trade models

7/23/2019 Trade Models

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Part 1: Neoclassical Trade Theory

Session A

Preliminaries: Two-SectorModels

Feenstra (Ch 1)

Trade & Investment Larry D. Qiu 2

Introduction

Analysis beginning from the equilibrium in a

single economy

Get familiar with the two basic international

trade models and the standard analysis


1. The Ricardian Model


Outline of the Ricardian model and

results.

The environment: labor, technology difference,

Question: Whats the pattern of trade?

Result: Comparative advantage determines thepattern of trade.

Home

Good 1

Good 2

Foreign

Good 1

Good 2


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The 2x1 model

Two goods: i

One factor: labor, L in Home and L* in Foreign

Technology:

Productivity:

Prices:

Labor is perfectly mobile b/w industries within each

country, but immobile b/w countries

*

productionofunitperneededlaborofunit

i

i

a

a

*

1and

1

ii aa

*

2

1* andpricerelative,, pp

pppp

ii =


Analysis 1: Autarky equilibrium

Social planners problem: utility maximization:

Def: Production possibility set (PPS) and

production possibility frontier (PPF):

(1)s.t.),(max 221121, 21 Lyayayyuyy +

2y

1y

2/ aL

1/ aL

Uay2

ay1

A

2

1

2

1

a

a

u

u=


A1: Perfect competition

Zero profit condition

Normalize

Then,

2

1

2

1

2

2

1

1 and,aa

pp

ap

apwap ii ===

12=p

22

and1

a

LwLI

aw ===


Analysis 2: International trade

H has comparative advantage in producing

good 1

Then,

Assumption: free trade and no transport costs

Question: what is the equilibrium p at which

world demand equals world supply?

Let us first use graphic analysis

*

2

*1

2

1

a

a

a

a

*app

At point A

A

B

Def: industry 1 (2) is labor

(capital) intensive

At point B: reverse

FIR: factor intensities change at different factor prices


Question: which

(w,r) (factor prices)for Home?

Answer: endowment

matters. Therefore,

we need to analyze

(1.6) (full

employment) as

well.

),(11 rwCp =

),(22 rwCp =

Ar

Aw

Br

Bw

r

w

A

B


Graphic analysis of (1.6)

Suppose A is the solution to (1.5). Then we have

),(),,( AAiKiKAA

iLiL rwaarwaa ==

K

LLa2 La1

Ka2

Ka1

Producing

one unit of

each good

K

LLa2 La1

Ka2

Ka1

Producing 21 , yy

)( 2,22 KLaay

)( 1,11 KLaay


What is the total endowment required to produce

21 and yy

AK

K

LA

L

?

A


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If are produced, A is the total factors

needed. In reverse, if the country has endowment A,there is a unique which will be produced.

This is how (1.6) is solved.

What if the countrys endowment is outside the cone

(next slide)?

Answer: only one good will be produced (with factor

prices being adjusted to satisfy (1.6)).

Def: Cone of diversification

21 and yy

21 and yy


K

L

Cone of diversification

A

C

D


Graphic analysis of (1.6)

Suppose B is the solution to (1.5). Then we have

),(),,( BBiKiKBB

iLiL rwaarwaa ==

1 in A

2 in A

2 in B1 in B

Note: there is no

overlappingK

L

K

L

B


K

L

Diversificationcone B

Diversification

cone A

Result: If H is a labor (capital) abundant country, A (B) is

the solution, with low (high) wage and high (low) rental

B

B

A

A

K

L

K

L>

A: labor abundant

B: capital abundant


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Case 2: No FIR (Factor Price Equalization)

Two iso-cost curves

from (1.5) No FIR: Factor

intensities do not

change

determine

, using

which in (1.6) to

determine

),(11 rwCp =

),(22 rwCp =

Ew

Er

r

w

E),( EE rw

and iKiL aa

21 and yy


EK

K

LE

L

E

Factor Price Equalization Theorem: Suppose 2 countries

have free trade, identical technologies, but different

endowments. If both countries are diversified and FIR does not

occur, then the factor prices (w,r) are equalized across these

countries.

F


Effects of goods price changes on factor

price

Comparative statics on the zero profit condition (1.5)

dradwadrr

Cdw

w

Cdp iKiL

iii +=

+

=

1,, iKiLiKiL =+=== i

iK

i

iL

C

wa

C

wa

x

dxx

Denote

Percentage change cost share

=

=

2

1

1L2L

1K2K

2K2L

1K1L

2

1

||

1

p

p

r

w

r

w

p

p

Then

1K2K2L1L|| ==where

(1.7)


Suppose industry 1 is labor intensive

2

2

1

1

K

L

K

L

a

a

a

a>

Also suppose the relative price of good 1 increases

Then 0|| >

Then

02

1 >p

pd

0 21 >= ppp

Then, from (1.7), we have

221

2122211221

1

12

2111122112

)()(

||

)()(

||

pppppp

r

pppppp

w

LL

LLLLL

KK

KKKKK

+=

=


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Stopler-Samuelson Theorem

An increase in the relative price of a good will

increase the real return to the factor usedintensively in that good, and reduce the real return

to the other factor.

