1. Lecture 1b. Classic and Neoclassic Trade Models: Heckscher-Ohlin Model
Carlos Llano
References:
Feentra y Taylor (2011). International Economics. Worth Publishers. Chapter 4.
Krugman P. Obsfeld and Melitz: International Economics. Prentice Hall, Chapter .
van Marrewijk C. (2009): The New Introduction to Geographical Economics. Cambridge University Press.

2. Introduction
In this chapter, we outline the Heckscher-Ohlin model, a model that assumes that trade occurs because countries have different resources.’
Our first goal is to describe the Heckscher-Ohlin (HO) model of trade.
The specific-factors model (Chapter 3) was a short-run model because capital and land could not move between the industries.
In contrast, the HO model is a long-run model because all factors of production can move between the industries.

3. Introduction
Our second goal is to examine the empirical evidence on the Heckscher-Ohlin model.
By allowing for more than two factors of production and also allowing countries to differ in their technologies, as in the Ricardian model, the predictions from the Heckscher-Ohlin model match more closely the trade patterns in the world economy today.
The third goal of the chapter is to investigate how the opening of trade between the two countries affects the payments to labor and to capital in each of them.

4. 1 Heckscher-Ohlin Model
Assumptions of the Heckscher-Ohlin Model
Assumption 1: Two factors of production, labor and capital, can move freely between the industries.
Assumption 2:
Two products: shoes vs computers;
Shoes production is labor-intensive; that is, it requires more labor per unit of capital to produce shoes than computers, so that LS /KS > LC /KC.
Computers are capital-intensive: KS / LS > KC / LC 4

5. 1 Heckscher-Ohlin Model
Labor Intensity of Each Industry The demand for labor relative to capital is assumed to be higher in shoes than in computers, LS/KS > LC/KC.
These two curves slope down just like regular demand curves, but in this case, they are relative demand curves for labor (i.e., demand for labor divided by demand for capital).
FIGURE 4-1

6. 1 Heckscher-Ohlin Model
Assumptions of the Heckscher-Ohlin Model
Assumption 3: Foreign is labor-abundant, by which we mean that the labor–capital ratio in Foreign exceeds that in Home, L*/K*> L/K. Equivalently, Home is capital-abundant, so that K/L >K*/L*.
Assumption 4: The final outputs, shoes and computers, can be traded freely (i.e., without any restrictions) between nations, but labor and capital do not move between countries.
Assumption 5: The technologies used to produce the two goods are identical across the countries.
Assumption 6: Consumer tastes are the same across countries, and preferences for computers and shoes do not vary with a country’s level of income.

7. 1 Heckscher-Ohlin Model
No-Trade Equilibrium
Production Possibilities Frontiers, Indifference Curves, and No-Trade Equilibrium Price
FIGURE 4-2 (1 of 3)
No-Trade Equilibria in Home and Foreign
The Home production possibilities frontier (PPF) is shown in panel (a),
and the Foreign PPF is shown in panel (b).
Because Home is capital abundant and computers are capital intensive, the Home PPF is skewed toward computers.

8. Why are Production Possibilities Frontiers skewed?
Home is capital-abundant and computer producing is capital-intensive .
Home is capable to produce more computers than shoes.
Production possibility frontier is skewed in the direction of computers.
Foreign is labor-abundant and shoes producing is labor-intensive.
 Production possibility frontier is skewed in the direction of shoes.

9. 1 Heckscher-Ohlin Model
No-Trade Equilibrium
Production Possibilities Frontiers, Indifference Curves, and No-Trade Equilibrium Price
FIGURE 4-2 (2 of 3)
No-Trade Equilibria in Home and Foreign (continued)
Home preferences are summarized by the indifference curve, U.
The Home no-trade (or autarky) equilibrium is at point A.
The flat slope indicates a low relative price of computers, (PC /PS)A.

10. Heckscher-Ohlin Model
Indifference curves are the same shape in both countries as required by assumption 6.
The slope of an indifference curve equals the amount that consumers are willing to pay for computers in terms of shoes given up.
In the equilibrium, the slope of an indifference curve equals the slope of a production possibility frontier.
A steeply sloped price line implies a high relative price of computers whereas a flat price line implies low relative price of computers.

