land, but little labor—grains. If capital and land are abundant, their prices will be low. As they are the main factors used in the production of grain, the price of grain will also be low—and thus attractive for both local consumption and export. Labor-intensive goods on the other hand will be very expensive to produce since labor is scarce and its price is high. Therefore, the country is better off importing those goods.

## Theoretical development

The Ricardian model of comparative advantage has trade ultimately motivated by differences in labour productivity using different "technologies". Heckscher and Ohlin did not require production technology to vary between countries, so (in the interests of simplicity) the "H–O model has identical production technology everywhere". Ricardo considered a single factor of production (labour) and would not have been able to produce comparative advantage without technological differences between countries (all nations would become autarkic at various stages of growth, with no reason to trade with each other). The H–O model removed technology variations but introduced variable capital endowments, recreating endogenously the inter-country variation of labour productivity that Ricardo had imposed exogenously. With international variations in the capital endowment like infrastructure and goods requiring different factor "proportions", Ricardo's comparative advantage emerges as a profit-maximizing solution of capitalist's choices from within the model's equations. The decision that capital owners are faced with is between investments in differing production technologies; the H–O model assumes capital is privately held.

### Original publication

Bertil Ohlin published the book which first explained the theory in 1933. Although he wrote the book alone, Heckscher was credited as co-developer of the model, because of his earlier work on the problem, and because many of the ideas in the final model came from Ohlin's doctoral thesis, supervised by Heckscher.

Interregional and International Trade itself was verbose, rather than being pared down to the mathematical, and appealed because of its new insights.

### 2×2×2 model

The original H–O model assumed that the only difference between countries was the relative abundances of labor and capital. The original Heckscher–Ohlin model contained two countries, and had two commodities that could be produced. Since there are two (homogeneous) factors of production this model is sometimes called the "2×2×2 model".

The model has "variable factor proportions" between countries—highly developed countries have a comparatively high capital-to-labor ratio compared to developing countries. This makes the developed country capital-abundant relative to the developing country, and the developing nation labor-abundant in relation to the developed country.

With this single difference, Ohlin was able to discuss the new mechanism of comparative advantage, using just two goods and two technologies to produce them. One technology would be a capital-intensive industry, the other a labor-intensive business—see "assumptions" below.

### Extensions

The model has been extended since the 1930s by many economists. These developments did not change the fundamental role of variable factor proportions in driving international trade, but added to the model various real-world considerations (such as tariffs) in the hopes of increasing the model's predictive power, or as a mathematical way of discussing macroeconomic policy options.

Notable contributions came from Paul Samuelson, Ronald Jones, and Jaroslav Vanek, so that variations of the model are sometimes called the Heckscher-Ohlin-Samuelson model or the Heckscher-Ohlin-Vanek model in the neo-classical economics.

## Theoretical assumptions

The original, 2×2×2 model was derived with restrictive assumptions, partly for the sake of mathematical simplicity. Some of these have been relaxed for the sake of development. These assumptions and developments are listed here.

### Both countries have identical production technology

This assumption means that producing the same output of either commodity could be done with the same level of capital and labour in either country. Actually, it would be inefficient to use the same balance in either country (because of the relative availability of either input factor) but, in principle this would be possible. Another way of saying this is that the per-capita productivity is the same in both countries in the same technology with identical amounts of capital.

Countries have natural advantages in the production of various commodities in relation to one another, so this is an "unrealistic" simplification designed to highlight the effect of variable factors. This meant that the original H–O model produced an alternative explanation for free trade to Ricardo's, rather than a complementary one; in reality, both effects may occur due to differences in technology and factor abundances.

