bernhofen-lect2-2

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Lecture 2: Testing comparative advantage

x David Ricardo (1817) discovered the principle of comparative advantage.

x Gottfried Haberler (1930) reformulated the theory of comparative advantage and provided its modern

opportunity cost formulation.x Alan Deardorff (1980) provided the modern general equilibrium formulation.

Revisiting Ricardos original formulation:

The quantity of wine which she [Portugal] shall give in exchange for the cloth of England, is not determined by the

respective quantities of labour devoted to the production of each, as it would be, if both commodities were manufactured inEngland, or both in Portugal.

England may be so circumstanced, that to produce the cloth may require the labour of100 men if she attempted tomake the wine, it might require the labour of120 men for the same time. England would therefore find it her interest toimport wine, and to purchase it by the exportation of cloth.

To produce the wine in Portugal, might require only the labour of80 men for one year, and to produce the cloth in thesame country, might require the labour of90 men for the same time, It would therefore be advantageous for her to export

wine in exchange for cloth.

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Ricardos modelling framework:- 2 commodities: cloth and wine,- 1 factor of production: labour,- fixed labour unit coefficients in each country: ac

E,aw

E,ac

P,aw

P

- cloth and wine are exchanged on an international market,- but commodities are valued by the labour embodied in them.

Ricardos logic (following Ruffin (2002) and Maneschi (2004))

- Denoting with Tc the trade of cloth and Tw the trade of wine, Ricardo assumed that Tc units of cloth areexchanged for Tw units of wine at the international market.=> the terms of international trade is then given by Tc/Tw .-Since commodities are valued by the labour embodied in them, England faces a labour exchange rate ofac

ETc/aw

ETw embodied in its commodity trade. This is the labour terms of trade line depicted in Figure 1.

England will only be willing to engage in trade if it obtains gains.Similarly, Portugal faces a labour exchange rate of ac

PTc/aw

PTw and will only trade if it gains from such

trade.


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- There are two possibilities about the direction of international trade(i) Tc>0, Tw England will import wine and export cloth because this generates a gain of 20 labour units..Similarly, Portugal will import cloth and export wine since Tcac

P-Twaw

P=90-80>0.

Ricardo established a direct link between the pattern of international trade and the gains from internationaltrade.

Modern 2-good formulation of comparative advantage

Assumptions:- we assume there are two regimes: autarky and freeinternational trade.- 2 goods are produced under constant returns to scale.- autarky: state of isolation, the economy can consume only what it produces.- autarky prices: the countrys equilibrium prices in isolation are p1

a,p2

a.

- free international trade: the economy is part of an international trading system andhas the option to trade with other trading partners.

- small country assumption: the country has no effect on the international prices.

- terms of trade: equilibrium prices under free trade are p1f

,p2f

.


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- Budget constraint/Balanced trade condition: If the country decides to engage in international trade, itmust be at the terms dictated by the world market:

p1

fT1+p2

fT2=0 (1)

or p1f

(C1-X1)+p2f

(C2-X2)=0Equation (1) is an implication of the small country assumption. If Ti>0, good i is imported (i.e. C1>X1) andif Ti0 and T2 good 1 is exported (T10)

C

ais the economys consumption point in autarky, which will coincide with its production point X

a.

Through international trade, the economy can obtain a consumption point Cfthat differs from its production

point Xf.

The comparative advantage slope prediction (2) can be captured more compactly in a single inequality:

Cf

Xf

good 2

good 1

p1 /p2

p1a

/p2a

Ca=X

a

T1

T2

C2

X2

C2 X1


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p1aT1+p2

aT2>0 (3)

Proof:The equivalence between (2) and (3) follows directly from rewriting the balance of trade condition (1) suchthat -(T2/T1)= p1

f/p2

f.

The general formulation of the law of comparative advantage (Deardorff, 1980)

The 2-good formulation of the comparative advantage prediction can be generalized to n goods under verygeneral conditions.Notation:

pi: n-vector of commodity prices.

pa

denotes the economys equilibrium price vector in autarky

pfdenotes the economys equilibrium price under trade

X

i

: n-vector of production Xa

denotes the economys equilibrium production vector in autarky X

fdenotes the economys equilibrium production vector under trade

Ci: n-vector of consumption

Cfdenotes the economys equilibrium consumption point under trade

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(in autarky Xa=C

a).

