Download Product Differentiation, and the Composition of Trade Across

Product Differentiation, and the Composition of Trade
Across Dissimilar Nations
Ahmad Lashkaripour∗
May 2015
First draft: November 2013
Abstract
Standard gravity models describe the volume of trade in a multilateral world, but overlook the commodity composition of trade. I develop a novel view of comparative advantage that reconciles the gravity
equation with three basic facts about the composition of trade: (i) the effect of geography on the price
composition of exports, (ii) the effect of GDP per capita on the price composition of exports, and (iii) the
systematically higher trade-to-GDP ratio of rich countries. My approach delivers a unified model, which
fully describes both the volume and the composition of trade among nations that are dissimilar in terms of
geography and income. A remarkable feature of the unified model is that, despite homothetic preferences,
rich and poor countries have systematically different consumption structures. I estimate the unified model
using bilateral trade data on 100 countries and compare it to a special case, which delivers the pure gravity
equation. The unified model fits the data significantly better with an R2 that is 43 percent higher than the
pure gravity model. The estimated gains from trade are substantially larger than the pure gravity model,
and more unequally distributed across nations. Importantly, when accounting for the role of composition,
further liberalization of trade systematically favors poor and remote nations.
1
Introduction
The contemporary theories of international trade deliver the gravity equation, by linking the characteristics
of a country to the volume of its trade. However, they do not deliver systematic predictions about how
country-specific characteristics determine the commodity composition of trade. With the dramatic growth
of trade between dissimilar nations, and the availability of microlevel data, it has become more evident that
dissimilar countries trade dissimilar goods. Evidence indicate that:
∗ I am grateful to my advisors Jonathan Eaton and Stephen Yeaple for their guidance, encouragement, and support. I am also grateful
to James Tybout for encouragement and various discussions on the topic. I wish to thank Bernardo Díaz de Asterloa, Alexandros
Fakos, Farid Farrokhi, Cecilia Fieler, Paul Grieco, Kala Krishna, Konstantin Kucheryavyy, Felix Tintelnot and seminar participants
at the University of British Columbia, Indiana University, Pennsylvania State University, University of California Santa Cruz, Drexel
University, and the New Faces in International Economics conference for helpful comments and suggestions. All errors are my own.
Correspondence: [email protected], http://pages.iu.edu/~alashkar/.
1
i. High-income countries import/export a higher share of their GDP.
ii. High-income countries have higher aggregate (and within category) export prices.
iii. Geographically distant nations trade higher-price goods (THE WASHINGTON A PPLES EFFECT ).1
The first two facts point to a systematic relationship between income per capita and the composition of a
nation’s trade. The third fact points to a systematic relationship between geography and the composition
of trade. All three facts are beyond the scope of standard gravity models. Three independent bodies of
literature have emerged, addressing each fact individually. However, there is no unified framework that
could reproduce all three facts.
This paper develops an novel view of comparative advantage that collectively reproduces all three facts
highlighted above. I combine this alternative view of comparative advantage with National Product Differentiation to construct a unified model of foreign trade. The unified model extends beyond standard gravity
models as it systematically pins down both the volume and the composition of trade. I estimate the unified
model and compare it to a special case, which delivers the pure gravity equation. I show that embedding
systematic production specialization into a pure gravity model (i.e. accounting for the role of composition)
tremendously magnifies the gains from trade. Moreover, when accounting for the role of composition, the
gains from trade depend crucially on two national characteristics: income per capita and remoteness.
To explain the commodity composition of trade across dissimilar nations, I take an alternative view from
the existing literature. Existing theories (usually) require non-homothetic demand to explain the effect of
per capita income and rely on additive (specific) trade costs to account for the effect of geography on the
composition of trade. The remaining void, however, is a general theory that reconciles the effect of per
capita income with that of geography. The unified model fills this void with a simple solution that requires
neither non-homotheticity nor additive trade costs. Indeed, I only relax one common assumption (of the
gravity models) that is inconsistent with micro level evidence. Standard gravity models assume that the
scope for product differentiation is the same across all goods.2 I relax this assumption, and allow for two
types of goods, which offer different scopes for product differentiation (a highly-differentiated, low-σ, type
and a less-differentiated, high-σ, type).3
In equilibrium, patterns of trade are determined by how countries concentrate their production and consumption across the two types of goods. Countries are characterized by their National Product Quality and
Labor endowment. Advanced countries (by definition) are endowed with higher National Product Qualities,
and produce more appealing varieties of both types. This entails more global demand, which drags up their
equilibrium wage. The higher wage paid by advanced countries makes them comparatively disadvantaged
in the less-differentiated type, which is highly price-sensitive. Consequently, high-wage countries have endogenously determined comparative advantage in the highly-differentiated (low-σ) type — i.e. the autarky
1 The first fact is documented by Limao and Venables (2001), Waugh (2010), and Fieler (2011). The second fact is documented
at various levels of aggregation: Schott (2004) shows that rich countries have higher within-category export prices; Hummels and
Klenow (2005) show that rich countries have higher aggregate export prices. The third fact is documented by Hummels and Skiba
(2004) and Baldwin and Harrigan (2011), among others.
2 Broda and Weinstein (2006) estimate that different HS10 product categories exhibit substantially different degrees of product differentiation. At an even more desegregated level, Berry, Levinsohn, and Pakes (1995) estimate that luxury cars have systematically lower
price elasticities of demand than economy cars. That is to say that luxury cars are more horizontally differentiated than economy cars.
3 Hanson and Xiang (2004) also exploit across-sector differences in the degree of product differentiation to identify the home market
effect.
2
relative price index of the highly-differentiated type is lower in high-wage countries.4 Low-wage countries,
meanwhile, have comparative advantage in the less-differentiated (low-σ) type. That being the case, in
equilibrium, high-wage countries concentrate their production on the highly-differentiated type, whereas
low-wage countries concentrate their production on the less-differentiated type.
Consumption patterns are determined by what I refer to as the Home Production Effect on local consumption. In the presence of trade costs, consumers spend relatively more on the locally competitive type as it
is relatively cheaper. Specifically, due to costly trade, The relative price index of the highly-differentiated
(low-σ) type is lower in rich countries versus poor countries. This induces households in rich countries to
consume relatively more of the low-σ type.5 So, remarkably, countries with identical (homothetic) preferences concentrate their consumption on different types of goods. This effect is the opposite of the Home
Market Effect formalized by Krugman (1980). The Home Market Effect states that local demand dictates patterns of local production. The present model states that, when trade is costly, local production determines
local consumption.6
In equilibrium, rich countries are both net exporters and the main consumers of the highly-differentiated
(low-σ) type. The low-σ type is subject to a low demand elasticity and exhibits two key properties: (i) it
comes with a higher markup, and (ii) it has a lower trade elasticity and is traded more heavily. Rich countries
have higher trade-to-GDP ratios because they produce and consume relatively more of the low-σ type,
which is traded more intensively. Rich countries have higher aggregate export prices dues to two reasons.
First, rich countries sell both types of goods at a higher price due to their higher National Product Quality.
Second, rich countries export relatively more of the highly-differentiated, high-markup type. The second
channel is novel and points to a purely compositional effect. Similarly, distant countries trade relatively
more of the highly differentiated, high-markup type. This follows from the fact that remote exporters face
higher trade costs and are price-disadvantaged. That being the case, they sell relatively more of the highlydifferentiated, high-markup type, which is price-insensitive. This gives rise to THE WASHINGTON A PPLES
EFFECT .
In the unified model, National Product Differentiation governs the trade of similar goods between similar
countries. I accommodate National Product Differentiation by letting firm-specific varieties from the same
country to be closer substitutes. The unified model, therefore, nests the Armington gravity model.7 Altogether, the unified model combines the neoclassical-type trade, between dissimilar nations, with the
gravity-type trade, between similar nations. This gives rise to two independent welfare-improving effects
of foreign trade. First, like gravity models, trade increases the number of differentiated varieties. Second, like neoclassical models, trade induces production reallocation, which lowers the relative price index
of the comparatively disadvantaged type in each country. More specifically, quality-abundant countries
reallocate production towards the highly differentiated type, whereas labor-abundant countries reallocate
4 Comparative advantage in the unified model is similar to the Heckscher-Ohlin model in that it is endogenously determined. It is
different from the Heckscher-Ohlin model in that it is regulated by demand. In the Heckscher-Ohlin model there are two goods, one
with a production that is labor-intensive and other has a production that is capital-intensive. In the present model there are two goods,
one (the low-σ type) has quality-intensive demand and the other (the high-σ type) has a quantity-intensive demand.
5 Preferences are nested CES, and consumers allocate expenditure across different types of goods based on their relative price.
6 The Home Market Effect relies on increasing returns to scale, the effect presented in this paper requires some degree of substitutability between different types of goods.
7 The Armington model implicitly assumes that varieties from the same country are perfect substitutes (which entails perfect competition). I relax this restriction, and develop a method that tractably combines National Product Differentiation with monopolistic
competition.
3
production towards the less-differentiated type. Welfare improves because the relative price index of the
highly-differentiated type falls in poor (labor-abundant) countries, and the relative price index of the lessdifferentiated type falls in rich (quality-abundant) nations.
