International Trade
The Gravity Equation and its Applications
Prof. Dr. Tobias Seidel
University of Duisburg-Essen
April 2014
Background Reading: Feenstra (2004) - Chapter 5
What Heckscher-Ohlin is (not) about
Heckscher-Ohlin is about
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The pattern (not the volume) of trade
Differences in structural characteristics of economies (like factor
endowments)
A country’s trade with the rest of the world
Heckscher-Ohlin is not (or less) about
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The volume of trade
The relative size of countries
Bilateral trade between single country pairs in a multi-country world
⇒ Explaining these latter things requires different (or enriched) theory
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An empirical observation: Intra-industry trade
Measure: Grubel-Lloyd index Γijs for each industry (sector) s and
countries i and j (Xsij and Msij denote sectoral exports and imports,
respectively)
|Xsij − Msij |
Γijs = 1 − ij
∈ [0, 1]
Xs + Msij
Measure of total intra-industry trade between i and j
Γ̄ijs =
X
s
Xsij + Msij
Γij
P ij
ij s
X
+
M
s
s s
Evidence: Large figures, sometimes well above 50%, in particular for
trade between similar advanced countries (EU - US, say)
⇒ Trade may be driven by things other than comparative advantage of
factor endowments
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Grubel-Lloyd indices of intra-industry trade, 2006
Source: WTO World Trade Report 2008
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Outline of the talk
In the previous lecture we checked whether factor endowments
advantage 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 a
theory-grounded workhorse for empirical research
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What drives the volume of world trade over time? Technology versus
policy
What determines the geographical structure of trade? Borders,
informal barriers to trade
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 distinct
subsets of goods
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Heckscher-Ohlin framework with a continuum of goods (many more
goods than factors)
Monopolistic competition and increasing returns to scale
Units of analysis are “country pairs” or dyads
The explanandum: Volume of bilateral trade , e.g., exports from
country 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 index
i, j = 1, ..., C
There are C (C − 1)/2 independent bilateral trade relations
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With approximately 225 countries and territories, the potential number
of independent trade relations amounts to 25, 200!
Explanatory variables: Countries’ GDP, trade costs (tariffs, transport
costs, ...)
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Frictionless trade
Assumptions
A1
A2
A3
A4
Countries are specialized in distinct subsets of goods
Representative consumers have identical, homothetic preferences
Countries are identical except for their size
Free trade (goods price equalization holds exactly, no trade costs)
Perfectly symmetric countries (identical symmetric preferences and
technology)
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Goods prices (k = 1, ..., N) can be normalized to unity
value = volume
The Krugman (1979) model
Since the monopolistic competition model is very well suited for this
analysis, we briefly review the original Krugman model
Love of variety” in consumption
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Consumers demand similar but different varieties of a product
Utility is increasing in the number of different varieties, ceteris paribus
Increasing returns to scale
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More costly for a firm to produce different varieties than to specialize
on a single variety due to fixed costs of production
Gains from trade
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Trade allows a country to specialize on the production of few varieties
while consuming many varieties
The Krugman (1979) model (cont’d)
Suppose there are i = 1, ..., N varieties that are endogenously
determined
There is a fixed number of consumers L sharing love-of-variety
preferences
N
X
U=
v (ci ) , v 0 > 0, v 00 < 0.
i=1
P
Given the budget constraint w = N
i=1 pi ci , each consumer
maximizes utility to get
v 0 (ci ) = λpi
where λ is the Lagrange multiplier.
Totally differentiating the first-order condition yields the elasticity of
demand for variety i
0 v
ηi = −
> 0, with dηi /dci < 0
ci v 00
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The Krugman (1979) model (cont’d)
On the production side, each firm requires the following labor to
produce output yi ,
Li = α + βyi .
This implies average costs ACi = wLi /yi and marginal costs βw .
With symmetric countries, we apply the following two equilibrium
conditions to solve the model
(1) MR = MC (profit maximization)
1
p 1−
= wβ
η
(2) P = AC (free entry drives profits to zero)
p=
wα
+ wβ
y
where we have substituted y = Lc.
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The Krugman (1979) model (cont’d)
Conditions (1) and (2) provide two equations in two unknowns, p/w
and 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 a
negative link (ZZ -schedule)
Finally, we can solve for the number of firms (varieties) by applying
the labor-market-clearing condition
L=
N
X
i=1
Li =
N
X
(α + βyi ) = N (α + βy ) = N (α + βLc)
i=1
This delivers
N=
11
1
(α/L) + βc
The Krugman (1979) model: Trade
p/w
Z
P
Z´
(p/w)0
Z
(p/w)1
P
Z´
c1
Source: Krugman (1979)
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c0
c
Frictionless trade: The ‘baby’ gravity equation
P
i
Country i 0 s GDP: Y i = N
k=1 yk
P
P
PC
i
i
World GDP: Y w = Ci=1 N
k=1 yk =
i=1 Y
Trade is assumed to be balanced
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Country j 0 s GDP equals its expenditure
Country j 0 s share in world expenditure is s̄ j = Y j /Y w
Perfect specialization and identical homothetic demand
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Xkij = s̄ j yki
Simplest form of the gravity equation
X ij =
N
X
s̄ j yki = s̄ j Y i = Y j Y i /Y w = s̄ j s̄ i Y w
k=1
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I.e., bilateral exports from country i to country j are proportional to
the product of their GDPs
Empirical application: Trade within and outside the OECD (Helpman,
1987, and Debaere, 2005)
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Theorem (Helpman, 1987)
Recall that X ij = X ji = s j s i Y w
Total bilateral trade volume X ij + X ji = 2s j s i Y 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 s A = Y A /Y w
We can rewrite the total bilateral trade volume V A = X ij + X ji
VA
sj si Y w
Yj Yi
Yj Yi YA
= 2s jA s iA s A
=
2
=
2
=
2
Yw YA
YA
YA
YA YA Yw
Since s iA + s jA = 1, we have
2
2
2
s iA + s jA = s iA + s jA + 2s jA s iA = 1
A theorem follows
2 2 VA
A
= s 1 − s iA − s jA
YA
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Bracketed expression is a ‘size dispersion index’ that we call disp A for
future reference
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
2
P
Then, disp A = 1 − i∈A s iA
The index is maximized for countries of the same relative size 1/N
X
disp A = 1 −
1/N 2 = 1 − 1/N = (N − 1)/N
i∈A
As any country has a share approaching unity, disp A approaches zero
The theorem says that the volume of trade in region A is related to
the relative size of countries – as measured by the dispersion index
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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
ij
X + X ji
i
j
+ ln disp A
ln
=
ln
s
+
s
Yi +Yj
Debaere runs the following regression
!
