Feenstra Taylor Econ CH04

The Heckscher-Ohlin Model

1 H-O Model

2Empirical

Evidence 3

Conclusions

4

© 2008 Worth Publishers ▪ International Economics ▪ Feenstra/Taylor 2 of 113

Introduction

• The Heckscher-Ohlin model (HO) shows how trade occurs because countries that have different resources.

• They wanted to explain this increase in trade during the “golden age” of international trade.

• H-O assumed that technologies were the same across countries, but had an uneven distribution of resources.


Introduction

• The specific factors model in the last chapter was a short run model since capital and labor could not move between industries.

• The HO model is a long run model because all factors of production can move between the industries.

• Generalizations Many factors and goods Differing productivities


Heckscher-Ohlin Model

• Two countries: Home and Foreign.• Two goods: computers and shoes.• Two factors of prod’n: labor (L) and capital (K).

• Resource constraint equations: Capital in each good for each country

K = KC + KS and K* = K*C + K*S

Labor in each good for each country L = LC + LS and L* = L*C + L*S


Assumptions of the Heckscher-Ohlin Model

1. Both factors can move freely between industries. R and W must be the same in both industries.

2. Shoe production is labor-intensive; it requires more labor per unit of capital to produce shoes than computers, so that LS/KS > LC/KC.

This means that computer production is capital-intensive.

Figure 4.1 shows relative demand curves for labor in each industry.



Figure 4.1



3. Foreign is labor abundant. Equivalently, Home is capital abundant L*/K* > L/K and K/L > K*/L* Here, we do not consider why the amount of

resources differs across countries. Take as given.

4. The final outputs, shoes and computers, can be traded freely, without restrictions, between nations, but labor and capital do not move between countries. Latter assumption will be relaxed in the next chapter.



5. The technologies used to produce the two goods are identical across the countries. This is opposite of the assumption in the Ricardian

model.

6. Consumer tastes are the same across countries, and preferences for computers and shoes do not vary with a country's level of income.

These are not realistic assumptions, but they allow us to focus on differences in factor endowments as the basis for trade.

APPLICATION


Are Factor Intensities the Same Across Countries?

• As part of our assumptions, we assume that factor intensities in each industry are the same in both countries. E.g. shoes are labor intensive in both countries

• Although all countries may have access to the same technologies, the machines used in the U.S. are different from those used in Asia and elsewhere.

• While the U.S. still produces some shoes, the production is different from the production in Asia.

APPLICATION


Are Factor Intensities the Same Across Countries?

• Asian production uses old technology and workers earn relatively little compared to the U.S. Labor intensive in Asia.

• In call centers, technologies and therefore factor intensities are similar across countries.

• So, shoes in India are labor intensive compared to the call center—the opposite of the U.S.

• This illustrates Reversal of Factor Intensities between the two countries. Holds for all Wage/Rental ratios. We will ignore the possibility of “factor intensity reversals.”


Heckscher-Ohlin ModelNo Trade Equilibrium

• As always, start with the no-trade equilibrium.

• Factor abundance and intensity (combined with total endowments) determine the shape of the PPFs: Home is capital abundant and computer production is capital

intensive. Home is capable of producing more computers than shoes.

Foreign is labor-abundant and shoe production is labor-intensive.

Foreign is capable of producing more shoes.

• Indifference Curves Consumer tastes are the same across countries, so the

shape of the indifference curves is the same in each country.


Heckscher-Ohlin ModelNo Trade Equilibrium

No-Trade Equilibria in Home and ForeignFigure 4.2



• No Trade Equilibrium Price The no-trade prices reflect the differing amounts of

resources found in the two countries. Foreign has abundant labor. Shoe production is labor intensive. The no-trade relative price of shoes is lower in Foreign.

People in Foreign are willing to give up more shoes for one computer since they have a lot of shoes.

The same logic applies to Home. Home has abundant capital. Computer production is capital intensive. The no-trade relative price of shoes is lower in Home.


Heckscher-Ohlin ModelFree Trade Equilibrium

• Three steps to finding free trade equilibrium Trace out the Home export supply of computers. Trace out the Foreign import demand for computers. Put together the export supply and the import demand

to determine equilibrium relative price of computers.

