1. Chapter 2: The Heckscher-Ohlin Model
Goal: Explaining comparative advantage and thus trade flows through different factor endowments.
Heckscher-Ohlin-Samuelson (HOS): Two countries, two goods, two factors.
Heckscher-Ohlin-Vanek (HOV): Two countries, many goods, many factors.
Explaining factor content of trade flows.
Gießen,

2. 2.1 Comparative Advantage and Trade Flows
Revealed preferences: An allocation y is directly revealed preferred to a different allocation z if z was in the budget set when y was chosen. Weak Axiom of revealed preferences: If allocation y is directly revealed preferred to z, then z cannot be directly revealed preferred to y. Let y be the choice at prices p. Then z cannot be chosen at prices p* if pz < py.
Gießen,

3. Application: Let m = (m1,m2) denote the import vector
Application: Let m = (m1,m2) denote the import vector. At autarky prices pa the preferred choice is point 0. No point below the budget line can be directly preferred to point 0.
pIm1 + m2 = 0 m2
-m1 m1
pam1+ m2 = 0
Figure 2.1
-m2

4. Implication for trade flows: Denote pa as relative price of good 1 in the autarky equilibrium, and pI as relative price of good 1 in the free trade equilibrium. In the latter pIm1 + m2 = 0 must hold. This implies together with the WARP:
pam1 + m2  0
pIm1 + m2 = 0
Subtracting the second equality from the first inequality yields
[pa – pI]m1  0,
i.e. good 1 will only be imported if its autarky price is greater than the world market price.

5. Extension to 3 goods:
pa1m1 + pa2m2 + m3 ≤ 0 cannot hold because of the WARP.
pI1m1 + pI2m2 + m3 = 0 must hold in the free trade equilibrium. Subtracting the second from the first expression implies
[pa1 – pI1]m1 + [pa2 – pI2]m2 ≤ 0 cannot hold, i.e. it cannot be true that a country exports all goods for which the autarky price was greater than the world market price.

6. 2.2 Factor Abundancy Heckscher-Ohlin Theorem:
Assumptions: Two goods, two factors, two countries, identical homothetic preferences, identical linear homogeneous production functions, no FIRs.
Each country exports the good that uses its abundant factor intensively.
Proof: Suppose w.l.g. that good 1 is labor intensive, and L/K > L*/K*. Let L = L* and K* > K.

7. Step 1: good 1 has lower autarky price in the home country than in the foreign country.
Step 2: H-O-Theorem implied by result on comparative advantage.
Identical relative prices would lead to a contradiction: Consider Figure 2. Suppose the home country equilibrium is at point A. If autarky prices are the same in the foreign country its equilibrium is at point B’. But because of identical homothetic preferences the consumption point must be on a ray from the origin through point A, e.g. C’. Thus B’ cannot be the autarky equilibrium in the foreign country. Because of the Rybczynski theorem B’ must be above and to the left of A, but C’ would have to be above and to the right of A – a contradiction.

8. Figure 2.2

9. At prices pa there would be an excess demand for good 1, hence the price of good 1 would go up and pa* > pa.
Next we show that the world market price (free trade equilibrium price) p satisfies pa* > p > pa. Denote world excess demand for good 1 as zI(p) = z(p) + z*(p). As shown above zI(pa) > 0. By an analogous argument zI(pa*) < 0, hence by continuity there exists some p satisfying pa* > p > pa such that zI(p) = 0.
Distribution effects of trade: the abundant factor gains, the scarce factor loses (Samuelson-Stolper).

10. Figure 2.3

11. Leontief‘s Paradox Empirical test of H-O-Model (1953):
Input-Output tables yield the following result:
Exports
Imports
Capital ($ million per $ 1 million value of output)
$ 2.5
$ 3.1
Labor(person-years per $ 1 million value of output)
182
170
Capital/Labor ($/person)
13700
18200

12. Explanations:
Measurement errors
Different demand functions (refuted by Houthakker)
Different technologies
Neglect of other factors of production
Factor intensity reversals (Minhas)
Labor not homogenous (different productivities)
Data too close to World War II
No free trade (Travis)

13. 2.3 Heckscher-Ohlin-Vanek Model
C countries, N goods, M factors.
identical technologies, factor price equalization,
identical homothetic preferences.
ajk = quantity of primary factor k needed per one unit of output j.
A = [ajk]‘…factor input coefficient matrix (MN);
rows: factors k = 1,…,M,
columns: outputs of industries j = 1,…,N.
Yi: output vector of country i, i = 1,…,C.

14. Di = demand vector of country i
Ti := Yi – Di = vector of net exports of country i.
Fi:= ATi = factor content of trade.
Goal of HOV-model: relate Fi to factor endowment

15. Fi  ATi = AYi – ADi = Vi – siVw.
Vi….vector factor endowments in country i.
AYi = Vi…full employment condition. Identical relative prices and homothetic preferences imply that consumption of country i is proportional to world consumption (and thus to world production):
Di = siDw, where Dw is world demand and si is the share of country i of world production.
HOV theorem:
Fi  ATi = AYi – ADi = Vi – siVw.