T: n-vector of net imports T=C

f-X

f; T is also called the economys net import vector.

If Ti>0, good i is imported; if Ti p

2C

1>p

2C

2. (A2)

(Note: C

1and C

2are the revealed choices under the price regimes p

1,p

2, respectively).

The weak axiom of revealed preference says: if C

1was chosen over C

2, although C

2was affordable at p

1(i.e.

C1

is revealed preferred to C2), then C

1must have been more expensive than C

2at p

1.

3) Balanced trade condition: p

fT=0. (A3)


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Theorem of comparative advantage (Deardorff, 1980, 1994)

If (A1)-(A3) => paT>0. (4)

Proof: (A1) and (A3) => p

fC

f=p

fX

f p

fX

a=p

fC

a. From (A2), we get p

aC

f>p

aC

a=p

aX

a. Since (A1)

implies pa

Xa

pa

Xf

, we finally obtain pa

Cf

>pa

Xf

,or pa

T>0.Figure 3: The general n-good prediction of comparative advantage

paT=0

importsof good 1

T1

A

paT>0

paT0, can beinterpreted as cutting the terms of trade hyperplane into half. The theory predicts that one should not observe trading vectors that liein the shaded area, i.e. paT0 is often called the correlation version of comparative advantage. The inequality is ofteninterpreted to say that a country will, on average, exports the goods with low autarky price and imports the goods with high autarkyprices. This stems from the fact that (after some normalization), p

aT>0 can be shown to imply cor(p

a-p

f, T)>0 (Deardorff, 1980, p.

951), i.e. there is a positive correlation between autarky-free trade price differences and net imports.(v) In his classical article Deardorff (1980) has shown that the law is robust to the incorporation of trade costs or government imposed

barriers to international trade, as long as export subsidies are ruled out (where the latter must only be ruled out in an average sense).In an extension Deardorff (1994) shows that this law does also hold under unbalanced trade (if one assumes homothetic preferences),production distortions and regional differences within a country (i.e. lumpiness within a country).

(vi) A key lesson of the theory of comparative advantage is that if n>2, it is not possible to pinpoint in which specific sector a country hasa comparative advantage or disadvantage. This has important implications for the policy making community since policy makersoften ask economists where they think the country has a comparative advantage. The theory implies that if there are more than twosectors, the fact that a specific good is exported/imported can not be linked to underlying comparative advantage fundamentals. Theappropriate answer is that the market will figure it out, if we allow the market to reign.


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(vii) The autarky price formulation of comparative advantage is the most general way to state the law of comparative advantage. The keypoint to recognize is that in a market economy autarky prices embody all the relevant information about economic fundamentals liketechnologies, endowments or tastes. In contrast, the Ricardian and the Heckscher-Ohlin models focus on specific fundamentals liketechnological differences (Ricardian framework) or endowment differences (Heckscher-Ohlin framework) that are thought ofdriving international specialization.

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A formal characterization of the comparative advantage gains from trade

The inner product paT embodies information about the gains from trade. More formally, the gains from

international trade can be captured by the Slutsky compensation measure of a welfare change. The Slutskycompensation measure asks the following question: What income is necessary to move from the autarkyconsumption point C

ato the free trade consumption point C

f, assuming that prices remain at the autarky

level pa? Formally, this can be written as

WSlutsky = pa

Cf

-pa

Ca

. (5)The first part of the proof of the law of comparative advantage has already established that p

aC

f>p

aC

a.

Positive gains from trade are a sufficient condition for the pattern of trade prediction. But we can also showthat p

aT provides an upper bound for the gains from trade:

WSlutsky= paC

f-p

aC

a= p

a(C

f-X

f)+p

a(X

f-C

a)

= paT-p

a(X

a-X

f)

paT. (6)

The latter inequality results from (A1), since p

aX

a p

aX

f. The inner product p

aT will be an exact measure of

the gains from trade for constant opportunity costs of production (i.e. paX

a=p

aX

f). Figure 4 illustrates the

relationship (6) in the two good case.