In addition to natural advantages in the production of one sort of output over another (wine vs. rice, say) the infrastructure, education, culture, and "know-how" of countries differ so dramatically that the idea of identical technologies is a theoretical notion. Ohlin said that the H–O model was a long-run model, and that the conditions of industrial production are "everywhere the same" in the long run.[2]

### Production output is assumed to exhibit constant returns to scale

In a simple model, both countries produce two commodities. Each commodity in turn is made using two factors of production. The production of each commodity requires input from both factors of production—capital (K) and labor (L). The technologies of each commodity is assumed to exhibit constant returns to scale (CRS). CRS technologies implies that when inputs of both capital and labor is multiplied by a factor of k, the output also multiplies by a factor of k. For example, if both capital and labor inputs are doubled, output of the commodities is doubled. In other terms the production function of both commodities is "homogeneous of degree 1".

The assumption of constant returns to scale CRS is useful because it exhibits a diminishing returns in a factor. Under constant returns to scale, doubling both capital and labor leads to a doubling of the output. Since outputs are increasing in both factors of production, doubling capital while holding labor constant leads to less than doubling of an output. Diminishing returns to capital and diminishing returns to labor are crucial to the Stolper–Samuelson theorem.

### The technologies used to produce the two commodities differ

The CRS production functions must differ to make trade worthwhile in this model. For instance if the functions are Cobb–Douglas technologies the parameters applied to the inputs must vary. An example would be:

Arable industry: ${\displaystyle A={{K}^{1/3}}{{L}^{2/3}}}$
Fishing industry: ${\displaystyle F={{K}^{1/2}}{{L}^{1/2}}}$

Where A is the output in arable production, F is the output in fish production, and K, L are capital and labor in both cases.

In this example, the marginal return to an extra unit of capital is higher in the fishing industry, assuming units of fish (F) and arable output (A) have equal value. The more capital-abundant country may gain by developing its fishing fleet at the expense of its arable farms. Conversely, the workers available in the relatively labor-abundant country can be employed relatively more efficiently in arable farming.

### Factor mobility within countries

Within countries, capital and labor can be reinvested and reemployed in order to produce different outputs. Similar to Ricardo's comparative advantage argument, this is assumed to happen without cost. If the two production technologies are the arable industry and the fishing industry it is assumed that farmers can shift to work as fishermen with no cost and vice versa.

It is further assumed that capital can shift easily into either technology, so that the industrial mix can change without adjustment costs between the two types of production. For instance, if the two industries are farming and fishing it is assumed that farms can be sold to pay for the construction of fishing boats with no transaction costs.

The theory by Avsar has offered much criticism to this.

### Factor immobility between countries

The basic Heckscher–Ohlin model depends upon the relative availability of capital and labor differing internationally, but if capital can be freely invested anywhere competition (for investment) will make relative abundances identical throughout the world. Essentially, free trade in capital would provide a single worldwide investment pool.

Differences in labour abundance would not produce a difference in relative factor abundance (in relation to mobile capital) because the labour/capital ratio would be identical everywhere. (A large country would receive twice as much investment as a small one, for instance, maximizing capitalist's return on investment).

As capital controls are reduced, the modern world has begun to look a lot less like the world modelled by Heckscher and Ohlin. It has been argued that capital mobility undermines the case for free trade itself, see: Capital mobility and comparative advantage Free trade critique.

Capital is mobile when:

Like capital, labor movements are not permitted in the Heckscher–Ohlin world, since this would drive an equalization of relative abundances of the two production factors, just as in the case of capital immobility. This condition is more defensible as a description of the modern world than the assumption that capital is confined to a single country.

### Commodity prices are the same everywhere

The 2x2x2 model originally placed no barriers to trade, had no tariffs, and no exchange controls (capital was immobile, but repatriation of foreign sales was costless). It was also free of transportation costs between the countries, or any other savings that would favor procuring a local supply.

If the two countries have separate currencies, this does not affect the model in any way—purchasing power parity applies. Since there are no transaction costs or currency issues the law of one price applies to both commodities, and consumers in either country pay exactly the same price for either good.

In Ohlin's day this assumption was a fairly neutral simplification, but economic changes and econometric research since the 1950s have shown that the local prices of goods tend to be correlated with incomes when both are converted at money prices (although this is less true with traded commodities). See: Penn effect.

### Perfect internal competition

Neither labor nor capital has the power to affect prices or factor rates by constraining supply; a state of perfect competition exists.

