Remodeling Trade Elasticities: Price and Quality in the

Global Economy

Ahmad Lashkaripour⇤

Abstract

I develop a novel approach of modeling trade elasticities and quality to address two well-established

facts about prices in trade data: (i) higher trade costs increase the price of traded goods, and (ii) high-wage coun-

tries trade (export) more despite charging higher prices. Leading trade theories, despite their massive success in

explaining trade volumes, fail to explain either of these price facts and many variants have been proposed

to account for each fact separately. I propose an extension of Krugman [1980] that accounts for both facts

in a unified framework, while preserving the tractability of conventional gravity models. Since my model

matches a richer set of facts, it also offers a richer set of implications regarding the scale and distribution

of the gains from trade across consumers. To evaluate my assumptions on quality and elasticity I fit the

model to highly disaggregated U.S. import data. To this end, I estimate trade elasticities for around four

hundred SITC industries. Then, I calibrate my model to Aggregate trade flows and demonstrate its merits,

relative to conventional gravity models, in terms of matching price data. My estimation results indicate

that within each industry, trade (i.e. demand) elasticities are lower in high-quality HS10 product codes.

Moreover, the estimated micro-elasticity between varieties manufactured in the same country is 1.3 times

higher than the cross-country macro-elasticity. I argue that disregarding the higher within-country micro-

elasticity, compared to the cross-country macro-elasticity, would result in underestimating trade costs by

38%. Finally, my counterfactual experiment suggests that the gains from variety in my model can be very

significant because trade increases the number varieties mostly in high-quality product categories, where

the elasticity of substitution is fairly low.

⇤I am grateful to my advisors Jonathan Eaton and Stephen Yeaple for their guidance, encouragement, and support. I am alsograteful to Jim Tybout for encouragement and various discussions on the topic. I wish to thank Russell Cooper, Kala Krishna, PeterNewberry, and Paul Grieco for helpful comments and suggestions. All errors are my own. Correspondence: azl153@psu.edu.

1

1 Introduction

Trade theory has been massively successful in explaining trade volumes. The volume of trade depends on

the number of goods traded, the quantity of each good that is shipped, and the prices they are sold for.

However, leading theories of international trade yield predictions about the composition of trade (quan-

tity, price and variety) which are inconsistent with empirical findings. Prices, in particular, are one key

component of trade flows that theories of international trade have not come to grips with.

It is well established in the empirical literature that exporters “ship out the good apples”. The higher the

trade costs a country/firm faces the higher the free on board (f.o.b) price1 of goods it exports to a foreign

market. Leading trade models (in their standard setting), all predict that higher trade costs will lower the

f.o.b price of exported goods2, which is at odds with empirical evidence. In these models it is usually

assumed that one exports if the variety they produce is the cheapest in the international market. In the

presence of high trade costs exporters could only export their cheapest products, so with the shipping cost

added up to the final price they would still remain competitive.

One other well documented fact is that high-wage countries export/import more than low-wage coun-

tries even though they do not charge lower prices.3 Again, his is at odds with the conventional practice in

trade literature; to match bilateral trade volumes, assuming countries import the cheapest variety, there is,

in the global market. Given that high wage countries export more (as seen in the data), conventional gravity

models would generate prices of traded goods that are lower (on average) when coming from high-wage

countries.4

Many variants of the mainstream trade models have been specifically developed to account for each one

of the above two price facts separately.5 However, what is missing is a unified framework that incorporates

both of these facts about the price of traded goods, without losing the explanatory power and tractability

of conventional gravity models when it comes to explaining bilateral trade volumes.

In this paper I develop a gravity model that accounts for both the effect of trade costs on the price of

traded goods, and the large trade share of high wage countries exporting expensive products. I argue that

digging deeper into the composition of trade and building a more comprehensive model of international

1Free on board price2See Baldwin and Harrigan [2011] for an extensive survey of literature on this matter.3Waugh [2010] provides a complete description of this fact.4In an Armington model countries that produce more appealing products (as determined by the CES weights) have higher wages

but have a similar trade share to that of low wage countries. In the Ricardian–Eaton and Kortum [2002]–model high wage countriestrade more but also charge lower prices.

5The fact that high wage countries trade more has been addressed by Fieler [2011] and Waugh [2010] among others. Both papersare variants of the Eaton and Kortum [2002] model. Fieler [2011] assumes a two-sector world with non-homothetic preferences,while Waugh [2010] assumes poor countries face higher export costs. The effect of trade costs on the price of traded goods hasbeen documented by Baldwin and Harrigan [2011]and Hummels and Skiba [2004]. Hummels and Skiba [2004] explain the fact withadditive trade costs or the so-called Alchian-Allen hypothesis. Baldwin and Harrigan [2011] makes the theoretical assumption thathigher prices reflect a more than proportional higher quality in a Melitz model.

2

trade would strongly enhance our understanding of both the scale and the distribution (across consumers)

of the the gains from trade. I also argue that relaxing the conventional structures imposed on trade elastici-

ties would result in better estimates of unobserved trade costs.

My point of departure is a multi country monopolistic competition model of trade with homogeneous

firms, as developed by Krugman [1980]. I depart from this baseline model along three dimensions: (1) I

allow for multi-product firms, (2) I incorporate quality into my CES preferences, and (3) I relax the assump-

tion that elasticities are the same across all varieties. A variety in my framework is characterized by the

HS10 product code it belongs to, the country it comes from and the firm that produces it. I define quality to

be any tangible or intangible attribute of a good that increases all consumers valuation of it. Quality in my

model appears as the weight consumers put on certain varieties in their CES preferences.

In my framework quality has two components: a country-level component (macro-quality) and an HS10-

level component (micro-quality). Consumers attach higher value (in terms of utils) to varieties from certain

countries, while some HS10 codes are also more appealing to consumers than others. The elasticity of

substitution is assumed to be lower, i.e. demand is less price sensitive, in high-quality HS10 codes. I also

assume that varieties manufactured by firms from the same country are closer substitutes than varieties

manufactured by firms in different countries.

Within my theoretical framework I show that high-quality HS10 codes are traded more intensively.

Furthermore, as trade costs become higher, export activity shifts more and more towards high-quality HS10

codes. I also show that countries which produce the highest quality varieties have higher equilibrium

wages and charge a higher price for their varieties. Yet, their varieties are the cheaper (compared to low-

wage countries) for every unit of quality they deliver. Therefore, high-wage (high-quality) countries have

absolute advantage in global markets.

The intuition behind my theoretical findings is the following. Since demand is less price sensitive in

high-quality HS10 codes, firms charge a higher markup for varieties sold in those product codes. Besides,

exporters who face high shipping costs will charge proportionately higher c.i.f prices for their products,

but the higher price will effect demand, for their varieties, to a lesser extent in high quality product codes.

These two effects together, and the fact that firms incur a fixed overhead cost for exporting in each HS10

code, make high-quality product codes more enticing to exporters.

Countries manufacturing higher quality products will export more because they charge a lower price

for every unit of quality, i.e. they have absolute advantage in global markets. These countries also have

higher market clearing wages and import more. If firms enter the market of wealthy countries, the scale

of sales will be larger. As a result, more foreign firms can overcome the fixed cost and break through into

wealthy markets. Foreign firms who break it through, specialize in high-quality HS10 codes, and the more

3

foreign varieties enter the market, the more demand is redistributed from low-quality product codes to

high-quality product codes, so consumers can benefit the most from their “love of variety”. That being the

case, not only high-wage countries spend a larger share of their income on high-quality HS10 codes, but

they also import relatively more foreign varieties.

Unlike Melitz [2003], in my model trade does not have an anti-variety effect at the aggregate level.

If one looks at the big picture, the overall number of varieties always rises when a country opens up to

trade. However at the HS10 product level the story can be very different. In high-quality HS10 codes

the market will experience a dramatic increase in the number of varieties, while in the low-quality HS10

codes the number of varieties will always fall. The anti-variety effects of trade in low-quality product codes

results from the fact that multi-product exporters crowd out multi-product domestic firms. However, multi-

product exporters, unlike domestic firms, will not sell in the lowest quality HS10 codes because generated

profits in low-quality codes are not enough to overcome the overhead cost. In a representative consumer

model this effect does not bear any welfare implication. When demand has a logit structure which is

isomorphic to the CES demand, however, this finding implies asymmetric gains from trade. The consumers

of high-quality products, i.e. HS10 codes, gain substantially while the consumers of low-quality products

lose from trade.

After developing a theoretical model that is consistent with empirical facts on the price of traded goods,

I take my model to data. First, I estimate demand elasticities (i.e. trade elasticities) separately for 390

5-digit SITC5 industries, using U.S. import data disaggregated at the 10-digit HS10 product level. When

estimating the gravity equation using aggregate trade data, one has to assume demand elasticities are the

same across all products to identify unobserved trade costs. Since the U.S. trade data documents price,

freight, and tariff data, it allows me to identify elasticities without imposing that restriction. My micro-

gravity estimation suggests that the elasticity of substitution is lower for high-quality HS10 codes. In the

average industry, the estimated elasticity is 8.9 for the lowest quality HS10 code, while it is only 0.34 for the

highest quality code. I also find that the elasticity of substitution is 1.3 times higher for varieties that are

manufactured in the same country.

In the second stage of my empirical inquiry, I use the demand elasticities I estimated in the previous

stage to calibrate my model to global bilateral trade volume data. My calibration exercise yields a couple

of interesting findings. First, I find that my calibrated model generates trade costs that are 38% larger

than the baseline model which assumes the same elasticity across all products. The result is not surprising

because of the following; when one enforces foreign and domestic products to have the same elasticity of

substitution, in order to match the high trade shares in data, they will generate lower trade costs. In a

world where foreign varieties are assumed to be less substitutable, the same trade shares could be matched

4

with higher trade costs. Second, my calibrated model generates country-level (macro) qualities that confirm

my theoretical findings; high-wage countries produce higher quality varieties such that their varieties are

cheaper for every unit of quality they deliver. For example, in the benchmark year, 2000, wages in the

U.S. were around 37 times higher than China, but when I adjust wages/prices for the quality of varieties

produced by both countries, the U.S. has a quality adjusted wage/price that is 10 times lower. Third,

I show that my model matches unit value data (of traded goods) better than the baseline model which

restricts elasticity to be the same across all product groups.

Within my framework, I then ask what kind of trade policy will benefit a country the most? I com-

pare two different scenarios: (1) a 50% reduction in variable trade costs/tariffs, and (2) removing the fixed

overhead cost of exporting. My counterfactual analysis implies that the number of varieties rises and the

purchasing power of consumers rises for all product codes when fixed costs are removed, while lowering

variable trade costs has an anti-variety effect in the low-quality product codes. In a world where the CES-

type demand is generated by discrete choice logit preferences, my results indicate asymmetric gains from

lowering variable trade costs–with consumers of low-quality product codes experiencing losses.

Explaining unit values (prices) in trade data has been an active area of ongoing research. The main

competitor to my model in this area is the Alchian-Allen hypothesis which assumes trade costs are additive.

In an earlier piece of work–Lashkaripour [2013]– I use highly disaggregated data to show that trade costs

resemble iceberg costs rather than additive costs. I argue that the results produced by Hummels and Skiba

[2004], on trade costs being additive, are driven by the fact that they misspecify unit values. An advantage

of my framework over the Alchian-Allen hypothesis is that by assuming iceberg trade costs, I stay in line

with the mainstream literature and generates tractable closed form results; something that models with

additive trade costs fail to produce.

