The Heckscher-Ohlin Model: Brief Review

The Heckscher-Ohlin Model: Brief Review giuseppe.dearcangelis@uniroma1.it 2015 1st Term

General Characteristics Explain trade with differences in endowments (also called factors proportion theory ) Technology (and preferences) are assumed identical among countries Perfect competition in all markets Important implications: Free trade implies factor price equalization (FPE) Effects of trade on the distribution of income (Stolper-Samuelson theorem)

Simple (2 2 2) Case Assumptions 2 goods (X and Y ) and 2 factors (L and T )

Simple (2 2 2) Case Assumptions 2 goods (X and Y ) and 2 factors (L and T ) Technology: CRS, no factors intensity reversal Perfect competition in all markets Mobile factors among sectors No frictions; full employment No full specialization, necessary for three theorems

Simple (2 2 2) Case Equations X = F X (L X, T X ) Y = F Y (L Y, T Y ) L X + L Y = L T X + T Y = T p X FL X = w p Y FL Y = w p X FT X = r p Y FT Y = r

Simple (2 2 2) Case Equations X = F X (L X, T X ) Y = F Y (L Y, T Y ) L X + L Y = L T X + T Y = T p X FL X = w p Y FL Y = w p X FT X = r p Y FT Y = r Hp: small country p X p Y are given. Resources are given: L and T.

Simple (2 2 2) Case Equations X = F X (L X, T X ) Y = F Y (L Y, T Y ) L X + L Y = L T X + T Y = T p X FL X = w p Y FL Y = w p X FT X = r p Y FT Y = r Hp: small country p X p Y are given. Resources are given: L and T. 8 equation in 8 unknowns: X, Y ; L X, L Y, T X, T Y ; w, r.

CRS Technology: Characteristics Homothetic isoquants independence on the production scale; hence, go for per-capita output CRS partial derivatives are homogeneous of degree 0 Same slopes of isoquants on arrays out of the origin MRTS = f (T /L) only Euler s theorem: F k (L, T ) = F k L L k + F k T T k p k Q k = wl k + rt k The efficiency locus in the Edgeworth box does not cross the diagonal; it coincides with the diagonal in case of linear, constant-coefficients technology

Simple (2 2 2) Case Theorems Unit-value isoquants

Simple (2 2 2) Case Theorems Unit-value isoquants Lerner-Pierce diagram can prove all the 4 theorems

Simple (2 2 2) Case Theorems Unit-value isoquants Lerner-Pierce diagram can prove all the 4 theorems Heckscher-Ohlin theorem: patterns of trade

Simple (2 2 2) Case Theorems Unit-value isoquants Lerner-Pierce diagram can prove all the 4 theorems Heckscher-Ohlin theorem: patterns of trade FPE theorem (needs absence of full specialization)

Simple (2 2 2) Case Theorems Unit-value isoquants Lerner-Pierce diagram can prove all the 4 theorems Heckscher-Ohlin theorem: patterns of trade FPE theorem (needs absence of full specialization) Stolper-Samuelson theorem: opening-up to trade and distribution of income (needs absence of full specialization)

Unit Value Isoquants and FPE Theorem K k Y C ( 1 pk ) EY Y e = 1 py k X EX X e = 1 px O α = pl pk D ( 1 pl ) L

HO Theorem K k Y Y 2 P 2 Y V 1 1 P 1... Q... 2 X2... Y1 D F 1 F 2 G 1 G 2 X1 D Y D 2 X D 2 V 2 k X 0 Q 1 X 1 L

Full Specialization K Y 1 V 1 k Y H 1... Y2... X 2 V 2 k X 0 L

Stopler Samuelson K C Y = 1 py k Y C ( 1 pk ) E Y EY k X EX E X X = 1 px X = 1 p X O D α = pl pk D ( 1 pl ) L

Rybczynski K k Y V... W. F N XV XW G M Y V k X X W 0 L

FPE Set 2 2 2 Model 4.3. Factor Price Equalization 87 Figure 4.10: The factor price equalization set of such vectors are the employment of L and K in each industry, denoted L A,L B andk A,K B. Naturally,thesumofthesectorialemploymentvectors gives the endowment Giuseppe vectors, De Arcangelis that is, L A HO +LModel B = L and K A +K B = K. (Gandolfo, 2014, p. 79)

90 Chapter 4. The Heckscher-Ohlin Model Heckscher-Ohlin-Vanek (Gandolfo, 2014, p. 81) Figure 4.11: The factor content of trade whose slope is given by the factor price ratio represents the GDP line (or budget constraint Giuseppe line) of Deeach Arcangelis country since it is obtained by multiplying

