International Trade And Income Differences

International Trade and Income Diﬀerences
JOB MARKET PAPER
Michael E. Waugh ∗
Revised Version: November 21, 2007
Abstract
Standards of living between the richest and poorest countries diﬀer by more than a factor
of 30. Is there a role for international trade in accounting for this fact? To answer this ques-
tion, I construct a multi-country general equilibrium model. Within this framework, I derive
an accounting procedure analytically decomposing income per worker into three components:
diﬀerences in capital-output ratios, productivity, and a contribution from trade. Since the con-
tribution from trade is measurable, I am able to quantify the variation in income per worker
attributable to trade. In a sample of 77 countries, I show that the contribution from trade is
negligible, less than 1 percent. That is, trade’s contribution is so small that relative incomes
are almost the same in a model with no trade. To further understand this result and how
cross-country income diﬀerences respond to changes in barriers to trade, I calibrate the model
by picking country speciﬁc productivity parameters and trade costs so the pattern of bilateral
trade implied by the model matches the data. I ﬁnd the calibrated trade costs are systemati-
cally asymmetric with poor countries facing higher costs to export their goods relative to rich
countries. Furthermore, my calibrated model generates both prices and cross-country income
diﬀerences consistent with the data. Through counterfactual exercises, I ﬁnd that by removing
the asymmetry in trade costs (i.e. provide poor countries with equivalent market access to rich
countries markets) cross-country income diﬀerences decline by up to 34 percent. Eliminating all
barriers to trade reduces cross-country income diﬀerences by up to 56 percent. By facilitating
a more eﬃcient allocation of production across countries, reductions in barriers to trade are
quantitatively important for economic development.
Key Words: trade, income, bilateral, total factor productivity, trade costs
JEL Classiﬁcations: F0; F1; O4
∗ Department of Economics, The University of Iowa, michael-waugh@uiowa.edu. Many people have provided useful
comments and suggestions including seminar participants at the Federal Reserve Bank of Minneapolis, 2006 German
Workshop in Macroeconomics, 2006 Midwest Trade and Theory Conference, 2006 Midwest Macro Meetings, NBER
Growth Conference, 2007 SED meetings, University of Iowa, and Trade and Development Workshop at the University
of Minnesota. Special thanks go to Timothy J. Kehoe, Samuel Kortum, and Kei-Mu Yi. Finally, I owe a debt of
gratitude to my advisors B. Ravikumar and Raymond G. Riezman for their invaluable encouragement and support.
1

1
Introduction
Standards of living between the richest and poorest countries diﬀer by more than a factor of 30. A
large literature has evolved attempting to explain this fact within the context of a standard (closed-
economy) neoclassical growth model. Beginning with Mankiw, Romer, and Weil (1992)—and the
competing views of Klenow and Rodriguez-Clare (1997), Hall and Jones (1999), and Parente and
Prescott (2002)—the consensus is that physical and human capital accounts for only 50 percent
of the variation in income per worker; the rest is unobserved productivity diﬀerences. Given this
ﬁnding, a growing literature has attempted to understand how diﬀerences in economic fundamentals
can result in large productivity diﬀerences across countries; see Caselli (2005) for a survey.
In most of this literature there is no explicit role for international trade. Yet there are many
reasons to think that international trade might be important to understand cross-country income
diﬀerences. For example, a majority of all trade is between rich countries, very little is between rich
and poor countries. Furthermore, there are many studies documenting the positive correlation be-
tween the amount a country trades and its income level; see Frankel and Romer (1999) for example.
In policy circles, various anti-globalization movements make claims suggesting rich countries exploit
poor countries through trade; see Oxfam International (2002). While international organizations
(e.g., The World Bank) emphasize trade as a means of development.
In this paper, I ask and answer the following question: What is the quantitative relationship
between international trade and a country’s standard of living? To answer this question, I bridge
the gap between existing quantitative closed-economy analysis of cross-country income diﬀerences
and international trade by studying their joint relationship in a quantitative multi-country general
equilibrium model. Focusing on the implications of international trade on income, I argue several
points: Given the current volume of trade, trade per-se is not an important factor in explaining
cross-country income diﬀerences; exogenous productivity diﬀerences are the driving force. However,
underlying the pattern of trade there are diﬀerences in the barriers to trade poor countries face
relative to rich countries. Eliminating these diﬀerences allows poor countries to gain relative to
rich countries reducing cross-country income diﬀerences through the reallocation of production both
within and across countries.
To argue these points, I construct a multi-country model of trade. In each country, there are
two sectors: an intermediate goods sector and a ﬁnal goods sector, both with constant returns
technologies. Labor, capital, and intermediate goods are used as factors of production. In the
intermediate goods sector there is a continuum of goods. As in Dornbusch, Fischer, and Samuelson
(1977), production technologies diﬀer across goods on the continuum only in their eﬃciency levels.
As in Eaton and Kortum (2002), eﬃciency levels are treated as random variables drawn from a
parameterized distribution. Each country’s distribution diﬀers in its average eﬃciency level. Trades
only occur within intermediate goods, which are purchased from the country with the lowest price
that includes “iceberg” costs to trade. The ﬁnal goods sector produces a non-traded consumption
good with a technology common to all countries.
To quantify the relationship between international trade and a country’s income level, I proceed
2

in two directions. First, using the model I derive an accounting procedure that analytically decom-
poses diﬀerences in income per worker into three components: diﬀerences in capital-output ratios,
diﬀerences in average eﬃciency, and a contribution from trade. The contribution from trade is a
function of a countries aggregate volume of trade and hence measurable. With this approach I am
able to quantify the variation in income per worker attributable to trade, circumventing otherwise
diﬃcult decisions necessary to calibrate and solve the entire model. Implementing this procedure,
I ﬁnd trade per-se is not quantitatively important in explaining cross-country income diﬀerences.
In a sample of 77 countries, there is a 26-fold diﬀerence in income per worker between the top 10th
percentile and bottom 10th percentile. The contribution from trade is only a factor of 1.13. That
is trade’s contribution is so small that relative incomes are almost the same in a model with no
trade.
It is important to emphasize the meaning and implications of this result. First, though relative
incomes would be similar if there was no trade, this result not about the level of trade but about
how the volume of trade covaries with level of development. Hence, this results says that the
observed volume of trade does not covary systematically enough for trade per-se to be quantitatively
meaningful. However, this raises the following question: Rich and poor countries seem very diﬀerent
in both the technologies and factors used, yet why is trade’s impact quantitatively similar? I argue
that the pattern of bilateral trade is distorted, the distortions poor countries face are systematically
diﬀerent than those faced by rich countries, and that cross-country income diﬀerences reﬂect these
distortions.
To argue these points, I proceed in a second direction to quantify the relationship between
international trade and a country’s income level. I calibrate the model by recovering trade costs
and each country’s average eﬃciency level from the pattern of bilateral trade. With the recovered
parameters, I compute the model’s equilibrium and study the model’s implications for cross-country
income diﬀerences. In contrast to alternative approaches, I ﬁnd that my model generates both
prices and diﬀerences in income per worker consistent with the data. Furthermore, similar to
the implications of the accounting exercise, my calibration results in large diﬀerences in average
eﬃciency across countries.
This is not the only impediment poor countries face. Consistent with the empirical trade
literature, there are signiﬁcant distortions in the form of trade costs present in the pattern of
trade; see Anderson and van Wincoop (2004) for a survey. In contrast to this literature, I allow
for asymmetries in trade costs. Using my approach, I ﬁnd that poor countries face systematically
higher costs to export relative to rich countries. Indirectly these distortions—both symmetric
and asymmetric—aﬀect cross-country income diﬀerences because the distribution of income across
countries depends on the entire general equilibrium allocation of production. Thus, changes in
trade policies and trade costs provide an avenue for poor countries to gain relative to rich countries
reducing cross-country income diﬀerences.
I illustrate this point through several counterfactual experiments by adjusting trade costs, but
ﬁxing the calibrated eﬃciency levels. In one experiment, trade costs are set so that between two
3

countries they both face the minimum of the calibrated trade costs between them. Given how
the recovered trade costs impact poor countries relative to rich countries, the question motivating
this counterfactual exercise is: If poor countries had equivalent market access to rich countries
markets, how would cross-country income diﬀerences change? In this experiment, the variance in
log income per worker is reduced from 1.43 to 1.18 and the diﬀerence between 90th percentile and
10th percentile in income per worker is reduced from 32 to 21. Providing poor countries with equal
market access reduces cross-country income diﬀerences by 17-34 percent.
In a second experiment all trade costs are eliminated. Here, the ratio of the variance in log
income per worker is reduced is reduced to 0.87 and the diﬀerence between 90th percentile and 10th
percentile in income per worker is reduced to 14. Removing all trade costs reduces cross-country
income diﬀerences by 40-56 percent. Admittedly, this is an extreme exercise. However, it is a
quantitative measure of trade’s potential to reduce cross-country income diﬀerences. For example,
even if one takes the position that much of the distortions to trade are outside of the policy realm,
this result suggests that non-policy related changes such as technological improvements in shipping,
infrastructure, and communications are quantitatively important to reducing cross-country income
diﬀerences.
As mentioned, these results relate to the income accounting literature. Klenow and Rodriguez-
Clare (1997), Hall and Jones (1999), Parente and Prescott (2002), and Caselli (2005) are examples
that ﬁnd cross-country income diﬀerences mostly result from diﬀerences in total factor productivity.
Extending these exercises to an open economy framework, I derive a relationship in which total
factor productivity is endogenous and decomposable into two components: an exogenous eﬃciency
level and an endogenous and measurable contribution from trade. As noted, I show that the latter is
not quantitatively important in explaining cross-country income diﬀerences. However, eliminating
barriers to trade reallocates production across countries allowing poor countries to close the gap in
income.
Most recent empirical studies of the relationship between international trade and a country’s
standard of living have focused on the statistical relationship between the aggregate volume of
trade and income level often ﬁnding a moderate positive correlation. These studies have faced two
diﬃculties. The ﬁrst diﬃculty is that both trade and income are endogenous. For example, a posi-
tive correlation between income level and trade may result from high income countries being more
productive, have better policies, etc. not because trade by itself raises income. After constructing
instruments to control for endogeneity, a moderate positive relationship often remains; see Frankel
and Romer (1999) and more recently Noguera and Siscart (2005). Rodriguez and Rodrik (2001),
Hallak and Levinsohn (2004), and others have questioned these ﬁndings, mostly criticizing the va-
lidity of their instruments, leaving the results inconclusive. The second diﬃculty is that they are
reduced-form studies. That is the estimated coeﬃcients in these studies only reﬂect correlations,
not policy statements regarding how income or welfare may change given a change in barriers to
trade. In a quantitative general equilibrium model, my accounting procedure explicitly accounts
for the role of international trade on a country’s standard of living while avoiding the statistical
4

diﬃculties previous studies have faced. Furthermore, with an explicit model and the quantiﬁcation
of its parameters, I am able to ask and answer how cross-country income diﬀerences would change
with the removal of barriers to trade.
Relative to recent quantitative models of international trade, such as Eaton and Kortum (2002)
and Alvarez and Lucas (2007), the key distinctions are the question and the methods. First, Eaton
and Kortum (2002) and Alvarez and Lucas (2007) are principally concerned with the model’s
implications for trade — with the former studying the bilateral pattern of trade for OECD countries
and the latter studying the aggregate volume of trade in a wide cross-section of countries. In
contrast, I am principally concerned with the implications of international trade for cross-country
income diﬀerences.
Another distinction lies in the procedures quantifying the model. First, I derive an accounting
procedure allowing me to evaluate the quantitative importance of trade, using only observed mea-
sures of trade, without having to make diﬃcult decisions that are necessary to quantify and solve
the whole model. Second, disciplining my approach I use equilibrium conditions in the model and
data on the pattern of bilateral trade to recover a country’s average eﬃciency level and trade costs
jointly. Third, I allow for asymmetries in trade costs and show how my model performs better
than alternative approaches at replicating the pattern of bilateral trade, prices, and cross-country
income diﬀerences.
Because my model is disciplined by the pattern of bilateral trade, my results are fundamentally
diﬀerent relative to Alvarez and Lucas (2007). First, in my model almost all the gains from trade
here yet to be realized. Second and more important, the available gains from trade systemati-
cally beneﬁt poor countries relative to rich countries reducing cross-country income diﬀerences. In
contrast, in the appendix I provide a direct comparison of the gains from trade in my model and
Alvarez and Lucas (2007) showing that in their calibration the available gains from trade are small
and they are allocated symmetrically across countries. These distinctions, i.e. the gains available
and the allocation, are nontrivial. The results of Alvarez and Lucas (2007) suggest that the gains
available from trade are small and they will do little to improve the plight of poor countries relative
to rich countries. In contrast, my results suggest a completely opposite assessment: The available
gains from trade are large and trade has the potential to improve the plight of poor countries
relative to rich countries reducing cross-country income diﬀerences.
As in Eaton and Kortum (2002), I estimate a structural relationship between observed bilateral
trade shares and trade costs resembling a “gravity equation” which has been a foundation of much
work in empirical international trade. To estimate these relationships, functional forms must be
assumed relating trade costs to observable data. This is restrictive because diﬀerent functional
forms result in diﬀerent quantitative implications for prices and cross-country income diﬀerences.
In Waugh (2007), I argue that for structural gravity models to account for both bilateral trade
volumes and relative price diﬀerences, trade costs must be systematically asymmetric. Given the
observed pattern of trade costs in Waugh (2007), I advocated an alternative trade cost speciﬁcation
relative to standard symmetric approaches or that of Eaton and Kortum (2002). In this paper, I
5