The existing literature that focuses on prices in international trade (e.g. Baldwin and Harrigan [2011],

Hummels and Skiba [2004], Waugh [2010], Hallak [2006], etc.), generate results that are consistent with

facts on either “the effect of trade costs on price of traded goods” or the fact that “high-wage (high-price)

countries export more”, but not both. The main advantage of my framework over the existing studies

is that it naturally explains both facts in one unified framework. Also, unlike the existing literature on

quality/price I do not impose systematic differences in demand (nor trade costs) across countries to achieve

non-homothiticity at the cost of loosing tractability. In my model high-wage countries buy higher qualities,

due to love of variety, even though preferences are assumed to be homothetic.

My paper also adds to another body of literature that imposes structure on demand elasticities to explain

trade patterns. My model is particularly related to Fajgelbaum et al. [2011] and Coibion et al. [2007]. Both

of these papers claim that high-quality varieties tend to have more attributes along which they can be

5

Figure 1: Price elasticity of demand for various car products in the U.S. (source: Berry et al. [1995]).

differentiated from other varieties of the same quality. They, therefore, assume demand elasticity is lower

for high-quality products. The first disadvantage with these models is that they apply their assumption

to an ad-hoc non-CES demand system. The second disadvantage is that they do not estimate the demand

elasticities explicitly. Not only my model incorporates the assumption that elasticity is lower in higher

qualities within a Dixit-Stiglitz framework, but I also estimate these elasticities.

My paper is also related to a rich body of empirical literature that estimates demand elasticities. In the

IO literature estimating demand elasticities for individual products, using highly disaggregated consumer

data has always been a topic of interest. Theses researches need not to impose any restriction on elasticities

since they usually have rich enough market data to back out elasticities for individual varieties. However,

the finding that high quality products have a lower elasticity implicitly exists in their finding. Berry et al.

[1995] for instance, estimate demand elasticities for the U.S. car market, and their findings (figure 1) suggest

a low elasticity for expensive luxury cars and a high elasticity for cheap economy cars.

In the trade literature measuring demand (i.e. trade) elasticities has also been a vibrant area of research.

Feenstra et al. [2012] and Broda and Weinstein [2006] are examples of studies that move away from the

standard assumption that elasticities are the same across all varieties. My paper is closest to Broda and

Weinstein [2006] since they also estimate a separate elasticity for each HS10 product code. My paper adds

to their findings in two ways. First, unlike Broda and Weinstein [2006] who look at only within-HS10

6

code variations in data, I also look at across-HS10 code variations which allows me to estimate systematic

quality differences between product codes. This, in turn, allows me to identify the dependence of demand

elasticities on the estimated qualities. Second, I allow for varieties manufactured in the same country to

have a lower elasticity, while Broda and Weinstein [2006] impose the same elasticity for all products (and

across all countries) in the same HS10 code. This restriction is fairly important because assuming the same

within source country elasticity can result in under-estimating trade costs when one takes the model to

aggregate data.

2 Theory

In this section I will introduce the main ingredients of my GE model. There are N asymmetric countries

that produce differentiated goods using only labor. Country i is populated with a mass Li of identical

agents, each endowed with one unit of labor. Firms in each country are multi-product and homogenous.

Geography is reflected in two kinds of barriers between countries: variable iceberg trade costs, and fixed

costs of exporting in each product category. Product categories differ in how appealing they are to the con-

sumers and how differentiated they are. Countries differ in endowments of labor and the quality/appeal

of their products. I assume a market structure characterized by monopolistic competition. I start with the

description of the commodity space and demand. Then, I turn to supply and the problem of the firm.

2.1 Commodity Space

I will refer to the final good an individual consumes as variety. A variety in my framework is characterized

by the category it belongs to, the country it was manufactured in, and the firm that manufactured it. A

product category is a 10-digit code from the HS10 product classification. For example, a 40” Samsung

TV is a variety that falls in the HS10 code that contains 40” TVs, is manufactured by Samsung in Korea.

Mathematically, the commodity space can be expressed as

⌅ = F|{z}

Manufacturing frim

⇥ C|{z}

Country

⇥ H|{z}

HS10 code

where F is the set of firms, C is the set of countries, and H = [0, ¯H] is a continuum of HS10 categories.

Variety fch will be a commodity that belongs to HS10 (product) code h, and is produced by firm f in

country c. A simple illustration of the commodity space is provided in figure 2.

7

0

¯H

h

County i

Country j

firm f

firm f 0

fih

f 0ih

firm g

firm g0

gjh

g0jh

Figure 2: The commodity space

2.2 Demand

As noted before, each country is populated with a mass Li of identical consumers. In a standard Dixit-

Stiglitz enviroment6 (e.g. Krugman [1980] ), the preferences of a representative agent can be denoted by a

three-level CES utility function

U =

ˆh2H

C��1�

h d✏

�

���1

where Ch is the sub-utility derived from the consumption of product h. � denotes the elasticity of

substitution among HS product categories. Ch has the following form

Ch =

2

4

X

j2C

Q��1�

jh

3

5

���1

where Qjh is the composite variety, i.e. sub-utility, from country j in HS code h

Qjh =

2

4

X

j2Fj

q��1�

gjh

3

5

���1

qgjh is the quantity of variety gjh that the consumers directly consume. In the standard Dixit-Stiglitz

framework, which is used by most leading models of international trade, the elasticity of substitution is the

same (equal to �) across all varieties.

In my framework I assume each consumer has the following CES utility function

6Dixit and Stiglitz [1977]

8

U =

ˆh2H

(↵hCh)��1� d✏

�

���1

where ↵h is the appeal or, as I will call it, “quality” of products in HS code h, i.e. product-level quality.

There is a one-to-one mapping from the product space (H) to the product-level quality space (i.e. [0, ¯H] !

[1, ↵̄] where ↵̄ is the highest quality). ✏ denotes the elasticity of substitution among HS product categories.

In my framework the second tier utility, sub-utility Ch, has the following form

Ch =

2

4

X

j2C

(µjQjh)

�h�1�h

3

5

�h�h�1

µj is the quality of varieties manufactured in country j, i.e. country-level quality. I would like to em-

phasize at this point that quality in my framework has a pure demand side interpretation.7 The elasticity of

substitution among (composite country-level) varieties in code h is �h, i.e. macro elasticity. The composite

imported variety, Qjh, is

Qjh =

2

4

X

j2Fj

q⌘

�(�h�1)

�(�h�1)+1

gjh

3

5

�(�h�1)+1

�(�h�1)

where ��h +(1� �) is the elasticity of substitution across varieties manufactured by firms from country

j in HS code h, i.e. micro elasticity. ⌘ captures the relative importance of quantity versus quality.8 A simple

depiction of the patterns of product substitution is given in figure 3. In my theoretical model, I impose two

restrictions on elasticities. The first restriction is that higher quality HS codes are more differentiated and

therefore have a lower elasticity of substitution.9

Assumption 1. (i) ↵h > ↵h0=) �h < �h0

(ii) lim↵h!1 �h = 1

The second restriction I impose on the elasticities is that varieties manufactured (by firms) in the same

country are closer substitutes than varieties manufactured in two different countries. In other words, the

micro-elasticity is assumed to be higher than the macro-elasticity.10

Assumption 2. � > 1

7The way I incorporate a country-level quality, i.e. µj , and a product-level quality, i.e. ↵h in my demand is similar to Hallak andSchott [2011]. However, they assume the same elasticity of substitution across all varieties in the same 2-digit sector.

8⌘ is not just a parameter that scales quality. A high ⌘ means demand is more sensitive to prices (than quality)-an effect identifiedby looking at across product variations in demand. The effect is explained in more detail in 2.2.1.

9Fajgelbaum et al. [2011] and Coibion et al. [2007] make a similar assumption, but in a non-CES demand structure.10If � > 1 then ��h + (1� �) > �h, given that �h > 1.

9

0

¯H

h

County i

Country j

firm f

firm f 0

fih

f 0ih

firm g

firm g0

gjh

g0jh

��h

�h

✏

Figure 3: Elasticity of substitution across different (product) nests

Each consumer in country i is endowed with one unit of labor and therefore will have an income equal

to wage, which I denote by wi. Utility maximization implies that the quantity demanded in country i of

variety gjh at price pigjh is

qigjh =

0

@

⇣

pigjh

⌘⌘

/↵hµj

P ijh

1

A

�(1��h)

P ijh

P ih

!1��h ✓

P ih

P i

◆1�✏wiLi

pigjh(1)

where P i is the aggregate price index, P ih is the price index for HS code h, and P i

jh is the price index of

country j (firm-level) varieties in code h, all in country i. The (quality-adjusted) price indices can be written

as

P ijh =

8

>

<

>

:

X

g02F ijh

2

4

⇣

pig0jh

⌘⌘

↵hµj

3

5

�(1��h)9

>

=

>

;

1�(1��h)

(2)

P ih =

8

<

:

X

k2Cih

�

P ikh

�1��h

9

=

;

11��h

(3)

P i=

⇢ˆh2H

�

P ih

�1�✏dh

�

11�✏

(4)

where F ijh is the set of firms exporting to country i from country j in code h. Ci

h is the set of countries

that export their variety to country i in code h.

In the following subsection, I turn to describing the global equilibrium. As a rule of thumb, in this paper

the superscript refers to the country that is importing the variety, and the subscript refers to the variety (e.g.

gjh).

10

2.3 Supply

On the supply side every country is populated with a big pool of homogenous multi-product firms which

can potentially enter various markets, and sell all the HS products. The entry scheme in my model is the

following

1. Every firm pays an (separate) entry cost fe to enter each market.

2. After entry, an exporting firm pays an (incremental) overhead cost f for every HS code it exports.11

Both the entry cost and the overhead cost are payed in terms of labor in the country of origin. The first

assumption on entry is also taken by Eaton et al. [2011], and the second assumption on the overhead cost is

also adopted by Arkolakis and Muendler [2010]. All the firms in a country share the exact same production

technology. For firms in country j, the cost of producing q units of product h and selling them in country i

is

cijh(q) = cij(q) =⇣

⌧jiwj↵1/⌘h

⌘

q + wjf

⌧jiwj↵1/⌘h is the marginal cost of production which I assume is linear in ↵1/⌘

h .12 ⌧ji is the iceberg trans-

portation cost from country j to i (⌧ij = ⌧ji). Note that the marginal labor requirements for producing one

unit of a variety in code h is the same everywhere. However with one unit of labor, some countries produce

higher quality varieties than others, which is captured by the term µj in the utility function. For domestic

firms in country i the cost of producing q units and selling it domestically will be

ciih(q) = wi↵1/⌘h q

Domestic firms pay neither fixed costs nor the iceberg transportation costs. The maximization problem

of firm g located in country j exporting to country i is the following

max

{pigjh}h2H

,Higj

ˆh2Hi

gj

0

B

B

@

⇥

pigjh � ⌧jiwj↵h

⇤

qigjh � wjf| {z }

⇡igjh

1

C

C

A

dh

11More specifically, I assume that firms pay a fixed cost equal to f✓ij(h)

where ✓ij(h) is the share of firms that sell category h, from the

total mass of firms which enter market i from country j . The assumption basically incorporates into the model, external economiesof scale when introducing a new variety into a foreign market. This is an out of equilibrium assumption and ensures that firms willact collectively, i.e. ✓ij(h) = 1 for every h that is exported, which makes the model much more tractable.

12This assumption assures that the quality adjusted price of varieties from various HS codes is the same. My results do not dependon this assumption, but it makes my model more tractable.

