the heckscher-ohlin model: brief revie · the heckscher-ohlin model: brief review giuseppe de...

2 × 2 × 2 ModelGeneralization

The short-run: the Factor-Specific ModelEmpirical Evidence

The Heckscher-Ohlin Model: Brief Review

Giuseppe De [email protected]

2014 1st Term

Giuseppe De Arcangelis HO Model



General Characteristics

I Explain trade with differences in endowments (also called“factors’ proportion theory”)

I Technology (and preferences) are assumed identical amongcountries

I Perfect competition in all markets

I Important implications:I Free trade implies factor price equalization (FPE)I Effects of trade on the distribution of income

(Stolper-Samuelson theorem)I Unequal effects of changes in factors’ quantities on sectors’

production (Rybczynski theorem)







I Perfect competition in all marketsI Important implications:

I Free trade implies factor price equalization (FPE)

I Effects of trade on the distribution of income(Stolper-Samuelson theorem)

I Unequal effects of changes in factors’ quantities on sectors’production (Rybczynski theorem)








I Free trade implies factor price equalization (FPE)I Effects of trade on the distribution of income

(Stolper-Samuelson theorem)

I Unequal effects of changes in factors’ quantities on sectors’production (Rybczynski theorem)








I Free trade implies factor price equalization (FPE)I Effects of trade on the distribution of income

(Stolper-Samuelson theorem)I Unequal effects of changes in factors’ quantities on sectors’

production (Rybczynski theorem)




Simple (2× 2× 2) Case – Assumptions

I 2 goods (X and Y ) and 2 factors (L and T )

I Technology: CRS, no factors’ intensity reversal

I Perfect competition in all markets

I Mobile factors among sectors

I No frictions; full employment

I No full specialization, necessary for three theorems




Simple (2× 2× 2) Case – Equations

X = FX (LX ,TX ) Y = FY (LY ,TY )LX + LY = L TX + TY = TpXF

XL = w pY F

YL = w

pXFXT = r pY F

YT = r

Hp: small country ⇒ pX pY are given. Resources are given:L and T .8 equation in 8 unknowns: X , Y ; LX , LY , TX , TY ; w , r .






XL = w pY F

YL = w

pXFXT = r pY F

YT = r

Hp: small country ⇒ pX pY are given. Resources are given:L and T .

8 equation in 8 unknowns: X , Y ; LX , LY , TX , TY ; w , r .






XL = w pY F

YL = w

pXFXT = r pY F

YT = r

Hp: small country ⇒ pX pY are given. Resources are given:L and T .8 equation in 8 unknowns: X , Y ; LX , LY , TX , TY ; w , r .




CRS Technology: Characteristics

I Homothetic isoquants

I Same slopes of isoquants on arrays out of the origin

I MRTS = f (T/L) only

I Euler’s theorem:F k(L,T ) = F k

L Lk + F kTTk ⇒ pkQk = wLk + rTk

I The efficiency locus in the Edgeworth box does not cross thediagonal; it coincides with the diagonal in case of linear,constant-coefficients technology

I Convexity of isoquants ⇒ concavity of the transformationcurve




Simple (2× 2× 2) Case – Theorems

I Unit-value isoquants

I Lerner-Pierce diagram can prove all the 4 theorems

I Heckscher-Ohlin theorem: patterns of trade

I FPE theorem (needs absence of full specialization)

I Stolper-Samuelson theorem: opening-up to trade anddistribution of income (needs absence of full specialization)

I Rybczynski theorem: changes in resources and effects onproduction and trade (needs absence of full specialization)




FPE Set4.3. 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, denotedLA, LB and KA,KB. Naturally, the sum of the sectorial employment vectorsgives the endowment vectors, that is, LA + LB = L and KA + KB = K.Recall that the slope of a vector is given by the ratio of its elements, thus,for instance, the slope of the sectorial employment vector measured on theL-axis for industry A is given by KA/LA which is the capital intensity inindustry A.