employ this trade cost speciﬁcation and show how my model correctly replicates salient features
of both prices and observed cross-country income diﬀerences — all while ﬁtting the bilateral trade
data equally well or better than alternative approaches.
The resulting trade costs suggests poor countries face systematic diﬃculties to selling their
goods in rich countries markets. This is a fundamentally diﬀerent view of the impediments present
in the pattern of trade relative to models with either symmetric trade costs or the formulation
of Eaton and Kortum (2002). Beyond helping the model replicate certain features of the data,
a natural counterfactual exercises arises from these results, i.e. if poor countries had equivalent
market access to rich countries markets, how would cross-country income diﬀerences change? The
results suggest that policies which provide equivalent market access for poor countries goods can
signiﬁcantly improve their plight and reduce cross-country income diﬀerences.
The paper proceeds as follows: Sections 2 and 3 describe the model and an equilibrium. Section
4 derives the accounting exercise and describes the calibration of the full model in addition to the
data used. Section 5, 6, and 7 present the results and section 8 concludes.
2
The Model
Consider a world with N countries. Each country has two sectors, an intermediate goods sector
and a ﬁnal goods sector. Only intermediate goods are traded. Within each country i, there is a
measure of consumers Li. Each consumer has one unit of time supplied inelastically in the domestic
labor market and are endowed with capital supplied to the domestic capital market. Furthermore,
each consumer has preferences only over the ﬁnal good which is non-traded. In the following, all
variables are normalized relative to the work force in country i.
2.1
Intermediate Goods Sector
As in Dornbusch, Fischer, and Samuelson (1977) there is a continuum of goods indexed by x ∈ [0, 1]
produced and traded. 1 In country i, capital ki, labor ni, and the aggregate intermediate good
qi are combined by the following nested Cobb-Douglas production function to produce quantity
mi(x):
mi(x) = zi(x)−θ[kα
i n1−α]β q1−β .
i
i
1A Ricardian model is a natural starting point for several reasons. First, diﬀerences in technology are the source
of comparative advantage in contrast to Heckscher-Ohlin models which emphasize diﬀerences in factor endowments.
Given the importance of technology diﬀerences relative to endowments in understanding cross-country income diﬀer-
ences, a Ricardian model is more suited to the question in this paper. Second, Ricardian models with a continuum
of goods have a prominent extensive margin. Hummels and Klenow (2005) and Kehoe and Ruhl (2003) document
the quantitative importance of the extensive margin in explaining trade ﬂows and trade liberalizations. “New trade
theory” models were designed to explain trade between similar countries and have no extensive margin, hence they
seem less appropriate for the question in this paper.
6

Power terms α and β control the factor shares.2 Across goods x, production technologies diﬀer
only in their eﬃciency level zi(x)−θ. The parameter θ is common to all countries.
The representative ﬁrm’s problem in country i is to minimize the cost of supplying mi(x) by
choosing capital, labor, and the aggregate intermediate good, given factor prices, ri, wi, and pq.
i
All ﬁrms in country i have access to the technology for any good x with the eﬃciency level zi(x)−θ.
Hence, in equilibrium ki, ni, and qi are allocated so that marginal products are equalized across
ﬁrms and goods are priced at unit cost.
In each country i, individual intermediate goods are aggregated according to a standard sym-
metric Dixit-Stiglitz technology producing the aggregate intermediate good with elasticity of sub-
stitution η > 0, speciﬁed in the next section.
2.2
Distribution of Eﬃciency Levels
Following Eaton and Kortum (2002), I parameterize the model by treating zi(x) as an idiosyncratic
random variable. In the setup above, I follow Alvarez and Lucas (2007) and assume that zi(x) is
distributed independently and exponentially with parameter λi diﬀering across countries. This is
analogous to a Type II extreme value distribution or Fr´echet distribution as in Eaton and Kortum
(2002).
In the production of intermediate goods, each country’s λi governs its average level of eﬃciency.
A country with a relatively larger λi is, on average, more eﬃcient. Given a draw z(x), it is taken
to the power −θ and yields good x’s eﬃciency level. θ controls the dispersion of eﬃciency levels.
Speciﬁcally, the coeﬃcient of variation for each country’s distribution of eﬃciency levels is controlled
only by θ. A larger θ yields more variation in eﬃciency levels relative to the mean. In this sense θ
controls the degree of comparative advantage and a country’s λi determines its absolute advantage.
Relabeling each good x by its eﬃciency level z, the production of the aggregate intermediate
good is
η
∞
η−1
η−1
qi =
m(z) η π(z)dz
.
0
Where π(z) is
N
N
π(z) =
λi exp −
λizi .
i=1
i=1
In country i, ﬁrms producing the aggregate intermediate good face the problem of minimizing
the cost of producing qi. The solution to this problem yields the following price of the aggregate
2It is worthwhile to contrast the use of intermediate goods here with the model of Yi (2003) in which there are
two stages of production, with individual goods x in the ﬁrst stage of production are used directly in the second stage
of production and then aggregated. It is this mechanism that is important for quantitatively explaining the growth
in world trade.
7

intermediate good:
∞
1
1−η
pq =
p
i
i(z)1−η π(z)dz
0
in which pi(z) = min[pi1(z), ..., piN (z)]. pij(z) is the price country i can purchase intermediate good
z from country j including costs to trade.
2.3
Final Goods Sector
In each country, a representative ﬁrm produces a homogenous good which is non-traded. Each ﬁrm
has access to the following nested Cobb-Douglas production function combining capital, labor, and
the aggregate intermediate good:
yi = [kα
i n1−α]γ q1−γ .
i
i
Factor shares, α and γ, are the same across countries.
The representative ﬁrm’s problem is to minimize the cost of producing yi, at price py, by
i
selecting the amount of capital, labor, and aggregate intermediate good, taking prices as given.
2.4
Trade Costs
To model trade costs, the standard iceberg assumption is made, i.e. τij > 1 of good z must be
shipped from country j for one unit to arrive in country i in which (τij − 1) “melts away” in transit.
Trade costs τij are thought to be composed of both policy and non-policy related barriers. In
addition, τii is normalized to equal one for each country.
3
Equilibrium
The goal is to ﬁnd allocation rules, prices, and trade shares to construct an equilibrium. Speciﬁcally,
the functions determining wages, the price of intermediate goods, and trade shares are the most
important objects. First, they determine all other equilibrium prices and quantities. Second, these
functions provide the basis for the calibration in section 4.
Allocation rules: Allocation rules for capital, labor, and the aggregate intermediate good are
easy to compute. Given the production technologies, it is straightforward to show a fraction γ
of capital, labor, and β of the aggregate intermediate good are allocated towards the ﬁnal goods
sector.
Price Index: I show in the appendix that each country faces the following price of intermediate
8

goods for each country i:
−θ
N
αβ
−1
θ
pq = k−αβΥ 
wβpq(1−β)τ
θ
kj
λ 
(1)
i
i
 j j ij
j 

ki
j=1

where Υ is a collection of constants. This expression is similar to those in Eaton and Kortum (2002)
or Alvarez and Lucas (2007). A diﬀerence is in how each country’s capital-labor ratio relative to
country i “weights” the importance of other countries in the determination of country i’s price of
intermediate goods. If country j has a relatively larger stock of capital, then its weight on the sum
will be higher in contrast to a country with a relatively small stock of capital.
Trade Shares: Mij is the fraction of all goods country i imports from country j. Since there is a
continuum of goods, computing this fraction boils down to ﬁnding the probability that country j is
the low-cost supplier to country i given the joint distribution of eﬃciency levels, prices, and trade
costs for any good z. In the appendix, I provide the details which follow the approach in Alvarez
and Lucas (2007). The result is the following expression for trade shares:
−1
k−αβwβpq(1−β)τ
θ
λ
j
j
j
ij
j
Mij =
.
(2)
−1
N
wβpq(1−β)τ
θ
λ
ℓ=1 k−αβ
ℓ
ℓ
ℓ
iℓ
ℓ
Note that the sum across j for a ﬁxed i must add up to one. Furthermore, with no barriers to
trade this relationship is independent of the importer i which implies that all countries purchase
the same fraction of goods from the same source.
Wage Function: An equilibrium wage vector is computed given trade shares and imposing bal-
anced trade. Imports are deﬁned as
N
Imports = Lipqq
M
i i
ij ,
j=i
which is the total value of all goods country i consumes from abroad. Similarly, exports are deﬁned
as
N
Exports =
MjiLjpqq
j j ,
j=i
which is the total value of all goods countries abroad purchase from country i.
Imposing balanced trade and including each country i’s consumption of goods produced at home
implies the following relationship must hold:
N
N
Lipqq
M
L
q
i i
ij =
j pq
j j Mji.
j=1
j=1
9

which says the aggregate value of intermediate goods purchased by country i is to equal the value
of intermediate goods all N countries purchase from country i.
Using the observation that each country allocates (1 − γ) of capital and labor to the production
of the intermediate goods sector and the relationship between factor payments and total revenue
(see Alvarez and Lucas (2007)), the equilibrium wage rate for each country i is:
N
L
w
j
i
=
w
L
j Mji.
(3)
i
j=1
At this point, the three key pieces of the model have been derived. Equation (1) describes the
equilibrium price of intermediate goods, equation (2) describes the fraction of goods countries
purchase from each other, and equation (3) describes the equilibrium wage rate for each country.
From these functions, all other prices and quantities are determined and an equilibrium constructed.
4
Quantiﬁcation
To quantify the relationship between international trade and cross-country income diﬀerences, I
outline two methods.
The ﬁrst is an accounting exercise analogous to standard income accounting procedures as
in Klenow and Rodriguez-Clare (1997) or Hall and Jones (1999). Below, I derive an equilibrium
relationship with income decomposed into a contribution from total factor productivity and capital-
output ratios. The key feature is that total factor productivity is now endogenous and is an
analytical function of how much each country trades. Given data on income per worker and trade,
I can account for the contribution of trade per-se to cross-country income diﬀerences.
The second is a calibration/estimation exercise enabling a deeper analysis of the model. Similar
to Eaton and Kortum (2002), I derive and estimate a structural relationship between bilateral
trade, technology parameters, and trade costs. With the recovered technology parameters and
trade costs, I can compute the cross-country income diﬀerences implied by the pattern of bilateral
trade and study the response of the economy given changes in costs to trade.
In both exercises, the model’s trade shares provide a convenient starting point as I can construct
an empirical counterpart Xij to the theoretical trade share Mij.
4.1
An Accounting Procedure
Suppressing some notation and rearranging the empirical counterpart of (2) and using (1) provides
an expression for each country’s home trade share:
−1
k−αβwβpq(1−β) θ λ
i
i
i
i
Xii =
.
(4)
q( −1 )
p
θ
Ψ
i
10

Further rearrangement of (4) provides the expression:
θ
wi
λ
β
= Ψ
i
kα
pq
X
i ,
(5)
i
ii
in which wages, deﬂated by the intermediate goods price, are a function of each country’s home
trade share and its capital-labor ratio.3
I deﬁne real income per worker as:
w
r
y
i
iki
i =
+
,
(6)
py
py
i
i
in which income from wages and capital are deﬂated by each country’s ﬁnal goods price and balanced
trade is imposed.4 Then using a representative ﬁrm’s ﬁrst order conditions determining the rental
rate as a function of the wage, I express income per worker as a function of only the wage and the
ﬁnal goods price:
1
w
y
i
i =
.
(7)
1 − α pyi
Since my interest is only in relative income diﬀerences, constant terms are abstracted from. Com-
bining the expression for the price of ﬁnal goods and (7), real income per worker is expressed
as:
w
1−γ
y
i
i =
kαγ.
(8)
pq
i
i
Combining equations (5) and (8), real income per worker is now:
−θ(1−γ)
θ(1−γ)
y
β
β
i = X
λ
kα
ii
i
i .
(9)
Here real income per worker is only a function of each countries home trade share Xii, its technology
parameter λi, and its capital-labor ratio.
Finally, I express income per worker relative to the U.S. following Hall and Jones (1999) with
income decomposed into terms of total factor productivity and capital-output ratios. But here
total factor productivity is decomposed into an endogenous trade factor and an exogenous domestic
3For reference, this is analogous to equation (15) in Eaton and Kortum (2002). I have to thank Sam Kortum for
directing my attention to this equation.
4This is the proper deﬁnition to compare the model to data on income per worker from the Penn World Table.
The key reason is that in benchmark years the Penn World Table deﬂates net-trade balance with the same deﬂator
for exports and imports in contrast to alternative approaches to computing real GDP; see Feenstra, Heston, Timmer,
and Deng (2004) for a discussion.
11