Xtij + Xtji
j
i
A
ln
=
α
+
γ
ln
s
+
s
ij
t + β ln dispt ,
t
j
i
Yt + Yt
where αij is a dyadic fixed effect
Econometric issues
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If sti + stj were constant over time, αij would capture their information
Debaere measures GDP in nominal USD and in PPP
GDP can be instrumented by population size
Debaere (2005) - Results
P. Debaere / Journal
International
66 (2005) 249–266
Note258that the dispersion
indexof shows
upEconomics
as ‘similarity’
Table 1
Eq. (2a) in logs with varying shares panel data
Fixed effects regression with time-specific effects
Dependent variable OECD
ln(similarity)
S.E.
ln(world share)
S.E.
ln(similarity) IV
S.E.
ln(world share) IV
S.E.
R2
Observ.
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
–
–
–
–
–
–
–
–
1.57
0.11*
1.3
0.13*
–
0.89
0.056*
0.47
0.05*
–
–
–
0.61
1820
0.45
1820
0.96
0.99
1.98
0.95*
–
0.25
0.66
0.06*
0.06*
0.62
0.98
–
0.25*
0.22*
0.56
0.41
0.02
1820
1820
1320
0.4
0.23
0.99
0.22*
–
–
0.14
1320
2.3
0.5
0.6*
0.26*
5.4
3.1
2.9
1.2*
0.03
0.14
1320
1320
Standard errors under the estimated coefficients.
* Significant at 95%.
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 e ij and simij
Source: Debaere (2005)
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Debaere (2005) - Results
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3
Theoretical prediction that β = 1 has a chance to be met only in the
OECD subsample
However, regardless of the exact specification (including ln sti + stj
or not) and regardless of the data (IMF versus PWT), β > 0 for the
OECD countries
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 less
so for developing countries. This is in line with intuition
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Estimating border effects (McCallum, 1995)
A second interesting application of this ”free-trade” gravity equation
compares intranational trade with international trade between
Canada and the US
What is the effect of the border on Canada-U.S. trade?
Sample of bilateral trade relations of Canadian provinces between
each other and with US states (trade between US states is not
present in McCallum’s original regressions)
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Estimating border effects (McCallum, 1995)
McCallum estimates a variant of the gravity equation using data for
1988
ln(X ij ) = α + β1 ln Y i + β2 ln Y j + γδ ij + ρ ln d ij + εij
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δ ij is an indicator variable that takes value 1 if the trade relation
involves Canadian provinces, and value 0 if it involves a Canadian
province and a US state. δ ij measures the border effect
d ij is the distance between any two provinces or states. It measures
distance related trade costs
Note that this equation proxies T ij by distance and border, but does
not relate those trade costs to prices
McCallum’s (1995) border puzzle
Estimates of coefficients to Y i , Y j and d ij are in line with theoretical
expectations 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 between
Canada and the US
These extraordinarily high effects remain if
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Data for 1993 are used (in 1990 NAFTA agreement was signed)
Trade between U.S. states are considered as well
⇒ “Border effect puzzle”
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Borders asymmetrically affect countries of different size
McCallum’s result is biased, since the size of border effects depends
on the size of the country in question
Example
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Assume that the US has a GDP 10 times as large as Canada
Without border effects (and transport costs), Canada exports 90% of
GDP to the US, it sells 10% internally
Suppose the border effect reduces cross-border trade by a factor of
one-half
Then, Canada exports 45% of GDP to the US and trades 55%
internally
So the border effect reduces external trade by the factor 2 and
increases internal trade by the factor 5.5. Total effect: internal trade is
11 times higher than external trade
Conversely, in the US, the border effect reduces external trade from
10% of GDP to 5% (factor 2) and increases internal trade from 90% of
GDP to 95% (factor 1.06). Total effect: internal trade is 2.1 times
higher than external trade
Towards a gravity equation that allows for trade costs
To avoid these huge biases, we need to carefully derive a gravity
equation that accounts for trade barriers
This introduces additional complications because prices are no longer
equalized across countries
Patterns of trade are more complex than in the ‘baby’ gravity equation
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A refresher of the monopolistic competition model
Special case: Dixit-Stiglitz preferences (Krugman, 1980)
Constant elasticity of substitution (CES) utility function
U=
N
X
(σ−1)/σ
c`
,σ > 1
`=1
Elasticity of substitution between products σ equals elasticity of
demand if N is large
Representative consumerP
in country j maximizes U subject to her
budget constraint Y j = N
`=1 p` c`
Lagrange function
L=
N
X
`=1
(σ−1)/σ
c`
+λ Yj −
N
X
`=1
!
