Essays in International Economics; Decomposing Episodes of Large Growth in International Trade.

Chapter 1

Introduction

My thesis consists of three essays in the field of international economics. The

first two essays examine trade growth during periods of large growth in inter-

national trade over the past 60 years. I use bilateral trade data to decompose

trade growth across goods classifications during rapid growth episodes and find

that trade growth is granular — the majority of overall trade growth between

given country-pairs is accounted for by a small number of goods classifications

exhibiting large growth in trade, while most goods exhibit small or negligible

growth. In the first essay (Chapter 2), I ask whether standard “Melitz-style”

international trade models, when supplemented with productivity and tariff

changes imputed from trade data, can generate the observed level of granu-

larity in bilateral trade data. In the second essay (Chapter 3), I add a choice

among multiple distribution technologies for exporting firms, with differing

fixed and variable costs, to quantify the model’s ability to match the observed

granularity of trade growth. The third essay (Chapter 4) examines how varia-

tion in transportation methods, which I denote “the supply network”, impacts

price dispersion across locations. I use a unique data set on weekly gasoline

prices across 44 Canadian cities to quantify how differences the available meth-

ods of transporting gasoline between locations (by pipeline, marine tanker, rail

or truck) account for observed mean and weekly price differences across cities.

International trade has grown nearly twice as fast as world GDP over the

past 60 years. For most countries, this growth in trade has occurred in a small

number of rapid growth episodes. Standard international trade models have

significantly under-predicted this large growth in international trade during

these periods of rapid growth. As such, recent Melitz-style trade models have

investigated the role of heterogeneity in trade growth across various industries

and goods. Chapter 2 analyzes bilateral trade data, at the 5-digit SITC classi-

fication level for Canada, Germany, Mexico, Japan, U.S., and U.K. (accounting

for 20–25% of global trade) between 1989 and 1999, in order to to decompose

the patterns of trade growth across various goods classifications. I find that

bilateral trade growth during these rapid growth episodes is granular — less

than 5% of goods classifications account for over 65% of overall bilateral trade

growth while the majority of goods exhibit little to no growth in trade.

Trade theory suggests that disproportionately large growth in this small

number of goods categories may be accounted for by the goods experiencing

the largest reductions in tariff rates. However, I find that tariff reductions

cannot account for the granularity of bilateral trade growth. Further, I find

that production growth and increases in trade intensity (defined as the share

of domestic production that is exported) are both significant factors in these

large-growth goods classifications.

I use a Melitz-style trade model, featuring heterogeneous productivity firms

facing CES demand under monopolistic competition, calibrated to match bilat-

eral trade flows, to quantify the predictions for trade growth across goods clas-

sifications during growth episodes. I find that for reasonable parameter values,

the model predicts less granular trade growth, generating only about 10% of

the granularity in the data, as measured by the share of total trade growth

accounted for by various quantiles of goods classifications. To better match

the observed granularity, I augment this standard model by incorporating het-

erogeneous productivity changes and tariff reductions imputed from the U.S.

production and export data. Doing so, I find that the model predicts roughly

70% of the granularity across goods observed in the trade data.

To account for the remaining heterogeneity of trade growth in the bilat-

eral trade data, I examine the role of heterogeneity in exporting methods in

accounting for differences in observed levels of trade and trade growth across

goods. Firms often choose between alternate methods of exporting their goods

to foreign countries. Generally, these can be grouped into two broad categories

— methods with high fixed costs and low variable costs, and those with low

fixed costs and high variable costs.

In Chapter 3, I use the standard Melitz-style model from Chapter 2, and

add a choice among multiple distribution technologies for exporting firms —

one low-fixed, high-variable cost option, and one high-fixed, low-variable cost

option. Solving the model, I find that, following productivity or tariff changes,

firms that switch from not-traded to traded, or from the low-fixed to high-fixed

cost method exhibit disproportionately larger growth than non-switching firms,

generating higher granularity in trade growth in the model. To quantify the

effect of this mechanism on trade growth granularity, I calibrate and simu-

late the model, incorporating heterogeneous productivity and tariff changes

imputed from trade data, to match data on bilateral trade flows and trade

growth. I find that the model with multiple distribution technologies increases

the predicted granularity of trade growth across goods to 90–95% of the level

observed in the data, as opposed to the 70% generated by a model with a single

distribution technology in Chapter 2.

Chapter 4 investigates how variation in available transportation methods

impacts observed price differences across locations in the Canadian gasoline

market. Price dispersion is often attributed to transportation costs — the

larger the costs of transporting goods between locations, the larger the price

gaps that can be sustained over time. Many studies use geographic distance

as a proxy for transportation costs.1However, little is known about the quan-

titative impact of variation in the methods used to transport goods between

locations on these relative price differences.

I use a unique data set on weekly average gasoline prices in 44 Canadian

cities between 2001 and 2017, as well as differences in the four main modes of

transporting gasoline — via pipeline, marine tanker, rail or truck — to quan-

tify the impact of the supply network on relative price differences between

locations. Controlling for distance, regional and market effects, I find that the

supply network has a significant impact on price dispersion in the Canadian

gasoline market. City-pairs connected via pipeline — a faster, lower cost-per-

unit method — exhibit 3.5% less mean-price dispersion than those connected

by higher cost-per-unit methods like rail or truck. Further, the existence of

pipelines connecting cities has the effect of reducing weekly price differences

by the equivalent of a 53% reduction in geographical distance, while a seaport

connection between cities reduces the effective distance by 38%, compared to

1See, for example, Burdett and Judd (1983), Crucini, Telmer and Zachariadis (2003), or

Engel and Rogers (1996).

land-route alternatives.

A brief case study of supply disruptions at the refinery level indicates that

unplanned refinery shut-downs result in price spikes that are higher in regions

closest to these supply disruptions, and that retail price shocks have lower

variation in cities that share a pipeline connection than in those that do not.

These results reinforce the finding that the structure of the supply network is

significant in accounting for observed price dispersion across locations.

1.1 References

BURDETT, K. AND K.L. JUDD (1983). “Equilibrium Price Dispersion”, Econo-

metrica , Vol. 51, No. 4, pp. 955-–969

CHANEY, T. (2008). “Distorted Gravity: The Intensive and Extensive Margins

of International Trade”. American Economic Review, 98:4, 1707–1721.

CRUCINI, M., C. TELMER AND M. ZACHARIADIS (2003). “Price Dispersion:

The Role of Borders, Distance and Location”, Tepper School of Business, Paper

490

ENGEL, C. AND J. ROGERS (1996). “How Wide Is the Border?”, American Eco-

nomics Review, Vol 86 No 5, pp. 1112–1125

MELITZ, M.J. (2003). “The Impact of Trade on Intraindustry Re-allocations

and Aggregate Industry Productivity.” Econometrica, Vol. 71.6 (2003): 1695–1725.

Chapter 2

Decomposing Episodes of Large

Growth in International Trade

2.1 Introduction

Over the past 50 years, international trade has grown nearly twice as fast as

world GDP.1For most countries, this growth has not been smooth and constant

over time, but rather occurred over a small number of rapid growth episodes.2

For some countries, episodes of large growth follow implementations of trade

liberalization, such as the North American Free Trade Agreement (NAFTA)

in the early 1990s. However, episodes of large trade growth also occur in the

absence of formal trade liberalizations.3

It is well-documented that in many instances, trade models significantly

1Source: IMF WEO 2012

available at: http://www.imf.org/external/pubs/ft/weo/2012/02/weodata/index.aspx.

2Figure A.1 shows bilateral trade for several countries over the past 30-–60 years, where

an average of roughly 70-–90% of overall growth over this period is accounted for by periods

spanning only 10% of the time span (i.e. 5 years).

3For example, between 1990 and 1999, Mexican exports to Canada quintupled, from $0.4

billion to $2.1 billion. By contrast, Mexico’s GDP grew by only 70% during this same period.

Over the same period, German exports to the U.S. grew from $25 billion to $49 billion while

German GDP grew by only 50%.

under-predicted the magnitude of trade growth during these episodes.4More

recently, papers like Melitz (2003) and Chaney (2008) have focused on the role

of heterogeneity in accounting for trade growth across industries and goods. As

a result, trade literature has examined responses to trade liberalization across

various types of goods and industries: previously-traded goods that become

traded in larger values — the intensive margin — and previously not-traded

goods that become traded — the extensive margin.5

Several questions remain to account for the large growth during these rapid

growth episodes:

1. What is the distribution of growth across goods during growth

episodes? What proportion of overall trade growth is attributable to

intensive margin growth as opposed to extensive margin growth? Kehoe

and Ruhl (2013) find evidence that the extensive margin is in fact large

and significant in accounting for overall trade growth. Further, within

these margins, is trade growth widely dispersed across a large number

of different goods, or is trade growth granular — i.e. is trade growth

concentrated in a small number of goods accounting for the majority of

overall trade growth?6

4For example, see Kehoe(2005) for a detailed examination of the erroneous predictions of

trade models following NAFTA.

5Although the terms “goods” and “industries” may have different connotations in other eco-

nomic literature, for brevity I will hereafter use the term “goods” to refer to various industries

and the goods they produce and trade.

6The use of the term “granular” in the literature is relatively recent and sparse — papers

like Gabaix (2011), DiGiovanni and Levchenko (2014) and DiGiovanni, Levchenko and Mejean

(2017) use granularity to refer to the “incompressible grains of economic activity” that result

from the idiosycratic shocks to the upper end of the fat-tailed distribution of firms within an in-

dustry, that pervade to aggregate economy-level shocks. For the purposes of this dissertation, I

extend my connotation of granularity to include two main properties: (1) the level of disaggre-

gation in cross-sectional trade that identifies idiosyncratic behavior across industries in a given

period, similar to Gabaix and others (as opposed to homogeneous behaviors across industries or

focusing on aggregate values, and (2) idiosyncratic behavior in trade growth across industries

2. What accounts for heterogeneity of growth across different goods?

Do tariff reductions account for overall trade growth for each good? Is

trade growth a function of production growth or increases in trade in-

tensity (or both)? That is, does trade growth for each good coincide with

increases in domestic production, with a constant share of output being

traded, or does the share of domestic output being traded increase?

3. Are the predictions of Melitz-style models consistent with the level

of granularity observed in international trade data? Do the mech-

anisms for tariff reductions and productivity changes in these models de-

liver similar patterns of trade growth across goods as observed in the

data?

In this paper, I document new data facts on bilateral trade growth across

goods during rapid growth episodes. I analyze 5-digit Standard International

Trade Classification (SITC) bilateral trade data, between 1989 and 1999, for

6 countries (Canada, Germany, Japan, Mexico, USA and UK) accounting for

20–25% of global trade during this period. Although data limitations restrict

the sample to this 10-year period, it does include the implementation of the

North American Free Trade Agreement (NAFTA) and the Canada-US Free

Trade Agreement (CUSFTA) in the early-to-mid 1990s, thus allowing a com-

parison of growth for trade-liberalization and non-liberalization country-pairs.7

I supplement this data with 8-digit Harmonized Tariff Schedule (HTS) data

— industries react differently across the distribution of trade, even from similar previous levels

of trade. The latter property contrasts with the connotation of terms like “lumpiness” of trade

(as in Armenter and Koren (2014), among others) which denotes the concentration of trade and

trade growth at the upper end of the distribution, where the majority of trade growth would

similarly be accounted for by those industries accounting for the majority of previous trade.

7Numerous papers, such as Caliendo and Parra (2014), Gould (1998), Romalis (2007), etc.,

examine the overall impact of NAFTA and CUSFTA, providing a large, diverse literature.

on U.S. tariff rates and 6-digit North American Industry Classification Sys-

tem (NAICS) data on U.S. manufacturing production. The U.S. tariff data is

matched to U.S. import data to analyze the impact of changes in tariff rates

on the growth in trade across goods classifications. U.S. manufacturing data

is matched to U.S. export data to decompose trade growth into changes in pro-

duction and changes in trade intensity.

I document four key facts during these rapid trade growth episodes:

1. Bilateral trade growth is granular across time and across goods — over

70% of total trade growth over time is accounted for by 10% of the total

time period (i.e. 5 of 50 years), and less than 5% of goods classifications

account for 65–110% of total bilateral growth across country-pairs8

2. Changes in tariffs do not account for episodes of large trade growth

3. Increases in trade intensity and domestic production each account for

large growth in trade across goods

4. The extensive margin is significant for overall bilateral trade, but is driven

by a relatively small number of extensive margin goods (<20%) that ac-

count for the majority of overall extensive margin growth

Across all bilateral country-pairs, trade growth is granular across time and

goods. Over the past 50 years, most of the total growth in bilateral trade is

accounted for by a small number of rapid growth episodes. Examining growth

for each year, the 5 largest-growth years (i.e 10% of the total time span) ac-

count for over 70% of the total growth in bilateral trade over the past 50 years.

8These goods can account for over 100% of trade growth due to negative growth in some

goods classifications.

Cross-sectionally, the majority of total bilateral trade growth is accounted for

by a small number of goods classifications exhibiting disproportionately large

growth.9Nearly all these large-growth goods had non-zero levels of trade prior

to rapid growth. Large growth from goods categories with zero previous trade

is rarely observed. Further, among this set of large-growth goods, there is large

variation in their level of trade prior to rapid growth.

Reductions in trade barriers alone are unable to account for these large-

growth goods categories which comprise the majority of trade growth across

country-pairs. Many episodes of trade growth occur in goods whose tariff rates

do not change, while most changes in tariff rates do not result in large trade

growth for those goods. As a result, there is no statistically significant corre-

lation between reductions in U.S. tariffs rates and U.S. bilateral trade growth

across goods categories. Of the 100 goods contributing the largest shares of bi-

lateral trade growth, over half exhibit no reduction in their ad valorem equiva-

lent (AVE) tariff rate. Further, of the goods with the largest reductions in tariff

rates, few (10-–20%) exhibit substantial growth in trade.

Examining U.S. manufacturing data, I find that episodes of large growth in

bilateral trade coincide with increases in both trade intensity and production.10

Controlling for changes in domestic production, observed increases in trade

9On average, across country-pairs, roughly 1% of goods classifications account for approxi-

mately 60% of total trade growth.