11

Where pigjh is the price the firm charges for variety gjh in country i, and Higj is the scope of exports

for firm g (i.e. the set of HS codes firm g exports to country i). The profit maximizing firms charge a

category/quality dependent markup over the marginal costs

pigjh = pijh =

1 + ⌘ [��h � 1]

⌘ [��h � 1]

�

⌧jiwj↵1/⌘h , 8j 2 Ci

h (5)

where again, Cih is the set of countries who have firms exporting their variety to country i in code h. The

markup ( 1+⌘[��h�1]⌘[��h�1] ) is decreasing in �h and, therefore, increasing in product-level quality ↵h. The quality

adjusted price, or as Hallak and Schott [2011] put it the pure price, of variety gjh is

pigjh

(↵hµj)1/⌘

=

1 + ⌘ [��h � 1]

⌘ [��h � 1]

�

⌧jiwj

µ1/⌘j

, 8j 2 Cih

Pure price is price per unit of quality and is the price that determines demand for every variety (equation

(1)). As seen in equation (5), firms from country j all charge the same price. They all also make the same

profits, i.e. ⇡igjh = ⇡i

g0jh = ⇡ijh 8g, g0 2 F i

jh, and have the same scope of exports, i.e. Higj = Hi

g0j =

Hij 8g, g0 2 F i

jh. Firms will export their variety in every HS code, as long as they make enough (marginal)

profit in that HS code to overcome the overhead cost f

Higj = Hi

j =�

h 2 H | ⇡ijh � 0

(6)

The above equation implicitly implies that domestic firms will sell their variety in all the HS codes (i.e.

Hii = H), given that they do not pay the fixed overhead cost.

2.4 Equilibrium

I denote the mass of firms that enter country i’s market from country j with M ij . M i

j is pinned down by the

free entry (FE) condition

ˆh2Hi

j

⇡ijhdh = wjf

e(FE)

wages in country i are pinned down by labor market clearing (LMC) condition

Li=

M ii f

e+

ˆh2Hi

i

↵hqiihM

ii dh

!

+

0

@

X

k 6=i

Mki f

e+

ˆh2Hk

i

�

⌧ik↵hqkih + f

�

Mki dh

1

A

(LMC)

12

The product market clearing condition is the following and clears by Walras’ law

X

k2C

ˆh2Hi

k

pikhqikhM

ikdh = wiLi

(PMC)

Given the market clearing conditions, now I can define the global equilibrium.

Definition. Given {Li}i2C , {⌧ij}i,j2C , {µj}j2C , {↵h}h2H , f , fe, �, ✏, ⌘ and {�h}h2H , a global equilibrium is

a set of wages wi, mass of firm M ij , price indices P i

h, P i, prices pijh, and consumer allocations qigjh, profits ⇡ijh and

scope of production Hij such that

(i) equation (1) is the solution of the consumer’s optimization problem.

(ii) pijh solves the firms’ profit maximization problem (equation (5))

(iii) The scope of production is given by equation (6)

(iv) P ih and P i are given by equations (3) and (4) respectively

(v) The free entry condition (FE) holds

(vi) The labor market clearing condition (LMC) holds

2.5 Gravity

In my model I have a two tier gravity equation. Let Xijh =

P

g pigjhq

igji be total spending on varieties from

country j in country i. Then the (second tier) gravity equation for product code h will be the following

�ij|h =

Xijh

P

k2CihXi

kh

=

�

M ij

�

1�

wj⌧ji

µ1/⌘j

��⌘(�h�1)

P

k2Cih

�

M ik

�

1�

wk⌧ki

µ1/⌘k

��⌘(�h�1), 8j 2 Ci

h (7)

�ij|h is the share of spending on varieties from country j 2 Cih in code h; where Ci

h is the set of countries

that export to i in code h (i.e. Cih =

�

j 2 C | h 2 Hij

). If j /2 Cih then clearly �ij = 0. One bold property of

my gravity equation is that the trade elasticities, i.e. elasticity of trade volumes wrt to iceberg trade costs,

are lower in high quality product codes (because �h is lower in high quality–high ↵h–HS codes).

The second layer of my gravity equation captures the relative spending on various HS product codes.

Let Xih =

P

k2CihXi

kh be total spending on varieties in category h, and Xi=

´hXi

hdh = wiLi be total

spending in country i. The share of spending on product code h, i.e. first tier gravity, will be given by the

following equation

13

�ih =

Xih

Xi=

h

1+⌘[��h�1]⌘[��h�1]

i�⌘(✏�1)(

P

k2Cih

�

M ik

�

1�

✓

wk⌧ki

µ1/⌘k

◆�⌘(�h�1))

✏�1�h�1

´h0

h

1+⌘[��h0�1]⌘[��h0�1]

i�⌘(✏�1)(

P

k02Cih0

�

M ik0

�

1�

✓

wk0⌧k0iµ1/⌘

k0

◆�⌘(�h0�1))

✏�1�h0�1

dh0

(8)

A novel future of the above equation is that love of variety is stronger in higher quality product codes.

Therefore, if the number of varieties in a country rises, spending will be redistributed towards the higher

quality categories so consumers can benefit the most from variety. For example, in country i, spending on

good h relative h0 is the following

�ih�ih0

=

h

1+⌘[��h�1]⌘[��h�1]

i�⌘(✏�1)(

P

k2Cih

�

M ik

�

1�

✓

wk⌧ki

µ1/⌘k

◆�⌘(�h�1))

✏�1�h�1

h

1+⌘[��h0�1]⌘[��h0�1]

i�⌘(✏�1)(

P

k2Cih0

�

M ik

�

1�

✓

wk⌧ki

µ1/⌘k

◆�⌘(�h0�1))

✏�1�h0�1

Suppose the number of varieties in market i increase by a factor t > 1, i.e.�

M ij

�0= tM i

j , then

�

�ih�

0

�

�ih0

�0 = t✏�1�

✓�h0��h

(�h�1)(�h0�1)

◆�ih�ih0

if ↵h > ↵h0 then �h < �h0 and (

�ih)

0

(

�ih0)

0 >�ih

�ih0

. Putting it into words; if the number of varieties in country

i increases, then country i will spend relatively more on high quality product codes. As we will see later,

the above condition implies that high wage countries spend relatively more on higher quality products; a

novel result that comes without the need to assume some type of non-homotheticity in demand.

2.5.1 On the Identified Effects of ⌘, �h, and ↵h

In this subsection I will briefly discuss the different effects of ⌘, �h, and ↵h on demand and how they are

identified. ⌘ can be separately identified from �h using the following strategy: increasing ⌘ and lowering �h

proportionately implies that, within the HS code, the conditional spending on varieties will not be affected,

while this change will increase the market share of code h relative to other HS codes.

�h and ↵h have similar, but yet different effects on demand. First, unlike �h, ↵h does not change the

relative spending within the HS code. Second, lowering �h increases spending on code h and the effect is

not sensitive to how high prices in code h are, because a lower �h suppresses the price effect (on spending)

within code h. A higher ↵h on the other hand increases spending on (varieties in) code h conditional on

prices in code h.

14

2.6 Shipping the Good Apples Out

One empirical regularity that the mainstream trade literature seems to not account for, is the fact that higher

trade costs are correlated with higher price/quality of traded goods.13 In this section I will explain how my

model accounts for this regularity.

For simplicity consider a world were iceberg costs are large enough so that domestic varieties are always

cheaper than their foreign counterparts (even after adjusting prices for quality). This will be the case if the

following condition holds14

Condition 1. ⌧ji

µ1/⌘j

> 1

µ1/⌘i

for all i, j 2 C

From equation (5) we know that firms will charge a higher markup in higher quality product codes.

Also, elasticity (�h) is lower in high-quality product codes, so demand is less sensitive to trade costs in the

high-quality codes. Given these two effects in higher qualities, i.e. (i) higher markups, and (ii) the price

disadvantage of exporters15 mattering less because their high-quality variety is not highly substitutable, I

can show that exporters collect higher profits in higher quality HS codes16

↵h > ↵h0=) ⇡i

jh > ⇡ijh0 , 8j 2 Ci � {i}

Firms charge zero markup for the lowest quality product category (lim↵h!1 �h = 1=) lim↵h!11+⌘[��h�1]⌘[��h�1] =

0) so they would not export their variety in the lowest quality HS code, but they would sell it domestically.

As demonstrated in figure 4, there is a source-specific quality cutoff, and firms export only the HS codes

which qualities fall above that cutoff

Hifj =

�

h 2 H | ↵h > ↵⇤ji

↵⇤ji is the cutoff for firms exporting from country j to i, where ⇡i

jh |↵h=↵⇤ji= 0. The cutoff is increasing in

iceberg trade costs ⌧ji which means that firms (or countries) facing higher trade costs will have a narrower

scope of exports which consists of only varieties in very high quality HS codes. The following proposition

summarizes this result regarding the effect of trade costs on the price and quality of the exported goods.

13Baldwin and Harrigan [2011] have a survey of the leading trade models and show that all the leading models generate resultsthat are inconsistent with this empirical regularity. As Hummels and Skiba [2004] show, the Alchian-Allen hypothesis can account forthe effect of trade costs on quality by assuming additive trade costs. However, the fact that trade costs are additive can be disputed(Lashkaripour [2013]) and moreover, assuming additive trade costs has the downfall of making trade models intractable.

14In proposition 2, I will show that wages are higher the higher µi. Therefore, condition 1 guarantees that ⌧jiwj

µ1/⌘j

> wi

µ1/⌘i

.

15Under condition 1, we will have foreign entry only if � > 1. If � < 1 then having additional foreign varieties will have the samevariety effect of having additional domestic varieties, but domestic firms/varieties will have absolute price advantage over foreignfirms/varieties.

16In the appendix I mathematicaly prove this claim.

15

�wjf = �wkf

⇡igjh

⇡ig0kh

↵h↵̄↵⇤ki↵⇤

ji

Figure 4: Profits graphed against HS10 qualities (↵h) for a typical firm exporting from countries k and j to country i, when ⌧ji < ⌧ki

and wj = wk . The dashed area under the profit (density) curve is total profits made by a typical firm from country k and is equal towkfe from the (FE) condition.

Proposition 1. Among foreign firms exporting to the same market, the one’s that incur the highest trade costs

(i) Have the narrowest scope of exports, and export their variety only in the highest quality product categories.

(ii) Export on average more expensive/higher quality varieties

Proof. see Appendix

Proposition 1 will still hold if I shut down product-level quality differences between the HS codes, i.e.

↵h = ↵h0 for all h, h 2 H , and allow for only variations in �h. In this case, firms facing higher trade costs

will again have the narrowest scope of exports, and will only export their most differentiated (i.e. low �h)

varieties. Moreover, since the the differentiated varieties are more expensive because of the higher markup

(equation 5), the firms facing higher trade costs will also be exporting, on average, more expensive goods.17

17

Corollary. Suppose ↵h = ↵h0 8h, h 2 H , then among foreign firms exporting to the same market, the one’s that incur the highest trade costs(i) Have the narrowest scope of exports, and export their variety only in the most differentiated product categories.(ii) Export on average more expensive/more differentiated varieties

16

In the next subsection I will show why high wage countries export more despite the fact that firms from

those countries charge higher prices.

2.7 Why Wealthy Nations Trade More

Waugh [2010] points out that, in the data, high wage countries trade more relative to their GDP, but in

contrast to what Ricardian models predict, they are not cheap producers. Actually, the price of exported

goods from high wage countries tends to be a bit higher . Waugh [2010] accounts for this by assuming that

poor countries face higher trade costs. Other papers (e.g. Fieler [2011]) have tried to address this fact by

assuming non-homothetic prefferences. In this subsection, I provide a novel and tractable (my preferences

are homothetic and iceberg trade costs are symmetric) explanation for why high wage countries trade more

relative to their GDP. I also show that within my model (even though preferences are homothetic) high

wage countries consume and trade on average higher qualities.

When a country produces high quality varieties (i.e has a higher µi) there will be more demand for

it’s varieties which results in higher wages. However, after deflating wages by the quality of the varieties

produced in each country, one can show that the high quality countries ends up producing every unit of

quality cheaper. This gives high-wage/high-quality countries absolute advantage in the global market,

which explains why high wage countries export more. Note that in a baseline Krugman model (�h = � and

� = 1) the quality adjusted wage ( wi

µ1/⌘i

) will be equalized across countries in equilibrium, so conditional on

geography all countries will trade the same. Proposition 2 captures the above result.