11. 1 Heckscher-Ohlin Model
No-Trade Equilibrium
Production Possibilities Frontiers, Indifference Curves, and No-Trade Equilibrium Price
FIGURE 4-2 (3 of 3)
No-Trade Equilibria in Home and Foreign (continued)
Foreign is labor-abundant and shoes are labor- intensive, so the Foreign PPF is skewed toward shoes.
Foreign preferences are summarized by the indifference curve, U*
The Foreign no-trade equilibrium is at point A*, with a higher relative price of computers, as indicated by the steeper slope of (P*C /P*S)A*.

12. Heckscher-Ohlin Model
We expect the equilibrium relative price of computers to lie between the no-trade relative prices in each country
This implies, hence, that Home will be exporting computers and Foreign will be exporting shoes
Importantly, in contrast to Ricardian model Home and Foreign are not completely specialized to produce only a single product.

13. 1 Heckscher-Ohlin Model
Free-Trade Equilibrium
Home Equilibrium with Free Trade
FIGURE 4-3 (1 of 2)
International Free-Trade Equilibrium at Home
At the free-trade world relative price of computers, (PC /PS)W,
Home produces at point B in panel (a) and consumes at point C,
exporting computers and importing shoes.
Point A is the no-trade equilibrium.
The “trade triangle” has a base equal to the Home exports of computers (the difference between the amount produced and the amount consumed with trade, (QC2 − QC3).

14. 1 Heckscher-Ohlin Model
Free-Trade Equilibrium
Home Equilibrium with Free Trade
FIGURE 4-3 (2 of 2)
International Free-Trade Equilibrium at Home (continued)
The height of this triangle is the Home imports of shoes (the difference between the amount consumed of shoes and the amount produced with trade, QS3 − QS2).
In panel (b), we show Home exports of computers equal to zero at the no-trade relative price, (PC /PS)A,
and equal to (QC2 − QC3) at the free-trade relative price, (PC/PS)W.

15. 1 Heckscher-Ohlin Model
Free-Trade Equilibrium
Foreign Equilibrium with Free Trade
FIGURE 4-4 (1 of 2)
International Free-Trade Equilibrium in Foreign
At the free-trade world relative price of computers, (PC /PS)W,
Foreign produces at point B* in panel (a) and consumes at point C*,
importing computers and exporting shoes.
Point A* is the no-trade equilibrium.)
The “trade triangle” has a base equal to Foreign imports of computers (the difference between the consumption of computers and the amount produced with trade, (Q*C3 − Q*C2).

16. 1 Heckscher-Ohlin Model
Free-Trade Equilibrium
Foreign Equilibrium with Free Trade
FIGURE 4-4 (2 of 2)
International Free-Trade Equilibrium in Foreign (continued)
The height of this triangle is Foreign exports of shoes (the difference between the production of shoes and the amount consumed with trade, Q*S2 – Q*S3).
In panel (b), we show Foreign imports of computers equal to zero at the no-trade relative price, (P*C /P*S)A*, and equal to (Q*C3 − Q*C2) at the free-trade relative price, (PC /PS)W.

17. 1 Heckscher-Ohlin Model
Free-Trade Equilibrium
Equilibrium Price with Free Trade Because exports equal imports, there is no reason for the relative price to change and so this is a free-trade equilibrium.
FIGURE 4-5
Determination of the Free-Trade World Equilibrium Price
The world relative price of computers in the free-trade equilibrium is determined at the intersection of the Home export supply and Foreign import demand, at point D.
At this relative price, the quantity of computers that Home wants to export, (QC2 − QC3), just equals the quantity of computers that Foreign wants to import, (Q*C3 − Q*C2).

18. 1 Heckscher-Ohlin Model
Free-Trade Equilibrium
Pattern of Trade
Home exports computers, the good that uses intensively the factor of production (capital) found in abundance at Home.
Foreign exports shoes, the good that uses intensively the factor of production (labor) found in abundance there.
This important result is called the Heckscher-Ohlin theorem.