Intuition:

Definition: magnification effect

Implications: income redistribution

rppw 21 >>>


Graphic analysis of SST

),(' 11 rwCp =

),(11 rwCp =

),(22 rwCp =

0r

0w

'r

'ww

r

0but0Suppose 21 => pp


Effects of endowment changes on output

Comparative statics on the full employment condition

(1.6)

1,1,, 2K1K2L1LiKiL =+=+== K

ay

L

ay iKiiLiDenote

=

=

K

L

y

y

y

y

K

L

||

1

1L1K

2L2K

2

1

2

1

2K1K

2L1L

Then

2L2K1K1L|| ==where

(1.8)


Suppose industry 1 is labor intensive

2

2

1

1

K

L

K

L

a

a

a

a>

Also suppose

Then 0|| >

0and0 => KL

Then, from (1.8), we have

0||

and0

||

12

21 >=

LyL

Ly KK


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Rybczynski Theorem

An increase in a factor endowment will increase

output of industry using it intensively, anddecrease the output of the other industry.

Intuition (see next slide):

Implications: Dutch disease


K

L

(L,K) (L,K)

),( 22 KL aa

),( 11 KL aa

),( 222 KL aay

),( 111 KL aay

),(' 222 KL aay

),(' 111 KL aay

Graphic analysis of the

Rybczynski Theorem


Conclusion

Ricardian model

2x2 model (the preliminary H-O model), with fixed

output prices: derive a set of results Provide tools to prove the theorems and intuitions,

for further study.


Session B

The Heckscher-Ohlin ModelFeenstra (Ch 2)


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Introduction

The environment: endowment difference.

Questions:

Pattern of trade?

Gains from trade?

Do data support the theory (next part)?


The Heckscher-Ohlin Theory

The HOS model

Keep the same assumptions as in the 2x2 modelin Ch 1 (two countries with identical technology,

identical demand (homothetic taste), free trade in

goods, no FIR, etc), but prices are determined

endogenously in international trade between two

countries: 2x2x2 model.

The Theorem

Each country will export the good that uses itsabundant factor intensively.


Analysis/Proof

Strategy:

Focusing on the case in which good 1 is labor

intensive, home is labor abundant, moreover

Procedure: autarky

Methodology: graphic analysis

KKLLK

L

K

L

a

a

a

a

K

L

K

L >=>> **,*

*,

2

2

1

1


Analysis

Autarky equilibrium

at home (slope):

What is ?

We prove

by contradiction

(next slide).

a

aa

p

pp

2

1=

apaa

pp >

Indifference curve

PPF

Budget line

GDP line

Home

1y

2y

A


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1y

2y

Homothetic taste

fixed share of income

spent on each good

F in point C

A

C

Rybcynzski Theorem

F should produce at

at point like B, not

C.

Contradiction!

aapp =Suppose

aapp

B

But should it be ? It must beaaaa

pppp >< or aa pp >


Where is the free trade equilibrium price p? Prove

Z(p)D(p)S(p) excess demand for good 1 at home

Z*(p)

D*(p)

S*(p)

excess demand for good 1 abroad Z(p)+Z*(p) excess demand for good 1 in the world

Since Z(pa) = 0, Z*(pa) > 0

Z(pa)+Z*( pa) > 0

also Z(pa*) < 0, Z*(pa*) > 0

Z(pa*) +Z*(pa*) > 0

Then by continuity of the excess demand functions, there must

be a price p, with such that Z(p)+Z*(p) = 0

),( aa ppp

),(

aa ppp


Welfare and gains from trade?

Whats the welfare implication of the HO

theorem?

The abundant factor in each country gains fromtrade, and the scarce factor loses.

Proof: and the SST.

Gains from trade?

),( aa ppp


Gains from trade for

each country


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Session C

Ricardian Model with a

Continuum of GoodsDornbusch, Fisher and Samuelson (AER, 1977)


Introduction

Continuum of goods vs. many discrete

commodities: simplification The distinguishing feature: a cut-off point

which determines imported and exported

goods

Tariffs and transport costs: a range of

commodities not traded

Useful framework for other applications


The model and issues

What is the pattern of trade?

Is every product traded?

How is pattern of trade affected by a change

in country size, technology progress, demand

shift, and unilateral transfer?

Home Foreign

Technology

a(z)

Technology

a*(z)


The model: Supply side

Discrete commodity case Constant unit labor requirement

Arrangement

Comparative advantages?