Proposition 2. Suppose ⌧ik = ⌧jk 8k 2 C, Li = Lj , but µi > µj then

(i) wi > wj : wages in country i are higher than j

(ii) wi

µ1/⌘i

<wj

µ1/⌘j

: quality-adjusted wages are lower in country i

(iii) Country i imports more (relative to its income) than country j

(iv) Country i consumes (and imports) relatively more from higher quality HS codes

Proof. see Appendix.

The intuition behind why rich countries import more (ad thus export more) is two-folded. If wages

in a country are high so is total spending; firms sell more in that country making it more likely for them

to overcome the entry and overhead cost (which is payed in terms of wages in their home country). More

varieties enter the market in high wage countries. In the presence of more varieties, due to the love of variety,

demand shifts towards high quality HS codes with low �h–so consumers can benefit the most from the

higher number of varieties. Hence, high wage countries spend relatively more on high quality HS codes.

17

This result contrasts the claim in Hallak [2006] that one has to assume systematic differences in demand

across countries (i.e rich countries value quality more) to explain the high quality/price of imports by rich

countries.

Thus far we know that high-wage countries spend relatively more on high-quality HS codes. Mean-

while, In high-quality HS codes, consumers also spend relatively more on foreign varieties (that are more

expensive) for two reasons: (i) demand is less price sensitive in high quality HS codes and (ii) foreign varieties are

present only in higher quality codes. As a result, not only high wage countries spend relatively more on high

quality product codes, but they also will spend relatively more on foreign varieties.

2.8 The Anti-variety Effects of Trade in Lower Qualities

Lowering iceberg trade costs in my model will lead to more foreign entry. Multi-product foreign firms will

enter the market and crowd out a portion of the multi-product domestic firms. In a baseline setting (�h = �

and � = 1) the total number of varieties will remain the same after lowering iceberg trade costs. Under the

specifications of my model (assumptions 1 and 2), I can show that the total number of varieties in a market,P

j2Ci M ij , will always rise–when trade costs are lowered. The intuition is following: lowering trade costs,

induces entry among foreign firms that specialize in high quality HS codes. More variety in high quality

codes encourages consumers to reallocate their spending from low quality HS codes to high quality ones.

As noted before, In high quality HS codes love of variety is more prominent, and spending is more evenly

distributed among varieties. This makes its possible that for every cheap domestic variety that leaves the

market, multiple expensive foreign varieties enter, which in total, leads to more variety in the market.

Looking at the big picture, trade always has pro-variety effects at the aggregate level–a result not cap-

tured by Melitz [2003].18 However, after lowering trade costs some multi-product domestic firms leave

to create room for the multi-product foreign firms. The multi-product domestic firms sell all the HS

codes/qualities while the multi-product foreign firms only sell the high-quality HS codes. As a result,

the number of varieties in low-quality codes drops, while the number of varieties increases substantially in

high-quality products codes.

Proposition 3. Suppose variable trade costs are lowered, there exists a quality cut-off ↵̃i in country i such that:

(i) if ↵h > ↵̃i then the number of varieties in code h rises (i.e. � dd⌧

P

j2CihM i

j > 0)

(ii) if ↵h < ↵̃i then the number of varieties in code h drops (i.e. � dd⌧

P

j2CihM i

j < 0)

(iii) The total number of varieties rises (i.e.� dd⌧

P

j2Ci M ij > 0)

18See Baldwin and Forslid [2010] for derivation of the anti-variety effects of trade in the Melitz [2003] framework.

18

In the CES context proposition 3 implies gains from trade for all households. In general, the CES frame-

work with identical consumers has no implications about the distribution of gains from trade (since every-

one gains the same). The CES interpretation behind the demand function in equation (1), is one extreme

interpretation. The other extreme is the logit interpretation where every consumer draws taste from a dis-

tribution and spends all his income on only one variety. In the appendix I show that according to the

logit interpretation, proposition 3 implies that when iceberg trade costs are lowered, consumers of the low-

quality products lose while the consumers of high -quality products gains substantially.

It is worth mentioning that if the fixed (overhead) cost of exporting–f–is lowered to zero, the pro-variety

effect of trade will be seen in all the HS codes or quality levels. When I map my model to data in section 3,

I will compare the two policies (lowering variable versus fixed cost of exporting) in terms of their effect on

variety in different quality levels.

Arkolakis et al. [2008] show that, in import data from Costa Rica, the number of varieties increase a

lot when trade is liberalized. However, they claim that since the new varieties absorb very low market

shares, the gains from variety are not significant. What proposition 3 tells us is that varieties do increase,

but they do so in high quality/low elasticity product codes. If one restricts elasticity to be the same across

all products, as in Arkolakis et al. [2008], the gains from these new varieties could be small. However, if one

takes into account the low elasticity of substitution for these new varieties, the gains from variety could be

much bigger.19

3 Mapping the Model to Data

In this section I discuss how I fit the model presented in Section 2 to data. First, I will describe the data

and provide some preliminary evidence on product differentiation across different HS codes. Then, I will

estimate my core demand parameters (by estimating a micro-gravity equation) for individual industries.

Finally, I will plug my estimated demand parameters into my model and calibrate it to global bilateral trade

data. I will first analyze the predictions of my calibrated model and then I perform a counterfactual analysis

to explore the variety effects of trade.

19Mathematically, the change in real wage, i.e. V i = wiP i , from lowering tarde cost is

�dV i/d⌧

V i=

�i +

fe

Li

X

k

dM ik

d⌧

!

| {z }V ariety effect

�

0

@X

k 6=i

1

⌧ki�ik

1

A+

0

@dwi/d⌧

wi(1� �ii)�

X

k 6=i

dwk/d⌧

wk�ik|h

1

A

| {z }Price effect

where �i is the extensive margin effect of new varieties on the price index. The intensive margin effect fe

Li

Pk

dMik

d⌧ is non-negative

and depends very much on how increasing �h is in product-level quality ↵h. Specificaly, if �h = � 8h then fe

Li

Pk

dMik

d⌧ = 0.

19

3.1 Data description and preliminary evidence

The dataset I use in this paper is the U.S. import data compiled by Schott [2008], which is publicly available.

The data, documents US import values and quantities from different source countries in various 10-digit

HS10 codes. Every HS10 code belongs to a 5-digit SITC5 industry, and every SITC5 industry itself belongs to

a two-digit SIC sector. Since the original data does not report SITC industry codes, I use the data compiled

by Feenstra et al. [2002] to map every HS10 codes into a SITC5 industries. I will use the data from 1989 to

1994.

An observation in my dataset is an import record for an HS10 product, from an exporting country, in a

given year to a given U.S. city. Each observation documents import quantities, values, and the number of

individual export cards associated with that observation. In addition, the data includes tariff and freight

charges and the units in which quantity was measured in. For my estimation, I consider only manufacturing

industries (SITC5 5-8) that are differentiated according to the classification proposed by Rauch [1999]. I take

the aggregate economic variables (population, GDP, etc.) from the Penn world tables and distance data from

the CEPII dataset compiled by Morey and Waldman [1998].

I trim the data along three different dimensions. First I drop all the observations reporting varieties in

which the quantity imported is one unit or the imported value is less than $5000 in 1989 dollars. Then,

within every industry I exclude varieties which report unit values that lie above the 99 percentile or below

the 1 percentile of that industry. Finally, since I need across HS10 code variations to identify �h and ↵h,

I drop all industries which contain less than four HS10 codes. In total I estimate the demand parameters,

separately, for 411 SITC5 industries.

For my estimation I need the share of spending on domestic (U.S.) varieties in every SITC industry. Like

Khandelwal [2010] I approximate this with the import penetration index estimated by Bernard et al. [2006].

I use the average price of exports by U.S. firms in every HS10 code as a proxy for the price of the U.S.

varieties in the local market.20

My model assumes that all firms that enter the U.S. market have the same scope and price. Therefore,

for every source country I need to have the number of firms that export to the U.S. in each SITC5 industry.

The assumption of my model is that all the firms have the same share from every import observation I see

in the data. In the data, I see the number of individual export lines, i.e. individual export cards filled in

by individual firms, associated with each observation. Since the number of export lines can be due to more

quantity sold throughout the year, I take the average number of export lines per quantity sold by country

j in a given SITC5 industry as a proxy for the number of firms exporting to the U.S. from country j in that

20Khandelwal [2010] uses the aggregate CPI to proxy for the price of the domestic variety.

20

industry (MUSj ).21

Before moving on to the demand estimation, there are three stylized facts in the data that are worth

mentioning

a) Within each SITC5 industry, the coefficient of variation of imported f.o.b prices are higher in HS codes

with a higher average f.o.b price

b) Within each SITC5 industry, countries that pay higher shipping costs export relatively more in more

(f.o.b) expensive HS10 codes

c) Within each SITC5 industry, more individual shipments (per quantity sold) leave for the U.S. market in

more (f.o.b) expensive HS10 codes.

The above facts and how they are derived is explained in details in appendix A. These stylized facts are

not accounted for in the mainstream firm-level trade models (e.g. Melitz [2003], and Eaton et al. [2011]). My

model explains fact (a) since in higher quality HS10 codes, more firms export including firms that charge

very high prices. Fact (b) documents across HS10 code effects of trade costs on the quality/f.o.b prices,

which again is consistent with the prediction of my model that high cost exporters only export the highest

quality HS10 codes (proposition 1). Finally, fact (c) is a crude confirmation of my model’s prediction that

high quality HS10 codes are more crowded due to high cost exporters selling their varieties in those product

codes.

3.2 Estimating Demand Elasticities

In this section I will try to identify and estimate demand elasticities �h, ✏, �, and ⌘. First, I perform my

estimation using a baseline specification where I shut down variations in �h across HS10 codes. Then, I will

estimate demand, allowing for �h to vary across HS10 codes and depend on quality ↵h.

3.2.1 Baseline Specification (�h = �̄)

In my baseline estimation I restrict the elasticity of substitution, in every SITC5 industry, to be the same

across all HS10 codes. More specifically, I let �h = �̄ for all h (HS10 codes) that belong to an SITC5 industry.

Then, I estimate demand (micro-gravity) for each one of the 411 industries in my sample, separately. In my

estimation I will be comparing product-level qualities, i.e. ↵h, across HS10 codes within the same industry.

21I normalize this number so that the exporter with the highest number of firms will have a mass of firms (MUSj ) equal to one. As

I will discuss later, I normalize the number of U.S. firms in every SITC5 industry to one too. This implies that the country with thelargest number of firms has the same number of firms, selling in the U.S. market, as the U.S. itself. If contrary to this restriction thenumber of U.S. firms is larger, then � will be underestiamted.

21

I will also be assuming that HS10 composite varieties are substitutes with elasticity ✏. Hallak and Schott

[2011] and Khandelwal [2010] among others also compare qualities across HS10 codes and assume varieties

in different HS10 codes are substitutable. The main reason is that to identify demand parameters one needs

to look at across HS10 code variations. Another reason is that an SITC5 industry is a very narrowly defined

class of HS10 codes. Hence, within an SITC5 industry, the 10-digit HS10 codes are comparable.

From equation (1), total U.S. spending on varieties from country j in HS10 code h (in a given SITC5

industry) will be

Xjh =

0

@

(Mj)� 1

�(�̄�1)

h

p⌘jh

µj↵h

i

Ph

1

A

1��̄✓

Ph

P

◆1�✏

wUSLUS (9)

where Mj is the number of firms in the SITC5 industry of interest exporting to the U.S. market from

country j. pjh is the c.i.f price set by these firms for variety jh. Ph is the price index of HS10 code h, given

by equation (3), and P is the aggregate price index in the SITC5 industry that I’m preforming the estimation

for.