19. 3 Effects of Trade on Factor Prices
Effect of Trade on the Wage and Rental of Home
Economy-Wide Relative Demand for Labor
FIGURE 4-10
Determination of Home Wage/Rental
The economy-wide relative demand for labor, RD, is an average of the LC /KC and LS /KS curves and lies between these curves.
The relative supply, L/K, is shown by a vertical line because the total amount of resources in Home is fixed.
The equilibrium point A, at which relative demand RD intersects relative supply L/K, determines the wage relative to the rental, W/R.
Relative supply
Relative demand

20. 3 Effects of Trade on Factor Prices
Effect of Trade on the Wage and Rental of Home
Increase in the Relative Price of Computers
FIGURE 4-11
Increase in the Price of Computers
Initially, Home is at a no-trade equilibrium at point A with a relative price of computers of (PC /PS)A.
An increase in the relative price of computers to the world price, as illustrated by the steeper world price line, (PC /PS)W, shifts production from point A to B.
At point B, there is a higher output of computers and a lower output of shoes,
QC2 > QC1 and QS2 < QS1.

21. 3 Effects of Trade on Factor Prices
Effect of Trade on the Wage and Rental of Home
Increase in the Relative Price of Computers
FIGURE 4-12 (1 of 2)
Effect of a Higher Relative Price of Computers on Wage/Rental
An increase in the relative price of computers shifts the economy-wide relative demand for labor, RD1, toward the relative demand for labor in the computer industry, LC /KC.
The new relative demand curve, RD2, intersects the relative supply curve for labor at a lower relative wage, (W/R)2.

22. 3 Effects of Trade on Factor Prices
Effect of Trade on the Wage and Rental of Home
Increase in the Relative Price of Computers
FIGURE 4-12 (2 of 2)
Effect of a Higher Relative Price of Computers on Wage/Rental (continued)
As a result, the wage relative to the rental falls from (W/R)1 to (W/R)2.
The lower relative wage causes both industries to increase their labor–capital ratios, as illustrated by the increase in both LC /KC and LS /KS at the new relative wage.
↑ ↓ ↑ ↓
Relative supply No change
Relative demand No change in total

23. 3 Effects of Trade on Factor Prices
Determination of the Real Wage and Real Rental
Change in the Real Rental
R = PC • MPKC
R = PS • MPKS
MPKC = R/PC ↑
MPKS = R/PS ↑
Change in the Real Wage
W = PC • MPLC
W = PS • MPLS
MPLC = W/PC ↓
MPLS = W/PS ↓

24. 3 Effects of Trade on Factor Prices
Determination of the Real Wage and Real Rental
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.
For our example, the Stolper-Samuelson theorem predicts that when Home opens to trade and faces a higher relative price of computers, the real rental on capital in Home rises and the real wage in Home falls. In Foreign, the changes in real factor prices are just the reverse.

25. 3 Effects of Trade on Factor Prices
Changes in the Real Wage and Rental: A Numerical Example

26. 3 Effects of Trade on Factor Prices
Changes in the Real Wage and Rental: A Numerical Example
General Equation for the Long-Run Change in Factor Prices The long-run results of a change in factor prices can be summarized in the following equation:
Real wage falls
Real rental increases
The equations relating the changes in product prices to changes in factor prices are sometimes called the “magnification effect” because they show how changes in the prices of goods have magnified effects on the earnings of factors:
Real rental falls
Real wage increases
Real rental falls
Real wage increases

27. The Sign Test in the Heckscher-Ohlin Model
K e y T e r m
A P P E N D I X T O C H A P T E R 4
The Sign Test in the Heckscher-Ohlin Model
Measuring the Factor Content of Trade
FIGURE 4A-1
Factor Content of Trade for the United States, 1947 This table extends Leontief’s test of the Heckscher-Ohlin model to measure the factor content of net exports. The first column for exports and for imports shows the amount of capital or labor needed per $1 million worth of exports from or imports into the United States, for The second column for each shows the amount of capital or labor needed for the total exports from or imports into the United States. The final column is the difference between the totals for exports and imports.
By taking the difference between the factor content of exports and the factor content of imports, we obtain the factor content of net exports, shown in the final column of Table 4A-1.