The integrated equilibrium yields the equilibrium values of factor priceswhich, as studied in section 4.1.1, allow to determine the factor intensity ineach industry. Given the factor intensities we can draw the sectorial employ-ment vectors by drawing two segments (from whichever corner) whose slopescorrespond to the factor intensities and whose length is such that the sum ofthem give the vector of world endowments.

In Fig. 4.10, the vectors O1EA and O1EB (or, equivalently, O2EA andO2EB) represent the sectorial employment vectors. Recalling the parallelo-gram rule of vectorial sum it is immediate that the sum O1EA +O1EB givesthe world endowment vector. The length of each sectorial employment vectoris proportional to factor inputs and, therefore, reflects the quantity of output;the longer the sectorial employment vector the larger the sector output.

We now split the world into two countries. Any point in the rectangle

(Gandolfo, 2014, p. 79)Giuseppe De Arcangelis HO Model



Heckscher-Ohlin-Vanek

90 Chapter 4. The Heckscher-Ohlin Model

Figure 4.11: The factor content of trade

whose slope is given by the factor price ratio represents the GDP line (orbudget constraint line) of each country since it is obtained by multiplyingfactor endowments by factor prices. The diagonal represents the vector offactor services embodied in the production the goods consumed by the worldeconomy.

Since preferences are identical and homothetic and since trade is balanced,each country will consume a share of world production of goods equal to itsshare of world income. Therefore, the vector representing factor servicesembodied in the goods consumed by a country will necessarily lie on thediagonal and will necessarily be a fraction of it. Its length is given by theintersection of the GDP line with the diagonal. In Fig. 4.11, O1C andO2C represent such vectors for country 1 and 2, respectively. The vectorCE is the factor content of trade vector for country 1. Its elements are(L1 − LC1) < 0 and (K1 −KC1) > 0. The first element is negative and thesecond is positive reflecting the fact that country 1 is relatively well endowedof K. The vector EC is the factor content of trade vector for country 2.As stated in the Heckscher-Ohlin-Vanek (henceforth H-O-V) theorem, eachcountry is the net exporter of the services of its abundant factor and the netimporter of the services of its scarce factor.

It is interesting to note that the H-O-V theorem does not require any

(Gandolfo, 2014, p. 81)Giuseppe De Arcangelis HO Model



HO-Vanek Equations

I X: vector (n × 1) of productions, n goods, xi i = 1, 2, . . . , n

I V: vector (m × 1) of factors, m factors, Vj j = 1, 2, . . . ,m

I A(w) : matrix (m × n) of factor coefficients, which vary withfactor prices in the vector w (m × 1); aj ,i : quantity of factor jto produce 1 unit of good i , j = 1, 2, . . . ,m and i = 1, 2, . . . , n

I p: vector (n × 1) of output prices, pi i = 1, 2, . . . , n but n − 1independent relative prices

General equilibrium for the competitive economy:

A′(w) w = p(n ×m) (m × 1) (n × 1)

A(w) X = V(m × n) (n × 1) (m × 1)




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 nquantities of output, X, as functions of the m endowments, V, andthe n (internationally given) prices, p.

Stolper-Samuelson andRybczynski as comparative-statics exercizes.




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 nquantities of output, X, as functions of the m endowments, V, andthe n (internationally given) prices, p. Stolper-Samuelson andRybczynski as comparative-statics exercizes.




Understanding the HOV Equationsn Efficiency conditions:

A′(w) w = p

Explicit first equation:

a1,1w1 + a2,1w2 + · · ·+ aj ,1wj + · · ·+ am,1wm︸︷︷︸cost of producing 1 unit of good 1

= p1

m Factors’ markets clearing conditions:

A(w) X = V


a1,1x1 + a1,2x2 + · · ·+ a1,ixi + · · ·+ a1,nxn︸︷︷︸demand of factor 1 from all sectors

= V1




Competitive Equilibrium

A′(w) w = pA(w) X = V

Given the (n − 1) relative prices in p, the system can beinterpreted in two ways:

I Equilibrium of the integrated world economy (givenrelative output prices); whatever n and m, there’s no problemsin solving for the n world output quantities in X and the mfactor prices in w; if the endowments of the two countries is inthe FPE set, then w holds for both countries (i.e. FPE holds);

I Equilibrium of the small open economy; the solution forthe quantities in X for each country depends on the relativevalues of m and n.




