International Trade

The Gravity Equation and its Applications

Prof. Dr. Tobias Seidel

University of Duisburg-Essen

April 2014

Background Reading: Feenstra (2004) - Chapter 5

1

What Heckscher-Ohlin is (not) about

Heckscher-Ohlin is aboutI The pattern (not the volume) of tradeI Differences in structural characteristics of economies (like factor

endowments)I A country’s trade with the rest of the world

Heckscher-Ohlin is not (or less) aboutI The volume of tradeI The relative size of countriesI Bilateral trade between single country pairs in a multi-country world

⇒ Explaining these latter things requires different (or enriched) theory

2

An empirical observation: Intra-industry trade

Measure: Grubel-Lloyd index Γijs for each industry (sector) s and

countries i and j (X ijs and M ij

s denote sectoral exports and imports,respectively)

Γijs = 1− |X

ijs −M ij

s |X ijs + M ij

s

∈ [0, 1]

Measure of total intra-industry trade between i and j

Γijs =

∑s

X ijs + M ij

s∑s X ij

s + M ijs

Γijs

Evidence: Large figures, sometimes well above 50%, in particular fortrade between similar advanced countries (EU - US, say)

⇒ Trade may be driven by things other than comparative advantage offactor endowments

3

Grubel-Lloyd indices of intra-industry trade, 2006

Source: WTO World Trade Report 2008

4

Outline of the talk

In the previous lecture we checked whether factor endowmentsadvantage shape the sectoral trade pattern according to theory

A key assumption was constant returns to scale in production

The gravity model relaxes that assumption and has proved atheory-grounded workhorse for empirical research

1 What drives the volume of world trade over time? Technology versuspolicy

2 What determines the geographical structure of trade? Borders,informal barriers to trade

3 What role for institutions, such as the WTO?

We will first develop a theoretical framework

And then discuss a number of empirical applications

5

Starting point: Models of perfect specialization

Trade models which predict that countries specialize in distinctsubsets of goods

I Heckscher-Ohlin framework with a continuum of goods (many moregoods than factors)

I Monopolistic competition and increasing returns to scale

Units of analysis are “country pairs” or dyads

The explanandum: Volume of bilateral trade , e.g., exports fromcountry i to country j : X ij (Note: X ij also the f.o.b. (free on board)value of imports of country j from country i); country indexi , j = 1, ...,C

There are C (C − 1)/2 independent bilateral trade relationsI With approximately 225 countries and territories, the potential number

of independent trade relations amounts to 25, 200!

Explanatory variables: Countries’ GDP, trade costs (tariffs, transportcosts, ...)

6

Frictionless trade

Assumptions

A1 Countries are specialized in distinct subsets of goodsA2 Representative consumers have identical, homothetic preferencesA3 Countries are identical except for their sizeA4 Free trade (goods price equalization holds exactly, no trade costs)

Perfectly symmetric countries (identical symmetric preferences andtechnology)

I Goods prices (k = 1, ...,N) can be normalized to unityI value = volume

7

The Krugman (1979) model

Since the monopolistic competition model is very well suited for thisanalysis, we briefly review the original Krugman model

Love of variety” in consumptionI Consumers demand similar but different varieties of a productI Utility is increasing in the number of different varieties, ceteris paribus

Increasing returns to scaleI More costly for a firm to produce different varieties than to specialize

on a single variety due to fixed costs of production

Gains from tradeI Trade allows a country to specialize on the production of few varieties

while consuming many varieties

8

The Krugman (1979) model (cont’d)

Suppose there are i = 1, ...,N varieties that are endogenouslydetermined

There is a fixed number of consumers L sharing love-of-varietypreferences

U =N∑i=1

v (ci ) , v ′ > 0, v ′′ < 0.

Given the budget constraint w =∑N

i=1 pici , each consumermaximizes utility to get

v ′ (ci ) = λpi

where λ is the Lagrange multiplier.

Totally differentiating the first-order condition yields the elasticity ofdemand for variety i

ηi = −(

v ′

civ ′′

)> 0, with dηi/dci < 0

9

The Krugman (1979) model (cont’d)

On the production side, each firm requires the following labor toproduce output yi ,

Li = α + βyi .

This implies average costs ACi = wLi/yi and marginal costs βw .

With symmetric countries, we apply the following two equilibriumconditions to solve the model

(1) MR = MC (profit maximization)

p

(1− 1

η

)= wβ

(2) P = AC (free entry drives profits to zero)

p =wα

y+ wβ

where we have substituted y = Lc .

10

The Krugman (1979) model (cont’d)

Conditions (1) and (2) provide two equations in two unknowns, p/wand c

From dηi/dci < 0, (1) establishes a positive link between p/w and c(PP-schedule)

(2) is simply the firm’s average cost curve and thus establishes anegative link (ZZ -schedule)

Finally, we can solve for the number of firms (varieties) by applyingthe labor-market-clearing condition

L =N∑i=1

Li =N∑i=1

(α + βyi ) = N (α + βy) = N (α + βLc)

This delivers

N =1

(α/L) + βc

11

The Krugman (1979) model: Trade

Z

Z

Z´

Z´P

P

p/w

cc1 c0

(p/w)0

(p/w)1

Source: Krugman (1979)

12

Frictionless trade: The ‘baby’ gravity equation

Country i ′s GDP: Y i =∑N

k=1 y ik

World GDP: Y w =∑C

i=1

∑Nk=1 y i

k =∑C

i=1 Y i

Trade is assumed to be balancedI Country j ′s GDP equals its expenditureI Country j ′s share in world expenditure is s j = Y j/Y w

Perfect specialization and identical homothetic demandI X ij

k = s jy ik

Simplest form of the gravity equation

X ij =N∑

k=1

s jy ik = s jY i = Y jY i/Y w = s j s iY w

I I.e., bilateral exports from country i to country j are proportional tothe product of their GDPs

Empirical application: Trade within and outside the OECD (Helpman,1987, and Debaere, 2005)

13

Theorem (Helpman, 1987)

Recall that X ij = X ji = s js iY w

Total bilateral trade volume X ij + X ji = 2s js iY w

Let i and j be part of the world region A : Y i + Y j = Y A

Denote s iA = Y i/Y A, and sA = Y A/Y w

We can rewrite the total bilateral trade volume V A = X ij + X ji

V A

Y A= 2

s js iY w

Y A= 2

Y j

Y w

Y i

Y A= 2

Y j

Y A

Y i

Y A

Y A

Y w= 2s jAs iAsA

Since s iA + s jA = 1, we have(s iA + s jA

)2=(s iA)2

+(s jA)2

+ 2s jAs iA = 1

A theorem follows

V A

Y A= sA

[1−

(s iA)2−(

s jA)2]

I Bracketed expression is a ‘size dispersion index’ that we call dispA forfuture reference

14

Size dispersion index

We have derived the Theorem for the case of two countries in a region

Helpman (1987) shows that it holds for a region A of many countries

Then, dispA = 1−∑

i∈A(s iA)2

The index is maximized for countries of the same relative size 1/N

dispA = 1−∑i∈A

1/N2 = 1− 1/N = (N − 1)/N

As any country has a share approaching unity, dispA approaches zero

The theorem says that the volume of trade in region A is related tothe relative size of countries – as measured by the dispersion index

15

Debaere (2005) - Setup

Let us specify the region A as any pair of countries, A = i , j

We can rewrite above theorem in natural logs

ln

(X ij + X ji

Y i + Y j

)= ln

(s i + s j

)+ ln dispA

Debaere runs the following regression

ln

(X ijt + X ji

t

Y it + Y j

t

)= αij + γ ln

(s it + s jt

)+ β ln dispA

t ,

where αij is a dyadic fixed effect

Econometric issuesI If s it + s jt were constant over time, αij would capture their informationI Debaere measures GDP in nominal USD and in PPPI GDP can be instrumented by population size

16

Debaere (2005) - Results

Note that the dispersion index shows up as ‘similarity’

not only affects the dependent variable in the regression, but also all the regressors that

are a function of countries’ GDP (and thus, of their trade), there is potentially an

endogeneity problem. As discussed, I therefore instrument for the measures eij and simij

as follows: I instrument for countries’ GDPs with their endowments and then use these

instruments (instead of the actual GDP numbers) to construct both the share and the

similarity measure. Each time, I report the regular estimates in the first rows before

turning to the instrumental variable estimates in the lower rows. Note that the regression

also includes year-specific effects, since there are two oil shocks during the period that is

studied.