I estimate the unified model using bilateral trade data for 100 countries. The sample represents more than
95% of the world trade. More importantly, the sample represents countries that are vastly dissimilar in
GDP per capita and geographical location. To demonstrate the merits of the unified model, I compare it
to a special case that delivers the pure gravity equation. The unified model fits the data better, with an R2
that is 43 percent higher than the pure gravity model. The superior fit of the unified model stems from
its ability to explain trade between both similar and dissimilar nations. Specifically, the unified model
matches two margins of the data that are beyond the scope of the pure gravity model. The first margin
corresponds to the sizable disparity in trade-to-GDP ratios across rich and poor countries. The unified
model correctly predicts that rich countries have higher trade-to-GDP ratios, whereas the gravity model
predicts the opposite. Second, the unified model allows for endogenously determined, country-specific
trade elasticities. That being the case, the unified model correctly predicts the smaller distance elasticity of
export flows from rich and remote countries. Moreover, in addition to better-explaining trade volumes, the
unified model also performs remarkably better than the gravity model in matching (out-of-sample) facts
about the price composition of exports.
The commodity composition of trade plays a central role in determining welfare. Arkolakis, Costinot, and
Rodriguez (2012) demonstrate that in gravity models the trade-to-GDP ratio and trade elasticity are sufficient statistics for evaluating the gains from trade relative to autarky. Gravity models mismatch tradeto-GDP ratios across rich and poor nations and counter-factually assume a common trade elasticity for all
countries. By characterizing the composition of trade, the unified model matches observed trade-to-GDP ratios and delivers country-specific trade elasticities that are endogenously determined. As a result, the gains
from trade (relative to autarky) are systematically larger in the unified model relative to the pure gravity
model. The gains are systematically larger for rich countries, because the unified model correctly predicts
that rich countries have higher trade-to-GDP ratios. The gains are systematically larger for poor countries
because they import relatively more of the highly-differentiated type and have systematically lower trade
elasticities.8 To quantitatively demonstrate this result, I estimate the gains from trade (relative to autarky)
in both models. In the unified model the estimated gains from trade are close to 200% larger than the pure
gravity model.
The composition of trade not only influences the overall size of the gains from trade, but also their distribution across countries. At the current levels of globalization, different countries are importing systematically
different goods. So the prospective gains from further trade liberalization depend crucially on the inherent
characteristics of each country. To quantify this dependence, I estimate the prospective gains from lowering
the existing trade costs by 10 per-cent. Two remarkable patterns emerge: (i) the prospective gains are systematically larger for poor countries, and (ii) compared to the pure gravity model, the prospective gains (in the
unified model) are distributed in favor of remote nations. Both patterns are due to the highly-differentiated
imports of poor and remote countries given the existing impediments to trade. Partially removing these
impediments allows poor and remote countries to import more of the highly-differentiated type. Highly8 Imported varieties increase welfare to a larger degree if they are highly-differentiated and less substitutable with domestic counterparts.
4
differentiated varieties are not easily substitutable with domestic counter-parts, so they bring along sizable
welfare gains.
This paper is closely related to a contemporary literature that describes the composition of trade. Hummels
and Skiba (2004), and Baldwin and Harrigan (2011) propose models that account for the effect of geography on the price composition of trade. Flam and Helpman (1987), Matsuyama (2000), and Fajgelbaum,
Grossman, and Helpman (2011) explain (based on non-homtheticity) the effect of GDP per capita on price
composition of exports. Fieler (2011), and Caron, Fally, and Markusen (2014) develop models (based on
non-homtheticity) that reproduce the higher trade-to-GDP ratios of rich countries. This paper contribute to
this literature along several key dimensions. First, it accounts for both the effect of geography and per capita
income on the composition of trade. Existing theories generally confront one aspect of the data in isolation,
and overlook the others. Second, the unified model preserves the standard assumptions that make gravity
models tractable (e.g. homthetic CES preferences and iceberg trade costs).9 The unified model, therefore, retains the parsimony of standard gravity models and is straightforward to estimated with multilateral trade
data. The main contribution of the paper, however, concerns the welfare gains from trade. I explicitly argue
that the composition margin has profound effects on the gains from trade. To my knowledge, this paper is
the first to show that embedding systematic specialization into a gravity model (to account for composition)
tremendously magnifies the gains from trade.10
Finally, this paper contributes to a literature that combines within-product trade with across-product trade
(Helpman and Krugman (1985); Markusen (1986); Davis (1995); Bernard, Redding, and Schott (2007)). The
contribution is along three directions: First, the driving force behind across-product specialization in the
present model is novel and consistent with micro-level evidence. Second, in the present model, acrossproduct trade delivers three principal facts regarding the composition of foreign trade—previous studies
of within- and across-product trade are mute about these principal facts.11 Third, existing theories are
generally confined to basic settings with two countries. This paper, however, develops and estimates a
multi-country, general equilibrium model that tractably combines within-product trade with across-product
trade across many dissimilar countries.
The paper is structured as follows. I present the model in Section 2 and the empirical analysis in Section 3.
Section 4 performs counterfactuals and quantifies the gains from trade. Section 5 concludes.
9 Competing theories usually deviate from these simple assumptions and, therefore, depend on a broader set of conditions to hold.
For example, the standard explanation for the effect of geography on the export price-mix (Hummels and Skiba (2004)) imposes two
conditions: (i) firms produce substitutable goods that exhibit different qualities, and (ii) trade costs are additive. The explanation
for higher trade-to-GDP in rich countries (Fieler (2011), and Caron et al. (2014)) relies on two assumptions: (i) preferences are nonhomothetic, and (ii) income elastic goods are subject to lower trade elasticities. Fajgelbaum et al. (2011) requires two conditions
to deliver the higher price of exports from rich countries: (i) preferences are non-homothetic, and (ii) high-quality goods are more
differentiated. T HE UNIFIED MODEL, developed here, only requires one non-standard assumption: different types of goods offer
different scopes for product differentiation. Yet, it collectively reproduces all three facts corresponding to composition. In THE UNIFIED
MODEL, the systematic difference in consumption structure across rich and poor countries is an endogenous outcome rather than an
assumption (of non-homotheticity).
10 Costinot, Donaldson, and Komunjer (2012) argue that accounting for sectoral specialization increases the gains from trade
marginally. They impose, however, that sectoral specialization is regulated by sector-specific technologies. That being the case, their
model does not deliver the three basic facts linking specialization to geography and income. Costinot and Rodríguez-Clare (2013) and
Ossa (2012) argue that embedding multiple sectors into a gravity model magnifies the gains from trade. In both studies, however, a
fixed share of income is spent on a particular sector, and intra-sector trade is governed by standard gravity forces. Therefore, while
both studies account for the composition margin, they overlook systematic specialization across sectors.
11 Markusen (1986) predicts that the volume North-North trade is larger than North-South trade. This result, however, does not imply
higher trade-to-GDP ratios in rich countries. As pointed out in Caron et al. (2014), one needs to further assume that income-elastic,
capital-intensive goods are subject to lower trade costs to achieve results corresponding to trade-to-GDP ratios.
5
2
Theory
The UNIFIED THEORY combines Monopolistic competition and National Product Differentiation in a multicountry general equilibrium framework with two types of goods. There are two driving forces behind trade:
international specialization and National Product Differentiation. International specialization is motivated by
comparative advantage across types, and governs across-product trade. National Product Differentiation governs within-product trade. The two forces, combined, determine the volume and the composition of foreign
trade.
2.1
The Environment
There are N countries; C = {1, ..., N } denotes the set of countries. Population Li , and National Product
Quality αi characterize country i ∈ C. There are two types of goods: H and L. Each type comes in a
continuum of firm-specific varieties. Firm-specific varieties are (horizontally) differentiated both at the firm
level and at the national level.
Demand.
Preferences are homothetic and described by a nested-CES utility. Consumers in country i max-
imize the following utility function


Ui = 
(Uiz )
∑
−1
−1

z∈{ H,L}
where Uiz is the sub-utility corresponding to type z ∈ { H, L}. Uiz is a CES aggregator across all national
varieties of type z
"
#1
ρz ρz
N
1−ρ z
z
z
Q ji
Ui = ∑ α j
j=1
The utility attained from varieties of type z produced in country j, is a Cobb-Douglas combination of the
aggregate quantity, Q zji , and the quality, α j , of the imported varieties. Henceforth, I will refer to α j as
the National Product Quality of country j—countries endowed with a higher α j , produce more appealing
varieties of both types (H and L).12 Q zji is a CES aggregator across all the firms exporting type z from
country j to i
"ˆ
Q zji
=
ω∈Ω ji
q zji
ρez
#
dω
1
ρez
1
= M jiρez q zji
12 The country-specific demand shifter, α , is not Hicks-neutral. This is essential for the results of the paper, and states that demand
j
for the highly-differentiated (low-σ) types is quality-intensive, whereas demand for the less-differentiated (high-σ) types is quantityintensive. Typically, to characterize trade across dissimilar countries one has to avoid Hicks-neutrality. In Fieler (2011), for example,
the country-specific technology parameters are not Hicks-neutral (i.e. better overall technology makes a country relatively better in
goods that have highly differentiated technologies). In the generalized framework developed by Costinot (2009), log-supermodularity
implies non-neutrality of technology. The fact that country-specific demand shifters are not Hick-neutral has theoretical roots. For
example, if consumers have heterogeneous tastes across varieties, and taste is Freshet-distributed, a CES-like demand will emerge
(Anderson, De Palma, and Thisse (1992)). Suppose ideas are used to develop varieties that match the taste of individual consumers. If
ideas arrive at constant rate and according to a Poisson distribution, then taste is Freshet-distributed. The non-neutral country-specific
demand shifter, α j , would then represent the stock of ideas in country j. This result is due to Kortum (1997).