In theory, the U.S. varieties were available in: (i) HS10 codes that are not imported, and hence the codes

not observed in import data, and (ii) HS10 codes that are imported, as an alternative to imported varieties

in those codes. In practice though, I do not observe U.S. sales by HS10 code, but I only have market share

of U.S. varieties at the SITC5 industry level. I therefore assume the U.S. varieties constitute an independent

HS10 code (i.e. outside variety). The price index associated with the U.S. product code will be

PUS = M�1

�(�̄�1)

US

✓

p⌘US

↵US

◆

I normalize the mass of firm (MUS), the price (PUS), and the quality (↵US) of U.S. firms to one so that

the price index for U.S. varieties will also be one (PUS = 1). Total spending on U.S. varieties will be

XUS =

✓

PUS

P

◆1�✏

wUSLUS (10)

Dividing equation (9) by (10) and replacing PUS = 1, we will have

Xjh

XUS=

0

@

(Mj)� 1

�(�̄�1)

h

pj(↵h)⌘

µj↵h

i

Ph

1

A

1��̄✓

1

Ph

◆✏�1

=

0

B

@

(Mj)� 1

�(�̄�1)

h

p⌘jh

µj↵h

i

M�1

�(�̄�1)

US

⇣

p⌘US

↵US

⌘

1

C

A

1�✏

0

B

B

B

B

B

@

(Mj)� 1

�(�̄�1)

h

p⌘jh

µj↵h

i

Ph| {z }

(

�j|h)�1�̄�1

1

C

C

C

C

C

A

✏��̄

(11)

22

where �j|h is the share of spending on varieties from country j in code h (i.e �j|h =

Xjh

Xh) . Taking logs

from equation (11) and adding a year subscript t will result in the following equation

ln

Xjht

XUS,t=

✏� 1

� (�̄ � 1)

ln

Mjt

MUS+(✏� 1) ln

↵ht

↵US,t�(✏� 1) ⌘ ln

pjhtpUS,t

+

1� ✏� 1

�̄ � 1

�

ln�ij|h,t+(✏� 1) lnµjt (12)

To identify �, I will have to assume that the country-level quality µjt varies across HS10 codes. However,

unlike Broda and Weinstein [2006], I still allow for the country-level qualities µjht’s to be clustered by

country, i.e. Cov[µjht, µjh0t] > 0 for all h and h0 in an SITC5 industry. However, I assume the µjht’s are not

corrolated across time.

Assumption 3. Cov[µjht, µjht0 ] = 0 8t, t0

Replacing lnµjt with lnµjht in equation (12) will give me the final demand, i.e. micro-gravity, equation

to estimate

ln

Xjht

XUS,t=

✏� 1

� (�̄ � 1)

ln

Mjt

MUS+ (✏� 1) ln

↵ht

↵US,t� (✏� 1) ⌘ ln

pjhtpUS,t

+

1� ✏� 1

�̄ � 1

�

ln�ij|h,t + (✏� 1) lnµjht

(13)

In the above equation I can not identify ⌘ and �̄ separately from ✏, but � is separately identified. Qual-

ity ↵ht

↵US,tis unobserved and needs to be estimated. One approach taken by Schott [2004] and Hummels

and Klenow [2005] is to proxy for quality with f.o.b prices. This approach can be inconsistent with my

framework, given that by definition high quality HS10 codes absorb a rather high market share conditional

on high prices. A second approach taken by Khandelwal [2010] (which is standard in the IO literature) is

to estimate quality as fixed effects. I cannot apply this approach since it will require estimating (13) with

HS10-year fixed effects, which will not allow me to identify �̄.22

My approach is a hybrid of the price-proxy approach and the fixed effect approach. I approximate the

fixed effect, a strategy also implemented by Blundell et al. [1999].23 To this end, I use my models theoretical

predictions about selection of firms into HS10 codes to find a proxy for product-level quality, i.e ↵ht, that

preserves the ordinality of the ↵ht, but approximates the cardinality. Theoretically, ln ↵ht

↵US,thas the following

representation

22The reason I cannot identify �̄ in the presence of HS10-year fixed effects is that I will be looking at only within HS10 codevariations, while �̄ is identified by looking at across HS10 code variations.

23Blundell et al. [1999] estimate a structural model of firm innovation and proxy for the firm fixed effect using pre-sample innova-tion data on individual firms.

23

(✏� 1) ln

↵ht

↵US,t= ln

Xht

XUS,t� ✏� 1

(�̄ � 1)

ln

X

j2Cht

✓

Mjt

MUS

◆

1�

pjht/µ1/⌘jht

pUS,t

!�⌘(�̄�1)

(14)

In the above equation ↵ht cannot be separately identified from the sequencen

µ1/⌘jht

o

j2Cht

, because a

transformation t↵ht and t�1n

µ1/⌘jht

o

j2Cht

will be identical to ↵ht andn

µ1/⌘jht

o

j2Cht

in the context of the above

equation. To disentangle the pure effect of ↵ht on prices and market shares, I use my model’s predictions

about the selection of firms, and thus lnµjht’s, into code h to find an order-preserving proxy for ↵ht. My

order-preserving proxy for quality is the following

(✏� 1) ln

↵̂ht

↵̂US,t=

8

<

:

ln

Xht

XUS,t� ✏� 1

� � 1

ln

X

j2Cht

✓

Mjt

MUS

◆

1�✓

pjhtpUS,t

◆�⌘(�̄�1)9

=

;

(15)

where is a parameter to be estimated, and ↵̂ht

↵̂US,tis my proxy for ↵ht

↵US,t. Equation (15) approximates

quality by attaching high quality to HS10 codes that have high market shares despite high average c.i.f

prices that are not adjusted with µjhts. In the context of my equilibrium, I show (proposition 4) that the

term in the braces in equation (15) has the same ordering as the actual product-level qualities (↵h), and

corrects for the scale. 24

Proposition 4. Let ˆA = {↵̂h}h2H , and A = {↵h}h2H ; then the sets A and ˆA have the same order type in my Global

equilibrium

↵̂h > ↵̂h0=) ↵h > ↵h0 8h, h0 2 H

Proof. see Appendix

Hence, the final (micro-gravity) equation to estimate is

ln

Xjht

XUS,t=

✏� 1

� (�̄ � 1)

ln

Mjt

MUS+ (✏� 1) ln

↵̂ht

↵̂US,t� (✏� 1) ⌘ ln

pjhtpUS,t

+

1� ✏� 1

�̄ � 1

�

ln�ij|h,t + (✏� 1) lnµjht

(16)

The first term, i.e. ✏�1�(�̄�1) ln

Mjt

MUS, tells us how much of country j’s sales in code h are due to the number

of firms exporting from country j. The second term, i.e. (✏� 1) ln

↵̂ht

↵̂US,ttells us how much of country j’s

sales in code h are due to quality rank of code h relative to other HS10 codes in that industry. The third

term, i.e. (✏� 1) ⌘ lnpjht

pUS,tcaptures the effect of prices on sales. The fourth term, i.e.

h

1� ✏�1�̄�1

i

ln�ij|h,t, tells

us how much of the sales by country j in code h are due to its market share within code h, and that clearly

24Given the structural expression for the product-level quality (equation 14), one would expect the scale parameter to be close toone.

24

depends on the magnitude of �̄ � 1 relative to ✏ � 1. If �̄ � 1 is very high relative to ✏ � 1 it implies that

because it is not possible to substitute varieties belonging to two different HS10 codes, a high conditional

market share within HS10 code h, i.e. �ij|h,t, would translate into a high nominal market share within the

industry, i.e. Xjht

XUS,t. Finally, whatever is left of country j’s sales, will be explained by the country-level

quality, i.e. (✏� 1) lnµjht.

3.3 Identification

To identify �̄�1✏�1 , ⌘ (✏� 1), �, and I will take the standard approach of using supply-shifters to identify the

demand curve. For this, I find a vector of instruments z that are uncorrelated with the quality lnµjht. Let

⇥ =

⇣

�̄�1✏�1 , ⌘ (✏� 1) , �,

⌘

be the vector of parameters I estimate, and X be data on Xht

XUS,t, Mjt

MUS, �ij|h,t, and

pjht

pUS,t, then the moment condition will be the following

E [zG(⇥;X)] = 0 (17)

where

G(⇥;X) = ln

Xjht

XUS,t� ✏� 1

� (�̄ � 1)

ln

Mjt

MUS� (✏� 1) ln

↵̂ht

↵̂US,t+ (✏� 1) ⌘ ln

pjhtpUS,t

�

1� ✏� 1

�̄ � 1

�

ln�ij|h,t

The above identification approach is also taken by Khandelwal [2010], while Broda and Weinstein [2006]

identify elasticity by assuming the supply shock (productivity) is uncorrelated with the demand shock

(quality). I estimate the ⇥ parameters using a non-linear GMM procedure

ˆ

⇥ = argmin

⇥ˆG(⇥;X)

0z0 ˆW2z ˆG(⇥;X)

The optimal weighting matrix ˆW2 is calculated in the conventional two-step procedure. As note before,

in constructing ˆW2 (i.e. variance-covariance matrix) I allow lnµjht’s to be clustered by source country.

Since Mjt

MUS, pjht

pUS,t, and ln�ij|h,t are all endogenous and correlated with lnµjht, I have to find instruments

that are correlated with these three variables but uncorrelated with lnµjht . To identify the price coefficient,

I will instrument price with total charges paid by exporters–which is equal to freight plus tariff charges.

As shown in proposition 1, freight charges are correlated with the HS code quality (↵h). However, freight

charges are not correlated with the country-level quality (µj) 25. µjht does affects wages which in turn can

25“Shipping the good apples out” effect, induces firms from the same country to export in higher quality (↵h) HS10 codes when theyface a higher freight rate. µj , on the other hand, does not affect the mix or price of the exported varieties directly, but affects the priceof all varieties from country j equally through wages.

25

influence freight rates. To take care of the possible endogeneity of freight rates, I run my main estimation

without using freight charges as an instrument . I also use exchange rate and oil price multiplied by distance

as additional instruments for c.i.f prices.✏�1�̄�1 , the coefficient of the nested share (�j|h,t), is identified by comparing varieties, belonging to dif-

ferent HS10 codes, which have similar prices but absorb different market shares. �j|h,t is endogenous and

correlated with µjht. I instrument �j|h,t with (1) the number of exporting countries in code h in year t

and (2) the number of distinct HS10 codes that country j exports throughout the years 1989 to 1994 in the

SITC5 industry that h belongs to. Both these variable are correlated with conditional nest share �j|h,t, but

uncorrelated with µjht.26 The number of distinct HS10 codes that country j exports throughout the years

1989 to 1994 is not correlated with µjht under the assumption that µjht’s are not clustered by year, but only

clustered by source country, i.e. Cov[µjht, µjht0 ] = 0 for all t, t0=1989-1994.

Finally, I instrument for Mjt

MUSwith population of country j,27 and the average number of export lines

per quantity sold by country j in the two-digit SIC sector which code h belongs to. I also use a dummy for

membership in WTO/GATT as an additional instrument for Mjt

MUS.

Table 1 shows the results from the baseline estimation. For 390 industries the two-step GMM estimator

converges which implies that for 390 industries I have enough variation in my data to identify all four

parameters in ⇥. For 82% of the industries the price coefficient is statistically significant and has the correct

sign. For around 75% of the industries, the estimated � is bigger than one and statistically significant,

while it’s very close to one or insignificant for the remaining industries. This implies that for the majority

of the SITC5 industries, varieties produced in the same country are more substitutable which confirms

assumption 2 in my theoretical model. the estimated �̄�1✏�1 is larger than one and statistically significant for

all 390 industries. Also nearly all the estimated values of are close to one as expected.