28. Computer Lab Ricardian Model: Testing the HOV Model:
A Practical Guide to Trade Policy Analysis:
Testing the HOV Model:
Feenstra, R Chapter 2

29. The Sign Test in the Heckscher-Ohlin Model
K e y T e r m
A P P E N D I X T O C H A P T E R 4
The Sign Test in the Heckscher-Ohlin Model
The Sign Test
We make use of the factor content of trade in developing a test for the Heckscher-Ohlin model, called the sign test. This test states that if a country is abundant in an effective factor, then that factor’s content in net exports should be positive, but if a country is scarce in an effective factor, then that factor’s content in net exports should be negative.
Sign of (country’s % share of effective factor − % share of world GDP) = Sign of country’s factor content of net exports

30. 1 Heckscher-Ohlin Model
Heckscher-Ohlin Theorem:
Assumption 1: Labor and capital flow freely between the industries.
Assumption 2: The production of shoes is labor-intensive as compared with computer production, which is capital-intensive.
Assumption 3: The amounts of labor and capital found in the two countries differ, with Foreign abundant in labor and Home abundant in capital.
Assumption 4: There is free international trade in goods.
Assumption 5: The technologies for producing shoes and computers are the same across countries.
Assumption 6: Tastes are the same across countries.

31. 3. Testing the Heckscher-Ohlin-Vanek (HOV)
HOV: Many countries, i = 1,…,C; Industries, j=1,…,N; Factors, k =1,..,M.
Technologies are identical across countries.
Tastes are identical and homothetic across countries.
Matrix A=[ajk]' , with dimensions (MxN), denotes the amounts of labor, capital, land,…needed for one unit of production in each industry.
Notice that this matrix applies in any country (same technology in all C).
Rows measure factors (k=1,…,M);
Columns measure industries (j=1,…,N).
Yi denotes the (Nx1) vector of outputs in each industry for country i,
Di denote the (Nx1) vector of demands of each good (equal for all countries)
Thus, Ti =Yi– Di equals the vector of net exports for country i.
The factor content of trade is: Fi ≡ ATi, which is an (Mx1) vector.
We denote individual components of this vector as Fik where:
A positive value indicates that the factor is exported,
A negative value indicates that the factor is imported.

32. HOV Theorem: Fi ≡ ATi = Vi– si Vw
3. Testing the HOV Model
HOVM relates the factor content of trade ATi to the endowments of country i.
To do so, we compute AYi and ADi.
AYi = demand for factors in country i. It is also, the endowments of country i,
AYi = Vi
ADi is simplified by using our assumption of identical and homothetic tastes.
Since product prices are equalized across countries by free trade, the consumption vectors of all countries must be proportional to each other.
Thus Di = si Dw,
where Dw = the world consumption vector
si = the share of country i in world consumption.
Thus: ADi= siADw.
If trade is balanced, si = country i’s share of world GDP.
Since world consumption must equal world production, then:
ADi= si ADw = siAYw = siVw.
HOV Theorem: Fi ≡ ATi = Vi– si Vw
HOV Theorem (for individual factors): Fik = Vik– si Vwk

33. 3. Testing the HOV Model Fi ≡ ATi = Vi– si Vw T i = A-1(V i – s i V w)
Partial tests
Complete test

34. 3. Testing the HOV Model <
The first test was performed by Leontief (1953).
He supposed that USA was abundant in capital relative to the rest of the world.
Thus, from the H-O theorem, US was expected to export capital-intensive goods and import labor-intensive ones.
He found the opposite: the capital–labor ratio for U.S. imports was higher than the one for U.S. exports!
This contradiction of the H-O is the Leontief’s paradox.
<
Each column shows the amount of capital or labor needed to produce $1 million worth of exports from, or imports into, the United States in 1947.

35. 3. Testing the HOV Model Leontief’s Paradox
Explanations
U.S. and foreign technologies are not the same, in contrast to what the HO theorem and Leontief assumed.
By focusing only on labor and capital, Leontief ignored land abundance in the United States.
Leontief should have distinguished between skilled and unskilled labor (because it would not be surprising to find that U.S. exports are intensive in skilled labor).
The data for 1947 may be unusual because World War II had ended just two years earlier.
The United States was not engaged in completely free trade, as the Heckscher-Ohlin theorem assumes.

36. 3. Testing the HOV Model Factor Endowments in the New Millennium
To determine whether a country is abundant in a certain factor, we compare the country’s share of that factor with its share of world GDP.
If its share of a factor exceeds its share of world GDP, then we conclude that the country is abundant in that factor, and
if its share in a certain factor is less than its share of world GDP, then we conclude that the country is scarce in that factor.