Various Extensions

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

I More goods than factors (m ≤ n):I FPE holds for the integrated economy (see above)I Indeterminate quantities and patterns of trade: for the

two-country free-trade case 2m + n equations (m equilibriumconditions for factors markets in each country and n efficiencyequations) for m + 2n unknowns (m equalized factor prices andn commodity outputs in each country) ⇒ too many unknowns

I The HO theorem must be reformulated in terms of the factorcontent of trade (HOV): although the T-abundant countrymay import the T-intensive good, when considering the totalfactor content of trade, it will export T services




Various Extensions

I More factors than goods (m > n): see sector-specific modelI More goods than factors (m ≤ n):

I FPE holds for the integrated economy (see above)I Indeterminate quantities and patterns of trade: for the






Various Extensions


I FPE holds for the integrated economy (see above)

I Indeterminate quantities and patterns of trade: for thetwo-country free-trade case 2m + n equations (m equilibriumconditions for factors markets in each country and n efficiencyequations) for m + 2n unknowns (m equalized factor prices andn commodity outputs in each country) ⇒ too many unknowns





Various Extensions


I FPE holds for the integrated economy (see above)I Indeterminate quantities and patterns of trade:

for thetwo-country free-trade case 2m + n equations (m equilibriumconditions for factors markets in each country and n efficiencyequations) for m + 2n unknowns (m equalized factor prices andn commodity outputs in each country) ⇒ too many unknowns





Various Extensions



two-country free-trade case 2m + n equations (m equilibriumconditions for factors markets in each country and n efficiencyequations)

for m + 2n unknowns (m equalized factor prices andn commodity outputs in each country) ⇒ too many unknowns





Various Extensions



two-country free-trade case 2m + n equations (m equilibriumconditions for factors markets in each country and n efficiencyequations) for m + 2n unknowns (m equalized factor prices andn commodity outputs in each country)

⇒ too many unknownsI The HO theorem must be reformulated in terms of the factor

content of trade (HOV): although the T-abundant countrymay import the T-intensive good, when considering the totalfactor content of trade, it will export T services




Various Extensions








Various Extensions




I The HO theorem must be reformulated in terms of the factorcontent of trade (HOV):

although the T-abundant countrymay import the T-intensive good, when considering the totalfactor content of trade, it will export T services




Various Extensions








HO-Vanek Equations

Factor requirements and factor availability:

A(w) X = V

or

X = A−1V




HO-Vanek Equations

The domestic consumption C is a fraction s of world consumptionbecause of homothetic and identical preferences:

C = sCW

Since the world economy is a closed economy, then CW = XW ;hence, given same technology everywhere and FPE:

C = sXW = sA−1VW




HO-Vanek Equations

Subtract domestic consumption from domestic production andobtain net exports:

X− C = A−1(

V − sVW)

or:

F ≡ A (X− C) = V − sVW

where F: factor content of net exports.




HO-Vanek Equations

F ≡ A (X− C) = V − sVW

F: factor content of net exports.


a1,1(x1 − c1) + a1,2(x2 − c2) + · · ·+ a1,i (xi − ci ) + · · ·+ a1,n(xn − cn)︸︷︷︸requirement of factor 1 from all net exports

=

= (V1 − sVW1 )

Note: the sign of each row of F depends on whether: Vi ≷ sVWi .




HO-Vanek Equations

F ≡ A (X− C) = V − sVW

F: factor content of net exports.Explicit first equation:

a1,1(x1 − c1) + a1,2(x2 − c2) + · · ·+ a1,i (xi − ci ) + · · ·+ a1,n(xn − cn)︸︷︷︸requirement of factor 1 from all net exports

=

= (V1 − sVW1 )

Note: the sign of each row of F depends on whether: Vi ≷ sVWi .