## Conclusions

The results of this work has been the formulation of certain named conclusions arising from the assumptions inherent in the model.

### Heckscher–Ohlin theorem

The exports of a capital-abundant country will be from capital-intensive industries, and labour-abundant countries will import such goods, exporting labour-intensive goods in return. Competitive pressures within the H–O model produce this prediction fairly straightforwardly. Conveniently, this is an easily testable hypothesis.

### Rybczynski theorem

Main article: Rybczynski theorem

When the amount of one factor of production increases, the production of the good which uses that particular factor of production intensively increases relative to the increase in the factor of production, as the H–O model assumes perfect competition where price is equal to the costs of factors of production. This theorem is useful in explaining the effects of immigration, emigration, and foreign capital investment. However, Rybczynski suggests that a fixed quantity of the two factors of production are required. This could be expanded to consider factor substitution, in which case the increase in production would be more than proportional.

### Stolper–Samuelson theorem

Relative changes in output goods prices will drive the relative prices of the factors used to produce them. If the world price of capital-intensive goods increases, it will increase the relative rental rate as well as decrease the relative wage rate (the return on capital as against the return to labor). Also if the price of labor-intensive goods increases, it will increase the relative wage rate as well as decrease the relative rental rate .

### Factor–price equalization theorem

Free and competitive trade will make factor prices converge along with traded goods prices. The FPE theorem is the most significant conclusion of the H–O model, but it is also the theorem which has found the least agreement with the economic evidence. Neither the rental return to capital, nor the wage rates seem to consistently converge between trading partners at different levels of development.

### Implications of factor-proportion changes

The Stolper–Samuelson theorem concerns nominal rents and wages. The Magnification effect on prices considers the effect of output-goods price-changes on the real return to capital and labor. This is done by dividing the nominal rates with a price index, but took thirty years to develop completely because of the theoretical complexity involved.

• The Magnification effect shows that trade liberalization will actually make the locally-scarce factor of production worse off (because increased trade makes the price index fall by less than the drop in returns to the scarce-factor induced by the Stolper–Samuelson theorem).
• The Magnification effect on production quantity-shifts induced by endowment changes (via the Rybczynski theorem) predicts a larger proportionate shift in output-quantity than in the corresponding endowment factor shift which induced it. This has implications to both labor and capital:
• Assuming fixed capital, population growth will dilute the scarcity of labor in relation to capital. If the population growth outpaces the growth in capital by 10% this may translate into a 20% shift in the balance of employment to the labor-intensive industries.
• In the modern world, money tends to be much more mobile than labor, so import of capital to a country will almost certainly shift the relative factor-abundances in favor of capital. The magnification effect says that a 10% increase in national capital may lead to a redistribution of labor amounting to a fifth of the entire economy (towards capital-intensive, high-tech production). Notably, employment patterns in very poor countries can be dramatically affected by a small amount of FDI, in this model. (See also: Dutch disease.)

## Econometric testing of H–O model theorems

Heckscher and Ohlin considered the Factor-Price Equalization theorem an econometric success because the large volume of international trade in the late 19th and early 20th centuries coincided with the convergence of commodity and factor prices worldwide.

Modern econometric estimates have shown the model to perform poorly, however, and adjustments have been suggested, most importantly the assumption that technology is not the same everywhere. This change would mean abandoning the pure H–O model.

In 1954 an econometric test by Wassily W. Leontief of the H–O model found that the United States, despite having a relative abundance of capital, tended to export labor-intensive goods and import capital-intensive goods. This problem became known as the Leontief paradox. Alternative trade models and various explanations for the paradox have emerged as a result of the paradox. One such trade model, the Linder hypothesis, suggests that goods are traded based on similar demand rather than differences in supply side factors (i.e., H–O's factor endowments).