p` c `
Deriving optimal demand
Maximization of L with respect to c` and ck delivers the following
first order conditions
σ − 1 −1/σ
c
= λp`
σ `
σ − 1 −1/σ
c
= λpk
σ k
Dividing leads to
−σ
c`
p`
=
ck
pk
Substituting into the budget constraint yields
−σ
N
N
X
X
p`
σ
Y =
ck p`
= ck pk
p`1−σ
pk
`=1
`=1
Hence, optimal demand is given by
ck =
25
pkσ
Y
PN
1−σ
`=1 p`
Simplifying the expression for demand
Introduce the exact price index P (the expenditure needed to
purchase one unit of utility)
1−σ
N N
N
X
X
X
p`
p` 1−σ
(σ−1)/σ
(σ−1)/σ
(σ−1)/σ
= c̄k
1 =
c̄`
=
c̄k
pk
pk
`=1
`=1
`=1
σ
#
" N X p` 1−σ σ−1
1 = c̄k
pk
`=1
σ
" N # 1−σ
# σ
" N
X p` 1−σ 1−σ
X
c̄k =
= pk−σ
p`1−σ
pk
`=1
`=1

σ 
1
"
# 1−σ
! 1−σ
N
N
N
N
X
X
X
X
p 1−σ
=
P =
p` c̄` =
p`1−σ
p`1−σ
`
`=1
`=1
`=1
This gives rise to demand functions
c` =
26
p`−σ
Y
P 1−σ
`=1
Production side
Labor is the only factor of production, with conditional labor demand
of 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` ) = w α + w βy`
This cost function is identical across sectors
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Constant marginal costs MC = w β
Decreasing average costs AC = w α/y` + w β
Characterizing the equilibrium
Firms behave as monopolists: they set marginal cost (MC ) equal to
marginal revenue (MR)
1
p`
σ
w β = p` 1 −
⇔
=β
σ
w
σ−1
Free entry forces prices to be equal to average costs (AC ) (zero
profits)
wα
p`
α
p` =
+ wβ ⇔
=
+β
y`
w
Lc`
Note that we have substituted y` by Lc` (identical households demand
c` units of each variety)
These two conditions determine
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Equilibrium firm size y = α
β (σ − 1)
Consumption per capita c = y /L =
α
Lβ (σ
− 1)
Characterizing the equilibrium (cont’d)
Labor market clearing
L=
N
X
(α + βy` ) = N (α + βy` ) ⇔ N =
`=1
L
ασ
Substituting this into the utility function, we get indirect utility
1 σ−1
L σ 1 σ−1 σ
U=
α
σ
β
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Increasing in L: love of variety
Variety represents the only source of gains from trade liberalization
(increase in L) – This is different to Krugman (1979)
Decreasing in fixed costs α and marginal costs β
Shortcomings
IO issues
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No strategic interactions of firms
Static model
Empirical issues
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Output per firm/variety is constant ⇒ no scale effect
Firms are symmetric. Selection (if occurring) is unmodeled, all firms
are exporters, only margin of adjustment to trade liberalization is
number of varieties consumed while number of varieties produced
remains unchanged ⇒ no selection effect
But: Scale and selection effects reappear if firms are heterogeneous in
their productivity levels (Melitz, 2003)
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Modeling trade costs – Iceberg trade costs and demand
A2’ Iceberg trade costs (Samuelson, 1952): p ij = T ij p i ; T ij ≥ 1, T ii = 1
We no longer have p ij = p ii for all i, j = 1, ..., C . Therefore need to model
demand
A4 Specific utility function: Constant elasticity of substitution (CES)
Now, we need to distinguish between quantities and values (as we can
no longer normalize p ij = 1 for all i, j = 1, ..., C
Let’s denote the quantity of exports from i to j of good k by ckij .
Perfect specialization implies that ckij is equal to the consumption of
good k in country j
Assuming that country i produces N i goods (varieties), country js
representative consumer has the utility
i
j
U =
C X
N X
i=1 k=1
ckij
σ/(1−σ)
,σ > 1
Modeling trade costs – Simplifications
To simplify, further assume that all exports of country i sell at the
same price p ij (c.i.f.) in country j. Then, by symmetry we have
ckij = c ij and
C
X
σ/(1−σ)
j
U =
N i c ij
,σ > 1
i=1
The representative consumer
in country j maximizes U j subject to her
P
C
budget constraint Y j = i=1 N i p ij c ij . This gives rise to demand
functions
−σ
p ij
ij
Yj
c =
1−σ
j
(P )
i
hP
1/(1−σ)
C
i
ij (1−σ)
is country j 0 s overall price
where P j =
i=1 N p
index.
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Modeling trade costs – Deriving the ‘core’ gravity equation
Total value of exports from country i to j is X ij = N i p ij c ij
Substituting from above and using A2’, we get
ij
i
X =N Y
j
T ij p i
Pj
1−σ
Recall that firm sizes are fixed by parameters
Hence, GDP in country i is Y i = N i p i ȳ
Combining both equations delivers
Y jY i
X = i σ
(p ) ȳ
ij
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T ij
Pj
1−σ
How do we estimate this gravity equation?