10To clarify this distinction, global growth of new technologies like smart-phones and laptop

computers, employed on a global scale, necessitates increased production of semi-conductors,

the key foundation of internal circuitry for modern electronics. A large increase in exports

for goods like semi-conductors may therefore be proportional to increases in their overall pro-

duction, with trade intensity (the share of domestic production that is exported) remaining

relatively constant. Alternatively, episodes of trade liberalization resulting in decreased bar-

riers to trade may lead to a larger share of domestic production being exported to a given

destination, representing an increase in trade intensity, even in the absence of large increases

in gross production.

intensity account for 35–90% of total bilateral trade growth across country-

pairs.11 Conversely, holding trade intensity constant, production growth ac-

counts for 30–40% of observed trade growth for some country-pairs, while for

others it accounts for virtually none of the overall bilateral trade growth.

Extensive margin growth is measured as changes in trade accounted for

by the goods classifications representing the bottom 10% of initial trade.12 I

find extensive margin growth is significant to overall bilateral growth for all

country-pairs. Additionally, within the extensive margin, large growth in a

small number of goods accounts for the majority of overall extensive margin

growth, mirroring the granularity of trade growth across goods in the intensive

margin, for trade-liberalizing and non-liberalizing countries alike.

I quantitatively compare these empirical findings on trade growth across

goods to the predictions of Melitz-style trade models. As in Melitz(2003), Help-

man, Melitz and Yeaple (2004) or Chaney (2008), these models typically feature

heterogeneous productivity firms, monopolistic competition pricing, and CES

demand, as well as fixed and variable costs of exporting. Since I am interested

in the quantitative results, I use reasonable parameter values and calibrate

this “standard model” to match observed trade flows and quantitatively assess

the model’s ability to match the observed granularity in bilateral trade data for

two main cases:

11Due to the data limitations of only having U.S. production data, I only consider 5 country

pairs — U.S. exports to Canada, Mexico, Japan, Germany and the U.K.

12This paper adopts the Kehoe and Ruhl (2013) definition of the extensive margin—the set

of goods that account for the bottom 10% of initial trade. This is due to reporting issues in

international trade—shipments with sufficiently low values need not be declared on Customs

reports for many countries, so distinguishing true zero-trade goods from small trade goods can

cause issues. For similar reasons, I follow the Kehoe and Ruhl approach of using the bottom

decile of goods, according to initial trade value to represent the extensive margin.

1. Standard model with uniform tariff reductions. A standard Melitz-

style model featuring firms with fixed productivities drawn from a Pareto

distribution, where trade liberalization takes the form of a uniform reduc-

tion in tariffs across all goods, a common approach in the trade literature.

2. Standard model with heterogeneous productivity changes and

tariff reductions. A standard Melitz-style which I augment by incorpo-

rating heterogeneous changes in productivity across goods imputed from

U.S. production data, as well as heterogeneous tariff reductions across

goods matched from U.S. import data.

I find that the predictions of the standard model with uniform tariff reduc-

tions do not match the stylized facts observed in the data. With a Pareto distri-

bution of productivities, and a fixed and variable cost of exporting, this model

produces much less granularity of trade growth than found in the data. In equi-

librium, goods are stratified into traded goods (those with sufficiently high pro-

ductivity to cover the fixed cost of exporting) and goods that are not-traded (i.e.

those where the fixed cost exceeds the potential profits from exporting). Fol-

lowing a uniform reduction in trade costs for all goods, the increase in exports

of previously traded is proportional to their productivities. As a result, growth

in the intensive margin of trade is smooth across previously-traded goods, not

granular. Extensive margin growth arises from a shift in the productivity cut-

off, resulting in some goods that were previously not-traded becoming traded,

as the reduction in variable cost makes it profitable to pay the fixed cost of

exporting.

The key result delivered by this standard mechanism is the smoothness

of trade growth — exports grow proportionally to the uniform reduction in

trade costs and proportionally to their productivity. The only disproportion-

ate growth in the standard model comes from extensive margin goods, jumping

from zero trade to non-zero levels. However, these goods become traded in such

small values (as a result of their relatively low productivities), that they ac-

count for a small proportion (<20%) of overall trade growth. This implies that

across goods, goods with similar initial levels of trade are predicted to grow

in similar magnitudes, and trade growth is only slightly more granular than

cross-sectional trade in any given period. Conversely, in the data trade growth

is highly granular and trade growth is substantially more granular than cross-

sectional trade.

Matching both the levels of cross sectional bilateral trade and the observed

level of granularity from the data is important for several reasons. For policy

analysis, it is necessary to identify the disparity in trade growth across indus-

tries so as to assess the welfare impact of trade policy across income distribu-

tions. It is important that the model capture the granularity of observed trade

to provide insight into heterogeneous responses across industries to policy pro-

posals such as trade liberalization. Matching the granularity of trade across

goods may also be important for quantifying the impact of shocks (both cyclical

and secular) on trade flows, sectoral output dynamics and the reallocations of

inputs across industries.

To attempt to better match the level of granularity observed in the data, I in-

troduce into the model heterogeneous tariff and productivity changes imputed

from U.S. manufacturing and export data. Heterogeneous productivity changes

across goods allow for large jumps in productivity for some goods classifications

that generates disproportionately large trade growth for these goods. Hetero-

geneous tariff reductions similarly allow for disproportionately large growth

in the goods exhibiting the largest tariff reductions, while goods experiencing

smaller reductions in trade costs exhibit much smaller growth.

To quantify this mechanism, I calibrate the standard model including het-

erogeneous productivity and tariff changes to match U.S. export data and com-

pare the granularity of trade growth across goods in the model to that in the

data. I find that incorporating these productivity and tariff changes signifi-

cantly increases the granularity of trade growth predicted in the model. Mea-

suring the proportion of overall bilateral trade growth accounted for by various

quantiles of large-growth goods, I find that this augmented model generates

roughly 70% of the granularity observed in the trade data, a marked improve-

ment from the 10% generated by the standard model with uniform tariff reduc-

tions.

2.2 Related Literature

Several empirical papers document the “lumpiness” of trade — a majority of

international trade in a given period is accounted for by a relatively small num-

ber of goods traded in large volumes, while a large proportion of domestically-

produced goods are not exported. Armenter and Koren (2010) suggest that

the concentration of large amounts of total bilateral trade in a small number of

goods categories may be systematic of the sparseness of trade data — in a given

period, the fact that there are relatively few international shipments (balls)

compared to the large number of potential goods classifications (bins) necessar-

ily results in this inherent “lumpiness” of trade across goods categories, with a

large number of goods being not-traded or traded in very small amounts, while

the majority of bilateral trade is concentrated in a small number of large-trade

goods. However, Blum, Claro and Horstmann (2016) argue that a key underly-

ing assumption driving the balls and bins model — that export shipment size

is randomly allocated across good categories, and is independent of firm size

— is inconsistent with shipment data and invalidates the Armenter and Koren

model’s findings. Alternatively, Fernandes et al (2015) argue that the granu-

larity of trade growth, particularly on the intensive margin, may arise from

a log-normal productivity distribution, as opposed to the Pareto distribution

commonly assumed in Melitz-style trade models, which causes firms to react

disproportionately in response to trade liberalization that lowers variable costs

of exporting. Alessandria, Kaboski and Midriggan (2010) attribute the lumpi-

ness of trade to economies of scale in transportation and delivery lags. They

find that large costs associated with international transportation of goods leads

firms “stock up” with larger and less frequent shipments, accounting for the

lumpiness of trade across goods and time.

While these papers focus on the patterns of cross-sectional trade, a cen-

tral contribution of this chapter is to document the fact that trade growth is

granular. Further, I find that the set of large-growth goods accounting for the

majority of trade growth is uncorrelated with the set of goods in which per-

period trade is concentrated. Finally, I find that trade growth is more granular

than cross-sectional trade, and that the level of trade growth across goods is

uncorrelated with initial levels of trade.

A large literature (e.g. Krugman (1979), Lancaster (1980), Deardorff (1984),

etc) documents recent growth in international trade. Most germane to this

chapter is the documented fact that the ratio of trade to GDP has increased

over the past 50 years. Bergoeing and Kehoe (2001) document key trade growth

facts and investigate the ability of standard trade models to quantitatively cap-

ture the patterns observed in international trade data. This chapter documents

that this trade growth is highly concentrated in a small number of rapid growth

episodes over this period.

This chapter is also related to empirical work identifying the effects of trade

liberalizations on bilateral trade flows. Romalis (2007) uses a difference-in-

difference approach to exploit variation between trade liberalizing and non-

trade liberalizing countries to estimate elasticities of traded goods. He reports

that trade liberalization has a significant impact on volume, but small impact

on prices and welfare. This chapter extends these data facts by investigating

trade growth variation across individual goods, and develops a model that can

deliver the patterns of trade observed in the data, which standard models do

not produce.

Kehoe and Ruhl (2013) find that the extensive margin plays a significant

role in accounting for bilateral trade growth, with a 10% increase in trade

between country-pairs being accompanied by a 36% increase in the extensive

margin, on average.13 While I find similar results on the impact of the overall

extensive margin, this chapter adds to Kehoe and Ruhl by decomposing exten-

sive margin growth between goods that were previously not traded and those

that were traded in very small amounts. I document that extensive margin

growth is quite granular, with less than 5% of extensive margin goods account-

ing for over 25% of growth in the extensive margin.

Many papers have used standard international trade models to examine the

impact of trade liberalizations (and other structural change) on trade volumes

13Kehoe and Ruhl’s interpretation of the extensive margin varies from the theoretical defini-

tion identified in Chaney (2008) — Kehoe and Ruhl classify the extensive margin as the growth

in trade among the set of least-traded goods, classified as the bottom decile of goods sorted by

initial trade value.

and the patterns of trade growth. However, these models do not produce the

high level of granularity of trade growth observed in the data. Melitz (2003)

introduces heterogeneous productivity across firms with a fixed cost of entry to

a model with monopolistic competition, which predicts that intensive margin

growth is smooth across goods. Chaney (2008) builds on the Melitz framework

to isolate the role of the extensive margin in trade growth, identifying the set

of goods that enter the exporting market following reductions in trade barriers.

However, in this framework, extensive margin growth is smooth across exten-

sive margin goods. Arkolakis (2010) builds a model of market penetration, in

which firms essentially choose their fixed cost in order to penetrate a market

and then face increasing marginal costs to reach additional consumers. How-

ever these models, whether employing a single fixed-cost export technology (as

in Melitz, Chaney), or a continuum of fixed cost options (as in Arkolakis), do not

produce the non-convexity of trade growth across goods observed in the data.

This chapter extends the literature by adding heterogeneous productivity and

tariff changes to investigate whether this standard framework can generate

the level of granularity of trade growth observed in the data across both the

intensive and extensive margins.

2.3 Data

2.3.1 Stylized Facts

I use data on bilateral trade values, ad valorem tariff rates, and manufacturing

data to decompose trade growth between the intensive and extensive margins

across goods classifications. Four key facts emerge from the data:

1. Trade growth is highly granular across time and across goods

classifications.

a. Across countries, bilateral trade growth over time occurs in short

periods of rapid growth. Rather than smooth, consistent growth

over time, growth is concentrated in a small number of rapid growth

episodes. Over the past 50 years, the 5 largest-growth years account

for roughly 75% of overall trade growth.

b. Across goods classifications, trade growth is concentrated in a small

number of goods classifications, with 5% of classifications accounting

for roughly 65–110% of total bilateral trade growth by country-pair.

In all bilateral pairs, there are many goods classifications that begin

with zero trade, and remain so over time.14 Goods that switch from

zero reported trade to positive trade remain at low values. The ma-

jority of goods that are initially traded grow very little — it is only

a small number of goods, growing from low levels of initial trade to

high levels of final trade, or from high levels of initial trade to very

high levels of final trade, that account for the majority of the growth

in bilateral trade.

2. Reductions in tariffs coincide with only 10–20% of the large-growth

goods.

Tariff reductions do not account for the granularity in trade growth. Among

the subset of large-growth goods which account for the majority of trade,

large decreases in tariff rates accompany only a small number (10–20%)

of these goods, while the remaining goods exhibit no change or small in-

creases in their ad valorem equivalent tariff rate.

14While this property is consistent across country-pairs, it is not true that it is the same set

of goods with zero trade across all country pairs. One good with zero trade for one country-pair

may be highly traded across other country-pairs, and vice-versa.

3. Trade intensity and production growth both account for large

growth in bilateral trade

Controlling for growth in production across goods classifications, increases

in trade intensity account for 35–90% of total observed trade growth across

various U.S. bilateral pairs. Conversely, fixing trade intensity at initial

levels, growth in domestic production accounts for 30–40% of U.S. export

growth to certain countries (such as Canada and Japan), whereas pro-

duction growth accounts for virtually none of the observed bilateral trade

growth in others (Germany, Mexico, U.K.).

4. Extensive margin growth is granular and a significant factor in

total bilateral trade growth The rise in trade growth of the least-

traded goods accounting for the bottom decile of initial bilateral trade is

significant in accounting for overall trade growth. A 10% increase in bilat-

eral trade is accompanied by a 24% increase in the extensive margin, on

average across country-pairs. Extensive margin growth is granular, with

a small number of extensive margin goods (<5%) accounting for roughly

25% of total extensive margin growth, but less granular than total bilat-

eral growth.