factor:
1
α
yi
A
1−α
k
1−α
=
i
i/yi
,
yus
Aus
kus/yus
θ(1−γ)
−θ(1−γ)
A
β
i
X
β
λ
=
ii
i
.
(10)
Aus
Xus,us
λus
trade−f actor
domestic−f actor
Closed Economy: When trade costs are inﬁnite, countries are unable to diversify production and
must import everything from home. Hence, Xii = 1 and relative income per worker is then:
θ(1−γ)
yclosed
λ
α
β
k
i
=
i
i
.
yclosed
us
λus
kus
Given how eﬃciency levels are distributed in the production of intermediate goods, each country’s
θ
average eﬃciency level relative to the U.S. is
λi
. Thus, each country’s closed-economy total
λus
factor productivity is its average eﬃciency level to the power (1−γ) . Hence, in equation (10), the
β
second term in brackets is termed the domestic factor.
Open Economy: When trade costs are ﬁnite, countries are able to diversify production and import
some goods from relatively more eﬃcient producers. Hence, Xii < 1 and each country’s gain from
−θ(1−γ)
trade, in the form of increased total factor productivity relative to the U.S., is
X
β
ii
and
Xus,us
termed the trade factor. This expression has several straightforward implications. First, if country
i has a smaller home trade share than the U.S., then country i gains relatively more from trade.
Second, the higher the share of intermediate goods in either sector results in a larger gain from
trade than otherwise. Finally, if the world has a larger θ and hence a higher degree of comparative
advantage, then trade will matter more than otherwise. Note as well, only through importing does
trade beneﬁt a county. A country’s exporting behavior is principally determined by its technology
parameter λ and trade costs.
This accounting procedure is a step forward relative to recent studies concerning the relation-
ship between international trade and a country’s standard of living. The principal focus of these
studies have been on the statistical relationship between the aggregate volume of trade and income
level. These studies face two diﬃculties. The ﬁrst diﬃculty is that both trade and income are
endogenous. To avoid this diﬃculty, Frankel and Romer (1999) and other authors have proposed
instruments to correct for these problems. However, as outlined in Rodriguez and Rodrik (2001),
there is some debate surrounding the validity of the instruments leaving the results inconclusive.
In contrast to these approaches, the derived accounting relationship in (10)—in conjunction with
careful measurement—allow for the quantiﬁcation of the relationship between trade and income
without dealing with these statistical issues.
The second diﬃculty behind these prior studies is that as reduced-form frameworks they are
12

unable to quantify the response from changes in fundamentals on income and trade. That is the
estimated coeﬃcients in these studies only reﬂect correlations, not statements regarding how income
may change in response to changes in barriers to trade. In contrast, this framework can ask and
quantitatively answer these questions. Depending on the question, however, the full model must
be quantiﬁed which the next section discusses.
4.2
Recovering Trade Costs and Technology
To further understand cross-country income diﬀerences, I want to understand the pattern of trade
and its implications for cross-country income diﬀerences. To do so, I will proceed in a second
direction and recover the unknown technology parameters and trade costs from the pattern of
trade. To recover these parameters, I derive and estimate structural equation which resembles a
reduced-form “gravity” equation widely used in empirical international trade.5
To derive the gravity equation, rearrange the empirical counterpart of (2), using (1) and then
αβ
−β
for convenience deﬁne c
θ
θ
i = k
w
λ
i
i
i, yielding following expression:
q( β )
X
θ
ii
= Ψ−1cip
,
(11)
i
q( β−1 ) −1
c
θ
θ
j p
τ
X
j
ij
ij
=
,
(12)
q( −1 )
p
θ
Ψ
i
As discussed in Eaton and Kortum (2002), the framework here nests a log-linear “gravity equation”
relationship. To derive this, divide each country i’s trade share from country j in (12) by country
i’s home trade share (11) yielding N − 1 equations for each country i:
q( β−1 ) −1
X
c
θ
τ θ
ij
j p
=
j
ij
.
(13)
Xii
q( β−1 )
c
θ
ipi
Taking logs yields the following linear relationship ready for estimation:
X
1
log
ij
= S
log τ
X
j − Si −
ij ,
(14)
ii
θ
q( β−1 )
in which S
θ
i is deﬁned as log
cip
.
i
To recover the technology parameters and trade costs, I estimate equation (14) with the Sis
recovered as the coeﬃcients on country speciﬁc dummy variables. Unfortunately, to recover trade
5In previous versions of this paper, I used an alternative approach to calibrate each country’s technology level
and trade costs by constructing an algorithm to recover the values that ﬁt the trade data in an exact manner. I
have deviated from this approach though an appendix is available upon request. The approach here has the beneﬁt
of being dramatically more transparent, easier to replicate, and quantiﬁes the eﬀect of distance—all while yielding
essentially the same results.
13

costs, I must assume a technological relationship between τij and observable data. I assume trade
costs take the functional form:
log(τij) = dk + bij + exj + ǫij.
(15)
Here trade costs are a logarithmic function of distance where dk with k = 1, 2, ...6 is the eﬀect
of distance between country i and j lying in the kth distance intervals. Intervals are in miles:
[0, 375); [375, 750); [750, 1500); [1500, 3000); [3000, 6000); and [6000, maximum]. bij is the eﬀect of
a shared border in which bij = 1, if country i and j share a border, zero otherwise. For estimation
purposes, I assume ǫij reﬂects barriers to trade arising from all other factors and is orthogonal to
the regressors. These features of the trade cost function are the same as in Eaton and Kortum
(2002).
An important diﬀerence lies in the term exj which is an exporter ﬁxed eﬀect. That is, the
estimate of exj is the extra cost country j faces to export a good to any country i. In Waugh
(2007), I argued that for structural gravity models to account for bilateral trade volumes and data
analogs to pq, costs to trade must be systematically asymmetric with poor countries facing higher
i
costs to export relative to rich countries. And I showed in an equilibrium decomposition exercise
systematic asymmetry is quantitatively important accounting for at least a third of the variation
in bilateral trade. Relative to distance and other symmetric relationships typically considered,
systematic asymmetry is quantitatively on par or more important in accusing for the pattern of
bilateral trade. With these observations, I then advocated a trade costs speciﬁcation—described
above with an exporter ﬁxed eﬀect—that can improve the equilibrium model’s ﬁt and result in
prices consistent with those observed.
In contrast, Eaton and Kortum (2002) employ a importer ﬁxed eﬀect mi in which the estimate
mi reﬂects the extra cost county i faces to import a good from any country j. As I show in this
paper and in Waugh (2007), when the model is estimated with a importer ﬁxed eﬀect, the resulting
prices are inconsistent with comparable international price indices for tradable goods. Eaton and
Kortum (2001) is a example of this outcome. They studied trade ﬂows in investment goods and the
model implied prices using an importer ﬁxed eﬀect and they ﬁnd poor countries face systematically
higher prices of investment goods relative to rich countries. This is in contrast to the data with
poor countries facing similar prices relative to rich countries. Hsieh and Klenow (2007) revisited
the data and argued that because these prices are roughly the same across countries, lower real
rates of investment for poor countries are not a result of distortions such as high tax rates and or
trade frictions as in Eaton and Kortum (2001). Instead poor countries face diﬃculties producing
investment goods and exportables. Between Eaton and Kortum (2001) and Hsieh and Klenow
(2007), the question is: How does one account for trade ﬂows with various trade frictions and
the fact that there is little variation in comparable price indices across countries? The trade cost
speciﬁcation I advocated in Waugh (2007) and employ here provides an answer to this question.
Equations (14) and (15) provide the basis for the estimation of trade costs τijs and Sis for which
14

I use ordinary least squares.6
Recovering the λis requires more work. Given the estimated Sis and τijs, the price of interme-
diate goods is then computed as:
−θ
N
−1
pq = Υ  eS

j τ θ
(16)
i

ij 
j=1 
Then given the pqs computed from (16), one can recover c
i
is from the estimates of Si.
With cis, more information is required to recover each country’s technology parameter λi. To
recover the λis, I determine wages from observed bilateral trade shares Xij, each country’s labor
endowment, and the empirical counterpart to equation (3):
N
L
w
j

i
= 
 w
L
j Xji
i
j=1
.
(17)
Wages are determined as a function of bilateral trade shares and labor endowments. Then, in
combination with aggregate capital-labor ratios, the recovered prices pq, and c
i
is, each country’s
technology parameter λi is recovered.
Notice the key parameters λi and τij are being determined primarily as a function of bilateral
trade shares. This approache diﬀerers substantially relative to Alvarez and Lucas (2007). For
example, Alvarez and Lucas (2007) pursue two calibrations and studied the implications of their
model for the aggregate volume of trade. Their ﬁrst calibration assumed that each country’s λi
is proportional to an unobservable endowment Li. This assumption in combination with balanced
trade, output data, and some proxies for trade costs such as average tariﬀ rates allowed them
to calibrate each country’s λi and Li jointly. Their second calibration built on the former, but
incorporated the use of relative price data and dropped the proportionality assumption of λi and
Li to identify each separately.
4.3
Data
To implement the accounting exercise and quantiﬁcation of the full model, I must take a stand on
the world economy and how the model corresponds to actual economies.
The model year is 1996 and table 5 details the countries considered.7 Beginning with the original
sample of countries in Parente and Prescott (1994), some countries were eliminated on the basis of
data availability. Thus, 77 countries remain and represent over 90 percent of World GDP.8
6I also experimented with the poisson pseudo maximum-likelihood estimator advocated by Silva and Tenreyro
(2006). The next section and footnote 10 contain a discussion.
7For the same exact set of countries, I also studied the year 1985. Similar results were obtained.
8The most important countries not included are Germany, due to data problems associated with East Germany’s
reintegration with West Germany, and Taiwan, again due to data problems as a result of political issues. The data
constraint is gross manufacturing production data used to construct bilateral trade shares. Hence other countries
were eliminated because the necessary data was unavailable.
15

I assume that the intermediate goods sector corresponds to the manufacturing goods sector.
This is a simpliﬁcation, but since all trade in the model is in intermediate goods and nearly 80
percent of all merchandise trade is in manufactured goods this assumption is reasonable as a ﬁrst-
order approximation to reality. Furthermore, Hummels, Rapoport, and Yi (1998) and Hummels,
Ishii, and Yi (2001) are studies that document the importance of trade in intermediate goods. The
ﬁnal goods sector is thought of as the sector producing all ﬁnal goods and services for each economy.
I constructed trade shares Xij following Bernard, Eaton, Jensen, and Kortum (2003). First,
I compiled manufacturing bilateral trade data from Feenstra, Lipsey, and Bowen (1997) for the
model 1996. Aggregating across all 34 BEA manufacturing industry codes provides the aggregate
value of manufactured goods each country purchases from each other. I then divided the value of
country i’s imports from country j by gross manufacturing production minus total manufactured
exports (for the whole world) plus manufactured imports (for only the sample) yielding bilateral
trade shares. Basically, this is just a way to map production and trade data into the unit interval,
by dividing inputs from country j used in country i divided by total inputs used in country i. In
table 5, I present the source for each country’s gross manufacturing production data. In table 6, I
present trade share’s for selected countries.
One may be concerned with the absence of agriculture. However, the data does include processed
agricultural goods. Most of the gross manufacturing data I employ corresponds with manufacturing
as deﬁned by ISIC revision 2 and the bilateral trade data is an approximation of this categoriza-
tion as well. Roughly any agricultural good that is manipulated shows up as manufacturing. For
example, code number 1531 which is “Manufacture of grain mill products” is considered an man-
ufactured product. Basically this activity encompasses the process of turning gains and mills into
edible and useful products. In contrast, goods not included are items such as code number 0111 or
“growing of cereals and other crops n.e.c.” This activity basically encompasses only the of growing
the grains.
The distance measures used to estimate trade costs are in miles from capital city in country i to
capital city in country j calculated by the great circle method.9 These measures and border data are
from from Centre D’Etudes Prospectives Et D’Informations Internationales (http://www.cpeii.fr).
I used aggregate capital-labor ratios from Caselli (2005). They were constructed using the
perpetual inventory method using purchasing power parity adjusted investment rates in Heston,
Summers, and Aten (2002). I used labor endowments from Caselli (2005) which are from informa-
tion in Heston, Summers, and Aten (2002) as well. Each country’s labor endowment relative to the
U.S. is presented in table 5.
I calibrated parameter values common to all countries as follows. I followed Alvarez and Lucas
(2007) in selecting the value for η. Other then satisfying the necessary assumptions detailed in the
appendix, this value plays no quantitative role.
Given the model’s structure resulting in equation (10), I want α to be consistent with the
9The great circle method is a way to calculate the shortest distance between two points along the surface of a
sphere.
16

Table 1: Common Parameter Values
Parameter
Description
Value
α
k’s share
1/3
β
k and n’s share in int. goods production
0.33
γ
k and n’s share in ﬁnal goods production
0.72
η
elasticity of substitution in aggregator
2.0
θ
variation in eﬃciency levels
0.15
exercises in the income accounting literature. To do so, I set α equal to 1/3. An argument for
setting α equal to 1/3 relies on Gollin (2002). He calculated labor’s share for a wide cross-section
of countries to be around 2/3.
The parameter β controls value added in intermediate goods production. With respect to the
data used, β corresponds with value added in the traded manufacturing goods sector. For OECD
countries in 1996 (http://www.sourceoecd.org), the average value added in the manufacturing goods
sector is 0.33. This is consistent with the value employed in Yi (2003).
The parameter γ controls value added in ﬁnal goods production. Since all trade is assumed to
be in manufactured goods, this implies (1 − γ) corresponds with traded manufacturing goods value
added in total output. Manufacturing’s value added as a fraction of GDP averaged across all coun-
tries in the sample is 0.17 as found in World Development Indicators (http://www.worldbank.org/data).
I adjusted this number by the fraction of all trade occurring in manufactured goods. Averaging
across the fraction of manufactured goods trade for the sample yields a value of 0.60. Together,
this implies traded manufactured goods share in ﬁnal goods production is 0.28 implying a value for
γ of 0.72.
The parameter θ controls the dispersion in eﬃciency levels across intermediate goods for all
countries. I selected a value of 0.15, which is the value used in Alvarez and Lucas (2007) as a
baseline. This value and the distributional assumptions imply a coeﬃcient of variation of approxi-
mately 0.22 for each country’s eﬃciency levels. The selected baseline value of θ lies in the middle of
empirical estimates. Eaton and Kortum (2002) found a range of 0.078 and 0.28 depending on their
approach in estimating θ. Furthermore, Eaton and Kortum (2002) and Anderson and van Wincoop
(2004) showed how θ is related to the elasticity of substitution in an Armington aggregator model of
international trade. Anderson and van Wincoop (2004) claimed reasonable values for this elasticity
are between 5 and 10, which implies a range for θ of 1/9 and 0.25. In the next sections, I discuss
the sensitivity of the results for other parameterizations of θ. Furthermore, I am currently pursuing
approaches to estimating my own value of θ.
An implication of the Eaton and Kortum (2002) framework is that, in aggregate, every country
should purchase some non-zero amount of goods from all other countries. In fact, the bilateral
trade matrix has many recorded zeros. For the sample considered there are 5,929 possible trading
combinations; 1,610 (27 percent) show no trade at all. This presents both an estimation issue and
computational issue.
17