We will study three approaches to estimate the resulting gravity
equation
1
2
3
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The use of price indexes (Baier & Bergstrand, 2001)
The use of estimated border effects (Anderson & van Wincoop, 2003)
The use of fixed effects (e.g. Redding & Venables, 2000; Rose & van
Wincoop, 2001)
Baier & Bergstrand (2001): Dissecting world trade growth
Specification issues
We have a panel data set with observations for Xtij and the other
variables (T ≥ 2)
Logarithms and first differences helps eliminate ȳ :
∆ ln X ij = ∆ ln Y j Y i − σ∆ ln p i + (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 p i
+ (1 − σ) ∆ ln T ij − (1 − σ) ∆ ln P j
The above equation attributes
growth in bilateral trade to income
j
i
growth, ∆ ln Y + Y , convergence in countries’ incomes,
∆ ln s i s j , changes in prices, ∆ ln p i and ∆ ln P j , and finally, changes
in trade costs, ∆ ln T ij
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Baier & Bergstrand (2001): Dissecting world trade growth
Data issues
To disentangle the different elements in T ij , Baier and Bergstrand
introduce two variables
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Gross c.i.f./f.o.b. factors published by the IMF, meant to measure
trade costs different than tariffs (i.e., transportation costs): 1 + aij
Gross tariff rate: 1 + tij
Data: Bilateral trade data averages for two points in time: 1958-1960
and 1986-1988. Log differences are interpreted as growth rates
36
Baier & Bergstrand (2001): Data
Real 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): Results
1
Income variables are the main drivers behind the growth of world
trade
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 yields
a contribution of 2.49
I Mean growth in importer income (1.03) has dampening effect on trade
growth 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 in
world 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 is
2.49 − 0.7 − 0.79 = 1 (100 percentage points); hence, income growth
explains 100/148 = 2/3 of the trade growth
I
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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
An alternative to using price data: Estimating border
effects
Using price measures has disadvantages: (i) difficult to compare levels
across countries and (ii) unlikely to capture border effect properly
So instead of using data to measure prices, we can model the
difference between c.i.f prices p ij form f.o.b. prices p i as a function of
distance 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 random
error
We would need to estimate τ ij ; this is tricky: substitution of T ij from
our gravity equation leads to a system of non-linear equations
estimation of which requires simulation
40
Anderson and van Wincoop’s (2003) gravity equation
Bilateral exports are given by
ij
X =
p ij
Pj
1−σ
Yj
Market-clearing implies that the sum of exports (including domestic
sales) equals total expenditure
i
Y =
X
j
ij
=X = p
i 1−σ
X T ij 1−σ
j
Pj
Yj
1−σ P T ij 1−σ j
P
Define Y = j Y j , s i = Y i /Y = p i
s and
j Pj
ij 1−σ
P
1−σ
sj
Πi
= j TP j
41
Anderson and van Wincoop’s (2003) gravity equation
Using these equations we get
pi
1−σ
=
si
1−σ
(Πi )
ij
⇒X =
T ij
Πi P j
1−σ
Y iY j
sY =
Y
i
j
T ij
Πi P j
This implies
P
j 1−σ
=
X T ij 1−σ
i
Πi
si
Under the assumption T ij = T ji it is clear that Πi = P i .
42
1−σ
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
ij X
ln
= ρ(1−σ) ln d ij +(1−σ)τ ij +ln(P i )σ−1 +ln(P j )σ−1 +(1−σ)ij
Y iY j
The multilateral resistance
terms can be solved from
PC i T ij 1−σ
1−σ
(Pi )
= j=1 s P j
once we know transport costs
The transport costs, in turn, are obtained from the lnT ij -equation
using the estimated value of ρ(1 − σ) ln d ij + (1 − σ)τ ij which comes
from the gravity equation above
As both sets of equations have to be used simultaneously, the
approach requires customized programming
43
Empirical implementation
A&vW work with an indicator 1 − δ ij , or unity for trade between the
U.S. and Canada, and zero otherwise
Introducing γ on this variable, they replace (1 − σ)τ ij with γ(1 − δ ij )
Let α = ρ(1 − σ)
Gravity equation becomes
ij X
ln
= α ln d ij + γ(1 − δ ij ) + ln(P i )σ−1 + ln(P j )σ−1 + (1 − σ)ij
Y iY j
Note that provincial and state GDP terms have their coefficients
constraint at unity
44
Results
Coefficient on the indicator variable is estimated at γ̂ = −1.65
h
i
ij )
Interpretation: exp(τ ij ) = exp γ(1−δ
1−σ
For cross-border trade we have δ ij = 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, indicating
border barriers of between 9% and 50% in terms of their implied
effect on price
45
How much more trade within than across the border?
Let (P̄ i )σ−1 be the multilateral resistance terms in the absence of the
border effect (thus using only distance to compute T ij )
Comparing equations with and without border effects
h
i P i P j σ−1
X ij
γ̂(1−δ ij )
=
e
X̄ ij
P̄ i P̄ j
Consider intra-Canadian trade (i = j = CAN, δ CAN,CAN = 1)
I
I
Intra-Canadian trade is 4.3 times larger with border effect than without
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 than
without
Thus, intra-Canadian trade is 4.3/0.41 = 10.5 times higher than
cross-border trade
Intra-U.S. trade is 1.05/0.41 = 2.6 times higher than cross-border
trade
⇒ Smaller economies have a much larger impact of the border effects
46
A fixed effects procedure
Drawback: Requires programming to solve unconstrained
minimization problem
Alternative procedure: Source and destination country fixed effects
With fixed effects ν i , ν j , we may estimate the equation
ij X
ln
= γ 1 − δ ij + α1 ln d ij + ν i + ν j + u ij
i
j
Y Y
This approach yields γ̂ = −1.55 which is close to the −1.65 reported
above
The implied average border effect is exp(1.55) = 4.7
47
Comparing border effects estimates
48
Comparing border effects estimates
Interestingly, the average border effect of the three approaches is very
similar
However, as McCallum ignores the price channels, his estimates are
inconsistent
This appears to have the effect that the border effect for Canada is
overstated, while it is understated for the US
49
Questions
1
50
h
2 i
2
as a dispersion index?