37. Country Factor Endowments, 2000. Feenstra and Taylor (2011)
3. Testing the HOV Model
Country Factor Endowments, Feenstra and Taylor (2011)

38. 3. Testing the HOV Model Differing Productivities across Countries
Feenstra and Taylor (2011)
Differing Productivities across Countries
Leontief found that the US was exporting labor-intensive products even though it was capital-abundant.
Why?
Labor is more productive in the US than in the rest of the world.
Then, the effective labor force in the US, the labor force times its productivity, is larger than it appears to be when we just count people.

39. 3. Testing the HOV Model Differing Productivities across Countries
Feenstra and Taylor (2011)
Differing Productivities across Countries
To allow factors of production to differ in their productivities across countries, we define the effective factor endowment as the actual amount of a factor found in a country times its productivity:
Effective factor endowment = Actual factor endowment * Factor productivity

40. 3. Testing the HOV Model Differing Productivities across Countries
Feenstra and Taylor (2011)
Differing Productivities across Countries
To determine whether a country is abundant in a certain factor, we compare the country’s share of that effective factor with its share of world GDP.
If its share of an effective factor exceeds its share of world GDP, then we conclude that the country is abundant in that effective factor;
if its share of an effective factor is less than its share of world GDP, then we conclude that the country is scarce in that effective factor.
Effective R&D Scientists
Effective R&D scientists = Actual R&D scientists • R&D spending per scientist

41. 3. Testing the HOV Model
Feenstra and Taylor (2011)
Differing Productivities across Countries. 2000
China: abundant in R&D scientists (14% > 11% of the world’s GDP) but scarce in effective R&D scientists (7% < 11% of the world’s GDP).
US: scarce in arable land (13% < 22% of the world’s GDP) but neither scarce nor abundant in effective land (21% = 22% ).

42. 3. Testing the HOV Model Leontief’s Paradox Once Again Labor Abundance
Feenstra and Taylor (2011)
Leontief’s Paradox Once Again
Labor Abundance
FIGURE 4-8
Labor Endowment and GDP for the United States and Rest of World, 1947
Shown here are the share of labor, “effective” labor, and GDP of the US and the rest of the world in The US had only 8% of the world’s population, as compared to 37% of the world’s GDP, so it was very scarce in labor. But when we measure effective labor by the total wages paid in each country, then the United States had 43% of the world’s effective labor as compared to 37% of GDP, so it was abundant in effective labor.

43. sign(Fik ) = sign ( Vik– si Vwk)
3. Testing the HOV Model. Feenstra (2004).
A complete test for HOV
Fi ≡ ATi = Vi– si Vw
T i = A-1(V i – s i V w)
Factor content of net exports data
A=technology data in country i
Factor Endowment data in country I and in the World
1. The sign test
sign(Fik ) = sign ( Vik– si Vwk)
2. The rank test

44. sign(Fik ) = sign ( Vik– si Vwk)
3. Testing the HOV Model
1. The sign test
sign(Fik ) = sign ( Vik– si Vwk)
Factor content of net exports data
Factor Endowment data
Sign of (country’s % share of factor − % share of world GDP) = Sign of country’s factor content of net exports
This test states that:
if a country is abundant in a factor, then that factor’s content in net exports should be positive,
but if a country is scarce in a factor, then that factor’s content in net exports should be negative.
What is the % of M*C observations that have the same sign?
The H-O is tested if this number is > 50%.

45. 3. Testing the HOV Model 2. The rank test
Factor content of net exports data
Factor Endowment data
This test implies a pairwise comparison of all factors for all sectors:
If the computed factor contents of one factor exceeds that of a second factor, then we check whether the relative abundance of that first factor also exceeds the relative abundance of the second factor.

46. 3. Testing the HOV Model Bowen, Leamer and Sveikaukas (1987).
27 countries and 12 factors.
Both sign and rank test failed.
Trefler (1995) performs several diagnostic tests on the data to determine which assumptions of the HOV model is most likely to be responsible for its failure:
Equal technologies across countries is especially unlikely.
Trefler (1993).
33 countries. 9 factors. A= US technological matrix (input-output tables)
Results:
Both sign and rank test failed when considering same technology for all countries (USA). Columns 2 and 4.

47. 3. Testing the HOV Model
Two ways to introduce technological differences in HOV:
to model the productivity of factors in different countries.
to model differences in the factor requirements matrix A.
Trefler (1993) follows the first approach:
33 countries. 9 factors. A= US technological matrix (input-output tables).
πik= the productivity of factor k in country i relative to its productivity in the U.S.
πik Vik = The effective endowment of factor k in country i.
Now, A denote the amount of effective factors needed per unit of output in each industry.