As one can see for the logarithmic specification in Table 1, a clear pattern emerges. The

logarithmic specification that is clearly the preferred one for the OECD countries explains,

as the block of columns to the left indicates, between 60% and 40% of the variation in the

data for both data sets. As the estimates in row two indicate, I obtain a positive coefficient

for both the similarity index and for the share of the country pairs in the world economy.

Both estimated coefficients are significant at the 95% level. Moreover, using instrumental

variables (reported in the fourth row) does not alter the picture. As Helpman (1987)

predicted, more country similarity makes developed countries trade a bigger fraction of

their output and so does an increase in their share of the world economy. The estimates in

Table 1 also illustrate that the estimated coefficients are statistically different from their

theoretical value of 1 in almost all cases—a feature that was clear already in the work of

Hummels and Levinsohn (1995) who like Helpman (1987) made the sign rather than the

exact magnitude of the estimated coefficients the yardstick for judging empirical support.

As noted before, one could argue that maybe because of the simplicity of the model (that

does not fully account for all possible trade frictions) and because of the presence of

measurement error, one should probably not expect a coefficient that is indistinguishable

from unity. Note also that the coefficients on the share and similarity variable are

statistically different in all cases.

Table 1

Eq. (2a) in logs with varying shares panel data

Fixed effects regression with time-specific effects

Dependent variable OECD Non-OECD

lnVT/Y lnVT/Y lnVT/Y lnVT/Y lnVT/Y lnVT/Y lnVT/Y lnVT/Y

Penn IMF Penn IMF Penn IMF Penn IMF

ln(similarity) 1.57 0.89 – – �0.96 0.4 – –

S.E. 0.11* 0.056* 0.99 0.23

ln(world share) 1.3 0.47 – – 1.98 0.99 – –

S.E. 0.13* 0.05* 0.95* 0.22*

ln(similarity) IV – – 0.25 0.66 – – �2.3 �0.5

S.E. 0.06* 0.06* 0.6* 0.26*

ln(world share) IV – – 0.62 0.98 – – 5.4 3.1

S.E. 0.25* 0.22* 2.9 1.2*

R2 0.61 0.45 0.56 0.41 0.02 0.14 0.03 0.14

Observ. 1820 1820 1820 1820 1320 1320 1320 1320

Standard errors under the estimated coefficients.

* Significant at 95%.

P. Debaere / Journal of International Economics 66 (2005) 249–266258

Source: Debaere (2005)

17

Debaere (2005) - Results

1 Theoretical prediction that β = 1 has a chance to be met only in theOECD subsample

2 However, regardless of the exact specification (including ln(

s it + s jt

)or not) and regardless of the data (IMF versus PWT), β > 0 for theOECD countries

3 For non-OECD countries, estimates of β either have the wrong sign,or are insignificant

=⇒ Bottom line: The gravity model works for OECD countries, but lessso for developing countries. This is in line with intuition

18

Estimating border effects (McCallum, 1995)

A second interesting application of this ”free-trade” gravity equationcompares intranational trade with international trade betweenCanada and the US

What is the effect of the border on Canada-U.S. trade?

Sample of bilateral trade relations of Canadian provinces betweeneach other and with US states (trade between US states is notpresent in McCallum’s original regressions)

19

Estimating border effects (McCallum, 1995)

McCallum estimates a variant of the gravity equation using data for1988

ln(X ij) = α + β1 ln Y i + β2 ln Y j + γδij + ρ ln d ij + εij

I δij is an indicator variable that takes value 1 if the trade relationinvolves Canadian provinces, and value 0 if it involves a Canadianprovince and a US state. δij measures the border effect

I d ij is the distance between any two provinces or states. It measuresdistance related trade costs

I Note that this equation proxies T ij by distance and border, but doesnot relate those trade costs to prices

20

McCallum’s (1995) border puzzle

Estimates of coefficients to Y i ,Y j and d ij are in line with theoreticalexpectations and of reasonable size

Very large coefficient on within-Canadian trade in interval [2.75, 3.09]

Interpretation: Within-Canadian trade is by a factor[exp (2.75) = 15.643, exp (3.09) = 21. 977] larger than trade betweenCanada and the US

These extraordinarily high effects remain ifI Data for 1993 are used (in 1990 NAFTA agreement was signed)I Trade between U.S. states are considered as well

⇒ “Border effect puzzle”

21

Borders asymmetrically affect countries of different size

McCallum’s result is biased, since the size of border effects dependson the size of the country in question

ExampleI Assume that the US has a GDP 10 times as large as CanadaI Without border effects (and transport costs), Canada exports 90% of

GDP to the US, it sells 10% internallyI Suppose the border effect reduces cross-border trade by a factor of

one-halfI Then, Canada exports 45% of GDP to the US and trades 55%

internallyI So the border effect reduces external trade by the factor 2 and

increases internal trade by the factor 5.5. Total effect: internal trade is11 times higher than external trade

I Conversely, in the US, the border effect reduces external trade from10% of GDP to 5% (factor 2) and increases internal trade from 90% ofGDP to 95% (factor 1.06). Total effect: internal trade is 2.1 timeshigher than external trade

22

Towards a gravity equation that allows for trade costs

To avoid these huge biases, we need to carefully derive a gravityequation that accounts for trade barriers

This introduces additional complications because prices are no longerequalized across countries

Patterns of trade are more complex than in the ‘baby’ gravity equation

23

A refresher of the monopolistic competition modelSpecial case: Dixit-Stiglitz preferences (Krugman, 1980)

Constant elasticity of substitution (CES) utility function

U =N∑`=1

c(σ−1)/σ` , σ > 1

Elasticity of substitution between products σ equals elasticity ofdemand if N is large

Representative consumer in country j maximizes U subject to herbudget constraint Y j =

∑N`=1 p`c`

Lagrange function

L =N∑`=1

c(σ−1)/σ` + λ

(Y j −

N∑`=1

p`c`

)

24

Deriving optimal demand

Maximization of L with respect to c` and ck delivers the followingfirst order conditions

σ − 1

σc−1/σ` = λp`

σ − 1

σc−1/σk = λpk

Dividing leads toc`ck

=

(p`pk

)−σSubstituting into the budget constraint yields

Y =N∑`=1

ckp`

(p`pk

)−σ= ckpσk

N∑`=1

p1−σ`

Hence, optimal demand is given by

ck =Y

pσk∑N

`=1 p1−σ`

25

Simplifying the expression for demandIntroduce the exact price index P (the expenditure needed topurchase one unit of utility)

1 =N∑`=1

c(σ−1)/σ` =

N∑`=1

c(σ−1)/σk

(p`pk

)1−σ= c

(σ−1)/σk

N∑`=1

(p`pk

)1−σ

1 = ck

[N∑`=1

(p`pk

)1−σ] σ

σ−1

ck =

[N∑`=1

(p`pk

)1−σ] σ

1−σ

= p−σk

[N∑`=1

p1−σ`

] σ1−σ

P =N∑`=1

p`c` =N∑`=1

p1−σ`

[N∑`=1

p1−σ`

] σ1−σ

=

(N∑`=1

p1−σ`

) 11−σ

This gives rise to demand functions

c` =p−σ`

P1−σY26

Production side

Labor is the only factor of production, with conditional labor demandof firm ` given by