Why can we interpret 1 − s iA + s jA
What does Helpman’s theorem imply?
2
Why is it important to control for multilateral resistance terms in
empirical 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 first
differencing or fixed effects (within) transformation suffice to control
for multilateral resistance terms when T ≥ 2?
5
Modify the trade costs specification such that it accounts for common
use of a currency!
6
What empirical applications of the gravity approach can you think of?
The Eaton-Kortum Model
Prof. Dr. Tobias Seidel
University of Duisburg-Essen
April 2014
Background Reading: Eaton, Kortum (2002), Technology, Geography, and
Trade, Econometrica 70, 1741-1779.
1
What’s the problem?
Ricardo (1817) provided a mathematical example that countries can
mutually benefit by specializing on their goods at which they have a
comparative advantage.
This changed the view in that also countries that were absolutely
better in producing all goods could benefit from trading with
technologically inferior countries.
The 2x2 model is a standard part of each introductory trade book,
but has played no influence in explaining the global pattern of
international trade.
Until recently! 200 years after its birth, the Ricardian theory
experiences a revival. Why???
2
Why?
Even in the most basic version of the Ricardo model, several equilibria
can 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 and
Kortum (2012) put it: “... stairways are trouble not only for wheeled
vehicles but for comparative statics.”
3
A continuum of goods...
Dornbusch, Fischer, and Samuelson (1977) had the idea of adding a
lot of goods to the list - ending up with a continuum. They replaced
the stairway with a ramp!
This smoothness makes the model very tractable.
For example, it is straightforward to introduce trade costs to explain
that countries buy more goods from themselves.
One limitation remains: There are only two countries.
4
5
Adding more countries...
Technically, we could add a continuum of countries (a finite integer
number would cause a stairway again).
While it might be justifiable to deal with a continuum of goods, it is
less plausible to introduce a continuum of countries – especially with
respect to empirical work.
Here’s where Eaton and Kortum (2002) comes in. They turn a messy
discreet problem into a tractable, continuous problem.
With many goods and many countries, it does not help to construct
chains of comparative advantage. Instead, they introduce a
probabilistic approach: Labor input requirements a(j) are realizations
of a random variable.
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 are
many, but only the parameters of which they are drawn, which can be
small in number.
Let’s see how it works in detail...
6
Preliminaries
Countries have differential access to technology, so efficiency varies
across 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 a
country (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 one
unit 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 ≤ dnk dki .
7
Preliminaries
Delivering an unit of good j produced in country i to country n costs
ci
dni .
pni (j) =
zi (j)
With perfect competition, pni is what consumers in n would have to
pay for good j imported from i.
But consumers would choose to buy the good from the country that
offers 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
ci
dni .
pni (j) =
zi (j)
With perfect competition, pni is what consumers in n would have to
pay for good j imported from i.
But consumers would choose to buy the good from the country that
offers 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) to
maximize a CES objective
Z
U=
1
Q(j)
σ−1
σ
σ
σ−1
dj
,
0
where σ > 0 represents the elasticity of substitution between goods.
Note: DFS (1977) order goods according to z1 (j)/z2 (j) where relative
wages determine the breakpoint in this “chain of comparative
advantage”. With more than two countries, there is no natural
ordering of commodities. Solution: Probabilistic approach!
10
Technology
Country i’s efficiency in producing good j is the realization of a
random variable Zi (drawn independently for each j) from its
country-specific probability distribution Fi (z) = Pr [Zi ≤ z]
By the law of large numbers, Fi (z) captures the fraction of goods for
which country i’s efficiency is below z.
The likelihood that country i supplies a particular good to country n
is the probability πni that i’s price turns out to be the lowest.
The probability theory of extremes provides a form for Fi (z) that
yields a simple expression for πni and the resulting distribution of
c
prices. EK assume FrÃchet
(type II extreme value distribution):
Fi (z) = e −Ti z
−θ
,
where Ti > 0 (absolute advantage) and θ > 0 (inverse of variability,
comparative advantage).
11
c
Why FrÃchet?
Central limit theorem implies (among other things): The highest or
lowest value in a large sample drawn from a well-behaved distribution
follows an extreme value distribution.
If technologies for making a good are the results of inventions that
occur over time and if the output per worker delivered by an invention
is drawn from a Pareto distribution, then output per worker using the
c
most efficient technology follow a FrÃchet
distribution (see Eaton
and Kortum, 1997, 1999).
c
Only for FrÃchet
does the distribution of prices inherit an extreme
value distribution.
12
Prices
What does this imply for the distribution of prices?
Country i presents country n with a distribution of prices
Gni (p) = Pr [Pni ≤ p] = 1 − Fi (ci dni /p) or
−θ ]p θ
Gni (p) = 1 − e −[Ti (ci dni )
.
Hence, the distribution Gn (p) for what country n actually buys is
Gn (p) = 1 − ΠN
i=1 [1 − Gni (p)] .
13
14
Prices
Inserting Gni (p) delivers
θ
Gn (p) = 1 − e −Φn p ,
where
Φn =
N
X
Ti (ci dni )−θ .
i=1
The price parameter Φn summarizes how (i) states of technology
around the world, (ii) input costs around the world, and (iii)
geographic barriers govern prices in each country n.
Prices
Three useful properties of price distributions:
1
Probability that country i provides a good at the lowest price in
country n given by
Ti (ci dni )−θ
πni =
Φn
With a continuum of goods, πni is also the fraction of goods that
country n buys from country i.
2
The price of a good that country n actually buys from any country i
also has the distribution Gn (p).