2.3.2 Data Sources

To study and decompose bilateral trade growth, I use annual UN Comtrade

data on bilateral trade from 1989–1999, at the 5-digit Standard International

Trade Classification (SITC) level, for 6 countries — Canada, Germany, Japan,

Mexico, U.S.A, and U.K. Trade between these country-pairs accounts for roughly

20–25% of global trade during this period. At the 5-digit SITC code level there

are 1836 different goods classifications.15 Since the 1989–1999 period includes

the implementation of NAFTA and CUSFTA — episodes of trade liberalization

for some country-pairs (Canada, Mexico, U.S.A.) but not for others (Germany,

Japan, U.K.) — I am able to examine the differential effects of trade liberaliza-

tion on trade growth across country-pairs.16

I use data on U.S. tariff rates and U.S. imports from Canada, Germany,

Japan, Mexico, and the U.K. to investigate the impact of trade liberalization,

and heterogeneous changes in tariff on trade growth across goods. The U.S. tar-

iff rate data is from the NBER database on international trade and reports the

ad valorem equivalent (AVE) tariff rates on U.S. imports between 1989–1999 at

the Harmonized Tariff Schedule (HTS) 8-digit level.17 This includes estimates

of AVE rates for all Most-Favored-Nation-status (MFN) trading partners, such

as Germany, Japan and U.K., as well as the tariff schedules for Canada and

Mexico following the implementation of NAFTA. I match this tariff data, with

data on U.S. imports, resulting in approximately 8000–10000 different goods

categories, depending on the import source country.18

15The UN uses a lexicographic ordering of SITC codes, with a parent category divided into up

to 10 subcategories at each stage of disaggregation — thus a 3 digit code 782 may be subdivided

into 7821 and 7822, and 7822 may be subdivided into 78221, 78223, 78225, 78227 and 78229,

etc. This may invokes concerns of endogeneity in the classifications — goods with larger trade

values may enable or necessitate more subdivisions, while goods with less trade may be lumped

into one broader parent category. However, the SITC codes underwent their most recent rounds

of revisions in 1986 and 2006 respectively — since the data in this work focuses on the time

periods 1989–1999, this concern should be reasonably mitigated. This is similarly true for the

NAICS and HTS classification systems. For a more detailed methodology, consult the United

Nations Statistic Divisions reports, available at http://unstats.un.org/unsd/family/default.asp.

16This trade data is particularly appropriate as it represents a subset of the Kehoe and Ruhl

(2013) data set, allowing for a comparison of the results on trade liberalizations and extensive

margin growth found in that paper.

17This data set is compiled by Feenstra, Romalis and Schott (NBER working paper), avail-

able at http://www.johnromalis.com/publications/.

18U.S. import data comes from a dataset on U.S imports and exports compiled by Pe-

ter Schott, containing data on U.S. imports at the 10-digit HTS level, which is then ag-

gregated up to the 8-digit level over the same time period, 1989–1999, available at http :

//faculty.som.yale.edu/peterschott/subinternational.htm.

To identify the relationship between trade and gross domestic production, I

include matched data on U.S. manufacturing and U.S. exports. I compile pro-

duction data from the NBER-CES Manufacturing Industry database to provide

data on 473 goods classifications at the 6-digit North American Industry Classi-

fication System (NAICS) level between 1989 and 1999. I match the production

data to U.S. export data at the 6-digit NAICS level for the same destination

countries as the tariff and bilateral trade data.19

Since international trade data often suffers from issues of sparseness and

lumpiness in shipments, I use a 3-yr average to control for reporting errors

in the timing of shipments, or instances of shipment and Customs reports be-

ing dispersed over multiple years. I classify the initial level of trade as the

1989–1991 average and the final level of trade as the 1997–1999 average for

each good classification. The difference in these 3-yr averages therefore repre-

sents the growth in trade over this period.

Descriptive Statistics

Tables 2.1 and 2.2 present summary statistics, for NAFTA country-pairs and

non-NAFTA country-pairs respectively, of the 5-digit SITC bilateral trade data.

There are three key facts to note. First, on average, the initial level of trade

for NAFTA and non-NAFTA pairs is approximately the same (roughly $36B),

in total shipment value in $US, while the average final level of trade is higher

in NAFTA country-pairs ($75B) than in non-NAFTA pairs ($57B). This reflects

the larger average growth in total trade for NAFTA country-pairs of 148%,

while non-NAFTA pairs average 63% growth over the same period. Second, the

bottom decile of goods, ordered by initial trade value, grow to account for 18%

19The NBER data comes from a database compiled by Becker, Gray and Marvakov, available

at http://www.nber.org/nberces/, while the export data comes from the Schott database (Ibid.).

of final trade in NAFTA country-pairs, while accounting for 13% of final trade

in non-NAFTA pairs. This implies a slightly larger role for the extensive mar-

gin in trade-liberalizing countries. Third, the 10 largest-growth goods in each

country pair (out of 1836 total good classifications) accounts for approximately

50% of total trade growth in NAFTA and non-NAFTA country-pairs alike. Sim-

ilarly, the 100 largest-growth goods account for 101% of total trade growth in

non-NAFTA countries, and 90% of total trade growth in NAFTA country-pairs.

Together, these three facts suggest that trade growth is highly concentrated

in a small number of goods classifications. This pattern is consistent across

all country-pairs, although it is slightly more prominent in trade-liberalization

country-pairs.

Table 2.1: Summary Statistics: NAFTA country-pairs

Bilateral Trade Statistics: 5-digit SITC codes

Variable Can-Mex Mex-Can Can-Usa Usa-Can Mex-Usa Usa-Mex NAFTA Avg

Initial trade 452451 1711096 83278894 71313846 28298716 25796112 35141852

Final trade 880883 5537384 160144152 123700777 93734628 70447948 75740962

Total trade growth 428432 3826288 76865257 52386931 65435912 44651836 40599109

%∆ in trade 94.7% 223.7% 92.3% 73.5% 231.2% 173.1% 148%

Share of trade growth 94.7% 61.3% 41.1% 29.4% 42.5% 29.6 51.9%

from 10 largest growers

Share of trade growth 136.5% 95.0% 77.6% 68.5% 85.2% 71.2% 91.8%

from 100 largest growers

Extensive margin 25.7% 26.4% 15.6% 11.5% 17.5% 13.3% 18.3%

share of final trade

Number of goods 1836

(All trade values in thousands of $US)

Table 2.2: Summary Statistics: Non-NAFTA country-pairs

Bilateral Trade Statistics: 5-digit SITC codes

Variable Ger-Usa Usa-Ger Jpn-Usa Usa-Jpn UK-Usa Usa-UK Non-NAFTA Avg

Initial trade 25828198 21430441 93940987 48749684 18021847 19532210 37917228

Final trade 47977038 34737504 124383525 67346115 33471956 34286200 57033723

Total trade growth 22148840 13307063 30442537 18596431 15450108 14753990 19116495

%∆ trade growth 85.7% 62.1% 32.4% 38.1% 85.7% 75.5% 63.3%

Share of trade growth 52.0% 56.1% 57.8% 58.1% 41.1 38.7% 50.6%

from 10 largest growers

Share of trade growth 85.3 107.9% 121.1% 118.7% 87.2% 85.9% 101.1%

from 100 largest growers

Extensive margin 13.0% 12.9% 12.3% 12.4% 11.9% 14.5% 12.8%

share of final trade

Number of goods 1836

(All trade values in thousands of $US)

2.3.3 Granularity of Trade Growth

Granularity Across Time

Over the past 50–60 years, trade growth across NAFTA and non-NAFTA country-

pairs exhibit similar patterns.20 All country-pairs show large overall growth

over this period, but exhibit large variation in the rate of growth between pe-

riods. In most cases, the majority of the overall trade growth over time is

accounted for by a small number of episodes of rapid growth.

To quantify the granularity in trade growth over time, I calculate the share

of total trade growth accounted for by each year, and calculate the proportion

of overall trade growth accounted for by the top 5, 10 and 15 years of growth.

Table 2.3 reports that the top 5 years of growth (representing only 10% of the

total time frame) account for roughly 75% of overall trade growth across time.21

The top 10 and 15 years of growth account for roughly 150% and 200%, re-

spectively, of total bilateral trade over this period, suggesting that most of the

overall growth over time is concentrated in a small number of rapid growth

episodes.

Table 2.3: Proportion of total bilateral trade from “X” top-growth years

Proportion of trade growth from top X%years

(5-digit SITC codes)

1-yr intervals 2-yr intervals 3-yr intervals

Country-Pair 5 yrs (10%) 10 yrs (20%) 15 yrs (30%) 3 yrs (10%) 6yrs (20%) 9yrs (30%) 2 yrs (10%) 4 yrs (20%) 6 yrs (30%)

Mex-Can 0.6856 0.9931 1.1836 0.7257 1.0360 1.1356 0.7146 0.9552 1.0612

Usa-Jpn 0.6781 1.0553 1.3400 0.6000 0.9775 1.2586 0.5747 0.8556 1.0261

Jpn-Usa 0.9172 1.5070 1.9293 0.8442 1.2970 1.5322 0.6426 0.9776 1.2874

Mean 0.7603 1.1852 1.4843 0.7233 1.1035 1.3088 0.6440 0.9295 1.1249

20Figure A.1 plots total bilateral trade values for exports over the past 50 years for Mexican

exports to the U.S. and Canada, as well as U.S. exports to Japan and Japanese exports to the

U.K. For some countries in the data set, such as Mexico, the data only extends back to 1980. For

brevity, only 4 countries are plotted here, but other the country-pairs exhibit similar growth

patterns over time.

21It should be noted that these need not be concurrent years, but rather the 5 individual

years demonstrating the largest growth across the entire time period.

Due to the inherent lumpiness and variability in reporting of international

shipments, using single year intervals to measure growth may potentially over-

estimate trade growth in any given year. I therefore repeat the exercise by

using 2-year and 3-year intervals for the length of each period in calculating

trade growth. I find similar results to those using 1-year intervals, with a high

degree of granularity across time periods, with the top 10% of time periods

accounting for 70–75% of total trade growth. This reinforces the finding that

trade growth is not smooth and uniform across time, but highly concentrated

in a small number of episodes of rapid growth.

Granularity across goods

To identify the properties of trade growth, I examine the share of total trade

growth accounted for by each good for each country pair. I arrange goods, in

ascending order, by initial value of exports for each bilateral pair and calcu-

late each good’s corresponding share of the total growth in bilateral trade. For

ease of exposition, I separate goods into 3 groupings — the least-traded goods

(comprising the bottom decile of total initial exports, by 5-digit SITC code); the

mid-traded goods (comprising the second through fifth deciles); and the most-

traded goods (comprising the top 50% of initial exports).. Across the various

bilateral country-pairs, the least-traded goods make up 75–90% of the goods

classifications. Roughly half of these categories are goods with zero reported

trade.22 The set of most-traded goods comprises a small number (5–40 of 1836)

of good classifications. This reflects the “lumpiness” in cross-sectional trade

data — many goods are not-traded or traded in small quantities, while a small

number of highly-traded goods accounts for a large portion of total bilateral

22Due to the fact that most countries exclude very small shipments (i.e. less than $2000)

from customs duties and reports, the term “not-traded” is used in this paper to refer to goods

with no recorded trade value in these customs reports.

trade in any given period.

Figure 2.1: Growth by Good: 5-digit SITC bilateral trade

(b) NAFTA county-pairs

To decompose trade growth across goods, I plot the trade growth accounted

for by each good as a share of total bilateral trade growth in Figures 2.1–2.2.23

The height of each bar represents that good’s contribution to the total growth

23Formally, the y-axis of Fig. A.2–2.2 is measured, for each good i, as: ∆Exports(i)

Pj∆Exports(j).

Figure 2.2: Growth by Good: 5-digit SITC bilateral trade

(b) Non-NAFTA county-pairs

in trade for that country-pair.24

Bilateral trade growth is highly granular, with a small number of goods

exhibiting large increases in trade values accounting for the vast majority of

total trade growth. Most of these goods originate from the mid- or most-traded

categories, and almost never from the least-traded category. The remaining

goods (90–95% of all goods classifications) exhibit small (<0.05% of total trade),

zero, or negative growth.

This finding can be summarized as follows: many goods begin and remain

not-traded; some not-traded goods become traded in small amounts, but al-

most never go from zero to large amounts of trade; most traded goods grow

very little; a small number of goods grow from small amounts of trade to large

amounts, or from large amounts to even larger amounts, the two cases that

account for the majority of trade growth between country-pairs.

The goods exhibiting large growth that account for the majority of trade

growth come from varying levels of initial trade across bilateral pairs. That

is, large growth goods (“growers”) do not all begin with similar levels of initial

trade, and goods with similar initial levels of trade do not necessarily grow in

similar proportions.25 Further, goods that begin with zero trade do not typically

become traded in large values, if they become traded at all.

To quantify this relationship, I calculate the share of total bilateral trade

growth accounted for by these high-growth goods. Table 2.4 lists the proportion

of overall trade growth accounted for by the top 1% of large-growth goods, as

24To more clearly illustrate the patterns of trade growth, I also plot groupings of goods indi-

vidually, as seen in Figures A.2–A.4. These figures represent the case for Canadian exports to

Mexico; Figures 2.1–2.2 show similar results for all country-pairs.

25One possible exception to this might be the U.S.-Canada pairing, which seems to exhibit

less concentration of trade growth and smoother growth in trade, according to initial value of

trade by good.

well as the top 2%, 5% and 10% of goods.26 The mean values, across all country-

pairs, identify the granularity in trade growth, with the top 1% of goods ac-

counting for 62% of total trade growth, while the top 2%, 5% and 10% of goods

accounting for 76%, 93% and 105% of total bilateral trade growth, respectively.

There is variability in the degree of granularity across country-pairs — the top

1% of Canadian exports to the U.S. account for 108% of total growth in trade,

while the top 1% of U.S. exports to Mexico account for only 39% of total trade

growth. However, all country-pairs exhibit granularity of trade growth across

goods, with a disproportionately high concentration of trade growth in a small

number of goods.

Table 2.4: Proportion of total bilateral trade concentrated in top “X00%of goods

Proportion of growth from top X%of goods

(5-digit SITC codes)

Country-Pair 1% (18 goods) 2% (36 goods) 5% (91 goods) 10% (183 goods)

Can-Usa 1.081 1.223 1.355 1.410

Can-Mex 0.491 0.606 0.760 0.884

Ger-Usa 0.589 0.692 0.837 0.955

Jpn-Usa 0.722 0.940 1.189 1.313

Mex-Can 0.718 0.818 0.940 1.004

Mex-Usa 0.551 0.681 0.836 0.935

Usa-Can 0.373 0.478 0.665 0.815

Usa-Ger 0.710 0.882 1.062 1.167

Usa-Jpn 0.753 0.928 1.165 1.311

Usa-Mex 0.396 0.518 0.692 0.834

Usa-UK 0.492 0.647 0.841 0.972

UK-Usa 0.516 0.653 0.853 0.974

Mean 0.616 0.756 0.933 1.048

While this pattern of granularity of trade growth is pervasive across all

country-pairs, it is not the same goods categories that account for the major-

ity of trade growth across different country-pairs. Rather, there is significant

26As there are 1836 goods classifications, the top 1% of goods consists of the top 18 goods

classifications, the top 2% consisting of 36 goods, etc.