• Home Equilibrium with Free Trade (Figure 4.3) The Home PPF will show a free trade or world relative

price of computers that is higher than the no-trade Home relative price.

They will produce more computers and fewer shoes. Home specializes in and exports computers.



Figure 4.3



• We can use the Home trade information to graph the exports of computers against the relative price.

Trace out the quantity of exports at each relative price.

This gives the Home export supply curve for computers.

It is upward-sloping since at higher relative prices, Home is willing to specialize further in computers and export more of them.



Figure 4.3



• Foreign Equilibrium with Free Trade The Foreign PPF will show a free trade or world

relative price of computers that is lower than the no-trade Foreign relative price.

• Foreign can now consume on any point along the world price line through point B*.

• We can now define the Foreign “trade triangle” which is the triangle that connects points B* and C*.



• Next, we run through the same steps for the Foreign country.

• Foreign specializes further in shoes and produces fewer computers.

• B* is where Foreign produces and C* is where Foreign consumes.

Figure 4.4



Figure 4.4

• We can use the Foreign trade information to graph the import of computers against the relative price.

• It is downward-sloping since at higher relative prices, Foreign is willing to specialize further in shoes and import more computers.



• The equilibrium free trade price is determined by the intersection of the Home export supply curve and the foreign import demand curve: Point D.

• At that relative price,

the quantity that Home wants

to export equals the amount

that Foreign wants to import.

• This is a free-trade

equilibrium since there is no

reason for the relative price

to change.

Figure 4.5



• Pattern of Trade This is the Heckscher-Ohlin Theorem:

With two goods and two factors, each country will export the good that uses intensively the factor of production it has in abundance, and will import the other good.

• When trade opens: The relative price of computers in Home rises from the

no-trade price. This gives Home an incentive to produce more computers and

export the difference. The relative price of computers in Foreign falls from the

no-trade price.



• Testing the HO Theorem: Leontief’s Paradox Wassily Leontief performed the first test of the HO

theorem in 1953 using data for the U.S. from 1947. He measured the amounts of labor and capital used in

all industries needed to produce $1 million of U.S. exports and to produce $1 million of imports into the U.S.



• Leontief used labor and capital used directly in the production of final good exports in each industry.

• Capital is high because we are measuring the whole capital stock—not the part actually used to produce exports.

• It was impossible for Leontief to get information on the amount of labor and capital used to produce imports.

• He used data on U.S. technology to calculate estimated amounts of labor and capital used in imports from abroad. Remember the HO model assume technologies are the same

across countries.



• Leontief assumed correctly that in 1947 the U.S. was capital abundant relative to the rest of the world. From the HO model, Leontief expected that the U.S.

would export capital intensive goods and import labor intensive goods.

• Leontief, however, found the opposite. The capital labor ratio for U.S. imports was higher than

for exports.

• This contradiction came to be called Leontief’s paradox.



• Why would this paradox exist?• U.S. and foreign technologies are not the same as

assumed.• By focusing only on labor and capital, land abundance

in the U.S. was ignored.• No distinction between skilled and unskilled labor.• The data for 1947 could be unusual due to the recent

end of WWII.• The U.S. was not engaged in completely free trade as

is assumed by the HO model.



• Several of the explanations depend on having more than two factors of production. The U.S. is land abundant, and much of what it was

exporting might have been agricultural products which use land intensively.

It might also be true that many of the exports used skilled labor intensively.

• More current research was aimed at redoing the Leontief test. The “extended” HO model works much better for the

same year of data.


Effects of Trade on Factor Prices

• How do the changes in pre-trade and post-trade relative prices affect the wage paid to labor in each country and the rental earned by capital? Remember the relative price of computers in Home increase,

causing them to export computers. The relative price of computers in Foreign decreases, causing

them to import computers.

• Effect of Trade on the Wage and Rental rate of Home Derive an economy-wide relative demand for labor. Compare it to the economy-wide relative supply of labor, L/K. This will determine Home’s relative wage and what happens after

the relative price of computers changes.



• Economy-Wide Relative Demand for Labor K = KC + KS and L = LC + LS

We can divide total labor by total capital to get the relative supply equal to the relative demand.

• The relative demand is a weighted average of the labor-capital ratio to each industry.