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Measuring real income in terms of units of good 1, WSlutsky is given by the line segment ST. Alsomeasured in units of good 1, the CA index is T1+(p2/p1)T2, which corresponds to X

fT=OT-OX

fin the graph.

But XfT exceeds ST by X

fS. In the case of a linear production possibility frontier, X

fwill coincide with S.

Figure 4: (Bernhofen & Brown (2005), Figure 1) Note X

a=C

a

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Testing the theory of comparative advantage: the natural experiment of Japan

Recall from Samuelsons foundations (1947, p.5):

...under ideal circumstances an experiment could be devised whereby one could refute thehypothesis.

Japans 19

thcentury opening up provided us with the ideal circumstances of a natural experiment.

POWER POINT SLIDES ON JAPANMotivation: Japans opening up to world commerce in 1853 after over 200 years of self-imposed autarky

provides an unusual opportunity to empirically investigate the theory of comparative advantage. Japans

trade liberalization experience is unique in several ways:

(i) Japans domestic production environment before and shortly after its trade liberalization was similar (i.e.

its production possibility set remained relatively unchanged).

(ii) While operating under autarky, the Japanese economy was predominantly a market economy. Bycontrast, virtually all other countries that opened up to international trade in the past (i.e. Latin America in


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the 1980s, Eastern Europe in the 1990s), were not market oriented before opening up. Hence, domestic

market reform often coincided with external trade liberalization, which makes it difficult to disentangle their

relative effects (i.e. what is caused by domestic market reform and what by trade liberalization). Japan is a

notable exception since it didnt experience significant domestic reforms in the early trade liberalization

period, i.e. during 1868-1875.

(iii) Given that Japan produced relatively homogeneous products in small scale production units, other

explanations for international trade like increasing returns to scale and imperfect competition- can be ruled

out as accounting for Japans pattern of trade.

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A test of the pattern of trade prediction of comparative advantage:

The attractiveness of the comparative advantage prediction (4) stems from its refutability. The null andthe alternative hypothesis can then be stated as follows:

H0: Pr(p

aT>0)=1; H1: p

aT is random and Pr(p

aT>0)=1/2 (7)

where Pr(.) denotes the probability measure. A great virtue of the opportunity cost formulation ofcomparative advantage is not only that it leaves us with an alternative hypothesis, CHANCE (i.e. p

aT is just

random), but also with a probability statement about that randomness. If all outcomes are equally likely, thelikelihood of getting a positive sign is exactly 0.5.Figure 6. (Figure 1 in Bernhofen (2005)) Counterfactual interpretation of the pattern of trade prediction)

Empirical challenge: How can we apply a static theory to a dynamic world?


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Theory requires information about p

a1870s, which is not observable. Under what conditions can we substitute

the observed pa1850s for the unobserved p

a1870s?

Identification condition: (p

a1850s- p

a1870s )T0, (8)

Cf1870s

Pf1870s

Ca1850s

pa1850s

good 2

PPF1850s PPF1870sgood 1

p 1870s

pa1870

Ca1870s

T1

T2

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(8) requires that the slope of pa1870s has not become larger than p

a1850s. Assuming unchanging preferences,

this condition can be interpreted that the economys growth path from PPF1850s to PPF1870s was eitherbalanced or biased towards its exportable.In the n-good case (8) says that the economy experienced, on average, a growth path which was eitherbalanced or biased towards the export goods.

The Composition of Japanese Trade, 1868-1875 (Table 1 in Bernhofen & Brown (2004))

Product Percent of Imports Percent of Exports

Agricultural: Non-Food

Silk 35.9

Silkworm Eggs 15.7

Other (Vegetable Wax and Cotton) 2.2 2.7

Agricultural: Food

Tea 28.2

Rice 10.8

Sugar 9.9


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Other Foods 4.2 8.2

Other Raw Materials

Fuel (Coal and Charcoal) 1.9

Other 3.1 2.9

Textiles 0.2

Cotton Yarn 15.1

Cotton Cloth 18.4

Woollens 19.2

Other textiles 1.8

Other manufactures 4.3

Weapons and ammunition 2.7

Machinery and instruments 1.4

Miscellaneous manufactures 11.2

Notes: The trade shares of each commodity group are based upon total imports and exports for the period 1868-1875.