6
where q zji is the quantity purchased from a typical firm ω from country j (note that firms are homogeneous).
M ji (Ω ji ) denotes the mass of firms (the set of firms) that sell from country j to i. In the above threetier nested-CES utility, is the elasticity of substitution between types H and L; σ z = 1/ (1 − ρ z ) is the
ez = 1/ (1 − ρez ) is the intraelasticity of substitution between (aggregated) national varieties of type z; σ
national elasticity of substitution between firm-specific varieties of type z.
ez = σ z there is no
The above demand structure nests both the Krugman and Armington models. When σ
scope for National Product Differentiation, and the demand structure (for each type) reduces to that of Krugez → ∞, the scope for National Product Differentiation is complete, similar to the Armington
man (1980). If σ
model. In this paper I adopt a middle ground. Specifically, I allow for some degree of National Product
Differentiation, which is the same for both types:
eH − 1
e −1
σ
σ
= L
≡η>1
σH − 1
σL − 1
The above specification indicates that firm-specific varieties produced in the same country are closer substitutes—
η → ∞ entails that varieties from the same country are perfect substitutes, like the Armington model.
Importantly, type H and type L goods are systematically different. Type H offers a greater scope for product
differentiation than type L:
σ H < σ L ⇐⇒ ρ H < ρ L
Hence, by definition, preferences for type L are quantity-intensive, whereas preference for type H are
quality-intensive, i.e. ρ H < ρ L . Henceforth, I will refer to to type H as the highly differentiated (low-σ)
type, and to type L as the less-differentiated (high-σ) type.
To summarize the demand-side, σ z regulates the scope for product differentiation in sector (or type) z, while
η regulates the degree of National Product Differentiation in the economy. In section 3, I estimate η without
imposing any restrictions, which delivers an η > 1.
Supply. As in Krugman (1980), firms are monopolistically competitive and homogeneous. Unlike the
Krugman model, entry cost is paid locally (and separately) for each market, so there are no economies of
scale. Labor is the only factor of production. One unit of labor is required to produce one unit of each type
z ∈ { H, L} . The unit labor cost is the same for both types and for all countries. Exports from country j to i
are subject to an additional iceberg cost, τ ji . Altogether, the marginal cost of producing type z in country j,
and selling in to country i is
mczji = τ ji w j
where w j denotes wage in country j. Let p zji denote the price of type z, produced in country j, and sold in
country i. A typical firm exporting q zji units of type z from country j to i collects a variable profit equal to
π jiz = p zji − τ ji w j q zji
7
The firms use the combined variable profits from selling both types to subsidize the local entry cost, which
is f e units of home labor. The free entry condition (for market i) is, therefore, given by
π jiz = w j f e
∑
z∈{ H,L}
The free entry condition determines M ji : the mass of firms that export from country j to i.
Equilibrium. Let X zji ≡ M ji p zji q zji denote the amount spent by country i on type z = { H, L} goods produced in country j. Utility maximization implies:
X zji
Pjiz
= αj
!1−σz Piz
Piz
Pi
1−
wi Li
(1)
where Pjiz denotes the price index of exports from country j to i of type z:
"ˆ
Pjiz ≡
ω∈Ω ji
p zji
1−σez
#
1
ez
1−σ
1
= M ji1−σez p zji ,
dω
Piz denotes the price index of type z in country i:
"
Piz ≡
#
∑
k ∈C
αk ( Pkiz )1−σz
1
1−σ z
,
Pi is the aggregate price index in country i (aggregated across both types):

Pi ≡ 

1
1−
( Piz )1− 
∑
z∈{ H,L}
In equation 1,
Piz
Pi
1−
is the share of spending on type z; α j
Pjiz
Piz
1−σz
is the share of spending on country
j varieties of type z. A typical firm from country j, therefore, sells x zji ≡ p zji q zji =
X zji
M ji
dollars of types z.
Firms are Monopolistically competitive, and charge a type-specific markup over marginal cost
p zji =
ez
σ
1
τ ji w j = 1 +
τ w
ez − 1
σ
η (σ z − 1) ji j
> η(σ 1−1) .
L
Plugging the equilibrium price into the demand equation (equation 1) delivers a type-specific gravity relationship:
1
1−σz
α j M jiη τ ji w j
X zji =
Xiz
(2)
1
1−σ z
η
∑k∈C αk Mki (τki wk )
Note that firms charge a higher markup on the highly differentiated (low-σ) type, i.e.
8
1
η(σ H −1)
where Xiz ≡
Piz
Pi
1−
wi Li , is total spending on type z in country i. The above gravity formulation indicates
that in the less-differentiated (high-σ) sector, L, trade shares are determined primarily on the basis of the
relative price. In highly-differentiated (low-σ) sector, H, trade shares are determined primarily by National
Product Quality.
The number of firms entering market i from country j, M ji , is pinned down by the FREE ENTRY CONDITION:
1
M ji =
wj f e
"
XH
ji
eH
σ
+
X Lji
#
(3)
eL
σ
ez − 1 = η(σ z − 1). Note that upon entry, firms collect higher profits from selling
where, by assumption, σ
the highly-differentiated, high-markup type, H. Therefore, countries that export relatively more of type H
are represented by more firms in the global markets. Finally, BALANCED TRADE implies that
wjLj =
∑ X Hji + X Lji
(4)
i ∈C
The above equation insures that total spending in country j equals totals sales (generated income) by country j.
2.2
Four Underlying Patterns that Describe the Global Economy
This section describes four underlying patterns that arise in the trade equilibrium. These underlying patterns shape the structure of production and consumption across dissimilar countries.
Pattern 1.
In the trade equilibrium, all else equal, countries with higher National Product Quality pay higher
wages. Basically, what separates the low- and high-income countries is their National Product Quality. To
demonstrate this, consider two geographically identical countries: N (North) and S (South). North is endowed with higher National Product Quality, which implies that all else equal there is more demand for
Northern varieties. Balanced trade (equation 4), therefore, entails that North pays higher equilibrium wages
than South:
α N > α S =⇒ w N > w S
Pattern 2.
High-wage countries have comparative advantage in type H. To see this, note that the gravity
relationship (equation 2) implies
L
XH
ji / X ji
XkiH / XkiL
=
τ ji w j
τki wk
σ L −σ H
(5)
The above relationship entail that high-cost countries sell relatively more of type H. Suppose North and
South are located at equal distance from some country i (τ Ni = τ Si ). Equation 5 indicates that North exports
relatively more of type H to i and South exports relatively more of type L
H /X L
XNi
Ni
H /X L
XSi
Si
=
wN
wS
9
σ L −σ H
>1
In summary, North has absolute quality-advantage in both types: α N > α S . This entails more demand for
Northern varieties, and drags up their equilibrium wage: w N > w S . That being the case, North becomes
comparatively disadvantaged in type L (which is price-sensitive), and has endogenously determined comparative advantage in type H.13 Comparative advantage in the unified model is similar to the Heckscher-Ohlin
model in that it is endogenously determined, but different in that it is regulated by demand. Specifically
demand for type H is quality-intensive, whereas demand for type L is quantity-intensive. Quality-abundant
North has comparative advantage in type H, whereas labor-abundant South has comparative advantage in
type L.14
Importantly, the above view of comparative advantage is more general than the classical view. In the classical view, a country has comparative advantage in a good for which the autarky relative price is lower in that
country (Deardorff (1980)). Here, comparative advantage can be defined in terms of the price index, which is
nominal price adjusted by quality and variety. To see this, note that the autarky relative price index of type
H in country i is given by
PiH
!Autarky
PiL
1 σ L1−1 − σ H1−1
A η
= φ αi Mii
where MiiA denotes the autarky number of firms in country i and φ ≡
(6)
eH (σ
eL −1)
σ
.
eL (σ
eH − 1 )
σ
equation 6 entails that the autarky relative price index of type H is lower in the
PNH
PNL
!Autarky
<
PSH
Given that α N > α S ,
North:15
!Autarky
(7)
PSL
Therefore, North’s comparative advantage in type H corresponds to a lower autarky relative price index of
type H. Moreover, the comparative advantage of North in type H implies that (i) North is the net exporter
of type H to the South, and (ii) North sells relatively more of type H and South sells relatively more of type
L to some country i, which is located at equal distance from both:
H
XNi
H
XSi
Pattern 3.
countries:
>
L
XNi
L
XSi
In the TRADE EQUILIBRIUM, the price index of type H relative to type L is lower in high-income
H
∂ Pi
∂αi P L
i
< 0. Like before, I will demonstrate this using the North-South example. Analogous to a
13 Note
that the underlying assumption generating pattern 2 is that demand for the highly differentiated type is quality-intensive
whereas demand for the less-differentiated type is quantity-intensive. Wage and patterns of comparative advantage are endogenously
determined.
14 Note that the model predicts incomplete specialization across types. More precisely, high-income countries are net exporters of
the highly-differentiated type (H), and net importers of the less-differentiated type (L). However (as opposed to neoclassical models),
high-wage countries not only produce type L, but export it. This behavior is driven by “national product differentiation,” and is
consistent with micro-level evidence (Schott (2004)).