Table 2.5: Common large-growth goods across all countries

Number of Goods with X% of Trade Growth

5-digit SITC codes (1836 goods)

Countries >3% >1% >0.5% >0.1%

All 0 1 2 9

Pass. Autos Switches/Fuses Unhardened rubber

Other auto parts Pipe valves

Metal mountings

Peripheral units

TV transmitters

Static converters

Elec. microcircuits

Gas instruments

Polarizing lenses

heterogeneity in which goods account for the majority of trade growth across

country-pairs. Table 2.5 shows that of the 1836 SITC 5-digit classifications,

none account for at least 3% of total trade growth in every country-pairs. Only

one category, passenger automobiles (excluding buses), accounts for at least 1%

of trade growth in every country-pair. Further, only a dozen of the 1836 goods

classifications account for at least 0.1% of total trade growth in every country-

pair. Examining bilateral pairs, of the small number of goods categories ac-

counting for the majority of trade growth, only a small proportion (roughly

5–20%) are common to both countries’ trade growth. Table 2.6 demonstrates

that for each bilateral pair, of the 1–6 goods categories accounting for at least

5% of bilateral trade growth for each country, none or only 1 of them is common

to both countries. Similarly, of the roughly 20–30 goods each accounting for at

least 1% of total bilateral trade growth, only 4–8 of these goods are common to

both countries.

Table 2.6: Common large-growth goods across country-pairs

Number of Goods with X% of Trade Growth

5-digit SITC codes (1836 goods)

Country >5% >3% >1% >0.5% >0.1%

Same Same Same Same Same

Canada 6 9 21 40 103

Mexico 4 117 118 426 6107 27

Canada 1 4 14 34 176

USA 1 012 115 532 15 202 108

Mexico 2 6 21 35 138

USA 1 016 118 836 15 190 76

Germany 2 3 12 31 165

USA 4 121 126 844 17 139 72

Japan 3 5 31 57 146

USA 3 121 325 853 19 178 62

UK 3 6 19 47 159

USA 3 014 222 642 18 182 91

2.3.4 Tariff Rates

Trade theory suggests that reductions in import tariffs should lower barriers to

trade and increase trade for those goods. To examine the relationship between

changes in tariff rates and corresponding trade growth across goods, I match

data on U.S. tariff rates to U.S. import data at the 8-digit HTS code level.27 I

calculate the change in the tariff rate for each good as the difference between

the initial and final ad valorem equivalent (AVE) tariff values calculated by

Romalis (2007). For each bilateral U.S. trade partner, I match the AVE tariff

change to the corresponding growth share in U.S. imports for each good. Across

all goods, the tariff changes show a wide range of values, from large increases

27To examine tariff data at the most disaggregated level available, I use 8-digit HTS data,

which has significantly more goods classifications than the 5-digit SITC data (>8000 vs. 1836)

— however, I find the pattern of trade growth granularity, while slightly more pronounced in

the HTS classifications, displays similar patterns of the concentration of trade growth as the

5-digit SITC code data. As in the 5-digit SITC data, trade growth is also slightly more granular

in NAFTA countries (Canada and Mexico) than it is in non-liberalizing countries (U.K.).

to no change to large decreases. Tariff changes are generally larger and more

negative in the trade liberalizing countries of Canada and Mexico than those

for Most Favored Nation (MFN) status countries like the U.K. However, for

each country-pair, the correlation between import growth and the change in

tariff rates across all goods is not significantly different from zero. Isolating

each set of least-, mid- and most-traded goods, this lack of correlation holds.28

Due to the granularity of trade growth across goods, I isolate the subset of

largest-growth goods contributing the majority of total trade growth and ex-

amine their corresponding tariff changes. Figure 2.3 plots the 100 goods clas-

sifications that contribute the most to import growth (accounting for ≈80% of

total growth). These large-growth goods display a wide range of tariff changes

— depending on the country-pair. Only 10 to 30 of these 100 largest “growers”

exhibit notable decreases in the AVE tariff rate. The remaining goods reflect no

change or an increase in the AVE rate, suggesting that tariff decreases alone

cannot account for the granularity in trade growth across goods.

Alternatively, in Figure 2.4, I isolate the subset of goods that exhibit the

largest decreases in tariff rates to examine their corresponding share of trade

growth. Roughly one-third of the goods experiencing the largest tariff reduc-

tions exhibit positive growth in trade. However, few of these goods (<10–15%)

contribute significant shares to the overall increase in imports. The majority of

goods with the largest tariff reductions exhibit no growth or slight decreases in

imports from initial to final trade levels, coinciding with the lack of statistically

significant correlation between tariff changes and import growth.

28Refer to Figures A.5–A.7.

Figure 2.3: Large-growth goods: Imports vs. Tariff changes

Figure 2.4: Large tariff decrease goods: Imports vs. Tariff changes

2.3.5 Production Growth and Trade Intensity

Trade theory predicts that increases in trade across goods may be related to

increases in overall domestic production, with the share of domestic production

being exported staying constant. Alternatively, increases in exports may be

driven by an increase in trade intensity — exporting a proportionally larger

share of domestic production, independent of the level of domestic production.

To examine the relationship between bilateral trade growth and domestic

production, I focus on U.S. data, due to the availability of U.S. production data

from the NBER manufacturing database at the 6-digit NAICS code level. The

trade data is therefore confined to U.S. exports to Canada, Germany, Japan,

Mexico, and U.K. I concord the U.S. export data from the 5-digit SITC codes to

the 6-digit NAICS classifications and match it to the corresponding production

data. This less disaggregated 6-digit NAICS code level results in less classifi-

cations (473 goods) than the 5-digit SITC level (1836 goods).29

One possibility is that these large-growth goods that account for the major-

ity of trade are simply due to large increases in domestic production, with a

constant share of domestic production being exported. To determine whether

these goods exhibit similar granularity in their domestic production, I calcu-

late the share of domestic production growth accounted for by each good. To be

consistent, I group the production data into the same categories of least-, mid-

and most-traded goods, that are arranged in the same fashion as the export

data. Specifically, the goods are grouped according to their initial trade levels,

and then analyzed for their growth in production. Thus, the “bottom decile”

29As seen in Figures A.9(a)–2.2 and 2.5. U.S. export data exhibits similar granularity at

the less disaggregated 6-digit NAICS code level as at the 5-digit SITC code level. Extensive

margin growth, represented by the set of least-traded goods, is still significant; however, due

to the less disaggregated data, the extensive margin accounts for a smaller fraction of final

bilateral trade (≈14%) than it does in the SITC data.

of production goods account for the bottom 10% of initial trade, and may not

account for the bottom 10% of initial domestic production.

Production growth is concentrated in a small number of goods for each

country-pair, but is less granular in the production data than in the export

data, particularly among the mid- and most-traded goods sets.30 Examining

the deciles of U.S. production, each decile primarily remains at its initial levels

in the final production data. In Figure 2.5, the value of final production appears

as the height of each bar, with the initial value plotted as the “+” in each decile.

Most deciles, across all country-pairs, demonstrate small to no change in their

fraction of total production from initial to final levels. Also, the bottom decile in

each country-pair accounts for a large share of overall production, both in ini-

tial and final levels, reflecting the fact that many domestically-produced goods

are not traded between each country-pair.

The production data suggests that the granularity in trade growth is not

merely a function of domestic production. To examine the effect of changes in

total production and changes in trade intensity in accounting for bilateral trade

growth, I construct the exports-to-production ratio for each good, for both ini-

tial and final levels of trade. I then create two separate measures to decompose

the effects of changes in trade intensity and production growth in contributing

to trade growth:

1. Holding production constant at initial levels, and multiplying by the final

level of trade intensity, I calculate the share of trade growth that can be

attributed to growth in trade intensity

2. Holding the trade intensity fixed at the initial level, and multiplying by

the final level of production, I calculate the share of trade growth that can

30See Figures A.9(a)–A.9(b).

Figure 2.5: Decile Growth (6-digit NAICS) bilateral trade

(a) NAFTA country-pairs

(b) Non-NAFTA country-pairs

be attributed to production growth

To illustrate this decomposition, Figure 2.6 plots the share of total trade growth

(in the top row of each figure) along with the corresponding trade intensity

share for each of the 473 6-digit NAICS goods classifications. Across all goods,

increases in trade intensity account for, on average, 30% to 72% of the observed

trade growth across country-pairs. However, there is little correlation between

the share of trade growth accounted for by each good and the corresponding

trade intensity share, as reported in Table 2.7. There is similarly no signifi-

cant correlations between initial trade values and the resultant trade intensity

share across goods.

Similarly, increases in production account for, on average, -5% to 33% of the

observed trade growth across country-pairs. For some destination countries

(Canada and Japan), production growth accounts for large portions of total

trade growth (30–40%), while for others (Germany, Mexico, U.K.) production

growth accounts for virtually none of the overall growth in trade, on average,

as seen in Figure 2.7. Across goods there is little correlation between the share

of trade growth and the corresponding production growth share for each good,

as reported in Table 2.7. However, unlike the trade intensity shares, goods with

higher initial trade values generally have higher production growth shares.

On average, increases in trade intensity are significant factors in account-

ing for episodes of large growth in bilateral trade across all country-pairs. Pro-

duction growth shares vary more widely across destination countries in their

significance in accounting for trade growth. There is no discernible difference

between trade-liberalizing destination countries and non-liberalizing destina-

tion countries for both the mean trade intensity and production growth shares.

Figure 2.6: Trade Intensity Share vs. Share of Trade Growth

(a) U.S.-Canada

(b) U.S.-U.K.

Figure 2.7: Production Growth Share vs. Share of Trade Growth

(a) U.S.-Canada

(b) U.S.-U.K.

Table 2.7: Correlations: Trade Intensity & Production Growth Shares vs.

Share of Trade Growth

Correlation US-Can US-Ger US-Jpn US-Mex US-UK

Trade Intensity Share vs

Share of Trade Growth -0.007 -0.052 -0.010 -0.015 -0.006

Production Growth Share vs

Share of Trade Growth 0.023 0.053 0.015 0.032 0.023

2.3.6 Extensive Margin Growth

Kehoe and Ruhl (2013) find that the extensive margin is significant in account-

ing for overall bilateral trade growth. Due to inconsistencies in the reporting

of small shipment values in international trade data, Kehoe and Ruhl examine

the set of least-traded goods in each bilateral country pair, represented by the

subset of goods accounting for the bottom decile of initial trade. Examining the

growth in the share of final trade accounted for by this set of least-traded goods

then gives a proxy for extensive margin growth in bilateral trade data.

To quantify the contribution of new or previously not-traded goods to over-

all trade growth, I calculate extensive margin growth in bilateral trade data

following the methodology of Kehoe and Ruhl (2013). Due to the large number

of goods that are not traded (30–50% of the 1836 classifications for most coun-

tries) between any given country-pair, it takes 75–90% of all goods classifica-

tions to account for 10% of initial trade. Mirroring Kehoe and Ruhl’s findings, I

find the extensive margin is significant in accounting for bilateral trade growth

across country-pairs in the 5-digit SITC trade data. Across all country-pairs,

the set of least-traded goods accounts for an average of approximately 16% of

final trade. A 10% growth in total trade between country-pairs is accompa-

nied by a 24% increase in the share of final trade accounted for by these goods.

However, there is also significant growth in other deciles by country-pair. For

example, the 6th decile of Canadian exports to Mexico grows to account for

over 20% of final trade, and the 5th decile of U.S. exports to Germany grows to

account for 18% of final trade, as seen in Figure 2.8.

Kehoe and Ruhl (2013) examine the overall role of the extensive margin in

contributing to total bilateral trade growth. I extend their findings by identi-

fying that within the set of least-traded goods, the majority of extensive mar-

gin growth comes from a small number of goods growing from small values to

slightly larger values of trade, not from not-traded goods becoming traded in

large amounts. Nearly half of the goods classifications contained within this

set of least-traded goods begin as not-traded.31 The majority of these remain

not-traded, while those that become traded only do so in small amounts. A

small number of goods (<10% of all extensive margin goods classifications) in

each bilateral pair exhibit relatively large growth, from a small value of initial

trade to large values of final trade. This result shows the granularity of trade

growth within the extensive margin that mirrors that in the intensive margin.

However, due to the exceedingly large number of goods classifications exhibit-

ing small growth, these large-growth extensive margin goods only contribute

5–25% of total extensive margin growth.

2.4 Model

I now ask whether the predictions of standard Melitz-style trade models are

consistent with the empirical findings in the data. The term “standard” here

31Refer to Figure A.2.

Figure 2.8: Decile Growth: 5-digit SITC bilateral trade

(a) NAFTA country-pairs

(b) Non-NAFTA country-pairs

refers to recently used models where firms differ in productivity, face fixed

and variable costs of exporting (as in Melitz (2003), Chaney (2008), etc.) and

CES demand under monopolistic competition. Specifically, I ask whether these

models, for reasonable parameter values, generate the high level of granularity

of trade growth across goods classifications observed in the data, in response

to both uniform and heterogeneous tariff reductions, and when incorporating

heterogeneous productivity changes imputed from the data.

I analyze a two-country model with firms indexed by heterogeneous produc-

tivities, facing CES demand under monopolistic competition, with fixed and

variable costs of exporting. I characterize the equilibrium objects for profit-

maximizing firms in their export decisions, and identify the stratification of

goods as exported or not-traded. I then introduce trade liberalization, repre-

sented as a reduction in the variable costs of exporting, for two main cases,

in order to determine the implications for bilateral trade growth across goods

classifications, to compare to the empirical findings. First, I follow an approach

common to many trade models, with firms exhibiting heterogeneous productiv-

ities that are fixed across periods, where trade growth is generated by trade

liberalization that takes the form of a uniform proportional reduction in tariff

rates across goods. Second, I augment this standard approach by incorporat-

ing heterogeneous tariff reductions, matched from global tariff data, as well as

heterogeneous productivity changes, imputed from U.S. production data, across

goods.