3.3.1 Alternative Specification

In this section I will re-estimate demand, this time assuming �h varies across HS10 codes. Like before, I

estimate demand (micro-gravity) separately for each SITC5 industry in my sample. The demand equation

is similar to the baseline case and has the following formulation

26Khandelwal [2010] uses the same set of instruments for �j|h,t.27In my model, everything else the same, a larger population lowers the wages and increase the number of exporting firms from a

country.

26

Statistic Median First quartile Third quartile

⌘ (✏� 1) .067 .034 .109

� 1.31 .979 1.85

�̄�1✏�1 10.38 8.499 12.93

.988 .979 .997

Two-step GMM p-value, ⌘ (✏� 1) .000 .000 .028

Two-step GMM p-value, � .000 .000 .000

Two-sepGMM p-value, �̄�1✏�1 .000 .000 .009

Two-step GMM p-value, .000 .000 .000

Number of SITC industries 390

Total observations across all estimations 270,327

Table 1: Summary of statistics from estimating the baseline demand equation (13) for 390 SITC industries

ln

Xjht

XUS,t=

✏� 1

� (�h � 1)

ln

Mjt

MUS+ (✏� 1) ln

↵ht

↵US,t� (✏� 1) ⌘ ln

pjhtpUS,t

+

1� ✏� 1

�h � 1

�

ln�ij|h,t + (✏� 1) lnµjht

(18)

As discussed in the theory section, �h � 1 is identified from ⌘ by looking at across-HS10 variations.

Hence, estimating �h with an HS10 dummy is not plausible. Since in my theoretical model I assume that �h

is lower in HS10 codes with a higher ↵h, I will identify �h by assuming a functional form for the dependence

of �h on ↵h. However, I do not impose any restrictions on the direction and scale (and of course significance)

of this dependence. More specifically, I assume �h depends on ↵h according to the following parametric

assumption

�h � 1

✏� 1

= ✓1 +

✓

↵ht

↵US,t

◆✓2(✏�1)

(19)

If ✓2 is negative and significant, then assumption 1 in my theoretical model is confirmed. To back out

quality I can use the equivalent of equation (15), which I used for the baseline specification

(✏� 1) ln

↵ht

↵US,t=

8

<

:

ln

Xht

XUS,t� ✏� 1

�h � 1

ln

X

j2Cht

✓

Mjt

MUS

◆

1�✓

pjhtpUS,t

◆�⌘(�h�1)9

=

;

(20)

The effect of ↵h (on spending/market share) cannot be identified through the above equation inde-

27

pendent of the effect of �h, for the following reason. A lower sigma in equation (18) will mechanically

overstate ↵h because �h and ↵h have similar but not identical effect on market share, Xht

XUS,t. A higher ↵h

leads to higher Xht

XUS,tconditional on prices, while a lower �h leads to a higher Xht

XUS,tunconditionally (since

it simultaneously deflates the effect of prices on spending). To account for this problem I approximate ↵ht

↵US,t

using the following equation

(✏� 1) ln

↵̂ht

↵̂US,t=

8

<

:

ln

Xht

XUS,t� ✏̄� 1

� � 1

ln

X

j2Cht

✓

Mjt

MUS

◆

1�✓

pjhtpUS,t

◆�⌘(✏�1) (�̄�1)✏̄�1

9

=

;

(21)

where �̄�1✏̄�1 is from the baseline estimation and the remaining parameters (�, ⌘(✏� 1), and ) are param-

eters to be estimated. In the above approximation of quality, according to proposition 4, the term in the

braces preserves the rank of HS10 qualities, ↵h, if ✏ = ✏̄. As before, corrects the scale, and since the above

proxy is very close to the structural representation of (✏� 1) ln

↵ht

↵US,t, I expect to be close to one.

Table 2 provides the results from estimating equation (17). given that I need more variation in the

data (in terms of price and market share) to identify the parameters using the alternative specification in

equation (17), the two-step GMM estimator converges for 322 industries, which is less than the baseline

estimation. The price coefficient is statistically significant and has the correct sign for 78% of the industries.

✓2 is negative and significant for 82% of the industries, while the estimated � is statistically significant and

bigger than one for 72% of the industries. � has on average the same estimated value in both specification.

Again, for nearly all industries the scale parameter is very close to one.

3.4 Discussion of Results

As shown in equation (7) trade elasticity is ⌘ (�h � 1) which can be calculated multiplying the two estimated

values, ⌘ (✏� 1) and �h�1✏�1 . The first result from the estimation of elasticities is that both specifications result

in somehow similar trade elasticities. Table 3 provides a summary of statistics for the trade elasticities

estimated according to both specifications. The composition of the trade elasticity is quite different in two

estimations. In the baseline estimation trade flows are more sensitive to price (i.e higher ⌘), while when I

allow for �h to vary across HS10 codes, conditional trade shares within HS10 codes (Xjht

Xh,t) are less sensitive

to prices, i.e. ⌘ is lower. The reason is that in the baseline estimation, I am trying to match the high variations

in trade shares (within the HS10 codes) with a relatively low elasticity (0.837), while some of these HS10

codes have an elasticity that goes as high as 8.936 on average. When I allow for elasticity to be high in low

quality HS10 codes I do not need a high ⌘ to match the within HS10 code trade shares, anymore.

28

Statistic Median First quartile Third quartile

⌘ (✏� 1) .014 .005 .032

� 1.33 .961 2.05

✓2 -.804 -1.27 -.512

✓1 15.9 7.35 28.2

.991 .984 .996

Two-step GMM p-value, ⌘ (✏� 1) .000 .000 .028

Two-step GMM p-value, � .000 .000 .000

Two-sepGMM p-value, ✓2 .000 .000 .009

Two-step GMM p-value, ✓1 .000 .000 .092

Two-step GMM p-value, .000 .000 .000

Number of SITC industries 322

Total observations across all estimations 246,777

Table 2: Summary of statistics from estimating equation (17) for 322 SITC industries

Parameter Median First quartile Third quartile

⌘ (�maxh � 1) 8.936 1.712 217.5

⌘�

�minh � 1

�

0.341 0.505 0.801

⌘ (�avgh � 1) 1.470 0.860 7.128

⌘ (�̄ � 1) 0.837 0.598 1.259

Table 3: The elasticity of demand wrt to price across SITC industries.

29

Sector Code Feenstra et al. 2012 Quality Dependent (median) Baseline (median)

Electronics 36 0.797 0.874 0.770

Chemicals 28 0.474 0.591 0.656

Food 20 0.792 0.637 0.670

Metals 33 0.496 0.695 0.628

Table 4: Comparison of estimated trade elasticities to Feenstra et al. [2012]

My estimated elasticities are close to the estimates found by Feenstra et al. [2012], who estimate trade

elasticities in an Amington model. In particular, they estimate a micro-gravity equation for various 2-digit

SIC sectors. To compare my results to Feenstra et al. [2012], I calculate the median value of my elasticity

estimates across all the SITC5 industries which belong to the same 2-digit SIC sector (under both specifica-

tions). In Table 4, for four sectors, I compare the median elasticity I estimate to the elasticity estimated by

Feenstra et al. [2012].

Trade elasticity ⌘ (� � 1) in my model has the same effect, but yet a very different interpretation, as

the Pareto shape parameter–✓–in the Eaton and Kortum [2002] model. Simonovska and Waugh [2011]

find an estimate value between 2.79 to 4.46 for ✓, under different specifications. The reason the estimated

elasticities are significantly lower in my model, compared to the estimated elasticities by Simonovska and

Waugh [2011] could be one of the following. First, they use a very different identification strategy. They

apply the simulated method of moments estimator that minimizes the distance between the trade volumes

generated by the EK model to real data. Second, in the EK model (and hence, in their simulation) mass of

firms/varieties is exogenously forced to be one. In my approach, Mass of firms is an endogenous variable,

and I use data on mass of firms to structurally estimate trade/demand elasticities. Ignoring the larger mass

of firms exporting from countries with high export intensities28, can result in over-estimating the spread of

productivity to capture the high variation in trade volumes across exporters.

Another result from my micro-gravity estimation is that quality (↵h) varies quite a lot across HS10 codes.

Consumers on average value some HS10 codes much more than others. I can calculate the (across HS10

code) quality ladder for each SITC5 industry, S, as below

LadderS = (✏� 1)

�

ln ↵̂maxS � ln ↵̂min

S

where ln ↵̂maxS = maxh2S {ln ↵̂h}. Since I estimate micro-gravity for 390 SITC industries, I will have 390

quality ladders. In figure 5 I plot the distribution of the quality ladder across all SITC5 industries in my

28In my model countries with lower (pure) wages and trade costs will have more firms exporting in equilibrium.

30

sample. The results suggest an average length of 5 for the quality ladder, which indicates a high level of

quality differentiation across HS10 codes. Note that there is also quality differentiation within every HS10

code due to µjh. Ignoring quality variation across HS10 codes can result in under-estimating the elasticity of

substitution in order to match the high market share absorbed by high quality HS10 codes–a result evident

in table 3.

Figure 5: The distribution of the quality ladder (length) across different SITC industries.

3.4.1 Robustness Checks

I perform various robustness checks. First, I redo the estimation with a sample that has been trimmed with

less restricting cutoffs. I rerun the estimation twice once for a sample of observations that report values

above $7500 and once I use $2500 as the cutoff. The overall magnitude and significance of the estimated

parameters is robust to how I trim the data. The same goes for within HS10 code trimming of the data. The

results are robust to not dropping the highest and lowest 1% c.i.f prices in each HS10 code.

Second, my results are robust to the choice of instruments. I redo my estimation by dropping each

instrument one at a time. The direction of the effects (� being bigger than one and ✓2 being negative) are

not affected by the choice of instruments. Third, I redo the estimation with the following functional form

assumption on �h

�h � 1

✏� 1

= ✓1 + ✓2

✓

↵ht

↵US,t

◆(✏�1)

Again, the direction of the estimates are not sensitive to the functional form assumption on �h. The rea-

son I always include ✓1 is that ln ↵ht

↵US,tis negative for nearly all observations, and dropping ✓1 will mechan-

31

ically force ✓2 to be negative, so that �h can be be positive. Finally, I estimate the model without clustering

the quality residual µjht by country. This doesn’t affect the direction of the results, but overestimates (the

median) � by around 0.15.

3.5 Calibration

In the second stage of my empirical inquiry, I will map my model to global trade flows to explore the

general equilibrium properties of my model. In this section, I calibrate the key parameters to the general

equilibrium outcomes of the model using data for many countries. Specifically, I calibrate iceberg trade

costs, country-level qualities, fixed costs of exporting varieties, and market entry cost to data on bilateral

trade flows, and per capita GDP/wages. I solve for the endogenous (relative) wages, price indices, and

mass of firms in every country.

3.5.1 Data

I use data on bilateral merchandise trade flows in 2000 from the U.N. Comtrade database , and data on

population and GDP from the World Bank database. I only consider the 50 largest economies (in terms of

Real GDP) that account for more than 80% of world trade in 2000. Each observation contains the total value

of trade for an importer–exporter country pair. Data specific to country pairs–distance, common official

language, and borders–are compiled by Mayer and Zignago [2011].

3.5.2 Calibration Strategy

Trade shares,�

�ij

i,j2C, are a function of the set of N countries, each with its population Li, wage wi,

quality µi and trade costs ⌧ji; parameters �, ⌘, ✏, and {�h}h2H that control the elasticity of substitution

across varieties; entry cost parameter fe that govern entry decision of firms into different markets, and

fixed cost f that govern entry decision of firms into different HS10 product codes in each market. I take the

set of countries, their population Li, and wages wi from the data, and I calibrate {⌧ji}Nj,i=1, {µi}Ni=1, f , fe to

match trade flow data.