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A continuum of goods

Relative unit labor requirement (decreasing in

z)

Comparative advantages? Competitiveness:

H produces z iff

].1,0[for z

Relative wageRelative costs


Define

Then, H and F efficiently produce

Relative price of z, produced at H, to z, also

produced at H

Relative price of z, produced at H, to z,

produced at F


In summary of the supply side: we use the

relative wage

To determine the borderline commodity,which gives indication of pattern of production

To determine the relative price structure,

because the we have known which countries

produce which goods.


The model: Demand side

Cobb-Douglas demand

Constant expenditure share (prove for 2 good

case)

Identical tastes between two countries


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The fraction of income spent on the goods

produced by H

The fraction of income spent on the goods

produced by H


Equilibrium relative wages and

specialization

What are the equilibrium conditions?

Hs labor market: income equals expenditure

The schedule starts at zero and approaches infinity as

approaches unity. It is a representation of the demandside: arise in results in a rise in relative wage


The previous condition is also a trade balance

condition

Another condition (supply side): the

specialization condition

zzA ~at)(=


Equilibrium relative

prices?


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Comparative statics

The importance of comparative statics in

economic analysis Based on Fig 1, we can see that the unique

equilibrium is determined jointly by tastes,

technology, and relative size. Hence we can

do comparative statics analysis with regard to

these changes.


Relative size:

Intuition?


Technical progress:

How?

A uniform

proportionalreduction in Fs unit

labor requirement

Intuition: loss in

comparative

advantages


Demand shifts:

How?

A shift from high z

commoditiestoward low z

commodities

Intuition


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Transport costs and nontraded goods

Samuelsons iceberg transport cost: a

fraction of the good arrives: g=g(z)


Supply side

Therefore H exports z iff

F exports z iff

Then, for any given


Demand side

Let be the fraction of H income spent on Hs goods.

Similarly, . Then,

The trade balance condition

And so the unique solution for relative wage as a

function of exogenous variables: relative size and

transport costs


Other applications

Tariffs

Exchange rates

Etc, e.g.,

Copeland and Taylor, Trade and transboundary

pollution,AER 1995

Eaton and Kortum, Technology, Geography, and

Trade, Econometrica, 70, 2002.

Matsuyama, Beyond Icebergs: Toward A Theory

of Biased Globalization (forthcoming), Review of

Economic Studies


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Session C

Technology transfer, FDI andinternational trade: A Ricardian

approachCheng, Qiu and Tan (JDE, 2004)


Introduction

An application of the continuum of goods

model to technology transfer via FDI Explore the implications on

Division of labor between local firms and MNEs;

NorthSouth wage gaps;

Regional and aggregate welfare;

Government incentives to promote or discourage

technology transfer via MNEs;

Pattern of product cycles.


Features and contributions

FDI arise due to technological differences

between two regions (as opposed to marketentry, etc)

Perfect competition (as opposed to

oligopolistic competition)

FDI and technology transfer requires specific

resources consisting of expatriate managers

and technicians


A continuum Ricardian trade model with

technology transfer

Goods and technology

South L, North L*

South a(z), North a*(z), z in [0, 1]

For simplification: a*(z)=1

Assumption: a(z)>1 and is increasing in z

Normalization: Southern wage rate =1

Notation: Northern wage rate w*>1.


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Technology transfer:

Efficiency loss, expatriates wage Unit cost of producing z by MNEs in the South

Preferences: a continuum version of Cobb-

Douglas utility function

Welfare


Equilibrium without technology transfer

We have the standard DFS model, in which

the equilibrium consists of and isdetermined by

Hence,


Equilibrium with technology transfer

Good z is produced by

For given w*


How to determine w*?

World income

Goods market equilibrium condition

Demand for expatriates

Substituting T to get Y


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The equilibrium is determined by

Then, we can conduct comparative statics

analysis to get some results/propositions

below


And more results

Part 2: Empirical Tests of Trade

Patterns and Flows

(A)

Leontief ParadoxFeenstra (Ch 2)


Introduction


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Leontief Paradox

It is a presumption that the US is capital-abundant but

yet it exports labor intensive goods. Leontief rejects the null hypothesis (H-O theory): Is the

theory wrong?

Three possibilities to explain the paradox: Assumptions are not realistic

Data problem

Methodology is wrong

Note (1) capital stock vs. capital flow

(2) Use US technology for both import and export

An half-century debate


HOV Model and Leamers Test

Vanek (1968): Extension to include many

countries, many goods and many factors, theMxN model. And consumption difference.

Essence of the HOV model

State the relationship between endowmentand pattern of trade in factor services.

The HOV theorem:

A country exports factor k services if its

endowment of factor k relative to the worldendowment exceeds its share of world GDP.