16. Definition: country i is abundant in factor k if the following inequality holds:
Vki/Vkw > si.
Capital is abundant relative to labor if
Ki/Kw > Li/Lw.
Theorem (Leamer 1980):
If capital is abundant relative to labor in country i, then the capital/labor ratio embodied in production for country i exceeds the capital/labor ratio embodied in consumption:
Ki/Li > (Ki – Fki)/(Li – Fℓi)

17. Proof:
One can rewrite F as
Fki = Ki – siKw
Fℓi = Li – siLw
This implies
Kw = (Ki - Fki )/si, Lw = (Li - Fℓi )/si, hence
Ki/Kw = siKi/(Ki - Fki ), Li/Lw = siLi/(Li - Fℓi ), and then
Ki/Kw > Li/Lw implies
Ki/(Ki - Fki ) > Li/(Li - Fℓi ), which yields the expression of the theorem.

18. Leamer‘s estimates (1980):
Figures show value of capital and amount of labor embodied in production and consumption
Production
Consumption
Capital ($ billion)
$ 327
$ 305
Labor (million person years) 47 45
Capital/Labor ($/person)
$ 6949
$ 6737

19. Figure 2.4: Vi: factor endowment of home country, ADi: domestic consumption, slope of line Vi to ADi equals ratio of factor prices.

20. Remark: Leamer’s test does not require balanced trade; trade deficit (imports > exports) implies that share of consumption exceeds share of world GDP, but consumption point is still on diagonal.
Empirical tests:
A complete test requires data on trade (Ti), technology (A) and factor endowments (Vi).
Partial tests (only two of those data available): Leontief, Leamer, Baldwin.
Complete tests: Bowen, Leamer and Sveikauskas; Trefler, Davis and Weinstein.

22. Complete test (Bowen, Leamer and Sveikauskas 1987):
Sign test: sign(Fki) = sign(Vki – siVkw).
Rank test: Fki > Fℓi  (Vki - siVkw) > (Vℓi – siVℓw).
Random pattern (flipping a coin) would generate correct signs 50% of the time – test should perform significantly better.
Results:
Sign test: satisfied 61% of the cases
Rank test: satisfied 49% of the cases

23. Different Technologies Across Countries
Least plausible assumption of HOV-model: Identical technologies.
Approaches to modeling technological differences
Different factor productivities
Different factor requirements (Ai  Aj)
Different factor productivities (Trefler 1993a)
Productivity of each factor in the U.S.A. as benchmark (= 1), productivity of factor k in country i is denoted as ki. In efficiency units the endowment of country i in factor k equals ki Vki.

24. A denotes factor requirements in efficiency units – identical for all countries. Modified HOV-equation:
MC equations, M(C–1) productivity parameters – but total factor exports must equal total factor imports, equations for one country (U.S.A.) can be dropped. From the above equation the productivities can be calculated; they have to be checked with respect to their plausibility (strictly positive, compatible with other data (e.g.factor prices).

25. Figure 2.5: Correlation between wages and estimated labor productivities.

26. Other Tests of Trade:
1. Comparative advantage:
paDf  paDa = paYa  paYf (country index i omitted)
Revealed preferences: free trade consumption vector cannot be affordable at autarky prices,
in autarky: consumption equals production,
profit maximization: at autarky prices autarky output vector has greater value than free trade output vector.
pa(Df – Yf)  0, T = Yf – Df, and because of balanced trade
pfT = 0, hence
(pa – pf)T  0.
Bernhofen & Brown(2001): confirmed for Japan ( )

27. 2. Factor prices and factor content
Helpman (1984): Suppose factor price equalization does not hold. Let Xij denote the vector of gross exports from country i to country j. The factor content of these exports, denoted as Fij, equals
Fij = AiXij.
Thought experiment: Suppose country j imports the factors Fij instead and produces the goods herself. Denote the GDP function as G(p,V). Recall the properties of the GDP-function:

28. Gross domestic product function: G(p,V) = maxpifi(vi) s.t. vi  V
By the properties of a maximum value function:
G/pi = fi(vi) = yi,
G/Vj = pifi/vij = wj.
Gießen,

29. Figure 2.6: concavity implies f(x‘)+fx(x‘)[x-x‘]  f(x)

30. p[Yj + Xij]  G(p,Vj + Fij)
 G(p,Vj) + [G(p,Vj)/Vj]Fij
= pYj + wjFij,
implying
pXij  wjFij.
The first inequality follows from the definition of G, the second from concavity of G (see figure 2.6), and the third from the property of a maximum value function Gv = w.
Using factor prices of the exporting country (wi), constant returns to scale imply pXij = wiFij.

31. Subtracting the equality from the inequality gives
[wj – wi]Fij  0.
Performing the same exercise for the exports of country j to country i yields
[wj – wi]Fji  0.
Now subtract the second from the first inequality :
[wj – wi][Fij – Fji] 0,
i.e. „on average“ factors embodied in traded goods will flow from countries where they are relatively cheap into countries where they are relatively expensive.
Empirical tests: e.g.Choi and Krishna (2001, 2004)