L`(y`) = α + βy`

I.e., the production function exhibits increasing returns to scale

y`(L`) = (L` − α)/β

yk(Lk) = (L` − α)/β

y`/yk = (L` − α)/(Lk − α) > L`/Lk

With wage rate w , the cost function is

K`(y`) = wα + wβy`

This cost function is identical across sectorsI Constant marginal costs MC = wβI Decreasing average costs AC = wα/y` + wβ

27

Characterizing the equilibrium

Firms behave as monopolists: they set marginal cost (MC ) equal tomarginal revenue (MR)

wβ = p`

(1− 1

σ

)⇔ p`

w= β

σ

σ − 1

Free entry forces prices to be equal to average costs (AC ) (zeroprofits)

p` =wα

y`+ wβ ⇔ p`

w=

α

Lc`+ β

Note that we have substituted y` by Lc` (identical households demandc` units of each variety)

These two conditions determineI Equilibrium firm size y = α

β (σ − 1)I Consumption per capita c = y/L = α

Lβ (σ − 1)

28

Characterizing the equilibrium (cont’d)

Labor market clearing

L =N∑`=1

(α + βy`) = N (α + βy`)⇔ N =L

ασ

Substituting this into the utility function, we get indirect utility

U =

(L

α

) 1σ 1

σ

(σ − 1

β

)σ−1σ

I Increasing in L: love of varietyI Variety represents the only source of gains from trade liberalization

(increase in L) – This is different to Krugman (1979)I Decreasing in fixed costs α and marginal costs β

29

Shortcomings

IO issues

I No strategic interactions of firmsI Static model

Empirical issuesI Output per firm/variety is constant ⇒ no scale effectI Firms are symmetric. Selection (if occurring) is unmodeled, all firms

are exporters, only margin of adjustment to trade liberalization isnumber of varieties consumed while number of varieties producedremains unchanged ⇒ no selection effect

But: Scale and selection effects reappear if firms are heterogeneous intheir productivity levels (Melitz, 2003)

30

Modeling trade costs – Iceberg trade costs and demand

A2’ Iceberg trade costs (Samuelson, 1952): pij = T ijpi ; T ij ≥ 1,T ii = 1

We no longer have pij = pii for all i , j = 1, ...,C . Therefore need to modeldemand

A4 Specific utility function: Constant elasticity of substitution (CES)

Now, we need to distinguish between quantities and values (as we canno longer normalize pij = 1 for all i , j = 1, ...,C

Let’s denote the quantity of exports from i to j of good k by c ijk .

Perfect specialization implies that c ijk is equal to the consumption of

good k in country j

Assuming that country i produces N i goods (varieties), country jsrepresentative consumer has the utility

U j =C∑i=1

N i∑k=1

(c ijk

)σ/(1−σ), σ > 1

31

Modeling trade costs – Simplifications

To simplify, further assume that all exports of country i sell at thesame price pij (c.i.f.) in country j . Then, by symmetry we havec ijk = c ij and

U j =C∑i=1

N i(c ij)σ/(1−σ)

, σ > 1

The representative consumer in country j maximizes U j subject to herbudget constraint Y j =

∑Ci=1 N ipijc ij . This gives rise to demand

functions

c ij =

(pij)−σ

(P j)1−σY j

where P j =[∑C

i=1 N i(pij)(1−σ)]1/(1−σ)

is country j ′s overall price

index.

32

Modeling trade costs – Deriving the ‘core’ gravity equation

Total value of exports from country i to j is X ij = N ipijc ij

Substituting from above and using A2’, we get

X ij = N iY j

(T ijpi

P j

)1−σ

Recall that firm sizes are fixed by parameters

Hence, GDP in country i is Y i = N ipi y

Combining both equations delivers

X ij =Y jY i

(pi )σ y

(T ij

P j

)1−σ

33

How do we estimate this gravity equation?

We will study three approaches to estimate the resulting gravityequation

1 The use of price indexes (Baier & Bergstrand, 2001)2 The use of estimated border effects (Anderson & van Wincoop, 2003)3 The use of fixed effects (e.g. Redding & Venables, 2000; Rose & van

Wincoop, 2001)

34

Baier & Bergstrand (2001): Dissecting world trade growthSpecification issues

We have a panel data set with observations for X ijt and the other

variables (T ≥ 2)

Logarithms and first differences helps eliminate y :

∆ ln X ij = ∆ ln(Y jY i

)− σ∆ ln pi + (1− σ) ∆ ln T ij − (1− σ) ∆ ln P j

Using s i = Y i/(Y i + Y j

)and s j = Y j/

(Y i + Y j

), the equation can

be rewritten as

∆ ln X ij = 2∆ ln(Y j + Y i

)+ ∆ ln

(s i s j)− σ∆ ln pi

+ (1− σ) ∆ ln T ij − (1− σ) ∆ ln P j

The above equation attributes growth in bilateral trade to incomegrowth, ∆ ln

(Y j + Y i

), convergence in countries’ incomes,

∆ ln(s i s j), changes in prices, ∆ ln pi and ∆ ln P j , and finally, changes

in trade costs, ∆ ln T ij

35

Baier & Bergstrand (2001): Dissecting world trade growthData issues

To disentangle the different elements in T ij , Baier and Bergstrandintroduce two variables

I Gross c.i.f./f.o.b. factors published by the IMF, meant to measuretrade costs different than tariffs (i.e., transportation costs): 1 + aij

I Gross tariff rate: 1 + tij

Data: Bilateral trade data averages for two points in time: 1958-1960and 1986-1988. Log differences are interpreted as growth rates

36

Baier & Bergstrand (2001): DataReal trade flows grow by 148 percentage points

Table : Statistics for the growth rates and the log-levels of selected variables

Source: Baier and Bergstrand (2001)

37

Baier & Bergstrand (2001): Results

38

Baier & Bergstrand (2001): Results1 Income variables are the main drivers behind the growth of world

tradeI Mean growth of the sum of the countries’ real incomes was 1.05 (or

105 percentage points); multiplying this by its coefficient of 2.37 yieldsa contribution of 2.49

I Mean growth in importer income (1.03) has dampening effect on tradegrowth by a factor of −0.68; the product of 1.03 and −0.68 yields−0.70

I The constant is related to the negative of the logarithmic change inworld per capita real GDP; combining the intercept estimate (0.05)with the effect from the lagged trade flow (−0.84 = −0.08× 11.08)yields −0.79

⇒ The estimate of the overall effect of income growth on trade growth is2.49− 0.7− 0.79 = 1 (100 percentage points); hence, income growthexplains 100/148 = 2/3 of the trade growth

2 Tariff reduction explains (−8.5×−4.49)/148 = 26% of trade growth.Transport cost reductions explain 8% of trade growth

3 Income convergence does not play any substantial role

39

An alternative to using price data: Estimating bordereffects

Using price measures has disadvantages: (i) difficult to compare levelsacross countries and (ii) unlikely to capture border effect properly

So instead of using data to measure prices, we can model thedifference between c.i.f prices pij form f.o.b. prices pi as a function ofdistance and other factors

ln T ij = τ ij + ρ ln d ij + εij

where d ij is geographical distance and τ ij measures the border effect(legal/monetary system, language, culture ,...) and εij is a randomerror

We would need to estimate τ ij ; this is tricky: substitution of T ij fromour gravity equation leads to a system of non-linear equationsestimation of which requires simulation

40

Anderson and van Wincoop’s (2003) gravity equation

Bilateral exports are given by

X ij =

(pij

P j

)1−σ

Y j

Market-clearing implies that the sum of exports (including domesticsales) equals total expenditure

Y i =∑j

= X ij =(pi)1−σ∑

j

(T ij

P j

)1−σ

Y j

Define Y =∑

j Y j , s i = Y i/Y =(pi)1−σ∑

j

(T ij

P j

)1−σs j and(

Πi)1−σ

=∑

j

(T ij

P j

)1−σs j

41

Anderson and van Wincoop’s (2003) gravity equation

Using these equations we get

(pi)1−σ

=s i

(Πi )1−σ

⇒ X ij =

(T ij

ΠiP j

)1−σ

s iY j =Y iY j

Y

(T ij

ΠiP j

)1−σ

This implies (P j)1−σ

=∑i

(T ij

Πi

)1−σ

s i

Under the assumption T ij = T ji it is clear that Πi = P i .