Regarding the estimation, I will omit any zero observed trade ﬂows from the estimation of
equation (14). This has been a standard approach in the empirical trade literature. Silva and
Tenreyro (2006) propose a poisson pseudo-maximum-likelihood (PPML) estimator to alleviate any
bias from log-linearizing equation (13) in the presence of heteroscedasticity and the omission of
zero observed trade ﬂows. I employed their technique estimating equation (13) including zero
observed trade ﬂows and I found the quantitative results and counterfactual exercises do not diﬀer
dramatically relative to using OLS.10 Furthermore, Helpman, Melitz, and Rubinstein (2007) build
on the model of Melitz (2003) with ﬁxed costs and ﬁrm heterogeneity and study similar biases
present in the estimation of traditional gravity equations. Their results suggest that any bias
arising from the omission zero trade ﬂows is quantitatively small.
Regarding the computation, when computing equilibrium prices and counterfactuals I will set
trade costs for the instances in which Xij is zero to an arbitrarily large value to approximate what
appears to be a trade cost of inﬁnity. In table 1, I summarize the selected parameter values.
5
Does Trade Explain Income Diﬀerences?
To answer this question, I use the framework outlined in section 4.1 to study trade’s contribution
to relative income diﬀerences. As discussed, I can express income per worker relative to the U.S.
with income decomposed into terms of capital-output ratios, an endogenous trade factor, and an
exogenous domestic factor:
1
α
yi
A
1−α
k
1−α
=
i
i/yi
,
yus
Aus
kus/yus
θ(1−γ)
−θ(1−γ)
A
β
i
X
β
λ
=
ii
i
.
Aus
Xus,us
λus
trade−f actor
domestic−f actor
A way to view this this accounting exercise is in the context of Caselli’s (2005) article on accounting
for cross-country income diﬀerence. Throughout his paper he asks the question: “how successful
is the factor-only model at explaining cross-country income diﬀerences?” That is given observed
factors what are the implied cross-country income diﬀerences. As mentioned in the introduction,
conventional measures of factors are not successful at explaining cross-country income diﬀerences.
In my accounting procedure income diﬀerences are a result of an observable trade factor, capital-
output ratios, and an exogenous TFP term represented by λi. Since the contribution from capital-
output ratios is well studied, the relevant question is: how successful is my trade factor in explaining
10 This does not contradict their ﬁndings. Consistent with their results, I ﬁnd that OLS exaggerates the distance
elasticity suggesting the bias they emphasize is present. For example using PPML, the percent eﬀect on cost are
129, 140, 141, 177, 223, and 263 percent for each distance category. Compared to table 8, shorter distances are more
costly and longer distances are less costly relative to OLS. This is consistent with a lower distance elasticity Silva
and Tenreyro (2006) ﬁnd when using PPML relative to OLS.
18

cross-country income diﬀerences? Figure 1 depicts trade factors versus income per worker data.
In ﬁgure 1 there is at best a slight negative relationship between trade factors and level of devel-
opment. This suggests that without trade income diﬀerences would actually be larger than those
observed. Ultimately, the magnitude of this relationship is small and trade factors contribute little
to explaining cross-country income diﬀerences. For example, the variance of log trade factors is
0.008 and the ratio of trade factors for the top 10th percentile and bottom 10th percentile in income
per worker is approximately 1. Recall, in data the variance of log income per worker is 1.38 and the
90/10 ratio of income per worker is 25.6. The success of my trade factor at explaining cross-country
income diﬀerences is negligible, less than one percent; moreover, this result suggests that if there
was no trade, then relative incomes would be almost the same.
This ﬁnding reﬂected in ﬁgure 1, is insensitive to diﬀerent values of θ. I performed the same
exercise with θ set equal to 0.10 and 0.20 at the low and high end for empirically plausible values.
Consistent with the prior results, trade factors showed little variation across income levels. That
is, trade per-se plays no quantitative role in explaining cross-country income diﬀerences as in the
baseline calibration. The reasons are straightforward. Figure 2 plots
Xus,us
versus income per
Xii
worker data (note this term is ﬂipped because a smaller Xii implies a larger gain from trade). The
correlation between income level and this measure of trade is −0.32 and is statistically diﬀerent
from zero. Hence any value of θ > 0 will result in then the implication that without trade income
diﬀerences would be larger than those observed. Second, though there is substantial variation in
Xus,us
, empirically plausible values for θ are too small and/or trade does not covary systematically
Xii
enough with level of development to have any quantitative meaning.
Despite the fact that relative incomes would be almost the same if there was no trade, this
result does not necessarily imply the world is in autarky. The distinction here is between the level
of Xii and how Xii covaries with level of development. For example, imagine a world where for all
countries Xii is small implying large volumes of trade. However, if Xii is similar across countries
then the same conclusion would be arrived at in this world, i.e. trade per-se plays little role in
accounting for cross-country income diﬀerences even though volumes of trade are large. Hence the
important observation from this exercise is that values of Xii are quite similar across countries.
However, this raises the following question: Rich and poor countries diﬀer in both the tech-
nologies and factors, yet why is trade’s impact quantitatively similar? For example, consider the
simplest Dornbusch, Fischer, and Samuelson (1977) economy with no trade costs. In this economy,
a country with an absolute disadvantage (i.e. small λi) should import a larger fraction of goods
(i.e. Xii should be smaller) relative to a country with an absolute advantage. Figure 2 faintly de-
picts the intuition of Dornbusch, Fischer, and Samuelson (1977), but ﬁgure 1 says the quantitative
importance is negligible. However, underlying the pattern of bilateral trade there are distortions
and costs to trade aﬀecting the pattern of observed Xii. In the next sections, I argue these dis-
tortions aﬀect poor countries diﬀerentially relative to rich countries and that cross-country income
diﬀerences reﬂect these distortions.
19

6
Calibration
The prior result is only a statement regarding the observed volume of trade, i.e. the volume of trade
does not covary systematically enough with level of development to be quantitatively meaningful.
To understand why the volume of trade does not covary enough or if it should and to study how
cross-country income diﬀerences would change if trade policies or trade costs were changed, I employ
the calibration procedure as detailed in section 4.2. That is, I recovered each country’s λi and trade
costs τij from pattern of bilateral trade. Table 7 presents summary statistics from the estimation
of the structural gravity equation. Tables 8 and 9 present the parameter estimates for trade costs
and technology parameters.
6.1
Trade Costs and Technology Parameters
Trade Costs: The parameter estimates in table 8 themselves are not of interest here, only the
reconstructed trade costs as inputs into the model. However, there are two features to note.
Consistent with the gravity literature, distance is an impediment and the estimates reported are
consistent with those in Eaton and Kortum (2001) which considers a similar sample of countries.
The overall size of the trade costs for a developed country are consistent with those reported in
Anderson and van Wincoop (2004). They survey the literature and report that for a representative
developed country, trade barriers fall in a range between 40-80 percent depending on the study
and elasticities of substitution. I ﬁnd that the median trade cost between for OECD countries is
equivalent to a 90 percent tariﬀ. This is above the upper-range of their survey, but not dramatically
so.
Second, the exporter ﬁxed eﬀect is negatively correlated with level of development. Figure 3
plots each country’s exporter ﬁxed eﬀect, expressed in terms of the percent eﬀect on cost, versus
income per worker data. The correlation between the exporter ﬁxed eﬀect and log income per
worker is −0.66 and statistically diﬀerent from zero. As the ﬁgure 3 depicts, poor countries appear
to have a serious disadvantage at exporting goods relative to rich countries. For example, a good
arriving from the United States costs 55 percent less than the average country. In contrast, a good
arriving from Rwanda will cost 130 percent more than the average country.
This is a fundamentally diﬀerent view of the world relative to standard approaches. For ex-
ample, most implementations of the gravity model never consider asymmetries in trade costs and
completely abstract from this issue. In terms of reconciling the bilateral pattern of trade, this is
a non-trivial abstraction. In Waugh (2007) I demonstrate that these asymmetries are quantita-
tively important accounting for at least a third of the variation in bilateral trade—on par or more
important than distance and other symmetric relationships typically considered. As mentioned,
an exception is Eaton and Kortum (2001, 2002) which generates asymmetries with an importer
ﬁxed eﬀect. As demonstrated here and in Waugh (2007), their procedure results in prices that
systematically deviate from the data and result in large cross-country income diﬀerences.
There is a simply policy story behind this “asymmetry” in trade costs. The idea is that though
20

rich countries have, on average, low tariﬀ and non-tariﬀ barriers, certain sectors were/are still highly
protected and poor countries are the predominant exporters in these sectors.11 A classic example
is the U.S. textile industry. Examining the bilateral trade data sector by sector for several poor
countries, a signiﬁcant fraction of the U.S. imports were in the industry classiﬁed as “Apparel and
Other Textile Products.” Hence it may not be a surprise that the U.S. looks relatively protected
towards poor countries. Anderson and van Wincoop (2004) provides some evidence regarding this
explanation. More explicit evidence along this front is presented in Kee, Nicita, and Olarreaga
(2006). They estimate trade restrictiveness indices from data on both tariﬀ and non-tariﬀ barriers
for a large set of countries developed and undeveloped countries. They ﬁnd that poor countries
systematically face the highest trade barriers on their export bundle — similar to the asymmetry
in trade costs here. Also relevant to these results, they estimate that non-tariﬀ barriers contribute
more than 70 percent to their trade restrictiveness indices. This suggests calibrating trade costs
based on average tariﬀ rates are bad approximations of the trade barriers countries actually face.
Technology: Table 9 presents the parameter estimates for the technology parameters. The key
observation here is that diﬀerences in average eﬃciency recovered from the pattern of trade are
consistent with inferences from the accounting exercise. From equation (10) and employing the
requisite data, I can recover values for λi with no assumptions regarding trade costs. In this
instance, the ratio of average eﬃciency between the top 10th percentile and bottom 10th percentile
is approximately 7.58. Similarly, when estimated from the pattern of bilateral trade, this ratio is
7.96. This an important observation, because two alternative procedures to recovering λi provide
similar answers suggesting the parameter estimates here are the correct values. Furthermore, the
ability of the model to replicate cross-country income diﬀerences further reinforces this point as
discussed next.
6.2
Prices and Income Diﬀerences
Prices: As one assessment of the model, I considered the model’s ability to quantitatively replicate
data on international prices of tradable goods. Note, that these are tradable goods not traded
goods since in equilibrium some goods may not be traded. To compare the model implied price
indices to data, I employed the benchmark price data available at the Penn World Table website
(http://pwt.econ.upenn.edu). From the benchmark price data, I constructed the appropriate price
indices of tradable goods which best matched the trade data employed; Waugh (2007) provides
more details concerning their construction.
Figure 4 plots the data on prices versus income per worker data. As the ﬁgure illustrate,
poorer countries have slightly lower prices of tradable goods. For the sample considered, the
elasticity of the price of tradable goods with respect to income level is 15 percent.12 These facts are
11Of course policies in poor countries could create this eﬀect as well. Export marketing boards are one possible
source of this distortion. These boards place a wedge between the price at which producers sell goods and the price
at which the good is exported. Export marketing boards are prevalent in African countries.
12To contrast this relationship, the elasticity of the price of non-tradable goods with respect to income is 60 percent
where non-tradable goods are deﬁned as the compliment of tradable goods.
21

consistent with Kravis and Lipsey (1988) which documents a similar relationships between the price
of tradable goods, price of non-tradeable goods, and level of development. Furthermore, Hsieh and
Klenow (2007) study similar price indices for only investment goods and the elasticities I report
are consistent with their ﬁndings.
Figure 5 plots the prices from the baseline calibration when trade costs are modeled with an
exporter ﬁxed eﬀect. The prices from the model with an exporter ﬁxed eﬀect are only slightly
higher for poor countries relative to rich countries. The elasticity with respect to income level is
approximately −0.04. In contrast, ﬁgure 6 plots the prices from a calibration using the trade cost
function of Eaton and Kortum (2002) with an importer ﬁxed eﬀect. These prices systematically
deviate from the data in a quantitatively important manner with poor countries facing higher prices
relative to rich countries. For example, the elasticity with respect to income level is −0.29, seven
times larger than my model with an exporter ﬁxed eﬀect. As discussed, this outcome is similar to
the results in Eaton and Kortum’s (2001) study of investment goods prices estimated from bilateral
trade data relative to data on investment goods prices. Using an importer ﬁxed eﬀect they ﬁnd
the estimated prices systematically deviate from the data with poor countries facing higher prices
relative to rich countries.
It is important to emphasize that both these two approaches estimate the same number of
parameters and ﬁt the data equally well, but my model performs signiﬁcantly better regarding its
implications for price data. In Waugh (2007), I provide a more complete discussion of structural
gravity models and their implications for price diﬀerences across countries.
Income Diﬀerences: As another assessment of the model, I considered the model’s ability to
quantitatively replicate the cross-country income diﬀerences seen in the data. With the λis and
τijs recovered from the pattern of bilateral trade, I computed an equilibrium and each country’s
income per worker as deﬁned in equation (6). Given this deﬁnition of income, the natural empirical
analog for comparison is purchasing power parity adjusted income per worker taken from Heston,
Summers, and Aten (2002).
Figure 7 depicts the model’s income levels versus the data relative to the U.S. along with the
45◦ line. If the model’s relative income per worker is the same as the data, then the ordered pairs
would map out the 45◦ line. In ﬁgure 7, the ordered pairs lie around the 45◦ line. For example,
the model predicts that Uganda has an income level 1/30 the U.S. level. In the data, Uganda has
an income level 1/32 the U.S. level. Table 2 provides some summary statistics: the variance of
log income, the 90/10 percentile ratio, and the Gini index.13 Except for the the Gini index, the
summary statistics indicate the model slightly over-predicts the variation in cross-country income
diﬀerences.
The model predicts incorrectly which countries within the rich are the richest. One potential
13For the year 1985, results in ﬁgure 7 and table 2 are similar. For the model calibrated using 1985 data but the
same common parameter values calibrated to 1996 data, the variance of log income is 1.25, in the data it is 1.11. The
results in ﬁgure 7 and table 2 are also insensitive to diﬀerent values of θ. I calibrated the model with θ set equal to
0.10 and 0.20 which are at the low and high end for empirically plausible values of θ. For a θ of 0.10, the variance of
log income is 1.38. For a θ of 0.20 the variance of log income is 1.34. Overall, the model performs well in capturing
the variation in income across countries for diﬀerent years and values of θ.
22