HO-Vanek Equations

F ≡ A (X− C) = V − sVW

F: factor content of net exports.Order the country’s factor endowment relative to the world asfollows:

V1

VW1

>V2

VW2

> · · · > Vm

VWm

> s >Vm+1

VWm+1

> · · · > VM

VWM

We can redefine the HO theorem in terms of factor contents: Thecountry net-exports goods that contains factors 1, . . . ,m andnet-imports the factors m + 1, . . . ,M.




Factor-Specific Model: Assumptions

Same as in HO, but with some factors that cannot freely moveamong sectors. Hence, the number of factors increases with factorsthat become specific to each sector.Case: 2 goods (X and Y ); mobile factor labor (L) andsector-specific land (TX and TY )

Tools:

I Basin graph with the value of marginal product of the mobilefactor for both sectors

I The wage bill

I Value of the product to each sector-specific land.




Factor-Specific Model: Assumptions

Same as in HO, but with some factors that cannot freely moveamong sectors. Hence, the number of factors increases with factorsthat become specific to each sector.Case: 2 goods (X and Y ); mobile factor labor (L) andsector-specific land (TX and TY )Tools:

I Basin graph with the value of marginal product of the mobilefactor for both sectors

I The wage bill

I Value of the product to each sector-specific land.




Factor-Specific Model: Comparative exercizes

I Effects of opening up to trade as a change in the domesticprice

I Changes in the endowments of the mobile factor and thespecific factors: effects on production (Rybczynski) and onthe factor prices

I E.g. Dutch disease

I Reformulate the HO theorem in terms of relative scarcity ofsector-specific factors




HO and HOV: Empirical Evidence

I The Leontieff paradox

I The new evidence by Leamer (1980)

I What goes wrong with HO? Which hp fails?

I Missing trade, Trefler (1995)




Leontieff Paradox

18 of 55 Copyright © 2011 Worth Publishers· International Economics· Feenstra/Taylor, 2/e.

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2 Testing the Heckscher-Ohlin Model

TABLE 4-1

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.

Leontief’s Paradox

Leontief’s Test

Possible explanations:

I Different labor productivity

I Other failures of HO hp’s




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’scontent in net exports should be positive, but if a country is scarcein a(n effective) factor, then that factor’s content in net exportsshould be negative:

I Sign of (country’s % share of effective factor - % share ofworld GDP) = Sign of country’s factor content of net exports




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’scontent in net exports should be positive, but if a country is scarcein a(n effective) factor, then that factor’s content in net exportsshould be negative:

I Sign of (country’s % share of effective factor - % share ofworld GDP) = Sign of country’s factor content of net exports




HOV Evidence


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Capital, Labor and Land Abundance

Factor Endowments in the New Millennium

FIGURE 4-6

Country Factor

Endowments, 2000

Shown here are

country shares of six

factors of production

in the year 2000, for

eight selected

countries and the rest

of the world.

In the first bar graph, we see that 24% of the world’s physical capital in 2000

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 States

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 tradeaccording to endowment differences, actual trade is too low!

Trefler (1995) calls is missing trade.What is the cause?

I Technology is different and then productivities are different

I Differences between North and South which impliesdifferences in effective factors





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

What is the cause?







When comparing actual international trade and the expected tradeaccording to endowment differences, actual trade is too low!Trefler (1995) calls is missing trade.What is the cause?









I Differences between North and South

which impliesdifferences in effective factors




HOV Evidence with Effective Factors


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Differing Productivities across Countries FIGURE 4-7 (2 of 2)

Shown here are country

shares of R&D scientists

and land in 2000, using

first the information from

Figure 4.6, and then

making an adjustment

for the productivity of

each factor across

countries to obtain the

“effective” shares.

The United States was scarce in arable land when using the number of acres

(since it had 13% of the world’s land as compared with 22% of the world’s GDP)

but neither scarce nor abundant in effective land (since it had 21% of the

world’s effective land, which nearly equaled its share of the world’s GDP).


“Effective” Factor Endowments, 2000




US Effective Labor


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Leontief’s Paradox Once Again

FIGURE 4-8

Shown here are the share of

labor, “effective” labor, and GDP

of the US and the rest of the

world in 1947. 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.

Labor Abundance


Labor Endowment and GDP for the United States and Rest of World, 1947


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