# Heckscher-Ohlin model

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Heckscher-Ohlin model

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 utilize their abundant and cheap factor(s) of production and import products that utilize the countries' scarce factor(s).

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 prices of goods are ultimately determined by the prices of their inputs. 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, for example. 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 of the model

The Ricardian model of comparative advantage has trade ultimately motivated by differences in labour productivity using different "technologies". Heckscher and Ohlin didn't 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 autarkies at various stages of development, 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 (i.e. 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 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.

The 2x2x2 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&times;2&times;2 model".

The model has "variable factor proportions" between countries: Highly developed countries have a comparatively high ratio of capital to labor in relation to developing countries. This makes the developed country capital-abundant relative to the developing nation, 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 modern synthesis.

Assumptions of the theory

The original, 2x2x2 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

As mentioned above, the H-O model differs from Ricardo's most drastically by assuming that the production functions available in each country are identical. The production functions simply convert labour and capital input to output.

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 actually 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 HO-model produced an alternative explanation for free trade to Ricardo's, rather than a complementary one). In reality, both effects may occur (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 HO-model was a long run model, and that the conditions of industrial production are "everywhere the same" in the long run. ( [http://www.econ.iastate.edu/classes/econ355/choi/ho.htm] ).

Production output must have constant Return to Scale

Both of the countries in the simple HO model produced both commodities, and both technologies have constant returns to scale (CRS). (CRS production has twice the output if both capital and labour inputs are doubled, so the two production functions must be 'homogeneous of degree 1').

These conditions are required to produce a mathematical equilibrium. With increasing returns to scale it would likely be more efficient for countries to specialize, but specialization is not possible with the Heckscher-Ohlin assumptions.

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: $A =$K}^{1/3L}^{2/3 : Fishing industry: $F =$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 labour in both cases.

In this example, the marginal return to an extra unit of capital is higher in the fishing industry, assuming units of F(ish) and A(rable) output 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 labour-abundant country can be employed relatively more efficiently in arable farming.

Labor mobility within countries

"Within" countries, capital and labor can be reinvested and re-employed to produce different outputs. Like the comparative advantage argument of Ricardo, this is assumed to happen costlessly.

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.

Capital mobility within countries

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.

Capital immobility between countries

The basic Heckscher-Ohlin model depends upon the relative availability of capital and labour 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:
* There are limited exchange controls
* Foreign Direct Investment (FDI) is permitted between countries, or foreigners are permitted to invest in the commercial operations of a country through a stock or corporate bond market

Labour immobility between countries

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 above. This condition is more defensible as a description of the modern world than the assumption that capital is confined to a single country.

Commodities have the same price 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 favour 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 labour nor capital has the power to affect prices or factor rates by constraining supply; a state of perfect competition exists.

Conclusions of the model

The results of this work has been the formulation of certain named conclusions arising from the assumptions inherent in the model. These are known as:

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

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.

tolper-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 relative to the rental rate as well as decreasing the relative wage rate (the return on capital as against the return to labour). Also if the price of labour intensive goods increases, it will increase relative to the wage rate as well as decreasing 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 HO-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.

The 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 labour. 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 labour and capital:
**Assuming fixed capital, population growth will dilute the scarcity of labour 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 labour-intensive industries.
**In the modern world, money tends to be much more mobile than labour, so import of capital to a country will almost certainly shift the relative factor-abundances in favour of capital. The magnification effect says that a 10% increase in national capital may lead to a redistribution of labour 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 US, 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).

ee also

*List of international trade topics
*Comparative advantage - An International trade model with varying technology between countries
*Balassa-Samuelson effect - An International trade model with traded and non-traded economic sectors
*Linder hypothesis
*Gravity model of trade