Table 2: Income per worker
var [log(y)]
y90/y10
Gini
Data
1.38
25.6
0.60
Model
1.43
31.9
0.59
reason is the absence of Germany. Inclusion of Germany would make European countries look a
bit less productive and reduce their income levels relative to the U.S. The model also misses on
Zaire (the Democratic Republic of the Congo) by a wide margin. In the data, the U.S. is richer
by a factor of 90, in the model it is 19.7. Overall, the model accurately captures the variation in
income across countries.
In the denominator of the bilateral trade shares there is data on domestic absorbtion, however,
this result is not by construction. The domestic absorbtion data does correlate strongly with
purchasing power parity GDP per worker data, but of 2.5 times more the variation. In simple
examples (like the one below) one can see how a correlation structure between domestic absorbtion
data and the resulting wage from balanced trade is possible. In general, the equilibrium wage
determined from (17) and how it relates to this piece of data is not clear. Furthermore, real income
per worker is not simply the wage but the wage deﬂated by the price of non-traded goods. The
price of non-traded goods depends on many diﬀerent pieces including how trade costs are modeled
and the resulting prices of tradable goods.
For example, had I used a trade cost function with an importer ﬁxed eﬀect instead of the
exporter ﬁxed eﬀect, then the variation of log income per worker is 2.60 and 90/10 percentile ratio
is 100. One reason why this results in diﬀerent implications for cross-country income diﬀerences
relates to the previous results regarding prices. The model with an importer ﬁxed eﬀect results
in systematically higher prices pq for poor countries resulting in higher prices of non-traded goods
i
py. Because real income per worker is deﬂated by py, this systematically lowers real income per
i
i
worker for poor countries resulting in an over prediction of income diﬀerences. This suggests that
the ability of my model to correctly replicate both prices and the variation in income per worker is
an important feature of my model relative alternative approaches to modeling trade patterns.
Where do these result arise from? A three country example. Understanding the features
of the data which drive the calibrated parameters and the resulting prices and income diﬀerences
can be a mystery. To alleviate this mystery, consider the following world with three countries where
labor is the only factor of production and labor endowments are the same. Normalize country 1’s
wage, λ1, and τ1 equal one. Finally, assume there is no distance cost and hence τj reﬂects only the
exporter ﬁxed eﬀect. Now consider the following trade share matrix
 X11 X21 X31 
X =
 X
 12 X22 0 
 X

13
0
X33 
23

in which Xij denotes the fraction of goods country i imports from country j. Hence, rows denote
an exporting country and columns denote an importing country.
In this trade share matrix assume that X12 > X13 but X21 = X31. Note that this pattern
is representative of the bilateral pattern of trade in the following sense; suppose country 1 is the
United States, then this says the United States exports similar shares to all countries, yet the U.S.
imports diﬀerent shares across countries depending upon level of development. Furthermore, think
of country 2 and country 3 as a middle income and poor country. Normalizing each column in the
trade share matrix by Xii, equation (2) implies the following relationship between the model and
the data
 1
1
1
−1
−1
(w2) θ λ2
(w3) θ λ3 
−1
X =



 (w2τ2) θ λ2
.

1
0
1




−1
(w3τ3) θ λ3
0
1

1
Given the assumptions made, lets work through a simple example to illustrate how the pattern
of trade and the model are informative regarding trade costs, aggregate prices, and technology
parameters.
−1
−1
First, notice that from X
θ
θ
21 = X31 then w2 λ2 = w3 λ3. Exponentiating both sides by −θ
implies that country 2 and country 3’s average unit cost of production are the same. The fact that
average unit costs are the same, yet country 1 purchases a large share of goods from country 2
relative to country 3 ( i.e. X12 > X13) implies that country 2 must have easier market access to
country 1 relative to country 3, τ2 < τ3. Otherwise country 1 should purchase the same share of
goods from both countries because country 2 and country 3 have the same average unit costs of
production.
Second, the price indexes in country 2 and country 3 are
−θ
−θ
−1
−1
pq
θ
θ
2 = Υ
w2 λ2 + 1
and pq3 = Υ w3 λ3 + 1
,
which are the same. Basically, this is another expression of the fact that average unit costs between
country 2 and 3 are the same. Here modeling trade costs with an exporter ﬁxed eﬀect is critical. If
they were modeled with an importer ﬁxed eﬀect, one can show this trade share matrix implies that
country 2 has a lower average unit cost relative to country 3. Furthermore, this would imply that
the aggregate price index in country 2 is lower relative to country 3 — similar to how prices covary
with level of development in ﬁgure 6 illustrates when the model is estimated with an importer ﬁxed
eﬀect.
At this point, all that is known is that average unit costs are the same between country 2 and
country 3. To say more about relative values of λ, one must determine relative wages between
country 2 and country 3. In this paper, I use balanced trade and bilateral trade data to determine
24

the wage. Balanced trade implies that:
X12
X
= w
13 = w
X
2 and
3.
21
X31
Given the structure of the trade share matrix with X21 = X31 and X12 > X13 then the wage in
−1
−1
country 2 is greater than the wage in country 3. Since w θ
θ
2
λ2 = w3 λ3, this observation implies
that country 2 must be more productive relative to country 3. Average unit costs are the same
across countries yet wages are diﬀerent. Therefore, there must be diﬀerences in productivity.
To understand this example relative to the data revisit table 6. Think of the U.S. as country
1, Japan as country 2, and Senegal as country 3. Notice that Japan and Senegal import similar
shares of goods from the U.S. But the U.S. imports a larger share of goods from Japan than from
Senegal. Ignoring the role of the diagonal, the fact the U.S. row does not vary between Japan and
Senegal implies unit costs are similar. Yet, the fact that the U.S. column does vary between Japan
and Senegal implies that Senegal faces higher barriers to export to the U.S. relative to Japan. With
balanced trade, the only way for unit costs to be similar across countries is for Senegal to be less
productive relative to Japan oﬀsetting the fact that wages are lower in Senegal.
7
How Do Trade Costs Inﬂuence Cross-Country Income Diﬀer-
ences?
As table 8 illustrates, there are signiﬁcant distortions present in the pattern of trade. Since the
distribution of income across countries depends on the general equilibrium allocation of production,
any distortion to the allocation of production suggests cross-country income diﬀerences reﬂect these
distortions. For example, trade costs may allow production of a good to exist in a country which
otherwise may have been imported. Reducing trade costs shuts down the production of goods a
country is relatively ineﬃciently at producing and these goods are now imported. As a result, do-
mestic resources are reallocated toward the production of goods that the country has a comparative
advantage in increasing output per worker. Thus, trade costs through the reallocation of produc-
tion both within and across countries may play an important role for economic development. To
quantify these possibilities, I performed two counterfactual exercises modifying trade costs while
ﬁxing the estimated eﬃciency levels and observed capital-labor ratios.
In the ﬁrst exercise, I adjusted trade costs so the new costs to trade between two countries are
ˆ
τij = min(τij, τji). The premise is that costs above this minimum reﬂect some extra distortion one
country faces while the other does not. Hence, the exercise is to remove these additional distortions
to trade. As discussed, a simply policy story lies behind this asymmetry in trade costs. The idea
is that rich countries are systematically protected in certain sectors and poor countries are the
predominant exporters in these sectors. Under this interpretation, this counterfactual exercise is to
provide poor countries with equivalent market access to rich countries markets. Furthermore this
issue, i.e. market access for poor countries goods, has been at the center of both past and recent
25

Table 3: Income Diﬀerences and Welfare Gains, Percent Change
var [log(y)]
y90/y10
Mean
Max
Min
Corr.
Baseline
1.43
31.9
—
—
—
—
min(τij, τji)
1.18
21.3
22.9
70.3 (Mali)
0.56 (Japan)
-0.69
τij = 1
0.87
13.9
118.2
267.8 (Rwanda)
16.8 (Belgium)
-0.83
multilateral trade negotiations.
With the new trade costs, the variation in log income per worker declines to 1.18 and the 90/10
percentile ratio of income per worker is only 21.3. Cross-country income diﬀerences decline by up
to 33 percent relative to the baseline model. Note that in this exercise trade costs are still large.
For example, distance is still an impediment to trade and the median trade cost is 142 percent for
all countries. This is signiﬁcantly larger than the value reported in Anderson and van Wincoop
(2004) for a developed country. Table 3 also reports the welfare gains and associated summary
statistics.14 Note, all countries gain—but poor countries gain relatively more than rich countries.
As a more extreme example, consider a world with no trade costs. In this world, the variation
in log income per worker is only 0.87. The 90/10 percentile ratio of income per worker in this world
is only 13.9. Recall, in the baseline model, the variation in log income per worker is 1.43 and the
90/10 percentile ratio is 31.9. Eliminating all trade costs reduces cross-country income diﬀerences
by up to 56 percent. Again, table 3 reports the welfare gains showing all countries gain and poor
countries gaining relatively more.15
Admittedly, this is an extreme exercise. However, it is a quantitative measure of trade’s potential
to eliminate cross-country income diﬀerences. For example, even if one takes the position that much
of the distortions to trade are outside of the policy realm, this result says that non-policy related
changes such as technological improvements in shipping, infrastructure, and communications are
quantitatively important to reducing cross-country income diﬀerences.
The Allocation of the Gains From Trade: The reason behind the reductions in cross-country
income diﬀerences results from the allocation of the gains from trade.16 Many models can generate
large welfare gains for all countries symmetrically. However, the results here show that reductions
in barriers to trade systematically beneﬁt poor countries more relative to rich countries — reducing
cross-country income diﬀerences.
14Welfare gains are deﬁned as the percentage increase in consumption across the two equilibria. If one assumes a
utility function with diminishing marginal returns, then poor countries gain even more relative to rich countries.
15In the two exercises with θ set to 0.20, the variance of log income declines to 1.05 and 0.80 and the average
welfare gain is 30 and 136 percent. With θ set to 0.10 the response is smaller. The variance of log income declines to
1.32 and 0.95 and the average welfare gain is 7.78 and 76.9 percent.
16This feature is the most relevant distinction between the gains from trade in this paper and in Alvarez and Lucas
(2007). Overall the key diﬀerences in the welfare gains are: (i) The welfare gains here are larger, (ii) almost all
the welfare gains here have yet to be realized, and (iii) the available welfare gains here are correlated with level of
development. The appendix provides a discussion.
26

Two reasons drive the reduction in cross-country income diﬀerences. First, section 5 shows
that based on observed volumes of trade, trade’s contribution to cross-country income diﬀerences
is negligible. That is, Xii are similar across countries so the current gains from trade are similar.
Second, the available gains are systematically allocated towards poor countries precisely because
of the reasons they are poor. To demonstrate this last point, consider each country’s trade share
Xi in frictionless trade
−1
αβ
(1
N
−α)β
θ
αβ
(1−α)β
θ
X
θ+β
θ+β
θ+β
θ+β
θ+β
θ+β
i = K
L
λ
K
L
λ
,
(18)
i
i
i
ℓ
ℓ
ℓ
ℓ=1
where Ki is the total stock of capital in country i. Note that with no trade costs, all countries
purchase the same fraction of goods from country i and hence Xi = Xii = Xij, ∀j. Equation (18)
says that in frictionless trade, countries with larger endowments or eﬃciency levels produce a larger
share of goods relative to countries with smaller endowments or are less productive.
Equations (10) and (18) together provide an expression for a country’s welfare gain when moving
from autarky to frictionless trade:
−θ(1 − γ)
Wi =
log (X
β
i) ,
(19)
where Wi is the welfare gain and equation (18) deﬁnes Xi. Now compare the welfare gains between
a representative rich and poor country assuming they have the same labor endowments. From (19)
and (18) the relative welfare gain is
θ(1−γ)
W
β
p
θ(1 − γ)
kα
θ
λ
=
log
r
+
log  r