K

K

K

L

K

K

K

L

K

LL

K

L S

S

SC

C

CSC

Relative Supply Relative Demand



• The relative demand curve is an average of the labor demand curves for each industry.

• The relative demand

curve therefore lies

between these two

curves.

• Where the curves

intersect gives the

wage to rental rate

ratio: W/R.

Figure 4.6



Figure 4.8

The increase in Pc/Ps

causes a shift in resources

from shoes into computer

production. This puts more

weight on the computer

sector.



• How does this happen? More labor per unit of capital is released from shoes than is

needed to operate that capital in computers. As the relative price of computers rises, computer output

rises while shoe output falls. Labor is “freed up” to be used more in both industries.

K

K

K

L

K

K

K

L

K

L S

S

SC

C

C

Relative Supply

No change

Relative Demand

No change in total



• Determination of the Real Wage and Real Rental Rate.

Who gains and who loses from the change in the relative price of computers?

We need to determine the change in the real wage and real rental. The change in the quantity of shoes and computers that

each factor of production can purchase. Real rental rate: R/PS and R/PC

Real wage: W/PC and W/PS



• Change in the Real Rental Rate Because the labor/capital ratio increases in both

industries, the marginal product of capital increases. There are more people to work with each unit of capital.

The rental rate of capital is determined by its marginal product. R = PC*MPKC and R = PS*MPKS

Rearranging we get: MPKC = R/PC and MPKS = R/PS

An increase in the relative price of a good will benefit the factor of production used intensively in producing that good.



• Change in the Real Wage Since the labor/capital ratio increases in both

industries, the marginal product of labor must decrease in both industries.

As before the wage is determined by the marginal product of labor and the price of goods. W = PC*MPLC and W = PS*MPLS

Rearranging MPLC = W/PC and MPLS = W/PS

Labor is clearly worse off due to the increase in the price of computers.



• The Stolper-Samuelson Theorem:

In the long run when all factors are mobile, an increase in the relative price of a good will increase the real earnings of the factor used intensively in the production of that good and decrease the real earnings of the other factor.

• Therefore, in the Heckscher-Ohlin model:

The abundant factor gains from trade, and the scarce factor loses from trade.



• A Numerical Example

Suppose we have the following data:

Computers Sales Revenue = PCQC = 100

Earnings of labor = WLC = 50

Earnings of capital = RKC = 50

Shoes Sales Revenue = PSQS = 100

Earnings of labor = WLS = 60

Earnings of capital = RKS = 40



• Shoes are more labor-intensive than computers. The share of total revenue paid to labor in shoes (60%)

is more than the share in computers (50%).

• When trade opens, the relative price of computers, PC, increases while the price of shoes, PS, does not change. Computers: % increase in price = ΔPC/PC = 10%

Shoes: % increase in price = ΔPS/PS = 0%

• Our goal is to see how the increase in the relative price of computers translates into long run changes in the wage and rental.



• The rental rate on capital is calculated by taking payments to capital and dividing by the amount of capital:

• Apply the following assumptions:

ΔPC > 0 and ΔPS = 0,

to the last equations:

C C C

C

S S S

S

P Q W LR

K

P Q W LR

K

0

C C C

C

S S

S

P Q W LR

K

Q W LR

K



• Rewrite the last

equation in

percentage

changes:

• Plugging in data from before:

C C C C

C C C

S

S

P P Q W LR WR P R K W R K

W LR WR W R K

40

60

50

50

50

100%10

W

W

R

R

W

W

R

R



• After solving we get: (ΔW/W) = -(20%/0.5) = -40% When the price of computers increases by 10%, the

wage falls by 40% The real wage, measured in terms of either good, has

fallen, so labor is worse off.

• We can also see: (ΔR/R) = -(ΔW/W)(60/40) = 60% Rental on capital increases by 60% when the price of

computers rises by 10% The real rental measured in terms of either good has

gone up, and capital owners are clearly better off.



• General Equation for the Long-Run Change in Factor Prices In summary, for an increase in PC

ΔW/W < 0 < ΔPC/PS < ΔR/R

Real wage falls, real rental increases

• We see what is referred to as a ‘magnification effect’ They show how changes in the prices of goods have

magnified effects on the earnings of factors. Even modest fluctuations in the relative prices of goods

on world markets can lead to exaggerated changes in the long-run earnings of both factors.