HO-Vanek Equations X: vector (n 1) of productions, n goods, x i i = 1, 2,..., n

HO-Vanek Equations X: vector (n 1) of productions, n goods, x i i = 1, 2,..., n V: vector (m 1) of factors, m factors, V j j = 1, 2,..., m

HO-Vanek Equations X: vector (n 1) of productions, n goods, x i i = 1, 2,..., n V: vector (m 1) of factors, m factors, V j j = 1, 2,..., m A(w) : matrix (m n) of factor coefficients, which vary with factor prices in the vector w (m 1); a j,i : quantity of factor j to produce 1 unit of good i, j = 1, 2,..., m and i = 1, 2,..., n p: vector (n 1) of output prices, p i i = 1, 2,..., n but n 1 independent relative prices

HO-Vanek Equations A (w) w = p (n m) (m 1) (n 1) A(w) X = V (m n) (n 1) (m 1) (n + m) equations to solve for the m prices of inputs, w, and the n quantities of output, X, as functions of the m endowments, V, and the n (internationally given) prices, p.

Understanding the HOV Equations n Efficiency conditions: A (w) w = p

Understanding the HOV Equations n Efficiency conditions: Explicit first equation: A (w) w = p a 1,1 w 1 + a 2,1 w 2 + + a j,1 w j + + a m,1 w m = p 1 }{{} cost of producing 1 unit of good 1

Understanding the HOV Equations n Efficiency conditions: Explicit first equation: A (w) w = p a 1,1 w 1 + a 2,1 w 2 + + a j,1 w j + + a m,1 w m = p 1 }{{} cost of producing 1 unit of good 1 m Factors markets clearing conditions: Explicit first equation: A(w) X = V a 1,1 x 1 + a 1,2 x 2 + + a 1,i x i + + a 1,n x n = V 1 }{{} demand of factor 1 from all sectors

Competitive Equilibrium A (w) w = p A(w) X = V

Competitive Equilibrium A (w) w = p A(w) X = V Given the (n 1) relative prices in p, the system can be interpreted in two ways:

Competitive Equilibrium A (w) w = p A(w) X = V Given the (n 1) relative prices in p, the system can be interpreted in two ways: Equilibrium of the integrated world economy (given relative output prices); whatever n and m, there s no problems in solving for the n world output quantities in X and the m factor prices in w; if the endowments of the two countries is in the FPE set, then w holds for both countries (i.e. FPE holds);

Various Extensions More factors than goods (m > n): see sector-specific model

Various Extensions More factors than goods (m > n): see sector-specific model More goods than factors (m n):

Various Extensions More factors than goods (m > n): see sector-specific model More goods than factors (m n): FPE holds for the integrated economy (see above)

Various Extensions More factors than goods (m > n): see sector-specific model More goods than factors (m n): FPE holds for the integrated economy (see above) Indeterminate quantities and patterns of trade: for the two-country free-trade case 2m + n equations (m equilibrium conditions for factors markets in each country and n efficiency equations) for m + 2n unknowns (m equalized factor prices and n commodity outputs in each country) too many unknowns The HO theorem must be reformulated in terms of the factor content of trade (HOV):

HO-Vanek Equations Factor requirements and factor availability: A(w) X = V

HO-Vanek Equations Factor requirements and factor availability: A(w) X = V or X = A 1 V

HO-Vanek Equations The domestic consumption C is a fraction s of world consumption because of homothetic and identical preferences: C = sc W

HO-Vanek Equations The domestic consumption C is a fraction s of world consumption because of homothetic and identical preferences: C = sc W Since the world economy is a closed economy, then C W = X W ; hence, given same technology everywhere and FPE: C = sx W = sa 1 V W

HO-Vanek Equations Subtract domestic consumption from domestic production and obtain net exports: X C = A 1 ( V sv W )

HO-Vanek Equations Subtract domestic consumption from domestic production and obtain net exports: X C = A 1 ( V sv W ) or: F A (X C) = V sv W where F: factor content of net exports.

HO-Vanek Equations F: factor content of net exports. F A (X C) = V sv W

HO-Vanek Equations F: factor content of net exports. Explicit first equation: F A (X C) = V sv W a 1,1 (x 1 c 1 ) + a 1,2 (x 2 c 2 ) + + a 1,i (x i c i ) + + a 1,n (x n c n ) = }{{} requirement of factor 1 from all net exports = (V 1 sv W 1 )

HO-Vanek Equations F A (X C) = V sv W F: factor content of net exports. Order the country s factor endowment relative to the world as follows: V 1 V W 1 > V 2 V W 2 > > V m V W m > s > V m+1 V W m+1 > > V M V W M We can redefine the HO theorem in terms of factor contents: The country net-exports goods that contains factors 1,..., m and net-imports the factors m + 1,..., M.