15 The free entry condition implies that dMii > 0—an increase in product quality induces consumption reallocation from type L to H
∂α
i
and, thus, creates a greater scope for firm entry. Therefore, inequality 7 follows from the fact that
"
α N > α S =⇒ φ α N
A
MNN
1
η
#
1
1
σ L −1 − σ H −1
"
< φ αS
10
A
MSS
1
η
#
1
σ L −1
<
1
1
σ L −1 − σ H −1
1
σ H −1
and α N > α S :
(two-country) Neoclassical trade model, if North and South (countries N and S) engage in trade, the relative
price of type H rises in North and Falls in South. However, due to trade costs, prices are not equalized across
countries. Specifically, the relative price of type H remains lower in North even after trade:
PNH
PNL
!Autarky
PH
PH
< NL < SL <
PN
PS
PSH
!Autarky
PSL
The above result follows from the fact that the price index under trade is a weighted CES average across all
international prices, with more weight put on the domestic price.16
Pattern 4.
All else equal, high-income countries consume relatively more of the highly differentiated, high
markup type H. In the context of the example used thus far, North (N) spends relatively more on type H,
than the South (S):
H
XSH
XN
>
L
XN
XSL
The above result is a direct consequence of pattern 3. The relative price index of type H is lower in the North.
Hence, the relative consumption of type H is higher. This result is novel and emerges despite the fact that
preferences are homothetic and independent of per capita income (existing theories generate consumption
disparity across nations by assuming non-homotheticity). Moreover, this pattern can be generalized as
follows: if type H and L exhibit some degree of substitutability and trade is costly, countries consume
relatively more of the locally competitive type. I refer to this pattern as the Home Production Effect on local
consumption. It is the opposite of the Home Market Effect highlighted by Krugman (1980). The Home Market
Effect states that local demand dictates patterns of local production. The Home Production Effect states that,
when trade is costly, local production determines local consumption.
2.3
The Three Stylized Facts Concerning the Composition of Trade
The four underlying patterns, highlighted in section 2.2, determine the composition of global trade. The
predicted composition collectively explains three stylized facts that are beyond the scope of pure gravity
models. Extensions to gravity models have been proposed to confront each fact individually. However, the
present framework is the first to collectively explain all three facts.
Income per capita × trade-to-GDP ratios.
Rich countries have systematically higher trade-to-GDP ratios
because they produce and consume relatively more of type H. Type H goods is highly-differentiated and
σ −1
subject to a lower effective trade cost: τ jiH
τ σjiL −1 . Let λiiz ≡
Xiiz
Xiz ,
denote share of domestic expenditure
16 Under free trade (τ = 1, ∀i, j), prices equalize in North and South, since they are geographically identical and have access to the
ji
same set of varieties:
!Free Trade
!Free Trade
PSH
PNH
=
PNL
PSL
11
on type z. The trade-to-GDP ratio of country i can be written as
Trade
GDP
i
XH
XL i
i
+ 1 − λiiH
= 1 − λiiL
Xi
Xi
In the South, consumption is dominated by type L:
XSL
XS
≈ 1. The effective trade costs, however, are sizable
in type L entailing negligible import flows
Trade
GDP
S
L
≈0
≈ 1 − λ SS
In the North, consumption is dominated by type H:
L
XN
XN
≈ 1. The effective trade costs, however, are negligi-
ble in type L sizable negligible import flows
Trade
GDP
≈
N
H
1 − λ NN
1+ η1
αN
≈ 1−
1+ η1
∑k αk
α 1+ 1
η
≈ α Nj
, when σ H approaches unity. The relationships above, indicate that the trade-to-GDP of the (low-wage) South is negligible relative to the (high-wage)
North. This result offers an important contribution to the existing literature. Existing studies either exogenously assume that rich countries face lower trade costs (Waugh (2010)), or assume that rich countries
consume more of the highly-tradable types with non-homotheticity (Fieler (2011); Caron et al. (2014)). In
the present model, rich countries specialize in the highly-tradeable type in equilibrium, and also consume
relatively more of the highly-tradable type by choice rather than assumption.
The above result follows from the fact that
XH
jN
H
XNN
Income per capita × the price composition of exports. In the UNIFIED MODEL, two factors contribute to
the higher price of exports from high-income countries. First, high-income countries sell each type of good
(H and L) at a higher equilibrium price. This is due to the higher National Product Quality in high-income
countries:
α N > α S ; τ Ni = τ Si =⇒
H
p Ni
H
p Si
=
p LNi
p LSi
=
wi
>1
wS
This channel corresponds to quality-differentiation, and presents a standard explanation, widely investigated in the literature (Schott (2004); Hallak and Schott (2011)).
The second channel, however, is novel and corresponds to a composition effect. High-income countries
export relatively more of the high-markup type H. That is to say, the North exports relatively more of the
highly-differentiated, high-markup type H, whereas the South exports relatively more of the less-differentiated,
low-markup type L. To show this, not that the average price of exports from country j to i is
p ji =
XH
ji
X ji
X Lji
!
pH
ji
+
X ji
12
!
p Lji ;
j = N, S
XH
L
Ni
Type H exhibits a higher price (p H
>
ji > p ji ), and North (N) sells relatively more of type H ( X
Ni
H
XSi
XSi ),
which
implies: p Ni > p Si . Generally speaking, all else the equal, the share of the highly-differentiated, high-price
type (H) increases in a nation’s export-mix, the higher the National Product Quality. This entails higher export
price from rich countries:17
H
∂p ji
∂ X ji
>
0
=⇒
>0
∂α j X Lji
∂α j
Distance × the price composition of exports According to the gravity relationship trade volumes decrease with bilateral distance. However, when one decomposes volume into quantity and price, exportquantity decreases with distance whereas export-price increases (Bernard, Jensen, Redding, and Schott
(2007)). The observation that export prices increase with distance is generally labeled as THE WASHING TON
A PPLES E FFECT. Surprisingly, despite being one of most-documented and robust patterns of trade,
THE
WASHINGTON A PPLES EFFECT is inconsistent with mainstream gravity models. A unique future of
the unified model is accommodating THE WASHINGTON A PPLES EFFECT. The unified theory offers a novel
explanation for the effect, which (unlike standard explanations) is consistent iceberg trade costs.18 Equation
5 implies that countries export relatively more of the highly-differentiated, high-markup-type (H) when
facing larger iceberg trade costs. More specifically, all else the same, higher trade costs increase the demand
for type H relative to L:
H
∂p ji
∂ X ji
>0
> 0 =⇒
L
∂τ ji X ji
∂τ ji
The above effect is driven by the higher price elasticity of type L. Demand for type L is extremely pricesensitive, which puts the high-cost exporters from distant countries at a disadvantage. As a result, distant
trading partner exchange relatively less of type L, and relatively more of type H.1920
17 For example, consider car exports from Korea and Germany. Suppose there are two types of cars: Luxury (high-markup) cars, and
Economy (low-markup) cars. The present model predicts that Germany sells both types of cars at a higher price point due to its higher
National Product Quality. Additionally, Germany sells relatively more luxury cars and Korea sells relatively more Economy cars. This
additional composition effect contributes to Germany’s higher export prices relative to Korea.
18 The standard explanation is founded on additive trade costs, and is due to Alchian and Allen (1983).
19 Additionally, firms collect higher profits from exporting type H (since type H offers a high markup). Introducing fixed exporting
costs would, therefore, introduce an additional channel that contributes to the “Washington Apples” effect. That is to say, when
incurring fixed costs, high-cost exporters would generate profits only from selling the type that offers high variable profits. Therefore,
firms export only the high-profit and high-price type, H, to faraway locations.
20 A real world example that corresponds to this effect, is car exports from Germany. Germany exports relatively more Luxury
(high-markup) cars to the US and relatively more Economy (low-markup) cars to France.
13
2.4
A Special Case: T HE P URE G RAVITY M ODEL
If both types of goods are identical (σ H = σ L = σ ), the present model reduces to a (one-sector) P URE
GRAVITY MODEL .21
The gravity equation, therefore, becomes
1
α j M jiη τ ji w j
X ji =
1−σ
1
η
∑k∈C αk Mki (τki wk )
1−σ
Xi
(8)
The pure gravity model, characterized by equation 8 , nests THE A RMINGTON MODEL. If firms are perfectly
competitive (η → ∞, and f e = 0), equation 8 reduces to the standard Armington gravity equation:
X ji =
α j τ ji w j
1−σ
∑k∈C αk (τki wk )
1−σ
Xi
Contrary to the unified model, the pure gravity model does not systematically characterize the composition of trade. As a result, the pure gravity model generates three counter-factual patterns: First, in THE
PURE GRAVITY MODEL , high-income countries have have lower trade-to-GDP ratios. High-income countries
have a lower equilibrium effective wage (wσi −1 /αi ), which makes them globally more competitive, but also
less likely to import. Second, in the gravity model, aggregate export flows from all countries are counterfactually subject to the same trade elasticity σ. Third, bilateral distance has no systematic effect on export
prices in the gravity model. In the pure gravity model, countries sell the same type of good at the same f.o.b.
price across all locations. Additionally, in the gravity model, higher income has no compositional effect on
export prices, which is inconsistent with micro-level evidence.22
3
Mapping the Model to Data
This section estimates the structural parameters of the model by fitting it to data on bilateral trade volumes
and per capita income. The UNIFIED MODEL matches the trade volumes remarkably better than the PURE
GRAVITY MODEL .