W
θ(1−γ)
r
(θ + β)
kα
p
(θ + β)
λ βp .
(20)
Equation (20) says diﬀerences in capital-labor ratios to the power α and closed-economy total factor
θ(1−γ)
productivity, λ β
, determine the relative gains. Poor countries have both lower capital-labor
ratios and λs relative to rich countries. Poor countries are poor because of these facts. Thus
equation (20) says that the poorer a country is the more it has to gain from trade relative to rich
countries.17
In section 5, observed relative volumes of trade and equation (10) show the current gains from
trade are quite similar across countries. Yet equation (20) shows poor countries have systematically
more to gain from trade than rich countries. These two observations imply that reductions in
barriers to trade not only deliver welfare gains but are an important force for reducing cross-
17There is a second feature that is more subtle — why poor countries are poor matters as well. Consider a simple
thought experiment, suppose cross-country income diﬀerences are entirely explained by capital-labor ratios to the
power α. Equation (20) implies a poor country in the 10 the percentile will gain 28 percent more relative to a
rich country in the 90th percentile. In contrast, suppose cross-country income diﬀerences are entirely explained by
θ(1−γ)
λ
β
. In this case, a poor country in the 10 the percentile will gain 100 percent more relative to a rich country in
the 90th percentile.
27

country income diﬀerences. Furthermore, the quantitative importance of this force is a function of
the variation in cross-country income diﬀerences.
8
Conclusion
In a quantitative general equilibrium model of trade, I argued three points. Decomposing income
per worker into components arising from trade, capital, and eﬃciency, I showed the contribution
from trade is not quantitatively important in explaining cross-country income diﬀerences. However,
preventing trade from playing any role are diﬀerences in the barriers to trade poor countries face
relative to rich countries. Eliminating these diﬀerences allows poor countries to gain relative to
rich countries reducing cross-country income diﬀerences through the reallocation of production both
within and across countries.
As the analysis here suggests, understanding how countries are quantitatively interrelated via
trade is an important topic for continued research. Fundamentally, cross-country income diﬀerences
and the bilateral of pattern of trade can be viewed as a function of diﬀerences in endowments, an
exogenous TFP term, and trade costs. Thus, understanding productivity diﬀerences takes on a
larger role in the sense that they are an important feature to understanding the bilateral pattern
of trade. Furthermore, understanding trade costs takes on a larger role in the sense that they are
an important feature to understanding cross-country income diﬀerences.
28

References
Alvarez, F., and R. J. Lucas (2007): “General equilibrium analysis of the Eaton-Kortum model
of international trade,” Journal of Monetary Economics, 54(6), 1726–1768.
Anderson, J., and E. van Wincoop (2004): “Trade Costs,” Journal of Economic Literature,
pp. 691–751.
Bernard, A., J. Eaton, J. B. Jensen, and S. Kortum (2003): “Plants and Productivity and
International Trade,” American Economic Review, 93, 1268–1290.
Caselli, F. (2005): “Accounting for Cross-Country Income Diﬀerences,” in Handbook of Economic
Growth, ed. by P. Aghion, and S. Durlauf.
Dornbusch, R., S. Fischer, and P. Samuelson (1977): “Comparative Advantage, Trade, and
Payments in a Ricardian Model with a Continuum of Goods,” American Economic Review, 67,
823–839.
Eaton, J., and S. Kortum (2001): “Trade in Capital Goods,” European Economic Review, 45,
1195–1235.
(2002): “Technology, Geography, and Trade,” Econometrica, 70, 1741–1779.
Feenstra, R., R. Lipsey, and H. Bowen (1997): “World Trade Flows, 1970-1992, with Pro-
duction and Tariﬀ Data,” Working Paper No. 5910, NBER.
Feenstra, R. C., A. Heston, M. P. Timmer, and H. Deng (2004): “Estimating Real Pro-
duction and Expenditures Across Nations: A Proposal for Improving the Penn World Tables,”
NBER Working Papers 10866, National Bureau of Economic Research, Inc.
Frankel, J., and D. Romer (1999): “Does Trade Cause Growth?,” American Economic Review,
89, 379–399.
Gollin, D. (2002): “Getting Income Shares Right,” Journal of Political Economy, 110, 458–474.
Hall, R., and C. Jones (1999): “Why Do Some Countries Produce So Much More Output Per
Worker Than Others?,” The Quarterly Journal of Economics, 114, 83–116.
Hallak, J. C., and J. Levinsohn (2004): “Fooling Ourselves: Evaluating the Globalization and
Growth Debate,” Working Paper No. 10244, NBER.
Helpman, E., M. Melitz, and Y. Rubinstein (2007): “Estimating Trade Flows: Trading
Partners and Trading Volumes,” NBER Working Papers 12927, National Bureau of Economic
Research, Inc.
Heston, A., R. Summers, and B. Aten (2002): “Penn World Table Version 6.1,” Discussion
paper, Center for International Comparisons at the University of Pennsylvania (CICUP).
29

Hsieh, C.-T., and P. J. Klenow (2007): “Relative Prices and Relative Prosperity,” American
Economic Review, 97(3), 562–585.
Hummels, D., J. Ishii, and K.-M. Yi (2001): “The nature and growth of vertical specialization
in world trade,” Journal of International Economics, 54(1), 75–96.
Hummels, D., and P. J. Klenow (2005): “The Variety and Quality of a Nation’s Exports,”
American Economic Review, 95(3), 704–723.
Hummels, D., D. Rapoport, and K.-M. Yi (1998): “Vertical specialization and the changing
nature of world trade,” Economic Policy Review, (Jun), 79–99.
Kee, H. L., A. Nicita, and M. Olarreaga (2006): “Estimating trade restrictiveness indices,”
Policy Research Working Paper Series 3840, The World Bank.
Kehoe, T. J., and K. J. Ruhl (2003): “How important is the new goods margin in international
trade?,” Staﬀ Report 324, Federal Reserve Bank of Minneapolis.
Klenow, P., and A. Rodriguez-Clare (1997): “The Neoclassical Revival in Growth Eco-
nomics: Has It Gone Too Far?,” in NBER Macroeconomics Annual 1997, ed. by B. Bernanke,
and J. Rotemberg. MIT Press.
Kravis, I. B., and R. E. Lipsey (1988): “National Price Levels and the Prices of Tradables and
Nontradables,” American Economic Review, 78(2), 474–78.
Mankiw, N. G., D. Romer, and D. N. Weil (1992): “A Contribution to the Empirics of
Economic Growth,” The Quarterly Journal of Economics, 107(2), 407–37.
Melitz, M. J. (2003): “The Impact of Trade on Intra-Industry Reallocations and Aggregate
Industry Productivity,” Econometrica, 71, 1695–1725.
Noguera, M., and M. Siscart (2005): “Trade raises income: a precise and robust result,”
Journal of International Economics, 65, 447–460.
Oxfam International (2002): Rigged Rules and Double Standards: trade, globalization, and the
ﬁght against poverty.
Parente, S., and E. Prescott (1994): “Changes in the Wealth of Nations,” Federal Reserve
Bank of Minneapolis Quarterly Review, pp. 3–16.
(2002): Barriers to Riches. MIT Press.
Rodriguez, F., and D. Rodrik (2001): “Trade Policy and Economic Growth: A Skeptic’s Guide
to the Cross-National Evidence,” in NBER Macroeconomics Annual 2000, ed. by B. Bernanke,
and K. Rogoﬀ. MIT Press.
30

Silva, J. M. C. S., and S. Tenreyro (2006): “The Log of Gravity,” The Review of Economics
and Statistics, 88(4), 641–658.
Waugh, M. (2007): “Bilateral Trade, Relative Prices, and Trade Costs,” Working Paper. Univer-
sity of Iowa.
Yi, K.-M. (2003): “Can Vertical Specialization Explain the Growth of World Trade?,” Journal of
Political Economy, 111, 52–102.
31

9
Appendix: Derivation of Price Indices and Trade Shares
In this section, I provide some details concerning the derivation of equations which describe the
the price index for intermediate goods and the share of goods purchased from each country. The
approach followed here largely follows Alvarez and Lucas (2007).
Rewrite the price of each good pi(z) as:
1
1
1
pi(z) θ = Ωθ min (rajwbj(pq)cjτij)θ zj .
(21)
j
Where a = αβ, b = (1 − α)β, and c = (1 − β). Note the following facts about the exponential
distribution:
• if z ∼ exp(λ), κ > 0, ⇒ κz ∼ exp( λ ).
κ
• if z = min(x, y), y ∼ exp(µ) and x ∼ exp(ξ) ⇒ z ∼ exp(µ + ξ).
This implies that each country i faces the following distribution for prices:
1
pi(z) θ
∼ exp(µi)
(22)
N
−1
−1
where µi = Ω θ
[rajwbj(pq)cτ
θ λ
j
ij ]
j .
(23)
j=1
This implies the price index for the representative country i is
∞
1
1
(pq)1−η =
µ
θ ]dp θ
.
(24)
i
ipi(z)(1−η) exp[−µipi(z)
i
0
1
Employing a change of variables by setting s = µipi(z) θ , the expression for (24) may be computed
as:
∞
(pq)1−η = µ−(1−η)θ
sθ(1−η) exp(−s)ds,
(25)
i
i
0
where the integral is the gamma function. Expanding what we have is:
−θ
N
1
−1
pq = ΩS(θ, η)


1−η
[ra
)cτ
θ λ
,
(26)
i
 jwbj(pqj ij] j
j=1

providing a more useful expression for the price index. S(θ, η) is the gamma function evaluated at
[1 + θ(1 − η)]. For S(θ, η) to exist, 1 > θ(η − 1) must hold which is assumed throughout. Finally, to
arrive at (1), note that from a representative ﬁrm’s ﬁrst order condition the following relationship
must hold:
α
ri =
w
.
1 − α ik−1
i
32

This implies the following expression for each countries price of intermediate goods:
−θ
N
pq = Υ  [k−αβwβ(pq)(1−β)τ
 ,
(27)
i
 j j j ij]−1θλj
j=1
αβ
1
α
1−η

Υ = ΩS(θ, η)
.
(28)
1 − α
From here, one can rearrange (27) as found in the paper:
−θ
N
αβ
−1
θ
pq = k−αβΥ 
wβ(pq)(1−β)τ
θ
kj
λ  .
(29)
i
i
 j j ij
j 
To compute the the probability so 
ki
j=1
me country j is the low cost supplier
for some good to country
i, just a couple more facts about the exponential distribution and order statistics are required:
• if z and y are independent and z ∼ exp(ξ), y ∼ exp(µ), ⇒ prob{z ≤ y} = ξ .
µ+ξ
Then note the following observation that
1
1
Prob pj(z) ≤ min[ps(z)] = Prob pj(z) θ ≤ min[ps(z) θ ] ,
(30)
j=s
j=s
then denoting Mij as the probability country j is the low cost supplier to country i, one may express
Mij as:
−1
k−αβwβ(pq)(1−β)τ
θ
λ
j
j
j
ij
j
Mij =
.
(31)
−1
N
wβ(pq)(1−β)τ
θ
λ
ℓ=1 k−αβ
ℓ
ℓ
ℓ
iℓ
ℓ
33

10
Appendix: Discussion of Alvarez and Lucas (2007)
The model in this paper is a variant of Alvarez and Lucas (2007) which in turn in a reformulation
of Eaton and Kortum (2002). The key distinctions here between my model and Alvarez and Lucas
(2007) lie in the calibration and the resulting welfare gains: (i) The gains here are larger, (ii) almost
all the gains here have yet to be realized, and (iii) the available gains here are correlated with level of
development. Below is a brief description of their calibration and then direct comparisons between
the welfare gains from my approach and Alvarez and Lucas (2007) are made.
In the calibration of Alvarez and Lucas (2007), λ and L are the unknown parameters of interest
and L is the number of eﬀective labor units in the economy. They do not calibrate trade costs and
instead construct them from data on average tariﬀ rates and a simple formulation of transportation
costs. They pursue two approaches to calibrating λ and L. First, they assume that λ is proportional
to L and calibrate both to match a countries share of nominal World GDP. The second approach
incorporates relative price data and allows them to calibrate each separately. To contrast the results
between this paper and Alvarez and Lucas (2007), I used their second calibration and recalibrated
my model with their values of β and γ — so the only diﬀerence in welfare gains arises from
diﬀerences in λ, L, and τ .18 The sample of countries between this paper and Alvarez and Lucas
(2007) are diﬀerent, however the assumption is that this margin is not quantitatively important.
Table 4 compares the welfare gains under two counterfactual exercises. The ﬁrst counterfactual
exercise is a move from the calibrated economy to frictionless trade and the ﬁrst two rows of table
4 present the results. In Alvarez and Lucas’s (2007) calibration the average welfare gain is only
16.5 percent. In this paper the average welfare gain is 61 percent — 270 percent larger. The second
column and third column report the slope coeﬃcient and standard error from a regression of the
welfare gains on log income per worker for each country in 1996. For Alvarez and Lucas (2007),
the slope coeﬃcient is eﬀectively zero. In my model, slope coeﬃcient implies that poor countries
gain systematically more relative to rich countries. For example, a country with income per worker
in the 10 percentile of the sample will experience a welfare gain 225 percent larger than a country
in the 90th percentile of the sample. Figure 8 plots the welfare gain versus income per worker data
summarizing these results — the gains from trade are larger and more correlated with a countries
level development. This means that in Alvarez and Lucas (2007) any potential gains from trade
are allocated the same across countries independent of a country’s level of development and hence
the gains from trade do nothing to reduce cross-country income diﬀerences.
The third distinction between the welfare gains regards the realization of the gains. In Alvarez
and Lucas (2007) almost all the gains are realized. A second counterfactual exercise illustrates
this point by computing the welfare gains for a move from autarky to frictionless trade given the
parameters L and λ.
The bottom two rows in table 4 compare the welfare gains for a move from autarky to frictionless
18They ﬁnd that the implications for the volume of trade and welfare gains are quite similar across the two
calibrations. To compute the gains, I used their programs which are available at Fernando Alvarez’s website at:
http://home.uchicago.edu/ falvare/workingp.html. The speciﬁc program used is welfare1.m
34