42

Empirical implementation

The estimation strategy is to move the GDP terms to the left side,take logs and substitute transport costs by ln T ij = τ ij + ρ ln d ij + εij

Dropping the constant term Y w yields

ln

(X ij

Y iY j

)= ρ(1−σ) ln d ij+(1−σ)τ ij+ln(P i )σ−1+ln(P j)σ−1+(1−σ)εij

The multilateral resistance terms can be solved from

(Pi )1−σ =

∑Cj=1 s i

(T ij

P j

)1−σonce we know transport costs

The transport costs, in turn, are obtained from the lnT ij -equationusing the estimated value of ρ(1− σ) ln d ij + (1− σ)τ ij which comesfrom the gravity equation above

As both sets of equations have to be used simultaneously, theapproach requires customized programming

43

Empirical implementation

A&vW work with an indicator 1− δij , or unity for trade between theU.S. and Canada, and zero otherwise

Introducing γ on this variable, they replace (1− σ)τ ij with γ(1− δij)Let α = ρ(1− σ)

Gravity equation becomes

ln

(X ij

Y iY j

)= α ln d ij +γ(1− δij) + ln(P i )σ−1 + ln(P j)σ−1 + (1−σ)εij

Note that provincial and state GDP terms have their coefficientsconstraint at unity

44

Results

Coefficient on the indicator variable is estimated at γ = −1.65

Interpretation: exp(τ ij) = exp[γ(1−δij )1−σ

]For cross-border trade we have δij = 0

Taking values for the elasticity of substitution of σ = 5, 10, and 20,we obtain estimates of exp(τ ij) of 1.5, 1.2, and 1.09, indicatingborder barriers of between 9% and 50% in terms of their impliedeffect on price

45

How much more trade within than across the border?

Let (P i )σ−1 be the multilateral resistance terms in the absence of theborder effect (thus using only distance to compute T ij)

Comparing equations with and without border effects

X ij

X ij=[e γ(1−δ

ij )](P iP j

P i P j

)σ−1Consider intra-Canadian trade (i = j = CAN, δCAN,CAN = 1)

I Intra-Canadian trade is 4.3 times larger with border effect than withoutI σ = 5 (but results not sensitive to changes in σ)

Intra-U.S. trade is 1.05 times larger with border effects than without

Cross-border trade is 0.41 times smaller with border effect thanwithout

Thus, intra-Canadian trade is 4.3/0.41 = 10.5 times higher thancross-border trade

Intra-U.S. trade is 1.05/0.41 = 2.6 times higher than cross-bordertrade

⇒ Smaller economies have a much larger impact of the border effects46

A fixed effects procedure

Drawback: Requires programming to solve unconstrainedminimization problem

Alternative procedure: Source and destination country fixed effects

With fixed effects ν i , ν j , we may estimate the equation

ln

(X ij

Y iY j

)= γ

(1− δij

)+ α1 ln d ij + ν i + ν j + uij

This approach yields γ = −1.55 which is close to the −1.65 reportedabove

The implied average border effect is exp(1.55) = 4.7

47

Comparing border effects estimates

Source: Feenstra (2004)

48

Comparing border effects estimates

Interestingly, the average border effect of the three approaches is verysimilar

However, as McCallum ignores the price channels, his estimates areinconsistent

This appears to have the effect that the border effect for Canada isoverstated, while it is understated for the US

49

Questions

1 Why can we interpret[1−

(s iA)2

+(s jA)2]

as a dispersion index?

What does Helpman’s theorem imply?

2 Why is it important to control for multilateral resistance terms inempirical gravity applications?

3 What are the advantages and disadvantages of the A&vW approach,the fixed effects approach, the Taylor-series approximation approach,and the ratio-of-ratios approach?

4 How does the gravity equation extend to panel data? Do firstdifferencing or fixed effects (within) transformation suffice to controlfor multilateral resistance terms when T ≥ 2?

5 Modify the trade costs specification such that it accounts for commonuse of a currency!

6 What empirical applications of the gravity approach can you think of?

50

The Eaton-Kortum Model

Prof. Dr. Tobias Seidel

University of Duisburg-Essen

April 2014

Background Reading: Eaton, Kortum (2002), Technology, Geography, andTrade, Econometrica 70, 1741-1779.

1

What’s the problem?

Ricardo (1817) provided a mathematical example that countries canmutually benefit by specializing on their goods at which they have acomparative advantage.

This changed the view in that also countries that were absolutelybetter in producing all goods could benefit from trading withtechnologically inferior countries.

The 2x2 model is a standard part of each introductory trade book,but has played no influence in explaining the global pattern ofinternational trade.

Until recently! 200 years after its birth, the Ricardian theoryexperiences a revival. Why???

2

Why?

Even in the most basic version of the Ricardo model, several equilibriacan emerge that need to be analyzed separately.

1 England makes only cloth and Portugal only wine.

2 England makes both cloth and wine and Portugal only wine.

3 England makes only cloth and Portugal both cloth and wine.

This is tedious as relative labor demand is “kinky”. As Eaton andKortum (2012) put it: “... stairways are trouble not only for wheeledvehicles but for comparative statics.”

3

A continuum of goods...

Dornbusch, Fischer, and Samuelson (1977) had the idea of adding alot of goods to the list - ending up with a continuum. They replacedthe stairway with a ramp!

This smoothness makes the model very tractable.

For example, it is straightforward to introduce trade costs to explainthat countries buy more goods from themselves.

One limitation remains: There are only two countries.

4

Adding more countries...

Technically, we could add a continuum of countries (a finite integernumber would cause a stairway again).

While it might be justifiable to deal with a continuum of goods, it isless plausible to introduce a continuum of countries – especially withrespect to empirical work.

Here’s where Eaton and Kortum (2002) comes in. They turn a messydiscreet problem into a tractable, continuous problem.

With many goods and many countries, it does not help to constructchains of comparative advantage. Instead, they introduce aprobabilistic approach: Labor input requirements a(j) are realizationsof a random variable.

5

Probabilistic approach

This way of thinking about technology has two advantages:

1 Distributions can be smooth (producing our ramp).

2 We do not need to keep track of all individual a(j)’s, of which there aremany, but only the parameters of which they are drawn, which can besmall in number.

Let’s see how it works in detail...

6

Preliminaries

Countries have differential access to technology, so efficiency variesacross countries and varieties.

Country i ’s efficiency in producing good j ∈ [0, 1] denoted by zi (j).

Cost of a bundle of inputs ci identical across commodities within acountry (mobile factors) – for now taken as given.

With CRS, the cost of producing good j in country i is ci/zi (j).

Geographic barriers introduced by iceberg trade costs. Delivering oneunit from country i to country n requires producing dni units in i .

Positive barriers imply dni > 1 and for all i it is assumed dii = 1.Also, it is imposed that dni ≤ dnkdki .