Additionally, in contrast to the gravity model, the unified model delivers factual out-
of-sample predictions regarding the price of aggregate tradeables. The improved explanatory power of
the unified model stems from matching both the composition and the volume of trade. To quantify the
importance of the composition margin, I perform a counter-factual analysis and estimate the gains from
trade within both models (the unified model and the pure gravity model). The results offer unique insight
into the size and distribution of the gains from trade across dissimilar countries.
21 Another special case rises when η = 1. In this case, National Product Differentiation is eliminated, and the only remaining force
behind trade is comparative advantage across types. Suppose there are a continuum of types, z ∈ [0, 1], and two countries: North (N)
and (South). In that case, the model becomes analogue to DFS. Specifically, let North have a higher national product quality: µ N > µ S .
There exist two cut-offs, σ and σ, such that North is the sole producer (and exporter) of type z if σ z < σ; South is the sole producer
(and exporter) if σ z > σ; and type z is not traded if σ < σ z < σ .
22 If one adopts the Ricardian framework to generate the standard gravity model (e.g. Eaton and Kortum (2002); Fieler (2011)),
the predicted export prices would be counter-factually lower from rich countries. Waugh (2010) proposes asymmetric trade costs to
overcome this counterfactual aspect of the Ricardian gravity model.
14
Data . I use data on bilateral merchandise trade flows in 2000 from the U.N. Comtrade database (Comtrade
(2010)). The data on population and GDP, and the price of tradeables are from the World Bank database
(World-Bank (2012)). My sample consists of the 100 largest economies (in terms of real GDP), which account
for more than 95% of the world trade in 2000. Data corresponding to country pairs–distance, common
official language, and borders–are compiled by Mayer and Zignago (2011).
3.1
Estimation Strategy
The section presents the estimation procedure and addressee identification issues. Equation 2 characterizes
bilateral trade flows for each type of good. I can, therefore, calculate total flows from country j to i as
L
X ji = X H
ji + X ji
(9)
where X H
and X Lji are given by equation 2. Aggregate trade flows are a function of the number of (exporting)
ji firms Mi j i, j∈C , population { Li }i∈C , wage {wi }i∈C , National Product Quality α ≡ {αi }i∈C , iceberg trade
costs T ≡ τ ji j,i∈C , and demand parameters σ L , σ H , and η.23 I take populations Li and wage wi from the
data, solve for the equilibrium number of firms M ji , and estimate αi , τ ji , σ L , σ H , , and η. The procedure is
the following:
i. I parametrize the iceberg trade costs:
τ ji = 1 + κconst + κdist dist ji κborderκlangκagreement
where dist ji is the distance (in thousands of kilometers) between countries j and i. κ border , is one if
countries do not share a border, and an estimated parameter otherwise. For example, if κ border is, say,
0.9, sharing a border reduces trade costs by 10%. Similarly, κAgreement and κlang are one if a country
pair
n do not have a trade agreementoor a common-language, and estimated otherwise. Hereafter, κ ≡
κborder , κlang , κagreement , κconst , κdist denotes to the vector of parameters corresponding to trade costs.
For any given κ, and data on distance, trade agreements and borders, I can construct a matrix of iceberg
trade costs.
ii. Given parameters κ, α, σ L , σ H , η; and data (D) on the wages, population, distance, trade agreements,
common languages and borders I can solve for the mass of firms using the free entry condition (equation 3):
M ji = M ji (κ, α, σ L , σ H , η; D), i, j ∈ C
iii. Given M ≡ { M ji }i, j∈C from the previous step, parameters κ, σ L , σ H , η, and data (D), I resolve for a
vector of National Product Qualities, α, that satisfy the trade balance condition (equation 4):
α j = α j (M, κ, σ L , σ H , η; D),
j∈C
23 The entry cost parameter, f e , governs the scale of entry and is normalized to one. The normalization does not affect trade flows ,
but normalizes the mass of firms in each markets. Putting it differently, f e cannot be identified from trade flows; it can be identified
with data on the number of firms.
15
More precisely, α j is chosen so that the market clearing wage equals data on GDP per capita. To this
end, I solve for the National Product Qualities that ensure balanced trade given the observed countryspecific wages.
iv. For any set of parameters {κ, σ L , σ H , η}, and data D, I iterate over steps 2 and 3 to find an implicit
solution for α j and M ji . Using the implicit solution, I calculate bilateral trade flows X ji from equation
9. Let λ ji =
X ji
Xi
denote the trade share of country j in i. The gravity equation 2 in stochastic form
becomes
λ ji = g(κ, σ L , σ H , η; D) + ε ji
(10)
The above equation indicates that trade shares (λ ji ) are a function of data D and the 8 parameters to be
n
o
estimated κborder , κlang , κagreement , κconst , κdist , σ L , σ H , η , plus the error term ε ji . I estimate equation 2
by minimizing the residual sum of squares (Non-linear Least Squares (NLLS)).24
Here, I explain how
of the eso
n trade flow data allows for the identification
timated parameters: κ, σ L , σ H , η. The vector κ = κborder , κlang , κagreement , κconst , κdist determines the size
Identification of parameters.
of the iceberg trade costs. Specifically, κ1 governs trade-to-GDP across all countries. κ2 and κ3 govern the
effect of bilateral distance on bilateral trade flows. η has a very different effect from iceberg trade costs (and
parameter κ1 , in particular). A higher κ1 reduces trade-to-GDP for all countries, whereas a lower η makes
imports more concentrated. As η approaches 1, countries import each type from the most competitive supplier. As η becomes large, imports are diversified. As in standard gravity models, the magnitude of trade
elasticities (σ H and σ L ) are not jointly identified. However, if I set σ L = 6, I can separately identify σ H . The
relative magnitude of σ L to σ H governs the differential effects of distance on export flows from rich and poor
countries. Parameter is the elasticity of substitution across types, which determines relative spending on
each type. That being the case, governs the size of the Home Production Effect on local consumption, which
gives rise to differences in trade-to-GDP ratios across rich and poor countries.
3.2
Results
The estimation results are presented in table 1. The first column reports the estimation results for the UNI FIED MODEL .
Column two reports estimation results corresponding to the PURE GRAVITY MODEL (described
in section 2.4). Column three reports estimation results for the A RMINGTON MODEL—a special case of the
general pure model. When estimating the unified model I normalize σ L (the elasticity of substitution for the
type L) to 6. When estimating the pure and restricted gravity models, I normalize the elasticity to 4.6: the
average of the estimated σ H and σ L = 6 from the unified model. This way, the trade elasticity in the gravity
model equals the average elasticity in the unified model. This, makes welfare comparison between the two
models plausible.
In both the unified model and the pure gravity model, countries diversify their imports due to National
Product Differentiation. All else equal, in the unified model countries have more incentive to concentrate
24 Anderson and Van Wincoop (2003) and Fieler (2011) also estimated a general equilibrium, multi-country model with NLLS by
simulating the whole economy and solving for endogenous variables. Both papers offer an extensive discussion on the unbiasedness
of the estimator.
16
their imports towards dissimilar partners. This is motivated by comparative advantage across types. Therefore, to match the observed levels of trade diversification, the unified model estimates a greater scope for
National Product Differentiation. In the Armington (restricted gravity) model, the scope for National Product
Differentiation is assumed to be complete, i.e. η → ∞. The only force that prevents countries from fullydiversifying across national varieties is, therefore, the distance effect. That being the case, the Armington
model over-estimates the distance elasticity to match the level of trade diversification observed in the data.
As illustrated in table 1, the unified model offers remarkable improvement over the pure gravity model in
matching trade flows across dissimilar countries. Specifically, the unified model has an R2 that is 43 percent
higher than pure gravity model (table 1) . The improved fit of the unified model comes from matching two
quantitatively important margins: (i) the lower trade-to-GDP ratios of poor countries and (ii) the higher
distance elasticity of exports from poor countries.
Parameters
U NIFIED MODEL
P URE GRAVITY
R ESTRICTED GRAVITY
(A RMINGTON MODEL )
σ L (Normalized)
6
4.6
4.6
σH
3.27
(0.025)
...
...
2.78
(0.011)
...
...
η
3.16
(0.024)
2.63
(0.019)
...
κconst
2.16
(0.017)
1.96
(0.020)
0.96
(0.027)
κdist
0.11
(0.002)
0.19
(0.003)
0.83
(0.006)
κborder
0.57
(0.01)
0.69
(0.013)
0.27
(0.009)
κlang
0.87
(0.007)
0.72
(0.006)
0.37
(0.005)
κagreement
0.71
(0.013)
0.80
(0.013)
1.17
(0.011)
Goodness of fit
(R-squared)
0.43
0.30
0.24
Table 1: Estimation Results – Standard error are reported in parenthesis.
17
Income per capita and trade-to-GDP ratios. Figure 2 displays the relationship between trade-to-GDP and
per capita income in the data, and compares it to the predicted values from the unified model and the
pure gravity model. The gravity model counter-factually predicts that trade-to-GDP drops with income per
capita. This feature of the gravity model makes it inapt for analyzing trade among rich and poor countries—
especially given that trade-to-GDP ratios are the metric that govern the gains from trade. The unified model,
on the other hand, correctly predicts the positive relationship between trade-to-GDP and per capita income.