### The Vanek formula

Various attempts in the 1960s and 1970s have been made to "solve" the Leontief paradox and save the Heckscher–Ohlin Theory from failing. From the 1980s a new series of statistical tests had been tried. The new tests depended on Vanek's formula.[3] It takes a simple form

${\displaystyle \mathbf {F_{C}} =\mathbf {V_{C}} -s_{C}\mathbf {V} }$

where ${\displaystyle \mathbf {F_{C}} }$ is the net trade of factor service vector for country ${\displaystyle c}$, ${\displaystyle \mathbf {V_{C}} }$ the factor endowment vector for country ${\displaystyle c}$, and ${\displaystyle s_{C}}$ the country ${\displaystyle c}$'s share of the world consumption and ${\displaystyle \mathbf {V} }$ the world total endowment vector of factors. For many countries and many factors, it is possible to estimate the left hand sides and right hand sides independently. To put it another way, the left hand side tells the direction of factor service trade. Thus it is possible to ask how this system of equations holds. The results obtained by Bowen, Leamer and Sveiskaus (1987) was disastrous.[4] They examined the cases of 12 factors and 27 countries for the year 1967. They found that the both sides of the equations had the same sign only for 61% of 324 cases. For the year 1983, the result was more disastrous. Both sides had the same sign only for 148 cases out of 297 cases (or the rate of correct predictions was 49.8%). The results of Bowen, Leamer, and Sveiskaus (1987) mean that the Hecksher–Ohlin–Vanek (HOV) theory has no predictive power concerning the direction of trade.

## Criticism

Although H-O model is normally thought to be basis for international trade theory, there are many points of criticism against the model.[5]

### Poor predictive power

The original Heckscher–Ohlin model and extended model such as the Vanek model performs poorly, as it is shown in the section "Econometric testing of H–O model theorems". Daniel Trefler and Susan Chun Zhu summarizes their paper that "It is hard to believe that factor endowments theory [editor's note: in other words, Heckscher–Ohlin–Vanek Model] could offer an adequate explanation of international trade patterns".[6]

A common understanding exists that in the national level HOV model fits well. In fact, Davis and others found that HOV model fitted extremely well with the regional data of Japan.[7] Even when the HOV formula fits well, it does not mean that Heckscher–Ohlin theory is valid. Indeed, Heckscher–Ohlin theory claims that the state of factor endowments of each country (or each region) determines the production of each country (respectively of each region) but Bernstein and Weinstein found that the factor endowments have little predictive power. The factor-endowments-driven model (FED model) has errors much greater than the HOV model.[8]

### Factor equalization theorem

The factor equalization theorem (FET) applies only to the most advanced countries. The average wage in Japan was once as big as 70 times the wage in Vietnam. These wage discrepancies are not normally in the scope of the H–O model analysis.[9]

Heckscher–Ohlin theory is badly adapted to the analyze South-North trade problems. The assumptions of H–O are unrealistic with respect to North-South trade. Income differences between North and South is the concern that third world cares most. The factor price equalization theorem has not shown a sign of realization, even for a long time lag of a half century.[10]

### Identical production function

The standard Heckscher–Ohlin model assumes that the production functions are identical for all countries concerned. This means that all countries are in the same level of production and have the same technology, yet this is highly unrealistic. Technological gap between developed and developing countries is the main concern for the development of poor countries. The standard Heckscher–Ohlin model ignores all these vital factors when one wants to consider development of less developed countries in the international context.[10] Even between developed countries, technology differs from industry to industry and firm to firm base. Indeed, this is the very basis of the competition between firms, inside the country and across the country. See the New Trade Theory in this article below.

### Capital as endowment

In the modern production system, machines and apparatuses play an important role. What is referred to as capital is nothing other than these machines and apparatuses, together with materials and intermediate products which will be consumed in the production process. Capital is the most important of factors, or one should say as important as labor. By the help of machines and apparatuses, the human being got a tremendous production capability. These machines, apparatuses and tools are classified as capital, or more precisely as durable capital, for one uses these items for many years. Their quantity is not changed at once. But the capital is not an endowment given by the nature. It is composed of goods manufactured in the production and often imported from foreign countries. In this sense, capital is internationally mobile and the result of past economic activity. The concept of capital as natural endowment distorts the real role of capital. Capital is a production power accumulated by the past investment.