I find that the standard model with uniform tariff reductions does not cap-

ture the granularity of trade growth — the model predicts trade growth is

widely dispersed across a large number of goods classifications. Additionally,

growth in the extensive margin, as represented by the set of least-traded goods,

does not match the pattern of growth in previously not-traded goods or the

small subset of goods growing from small values of trade to much larger val-

ues. Adding heterogeneous productivity changes and tariff reductions allows

the model to to better match the lumpiness of initial trade values across goods

seen in the trade data, as well as predicting significantly more granularity in

trade growth across goods. This version of the model also better captures the

granularity of growth within the extensive margin, as well as better capturing

the contribution of the extensive margin to overall trade growth.

2.4.1 Model Set-up

The model builds on the standard trade model framework, with 2 symmetric

countries, Home(H) and Foreign(F).32 Firms are heterogeneous in their labor

productivity, with each firm producing a differentiated good using only labor as

an input. Firms are indexed by their productivity, 1

a, where ais the amount of

labor required to produce one unit of output. Pricing follows the Dixon-Stiglitz

(1977) model of monopolistic pricing with firms facing CES demand in both a

home and foreign country. Firms may sell in the domestic market only, or may

choose to also export to the foreign market via a common distribution technol-

ogy that requires a fixed cost of exporting, and an iceberg variable cost per unit

shipped to the destination market. Following the literature, episodes of trade

liberalizations can be represented by a uniform reduction in the variable cost

of exporting in the second period.

32For brevity, I will consider the problem of Home’s exports to Foreign — by symmetry, the

Foreign country faces the same problem as the Home country in its exporting decisions.

Consumers

Preferences of consumers in country i∈ {H, F }can be represented by the CES

utility function

Ui=Za∈A

c(a)−1

da

−1

(2.1)

where c(a)is consumption of good variety a,is the elasticity of substitution

across goods ( > 1) and Ais the set of available goods.

Firms

I assume firms maximize profits under monopolistic competition pricing, as

in Dixon-Stiglitz (1977) while facing this CES demand. Firms first draw their

labor requirement from a Pareto distribution, G(a), which they hire at domestic

wage rate, ωiin country i. Firms then choose whether or not to service the

foreign market by paying a fixed cost of exporting, f, and a variable cost of

exporting, τin the form of an iceberg transportation cost.

2.4.2 Characterizing Equilibrium

Demand

Due to the symmetry of the two-country model, I consider only the demand

from Foreign for product varieties produced in Home, and set aside the de-

mand from the domestic market. For utility-maximizing consumers with this

common CES utility specification, the demand in Foreign for Home variety a

is:

cF(a) = EFp(a)−

PF1−(2.2)

where EFis national income in Foreign and PFis the Foreign aggregate price

level.

Firm’s Decision

Under monoplistic competition, firms price at a constant mark-up over marginal

cost. In the Home market, the marginal cost of production is ωHa, while the

marginal cost for firm ato service the foreign market is ωHτa, as each exporting

firm must pay the additional variable export cost τper unit. This results in a

price in Foreign for variety aproduced in Home of

pF(a) = 

−1ωHτa (2.3)

For a firm with labour requirement a, domestic profits for profit maximizing

firms are:33

πD(a)=(ωHa)1−DH(2.4)

Under CES demand and monopolistic competition pricing, these profits are

proportional to the firm’s productivity.

For a firm with labour requirement a, the additional profits from exporting

are:

πX(a) = (ωHτa)1−DF−ωHf(2.5)

That is, firms generate sales that are proportional to their productivity and

the variable transportation costs τ, but must pay the fixed cost, f, in order to

access the foreign market. 34

Productivity thresholds

These profit functions result in productivity thresholds dictating which firms

will choose to export and which will only be produced domestically. With no

33DH=EH−

[PH(−1)]1−and is a constant w.r.t. a.

34DF=EF−

[PF(−1)]1−.

fixed cost of entry, domestic profits are always non-negative, so all firms choose

to produce domestically.35 To export, additional profits must be non-negative:

πX(a)≥0. This leads to productivity cut-off, 1

¯a, that satisfies:

¯a=ωHfτ −1

DF

−1

(2.6)

The productivity cut-off for exporting is increasing in both fand τ.

The top panel of Figure 2.9 shows the stratification of goods according to

the exporting choice. Arranging goods by increasing productivity 1

a, the least

productive goods will only be produced for domestic consumption. Firms pro-

ducing good awith productivity higher than 1

¯awill choose to export.

2.4.3 Trade Liberalization

In order to examine whether the standard model can match observed patterns

of trade growth in the data, I characterize equilibrium in the static standard

model in two cases: an “initial” period and a “final” period. I categorize the

difference in the equilibrium trade values for each good across periods as the

corresponding growth in trade for each good. Following the trade growth lit-

erature, I consider the counter-factual of an episode of trade liberalization be-

tween periods, represented as a reduction in the variable cost of exporting, to

determine the patterns of trade growth across goods.36

A fall in iceberg transportation costs lower the marginal cost of servicing

the foreign market. This results in a lower price offered to the foreign market.

35πD(a)=(ωHa)1−DH≥0implies productivity cut-off 1

a= 0.

36The work here addresses a period of trade liberalization in the standard context of reducing

τ. However, it is noted that τ, the variable cost of exporting, can be decomposed into τ=M C +

tar, where MC represents the distribution costs of production and transportation to reach the

foreign market, and tar is the tariff rate. Thus examining a decrease in τprovides insight

into cases of pure trade liberalization, captured by a decrease in tar or cases like technological

improvements in the distribution network, MC.

Figure 2.9: Standard model with uniform tariff reductions

(a) Initial export sales

(b) Final export sales

With an elasticity of substitution greater than 1, this generates an increase

in export sales for all exported goods that is proportional to the fall in tariffs

and the firm’s productivity — this is growth in the intensive margin. Addition-

ally, the decrease in variable costs lowers the productivity threshold, as the

increase in variable profits resulting from the lower marginal costs of reaching

the foreign market allow a subset of goods that were previously not-traded to

overcome the fixed cost of exporting and enter the foreign market — this is

growth in the extensive margin.

The bottom panel of Figure 2.9 demonstrates the change in export sales re-

sulting from a decrease in trade costs for the standard model with uniform tar-

iff reductions. First, all previously exported goods increase their export sales

due to the direct decrease in variable costs, proportional to their productivity.

The model predicts that the largest intensive margin growth will occur among

goods with the largest initial level of trade, with goods traded at lower lev-

els exhibiting smaller growth in trade. Second, as the productivity threshold

shifts to the left, lower productivity firms enter the export market, represent-

ing the extensive margin. As these were the marginally excluded firms before

the trade liberalization, the model predicts the final level of trade for these

goods to be similar to that of the goods previously least-traded. As these goods

all previously accounted for zero export sales, the model predicts the growth in

trade for the extensive margin goods to be relatively larger than that of other

previously traded goods with similar productivities, i.e. those previously just

above the cut-off.

Implications for trade growth

The standard model predictions for growth in bilateral trade are inconsistent

with the empirical findings. Growth is smooth across all previously traded

goods, and neither the intensive nor extensive margins display the high level

of granularity of a small number of goods accounting for the majority of trade

observed in the data.

First, the standard model delivers much less granularity of trade growth

than observed in the data. The model predicts that trade growth for previously

traded goods will be much less concentrated, as the growth in trade is pro-

portional to the initial level of trade, reflecting each good’s productivity. With

a common fixed and variable cost of exporting, goods with similar productiv-

ities, and thus similar initial levels of trade, will have similar levels of trade

following homogeneous reductions in trade costs, and thus contribute similar

shares of total trade growth. Additionally, no goods with low levels of initial

trade exhibit disproportionately large growth, as seen in the data. Further, all

goods with high initial levels of trade grow similarly, with none of these goods

exhibiting zero or negligible trade growth as seen in the data.

Second, growth in the extensive margin does not match the stylized facts

from the data. The model predicts that most extensive margin growth, in terms

of the Kehoe-Ruhl representation of the set of least-traded goods, comes from

large increases in previously not-traded goods becoming traded in relatively

high values. All previously-traded goods within the extensive margin grow

proportionally to their productivity and the reduction in tariffs, similar to in-

tensive margin goods. The standard model predicts that due to the relatively

large growth in the intensive margin, the extensive margin accounts for a small

portion of overall total trade growth.

Finally, standard models often use the simplifying assumption that trade

liberalization takes the form of a decrease in the marginal cost of exporting

that is constant and proportional across all goods. The tariff data shows that

periods of trade liberalization tend to exhibit high levels of heterogeneity in the

magnitude of AVE tariff reductions across goods, which will not be captured by

a homogeneous reduction of the marginal costs of exporting across all goods in

the model.

2.5 Numerical Exercises: Trade Growth

Characterizing equilibrium in the standard model generates smooth growth

across goods, which is proportional to each firm’s productivity and the reduc-

tion in variable costs from trade liberalization. The standard model does not

generate the granularity of trade growth observed in the data. To quantify the

level of granularity generated by the standard model, I use reasonable param-

eters from trade literature to calibrate the standard model. I compare both the

level of granularity in trade growth and the correlations of trade growth with

production growth and trade intensity predicted in the model against those

observed in the data.

I simulate the model for two main cases:

1. The standard model with uniform tariff reductions.

Firms in the model exhibit productivities drawn from a Pareto distribu-

tion, which are fixed for each good category across the initial and final

periods. As is common in may standard trade models, trade growth is

driven by trade liberalization between the initial and final periods that

takes the form of a uniform proportional reduction in tariffs across all

goods.

2. The standard model with heterogeneous productivity changes and

tariff reductions.

Firms again take Pareto productivities in the initial period. However, fi-

nal period productivities are calculated by incorporating heterogeneous

productivity changes to the Pareto distribution as calculated by the im-

puted changes in productivity backed out from the U.S. production data.

This simulation also introduces trade liberalization between periods by

incorporating heterogeneous tariff reductions across goods, imputed from

tariff data.

2.5.1 Parameterization and Calibration

The numerical strategy is to select reasonable parameter values for the elas-

ticity of substitution across goods classifications, productivity parameters, and

fixed and variable costs of exporting, within the estimated ranges of the leading

trade literature.

The model predictions are compared to those of the 5-digit SITC bilateral

trade data with 1836 goods classifications, as well as the 6-digit NAICS data,

with 473 classifications, in order to match production data. To represent these

goods in the model, I draw each firm’s productivity from a Pareto distribution,

and map each firm to the production of one good.37 I arrange firms according

37The Pareto distribution is commonly used in a vast literature on international, (i.e. Melitz

(2003), Chaney(2008), Gabaix (2008), Helpman, Melitz and Rubenstein (2008), among many

others), both for its computational expediency and its ability to match certain stylized facts,

such as the upper-right tail of the firm distribution, which motivates the choice of a Pareto

distribution employed here. However, although not employed in this chapter, recent work has

begun to explore alternate distributions, such as log-normal (Eeckhout (2004), Fernandes et

al(2014), etc) or a mixed distribution of the two (Nigai (2017) that match other salient proper-

ties of firm-level productivity distributions.

to their heterogeneous productivity levels, in ascending order.38 The iceberg

cost, representing the variable cost of exporting, is set at 2.0. The elasticity of

substitution across goods in the CES demand function is set toward the high

end of estimated values in the literature, at 6.0, in order to give the model a

better chance to match the granularity of growth across traded goods observed

in the data.39

The fixed cost in the model determines the productivity threshold beyond

which firms will enter into the exporting market. As such, the fixed cost is

calibrated to match the number of non-exported goods classifications in each

bilateral trade pair. Finally, DF, the constant which contains foreign income

and price levels as well as other constants in the model set-up, is calibrated to

match the total level of initial bilateral trade for each country-pair.

For the standard model with uniform tariff reductions, I calibrate the pro-

portional reduction in tariffs (as represented by a reduction in the variable

costs of exporting) necessary to match the total growth in exports for each coun-

try.40

For the standard model with heterogeneous productivity and tariff changes,

I first determine the distribution of productivity changes across goods classifi-

cations imputed from U.S. production data. I use the 6-digit NAICS data to

38Thus “good 1” will be least productive firm, “good 2” will be the next least-productive firm,

etc.

39See, for example, Imbs and Mejean(2010), who estimate elasticities for more than 30 coun-

tires between 1 and 7.5, and supported by McDaniel and Balistreri (2003) who summarize

the literature’s findings that estimated elasticities are higher with more highly disaggregated

data.

40Specifically, I take the observed change in AVE tariff rates from the data, and scale them

by the factor necessary to match the observed change in exports for each bilateral country

pair. This method implicitly assumes that DFis constant across periods, thus all growth is

generated via the uniform tariff reduction. However, since I am concerned with the share of

trade growth accounted for by each good category, this method is computationally equivalent

to choosing a set reduction in tariffs (i.e. 10%) and calibrating DFto match the overall level of

trade growth.

back out the implied productivities for each good in the U.S. production data,

in both the initial and final periods. I then calculate the growth in productivity,

and apply the imputed productivity change onto the initial Pareto distribution

of firms in the model, in order to calculate the new productivities for the final

period. I then determine the distribution of tariff changes across goods im-

puted from tariff data from U.S. export destinations (e.g. Canada, Germany,

Mexico, Japan and the U.K.). I normalize this distribution of tariff changes

and calibrate it to match the overall level of bilateral trade growth for each

country-pair, as in the case of the uniform tariff distribution, given the produc-

tivity changes already imposed.41

2.5.2 Standard Model with Uniform Tariff Reductions

Figure 2.10 presents the results of the model simulation for Canadian exports

to Mexico using the 5-digit SITC data.42 In the bottom row of each column, the

standard model specification is unable to match the patterns of trade observed

in the actual bilateral trade data presented in the top row. The overall gran-

ularity of trade growth, with the majority of growth concentrated in a small

number of goods is not produced in the standard model with uniform tariff re-

ductions. The model delivers smooth growth across goods, with each previously

traded goods experiencing trade growth proportional to its initial level of trade,

reflective of its productivity. Further, growth in the extensive margin, repre-

sented by the bottom decile of initial trade, occurs solely in previously traded

goods (represented in blue), with virtually none of the overall trade growth

41Similar to the case of uniform tariff reductions, for the sake of calculating the share of trade

growth across goods, this method is computationally equivalent to calibrating DFto match the

overall level of trade growth, or scaling the productivity changes proportionally to match the

observed trade growth.