Note that the unified model delivers this pattern under homothetic preferences, whereas alternative theories
rely on both non-homotheticity and sectoral heterogeneity. That said, the main advantage of the unified
theory over existing alternatives is reconciling higher trade-to-GDP ratios with higher aggregate export
prices in rich countries.
Income per capita and trade elasticities. Figure 3 plots the normalized export flows
X ji
Xi X j
against bilateral
distance dist ji . Exporters are divided in to two groups: North and South. North consists of the richest 50
countries, and South is the poorest 50. In the data, export flows from the North are less sensitive to distance
compared to export flows from the South.25 The unified model correctly captures this patterns. The pure
gravity model, in contrast, counter-factually predicts similar elasticities for North and South. This result
points to another key contribution of this paper. In the unified model trade elasticities are country-specific
and endogenously determined by sectoral specialization. As the estimation results indicate, this feature of the
unified model is qualitatively important.
3.3
Out-of-sample performance
When estimating the model, I exclusively targeted trade volumes. One of the main merits of the unified
model, however, is collectively explaining patterns regarding the price of tradeables. This section demonstrates the unified model’s performance in delivering such out-of-sample patterns.
Income per capita and the price composition of exports. High-income countries export higher price
goods within narrowly defined categories and, therefore, have a higher aggregate export-prices. This observation is partially due to the distinct composition of exports from rich countries (Schott (2004)). Workhorse
gravity models that allow for international productivity differences (e.g. Chaney (2008); Eaton and Kortum
(2002)), counterfactually predict that high-income countries have lower export prices. The Armington gravity model asserts that export prices are determined solely by exporter-wage. None of workhorse gravity
models characterize a systematic relationship between exporter-wage and the composition of trade. In the
unified model, however, export prices are determined jointly by both exporter-wage and the composition of
exports. High-income countries have higher export prices due to: (1) their higher National Product Quality,
25 To formally illustrate the (mediation) effect of income per worker on trade elasticities, I can run a conventional gravity regression
on my sample of 100 countries. Specifically, I allow for interaction between bilateral distance and the exporter’s income per worker:
!
ln X ji =
−3.26 + 0.20 ln w j
(0.15)
(0.02)
ln DIST ji + S j + Mi + ji
where S j and Mi are exporter and importer fixed effects. The robust standard errors are reported in the parenthesis, and the R2 is 0.47.
The results confirm that export flows from rich countries are significantly less sensitive to distance.
18
which is reflected in their higher wage, and (2) their markup-intensive exports. The latter effect is novel and
purely compositional. Figure 4 illustrates the estimated effect of export composition on export prices in the
unified model.
T HE WASHINGTON A PPLES EFFECT.
Countries export higher-price goods to far-way markets. Workhorse
gravity models predict the opposite pattern. Specifically, in heterogeneous gravity models (e.g. Chaney
(2008); Eaton and Kortum (2002)) bilateral distance lowers the f.o.b. price of exports. In homogenous gravity
models (e.g. the Armington model), f.o.b. export prices are the same across all the export destinations. In
the present model, bilateral distance determines the composition of exports. Specifically, when facing higher
trade costs, exporter sell relatively more of the highly-differentiated, high-markup type H. This gives rise
to THE WASHINGTON A PPLES EFFECT in the presence of ad-valorem trade costs. Figure 5 illustrates this
result; the model predicts that aggregate exports prices from Germany and the US significantly increases
with distance to a given market.
4
4.1
The Gains from Trade
The realized gains from trade
In the pure gravity model, when η is sufficiently large, the gains from trade relative to autarky are determined solely by the intensity of trade. Specifically, Let λii denote the share of domestic consumption in the
GDP (one minus trade-to-GDP ratio) of country i. The gains from trade relative to autarky in the gravity
model are given by
− 1e
Gainsi = λii
where e = σ − 1 is the trade elasticity, and common across countries. Arkolakis et al. (2012) show that the
the above equation characterizes the gains from trade in all the workhorse gravity models.
Unlike gravity models, in the unified model the gains from trade not only depend on the intensity of trade,
but also the composition of trade. Specifically, trade elasticities are endogenously determined by the composition of a nations’ imports, and are country-specific. When η is sufficiently large, the gains from trade in
the unified model are given by
−1
− −1 −1 1
− σ −1
σ L −1
H
H
Gainsi = µi λii
+ (1 − µi ) λiiL
−1
σ −1
where µi ≡ αi H
(11)
−1
−1 σ −1
σ −1
/ αi H + αi L
is the autarky share of expenditure on type H in country i. Equation
11 indicates that the gains from trade in the unified model are a weighted average of gains across the two
sectors. The gains form trade are systematically larger in the highly differentiated sector, H. The overall
− 1
gains from trade are, therefore, dominated by the magnitude of the term µi λiiH σ H −1 .
In the unified model the gains from trade are sizable for both rich and poor countries. The gains are sizable
for rich countries as they consume relatively more of type H, which corresponds to a high µi . That being
19
the case, rich countries have higher overall trade-to-GDP ratios, which results in sizable gains. For poor and
remote countries, the gains are sizable as their imports are concentrated on the highly-differentiated type.
This corresponds to a high
λiiH
λiiL
and, therefore, sizable gains.
Importantly, the gravity models systematically understate the gains from trade compared to the unified
model. For rich countries the gravity model systematically under-states the gains, since it counterfactually
asserts that rich countries have lower trade-to-GDP ratios. The gravity model systematically understates
the gains for poor countries as it forces their imports to have the same elasticity as rich countries. In general, the understatement of the gains from trade in gravity models are due to the absence of international
specialization.26 Specifically, gravity models overlook the gains that arise due to systematic differences in
production and consumption composition across countries.27
To quantify the importance of the composition margin, I estimate the gains from trade in the unified model
and compare them with the gains implied by the gravity model. To this end, I compare the factual real wage
with the counter-factual autarky real wage in both models. I solve for the counter-factual real wages by
resolving the general equilibrium with no trade. The estimated gains are presented in figure 6. A summary
of the estimated gains is reported in table 2. Expectedly, the gains from trade are about two-times larger in
the unified model and more unequally distributed across countries. Simply put, the composition of foreign
trade plays a central role in determining both the size and the distribution of the gains across nations.
The average gains from trade
relative to autarky
The coefficient of variation of the
gains (across countries)
T HE UNIFIED MODEL
4.45 (per cent)
1.10
T HE PURE GRAVITY MODEL
2.38 (per cent)
0.84
Table 2: Summary statistics of the estimated gains from trade relative to autarky. The gains from trade correspond to percentage
changes in real wage when moving from the counter-factual autarky equilibrium to the factual trade equilibrium.
4.2
The prospective gains from trade
The previous section estimated the realized gains from trade by comparing the factual real wage with the
autarky real wage. In this section, I ask a more policy-relevant question: how large are the prospective gains
from lowering the trade costs by 10%? To address this question, I first perform a counterfactual analysis to
estimated the prospective gains. I then compare the prospective gains implied by the unified model with
those implied by the pure gravity model. Two systematic patterns emerge:
26 The unified model offers two welfare-improving channels: First, liberalizing trade enables consumers to add more national varieties to their consumption bundle (re-allocation of consumption). This channel prevail in any model with “national product differentiation.” Second, opening to trade enables countries to reallocate production from their less competitive sector to the more competitive
one. As a result of systematic specialization global production becomes more efficient. This additional channel, which corresponds to
systematic specialization, is missing in gravity models and explains the larger gains from trade in the unified model.
27 Surprisingly, Neoclassical trade models focus exclusively on characterizing the composition of foreign trade.
20
i. The unified model predicts that the prospective gains from trade are substantially larger for poor countries. The gravity model predicts a weak relationship between income per capita and the prospective
gains. (figure 7).
ii. The gravity model systematically understates the prospective gains for geographically remote countries (figure 8).
The above patterns indicate that at the prevailing levels of globalization, poor and remote countries are
the main beneficiaries from further globalization. Given the existing impediments to trade, poor and remote countries are predominantly importing the highly-differentiated type. Foreign varieties of the highlydifferentiated type are not easily substituted with domestic counter-parts. That being the case, liberalizing
trade furthermore allows these countries to import more of the highly-differentiated type, which would improve their welfare dramatically. In the gravity model, such patterns are absent since all countries import
the same type of good. This result could have important applications for a vibrant literature that studies
trade negotiation between dissimilar countries.
5
Conclusion
This paper develops a unified framework that combines within-product trade in differentiated goods with
trade resulting from across-product specialization. The driving force behind across-product specialization
is novel and collectively delivers three principle facts about the composition of foreign trade. While these
principle facts have been approached individually by the previous literature, the unified framework is the
first to collectively explains all three facts, while retaining the standard assumptions that ensure tractability.
Specifically, the unified theory (i) explains the effect of income per capita on the composition of imports and
exports assuming standard homothetic preferences, and (ii) explains the effect of distance on the composition of trade assuming standard iceberg trade costs. That being the case, the unified model offers a tractable
framework that, unlike standard gravity models, permits the analysis of trade between vastly dissimilar
countries (e.g. trade between developed and developing countries).