### Homogeneous capital

Capital goods take different forms. It may take the form of a machine-tool such as lathe, the form of a transfer-machine, which you can see under the belt-conveyors. It may take the form of oil or iron core. Despite these facts, capital in the Hechscher–Ohlin model is assumed as homogeneous and transferable to any form if necessary. This assumption is not only far from the reality, but also it includes logical flaw. Capital has a measure, just like anything has weight. How can an amount of various goods be measured?[9]

Usually by a system of prices. But prices depend on profit rate. In the Heckscher–Ohlin model, the rate of profit is determined according to how abundant capital is. If capital is scarce, it has a high rate of profit. If it is abundant, the profit rate is low. Here is a logical circle. Before the profit rate is determined, the amount of capital is not measured. This logical difficulty was the subject of academic controversy which took place many years ago. In fact, this is sometimes named Cambridge Capital Controversies. The conclusion of the controversies was that the concept of homogeneous capital was untenable. Heckscher–Ohlin theorists ignore all these stories without providing any explanation how capital is measured theoretically.[11]

### No unemployment

Unemployment is the vital question in any trade conflict. Heckscher–Ohlin theory excludes unemployment by the very formulation of the model, in which all factors (including labour) are employed in the production.[12]

### No room for firms

Standard Heckscher–Ohlin theory assumes the same production function for all countries. This implies that all firms are identical. The theoretical consequence is that there is no room for firms in the H–O model. By contrast, the New Trade Theory emphasizes that firms are heterogeneous.[13][14]

### Political background

From the middle of the 19th century to 1930s, giant flow of immigration took place from Europe to North America. It is estimated that more than 60 million people crossed the Atlantic Ocean. Some politicians worried if these immigrants may cause various troubles (including cultural conflicts). For those politicians HO-theory provided a good reason “in support of both restrictions on labor migration and free trade in goods”.[15]

New Trade theorists challenge the assumption of diminishing returns to scale, and some argue that using protectionist measures to build up a huge industrial base in certain industries would then allow those sectors to dominate the world market via a network effect.

New New Trade Theory analyses individual enterprises and plants in an international competitive situation. The classical trade theory—i.e., the Heckscher–Ohlin model—has no enterprises in mind. The new trade theory treats enterprises in an industry as identical entities. New New Trade Theory gives focus on the diversity of enterprises. It is a stylized fact that there are enterprises which engage in export and ones which do not. Some enterprises invest directly in the foreign country in order to produce and sell in that country. Some other enterprises engage only in export. Why does this kind of differences occur? New New Trade Theory tries to find out the reasons of these well observed facts.[14]

The gravity model of international trade predicts bilateral trade flows based on the economic sizes of two nations, and the distance between them.

Ricardian theory is now extended in a general form which includes not only labor but also inputs of materials and intermediate goods. In this sense, it is much more general and plausible than the Heckscher–Ohlin model and escapes the logical problems such as capital as endowments, which is in reality produced goods.[16]

As the theory permits different production processes to coexist in an industry of a country, the Ricardo–Sraffa theory can give a theoretical bases for the New Trade Theory.