42All other country-pairs present similar results, and are omitted here for brevity.

attributable to previously not-traded goods becoming traded.

Figure 2.10: Standard Model with uniform tariff reductions (Can-Mex)

To quantify the degree of granularity of trade growth, Table 2.8 reports

the proportion of overall trade growth accounted for by various quantiles of

goods classifications. On average, across country-pairs, the top 1% of goods

classifications accounts for 32% of overall trade growth in the data, but only 3%

of overall trade growth in this model simulation.43 The standard model with

uniform tariff reductions delivers only roughly 10% of the granularity observed

in the data, as measured by the fraction of overall trade growth accounted for

by the various quantiles of largest-growth goods.

This lack of granularity is not surprising — by construction, with all firms

exhibiting fixed productivities and a uniform reduction in tariffs across goods,

the majority of trade growth is evenly dispersed across previously traded goods.

43It should be noted that this level of concentration is less than the 65% of trade growth

accounted for by the top 1% of goods in the 5-digit SITC data. This is mainly due to the

necessity of switching to the less disaggregated NAICS data (with only 473 goods) in order to

impute productivities from U.S. production data, where 1% of goods is only 5 goods, as opposed

to 18 goods in the SITC classification data.

Table 2.8: Standard Model with Uniform Tariff Reductions

Proportion of growth from top X%of goods

(6-digit NAICS codes)

Model 1% (5 goods) 2% (10 goods) 5% (24 goods) 10% (47 goods) 20% (94 goods)

Data 0.318 0.473 0.696 0.852 0.988

Standard 0.032 0.062 0.143 0.259 0.4490

The only disproportionate growth comes from the extensive margin — firms

which cross the productivity threshold switch from not-traded to trade, but

become traded only in relatively small volumes. Trade growth from these ex-

tensive margin goods is outweighed in the share of total trade growth by the

increases in goods at the upper ends of the productivity distribution. In all

cases, growth is smooth and proportional to productivity, and fails to produce

the granularity of trade growth observed in the data.

2.5.3 Standard Model with Heterogeneous Productivity

Changes and Tariff Reductions

The standard model with uniform tariff reductions fails to generate the granu-

larity in trade growth found in the trade data due to the smoothness in the pro-

ductivity distribution, and the uniformity of tariff reductions with are common

across all goods. A possible solution is adding heterogeneity in the productivity

distribution and in the reductions in tariff rates across goods. If some goods

categories experience large increases in productivity, it may lead to dispropor-

tionately larger growth in production and trade for those goods. Similarly, large

decreases in tariff rates for some goods may lead to disproportionately larger

growth in those categories. Combining these effects may be able to generate

the level of granularity observed in the data, due to the large growth in a small

subset of goods experiencing the complementarity of these effects. I re-simulate

the standard model incorporating heterogeneous productivity changes and tar-

iff reductions imputed from U.S. production and export data, to determine if

this augmented standard model can produce the documented patterns of trade

growth.

Figure 2.11 demonstrates the distribution of productivity changes imputed

from U.S. production data. There is a great deal of heterogeneity across the

final distribution (in blue), once applied to the initial Pareto distribution (in

red). This suggests there may be some ability for the model to capture a higher

degree of granularity of trade growth as in the data, due to the relatively small

number of goods exhibiting disproportionately large productivity shocks, aris-

ing from varying levels of initial trade.

Figure 2.11: Productivity Distributions: Productivity Shocks

Once applied to the standard model, the heterogeneous productivity changes

and tariff reductions generate a larger degree of granularity in trade growth,

similar to that in the data. As can be seen in the bottom row of Figures

2.12(a)–2.12(b), the standard model with productivity shocks generates much

more heterogeneity across goods in the level of trade growth than the standard

model, due primarily to the large degree of heterogeneity in the productivity

shocks. Contrasting with the observed patterns of trade growth in the bilat-

eral trade data in the top row, there are typically a larger number of large

growth goods in the most-traded goods, and fewer large spikes among the mid-

traded goods in the model than what is observed in the data. This model sim-

ulation does appear to generate similar patterns of trade growth among the

least-traded goods, although there is a larger role of the traditional extensive

margin goods — those switching from not-traded to traded — in the model

than is observed in the data. Overall, there appear to be a larger number of

goods exhibiting relatively large growth in the model, such that the degree of

concentration of a large proportion of overall trade growth in a small number

of goods is slightly less than in the data, and thus the magnitude of growth

concentrated in each large-growth good is less in this model simulation.

Table 2.9 quantifies the degree of granularity generated in this model sim-

ulation. Across various country-pairs, including heterogeneous productivity

changes and tariff reductions greatly improves the standard model’s ability to

generate the granularity observed in the data. Analyzing the share of trade

growth accounted for by various quantiles of large-growth goods, the model

now generates roughly 70% as much granularity as in the data, a marked im-

provement from the 10% generated in the standard model with uniform tariff

reductions. In many cases, this improves to 80–90% of the granularity ob-

served in the data as more goods are included (i.e. the top 10% or 20% of

largest-growth goods).

Figure 2.12: Standard Model with Heterogeneous Productivity Changes and

Tariff Reduction

(a) U.S.-Canada

(b) U.S.-Japan

Table 2.9: Heterogeneous Productivity Changes and Tariff Reductions

Share of growth from top X%of goods

(6-digit NAICS codes)

US Exports to Mexico

Model 1% 2% 5% 10% 20%

Data 25% 36% 57% 74% 89%

Productivity &

Tariff Changes 18% 26% 39% 53% 71%

US Exports to Canada

Model 1% 2% 5% 10% 20%

Data 26% 38% 56% 71% 86%

Productivity &

Tariff Changes 14% 22% 39% 58% 80%

US Exports to Japan

Model 1% 2% 5% 10% 20%

Data 37% 56% 86% 101% 114%

Productivity &

Tariff Changes 25% 37% 60% 82% 105%

2.5.4 Quantitative Analysis

To further illustrate the granularity generated by the standard model, I plot

the histograms of the share of total trade growth accounted for by each good, for

each of the various iterations of the model, in Figure 2.13. For all country-pairs,

the high level of granularity in the trade data results in a bimodal distribution,

with large spikes at small positive values, and at the top end of the distribution.

This reflects the empirical findings that most goods grow very little, and the

majority of trade growth is concentrated in a small subset of goods exhibiting

large growth.

The standard model with uniform tariff reductions produces a flatter, smoother

distribution of trade growth shares, reflecting much less granular growth across

Figure 2.13: Histograms of Trade Growth by Goods

goods, and much less growth at the top end of the distribution. The stan-

dard model with heterogeneous productivity changes and tariff reductions pro-

duces comparable growth at the top end of the distribution, reflecting the large

growth among the small subset of goods accounting for the majority of trade

growth. However, the remainder of the distribution is less granular than in

the data, with growth more evenly dispersed across the remaining goods.

To quantify this dispersion of growth across goods, Table 2.10 provides sum-

mary statistics of trade growth across goods classifications for the various it-

erations of the model. The standard deviation gives an idea of the dispersion

across goods in the share of trade growth accounted for by each good, while the

kurtosis provides insight into the steepness of the distribution, both of which

reflect the granularity of trade growth. Notably, the variation across goods in

their share of total trade growth is higher in the data than in any of the model

iterations, and the kurtosis is significantly higher. The standard model with

heterogeneous productivity changes and tariff reductions performs best, with

a standard deviation 65% as large and a kurtosis 45% of that of the data. The

Table 2.10: Summary Statistics: Growth by Goods — Data vs. Models

Standard Deviation and Kurtosis

Model US/Can US/Ger US/Jpn US/Mex US/UK

Data Std 0.0072 0.0094 0.0107 0.0065 0.0092

Kurt 142.2410 34.0410 89.1526 62.6012 127.3663

Standard Std 0.0016 0.0015 0.0015 0.0017 0.0016

Kur 3.0950 3.0340 3.0825 3.0545 3.1281

Prod. shock Std 0.0043 0.0077 0.0072 0.0037 0.0052

Kur 39.9845 42.2558 42.2955 37.3227 41.5337

standard model with uniform tariff reductions generates standard deviations

and kurtosis that are much lower than those observed in the data.

Table 2.11 reports correlation coefficients between the initial level of trade

for each good and the resultant share of total trade growth accounted for by

each good. In the data, this correlation is statistically insignificant, ranging

from -0.02 to 0.05 across country-pairs, signifying that the high degree of con-

centration of growth in a small subset of goods is independent of those goods’

initial trade values. In the standard model with uniform tariff reductions, in

which goods have fixed productivities, this correlation is very high, greater

than 0.85 for all country-pairs. This characterizes the “smooth” productivity

distribution in the model, which results in all goods growing proportionally to

the tariff decrease and their initial productivity. The model with heterogeneous

productivity changes perform better, though the correlation coefficients are still

statistically non-zero, and in some countries much higher than observed in the

data. Again, the inherent smoothness in the initial productivity distribution

passes through in at least some degree to the levels of initial and final trade,

even when including heterogeneous productivity changes, generating stronger

correlation between initial trade levels and trade growth across goods.

Table 2.11: Correlations: Initial Trade vs Share of Total Trade Growth

Model US/Can US/Ger US/Jpn US/Mex US/UK

Data -0.0113 -0.0063 -0.0193 0.0453 -0.0155

Standard 0.9795 0.9114 0.9255 0.9869 0.9674

Prod. shock 0.3620 0.1715 0.1886 0.4405 0.2903

2.6 Conclusions

This chapter identifies key facts of trade growth during episodes of large growth

in bilateral trade. Bilateral trade growth is granular across goods classifica-

tions, with less than 5% of goods categories accounting for over 65% of total

trade growth during these periods. Tariff changes do not account for the large

growth in this subset of large growth goods, and many goods experiencing large

drops in their AVE tariff rates exhibit little to no growth. For all U.S. exporting

partners, increases in trade intensity, on average, account for a large share of

total trade growth, while production growth, on average, accounts for signifi-

cant portions of trade growth for some country-pairs, but virtually none of the

overall trade growth for others.

Characterizing the predictions of the a Melitz-style model with uniform tar-

iff reductions shows that it does not generate the granularity observed in the

data. Trade growth is much less granular in this model, generating only 10%

as much granularity as in the data, as measured by the share of total trade

growth accounted for by various quantiles of goods classifications. Adding het-

erogeneous productivity changes and tariff reductions to the model generates

a higher degree of granularity in trade growth in the model, capturing approx-

imately 70% of the granularity observed in the data.

Further research is needed to match the model to the level of granularity

generated by the data. More detailed data on tariff and production levels, for

a larger collection of countries, at this level of disaggregation across goods may

improve the model’s ability to match the observed level of granularity. Simi-

larly, examining non-tariff trade barriers may help to account for the remaining

25–30% of trade growth concentrated in a small subset of large-growth goods.

Finally, examining variation in the methods of transportation and distribution

of exported goods may help account for the granularity of trade growth, as

goods exported via different distribution methods may respond differently to

trade liberalization, leading to a larger degree of granularity generated when

these factors are considered in a Melitz-style model environment.

2.7 References

ABEL-KOCH, J. (2013) “Who Uses Intermediaries in International Trade? Ev-

idence from Firm-level Survey Data,” The World Economy. 36(8),1041–1064.

AHN, J., A. KHANDELWAL,AND S. WEI (2011). “The Role of Intermediaries in

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Chapter 3

The Role of Multiple Distribution

Technologies in Accounting for

Trade Growth

3.1 Introduction

Fixed and variable costs of exporting have been found to play a significant

role in accounting for international trade flows.1A wide literature establishes

the role of geographic barriers, international borders, and tariffs and quotas

in accounting for variation in bilateral trade growth across countries.2It is

well-documented, in papers like Anderson (1979), or Parsley and Wei (1996),

that trade flows generally decrease with distance — the larger the geographic

distance, the higher the presumed transportation costs of shipping goods to

foreign locations, resulting in smaller trade flows, ceteris paribus.

While a large literature examines the impact of transportation costs in ac-

counting for bilateral trade flows across countries, many studies assume a

1See, for example Melitz (2003), Chaney (2008), or Bernard et al (2007) for prominent

examples.

2See Eaton, Kortum (2002), Engel, Rogers (1996), among others.

singular exporting technology, with a common fixed and variable cost. How-

ever, when exporters ship their goods internationally, they typically compare

the costs of multiple available technologies to choose their optimal distribution

networks.3In many cases, these can be divided into two broad categories: (1)

methods with low-fixed and high-variable costs, and (2) methods with high-

fixed and low-variable costs. For example, firms exporting large volumes may

opt to build their own infrastructure, complete with marine or air transport and

offices at home and abroad to handle shipments, incurring large fixed costs, but

relatively low per-unit costs. Conversely firms with relatively small or infre-

quent shipments may choose to export using an intermediary like FedEx, with

minimal fixed costs, but higher per-unit costs incurred.

One of the main findings of Chapter 2 is that trade growth is granular —

that the majority of bilateral trade growth is accounted for by a small number

of large-growth goods classifications. I find that using a standard Melitz-style

trade model, and including heterogeneous productivity and tariff changes im-

puted from U.S. production and tariff data, generates roughly 70% as much

granularity as in bilateral trade data. Can incorporating heterogeneity in

available exporting technologies help account for the remainder of this gran-

ularity? How do the differences in available transportation options, and their

associated costs, affect suppliers exporting decisions and account for increased

granularity in trade growth across goods?

To answer these questions, I build a model of bilateral trade with standard

features such as heterogeneous productivities across firms, CES preferences

and monopolistic competition pricing similar to Chapter 2. In this chapter, I

3For a general overview of recent developments in the strategic supply network formation

literature, see Mills, Schmitz and Frizelle (2004), or work on optimal supply network design,

such as Nagurney, Dong and Zhang (2004).

add a choice for exporters among multiple distribution technologies — one low-

fixed, high variable cost method, and one high-fixed, low-variable cost method

— to examine how variation in the available distribution technologies impacts

bilateral trade flows and trade growth across goods classifications. This model

framework generates three main channels for generating large trade growth

across goods:

1. Large increases in productivity that lower the marginal costs of produc-

tion

2. Large reductions in tariff rates that lower the marginal costs of servicing

the foreign market

3. The ability for firms to switch distribution technologies, from a high vari-

able cost method to a lower variable cost method

The contribution of this chapter is to examine the impact of this third chan-

nel. In Chapter 2, I find that a Melitz-style generates only 70% as much gran-

ularity in trade growth as bilateral trade data. Including this “switching”

mechanism may allow the model to bridge this gap, which requires a higher

concentration of overall trade growth in a smaller number of goods exhibiting

disproportionately larger growth.