48. 3. Testing the HOV Model
Trefler (1993) follows the first approach. Results:
Allowing for all factors in all but one country to differ in their productivities the HOV becomes an equality.
However HOV is not testable.
So how to check the HOV. Two ways:
Check whether the productivity parameters are positive;
We might compare these parameters to other economic data to evaluate how “reasonable” the productivity parameters are.
For example, it makes sense to compare the labor productivity parameters to wages across countries.

49. 3. Testing the HOV Model Labor Productivity
Feenstra and Taylor (2011)
Labor Productivity
Feenstra and Taylor (2011), FIGURE 4-9
We expect this close connection between wages and labor productivity from the Ricardian model, in which technology differences across countries determine wages, and this is also what we expect to hold in the Heckscher-Ohlin model once we drop the assumption of identical technologies.
Labor productivities across countries and their wages, relative to the United States in 1990, are highly correlated (0.9).
Then the effective amount of labor found in each country equals the actual amount of labor times the wage.

50. 3. Testing the HOV Model
Feenstra (2004)
Trefler (1993) follows the first approach. Results:
To implement this, we need to model Ai in terms of some productivity differences across countries.
Trefler considers that the matrices Ai differ by a uniform amount across countries:
If country i is less productive than the US.
Now the HOV expression becomes:

51. 3. Testing the HOV Model
Source: Trefler (1995); Feenstra (2004). Ex. 2.1 and 2.2.
Columns (1) is per-capita GDP relative to U.S. per-capita GDP.
Columns (2) and (4): the sign and rank tests, assuming that all countries have the U.S. technology.
Columns (3) and (5): the sign and rank tests, allowing for uniform technological differences δi across countries.
Column (6): estimates of δi and column (7) their asymptotic t-statistic for the null hypothesis δi= 1.

52. 3. Testing the HOV Model
Source: Trefler (1995);

53. 3. Testing the HOV Model The Sign Test in the Heckscher-Ohlin Model
Feenstra and Taylor (2011)
The Sign Test in the Heckscher-Ohlin Model
The Sign Test in a Recent Year
FIGURE 4A-2
The Sign Test for 33 Countries with Differing Technologies, 1990 This table shows the sign test for the Heckscher-Ohlin model for 1990, allowing for different technologies across countries. There are 33 countries included in the study and 9 factors of production. All countries have more factors passing the sign test than failing it, especially the low- and medium-income countries. These results show that the sign test holds true when we allow productivities to differ across countries.
Note: The countries with low GDP per capita are Bangladesh, Pakistan, Indonesia, Sri Lanka, Thailand, Colombia, Panama, Yugoslavia, Portugal, and Uruguay. The countries with middle GDP per capita are Greece, Ireland, Spain, Israel, Hong Kong, New Zealand, and Austria. The countries with high GDP per capita are Singapore, Italy, the United Kingdom, Japan, Belgium, Trinidad, the Netherlands, Finland, Denmark, former West Germany, France, Sweden, Norway, Switzerland, Canada, and the United States.

54. 4. Conclusions
Feenstra and Taylor (2011)
In the Heckscher-Ohlin model, we assume that the technologies are the same across countries and that countries trade because the available resources (labor, capital, and land) differ across countries.
The Heckscher-Ohlin model is a long-run framework, so labor, capital, and other resources can move freely between the industries.
With two goods, two factors, and two countries, the Heckscher-Ohlin model predicts that a country will export the good that uses its abundant factor intensively and import the other good.
The first test of the Heckscher-Ohlin model was made by Leontief using U.S. data for He found that U.S. exports were less capital-intensive and more labor-intensive than U.S. imports. This was a paradoxical finding because the United States was abundant in capital.

55. 4. Conclusions
Feenstra and Taylor (2011)
The assumption of identical technologies used in the Heckscher-Ohlin model does not hold in practice.
Current research has extended the empirical tests of the Heckscher-Ohlin model to allow for many factors and countries, along with differing productivities of factors across countries.
When we allow for different productivities of labor in 1947, we find that the United States is abundant in effective—or skilled—labor, which explains the Leontief paradox.