I estimate the unified model to study the welfare consequences of trade across rich and poor countries. Allowing for systematic across-product specialization magnifies the gains from trade for all countries. Specifically, the gains from trade in the unified model are two-times larger than a standard gravity model that
only permits within-product trade. Moreover, the prospective gains from further liberalization of trade
depend crucially on the characteristics of a country and the composition of its imports. Relative to the
standard gravity model, the prospective gains from trade in the unified model are pro-poor and remote
countries. This finding could have substantial implications for a vibrant literature that studies international
trade agreements.
Two aspects of the unified model merit further research. In the unified model National Product Quality determines the composition a nation’s trade. The model, however, is mute on the determinants of National
Product Quality. One could extend the unified model so that National Product Quality is endogenously determined by the capital- or skill-abundance of a country. Second, the unified model can be extended to allow
21
for intermediate trade and multi-national production. Such extensions could provide a tractable framework for studying those phenomena across dissimilar countries. Existing models of intermediate trade and
multi-national production are generally implemented within standard gravity frameworks and, therefore,
miss out on principal moments when applied to trade between rich and poor countries.
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24
TZA
UGA
LUX
−5
0
USA
JPN
ISL
CHE
QAT
NOR
DNK
HKG
IRL
AUT
DEU
BEL
SWE
GBR
FRA
NLD
CAN
SGP
FIN
ITA
ARE
AUS
ISR
KWT
ESP
TWN
CYP
BHR
KOR
PRTNZL
GRC
SVN
ARG
SAU
URY
OMN
LBY
TTO
MEX
CHL
CZE
BRA VEN
POL
HUN
LBN
CRI
HRV
BWA
MYS
SVK
LVA
ZAF
TUR
LTU
JAM
DOM
PER
COL
THA
SLV
TUN
PRY RUS
DZA
JOR
IRN
ROM
BGR
EGY
ECU
BLR
KAZ
CHN
BOL
MAR
SYR
YUG
PHL
IDN
LKA
CMR
AGO
UKR
ZWE
IND
PAK
CIV
UZB
YEM
VNM
KEN
BGD
NGA
SDN
−10
Log( relative production of type H )
0
−2
CMR
AGO
CIVUKR
ZWE
UZB
YEM
PAK
IND
KEN
VNM
NGA
SDN
BGD
−4
Log( GDP per worker (US=1) )
Pattern 2
LUX
NORJPN
USA
CHE
ISL
DNK
QAT
SWE
HKG
IRL
NLD
AUT
GBR
SGP
DEU
FIN
BEL
CAN
ARE
FRA
AUS
ISR ITA
KWT
TWN
ESP
CYPNZL
BHR
PRTKOR
GRC
SVN
OMN SAU
ARG
LBY
URY
TTO
CZEMEX
CHL
VEN
HUN
LBN
POL
CRI
HRV
MYS BRA
SVK
BWA
LVA
LTU
JAM
TUR
ZAF
DOM
SLV
PER
COL
TUN
THA
DZA
JOR
RUS
ROM
BGR
IRN
EGY
PRY
ECU
BLR
KAZ
MAR
SYR
YUG
BOL
PHL
LKAIDN CHN
5
Pattern 1
TZA
UGA
ETH
−6
−15
ETH
−20
−10
0
−6
−2
0
Pattern3
Pattern 4
.5
SAU BHR
NZL
SVN CYP
GRC
KOR
KWT
PRT
TWN
ISR
ARE
SGP QAT
ISL
ESP
AUSHKG
FIN
IRL
AUT
LUX
ITABEL
SWE
NLD
DNK
NOR
FRA
GBR
CAN
CHE
DEU
JPN
0
DEU CHE
CAN
GBR
FRA
NOR
DNK
NLD
SWE
ITABEL
LUX
AUT
IRL
FIN
AUSHKG
−1
1
MEX
JPN
MEX
−2
CZE
USA
ETH
−3
1.5
ETH
PER
IDN BOL PRY
COL ZAF
ECU THA
IND
BGD
BRA CHL
VNM
CHN
AGO LKA
ZWE
BWA
URY
PHL
SLV
PAK
IRN
KAZ
TZA NGA
CRI
DOM
KEN UZB
UGA SDN
CIV
TUR MYS VEN
YEM
EGY
CMR
ROM
UKR
SYR
MAR RUS
DZA
JAM
JOR
YUGBLRBGR
LTU
TUN
LVAHRV
LBY
TTO
LBN
ARG
HUN
SVKPOL
OMN
Log( relative consumption of type H )
1
Log( GDP per worker (US=1) )
0
Log( relative price index of type H )
−4
Log( National Product Quality )
2
−30
USA
−6
−4
−2
0
−6
Log( GDP per worker (US=1) )
ESP
ISL
SGP QAT
ARE
ISR
TWN
PRT
KWT
KOR
GRC
SVN CYP
NZL
SAU BHR
CZE
OMN
POL
SVKLBN
HUN TTO
ARG
LBY
HRV
LVA
TUN
LTU
YUGBLRBGR
JOR
RUS
JAM
DZA
MAR ROM
SYR
UKR
CMR
EGY
YEM
TUR MYS VEN
CIV
UGA SDN
KEN UZB
DOM
CRI
TZA NGA
PAK
PHLKAZ IRN SLV
URY
BWA
ZWE
AGO LKA
CHN
VNM
BRA CHL
BGD IND
ECU THA
COL ZAF
IDN BOL PRY
PER
−4
−2
Log( GDP per worker (US=1) )
Figure 1: The four underlying patterns that characterize the global economy: (i) countries with high national product quality, pay
higher wages; (ii) high-wage countries relatively more competitive in production of type H, and specialize in the production of type
H (type H is the highly differentiated, high markup type); (iii) due to trade costs, the relative price of type H is lower in
high-income countries; (vi) high-income countries spend relatively more on type H.
25
0
Data
SGP
0
MYS
PHL BLR
AGO
BEL
IRL
HUN
THA
CZE
TWN
SVNBHR
ARE
NLD
LUX
QAT
OMN
SAU
KWT CAN
CHE
SWE
AUT
LKA
KOR
FIN
ROM
IDN
NGA YEM
HRV MEX
ECU JOR
MAR
CIV
PRT
DOM JAM
YUG
NZL ISR DEU DNK
ISL NOR
RUS
CHN
CYP
LBY
DZA
CHL
SYRPRY
BWAPOL
ZAF
FRA
IRN
ESP
GBR
SLV TUR LBN
ZWE
ITA
CMR
VEN
KEN
GRC
AUS
BOL
COL
BGD
URY
SDN PAK
UZB
PER
VNM
−1
UKR
−2
Log( trade−to−GDP ratio )
HKG
SVK
ETH
BGR
TUN
KAZ
LTU CRI
LVA
TTO
TZA
UGA
EGY
BRA
USA
JPN
ARG
−3
IND
−6
−4
−2
0
Log( GDP per worker: US=1 )
0
The Unified model
−1
ISL
QAT
IRL
BEL
AUT DNK
CHE
FIN
NOR
CAN
HKG
NLD
SWE
SGP
−2
PRY
ETH
UGA
JOR
YUGBLRBGR
BOL
SYR
TUN
KAZ
SDN
KENYEM
UKR
ZWE
CMR
TZA
−3
Log( trade−to−GDP )
LUX
ARE
URY SVN CYP KWTFRA
BHR
PRT
ISR DEU
LVA
MEX
LTU
GRC ESP ITA
SVK
CZE OMN
MYS
LBN
HRV
BWA
GBR
LBY
HUN TTO
JAM POL
MAR ROM
DZA
RUS
ECU
EGY
DOM
SLV
CRI
IRN COL
PER TUR
VEN
THA
CHL
UZB
VNM PAK
CIV
AGO
NGA
BGD
LKAPHL
CHN
IDN
IND
SAU
ARG
NZL
TWN
KOR
ZAF
AUS
USA
BRA
−4
JPN
−6
−4
−2
0
Log( GDP per worker (US=1) )
0
The Pure Gravity Model
−2
ETH
PRY
JOR
BEL
YUG
LVA
TUN
BOL
LTU
LBN URY SVNBHR
YEM
IRLQAT
BLRBGR
AUT
CMR
SYR
CYP
JAM
SVK
BWA
ZWE
HRV
TTO OMN
KEN
ISLCHE
LBY
TZA
MAR
UKR
ECU DZA
KAZ
FIN
CZE
KWT
CAN
CIV
HUN
SLV
DNK
ROM
UZB
PAK
CRI
PRT
DOM
NLD
ARE
GRC
AGO
MYS
SWE
EGY
SGP
VNM
PER
NGA
POL
ISRFRA
COL
HKG
LKA
DEU
SAU
CHL
NOR
PHL
BGD
ESP
IRN
VEN
RUS
TUR
ITA
ARG
GBR
THA
MEX
IND
UGA
SDN
ZAF
IDN
−4
Log( trade−to−GDP )
LUX
CHN
TWN
NZL
BRA
KOR
USA
AUS
−6
JPN
−6
−4
−2
0
Log( GDP per worker (US=1) )
Figure 2: Trade-to-GDP ratio increases with GDP per capita in the data. The unified model captures this pattern, whereas the
gravity model does not.