With CES demand and monopolistic competition pricing, the fixed costs of

exporting generate productivity thresholds — the least productive firms do

not export, firms with sufficiently high productivities export via the low-fixed

cost method, and the most productive firms find it profitable to export via the

higher-fixed cost method. As trade barriers fall (commonly represented by re-

ductions in the variable costs of exporting), the productivity thresholds shift —

some previously not-traded goods now become exported, and some previously

traded goods switch from the low-fixed/high-variable cost method, to the high-

fixed/low-variable cost method. These “switchers” may exhibit disproportion-

ately larger trade growth, due to double effect of the original reduction in trade

costs, combined with the switch to a lower variable cost exporting method.

To quantitatively assess the ability of this channel to generate granularity

in trade growth, I calibrate the model to match observed trade shares across

goods in bilateral trade data. As in Chapter 2, I use 6-digit North American In-

dustry Classification System (NAICS) data on U.S. exports to Canada, Japan,

and Mexico between 1989 and 1999, to determine the share of cross-sectional

trade and trade growth accounted for by each good category.4I target the level

of granularity in trade growth, which I quantify by calculating the share of

bilateral trade growth accounted for by each of the 473 NAICS goods classifica-

tions. I find that trade growth is highly granular in the data, with the top 5% of

large-growth goods accounting for, on average, 66% of bilateral trade growth.5

Most goods account for very little of the overall growth in trade — it is only a

small number of goods, growing from small initial levels of trade to large levels

of trade, or from large initial levels to much larger levels, that account for the

majority of growth.

4The analysis in this chapter is confined to these three destination countries due to data

limitations — in order to include heterogeneous productivity changes at this disaggregated

level of goods classifications, I use 6-digit NAICS production data for the United States, mak-

ing the U.S. the only source country for bilateral trade; in order to include heterogeneous tariff

reductions at this level of disaggregation, I use 8-digit Harmonized Tariff Schedule (HTS) im-

port tariff data, corcorded to 6-digit NAICS classifications, that is only available during this

period for Canada, Japan and Mexico.

5Further, I find that trade growth is more granular than cross-sectional trade — that is, the

top 5% of large-trade goods categories accounts for 52% of trade in a given period, but the top

5% of large-growth categories accounts for, on average, 66% of trade growth across countries.

Note: these top 5% categories need not be the same — the top 5% of traded goods in one period

are not necessarily the largest growth goods in the next period.

I quantitatively assess whether this model with multiple distribution tech-

nologies can generate the high degree of granularity observed in the data. As

in Chapter 2, each firm produces a single, unique good using labour as the

sole input, indexed by its productivity, 1

a, where ais the per-unit labor require-

ment, facing CES demand with monopolistically competitive markets. In this

chapter, I add a discrete choice among multiple distribution technologies for

exporting firms — X1: a low-fixed, high-variable cost method (f1, τ1), and X2: a

high-fixed, low-variable cost method (f2, τ2). Given a productivity drawn from a

Pareto distribution, firms profit maximize by deciding whether to export, and

if so, choosing their optimal distribution technology.

Characterizing equilibrium, I find that with CES preferences, foreign de-

mand for each good produced in the home country is inversely proportional

to that good’s price offered in the foreign market. Monopolistic competition be-

tween firms implies that each good is priced in the foreign market at a constant

mark-up over marginal cost. This marginal cost has multiple components —

the marginal cost of domestic production, a, which is a function of each firm’s

productivity; and the marginal cost of reaching the foreign market, which itself

has two components — the variable costs of the distribution method employed,

τ, and any tariffs imposed by the destination country, which is treated similar

to a change in the variable transportation cost. However, with multiple dis-

tribution technologies, the variable distribution cost can take two values — τ1

or τ2, allowing for greater heterogeneity across goods in the growth in trade

generated by productivity changes or trade liberalization.

Exporting profits are thus a function of the firm’s productivity and the fixed

and variable costs of the chosen distribution method. The existence of fixed

costs of exporting generates productivity thresholds — only goods with suffi-

ciently high productivities will find it profitable to export, and only goods with

productivities high enough to cover the higher fixed cost will find it profitable

to export via method X2, while all other exported goods will be exported via

the lower-fixed cost method X1. Goods are stratified in the model according to

their optimal distribution choice, and trade flows are a function of the relative

productivities and export costs across goods.

To quantify the granularity of trade growth generated by this model, I first

solve the model for given values of fixed and variable costs, productivities and

tariff rates, to determine export sales and optimal distribution choices across

goods. To analyze growth in this static model, I follow a common approach

of representing trade liberalization as a fall in trade costs which reduce the

variable costs of exporting, and then re-solve the model to determine changes

in the model’s predictions for export sales and distribution choice.

With CES demand, monopolistic competition pricing, and a single distri-

bution technology, a fall in trade costs results in a proportional increase in

exports for each previously-traded good. However, with multiple distribution

technologies, the fall in variable costs also shifts the productivity thresholds for

the high- and low-fixed cost distribution methods. Some previously not-traded

goods become traded, as the reduction in variable costs makes paying the fixed

cost to export profitable. This is extensive margin growth, and leads to dispro-

portionately larger growth than the size of the tariff reduction for these goods,

as they grow from zero to larger share of total trade by crossing the exporting

threshold. Further, some goods previously traded via the low-fixed cost method

now profitably switch to the higher-fixed cost method, accessing the lower vari-

able cost. These “switchers” exhibit disproportionately larger export growth

due to a double effect — the direct effect of a reduction in the variable costs

due to tariff decreases, and the indirect effect of switching to a distribution

method with a lower variable cost.

To compare the predictions of the multiple distribution technologies model

to the data, I calibrate and simulate the model and calculate the share of to-

tal trade growth accounted for by each good. I first simulate the model with

each good classification drawing a heterogeneous productivity from a Pareto

distribution, and determine the share of trade accounted for by each good. I re-

simulate the model, adding heterogeneous productivity changes for each good

that I impute from U.S. production data, and heterogeneous tariff reductions

concorded from destination-country tariff data. The changes in the model’s pre-

dictions for each good’s level of exports between the two simulations are then

compared to the changes in trade for each good in the data.

A key issue is how to calibrate the fixed and variable costs, f1, f2and τ1, τ2.

Since data on direct measures of shipping and distribution costs is limited at

this level of disaggregation, I calibrate the fixed and variable costs in the initial

simulation to match the granularity of cross-sectional trade in the data for

the 1989–1991 average for each country-pair. For a given τ1, the lower fixed

costs, f1is calibrated to match the number of not-traded goods categories.6The

higher fixed cost, f2and lower variable cost τ2are calibrated to best match the

granularity in cross-sectional trade, as measured by the share of total trade

accounted for by top quantiles of goods categories (i.e. the top 2, 5, and 10%)

in a given period. I retain these values for the fixed and variable costs in the

second simulation.

Simulating the model, I find the multiple distribution technologies model

6This is determined by the equation for the lower productivity cut-off, Eq.(5).

closely matches the degree of granularity in cross-sectional trade. On average

across country-pairs, the top 2, 5 and 10% of goods categories, respectively,

account for 33, 56 and 64% of cross-sectional trade, as compared to 35, 52 and

67% of cross-sectional trade in the data. Achieving this granularity requires

a relatively high ratio of fixed costs, with f2

f1calibrated anywhere from 670

for U.S. exports to Mexico, up to 1840 for U.S. exports to Japan. The ratio of

variable costs for the two methods is fairly consistent, calibrated near τ2

τ1=0.60

for all country-pairs.

I find that the two-method model generates a higher degree of granularity,

with the top quantiles of goods categories accounting for roughly 90–95% of the

share of total trade growth as in the corresponding trade data. Specifically, the

top 2, 5 and 10% of goods categories account for 43, 57 and 81%, respectively,

of total trade growth in the two-method model, compared to 43, 66 and 82% in

the data. Conversely, performing similar model simulations with only a single

distribution technology, as in Chapter 2, accounts for only 23, 46 and 64% of

total trade growth, roughly 60–70% of the granularity observed in the data.

Examining the choices of distribution methods in the simulations, I find

that switching behaviour generates increased granularity in trade growth in

the model. Goods that begin and remain traded via method X1account for an

average of less than 0.01% of total trade growth. Goods that begin and remain

traded via method X2contribute a larger share of total trade growth, on aver-

age 0.40% of total trade growth for each good in this group. However, goods

that switch from not-traded to traded via either method contribute an average

of 0.39% of total trade growth, while goods that switch distribution methods

from X1to X2contribute an average of 0.60% of total trade growth. This sup-

ports the theory that the ability for firms to choose among multiple distribution

technologies in the exporting process increases the granularity predicted by

the model, more closely matching the level of granularity observed in bilateral

trade data.

3.2 Related Literature

As in Chapter 2, this chapter contributes to the “trade lumpiness” literature, in

multiple ways.7First, this chapter provides a novel mechanism of incorporat-

ing multiple exporting technologies into a standard Melitz-style trade model,

that is capable of matching a high degree (roughly 90–95%) of the granularity

of cross-sectional trade observed in the data. Second, a central contribution

of Chapter 2 was to document the fact that trade growth is more granular

than cross-sectional trade, and that the set of large-growth goods is uncorre-

lated with the set of goods that were previously most highly traded. Including

multiple exporting technologies in the model generates a mechanism whereby

firms may switch distribution technologies, leading to disproportionately larger

trade-growth than non-switching firms, and helping to account for the granu-

larity of both cross-sectional trade and trade growth over time.

This chapter builds a framework similar to that of Helpman, Melitz and

Yeaple (2004), in which firms face a choice of exporting versus foreign direct in-

vestment (FDI). In their model, firms face different fixed costs of exporting and

FDI, and become stratified: domestic-only producers, firms productive enough

to pay the relatively lower fixed costs of exporting, and firms that are most

productive and can pay the relatively higher fixed costs of FDI to profit from

the lower marginal costs of production in FDI rather than exporting. However,

7See Armenter, Koren (2010), Hornok, Koren (2015) or Alessandria, Kaboski and Midraggan

(2010), for example.

since FDI is not observed in trade data as exports, this mechanism would not

be present in accounting for the granularity of export growth. This chapter

introduces a similar mechanism, with goods stratified according to their opti-

mal distribution technology, but which allows for the model to account for the

granularity of trade growth observed in export data.

A wide literature investigates optimal supply network design, to identify

how firms choose their distribution networks when confronted with options

across multiple distribution technologies. Nagurney (2010), and subsequent

papers related to this work, investigate the formation, and potential re-optimization,

of firms’ optimal supply networks. This work focuses on channels such as the

role of excess capacity — firms strategically choose distribution network capac-

ity and usage, to dynamically optimize around potential changes in the econ-

omy. Similarly, Santoso et al (2005) propose an algorithmic approach, similar

to Nagurney, for solving optimal supply network design across firms. While

this chapter abstracts from innovation in new supply network design or ca-

pacity constraints, it contributes to the supply network literature by quantita-

tively assessing the impact of distribution options in accounting for observed

patterns of trade growth.

Another literature related to optimal distribution networks focuses on the

role of wholesalers as intermediaries in international trade. Abel-Koch (2013)

uses firm-level data to empirically examine the relationship of firm size and

production to the use of trade intermediaries in Turkish exporting firms, and

find that intermediary use is decreasing in firm size, and that newly traded

goods are more likely to use trade intermediaries to export their products. Ahn,

Khandlwal and Wei (2011) incorporate an intermediary sector into a model

with heterogeneous firms, and find that firms are stratified into non-traded,

use of trade intermediary, and direct exporting firms, according to productivity.

This chapter finds a similar result of the stratification across the multiple tech-

nologies in firms’ distribution choice; however, these previous works largely

seek to match data on cross-sectional trade, not on trade growth. Further, they

primarily focus on matching which firms employ each method of trade, and do

not examine the possible change in these optimal choices following a reduc-

tions in trade barriers and the resultant impact on trade growth across firms.

This chapter extends this literature by allowing for possible changes in distri-

bution choice across multiple exporting technologies as trade barriers fall or

other structural changes may take place.

A large literature highlights the role of heterogeneity in accounting for

trade growth in international trade models. However, the focus of these models

is typically in matching overall trade flows and growth in trade. This chapter

focuses not only on matching overall bilateral trade growth, but also the distri-

bution of growth across goods, in matching the observed granularity of bilateral

trade data. Melitz (2003) and Chaney (2008), both pre-eminent works in this

literature, document the role of heterogeneous productivities across firms, as

well as fixed and variable costs of exporting, to identify the roles of the inten-

sive and extensive margins in accounting for overall trade growth. Freund and

Pierola (2015) empirically determine that the majority of cross-sectional trade

can be attributed to a small number of the largest firms in a given sector, which

can account for variation in the sectoral distribution of exports relative to in-

come across countries. Arkolakis (2010) focuses on market penetration, build-

ing a model in which firms essentially choose their fixed cost in order to access

a foreign market. Depending on this choice of fixed costs, they then face vary-

ing options of increasing marginal costs to reach additional consumers and in-

crease sales. However, as documented in Chapter 1, even adding heterogeneous

productivity and tariff changes to these types of models does not generate suf-

ficient granularity of trade growth. By adding a discrete choice across multi-

ple distribution technologies in the exporting process, allowing some firms to

switch technologies and leading to disproportionately larger growth for these

goods, the model in this chapter is better able to match the granularity of trade

growth across goods observed in the data.

3.3 Data

To decompose trade growth across goods, I use 6-digit North American Indus-

try Classification System (NAICS) data for U.S. exports to Canada, Mexico and

Japan, from 1989 to 1999. Unlike Chapter 2, the bilateral trade data is con-

fined to this subset of country-pairs by data limitations. In order to include het-

erogeneous productivity changes imputed from production data, I confine the

analysis to U.S. exports, as data at this level of disaggregation is only avail-

able for U.S. production. Similarly, in order to include heterogeneous tariff

changes across goods, I confine the analysis to U.S. exports to Canada, Mexico

and Japan, as tariff data at this level of disaggregation is only available for

this subset of the countries used in Chapter 2 for this time period.