3
The exact price index for the CES objective (assuming σ < 1 + θ) is
pn = γΦ−1/θ
,
n
where
15
1
1−σ
θ+1−σ
γ= Γ
θ
A gravity equation
A corollary of property (2) is that country n’s average expenditure per
good does not vary by source. Hence,
Xni
Ti (ci dni )−θ
Ti (ci dni )−θ
=
= PN
,
−θ
Xn
Φn
T
(c
d
)
k
k
nk
k=1
This expression resembles the standard gravity equation! Let Qi be
total export sales of i to write
Qi =
N
X
m=1
Xmi =
Ti ci−θ
N
−θ
X
dmi
Xm
Φm
m=1
Solving for Ti ci−θ and substituting in the above expression delivers
−θ
dni
Xn
pn
Qi .
Xni =
−θ
PN
dmi
Xm
m=1 pm
16
Confronting the model with data
Model exhibits a direct link between trade flows and price differences:
Φi −θ
Xni /Xn
=
d =
Xii /Xi
Φn ni
pi dni
pn
−θ
This equation can be used to estimate θ.
But let us first plot normalized import shares against distance (as a
crude measure of geographical barriers) based on bilateral trade in
manufactures among 19 OECD countries...
17
Trade and geography
1752
J. EATON AND S. KORTUM
~~+
0.1~
~
x~~...
A,..Ue
4
*
',.
,
*
e
.
*
00
E
.
..,.
..
**
v
0.0
..
* *
*
0.001
.
c
t
t;
*0
-
.
.
.v
5 .
v
.
*
..
0.0001
100
1000
10000
distance (in miles) between countries n and i
FIGURE 1.-Trade and geography.
18
100000
Identifying θ
EK measure the term (pi dni )/pn by using retail prices for 50
manufactured products in 19 OECD countries.
The price measure reflects what the price index in destination n would
be for a buyer there who insisted on purchasing everything from
source i, relative to the actual price index in n (based on the cheapest
source).
Insights: (i)The cheapest foreign source is usually nearby and the
most expensive far away. (ii) Large countries usually suffer the most if
required to buy everything from a given foreign source.
From plotting the data, the implied θ is 8.28.
19
1754
Price measure
statisticsJ. EATON AND
S. KORTUM
TABLE II
PRICE
MEASURE
STATISTICS
Foreign Sources
Country
Australia (AL)
Austria (AS)
Belgium (BE)
Canada (CA)
Denmark (DK)
Finland (FI)
France (FR)
Germany (GE)
Greece (GR)
Italy (IT)
Japan (JP)
Netherlands (NE)
New Zealand (NZ)
Norway (NO)
Portugal (PO)
Spain (SP)
Sweden (SW)
United Kingdom (UK)
United States (US)
Minimum
Maximum
NE (1.44)
SW (1.39)
GE (1.25)
US (1.58)
Fl (1.36)
SW (1.38)
GE (1.33)
BE (1.35)
SP (1.61)
FR (1.45)
BE (1.62)
GE (1.30)
CA (1.60)
Fl (1.45)
BE (1.49)
BE (1.39)
NO (1.36)
NE (1.46)
FR (1.57)
PO (2.25)
NZ (2.16)
JP (2.02)
NZ (2.57)
PO (2.21)
PO (2.61)
NZ (2.42)
NZ (2.28)
NZ (2.71)
NZ (2.19)
PO (3.25)
NZ (2.17)
PO (2.08)
JP (2.84)
JP (2.56)
JP (2.47)
US (2.70)
JP (2.37)
JP (3.08)
Foreign Destinations
Minimum
BE
UK
GE
AS
NE
DK
BE
BE
NE
AS
AL
DK
AL
SW
SP
NO
FI
FR
CA
(1.41)
(1.47)
(1.35)
(1.57)
(1.48)
(1.36)
(1.40)
(1.25)
(1.48)
(1.46)
(1.72)
(1.39)
(1.64)
(1.36)
(1.59)
(1.51)
(1.38)
(1.52)
(1.58)
Maximum
US (2.03)
JP (1.97)
SW (1.77)
US (2.14)
US (2.41)
US (2.87)
JP (2.40)
US (2.22)
US (2.27)
JP (2.10)
US (3.08)
NZ (2.01)
GR (2.71)
US (2.31)
JP (3.25)
JP (3.05)
US (2.01)
NZ (2.04)
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.
20
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
Trade and geography
TECHNOLOGY,
GEOGRAPHY,
1755
AND TRADE
0 -
X -2 *-
X
*
-
*
-10 -
0
0.2E0.4
0
01
u
-8
*%
*
0M-10
0~~~~~~~~~~~~~~~
E~~~~~
I
~FGR
2.
Trd
an prices
-12
0
0.2
0.6
0.4
0.8
price measure: Dni
FIGURE
21
2.-Trade and prices.
1
1.2
1.4
Endogenizing input costs
To close the model, (i) the input bundle is decomposed into labor and
intermediates. (ii) Then, EK determine prices given wages. (iii)
Finally, wages are determined.
Cobb-Douglas with labor cost share β. Intermediates comprise the
CES-aggregated good with the overall price index as the appropriate
index of intermediate goods prices.
The cost of an input bundle in country i is thus
ci = wiβ pp1−β
Note: ci depends on prices in i and hence on Φi which summarizes
input costs in all countries!
22
Determining price levels
Due to rich interactions of costs in prices via the price index, we
obtain a system of equations that generally requires numerical
methods:
" N
#
−θ 1/θ
X pn = γ
Ti dni wiβ pp1−β
(1)
i=1
Expanding the trade-shares equation delivers
Xni
= πni = Ti
Xn
γdni wiβ pi1−β
pn
!−θ
(2)
The pi ’s are determined from the system of equations above. Finally,
conditions for the labor market equilibrium are needed to determine
wages.