In the previous section I estimated demand elasticities for 390 SITC industries. To calibrate my model to

global trade data, I normalize ✏ to two, as in Khandelwal [2010] or Berry et al. [1995]. I then use the median

estimated value for the remaining demand parameter–�, ⌘, and {�h}h2H . More specifically, I let � = 1.33,

�h � 1 = 15.9 + (↵h)�0.804, ⌘ = 0.014, and ln ↵̄ = 5.29

29The lowest quality is normalized to one.

32

Before, I assumed domestic and foreign firms all pay the same entry cost fe, and foreign firms pay an

extra overhead cost f for each HS code they export. In my calibration exercise I assume that the entry cost

by foreign firms is also different and equal to fe+ fx. I normalize fe to one since the scale of fe only affects

the scale of firm entry (M ij ), but not the relative mass of firms in the market. In the following, I will describe

my strategy for identifying iceberg trade costs–{⌧ji}Nj,i=1–and country level qualities–{µi}Ni=1.

Iceberg trade costs I assume that iceberg trade costs take the form

⌧ji = 1 + ⌧dist ⇤ ⌧border ⇤ ⌧lang ⇤ ⌧agreement

where

8

>

>

>

>

>

>

>

>

>

>

<

>

>

>

>

>

>

>

>

>

>

:

⌧distance = 1 + distDji

⌧border = [border � 1] dborder + 1

⌧lang = [lang � 1] dlang + 1

⌧agreement = [agreement � 1] dagreement + 1

The term ⌧dist ⇤⌧border ⇤⌧lang ⇤⌧agreement is the proxy for geographic barriers, and the number 1 added to

it is the production cost. Variable Dji is the distance (in thousands of kilometers) between countries j and

i. So ⌧dist is the effect of distance on trade costs. Parameter ⌧border equals 1 if countries j and i do not share

a border, and border otherwise. If border is, say, 0.8, sharing a border reduces trade costs by 20%, but it

does not affect production costs; if border > 1, sharing a border increases trade costs. Similarly, parameters

lang an agreement refer, respectively, to whether countries j and i share a language, and whether they

have a trade agreement. Henceforth, ⌥ = {dist,border,lang,agreement, f, fe, fx} refers to the set of trade

cost parameters and ¯

⌥ refers to the set of data on countries’ pairwise geopolitical characteristics—distance,

common border, language, and trade agreement.

Country-level qualities I identify the vector of country-level qualities in an inner-loop with wage data,

using the following algorithm.30 Given parameters {⌥, �,�h, ↵̄, ⌘}, data on population L = {Li}Ni=1, and

geopolitical characteristics ¯

⌥, the product market clearing condition (PMC) pins down a relation between

country-level qualities {µi}Ni=1 and market clearing wages�

wi N

i=1. Therefore, fixing other parameters, I

can uses wages directly to back out the country-level qualities–{µi}Ni=1. I take per capita income from the

data as a proxy for wages. Then, for each guess of the parameters, I simulate the whole economy, generating

30Fieler [2011] uses the same strategy to pin down the technology parameters in a Ricardian model.

33

Parameters value

dist 0.221

lang 0.591

border 0.477

agreement 0.607

f 0.079

fx 2.760

f 1

Goodness of fit (R-squared) 0.33

Table 5: Calibrated trade cost parameters

trade flows Xij , and therefore trade shares �ij , until I find a vector of country-level qualities –µ–that satisfies

equilibrium conditions.

After substituting fixed and variable trade costs and the implicit solutions for country-level qualities,

{µi}Ni=1, the moment condition (minimized in the outer-loop) can be written as

⇥

�ij(w,L,¯

⌥,⌥, �,�(↵h), ↵̄, ⌘)� �ij⇤N

i 6=j=1

where, �ij is share of spending on varieties from country j in country i. Each element in the above (N �

1)⇤ (N �1) vector characterizes the distance between the respective model outcome (given the parameters)

and the outcome in the data.The calibration’s objective is to minimize the sum of the squared differences

between the model outcomes and the data targets for these outcome. I normalize the wage and quality of

the US varieties to 1 and 100 respectively.

Table 5 provides the calibrated trade cost parameters, and table 6 presents the calibrated country-level

qualities (µ1/⌘i ) and quality-adjusted wages (wi/µ

1/⌘i ). The rank of countries in terms of their quality (µi) is

the same as their technology (Ti) rank in the Eaton and Kortum [2002] model. This is quite intuitive given

that the effect of technology (Ti) in my model is captured by (1) the quality of a country’s products (µi), and

(2) the mass of varieties/firms that enter various markets form country i (M ij ).

34

Country µ1/⌘i

wi

µ1/⌘i

Country µ1/⌘i

wi

µ1/⌘i

Country µ1/⌘i

wi

µ1/⌘i

Country µ1/⌘i

wi

µ1/⌘i

USA 100 1 Russia 0.45 11.44 Greece 4.99 6.08 Taiwan 10.05 4.18

Japan 93.53 1.13 Switzerland 22.80 4.34 Portugal 5.07 6.28 Venezuela 1.39 10.04

Germany 33.97 1.97 Sweden 24.80 3.18 Iran 0.30 15.36 New Zealand 5.03 7.84

UK 31.89 2.19 Belgium 12.30 5.31 Egypt 0.24 17.85 Argentina 4.00 5.56

France 29.43 2.21 Turkey 0.88 9.73 Ireland 10.80 6.76 Israel 8.61 6.17

China 0.26 10.37 Austria 15.54 4.50 Singapore 10.85 6.14 Netherlands 22.73 3.08

Italy 23.30 2.39 S Arabia 4.69 5.62 Malaysia 0.94 12.12 Finland 15.15 4.44

Canada 20.41 3.29 Poland 1.44 8.95 Colombia 0.33 17.83 Peru 0.28 20.86

Brazil 1.79 5.97 Hong Kong 14.65 4.99 Philippines 0.10 27.90 Australia 19.65 3.07

Mexico 3.37 5.09 Norway 35.07 3.06 Chile 1.21 11.69 Thailand 0.46 12.63

Spain 12.35 3.37 Indonesia 0.13 18.03 Pakistan 0.03 43.21 Algeria 0.19 26.99

Korea Rep. 8.34 3.77 Denmark 24.57 3.53 UAE 11.93 5.27

India 0.06 21.55 South Africa 0.74 11.84 Czech Rep. 1.23 13.01

Table 6: Calibrated country level quality parameters

Figure 6: Comparison of country-level quality estimates by Hallak and Schott [2011] with the calibrated value in this paper. I usethe average value estimated by Hallak and Schott [2011] for years 1998 and 2003, and normalize the quality of Argentina to zero.

35

3.5.3 Quantitative predictions

In this section I will illustrate the quantitative predictions of my calibrated mode. The first and most im-

portant result of my calibrated model is the scale of iceberg trade costs. Anderson and Van Wincoop [2004],

in their seminal paper, raise the question of why unobserved trade costs are so high?

Forcing � (the relative scale of the micro-elasticity to the macro-elasticity) to be equal to one, which is

the conventional practice in the existing literature, will result in under-estimating the already high iceberg

costs. The intuition is simple; suppose the elasticity of substitution between Home and Foreign varieties

is not lower than the elasticity of substitution between different Home varieties. Then, there will be less

incentive to trade since the foreign varieties are not bringing anything to the table that the Home varieties

cannot offer. As a result, to match the high volume of trade, the estimated trade costs should be sufficiently

low. Actually, if iceberg costs are high enough so that the Home variety is always cheaper than the Foreign

variety, there will be no trade at all under the assumption that � = 1.

To test this claim, I calibrate a baseline model with � = 1 and ⌘(� � 1) = 0.837 to the global bilateral

trade data. The calibrated iceberg trade costs are around 38% lower than the calibrated values from my

main specification where the within source country micro-elasticity is 33% higher than the across country

macro-elasticity (� = 1.3). This result is quite striking given that it adds up even more to the mystery of

why trade costs are so high. The result also suggests that if one decomposes the gains from trade into gains

from variety and gains from price; the gains from variety will be relatively higher under the correct demand

structure.

One shortcoming of the mainstream trade models is that they either predict lower prices for varieties

exported from high wage countries (Ricardian models) or they predict the same price per unit of quality

for all countries, conditional on geography (baseline Krugman model). In proposition 2, I showed that my

model theoretically overcomes this problem. Here, I demonstrate how my model performs quantitatively in

explaining the higher export share of high wage countries. In figure 7, I plot the log of wages (lnwi) against

the log of country-level qualities (lnµi), for my 50-country sample. As expected, from proposition 2, high

quality countries have higher wages. However, what my model brings to the table is that wage per unit of

quality ( wi

µ1/⌘i

) is lower in high quality countries, which give them absolute advantage in the global market.

To depict this point I plot the log of quality adjusted wages (ln wi

µ1/⌘i

) against the nominal country wages

(lnwi) in figure 8. The resulting scatterplot indicates that (firms from) high-quality/high-wage countries

charge a lower price for every unit of quality they sell,, which explains why they export more.

One other quantitative property of the model, that I explore, is how good my model matches data on

the price of traded goods in general. There are two effects that my model captures theoretically: (i) the

36

ARE

ARG

AUSAUTBEL

BRA

CAN

CHE

CHL

CHN

COL

CZE

DEU

DNK

DZAEGY

ESP

FIN FRAGBR

GRC

HKG

IDN

IND

IRL

IRN

ISR ITA

JPN

KOR

MEX

MYS

NLD

NOR

NZL

PAK

PER

PHL

POL

PRT

RUS

SAU

SGPSWE

THA

TUR

TWN

USA

VEN

ZAF

!4

!3

!2

!1

0

log(w

)

!4 !2 0 2 4

log(mu)

Figure 7: Estimated country-level quality (lnµi) against country wage (lnwi) in 2000.

AREARG

AUS

AUTBEL

BRA

CAN

CHE

CHLCHN

COL

CZE

DEU

DNK

DZA

EGY

ESP

FIN

FRAGBR

GRC

HKG

IDNIND

IRL

IRN

ISR

ITA

JPN

KOR

MEX

MYS

NLD NOR

NZL

PAK

PER

PHL

POL

PRT

RUS

SAUSGP

SWE

THA

TUR

TWN

USA

VENZAF

!5

!4

!3

!2

!1

log(w

/mu)

!4 !3 !2 !1 0

log(w)

Figure 8: Absolute advantage of high wage countries in the global market: Estimated quality-adjustedwage (ln wi

µ1/⌘i

) against wage (lnwi) in 2000.

37

Correlation of simulated prices with unit values observed in data

My model 0.414

Baseline model 0.228

Table 7: Comparing the fit of my model to observed unit values of trade in data, to the baseline model ((i.e.� = 1 and ⌘(� � 1) = 0.837 ))

effect of trade costs on prices, and (ii) the higher price of high wage exporters. To demonstrate the merits of my

model relative to the baseline (Krugman) model, quantitatively, I look at the correlation between the price

of traded goods generated by my calibrated model and the unit value of traded goods as seen in the data.31

Note that when calibrating my model I have only matched data on trade volumes, so this will be an out of

sample prediction. I do the same for a baseline calibrated model (i.e. � = 1 and ⌘(� � 1) = 0.837 ), and

compare the fit of my model to the baseline model. The results are provided in table 7, showing that my

model fits the price data significantly better than the baseline model.