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Empirical evidence: Table 2 from Bernhofen and Brown (2004)

The Approximate Inner Product in Various Test Years

(in million Ry)

Year of Net Import VectorComponents

1868 1869 1870 1871 1872 1873 1874 1875

(1) Imports withobservedautarky prices

2.24 4.12 8.44 7.00 5.75 5.88 7.15 7.98

(2) Imports ofwoollen goods 0.98 0.82 1.29 1.56 2.16 2.50 1.56 2.33

(3) Imports withapproximatedautarky prices(Shinbo index)

1.10 0.95 0.70 0.85 1.51 2.08 1.60 2.65

(4) Exports withobservedautarky prices

-4.07 -3.40 -4.04 -5.16 -4.99 -4.08 -5.08 -4.80

(5) Exports withapproximatedautarky prices(Shinbo index)

-0.09 -0.03 -0.07 -0.07 -0.15 -0.07 -0.11 -0.10

Total inner

product (sum

of ((1)-(5))

0.18 2.47 6.31 4.17 4.28 6.31 5.11 8.06


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Notes: All values are expressed in terms of millions of ry. The ry equaled about $1 in 1873 and was equivalent to the yen when it was

introduced in 1871. The estimates are of the approximation of the inner product ( Tp a~~

1 ) valued at autarky prices prevailing in 1851-1853. For an

explanation of the assumptions underlying the approximation, please see the text.Source: For sources of price data, see footnotes 18 and 21. For numbers (3) and (5), current silver yen values are converted to values of 1851-1853 by deflating them with the price indices for exports and imports found in Shinbo (1978, Table 5-10).

Summary:

The fact that each of the 8 inner products had a positive sign provides a strong empirical case for theprediction of the theory. The alternative CHANCE, i.e. H1:Pr(p

aT>0)=1/2, can be rejected with the

likelihood of 99.6%.

An empirical assessment of the comparative advantage gains from trade

We consider now the empirical implementation of (6), which leads to the following counterfactual:

By how much would real income have had to increase in Japan during its final autarky years of 1851-1853to afford the consumption bundle the economy could have obtained if it were engaged in international tradeduring that period?

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Figure 7: (Figure 2 in Bernhofen (2005)): The counterfactual gains from trade)

Cf1870s

Cf1850s

Ca1850s

good 1

good 2

WSlutskyP

f1870s

PPF1850s PPF1870s

pa1850s

Pa1850s


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Alternative Estimates of the Gains from Trade for the Autarky Years of 1851- 1853 as a Percentage of

GDP (Table 4 in Bernhofen and Brown (2005))

Assumed annual growth rate of GDP per

capitaMethod and Period

0.15% 0.4% 1.5% 2.0%

Using the backcast

estimates of GDP5.4 5.8 7.8 9.0

Using the forecast

estimates of GDP9.1 8.9 7.8 7.3

Summary: The counterfactual gains from trade were between 6 and 9% of Japans GDP at the time.

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References:

Bernhofen, D.M. and J.C. Brown, 2004. A direct test of the theory of comparative advantage: the case ofJapan. Journal of Political Economy 112(1), 48-67.

Bernhofen, D.M., Brown J.C., 2005. An empirical assessment of the comparative advantage gains from

trade: evidence from Japan. American Economic Review 95(1), 208-225.Bernhofen, D. M. 2005, The empirics of comparative advantage: overcoming the tyranny ofnonrefutability, Review of International Economics 13(5), 1017-1023,

Bernhofen, D. M. 2009. On predictability in the neoclassical trade model: a synthesis, forthcoming inEconomic Theory.

Deardorff, A.V, 1980. The general validity of the law of comparative advantage. Journal of PoliticalEconomy 88, 941-57.

Deardorff, Alan, 1994, "Exploring the Limits of Comparative Advantage", Weltwirtschaftliches Archiv130:1-19.

Maneschi, Andrea, 2004. The true meaning of David Ricardos four numbers. Journal of InternationalEconomics 62, 433-443.

Ruffin, R.J., 2002. David Ricardos discovery of comparative advantage.History of Political Economy 34,

727-748.

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