7

Preliminaries

Delivering an unit of good j produced in country i to country n costs

pni (j) =

(ci

zi (j)

)dni .

With perfect competition, pni is what consumers in n would have topay for good j imported from i .

But consumers would choose to buy the good from the country thatoffers the lowest price, that is

pn(j) = min{pni (j); i = 1, ...,N},

where N is the number of countries.

8

Preliminaries

Delivering an unit of good j produced in country i to country n costs

pni (j) =

(ci

zi (j)

)dni .

With perfect competition, pni is what consumers in n would have topay for good j imported from i .

But consumers would choose to buy the good from the country thatoffers the lowest price, that is

pn(j) = min{pni (j); i = 1, ...,N},

where N is the number of countries.

9

Preliminaries

Buyers (final consumers or firms) purchase quantities Q(j) tomaximize a CES objective

U =

[∫ 1

0Q(j)

σ−1σ dj

] σσ−1

,

where σ > 0 represents the elasticity of substitution between goods.

Note: DFS (1977) order goods according to z1(j)/z2(j) where relativewages determine the breakpoint in this “chain of comparativeadvantage”. With more than two countries, there is no naturalordering of commodities. Solution: Probabilistic approach!

10

Technology

Country i ’s efficiency in producing good j is the realization of arandom variable Zi (drawn independently for each j) from itscountry-specific probability distribution Fi (z) = Pr [Zi ≤ z ]

By the law of large numbers, Fi (z) captures the fraction of goods forwhich country i ’s efficiency is below z .

The likelihood that country i supplies a particular good to country nis the probability πni that i ’s price turns out to be the lowest.

The probability theory of extremes provides a form for Fi (z) thatyields a simple expression for πni and the resulting distribution ofprices. EK assume FrA c©chet (type II extreme value distribution):

Fi (z) = e−Tiz−θ,

where Ti > 0 (absolute advantage) and θ > 0 (inverse of variability,comparative advantage).

11

Why FrA c©chet?

Central limit theorem implies (among other things): The highest orlowest value in a large sample drawn from a well-behaved distributionfollows an extreme value distribution.

If technologies for making a good are the results of inventions thatoccur over time and if the output per worker delivered by an inventionis drawn from a Pareto distribution, then output per worker using themost efficient technology follow a FrA c©chet distribution (see Eatonand Kortum, 1997, 1999).

Only for FrA c©chet does the distribution of prices inherit an extremevalue distribution.

12

Prices

What does this imply for the distribution of prices?

Country i presents country n with a distribution of pricesGni (p) = Pr [Pni ≤ p] = 1− Fi (cidni/p) or

Gni (p) = 1− e−[Ti (cidni )−θ]pθ .

Hence, the distribution Gn(p) for what country n actually buys is

Gn(p) = 1− ΠNi=1 [1− Gni (p)] .

13

Prices

Inserting Gni (p) delivers

Gn(p) = 1− e−Φnpθ ,

where

Φn =N∑i=1

Ti (cidni )−θ.

The price parameter Φn summarizes how (i) states of technologyaround the world, (ii) input costs around the world, and (iii)geographic barriers govern prices in each country n.

14

Prices

Three useful properties of price distributions:

1 Probability that country i provides a good at the lowest price incountry n given by

πni =Ti (cidni )

−θ

Φn

With a continuum of goods, πni is also the fraction of goods thatcountry n buys from country i .

2 The price of a good that country n actually buys from any country ialso has the distribution Gn(p).

3 The exact price index for the CES objective (assuming σ < 1 + θ) is

pn = γΦ−1/θn ,

where

γ =

[Γ

(θ + 1− σ

θ

)] 11−σ

15

A gravity equation

A corollary of property (2) is that country n’s average expenditure pergood does not vary by source. Hence,

Xni

Xn=

Ti (cidni )−θ

Φn=

Ti (cidni )−θ∑N

k=1 Tk(ckdnk)−θ,

This expression resembles the standard gravity equation! Let Qi betotal export sales of i to write

Qi =N∑

m=1

Xmi = Tic−θi

N∑m=1

d−θmi Xm

Φm

Solving for Tic−θi and substituting in the above expression delivers

Xni =

(dnipn

)−θXn∑N

m=1

(dmipm

)−θXm

Qi .

16

Confronting the model with data

Model exhibits a direct link between trade flows and price differences:

Xni/Xn

Xii/Xi=

Φi

Φnd−θni =

(pidnipn

)−θ

This equation can be used to estimate θ.

But let us first plot normalized import shares against distance (as acrude measure of geographical barriers) based on bilateral trade inmanufactures among 19 OECD countries...

17

Trade and geography1752 J. EATON AND S. KORTUM

0.1~ ~~+

e * . x~~ ~ ... . * 4

A,..Ue * ',. , ..,. .. **

00 v *0 t; t

E 0.0 - * * . . *

0.001 c . . . .v

v .

5 . * ..

0.0001

100 1000 10000 100000

distance (in miles) between countries n and i

FIGURE 1.-Trade and geography.

An obvious, but crude, proxy for dni in equation (12) is distance. Figure 1 graphs normalized import share against distance between the correspond- ing country-pair (on logarithmic scales). The rrelationship is not perfect, and shouldn't be. Imperfections in our proxy for geographic barriers aside, we are ignoring the price indices that appear in equation (12). Nevertheless, the resis- tance that geography imposes on trade comes through clearly.

Since we have no independent information on the extent to which geographic barriers rise with distance, the relationship in Figure 1 confounds the impact of comparative advantage (0) and geographic barriers (dni) on trade flows. The strong inverse correlation could result from geographic barriers that rise rapidly with distance, overcoming a strong force of comparative advantage (a low 0). Alternatively, comparative advantage might exert only a very weak force (a high 0), so that even a mild increase in geographic barriers could cause trade to drop off rapidly with distance.

To identify 0 we turn to price data, which we use to measure the term pid"i/p" on the right-hand side of equation (12). While we used standard data to calculate normalized trade shares, our measure of relative prices, and particularly geo- graphic barriers, requires more explanation. We work with retail prices in each of our 19 countries of 50 manufactured products.24 We interpret these data as

24 The United Nations International Comparison Program 1990 benchmark study gives, for over 100 products, the price in each of our countries relative to the price in the United States. We choose 50 products that are most closely linked to manufacturing outputs.

18

Identifying θ

EK measure the term (pidni )/pn by using retail prices for 50manufactured products in 19 OECD countries.

The price measure reflects what the price index in destination n wouldbe for a buyer there who insisted on purchasing everything fromsource i , relative to the actual price index in n (based on the cheapestsource).

Insights: (i)The cheapest foreign source is usually nearby and themost expensive far away. (ii) Large countries usually suffer the most ifrequired to buy everything from a given foreign source.

From plotting the data, the implied θ is 8.28.