3.6 The Effect of Trade on Variety: a Counterfactual Analysis

As noted in section 2 of the paper, lowering iceberg trade costs will decrease the number of varieties in

the low-quality HS10 codes, but will dramatically increase the number of high-quality varieties. With the

logit interpretation of demand, consumers who buy only one variety from one HS10 code, will be affected

according to the price index in that HS10 code. Hence, the anti-variety effect of trade in low-quality HS10

codes can have anti-welfare effects for a portion of the consumers who strongly prefer the low-quality HS10

codes.

In this section, I perform a counterfactual analysis based on my calibrated model of the global economy

to quantify the variety effects of trade. I will first analyze the effect of a 50% drop in variable trade costs

on purchasing power (i.e. wi

P ih

) in different HS10 codes in each country. In the counterfactual experiment,

the general equilibrium is resolved for the new trade values, and the new measure of purchasing power

is calculate using the counterfactual wage and (quality adjusted) price index. In table 8, the first column

reports changes in wage when iceberg trade costs fall by 50%. The remaining columns report the change

in purchasing power (wi

pih

) for five different HS10 codes or quality levels. With a logit interpretation of

demand32, the first HS10 code (h = 1) could be thought of as the group of consumers who have a strict

preference (taste) for product one ( h = 1), and so forth.

31Since the U.N. Comtrade data base does not report quantity of trade, I use the data compiled by Feenstra et al. [2005] to calculateunit values in the benchmark year, 2000.

32In the appendix I show that logit preferences are isomorphic to CES preferences and produce the same demand function. How-ever, there is avery different interpretation behind each one of them.

38

The results in table 8 suggest that lowering iceberg trade costs can result in very unevenly distributed

equilibrium gains/losses. The purchasing power always drops in the low qualities, while in the high-

est quality product code, the purchasing power doubles on average. Another expected pattern is that

asymmetric effects of trade hit smaller economies, and marginal qualities harder. In Austria, for example,

purchasing power for high quality products increases around 300%–more so for products of medium-high

quality–while purchasing power for low-quality products drops up to 20%–again more so for medium-low

qualities.

As noted before, removing the fixed exporting cost–f–will, on the other hand, have pro-variety effects

in all product codes/qualities. To demonstrate this result, I perform a second counterfactual experiment

where I lower the fixed cost of exporting–f . The results is provided in table 9 suggesting that the purchasing

power (and also the number of varieties) increases evenly in all product codes/qualities.

39

Countryw0

iwi

V ih

V i0h

|h=1V ih

V i0h

|h=2V ih

V i0h

|h=3V ih

V i0h

|h=4V ih

V i0h

|h=5

USA 0.933 0.988 0.968 0.944 0.996 1.050

Japan 0.916 0.992 0.979 0.963 0.964 0.989

Germany 1.008 0.972 0.928 0.876 1.204 1.321

UK 1.103 0.953 0.882 0.801 1.700 1.734

France 1.031 0.967 0.916 0.857 1.299 1.415

China 0.977 0.978 0.944 0.903 1.247 1.203

Italy 0.981 0.977 0.942 0.899 1.110 1.219

Canada 1.275 0.925 0.814 0.695 2.813 2.672

Brazil 0.930 0.988 0.970 0.948 1.008 1.038

Mexico 1.002 0.973 0.931 0.881 1.250 1.297

Spain 1.034 0.967 0.914 0.854 1.282 1.427

Korea Rep. 0.985 0.977 0.939 0.896 1.176 1.234

India 1.098 0.954 0.884 0.805 1.976 1.704

Russia 1.016 0.970 0.923 0.869 1.327 1.352

Switzerland 1.271 0.925 0.815 0.697 2.643 2.647

Sweden 1.066 0.960 0.899 0.828 1.417 1.566

Belgium 1.251 0.929 0.822 0.708 2.534 2.525

Turkey 1.038 0.966 0.912 0.851 1.392 1.443

Austria 1.217 0.934 0.835 5.312 2.353 2.326

S Arabia 1.028 0.968 0.918 0.859 1.281 1.402

Poland 1.114 0.951 0.877 0.793 1.792 1.785

Hong Kong 1.251 0.929 0.822 0.708 2.464 2.526

Norway 1.095 0.955 0.885 0.807 1.510 1.697

Indonesia 0.947 0.985 0.960 0.931 1.075 1.095

Denmark 1.118 0.951 0.875 0.790 1.680 1.805

South Africa 1.143 0.946 0.865 2.472 2.119 1.922

Greece 1.067 0.960 0.898 0.828 1.427 1.569

Portugal 1.126 0.949 0.872 0.785 1.751 1.845

Iran 1.017 0.970 0.923 0.867 1.306 1.360

Egypt 1.113 0.952 0.878 0.794 1.855 1.777

Ireland 1.279 0.924 0.812 2.363 2.736 2.697

Singapore 1.239 0.930 0.827 3.700 2.399 2.451

Malaysia 1.171 0.942 0.853 0.756 2.009 2.071

Colombia 1.183 0.939 0.848 0.748 2.217 2.136

Philippines 1.213 0.935 0.837 2.872 2.467 2.297

Chile 1.176 0.941 0.851 0.752 2.132 2.097

Pakistan 1.240 0.930 0.826 3.012 2.602 2.459

UAE 1.140 0.947 0.866 2.124 1.801 1.913

Czech Rep. 1.215 0.934 0.836 2.423 2.354 2.311

Taiwan 1.119 0.951 0.875 0.790 1.636 1.808

Venezuela 1.156 0.944 0.859 0.765 2.009 1.992

New Zealand 1.209 0.935 0.837 2.551 2.375 2.278

Argentina 1.042 0.965 0.910 0.847 1.357 1.461

Israel 1.232 0.931 0.829 2.708 2.463 2.409

Netherlands 1.098 0.954 0.884 0.805 1.625 1.708

Finland 1.139 0.947 0.866 1.706 1.825 1.908

Peru 1.201 0.936 0.841 0.737 2.298 2.235

Australia 1.029 0.968 0.917 0.858 1.332 1.407

Thailand 0.975 0.979 0.945 0.905 1.138 1.197

Algeria 1.238 0.931 0.827 2.606 2.492 2.447

Table 8: Gains from lowering iceberg trade costs by 50%, across different consumer groups.

40

Countryw0

iwi

V ih

V i0h

|h=1V ih

V i0h

|h=2V ih

V i0h

|h=3V ih

V i0h

|h=4V ih

V i0h

|h=5

USA 0.9999 1.0000 1.0006 1.0103 1.0000 1.0000

Japan 1.0004 1.0000 1.0000 1.0006 1.0001 1.0002

Germany 1.0000 2.8375 2.5204 1.2864 1.0003 1.0004

UK 0.9999 1.0663 1.1178 1.2261 1.0001 1.0002

France 0.9999 1.0000 1.0081 1.0635 1.0000 1.0001

China 1.0001 1.3903 1.1747 1.1640 1.0001 1.0001

Italy 0.9999 1.0000 1.0045 1.0361 1.0000 1.0000

Canada 1.0000 2.9064 2.8635 2.9914 1.0004 1.0004

Brazil 1.0000 2.5901 2.9967 3.8997 1.0004 1.0004

Mexico 0.9999 1.0061 1.0246 1.0745 1.0000 1.0000

Spain 0.9999 1.0000 1.0081 1.0635 1.0000 1.0001

Korea Rep. 1.0002 1.0026 1.0172 1.0437 1.0001 1.0001

India 0.9999 5.0851 3.1160 2.1566 1.0002 1.0001

Russia 0.9999 1.0073 1.0687 1.2305 1.0001 1.0001

Switzerland 1.0001 2.1483 2.6844 3.7658 1.0004 1.0005

Sweden 1.0001 1.5606 1.6243 2.1790 1.0004 1.0005

Belgium 1.0000 2.5901 2.9967 3.8997 1.0004 1.0004

Turkey 1.0000 1.0103 1.0152 1.0416 1.0000 1.0001

Austria 1.0000 1.9971 2.0413 2.3556 1.0003 1.0003

S Arabia 0.9999 1.0108 1.0402 1.1053 1.0000 1.0001

Poland 1.0000 11.6559 8.3114 1.3110 1.0004 1.0004

Hong Kong 1.0002 1.4388 1.5314 2.0868 1.0004 1.0005

Norway 0.9999 1.0099 1.0760 1.2303 1.0001 1.0001

Indonesia 1.0000 1.0227 1.0147 1.0319 1.0000 1.0000

Denmark 0.9999 1.0051 1.0603 1.2144 1.0001 1.0002

South Africa 0.9999 1.2340 1.3333 1.5803 1.0002 1.0002

Greece 0.9999 1.0002 1.0168 1.1034 1.0000 1.0001

Portugal 0.9999 1.0073 1.0687 1.2305 1.0001 1.0001

Iran 0.9999 1.0033 1.0301 1.0976 1.0000 1.0000

Egypt 0.9999 2.0079 1.6933 1.6778 1.0001 1.0001

Ireland 1.0001 3.6251 4.1091 1.0384 1.0006 1.0006

Singapore 1.0001 1.5606 1.6243 2.1790 1.0004 1.0005

Malaysia 1.0001 1.6377 1.5549 1.7401 1.0002 1.0003

Colombia 0.9999 2.0587 2.0259 2.2409 1.0002 1.0002

Philippines 1.0000 11.6559 8.3114 1.3110 1.0004 1.0004

Chile 0.9999 1.6991 1.6710 1.9045 1.0002 1.0002

Pakistan 1.0000 11.6559 8.3114 1.3110 1.0004 1.0004

UAE 1.0000 1.0152 1.1110 1.3004 1.0001 1.0002

Czech Rep. 1.0000 2.8375 2.5204 1.2864 1.0003 1.0004

Taiwan 1.0001 1.0007 1.0277 1.1550 1.0001 1.0003

Venezuela 0.9999 1.2340 1.3333 1.5803 1.0002 1.0002

New Zealand 1.0000 2.0419 1.9893 1.0398 1.0004 1.0004

Argentina 0.9999 1.0001 1.0160 1.0975 1.0000 1.0001

Israel 1.0000 2.2571 2.2290 1.2336 1.0004 1.0004

Netherlands 0.9999 1.0099 1.0760 1.2303 1.0001 1.0001

Finland 0.9999 1.0000 1.0081 1.0635 1.0000 1.0001

Peru 1.0000 11.6559 8.3114 1.3110 1.0004 1.0004

Australia 0.9999 1.0030 1.0288 1.0910 1.0000 1.0001

Thailand 1.0000 1.0103 1.0152 1.0416 1.0000 1.0001

Algeria 0.9999 1.0051 1.0603 1.2144 1.0001 1.0002

Table 9: Gains from removing the fixed cost of exporting varieties, across different consumer groups.

41

4 Conclusion

In this paper I have shown that instead of imposing restrictive assumptions on demand elasticities to back

out unobserved trade costs, using aggregate trade data, one could first back out the correct demand struc-

ture using disaggregated data were trade costs are observable. Then using the correct demand structure we

can identify the correct trade costs in aggregate data. The advantage of implementing this strategy is that

(i) I can also match price moments in the trade data rather than just moments on trade volumes, and (2) I

will have a better estimate of the unobserved trade costs at the aggregate level. In particular, I have show

that when one ignores the higher degree of substitutability between varieties manufactured in the same

country, they will underestimate trade costs by a big margin.

The main merit of my model, theoretically and empirically, is generating results that are consistent with

not only data on bilateral trade volumes, but also data on the price (and quality) of traded goods. In my

model this property is achieved in a Dixit-Stiglitz (CES) framework without imposing any kind of non-

homotheticity assumption on demand.

Another aspect of my model that I do not fully explore in this paper is the distribution of gains from

trade. Since the model matches the fact that trade favors high quality products, it generates a richer set

of results regarding the gains from trade. As a result of lowering iceberg trade costs, purchasing power in

high quality products rises dramatically at the cost of lower purchasing power in low quality products.

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