Table 4: Welfare Gain Comparison
Calibrated Model to Frictionless Trade
µ(Wi)
ˆ
β
s.e. ˆ
β
# Obs.
Alvarez and Lucas (2007)
16.5
-0.009
.0001
60
My Model
60.9
-0.21
.0006
77
Autarky to Frictionless Trade
Alvarez and Lucas (2007)
47.8
-0.08
.0002
60
My Model
67.2
-0.21
.0002
77
trade. For Alvarez and Lucas (2007), the gains are substantially larger relative to those moving
from the calibrated model to frictionless trade. For example, the mean value is 47.8 percent for a
move from autarky to frictionless trade while the mean value moving from the calibrated model to
frictionless trade is only 16.5 percent. In terms of welfare gains, the world of Alvarez and Lucas
(2007) is only 35 percent away from frictionless trade. In contrast, the ﬁnal row in table 4 presents
the welfare gains in this paper. These welfare gains are quite similar to those for a move from
the calibrated model to frictionless trade. In terms of welfare gains, the world in this paper is 90
percent away from frictionless trade.
The distinctions highlighted here, i.e. the gains available and how the welfare gains are allocated,
are nontrivial. Regarding the gains available, the results in Alvarez and Lucas (2007) suggest that
further removal of existing trade barriers are small relative to those gains already achieved. Even
if one takes the position that much of the distortions to trade are outside of the policy realm, this
result says that any non-policy related changes such as technological improvements in shipping,
infrastructure, communication are of little consequence to those gains already achieved. Regarding
the allocations of the gains, the results in Alvarez and Lucas (2007) suggest they will do little to
improve the plight of poor countries relative to rich countries. In contrast, the calculations from
this paper suggest a completely opposite assessment: The available gains from trade are large and
trade has the potential to improve the plight of poor countries relative to rich countries reducing
cross-country income diﬀerences.
35

X−θ(1−γ)/β(1−α)
ii
4
2
NER
MOZ
PAN
SLE
PNG
BEL
GHA
IRL
ETH
ZMB
LKA
MWI
BEN
HNDJAM
SLV
NLD
TGO KEN
MUS
ZAR
MLI
SEN
BOL
DOM
PHL
PRY
MYS
CAN
ISR
VEN
CAF
CMR
NIC
CRI
UGA
NPL
ZWE PAK
ECU
GTM JOR
THA
TUN MEX
URY
PRT
CHE
CHL
DNK
GRC NZL
SWE
NOR
1
BGD
RWA
CHN
PER COL
EGY TUR IRN
ZAF ARG
ESP
FIN AUS
AUT
FRA
GBR
IND
SYR BRA
KOR
ITA USA
JPN
3
U.S. = 1
6
1/2
1/4
1/128
1/64
1/32
1/16
1/8
1/4
1/2
1
1996 PPP GDP Per Worker: U.S. = 1
Figure 1: Trade Factors versus Income Data

X
/ X Data
us,us
ii
16
NER
8
MOZ
PAN
4
BEL
PNG
SLE
U.S. = 1
IRL
3
7
GHA
LKA
ZMB
2
NLD
ETH
MWI
HNDJAM
SLV
BEN
MUS
TGO
DOM
KEN
CAN
ISR
MYS
ZAR
PHL
SEN
MLI
BOL
PRY
VEN
CRI
JOR
DNK
CMR
NIC
ECU
GTM
MEX
CHE
ZWE PAK
NOR
CAF
NPL
THA
TUN
CHL
GRC
PRT
AUT
GBR
UGA
URY
NZL
SWE
BGD
COL
FIN
PER
AUS
FRA
RWA
CHN
EGY TUR
ESP
ZAF ARG
1
IRN
KOR
ITA USA
IND
SYR BRA
JPN
1/128
1/64
1/32
1/16
1/8
1/4
1/2
1
1996 PPP GDP Per Worker: U.S. = 1
Figure 2: Home Trade Shares versus Income Data

140
RWA
SYR
120
MLI
100
CAF TGO
80
BEN
NPL
NIC
UGA
60
MWI
HND
BOL
EGY
ETH
SLV
40
SEN
PRY
GTM
IRN
JOR
TUN
JAM
NER
ZWE
Percent
3
CMR
DOM
8
20
SLE
ECU
CRI
MOZ
KEN
ZAR
ZMB
GRC
GHA
BGD PNG
COL
MUS
0
TUR
VEN
PAN
URY
PRT
NOR
PER
FIN
LKA
PHL
−20
AUT
PAK
MEX ARG
DNK
IND
ISR
SWE
BRA ZAF
CHE
CHL
NZL
AUS
THA
IRL
ESP
−40
CAN
KOR
FRAITA
CHN
MYS
GBR
JPN NLD
USA
BEL
−60
1/128
1/64
1/32
1/16
1/8
1/4
1/2
1
1996 GDP Per Worker: U.S. = 1
Figure 3: Exporter ﬁxed eﬀect, Percent Eﬀect on Cost

16
8
4
2
SYR
UGA
JPN
CHE
DNK
RWA
FIN
SWE
NOR
MOZ
GHA
AUT
BEL
FRA
IRL
GRC
ITA
CRI
NZL
ZAF
AUS
PRT
ESP
GBRNLD
ISR
1
ZAR
GTM
PNG
SLV
DOM
KOR
USA
CAF
CAN
ETH
NER
COL
PRY
BRA
URY
ARG
HNDJAM
MYS
TGO
NIC
THA
ZMB
LKA
PER
TUR
CHL
ECU PAN
BEN
VEN
3
IRN MEX
9
MLI
SEN
CMR
CHN
IND
BOL
JOR
MUS
1/2
SLE
TUN
MWI
KEN
PAKPHL
BGD
ZWE
EGY
Price of Tradables: U.S. = 1
1/4
NPL
1/8
Data
1/16
1/128
1/64
1/32
1/16
1/8
1/4
1/2
1
1996 PPP GDP Per Worker: U.S. = 1
Figure 4: Price Data

16
8
My Model
4
2
SYR
UGA
JPN
CHE
DNK
RWA
FIN
SWE
NOR
FRA
MOZ
MOZ
AUTBEL
GHA
IRLITA
ETH
MWI
NER
SLE
GRC
NZL
NLD
BEN GHA
KEN
LKA
PNG
PAN
GBR
ZAF
AUS
ZAR
ZMB
CRI
CHLMUS
TGO
CMR
PRT
NZL
ESP ISR
MLI
RWA
UGA
SEN
ZAR
ZWE PAK
PER
CRI
SLV
URY
MYS
1
HNDJAM
PHL
GTM
PRY
GTM
SLV
VEN
ZAF
ISR
CAN
PNG
NER CAF
NPL
CHN BGD
BOL
DOM
ECU
THA JOR
DOM
ARG
AUS
NIC
COL
KOR GBR
USA
USA
ETH
CAF
IND
COL
PRY
BRA
ESP
MEX
BRAURY
ARG
GRC
TUR
PRTKOR
AUT
SWE
BEL
DNK
IRL
NLD
HNDJAM
EGY
IRN
MYS
FIN
JPN CHE
FRAITA
NOR
TGO
THA
TUN
NIC
CAN
PER
SYR
ZMB
LKA
TUR
CHL
ECU
PAN
BEN
VEN
IRN
MEX
4
0
MLI
SEN
CMR
CHN
IND
BOL
JOR
MUS
1/2
SLE
TUN
MWI
KEN
PHL
PAK
BGD
ZWE
EGY
Price of Tradables: U.S. = 1
1/4
NPL
1/8
Data
1/16
1/128
1/64
1/32
1/16
1/8
1/4
1/2
1
1996 PPP GDP Per Worker: U.S. = 1
Figure 5: Price Data and My Model

16
Approach of Eaton and Kortum (2001, 2002)
8
RWA
MLI
SYR
CAF BEN
TGO
MWI
UGA
ETH
NPL
NIC BOL
HND
4
SEN
PRYSLV
MOZ
NER
CMR
ZWE
JAM
EGY
GTM
KEN
SLE
IRN
JOR
ZAR
ZMB
GHA
PNG
CRI
DOM
ECU
TUN
MUS
BGD
COL
PAN
URY
VEN
GRC
LKA
PER
TUR
PHL
PRT
NOR
2
PAK
ZAF ARG
CHL
FIN
NZL ISR
UGA
IND
SYR
MEX
JPN
AUS
AUT
DNK
BRA
SWE
THA
RWA
FIN CHE
DNK
ESP
SWE
IRL
CHE NOR
MOZ
MYS
AUT
FRA BEL
GHA
IRL
GRC
ITA
KOR
ITA
GBR
NZL
NLD
CHN
CRI
ZAF
PRT
ESP FRA
AUS
CAN
GBRNLD
ISR
1
GTM
SLV
ZAR
JPN CAN
PNG
DOM
KOR
USA
BELUSA
NER CAF
ETH
COL
PRY
BRAURY
ARG
HNDJAM
MYS
TGO
NIC
THA
ZMB
LKA
PER
TUR
CHL
ECU
PAN
BEN
VEN
IRN
MEX
4
1
MLI
SEN
CMR
CHN
IND
BOL
JOR
MUS
1/2
SLE
TUN
MWI
KEN
PHL
PAK
BGD
ZWE
EGY
Price of Tradables: U.S. = 1
1/4
NPL
1/8
Data
1/16
1/128
1/64
1/32
1/16
1/8
1/4
1/2
1
1996 PPP GDP Per Worker: U.S. = 1
Figure 6: Price Data and Modeling approach of Eaton and Kortum (2002)

2
JPNCHE
FIN
BEL
CAN
FRAITA
SWE
KOR
AUT
DNK
IRL
NLD
NOR
1
USA
ESP
GBR
MYS
ISR
PRT NZL AUS
GRC
1/2
BRAMEX
TUN
ARG
THA
CHL
TUR
URY
ZAF MUS
CRI
1/4
PER DOM
JOR
CHN
ECU
IRNVEN
JAM
PHL
SYR
COL
IND
PAN
NIC
PAK
PRY
EGY
BGD
ZWE
GTM
HND
PNG
1/8
BOLLKA
SLV
ZMB
CAF
NPL
SEN CMR
4
2
Model: U.S. = 1
1/16
GHA
KEN
SLE
ZAR
TGO
MLI
MWI
BEN
1/32
UGA
RWA
MOZ
NER
ETH
1/64
1/128
1/128
1/64
1/32
1/16
1/8
1/4
1/2
1
2
1996 PPP GDP Per Worker: U.S. = 1
Figure 7: Income Per Worker: Data and Model

140
RWA
This Paper
120
BEN
MLI
MWI
TGO
NER
MOZ
ETH
100
CAF
UGA
SLE
SLV
KEN
HND
SEN
NIC
ZMB NPL
BOL
CMR
PNG
PRY
80
GHA
GTMPAN
JAM
JOR
MUS
ZAR
ZWE
CRI
SYR
LKA
DOM
ECU
EGY
URY
VEN
4
60
IRN
BGD
PER
3
COL
TUN
PAK
CHL
GRC NZL
PHL
ZAF
ISR
Welfare Gain, Percent
TUR
ARG
40
PRT
AUS
NOR
Alvarez and Lucas (2007)
THA
FIN AUT
DNK
IND
MEX
MYS
BRA
SWE IRL
CHE
ESP
20
PAK
IND
CHN
EGY
TUN
KOR
BGD
MAR
NGA
ITA
VNM
PHL
LKA
IDN
UKR PER
ROM COL
BLRKAZ TUR
THADZA POL
IRN
ZAF
VEN
SVKCZE
HUN
NZL SGP
NLD
ARG
MYS
CHL
GRC
PRT
FINCHE
SWE
SAU
ISR
GBR
BEL
AUT
DNKHKG
NOR
IRL
CHN
RUS
BRAMEX
ESP CAN
AUS
NLD
FRA
ROW
DEU
FRA
GBR
ITA USA
JPN
BEL
CAN
USA
0
1/128
1/64
1/32
1/16
1/8
1/4
1/2
1
1996 PPP GDP Per Worker
Figure 8: Welfare Gains: Calibrated Model to Frictionless Trade