26
Data
−10
−15
X
ln X i Xi j j
−20
−25
North
South
South
North
−30
−35
−3
−2
−1
0
1
2
3
1
2
3
1
2
3
ln( d i s t i j)
The unified model
−12
−14
−18
X
ln X i Xi j j
−16
−20
−22
North
South
South
North
−24
−26
−3
−2
−1
0
ln( d i s t i j)
The Gravity model
−15
−20
X
ln X i Xi j j
−25
−30
−35
North
South
South
North
−40
−45
−3
−2
−1
0
ln( d i s t i j)
X
Figure 3: Normalized export flows ( X j Xji i ) from the North (the richest 50 countries) are less elastic to distance than export flows of
the South (the poorest 50 countries). The unified model captures this pattern, whereas the gravity model does not.
27
1.14
1.12
CYP
CAN
BEL
FRA
ITADEU
BHR
KOR
1.1
ESP
PRT
ARG GRC
SVN
OMN
SAU
1.08
URY
TTO
CHL
VEN
LBY
CRI CZE
HUNMEX
BRA
LBN
BWA
POL
HRV
ZAF
JAM
SVK
LVA
LTUMYS
TUR
DOM
SLV
PER
COL
THA
TUN
DZA
ROM
IRN
JOR
ECU
BGR
PRY
EGY
RUS
KAZ
BLR
BOL
MAR
PHL
YUG
SYR
LKA
CHN
IDN
AGO
CMR
ZWE
CIV
UKR
UZB
PAK
YEM
IND
NGA
VNM
KEN
UGA
TZA BGD
SDN
ETH
1.06
Export price (net of wage and trade cost)
JPN
ISL NOR
QAT
LUX
AUSHKG
SGP CHE
USA
ARE DNK
ISR SWE
IRL
NZL KWT GBR
TWN
NLD
FIN
AUT
−6
−4
−2
0
Log(GDP per worker (US=1) )
Figure 4: The unified model predicts that export prices (net of trade costs and wage) strongly increase with GDP per capita. The
above figure displays the compositional effect of GDP per capita on export prices in the (estimated) unified model.
Germany’s exports
.76
1.14
U.S. exports
QAT
NOR
1.13
LUX
GBR
CZE
QAT
NOR
SWE FIN
FRA
AUS
NZL
IRL
ISL
NLD
CHE
BEL
AUT
DNK
.72
ISL
BRA
IND CHN
IDN
ARG
ZAF
CHL
THA
COL
VEN
MEX
PPER
HL
KOR
MYS
PAK BGD
URY
TUR
VNM
RUS
TWN
ECU
PRY
EGY IRNSAU
NGAUSA DOM
LKA
C
RIBOL
SLV
JPN
KAZ KEN
DZA MAR
ZWE
BWA
AGO
TZA
ROM
HKG
UZB
CAN
UKR LBY
SGP
SDN
HUN
CIV
CMR
JAM
SYR
ETH
YEM
UGA
OMN
TTO
TUN
LBN
BGR
ESP
ISR
BLR
HRV
SVK
POLITALTU
JOR
KWTARE
GRC
YUG
LVA
PRT
SVN
BHR
CYP
.75
MEX
TTO
.74
JAM
Aggregate price of German exports
1.135
CRI
SLV
IRL
1.125
Aggregate price of US exports
DOM
.73
CHN
BRA
IDN
IND
THA
ARGIRNKOR
ZAF
TUR
MYS
RUS
CHL
PHL
VNM
EGYSAU
PAKBGD
PERPOL
LKA
URY KAZ TWN
DZA
NGA
ESP
ROM
ITA
JPN
AUS
UKR
GRC
PRY
DEU
UZB
HUN
SDN
AGO
MAR
BOL
ECU FRA
CZELBY SYR YEM
KEN
OMN
NZL
ZWE
LBN
TZA
TUN
PRT
BWA
CIV
BGR
HRV
BLR
GBR SVK
HKG SGP
ETH
JOR
LTU
CMR
UGA
ARE
YUG ISR
KWT
NLDLVA
AUT
BEL SVN
BHR
SWE
FIN
CYP
CHE
DNK
VEN COL
LUX
CAN
6
7
8
9
10
5
6
7
8
Log( distance to Germany )
Log( distance to the US )
Figure 5: The unified model delivers the “Washington Apples” effect: export prices (net of trade costs) increase with bilateral
distance.
28
9
10
JPN
USA
BRA
ARG
AUS
KOR
CHL
ZAF
TWN
VEN
NZL
IDN
PER
COL
THA
IND
CHN
LKA
BGD
CRI
ECU
PHL
SAU
IRN
AGO
TUR
SLV
VNM
DOM
NGA
PAK
BWA
TZA
ZWE
EGY
CIV
GBR
UZB
BOL
KAZ
KEN
LBY
MYS
ROM
CMR
YEM
DZA
RUS
MAR
URY
POL
TTO
JAM
UKR
OMN
ETH
ISR
HUN
UGA
SDN
ITA
SYR
HRV
LBN
TUN
ESP
BGR
SGP
BLR
LTU
DEU
ARE
YUG
KWT
LVA
HKG
GRC
JOR
SVK
CZE
BHR
PRY
FRA
PRT
CYP
SVN
MEX
NOR
SWE
NLD
FIN
CAN
CHE
DNK
AUT
QAT
BEL
IRL
ISL
LUX
Th e u n ified m odel
Th e gen er a l gr a vit y m odel
0
10
20
30
40
50
Th e ga in s fr om t r a de r ela t ive t o a u t a r ky
Figure 6: The estimated gains from trade relative to autarky. The gains from trade are both systematically larger and more
dispersed in UNIFIED MODEL relative to the PURE GRAVITY MODEL.
29
The Unified model
PRY
JOR
CZE
YUGBLR
JAM
LVA POL
LTU
SYR BGRTUN
UGA
SVK
BOL
YEMUKR
LBN
HRV
DZA
MAR ROM
CMR
PRT
KEN
KAZEGY
HUN
SVN
RUS DOM
UZB
ZWE
TZA NGA PAK
TTO
SLV TUR
URY
PHL ECU
VNM CIV
GRC
MYS
BWA
IRN COL
CRI
BGDIND AGO LKA
LBY
THA
CHN
OMN
PER
IDN
ESP
ZAF
VEN
SAU
BRA CHL
SDN
5
ETH
ARG
0
The prospective gains from trade
10
MEX
CAN
BEL
IRL ISL
AUT
QAT
FIN DNK
ITAFRA
NLD
DEU
KOR
CHE
NZL
BHR
GBR
TWN
CYP
SWE
AUS
JPN
USA
ISR
KWT
NOR
ARE
−5
SGP
HKG
−6
−4
−2
0
Log( GDP per worker (US=1) )
15
The Pure Gravity Model
10
JOR
BEL
BOL
YUG
UGA
SDN
5
ETH
TZA
0
The prospective gains from trade
PRY
−6
YEM
CMR
ZWE
TUN
BLRBGR
SYR
LVA
LTU
JAM
IRL
URY
LBN
BWA
SVK
HRV
TTO
SVNBHR
CYP
AUTQAT
OMN
ISLCHE
CAN
ECU
KAZ
LBY
UKR
MAR
FIN
CZE
SLV
DZA
KWT
PAK
CRI
DNK
CIV
UZB
PRT
ROM DOM
MYSHUN
VNM
SGP
GRC
HKG
AGO
PER
ARE
NLD
SWE
COL
NGA
POL
ISRFRA
LKAPHL
EGY
CHL
BGD
NOR
VEN
ESP
MEXARG
IRN
RUS
SAUKORNZL
THA
TUR
TWN ITA
IND
DEU
IDN
GBR USA
CHN
ZAF
BRA
AUS
JPN
KEN
−4
−2
0
Log( GDP per worker (US=1) )
Figure 7: The prospective gains from lowering trade cost by 10% versus GDP per worker. In the UNIFIED MODEL the prospective
gains increase strongly as GDP per worker decreases. This patterns is substantially weaker in the PURE GRAVITY MODEL.
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30
ZAF
20
CHN
MEX
IDN
IND
10
RUS
TUR
IRN
THA
KOR
POL
SAU
EGY
PHL
NGA
BGD
VEN
LKA
COL
FRA
AGO
PER
PRT
HUN GRCGBR
CZE ROM
VNM
MYS
UZB PAK
DOM
DZA
CIV
CAN
UKR
MAR
CRI
SLV
KAZ
KEN TZA
HRV BGR LBY NLDISL
ECUTWN
SYR
SVK
BLR
JAM
SDN
ZWE
LUX
CMR
LBN
ETH
LTU
TTO
YEM
DNK
TUN
OMN
AUT
YUG
UGA
LVASVN
PRY
BWA
BEL
JOR QAT BOL
URY
SWE FIN IRL
CHE
BHR CYP
ITAESP
DEU
0
The prospective gains from trade (unified/gravity)
BRA
0
5
CHL
NZL
ARG
10
Remoteness
The prospective gains in the unified model
Figure 8: The prospective gains fin the gravity model × remoteness. The prospective gains correspond to welfare improvements from
lowering trade costs by 10%. The PURE GRAVITY MODEL systematically understates the prospective gains for remote countries.
The y-axis corresponds to the prospective gains from the UNIFIED MODEL relative to the PURE GRAVITY MODEL. The x-axis
corresponds to remoteness, which is calculated as weighted distance (in thousands of kilometers) from trading partners.
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