19

Price measure statistics1754 J. EATON AND S. KORTUM

TABLE II

PRICE MEASURE STATISTICS

Foreign Sources Foreign Destinations

Country Minimum Maximum Minimum Maximum

Australia (AL) NE (1.44) PO (2.25) BE (1.41) US (2.03) Austria (AS) SW (1.39) NZ (2.16) UK (1.47) JP (1.97) Belgium (BE) GE (1.25) JP (2.02) GE (1.35) SW (1.77) Canada (CA) US (1.58) NZ (2.57) AS (1.57) US (2.14) Denmark (DK) Fl (1.36) PO (2.21) NE (1.48) US (2.41) Finland (FI) SW (1.38) PO (2.61) DK (1.36) US (2.87) France (FR) GE (1.33) NZ (2.42) BE (1.40) JP (2.40) Germany (GE) BE (1.35) NZ (2.28) BE (1.25) US (2.22) Greece (GR) SP (1.61) NZ (2.71) NE (1.48) US (2.27) Italy (IT) FR (1.45) NZ (2.19) AS (1.46) JP (2.10) Japan (JP) BE (1.62) PO (3.25) AL (1.72) US (3.08) Netherlands (NE) GE (1.30) NZ (2.17) DK (1.39) NZ (2.01) New Zealand (NZ) CA (1.60) PO (2.08) AL (1.64) GR (2.71) Norway (NO) Fl (1.45) JP (2.84) SW (1.36) US (2.31) Portugal (PO) BE (1.49) JP (2.56) SP (1.59) JP (3.25) Spain (SP) BE (1.39) JP (2.47) NO (1.51) JP (3.05) Sweden (SW) NO (1.36) US (2.70) FI (1.38) US (2.01) United Kingdom (UK) NE (1.46) JP (2.37) FR (1.52) NZ (2.04) United States (US) FR (1.57) JP (3.08) CA (1.58) SW (2.70)

Notes: The price measure Di is defined in equation (13). For destination country n, the minimum Foreign Source is mini#n exp D,i. For source country i, the minimum Foreign Destination is minn7i exp Dni.

Figure 2 graphs our measure of normalized import share (in logarithms) against Dni. Observe that, while the scatter is fat, there is an obvious negative relationship, as the theory predicts. The correlation is -0.40. The relationship in Figure 2 thus confirms the connection between trade and prices predicted by our model.

Moreover, the slope of the relationship provides a handle on the value of the comparative advantage parameter 0. Since our theory implies a zero intercept, a simple method-of-moments estimator for 0 is the mean of the left-hand-side variable over the mean of the right-hand-side variable. The implied 0 is 8.28. Other appropriate estimation procedures yield very similar magnitudes.27 Hence

27 A linear regression through the scatter in Figure 2 yields a slope of -4.57 with an intercept of -2.17 (with respective standard errors 0.6 and 0.3). The fact that OLS yields a negative intercept is highly symptomatic of errors in variables, which also biases the OLS estimate of H toward zero. (The reasoning is that in Friedman's 1957 critique of the Keynesian consumption function.) There are many reasons to think that there is error in our measure of pidni/pn. Imposing a zero intercept, OLS yields a slope of -8.03, similar to our method-of-moments estimate. (Instrumental variables provide another way to tackle errors in variables, an approach we pursue in Section 5, after we complete the general equilibrium specification of the model.) We also examined how the three components ln pi, ln pn, and ln dni contributed individually to explaining trade shares. Entering these variables separately into OLS regressions yielded the respective coefficients -4.9, 5.5, -4.6 (with a constant) and -9.0, 6.4, -6.8 (without a constant). All have the predicted signs. For 42 of our 50 goods similar price data are available from the 1985 Benchmark Study. Relating 1985 trade data to these price data yields very similar estimates of 6.

20

Trade and geographyTECHNOLOGY, GEOGRAPHY, AND TRADE 1755

0 -

X -2 - *- * -

X -10 - *

0 0.2E0.4 01

E~~~~~ ~FGR 2. Trd an prices

0 u -8 * *%

0M -10 I 0~~~~~~~~~~~~~~~

-12 0 0.2 0.4 0.6 0.8 1 1.2 1.4

price measure: Dni

FIGURE 2.-Trade and prices.

we use this value for 6 in exploring counterfactuals. This value of 6 implies a standard deviation in efficiency (for a given state of technology T) of 15 percent. In Section 5 we pursue two alternative strategies for estimating 6, but we first complete the full description of the model.

4. EQUILIBRIUM INPUT COSTS

Our exposition so far has highlighted how trade flows relate to geography and to prices, taking input costs c1 as given. In any counterfactual experiment, however, adjustment of input costs to a new equilibrium is crucial.

To close the model we decompose the input bundle into labor and intermedi- ates. We then turn to the determination of prices of intermediates, given wages. Finally we model how wages are determined. Having completed the full model, we illustrate it with two special cases that yield simple closed-form solutions.

4.1. Production

We assume that production combines labor and intermediate inputs, with labor having a constant share f3.28 Intermediates comprise the full set of goods

28 We ignore capital as an input to production and as a source of income, although our intermediate inputs play a similar role in the production function. Baxter (1992) shows how a model in which capital and labor serve as factors of production delivers Ricardian implications if the interest rate is common across countries.

21

Endogenizing input costs

To close the model, (i) the input bundle is decomposed into labor andintermediates. (ii) Then, EK determine prices given wages. (iii)Finally, wages are determined.

Cobb-Douglas with labor cost share β. Intermediates comprise theCES-aggregated good with the overall price index as the appropriateindex of intermediate goods prices.

The cost of an input bundle in country i is thus

ci = wβi p

1−βp

Note: ci depends on prices in i and hence on Φi which summarizesinput costs in all countries!

22

Determining price levels

Due to rich interactions of costs in prices via the price index, weobtain a system of equations that generally requires numericalmethods:

pn = γ

[N∑i=1

Ti

(dniw

βi p

1−βp

)−θ]1/θ

(1)

Expanding the trade-shares equation delivers

Xni

Xn= πni = Ti

(γdniw

βi p

1−βi

pn

)−θ(2)

The pi ’s are determined from the system of equations above. Finally,conditions for the labor market equilibrium are needed to determinewages.

23

Labor market

Manufacturing labor income in country i is labor’s share of country i ’sexport around the world, including to itself (domestic sales).

wiLi = β

N∑n=1

πniXn

Denoting aggregate final expenditures as Yn with α the fraction spenton manufactures, total manufacturing expenditures are then

Xn =1− ββ

wnLn + αYn,

where the first term captures demand for manufactures as inputs bythe manufacturing sector itself.

Also, we haveYn = wnLn + Y O

n

24

Case 1: Labor is mobile

Workers can move freely between manufacturing andnon-manufacturing.

Wage wn is given by productivity in non-manufacturing and totalincome Yn is exogenous.

Combining total labor income with total manufacturing expendituredelivers

wiLi =N∑

n=1

πni [(1− β)wnLn + αβYn] , (3)

determining manufacturing employment Li .

25

Case 2: Labor is immobile

Number of manufacturing workers is fixed at Ln. Non-manufacturingincome Y O

n is exogenous. We now get

wiLi =N∑

n=1

πni

[(1− β + α)wnLn + αβY O

n

], (4)

determining manufacturing wages wi .

26

Estimation

Equations (1) and (2), along with either (3) or (4), comprise the fullgeneral equilibrium.

Equation (2) allows us to learn about states of technology Ti andgeographic barriers dni .

Normalizing by the importer’s home sales delivers

Xni

Xnn=

Ti

Tn

(wi

wn

)−θβ ( pipn

)−θ(1−β)

d−θni

27

Estimation

Further, we can use (2) for both country i and n to get

pipn

=wi

wn

(Ti

Tn

)−1/θβ ( Xi/Xii

Xn/Xnn

)−1/θβ

Plugging this into the previous equation yields

lnX ′niX ′nn

= −θln(dni ) +1

βlnTi

Tn− θln wi

wn

where X ′ni ≡ lnXni − [(1− β)/β]ln(Xi/Xii ).

28

Estimation

Defining Si ≡ 1β ln(Ti )− θln(wi ), we arrive at the baseline equation

that is estimated by GLS

lnX ′niX ′nn

= −θln(dni ) + Si − Sn

where we can think of Si as country i ’s “competitiveness”, its state oftechnology adjusted for labor costs.

Taking β = 0.21 from the data, the LHS can be directly computed. Siand Sn are captured by the coefficients on source-country dummies.

Proxies for geographic barriers are distance dk (lying in the kthinterval, k = 1, ..., 6), border b, language l , trading area eh, an overalldestination effect mn. δni captures all other factors such that

ln(dni ) = dk + b + l + eh + mn + δni

29

Results1762 J. EATON AND S. KORTUM

TABLE III

BILATERAL TRADE EQUATION

Variable est. s.e.