The HOV model

=

=

=

i

i

i

i

i

i

KK

LL

D

DD

y

yy

aa

aaA

2

1

2

1

21

21Let Technology matrix

Output vector for country i

Demand/consumption vector for country i

is the net export (of goods) vector for country i

is the factor content of trade

then, country i exports labor services

then, country i exports capital services

Then

ii

iii

ATF

DyT

=

=

0

0

>

>i

K

i

L

F

FIf

If


The HOV theorem

wiiiiVsVATF ==

w

ii

w

i

K

i

Li

D

Ds

VVVV

VV

=

+=

= 21,

whereEndowment vectors

Share of world consumption


22/25


Leamers test (1980)

There is no paradox!: US K/L ratio in production exceedsthat in consumption

Why?


Explanations: Leamer vs Leontief

What is source of the paradox?

It must be the methodology problem, because Leamerused the same data and assumptions.

Where did Leontief go wrong?

Leontief had performed the wrong test! (Leamer): we

should not compare the K/L ratios in the export and

import. Why?

There are more than 2 factors

Trade is not balanced: US is a net exporter of both

capital and labor services Leontief calculated only production, Leamer calculated

both production and consumption


No paradox for the US, but what about

other countries?

Bowen, Leamer, and Sveikauskas (AER, 1987):

Many countries

.,...1;,...1),()( MkCiVsVsignFsign wkii

k

i

k ===

.,...1;,...1;,...1),()( MlMkCiVsVVsVFF wlii

l

w

k

ii

k

i

l

i

k ===>>

Sign test

Rank test

Result? 50% success. FAIL again! No better than flipping a coin.

Implications: HOV model fails to meet the data. Some assumptions of the

model are wrong. Which one?


Treflers diagnostic test

The assumption of equal technology across

countries is especially bad!

Trefler (JPE, 1993) estimates technologydifference across countries and makes

adjustment:

There is no reason to requires the data to

match the HO model

US is abundant in adjusted labor => Leontief

was right!


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Conclusions

Tests directly on HO model as Leontief did giveunsatisfactory results.

Empirical studies after Leontief try to improve it Leamer (and others) uses HOV model: factor content

Trefler introduces technology differences

Both technology and endowment differences aremajor determinants of trade patterns

Further research in empirical studies: explainingtech differences Increasing returns to scale

Geography and climate Colonial institutions

Social capital

Part 2: Empirical Tests of Trade

Patterns and Flows(B)

The Case of Missing Trade

Trefler (AER, 1995)


Motivation of the study

The H-O theorem and the HOV theorem have been

widely accepted in international trade theory.

BUT, the HOV theorem has been repeatedly

rejected, empirically.

In other fields of economics, the poor performance of

a major theory leads to

More careful consideration of the data, and

New theories that can accommodate the anomalies.

But, not for the HOV theorem.

This paper attempts to do both.


Contribution of the paper

First, it demonstrates that the HOV theorem isrejected because factor service trade departsfrom its endowments-based prediction insystematic and informative way.

Second, it shows that the HOV is rejectedempirically in favor of a modification thatallows for home bias in consumption andinternational technology difference.

Literature Review (omitted)


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Testing the HOV theorem against

statistical alternative

Sample: 33 countries and 9 factors

Notation: = the factor content of country cs net exports.

= the endowment of factor f in country c.

= the endowment of factor f in the world.

= the consumption share of country c in the world.

HOV equation:

If country c is abundant in factor f (i.e., ),

then it exports the services of factor f (i.e., >0 ).

Result (there are 297 observations): the correlation between

and is 0.28, very poor.

fcF

fcV

fwV

cs

fwcfcfc VsVF =

cfwfc sVV >/

fcF

fcF

fwcfc VsV


A view through the HOV window

Fig. 1: define

Plot it against

By HOV equation, = 0 (not shown).

At least and should have the same

sign (but only 50%).

The main feature: = 0 (the diagonal), called

the case of the missing trade

)( fwcfcfcfc VsVF =

fwcfc VsV

fc

fcF fwcfc VsV

fcF

Trade & Investment Larry D. Qiu 95 Trade & Investment Larry D. Qiu 96

Fig. 2: the endowment paradox

The left panel of Fig 2: Poor countries tend to have

negative deviations, and rich countries tend to have

positive deviations. (The correlation of the number of

negative deviations per country with per capita GDP

is 0.87).

The right panel of Fig 2: Rich countries tend to be

scarce in most factors, and poor countries tend to be

abundant in all factors. (The correlation with per

capita GDP is 0.89).


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Trade & Investment Larry D. Qiu 97 Trade & Investment Larry D. Qiu 98

Suggestion/indication

The pattern of Fig 2 would occur if rich countries rantrade deficits and poor countries ran trade surpluses.

But if anything, the opposite is true.

Thus, the HOV theorem must have omitted somefactors in the endowment set and for those factors therich countries are abundant.

What are they? It suggests alternative theories(hypotheses).

Alternat ive hypotheses: technology andconsumption.

trade models

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