## References

1. ^ Blaug, Mark (1992). The methodology of economics, or, How economists explain. Cambridge University Press. p. 190. ISBN 0-521-43678-8.
2. ^ http://www.econ.iastate.edu/classes/econ355/choi/ho.htm
3. ^ Vanek, J. (1968), "The Factor Proportions Theory: the N-Factor Case", Kyklos, 21 (4): 749–756, doi:10.1111/j.1467-6435.1968.tb00141.x
4. ^ Bowen, Harry P.; Leamer, Edward E. & Sveiskaus, Leo (1987), "Multicountry, Multifactor Tests of the Factor Abundance Theory", American Economic Review, 77 (5): 791–809, JSTOR 1810209
5. ^ The Heckscher–Ohlin theorem is one of the four critical theorems of the Heckscher–Ohlin model. It states that a country will export goods that use its abundant factors intensively, and import goods that use its scarce factors intensively. In the two-factor case, it states: "A capital-abundant country will export the capital-intensive good, while the labor-abundant country will export the labor-intensive good." The critical assumption of the Heckscher–Ohlin model is that the two countries are identical, except for the difference in resource endowments. This also implies that the aggregate preferences are the same. The relative abundance in capital will cause the capital-abundant country to produce the capital-intensive good cheaper than the labor-abundant country and vice versa. Initially, when the countries are not trading: the price of the capital-intensive good in the capital-abundant country will be bid down relative to the price of the good in the other country, the price of the labor-intensive good in the labor-abundant country will be bid down relative to the price of the good in the other country. Once trade is allowed, profit-seeking firms will move their products to the markets that have (temporary) higher price. As a result: the capital-abundant country will export the capital-intensive good, the labor-abundant country will export the labor-intensive good. The Leontief paradox, presented by Wassily Leontief in 1951,[1] found that the U.S. (the most capital-abundant country in the world by any criterion) exported labor-intensive commodities and imported capital-intensive commodities, in apparent contradiction with the Heckscher–Ohlin theorem. However, if labor is separated into two distinct factors, skilled labor and unskilled labor, the Heckscher–Ohlin theorem is more accurate. The U.S. tends to export skilled-labor-intensive goods, and tends to import unskilled-labor-intensive goods.Miberg, William (1996), "The rhetoric of policy relevance in international economics", Journal of Economic Methodology, 3 (2): 237–259, doi:10.1080/13501789600000017
6. ^ Trefler, Daniel & Zhu, Susan Chun (2000), "Beyond the Algebra of Explanation: HOV for the Technology Age", American Economic Review, 90 (2): 145–149, doi:10.1257/aer.90.2.145, JSTOR 117209
7. ^ Davis, D. R.; Weintein, D. E.; Bradford, S. D.; Shimpo, K. (1997), "Using International and Japanese Regional Data to Determine When the Factor Abundance Theory of Trade Works", American Economic Review, 87 (3): 421–446, JSTOR 2951353
8. ^ Bernstein, J. R. & Weinstein, D. E. (2002), "Do endowments predict the location of production?: Evidence from national and international data", Journal of International Economics, 56 (1): 55–76, doi:10.1016/S0022-1996(01)00108-8
9. ^ a b Edwards, Chris (1985), "§2.3 The Fall of The Hecksher-Ohlin Theory", The fragmented world: competing perspectives on trade, money, and crisis, London and New York: Methuen, pp. 29–40, ISBN 0-416-73390-5
10. ^ a b Stewart, Frances (1989), "Recent Theories of International Trade: Some Implications for the South", in Kierzkowski, Henryk, Monopolistic Competition and International Trade, Oxford: Clarendon Press, pp. 84–108, ISBN 0-19-828726-7
11. ^ Cohen, Avi J. & Harcourt, Geoffrey C. (2003), "Whatever Happened to the Cambridge Capital Theory Controversies?", Journal of Economic Perspectives, 17 (1): 199–214, doi:10.1257/089533003321165010
12. ^ Shiozawa, Y. (2009), "Samuelson's Implicit Criticism against Sraffa and the Sraffians and Two Other Questions", The Kyoto Economic Review, 78 (1): 19–37
13. ^ Melitz, M. (2003), "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity", Econometrica, 71 (6): 1695–1725, doi:10.1111/1468-0262.00467
14. ^ a b Greenaway, David & Kneller, Richard (2007), "Firm heterogeneity, exporting and foreign direct investment", The Economic Journal, 117 (517): F134–F161, doi:10.1111/j.1468-0297.2007.02018.x
15. ^ Edwards, Cris (1985), The Fragmented World, Competing Perspective on Trade, Money and Crisis, London and New York: Methuen, p. 28
16. ^ Shiozawa, Y. (2007), "A New Construction of Ricardian Trade Theory—A Many-country, Many-commodity Case with Intermediate Goods and Choice of Production Techniques", Evolutionary and Institutional Economics Review, 3 (2): 141–187, doi:10.14441/eier.3.141