APPLICATION


Opinions Toward Free Trade

• A survey was conducted in the U.S. by the National Elections Studies (NES) in 1992 to see how citizens viewed trade. Respondents could either answer that they favor

placing limits on imports, not supporting free trade, or they could oppose limits on imports, supporting free trade.

How do these answers compare with characteristics of the respondents, such as their wages, skills, or the industries they work in?

APPLICATION



• If labor earns some of the return to capital, then workers in exporting (importing) industries will support (oppose) free trade.

• In the short run, the industry of employment of workers will affect their attitudes toward free trade.

• In the long run HO model, the industry of employment should not matter.

• In the long run then, the skill level of workers should determine their attitudes toward free trade.

APPLICATION



• In the NES survey, the industry of employment was somewhat important in explaining respondents’ attitudes toward free trade, but skill level was much more important. Workers in export-oriented industries are somewhat more likely to

favor free trade. Those in import-competing industries favoring import restrictions.

• A much more important determinant of the attitudes toward free trade is the skill level of workers, measured by wages or years of education. This suggests respondents are considering long run earnings as

predicted by HO and Stolper-Samuelson.

APPLICATION



• Respondents were also asked if they owned a home.• People who owned homes in communities where the local

industries face a lot of import competition are much more likely to oppose free trade.

• People who owned homes in communities where the industries benefit from export opportunities are more likely to support free trade.

• People are concerned about the asset value of their homes, just like the owners of specific-factors in our model are concerned about the rental earned by the factor of production they own.


Extending the Heckscher-Ohlin Model

• We need to make the HO model more realistic by allowing for more than two goods, factors, and countries.

• As the second modification, we will allow the technologies used to produce each good to differ across countries.

• Many Goods, Factors, and Countries The predictions of the HO model depend on knowing what

factor a country has in abundance, and which good uses that factor intensively.

When there are more than two goods, it is more complicated to evaluate factor intensity and factor abundance.



• Measuring the Factor Content of Trade How do we measure the factor intensity of exports and

imports when there are thousands of products traded between countries?

How can we use this to test the HO model?

• Measuring the Factor Content of Trade Using Leontief’s test, we can look at similar data. We can multiply his numbers shown in Table 4.2 by the

actual value of U.S. exports and U.S. imports. This gives values for “total exports” and “total imports.”



• These values are called the factor content of exports and factor content of imports.

• By taking the difference between the factor content of exports and factor content of imports.

This gives factor content of net exports, shown in the final column of 4.2.



• Measuring the Factor Content of Trade Since both these factor contents are positive, we see

that the U.S. was running a trade surplus.

• Measuring Factor Abundance How should we measure factor abundance when there

are more than two factors and two countries? Compare the country’s share of that factor with its

share of world GDP. If the share of a factor > share of world GDP.

The country is abundant in that factor. If the share of factor < share of world GDP.

The country is scarce in that factor.



Country Factor Endowments, 2000 Figure 4.9



• Capital Abundance

For example, 24% of the world’s physical capital is located in the U.S., which had 21.6% of world GDP.

We can conclude that the U.S. was abundant in physical capital in 2000.

• Labor and Land Abundance U.S. is abundant in R&D scientists: 26.1% of the world’s total

as compared to 21.6% of the world’s GDP. The U.S. is also abundant in skilled labor but is scarce in less-

skilled labor and illiterate labor. India is scarce in R&D scientists: 2.5% of world’s total as

compared to 5.5% of the world’s GDP.



• Labor and Land Abundance The U.S. is also scarce in arable land which is

surprising since we think of the U.S. as a major exporter of agriculture.

Another surprise is that China is abundant in R&D scientists.

These findings seem to contradict HO model.

It is likely that the productivity of R&D scientists and arable land are not the same in both countries.

We need to allow for differences in productivity.



• Differing Productivities Across Countries Remember that Leontief found that the U.S. was

exporting labor-intensive products even though it was capital-abundant at that time.

One explanation is that labor is highly productive in the U.S. and less productive in the rest of the world. Then the effective labor force in the U.S. is much larger than if

we just count people. Effective labor force is the labor force times its productivity.