Distance [0, 375) -0d1 -3.10 (0.16) Distance [375, 750) -6d2 -3.66 (0.11) Distance [750, 1500) -Od3 -4.03 (0.10) Distance [1500,3000) -Od4 -4.22 (0.16) Distance [3000, 6000) -Od5 -6.06 (0.09) Distance [6000, maximum] - Od6 -6.56 (0.10) Shared border -Ob 0.30 (0.14) Shared language -01 0.51 (0.15) European Community -0e1 0.04 (0.13) EFTA -Oe2 0.54 (0.19)

Source Country Destination Country

Country est. s.e. est. s.e.

Australia S, 0.19 (0.15) -Om, 0.24 (0.27) Austria S2 -1.16 (0.12) - m2 -1.68 (0.21) Belgium S3 -3.34 (0.11) - m3 1.12 (0.19) Canada S4 0.41 (0.14) - m4 0.69 (0.25) Denmark S5 -1.75 (0.12) -6m5 -0.51 (0.19) Finland S6 -0.52 (0.12) - m6 -1.33 (0.22) France S7 1.28 (0.11) -6m7 0.22 (0.19) Germany S8 2.35 (0.12) - m8 1.00 (0.19) Greece S9 -2.81 (0.12) -6m9 -2.36 (0.20) Italy S1( 1.78 (0.11) -6m10 0.07 (0.19) Japan Sil 4.20 (0.13) -6m11 1.59 (0.22) Netherlands S12 -2.19 (0.11) -6m12 1.00 (0.19) New Zealand S13 -1.20 (0.15) -Om13 0.07 (0.27) Norway S14 -1.35 (0.12) -Om14 -1.00 (0.21) Portugal S15 -1.57 (0.12) -6m15 -1.21 (0.21) Spain S16 0.30 (0.12) -6m16 -1.16 (0.19) Sweden S17 0.01 (0.12) -6m17 -0.02 (0.22) United Kingdom S18 1.37 (0.12) -6m18 0.81 (0.19) United States S19 3.98 (0.14) -6m19 2.46 (0.25)

Total Sum of squares 2937 Error Variance: Sum of squared residuals 71 Two-way (02o2) 0.05 Number of observations 342 One-way (02o-2) 0.16

Notes: Estimated by generalized least squares using 1990 data. The specification is given in equation (30) of the paper. The parameter are normalized so that E!9 Si = 0 and E19 mn = 0. Standard errors are in parentheses.

On their own, the competitiveness measures and the coefficients on the proxies for geographic barriers reflect a combination of underlying factors. Below we use estimates of 0 to extract from them the parameters that we need for our counter- factuals. We now provide two alternative estimates of 0 to the one from Section 3.

5.2. Estimates using Wage Data

One approach brings data on wages to bear in estimating (26). The coefficient on relative wages in the bilateral wage equation provides the first alternative

30

Results

1762 J. EATON AND S. KORTUM

TABLE III

BILATERAL TRADE EQUATION

Variable est. s.e.

Distance [0, 375) -0d1 -3.10 (0.16) Distance [375, 750) -6d2 -3.66 (0.11) Distance [750, 1500) -Od3 -4.03 (0.10) Distance [1500,3000) -Od4 -4.22 (0.16) Distance [3000, 6000) -Od5 -6.06 (0.09) Distance [6000, maximum] - Od6 -6.56 (0.10) Shared border -Ob 0.30 (0.14) Shared language -01 0.51 (0.15) European Community -0e1 0.04 (0.13) EFTA -Oe2 0.54 (0.19)

Source Country Destination Country

Country est. s.e. est. s.e.

Australia S, 0.19 (0.15) -Om, 0.24 (0.27) Austria S2 -1.16 (0.12) - m2 -1.68 (0.21) Belgium S3 -3.34 (0.11) - m3 1.12 (0.19) Canada S4 0.41 (0.14) - m4 0.69 (0.25) Denmark S5 -1.75 (0.12) -6m5 -0.51 (0.19) Finland S6 -0.52 (0.12) - m6 -1.33 (0.22) France S7 1.28 (0.11) -6m7 0.22 (0.19) Germany S8 2.35 (0.12) - m8 1.00 (0.19) Greece S9 -2.81 (0.12) -6m9 -2.36 (0.20) Italy S1( 1.78 (0.11) -6m10 0.07 (0.19) Japan Sil 4.20 (0.13) -6m11 1.59 (0.22) Netherlands S12 -2.19 (0.11) -6m12 1.00 (0.19) New Zealand S13 -1.20 (0.15) -Om13 0.07 (0.27) Norway S14 -1.35 (0.12) -Om14 -1.00 (0.21) Portugal S15 -1.57 (0.12) -6m15 -1.21 (0.21) Spain S16 0.30 (0.12) -6m16 -1.16 (0.19) Sweden S17 0.01 (0.12) -6m17 -0.02 (0.22) United Kingdom S18 1.37 (0.12) -6m18 0.81 (0.19) United States S19 3.98 (0.14) -6m19 2.46 (0.25)

Total Sum of squares 2937 Error Variance: Sum of squared residuals 71 Two-way (02o2) 0.05 Number of observations 342 One-way (02o-2) 0.16

Notes: Estimated by generalized least squares using 1990 data. The specification is given in equation (30) of the paper. The parameter are normalized so that E!9 Si = 0 and E19 mn = 0. Standard errors are in parentheses.

On their own, the competitiveness measures and the coefficients on the proxies for geographic barriers reflect a combination of underlying factors. Below we use estimates of 0 to extract from them the parameters that we need for our counter- factuals. We now provide two alternative estimates of 0 to the one from Section 3.

5.2. Estimates using Wage Data

One approach brings data on wages to bear in estimating (26). The coefficient on relative wages in the bilateral wage equation provides the first alternative

31

Estimation

EK use wage and price data to provide to alternative estimates for θ.They apply θ = 3.60, θ = 8.28, and θ = 12.86.

For each of these values, they derive estimates for Ti and geographicbarriers.

Based on the definition of Si and using wages, one can back out Ti .

Geographic barriers can be obtained by dividing the coefficients in theresults tables above by the respective value of θ and exponentiate.

We are now ready to study a number of counterfactuals.

32

Counterfactuals

Objective: Real GDP Yn/pαn , where the manufacturing sector share is

α = 0.13.

1 Gains from trade: Autarky vs. Status Quo vs. Free Trade

2 How do technology and geography shape the pattern ofspecialization?

3 How does trade help spreading technological know-how?

4 What are the implications of tariff reductions?

33

1. Raising geographic barriersTECHNOLOGY, GEOGRAPHY, AND TRADE 1769

TABLE IX

THE GAINS FROM TRADE: RAISING GEOGRAPHIC BARRIERS

Percentage Change from Baseline to Autarky

Mobile Labor Immobile Labor

Country Welfare Mfg. Prices Mfg. Labor Welfare Mfg. Prices Mfg. Wages

Australia -1.5 11.1 48.7 -3.0 65.6 54.5 Austria -3.2 24.1 3.9 -3.3 28.6 4.5 Belgium -10.3 76.0 2.8 -10.3 79.2 3.2 Canada -6.5 48.4 6.6 -6.6 55.9 7.6 Denmark -5.5 40.5 16.3 -5.6 59.1 18.6 Finland -2.4 18.1 8.5 -2.5 27.9 9.7 France -2.5 18.2 8.6 -2.5 28.0 9.8 Germany -1.7 12.8 -38.7 -3.1 -33.6 -46.3 Greece -3.2 24.1 84.9 -7.3 117.5 93.4 Italy -1.7 12.7 7.3 -1.7 21.1 8.4 Japan -0.2 1.6 -8.6 -0.3 -8.4 -10.0 Netherlands -8.7 64.2 18.4 -8.9 85.2 21.0 New Zealand -2.9 21.2 36.8 -3.8 62.7 41.4 Norway -4.3 32.1 41.1 -5.4 78.3 46.2 Portugal -3.4 25.3 25.1 -3.9 53.8 28.4 Spain -1.4 10.4 19.8 -1.7 32.9 22.5 Sweden -3.2 23.6 -3.7 -3.2 19.3 -4.3 United Kingdom -2.6 19.2 -6.0 -2.6 12.3 -6.9 United States -0.8 6.3 8.1 -0.9 15.5 9.3

Notes: All percentage changes are calculated as 100ln(x'/x) where x' is the outcome under autarky (d,j oo for n :A i) and x is the outcome in the baseline.

when trade is shut down could be seen as indicating their overall comparative advantage in manufactures.