23
Labor market
Manufacturing labor income in country i is labor’s share of country i’s
export around the world, including to itself (domestic sales).
wi Li = β
N
X
πni Xn
n=1
Denoting aggregate final expenditures as Yn with α the fraction spent
on manufactures, total manufacturing expenditures are then
Xn =
1−β
wn Ln + αYn ,
β
where the first term captures demand for manufactures as inputs by
the manufacturing sector itself.
Also, we have
Yn = wn Ln + YnO
24
Case 1: Labor is mobile
Workers can move freely between manufacturing and
non-manufacturing.
Wage wn is given by productivity in non-manufacturing and total
income Yn is exogenous.
Combining total labor income with total manufacturing expenditure
delivers
N
X
wi Li =
πni [(1 − β)wn Ln + αβYn ] ,
(3)
n=1
determining manufacturing employment Li .
25
Case 2: Labor is immobile
Number of manufacturing workers is fixed at Ln . Non-manufacturing
income YnO is exogenous. We now get
wi Li =
N
X
h
i
πni (1 − β + α)wn Ln + αβYnO ,
n=1
determining manufacturing wages wi .
26
(4)
Estimation
Equations (1) and (2), along with either (3) or (4), comprise the full
general equilibrium.
Equation (2) allows us to learn about states of technology Ti and
geographic barriers dni .
Normalizing by the importer’s home sales delivers
Xni
Ti
=
Xnn
Tn
27
wi
wn
−θβ pi
pn
−θ(1−β)
dni−θ
Estimation
Further, we can use (2) for both country i and n to get
pi
wi
=
pn
wn
Ti
Tn
−1/θβ Xi /Xii
Xn /Xnn
−1/θβ
Plugging this into the previous equation yields
ln
Xni0
1 Ti
wi
= −θln(dni ) + ln
− θln
0
Xnn
β Tn
wn
where Xni0 ≡ lnXni − [(1 − β)/β]ln(Xi /Xii ).
28
29
Estimation
Defining Si ≡ β1 ln(Ti ) − θln(wi ), we arrive at the baseline equation
that is estimated by GLS
ln
Xni0
= −θln(dni ) + Si − Sn
0
Xnn
where we can think of Si as country i’s “competitiveness”, its state of
technology adjusted for labor costs.
Taking β = 0.21 from the data, the LHS can be directly computed. Si
and Sn are captured by the coefficients on source-country dummies.
Proxies for geographic barriers are distance dk (lying in the kth
interval, k = 1, ..., 6), border b, language l, trading area eh , an overall
destination effect mn . δni captures all other factors such that
ln(dni ) = dk + b + l + eh + mn + δni
Results
1762
J. EATON AND S. KORTUM
TABLE III
BILATERAL
TRADE
EQUATION
Variable
-0d1
-6d2
-Od3
-Od4
-Od5
- Od6
-Ob
-01
-0e1
-Oe2
Distance [0, 375)
Distance [375, 750)
Distance [750, 1500)
Distance [1500,3000)
Distance [3000, 6000)
Distance [6000, maximum]
Shared border
Shared language
European Community
EFTA
30
Australia
Austria
Belgium
Canada
Denmark
S,
S2
S3
S4
S5
s.e.
-3.10
-3.66
-4.03
-4.22
-6.06
-6.56
0.30
0.51
0.04
0.54
(0.16)
(0.11)
(0.10)
(0.16)
(0.09)
(0.10)
(0.14)
(0.15)
(0.13)
(0.19)
Destination Country
Source Country
Country
est.
est.
s.e.
0.19
-1.16
-3.34
0.41
-1.75
(0.15)
(0.12)
(0.11)
(0.14)
(0.12)
-Om,
- m2
- m3
- m4
-6m5
est.
s.e.
0.24
-1.68
1.12
0.69
-0.51
(0.27)
(0.21)
(0.19)
(0.25)
(0.19)
0.51
0.04
0.54
-01
-0e1
-Oe2
Shared language
European Community
EFTA
Results
Destination Country
Source Country
Country
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Greece
Italy
Japan
Netherlands
New Zealand
Norway
Portugal
Spain
Sweden
United Kingdom
United States
Total Sum of squares
Sum of squared residuals
Number of observations
31
S,
S2
S3
S4
S5
S6
S7
S8
S9
S1(
Sil
S12
S13
S14
S15
S16
S17
S18
S19
2937
71
342
(0.15)
(0.13)
(0.19)
est.
s.e.
est.
s.e.
0.19
-1.16
-3.34
0.41
-1.75
-0.52
1.28
2.35
-2.81
1.78
4.20
-2.19
-1.20
-1.35
-1.57
0.30
0.01
1.37
3.98
(0.15)
(0.12)
(0.11)
(0.14)
(0.12)
(0.12)
(0.11)
(0.12)
(0.12)
(0.11)
(0.13)
(0.11)
(0.15)
(0.12)
(0.12)
(0.12)
(0.12)
(0.12)
(0.14)
0.24
-1.68
1.12
0.69
-0.51
-1.33
0.22
1.00
-2.36
0.07
1.59
1.00
0.07
-1.00
-1.21
-1.16
-0.02
0.81
2.46
(0.27)
(0.21)
(0.19)
(0.25)
(0.19)
(0.22)
(0.19)
(0.19)
(0.20)
(0.19)
(0.22)
(0.19)
(0.27)
(0.21)
(0.21)
(0.19)
(0.22)
(0.19)
(0.25)
-Om,
- m2
- m3
- m4
-6m5
- m6
-6m7
- m8
-6m9
-6m10
-6m11
-6m12
-Om13
-Om14
-6m15
-6m16
-6m17
-6m18
-6m19
Error Variance:
Two-way (02o2)
One-way (02o-2)
0.05
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.