Table 5: Country Data
Country
yus
Lus
k
Xii
Data Source
y
i/yi
i
Li
Xus,us
United States
1.00
1.00
2.19
1.00
O
Argentina
2.23
9.25
1.91
0.95
I
Australia
1.23
15.0
2.56
0.88
O
Austria
1.25
35.8
2.96
0.78
O
Belgium
1.13
31.9
2.80
0.24
O
Benin
25.0
49.6
0.76
0.54
W
Bangladesh
9.15
4.61
0.97
0.85
I
Bolivia
8.54
45.2
1.06
0.66
I
Brazil
3.05
2.28
2.05
1.06
I
Central African Republic
30.4
84.6
0.93
0.78
W
Canada
1.26
8.94
2.70
0.59
O
Switzerland
1.30
34.5
3.59
0.74
I
Chile
2.46
24.3
1.58
0.79
I
China-Hong Kong
11.2
0.18
1.54
0.93
I
Cameroon
14.9
20.2
0.98
0.71
I
Colombia
4.70
7.58
1.25
0.87
I
Costa Rica
4.30
102
1.74
0.67
O
Denmark
1.27
48.1
2.71
0.68
W
Dominican Republic
4.58
54.0
1.29
0.56
I
Ecuador
4.52
37.8
1.99
0.73
W
Egypt
4.52
7.80
0.63
0.94
I
Spain
1.47
8.65
2.83
0.92
I
Ethiopia
45.1
5.34
0.48
0.50
O
Finland
1.45
53.5
3.13
0.86
O
France
1.27
5.06
2.99
0.89
W
United Kingdom
1.41
4.64
2.16
0.77
O
Ghana
21.5
16.0
0.79
0.42
I
Greece
1.83
31.7
2.81
0.79
W
Guatemala
4.27
46.1
0.83
0.72
I
Honduras
8.34
75.2
1.46
0.51
O
India
10.6
0.37
1.04
1.06
I
Ireland
1.19
96.6
1.77
0.36
I
Iran
3.19
7.58
1.85
1.01
O
Israel
1.31
63.1
2.49
0.58
W
Italy
1.12
5.87
2.72
0.99
I
Jamaica
7.44
108
2.31
0.51
O
Jordan
3.53
135
1.59
0.69
I
Japan
1.51
1.69
3.51
1.11
O
Kenya
22.7
9.85
0.96
0.57
I
Republic of Korea
1.67
7.11
2.86
0.98
O
Sri Lanka
7.44
17.7
1.14
0.43
W
Mexico
2.67
4.26
2.06
0.73
I
Mali
33.8
28.2
0.92
0.66
I
Mozambique
32.7
17.1
0.39
0.15
I
Mauritius
2.19
263
1.14
0.54
I
44

Table 5: Country Data contd.
Country
yus
Lus
k
Xii
Data Source
y
i/yi
i
Li
Xus,us
Malawi
34.0
31.6
1.06
0.50
I
Malaysia-Singapore
1.91
18.2
2.38
0.60
W
Niger
34.7
29.5
0.86
0.07
O
Nicaragua
10.0
95.4
1.72
0.71
O
Netherlands
1.25
18.6
2.66
0.48
W
Norway
1.14
62.2
3.22
0.74
O
Nepal
18.8
14.8
1.43
0.77
I
New Zealand
1.52
77.1
2.55
0.79
I
Pakistan
8.19
3.86
1.07
0.75
I
Panama
3.74
136
2.05
0.16
I
Peru
5.59
13.0
2.24
0.88
W
Philippines
7.34
4.69
1.66
0.62
O
Papua New Guinea
7.66
65.0
1.20
0.26
W
Portugal
1.90
30.2
2.36
0.78
W
Paraguay
4.69
62.2
1.18
0.64
I
Rwanda
34.2
40.9
0.62
0.92
W
Senegal
18.5
33.1
0.80
0.63
O
Sierra Leone
22.5
80.5
0.53
0.26
O
El Salvador
4.22
74.6
0.85
0.51
O
Sweden
1.43
29.4
2.73
0.78
I
Syrian Arab Republic
3.54
37.9
1.05
1.05
W
Togo
26.2
78.8
0.96
0.56
I
Thailand
4.28
4.25
2.78
0.77
I
Tunisia
3.23
45.2
1.45
0.77
I
Turkey
3.86
4.96
1.71
0.92
W
Uganda
32.5
14.1
0.24
0.80
O
Uruguay
2.76
93.2
1.42
0.79
I
Venezuela
2.88
17.4
1.94
0.65
I
South Africa
2.61
10.0
1.27
0.94
I
Zaire (DRC)
90.9
6.08
1.07
0.62
W
Zambia
22.8
43.8
1.93
0.45
W
Zimbabwe
9.71
24.8
1.82
0.75
W
Note: Column’s 2, 3, and 4 are constructed from Heston, Summers, and Aten (2002) describing
relative income per worker, relative labor endowments, and each country’s capital-output ratio.
Column 5 is the relative home trade share for each country—the inverse is depicted in log base
2 scale in ﬁgure 2. Column 5 denotes the source of gross manufacturing production data. “O”
denotes the OECD. “I” denotes data from the International Yearbook of Industrial Statistics from
various years published by the United Nations Industrial Development Organization. “W” denotes
the World Bank and gross manufacturing production is computed from value added. China and
Hong Kong and Malaysia and Singapore are aggregated together following Bernard, Eaton, Jensen,
and Kortum (2003) to avoid problems with entrepot trade.
45

Table 6: 1996 Trade Shares Xij in Percent
U.S. Can. Japan Mexico China Senegal Malawi Zaire
U.S.
83.25 39.73 2.27
31.62
3.63
2.16
1.57
2.93
Can.
3.78 49.21 0.21
0.72
0.32
0.56
0.67
0.51
Japan
3.04 2.01 92.56
1.59
6.99
1.34
2.65
0.82
Mexico 1.88 1.33
0.02
61.09 0.057
0.01
0
0.007
China
1.78 1.41
1.44
0.30
77.61
2.69
2.50
6.81
Senegal
0∗
0∗
0∗
0
0∗
52.68
0
0
Malawi
0∗
0∗
0∗
0
0
0
41.52
0
Zaire
0.003 0.005 0.003
0∗
0∗
0
0
51.53
Note: Zeros with stars indicate the value is less than 10−4. Zeros
without stars are recorded zeros in the data. Entry in row i,
column j, is the fraction of goods country j imports from country
i.
46

Table 7: Summary Statistics
No. Obs TSS SSR
σ2ǫ
4242
4924 851
2.08
Table 8: Geographic Barriers, θ = 0.15
Barrier
Parameter Estimate S.E. %eﬀect on cost
[0, 375)
−4.66
0.60
101.1
[375, 750)
−5.60
0.30
131.9
[750, 1500)
−6.16
0.17
151.9
[1500, 3000)
−7.22
0.12
195.2
[3000, 6000)
−8.44
0.09
254.8
[6000, maximum]
−9.37
0.10
308.1
Shared Border
0.69
0.37
−10.8
Arrival Country
United States
5.40
0.43
−55.5
Argentina
1.62
0.53
−22.0
Australia
2.50
0.53
−31.2
Austria
1.35
0.34
−18.4
Belgium
5.13
0.51
−53.7
Benin
−3.71
0.87
74.5
Bangladesh
−0.43
0.58
6.58
Bolivia
−2.61
0.66
47.9
Brazil
2.21
0.45
−28.2
Central African Republic
−4.04
1.83
83.4
Canada
3.32
0.39
−39.2
Switzerland
2.19
0.44
−28.0
Chile
2.40
0.49
−30.1
China-Hong Kong
4.40
0.39
−48.3
Cameroon
−1.50
0.80
25.3
Colombia
−0.45
0.44
6.97
Costa Rica
−0.96
0.60
15.5
Denmark
1.67
0.40
−22.1
Dominican Republic
−1.45
0.62
24.3
Ecuador
−1.09
0.52
17.7
Egypt
−2.66
0.50
48.9
Spain
2.82
0.38
−34.5
Ethiopia
−2.45
0.63
44.3
Finland
0.82
0.41
−11.5
France
3.69
0.41
−42.5
United Kingdom
4.60
0.42
−49.8
Ghana
−0.51
0.75
8.00
Greece
−0.68
0.41
10.7
Guatemala
−2.28
0.63
40.7
Honduras
−2.96
0.78
55.8
India
1.86
0.49
−24.3
47

Table 8 Contd.
Arrival Country
Parameter Estimate S.E. % eﬀect on cost
Ireland
2.54
0.42
−31.7
Iran
−2.35
0.76
42.3
Israel
1.78
0.51
−23.4
Italy
3.48
0.37
−40.7
Jamaica
−2.04
0.94
35.8
Jordan
−2.22
0.71
39.4
Japan
4.35
0.36
−47.9
Kenya
−0.82
0.65
13.1
Republic of Korea
3.64
0.41
−42.0
Sri Lanka
0.98
0.56
−13.7
Mexico
1.49
0.46
−20.0
Mali
−4.83
0.65
106
Mozambique
−0.87
0.85
13.9
Mauritius
−0.26
0.66
3.84
Malawi
−3.04
0.92
57.7
Malaysia-Singapore
4.25
0.43
−47.1
Niger
−1.64
0.99
27.9
Nicaragua
−3.55
0.86
70.2
Netherlands
4.38
0.39
−48.1
Norway
0.38
0.50
−5.55
Nepal
−3.68
0.68
73.6
New Zealand
2.52
0.51
−31.5
Pakistan
1.55
0.53
−20.7
Panama
0.14
0.63
−2.11
Peru
0.77
0.52
−11.0
Philippines
1.03
0.54
−14.3
Papua New Guinea
−0.53
1.05
8.30
Portugal
0.37
0.40
−5.38
Paraguay
−2.38
0.65
43.0
Rwanda
−5.76
1.01
137
Senegal
−2.37
0.82
42.6
Sierra Leone
−1.14
1.05
18.6
El Salvador
−2.41
0.88
43.6
Sweden
1.86
0.38
−24.3
Syrian Arab Republic
−5.55
0.59
130
Togo
−4.12
0.82
86.5
Thailand
2.61
0.52
−32.4
Tunisia
−2.26
0.60
40.4
Turkey
−0.13
0.39
1.98
Uganda
−3.35
0.81
65.2
Uruguay
0.14
0.47
−2.07
Venezuela
−0.19
0.63
2.82
South Africa
2.24
0.43
−28.5
Zaire (DRC)
−0.68
0.82
10.8
Zambia
−0.79
0.85
12.5
Zimbabwe
−1.73
0.66
29.5
Note: The parameters were estimated by OLS. For an estimated
parameter ˆb, the implied percentage eﬀect on cost is 100 × (e−θˆb −
1). Heteroskedasticity-robust standard errors reported
48

Table 9: Technology, λi
θ
Country
ˆ
Si
S.E.
λus
λi
United States
0.54
0.33
1.00
Argentina
0.69
0.34
1.61
Australia
0.11
0.38
1.38
Austria
0.77
0.26
0.95
Belgium
-1.55
0.45
1.15
Benin
-0.25
0.50
9.98
Bangladesh
0.54
0.43
2.91
Bolivia
-0.09
0.39
3.71
Brazil
1.27
0.38
1.34
Central African Republic
0.33
0.53
3.40
Canada
0.11
0.32
1.00
Switzerland
0.75
0.35
0.77
Chile
-0.39
0.35
1.79
China-Hong Kong
0.76
0.31
1.88
Cameroon
-0.43
0.46
4.52
Colombia
0.63
0.29
2.62
Costa Rica
0.01
0.42
2.44
Denmark
0.81
0.33
0.90
Dominican Republic
-0.49
0.39
2.18
Ecuador
0.06
0.36
2.69
Egypt
1.17
0.29
2.93
Spain
0.53
0.30
1.03
Ethiopia
-1.15
0.42
11.74
Finland
1.39
0.32
0.67
France
0.68
0.32
0.85
United Kingdom
-0.08
0.34
1.10
Ghana
-1.50
0.47
5.47
Greece
0.75
0.29
1.68
Guatemala
-0.03
0.36
3.72
Honduras
-0.46
0.43
3.88
India
1.24
0.42
2.17
Ireland
-0.33
0.35
0.88
Iran
1.20
0.63
3.07
Israel
-0.01
0.37
1.26
Italy
0.85
0.30
0.77
Jamaica
-0.50
0.36
2.63
Jordan
-0.01
0.37
2.74
Japan
1.44
0.31
0.62
Kenya
-0.58
0.39
6.91
Republic of Korea
1.00
0.32
0.78
Sri Lanka
-1.48
0.38
4.03
Mexico
0.76
0.28
1.36
Mali
0.08
0.44
8.93
Mozambique
-2.32
0.54
12.01
Mauritius
-1.04
0.46
2.28
49

Table 9: Technology, λi contd.
θ
Country
ˆ
Si
S.E.
λus
λi
Malawi
-0.71
0.58
9.75
Malaysia-Singapore
-0.33
0.30
1.05
Niger
-2.94
0.52
18.43
Nicaragua
0.09
0.47
2.96
Netherlands
-0.75
0.32
1.14
Norway
0.92
0.39
0.96
Nepal
0.62
0.41
4.69
New Zealand
-0.27
0.32
1.33
Pakistan
-0.01
0.41
2.94
Panama
-1.71
0.42
5.58
Peru
-0.08
0.35
2.53
Philippines
-0.12
0.36
2.36
Papua New Guinea
-1.51
0.55
3.80
Portugal
0.61
0.27
1.18
Paraguay
0.26
0.43
3.48
Rwanda
0.24
0.58
9.96
Senegal
-0.36
0.43
3.87
Sierra Leone
-2.01
0.55
5.67
El Salvador
-0.64
0.46
4.59
Sweden
1.07
0.30
0.73
Syrian Arab Republic
1.75
0.36
2.45
Togo
-0.49
0.43
7.10
Thailand
0.15
0.46
1.67
Tunisia
1.29
0.40
1.28
Turkey
1.23
0.30
1.81
Uganda
-0.27
0.39
6.01
Uruguay
-0.31
0.27
1.96
Venezuela
-0.16
0.36
3.27
South Africa
0.16
0.32
1.93
Zaire (DRC)
-0.57
0.56
4.32
Zambia
-1.05
0.45
3.90
Zimbabwe
0.14
0.40
3.55
Note:
Technology parameters, λi, are re-
covered as detailed in section 4.2 and θ =
0.15.
Heteroskedasticity-robust standard errors
reported
50

International Trade And Income Differences

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