Factor-Specific Model: Assumptions Same as in HO, but with some factors that cannot freely move among sectors. Hence, the number of factors increases with factors that become specific to each sector. Case: 2 goods (X and Y ); mobile factor labor (L) and sector-specific land (T X and T Y ) Tools: Basin graph with the value of marginal product of the mobile factor for both sectors The wage bill Value of the product to each sector-specific land.

Factor-Specific Model: Comparative exercizes Effects of opening up to trade as a change in the domestic price Changes in the endowments of the mobile factor and the specific factors: effects on production (Rybczynski) and on the factor prices E.g. Dutch disease Reformulate the HO theorem in terms of relative scarcity of sector-specific factors

HO and HOV: The Leontieff paradox The new evidence by Leamer (1980) What goes wrong with HO? Which hp fails? Missing trade, Trefler (1995)

Chapter 4: Trade and Resources: The Heckscher-Ohlin Model 2 Testing the Heckscher-Ohlin Model Leontieff Paradox 2 2 2 Model Leontief s Paradox TABLE 4-1 Leontief s Test Leontief used the numbers in this table to test the Heckscher-Ohlin theorem. 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. As shown in the last row, the capital labor ratio for exports was less than the capital labor ratio for imports, which is a paradoxical finding. Copyright 2011 Worth Publishers International Economics Feenstra/Taylor, 2/e. 18 of 55

Chapter 4: Trade and Resources: The Heckscher-Ohlin Model 2 Testing the Heckscher-Ohlin Model Leontieff Paradox 2 2 2 Model Leontief s Paradox TABLE 4-1 Leontief s Test Leontief used the numbers in this table to test the Heckscher-Ohlin theorem. 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. As shown in the last row, the capital labor ratio for exports was less than the capital labor ratio for imports, which is a paradoxical finding. Possible explanations: Different labor productivity Copyright 2011 Worth Publishers International Economics Feenstra/Taylor, 2/e. Other failures of HO hp s 18 of 55

Leamer s Sign test Leamer (1980) applies the Vanek interpretation of HO.

Leamer s Sign test Leamer (1980) applies the Vanek interpretation of HO. If a country is abundant in a(n effective) factor, then that factor s content in net exports should be positive, but if a country is scarce in a(n 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

Chapter 4: Trade and Resources: The Heckscher-Ohlin Model HOV Evidence 2 2 2 Model 2 Testing the Heckscher-Ohlin Model Factor Endowments in the New Millennium Capital, Labor and Land Abundance FIGURE 4-6 Country Factor Endowments, 2 Shown here are country shares factors of produ in the year 2000 eight selected countries and th of the world. In the first bar graph, we see that 24% of the world s physical capital in 20 was located in the United States, with 9% located in China, 13% located in Japan, and so on. In the final bar graph, we see that in 2000 the United St had 22% of world GDP, China had 11%, Japan had 8%, and so on.

Trefler s Missing Trade When comparing actual international trade and the expected trade according to endowment differences, actual trade is too low!

Trefler s Missing Trade When comparing actual international trade and the expected trade according to endowment differences, actual trade is too low! Trefler (1995) calls is missing trade.

Trefler s Missing Trade When comparing actual international trade and the expected trade according to endowment differences, actual trade is too low! Trefler (1995) calls is missing trade. What is the cause? Technology is different and then productivities are different

apter 4: Trade and Resources: The Heckscher-Ohlin Model 2 2 2 Model 2 Testing the Heckscher-Ohlin Model HOV Evidence Differing withproductivities Effective Factors across Countries FIGURE 4-7 (2 of 2) Effective Factor Endowments, 2000 Shown here ar shares of R&D and land in 200 first the informa Figure 4.6, and making an adju for the product each factor acr countries to ob effective shar The United States was scarce in arable land when using the number o (since it had 13% of the world s land as compared with 22% of the wor but neither scarce nor abundant in effective land (since it had 21% of t

hapter 4: Trade and Resources: The Heckscher-Ohlin Model 2 2 2 Model US Effective FIGURE Labor 4-8 Leontief s Paradox Once Again Labor Abundance Labor Endowment and GDP for the United States and R Shown here labor, effec of the US a world in 194 8% of the w compared t GDP, so it w labor. But w effective lab wages paid then the Un of the world compared t was abunda