The remaining columns consider the effects of moving to autarky with immo- bile labor. Column four reports the welfare loss. The effect on welfare is more negative than when labor is mobile, but usually only slightly so.

The net welfare effects mask larger changes in prices and incomes. In all but the four "natural manufacturers" (Germany, Japan, Sweden, the United Kingdom), the price rise is greater when manufacturing labor is immobile. (In Germany and Japan manufacturing prices actually fall.) But these greater price changes lead to only slightly larger effects on welfare because they are mitigated by wage changes (reported in column six): The wage in manufacturing rises in all but the four "natural manufacturers."44

44 How much labor force immobility exacerbates the damage inflicted by autarky depends on the extent of specialization in manufacturing. A move to autarky raises the manufacturing wage the most in Greece, with the smallest manufacturing share. But since its share of manufacturing labor income (reported in Table I) is so small, the overall welfare effect is swamped by the large increase in manufacturing prices. In Germany, with the largest manufacturing share, a move to autarky lowers the manufacturing wage. But since the share of manufacturing is so large, the welfare cost of this loss in income is not offset by the drop in manufacturing prices. For countries that are less specialized (in or away from manufactures), labor mobility makes less difference for overall welfare.

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2. Lowering geographic barriers1770 J. EATON AND S. KORTUM

TABLE X

THE GAINS FROM TRADE: LOWERING GEOGRAPHIC BARRIERS

Percentage Changes in the Case of Mobile Labor

Baseline to Zero Gravity Baseline to Doubled Trade

Country Welfare Mfg. Prices Mfg. Labor Welfare Mfg. Prices Mfg. Labor

Australia 21.1 -156.7 153.2 2.3 -17.1 -16.8 Austria 21.6 -160.3 141.5 2.8 -20.9 41.1 Belgium 18.5 -137.2 69.6 2.5 -18.6 68.8 Canada 18.7 -139.0 11.4 1.9 -14.3 3.9 Denmark 20.7 -153.9 156.9 2.9 -21.5 72.6 Finland 21.7 -160.7 172.1 2.8 -20.9 44.3 France 18.7 -138.3 -7.0 2.3 -16.8 15.5 Germany 17.3 -128.7 -50.4 1.9 -14.3 12.9 Greece 24.1 -178.6 256.5 3.3 -24.8 29.6 Italy 18.9 -140.3 6.8 2.2 -16.1 5.7 Japan 16.6 -123.5 -59.8 0.9 -6.7 -24.4 Netherlands 18.5 -137.6 67.3 2.5 -18.5 65.6 New Zealand 22.2 -164.4 301.4 2.8 -20.5 50.2 Norway 21.7 -161.0 195.2 3.1 -22.9 69.3 Portugal 22.3 -165.3 237.4 3.1 -22.8 67.3 Spain 20.9 -155.0 77.5 2.4 -18.0 -4.4 Sweden 20.0 -148.3 118.8 2.7 -19.7 55.4 United Kingdom 18.2 -134.8 3.3 2.2 -16.4 28.5 United States 16.1 -119.1 -105.1 1.2 -9.0 -26.2

Notes: All percentage changes are calculated as 1001n(x'/x) where x' is the outcome under lower geographic barriers and x is the outcome in the baseline.

Three of the four countries we have identified as "natural manufacturers," where manufacturing shrinks in moving to autarky, are quite large. A question is whether these countries' manufacturing prowess results from their state of tech- nology relative to the cost of labor, or because of their size and location. In the first case a total elimination of geographic barriers would continue to favor these countries. In the second the elimination of geographic barriers would remove their advantage. Table X shows, in its first three columns, what out model says would happen in a zero-gravity world (setting all dni = 1). Looking at manufac- turing employment in the case of mobile labor (column three), Germany and Japan experience large drops while Sweden continues to gain. Little happens in the United Kingdom. At the same time smaller, peripheral countries all experi- ence expansion.

Our welfare measure indicates that we are very far from a world of zero gravity. Furthermore, world trade would be about five times its current level in such a world. The last three columns of Table X report an experiment closer to reality: What happens if geographic barriers fall to 69 percent of their baseline levels across the board, leading to a doubling of world trade?45 Welfare rises by 1 to 3 percent as the price of manufactures falls by 10 to 20 percent. These effects are

45 We find an elasticity of trade volume with respect to overall geographic barriers of around 2 to 3.

35

3. Technology vs. geography

1772 J. EATON AND S. KORTUM

0.9

0.8

c o|! 0.7-

E 0.6

o 0.5

o 0.4 o 0.4- / J ~~~~~~~~~~~~~~~~~~Denmark|

0 r 0.3 Germany -0

0.2

0.1

0 l l l l l l l l l l l l l l l l l l l l l l I

16 8 4 2 1 0.5 0.25 0.125 0.0625

(toward autarky) factor increase In geographic barriers (toward zero gravity)

FIGURE 3.-Specialization, technology, and geography.

technology T1 by 20 percent, first for the United States and then for Germany. Table XI reports what happens to welfare in different countries of the world as a percentage of the effect locally. Other countries always gain through lower prices. With labor mobile there is no additional income effect, so the net welfare effect is always positive. When labor is immobile, foreign countries also experience a negative income effect through lower wages in manufacturing. Hence the overall welfare effect is generally lower when countries can't downsize their manufactur- ing labor forces.47 Germany and Japan, with large manufacturing shares, actually suffer welfare losses in response to technological improvements elsewhere.

The percentage benefits decay dramatically with distance and size. With labor mobile the gain in nearby countries approaches that where the improvement occurred. Canada, for example, benefits almost as much as the United States from a U.S. technological improvement. Germany's smaller neighbors experience more than half the gain from an improvement in German technology as Germany itself. At the other extreme, Japan, which is both distant and large, gets little from either Germany or the United States.

The results point to the conclusion that trade does allow a country to bene- fit from foreign technological advances. But for big benefits two conditions must be met. First, the country must be near the source of the advance. Second, the

47 The exception is Greece. In the case of immobile labor the added benefit of lower wages in suppliers nearby more than offsets the reduction in the wages earned by its own small fraction of workers in manufacturing.

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Technology vs. geography

For smaller countries, manufacturing shrinks as geographic barriersdiminish.

Production shifts to larger countries where inputs are cheaper.

As geographic barriers continue to fall, however, the forces oftechnology take over and manufacturing employment grows.

37

Conclusions

Eaton and Kortum (2002) develop a model with N countries and acontinuum of goods incorporating realistic geographic features intogeneral equilibrium.

Their model can explain that

I trade diminishes dramatically with distance;

I prices vary across locations, with greater differences between placesfarther apart;

I factor rewards are far from equal across countries

I countries’ relative productivities vary substantially across industries.

Shortcoming: Proper model of labor market. Alvarez and Lucas(2006, JME) add this aspect to the EK-model.

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