We can now look at differing productivities into the HO model.



• Measuring Factor Abundance Once Again

Effective Factor Endowment is the actual factor endowment times the factor productivity.

To determine if a country is abundant in a certain factor, we compare the country’s share of that effective factor with share of world GDP. If share of an effective factor is less than its share of world GDP

then that country is abundant in that effective factor. If share of an effective factor is less than its share of world

GDP, then that country is scarce in that effective factor.



• Effective R&D Scientists On way to measure this is through a country’s R&D spending per

scientist. Take the total number of scientists and multiply that by the R&D

spending per scientists With these productivity corrections, the U.S. is more abundant in

effective R&D scientists and China is lower.

• Effective Arable Land Effective arable land is the actual amount of arable land times the

productivity in agriculture. The U.S. has a very high productivity in agriculture where China

has a lower productivity. The U.S. is neither scarce nor abundant in effective arable land.



“Effective” Factor Endowments, 2000 Figure 4.10

HEADLINES


Food Imports Close to Matching Level of Exports

• It is expected that by about 2010, U.S. imports of agricultural goods will be about equal to exports.

• That is what the HO model would predict, given our finding that the U.S. is neither abundant nor scarce in effective land.


Extending the Heckscher-Ohlin Theorem

• We have now abandoned many of the assumptions we previously made. We allow for many goods, factors, and countries. We also allow for factors to differ in productivity. A new version called the “sign test” is available. If a country is abundant in an effective factor, then the

factor’s content in net exports should be positive. If a country is scarce in an effective factor, then that

factor’s content in net exports should be negative.



• The sign test is as follows Sign of (country’s % share of effective factor minus the %

share of world GDP) equals Sign of (Country’s factor content of net exports).

Using 35 countries, the U.S. share of GDP of those countries was 33%.

Given the timing after WWII, we can assume that the U.S. share of world capital was more than 33%.

Therefore, the U.S. was abundant in capital and since that factor’s content of net exports was positive, it passes the sign test.

The U.S. share of population for the 35 countries was about 8%.

Therefore, the U.S. was scarce in labor.



• But labor’s factor content of net exports was positive.

• The sign test seems to fail for the U.S. in 1947 in labor.

• However, the U.S. share of the population is not the right way to measure the U.S. labor endowment.

• One way to measure productivity is to use wages paid to workers.

• The effective amount of labor found in each country equals the actual amount of labor times the wage. The amount of labor in each country times the average

wages gives total wages paid to labor.



Figure 4.11



• Doing this for 30 countries and comparing it to the U.S. we find that the U.S. was abundant in effective labor.

• Given that the U.S. was abundant in effective factor, then labor also passes the sign test, in addition to capital.

• There is no “paradox” in the U.S. pattern of trade.• This explanation for Leontief’s paradox relies on taking

into account the productivity differences in labor across countries. As Leontief himself proposed, once we take into account

differences in the productivity of factors across countries, there is no “paradox” after all.

APPLICATION


Why does India Import Cotton Textiles?

• From the 17th century until the early 19th century, India was a major world producer of cotton textiles and exported those goods to Britain and elsewhere.

• By the early 19th century, however, Britain had overtaken India as the world’s dominant producer of cotton textiles and was exporting to India.

• India still produced raw cotton needed to manufacture cotton cloth—the raw cotton was exported to Britain.

• A similar trade pattern held for China and Egypt.

APPLICATION



• These countries are all labor abundant rather than land abundant, therefore it is puzzling why they seem to be net exporters of land and net importers of labor.

• Two explanations

1. Britain’s rise as the world’s leading exporter of cotton textiles was related to technological improvements.

However India was able to gain access to this technology. Then the importing of textiles is contrary to the HO model.

APPLICATION



2. The poor countries used this new technology to make textiles inefficiently.

Large differences in efficient use of technology across countries remained. .

• This inefficiency applied more strongly to labor than it did to other factors such as land.

• Estimates from 1910 and 1990 show that labor was not necessarily the abundant factor in India once we take into account its low productivity.

• India could be considered land-abundant if land and labor are measured by their “effective” amounts.

• This can explain the switch from exporter to importer.

Feenstra Taylor Econ CH04

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