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 geographic
barriers.
Based on the definition of Si and using wages, one can back out Ti .
Geographic barriers can be obtained by dividing the coefficients in the
results 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 /pnα , where the manufacturing sector share is
α = 0.13.
33
1
Gains from trade: Autarky vs. Status Quo vs. Free Trade
2
How do technology and geography shape the pattern of
specialization?
3
How does trade help spreading technological know-how?
4
What are the implications of tariff reductions?
TECHNOLOGY,
1769
AND TRADE
GEOGRAPHY,
1. Raising geographic barriers
TABLE IX
THE GAINS
FROM TRADE:
RAISING
GEOGRAPHIC
BARRIERS
Percentage Change from Baseline to Autarky
Mobile Labor
Country
Welfare
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Greece
Italy
Japan
Netherlands
New Zealand
Norway
Portugal
Spain
Sweden
United Kingdom
United States
-1.5
-3.2
-10.3
-6.5
-5.5
-2.4
-2.5
-1.7
-3.2
-1.7
-0.2
-8.7
-2.9
-4.3
-3.4
-1.4
-3.2
-2.6
-0.8
Immobile Labor
Mfg. Prices
Mfg. Labor
11.1
24.1
76.0
48.4
40.5
18.1
18.2
12.8
24.1
12.7
1.6
64.2
21.2
32.1
25.3
10.4
23.6
19.2
6.3
48.7
3.9
2.8
6.6
16.3
8.5
8.6
-38.7
84.9
7.3
-8.6
18.4
36.8
41.1
25.1
19.8
-3.7
-6.0
8.1
Welfare
-3.0
-3.3
-10.3
-6.6
-5.6
-2.5
-2.5
-3.1
-7.3
-1.7
-0.3
-8.9
-3.8
-5.4
-3.9
-1.7
-3.2
-2.6
-0.9
Mfg. Prices
Mfg. Wages
65.6
28.6
79.2
55.9
59.1
27.9
28.0
-33.6
117.5
21.1
-8.4
85.2
62.7
78.3
53.8
32.9
19.3
12.3
15.5
54.5
4.5
3.2
7.6
18.6
9.7
9.8
-46.3
93.4
8.4
-10.0
21.0
41.4
46.2
28.4
22.5
-4.3
-6.9
9.3
Notes: All percentage changes are calculated as 100ln(x'/x) where x' is the outcome under autarky (d,j
x is the outcome in the baseline.
34
oofor n :Ai) and
when trade is shut down could be seen as indicating their overall comparative
1770
J. EATON AND S. KORTUM
2. Lowering geographic barriers
TABLE X
THE GAINS
FROM TRADE:
LOWERING
GEOGRAPHIC
BARRIERS
Percentage Changes in the Case of Mobile Labor
Baseline to Doubled Trade
Baseline to Zero Gravity
Country
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Greece
Italy
Japan
Netherlands
New Zealand
Norway
Portugal
Spain
Sweden
United Kingdom
United States
Welfare
21.1
21.6
18.5
18.7
20.7
21.7
18.7
17.3
24.1
18.9
16.6
18.5
22.2
21.7
22.3
20.9
20.0
18.2
16.1
Mfg. Prices
-156.7
-160.3
-137.2
-139.0
-153.9
-160.7
-138.3
-128.7
-178.6
-140.3
-123.5
-137.6
-164.4
-161.0
-165.3
-155.0
-148.3
-134.8
-119.1
Mfg. Labor
Welfare
153.2
141.5
69.6
11.4
156.9
172.1
-7.0
-50.4
256.5
6.8
-59.8
67.3
301.4
195.2
237.4
77.5
118.8
3.3
-105.1
2.3
2.8
2.5
1.9
2.9
2.8
2.3
1.9
3.3
2.2
0.9
2.5
2.8
3.1
3.1
2.4
2.7
2.2
1.2
Mfg. Prices
-17.1
-20.9
-18.6
-14.3
-21.5
-20.9
-16.8
-14.3
-24.8
-16.1
-6.7
-18.5
-20.5
-22.9
-22.8
-18.0
-19.7
-16.4
-9.0
Mfg. Labor
-16.8
41.1
68.8
3.9
72.6
44.3
15.5
12.9
29.6
5.7
-24.4
65.6
50.2
69.3
67.3
-4.4
55.4
28.5
-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.
35
Three of the four countries we have identified as "natural manufacturers,"
3. Technology vs. geography
J. EATON AND S. KORTUM
1772
0.9
0.8
o|!
c 0.7-
E 0.6
o 0.5
o o0.40.4-
/
J
~~~~~~~~~~~~~~~~~~Denm
0
r 0.3
-0
Germany
0.2
0.1
0
l
16
l
l
l
8
l
l
l
l
4
(toward autarky)
l
l
l
l
l
l
2
l
l
1
l
l
l
l
0.5
factor increase In geographic barriers
FIGURE 3.-Specialization,
l
I
l
0.25
0.125
0.0625
(toward zero gravity)
technology, and geography.
technology T1by 20 percent, first for the United States and then for Germany.
36
Technology vs. geography
For smaller countries, manufacturing shrinks as geographic barriers
diminish.
Production shifts to larger countries where inputs are cheaper.
As geographic barriers continue to fall, however, the forces of
technology take over and manufacturing employment grows.
37
Conclusions
Eaton and Kortum (2002) develop a model with N countries and a
continuum of goods incorporating realistic geographic features into
general equilibrium.
Their model can explain that
I
trade diminishes dramatically with distance;
I
prices vary across locations, with greater differences between places
farther 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.
38