To combine these disparate data sources, I map all data to the 6-digit NAICS

classification system. While these limitations restrict the analysis to a smaller

set of countries, I am still able to analyze trade growth across goods at a rel-

atively high level of disaggregation, and for countries that experience formal

trade liberalization (U.S.-Canada, U.S.-Mexico) as well as those that do not

(U.S.-Japan).

In Chapter 2, I used 5-digit Standard International Trade Classification

(SITC) data to document the granularity of trade growth across goods. One

key distinction between the two goods classification systems is the level of dis-

aggregation — there are 1836 goods categories in the 5-digit SITC data, while

the NAICS data is less disaggregated, with only 473 goods classifications. Since

the level of disaggregation has a potential impact on the level of granularity, I

re-calculate the shares of total trade growth accounted for by top quantiles of

goods categories for each country-pair in the 6-digit NAICS data.

As in Chapter 2, I use a 3-year average for measuring trade flows, to account

for issues such as shipping delays and customs reporting irregularities. For

each 6-digit NAICS good, I calculate the average export value from 1989–1991,

which I label as the “initial” trade value, and similarly calculate the average

export value from 1997–1999, which I label as the “final” trade value. Trade

growth is thus measured as the difference in these three-year averages for each

good.

3.3.1 Bilateral Trade Data

Descriptive Statistics

Table 3.1 presents summary statistics for U.S. exports to Canada, Mexico and

Japan, between 1989 and 1999. Countries experiencing formal trade liberal-

ization (U.S./Canada, U.S./Mexico around NAFTA) exhibit larger total growth

in trade than those non-liberalizing countries (U.S./Japan). Additionally, this

trade growth represents a larger percentage increase in trade over initial lev-

els, with U.S. exports to Canada and Mexico growing by 115% and 189% re-

spectively, while U.S. exports to Japan grew by 44% over this period.

Table 3.1: Summary Statistics: Bilateral Trade Data

(6-digit NAICS codes)

Variable USA-CAN USA-MEX USA-JPN

Initial Trade 65196.99 24536.51 34976.65

Final Trade 139880.12 70818.53 50320.17

Trade Growth 74683.13 46282.01 15343.51

%∆ in Trade 115% 189% 44%

Share of initial trade from top X%of goods

2% 37% 27% 41%

5% 53% 45% 59%

10% 66% 62% 74%

Share of trade growth from top X%of goods

2% 38% 36% 56%

5% 56% 57% 86%

10% 72% 74% 102%

Median share of 0.05% 0.03% 0.03%

trade growth

Number of goods: 473

(All trade values in thousands of $US)

Trade Growth Granularity

I re-calculate the share of total trade growth between country-pairs that is ac-

counted for by each 6-digit NAICS classification. Table 3.1 reports the share of

total trade growth accounted for by the top 2, 5 and 10% of goods. At this lower

level of disaggregation, trade growth remains granular, with a small number

of goods (roughly 10, 25 and 50 goods) accounting for 43%, 66% and 82% of

total trade growth, respectively, but is not as pronounced as in the 5-digit SITC

data from Chapter 2.8However, trade growth is still highly concentrated in

a small number of goods, while the majority of goods account for very little of

the overall growth in trade. Further, for each country-pair, the median share

of trade growth per good (0.03–0.05%) is well below the mean share of trade

growth (2.1% for each of the 473 goods categories), signifying a highly skewed

distribution of trade growth across goods. Finally, trade growth remains more

granular than cross-sectional trade — the top 2, 5 and 10% of goods categories

account for 43%, 66%, and 82% of trade growth, but only 35%, 52% and 67% of

trade in the initial period.9

Figure 3.1 illustrates the granularity of trade growth across goods at this

lower level of disaggregation. As in Chapter 2, this is shown by the small num-

ber of spikes representing goods exhibiting large growth shares, while most

goods exhibit little negligible growth shares.10 Further, trade growth shares

remain uncorrelated with initial levels of trade — the small number of goods

8For example, in the SITC data, the top 1% of goods categories accounted for roughly 60%

of total trade growth, on average across country-pairs — accounting for 60% of trade growth in

the NAICS data would require 2–5% of largest-growth goods categories.

9These 2,5 and 10% of goods categories need not be the same in accounting for trade growth

versus cross-sectional trade — that is, the most-traded goods in the initial period are not nec-

essarily the same goods that exhibit the largest growth in trade.

10Figure 3.1 illustrates this case for U.S. exports to Canada — similar examples for U.S.

exports to Mexico and Japan can be found in Appendix B.

accounting for the majority of overall trade are not necessarily just the largest,

or smallest, initially traded-goods, but rather arise from varying levels of ini-

tial trade.

Figure 3.1: Growth by Goods Category: US Exports to Canada

3.3.2 Production Data

To quantitatively assess the the model’s predictions for the trade growth across

goods, I include heterogeneous productivity changes, imputed from U.S. pro-

duction data, and compare the granularity of trade growth predicted by the

model to that observed in the bilateral trade data. I use 6-digit NAICS data

on U.S. production from the NBER-CES Manufacturing Industry Database,

for the initial period (1989–1991 average) and the final period (1997–1999 av-

erage), to calculate the changes in imputed productivity between periods. I

match the changes in productivity to the data on bilateral trade growth for

each 6-digit NAICS good category.

Figure 3.2: Productivity Distributions: Implied Productivities

Figure 3.2 demonstrates the changes in the imputed productivities for U.S.

production. For each good category, I use the observed level of domestic produc-

tion to back out the implied productivity from the production function for the

initial period and arrange goods in order of ascending productivity. I repeat

the process for the final period and map the change in imputed productivity

to each corresponding good from the initial period productivity distribution.11

There is a large degree of heterogeneity of productivity changes across goods.

Further, the changes in productivity are uncorrelated with the initial produc-

tivities — that is, it is not just the most productive firms that become even

more productive, or vice-versa.

11I also normalize the changes in productivity to mean zero to highlight the heterogeneity in

productivity changes across goods, rather than merely an increase in mean productivity.

3.3.3 Tariff Data

As in Chapter 2, I analyze the role of heterogeneous tariff changes in account-

ing for trade growth granularity in a standard trade model. To do so, I map

changes in the ad valorem equivalent (AVE) tariff rates for U.S. export desti-

nations to each good category in the model. I use 8-digit Harmonized Tariff

Schedule data from the World Bank’s World Integrated Trade Solution (WITS)

database on AVE import tariff rates on U.S. exports for Canada, Mexico and

Japan, from 1989–1991 and 1997–1999 to match the initial and final periods

in the bilateral trade data. I use concordances provided by Pierce and Schott

(2012) to map the 8-digit HTS tariff rates to the 6-digit NAICS classifications.

Figure 3.3: Heterogeneous Tariff Changes: Canada

Figure 3.3 shows the changes in the AVE tariff rates between the initial

and final periods for each concorded 6-digit NAICS good category for Canada.12

12Similar tariff changes for Mexico and Japan are shown in Figures B.4–B.6.

There is a large degree of heterogeneity across goods in the AVE tariff changes,

with most goods falling somewhere in the range between zero change and a

25% reduction tariffs.13 The mean reduction in tariffs are largest in Canada,

followed by Mexico and finally Japan, reinforcing that countries engaged in for-

mal trade liberalization policy over this period (U.S./Canada, U.S./Mexico) have

larger overall reductions in tariffs than those countries that lack a formal trade

liberalization agreement (U.S./Japan). Further, there are a larger proportion

of goods categories exhibiting large decreases in tariffs for Canada and Mexico,

and relatively more goods with small or zero reductions in tariffs for Japan.

3.4 Model

To account for the granularity of trade growth in the data, I extend the Melitz-

style model framework from Chapter 2 by including a choice among two ex-

porting technologies — one low-fixed, high-variable cost method, and one high-

fixed, low-variable cost method. The model includes heterogeneous produc-

tivities across firms, monopolistic competition, and CES preferences for con-

sumers. I characterize consumer demand and firms’ profit maximization in

equilibrium, including firms’ export decisions and distribution method choice.

As in Chapter 2, I use a static two-country model, and characterize par-

tial equilibrium to predict export sales of home-produced goods in the foreign

market. To analyze growth in this static environment, I solve the model for

two cases: first, I solve the model with a Pareto distribution of firms facing

CES demand, under monopolistic competition, given a choice among the two

13There is a notable exception, with an outlier of Mexican tariffs on U.S. exports of NAICS

311213 — “Malt Manufacturing, from barley, rye or other grains” rising by over 130%.

distribution technologies— this will serve to represent the “Initial period”; sec-

ond, I re-solve the model, incorporating heterogeneous productivity and tariff

changes across goods, under the same choice of distribution methods for export-

ing firms — this will serve as the “Final period”. Trade growth for each good

is calculated as the changes in the model’s predictions for exports between the

two cases.

In the Initial period, I find that the model generates productivity thresh-

olds for exporting, and goods are stratified according to their initial produc-

tivities. The least productive goods are not exported, as the fixed costs of ex-

porting make exporting unprofitable regardless of distribution method. Goods

with sufficiently high productivity find it profitable to export via the low-fixed,

high variable cost method. The most productive goods exhibit the largest ex-

port sales, finding it more profitable to export the high-fixed, low-variable cost

method.

In the Final period, I find that adding productivity and tariff changes across

goods generates a large degree of heterogeneity in trade growth across goods.

The model produces three channels for disproportionately larger growth in cer-

tain goods, generating the granularity of trade growth:

1. Goods with large increases in productivity

2. Goods with large decreases in tariffs, represented by a reduction in the

variable costs of exporting

3. The ability for firms to switch distribution technologies, from a high-

variable to a low-variable cost method

With productivity increases or tariff reductions (or a combination of the two),

some goods that were previously not-traded now find exporting profitable, via

the low-fixed cost method, or via the high-fixed cost method if these shocks

are sufficiently large. Similarly, some goods that were previously exported via

the low-fixed cost method now find it profitable to switch to the high-fixed cost

method, with a corresponding reduction in variable costs. These “switching”

goods exhibit disproportionately larger growth, as they benefit directly from

the productivity increase or tariff reduction, but also indirectly from the choice

of switching to a lower-variable cost method, leading to larger export sales.

This “switching” mechanism generates more granularity than the standard

model with a single distribution technology, as a larger share of total trade

growth is concentrated in these disproportionately larger-growth goods.

3.4.1 Model Set-up

The model builds on the standard Melitz-style framework, adding a discrete

choice among multiple exporting technologies. I use a static, two-country model

with symmetric countries, Home (H) and Foreign (F). As in Chapter 2, firms are

heterogeneous in their productivities, 1

awhere ais the per-unit labour require-

ment. Firms engage in monopolistic competition pricing, facing CES prefer-

ences generating consumer demand from each country. Firms choose whether

to sell to the foreign market by utilizing one of two distribution methods — one

with a lower fixed and higher variable (iceberg) cost of exporting, and the other

with a higher fixed and lower variable cost of exporting.

Firms

I assume each firm produces a differentiated good, so that each good category

in the model is synonymous with one firm, indexed by its per-unit labour re-

quirement, a. Firms use labour as the single input, paying the domestic wage

rate ωito produce in country i∈ {H, F }. For simplicity, I consider the case of

Home exports to Foreign, though the symmetric problem is equivalent. Firms

draw their productivity, 1

a, from a Pareto distribution, G(1

a). Firms engage in

monopolistic competition pricing, as in Dixit-Stiglitz (1977), facing CES de-

mand from each country. Given foreign demand for their product, cF(a), firms

choose whether or not to service the foreign market. If they choose to export,

firms must choose their optimal distribution technology among:

1. Method X1(f1, τ1): a low-fixed, high-variable cost option

2. Method X2(f2, τ2): a high-fixed, low-variable cost option

For a firm with labour requirement a, given foreign demand cF(a), the firm’s

profit maximization problem is:

max

Xj,j∈{1,2}{max

p(a){p(a)cF(a)−h(a, Xj)cF(a)}} (3.1)

where h(a, Xj)is the cost function, depending on the choice of distribution

method Xj, j ∈ {1,2}. These costs include the fixed cost of exporting, fj, as well

as the marginal cost of exporting, which embeds the marginal cost of produc-

tion, ωHa, and the variable cost of exporting, τj. The variable cost can be further

decomposed into two components: the shipping costs of physically transporting

goods between locations, and trade barrier costs, such as tariffs. By assump-

tion, there is no fixed cost for domestic production.

Consumers

Preferences of consumers in country i∈ {H, F }are represented by the CES

utility function,

Ui=Za∈A

ci(a)−1

da

−1

(3.2)

where ci(a)is consumption of good variety a,is the elasticity of substitution

across goods ( > 1) and Ais the set of available goods. Since the two countries

are symmetric, I solve the case of Home exports to Foreign, and therefore only

consider the utility function UFto derive demand for Home-produced goods in

the Foreign market, cF(a).

3.4.2 Characterizing Equilibrium

I solve the model to characterize equilibrium export flows for all goods vari-

eties, a∈A. With no fixed cost of production, all goods are produced in Home,

and consumers in Foreign have demand for these varieties that is given by the

well-known demand function for CES preferences:

cF(a) = EFp(a)−

PF1−(3.3)

where EFis national income in Foreign and PFis the aggregate price level

in Foreign. With  > 1, demand in the Foreign market, cF(a), is inversely

proportional to the price offered in the Foreign market for each Home-produced

good.

Monopolistic competition implies that firms price at a constant mark-up

over marginal cost. The marginal cost of servicing the foreign market has mul-

tiple components. The marginal cost of domestic production is ωHa— how-

ever, in order to have a full unit reach the foreign market, the firm must ship

τ > 1units (where τis commonly referred to as the iceberg transportation cost).

Thus the marginal cost of exporting is ωHτja, where j∈ {1,2}depending on the

distribution method employed by the firm. This results in a price in Foreign

for Home-produced variety aof:

pF(a, Xj) = 

−1ωHτja(3.4)

Export sales, pF(a, Xj)cF(a), are proportional to productivity and inversely

proportional to the variable cost of exporting:

ExSales(a, Xj) = 

−1EF

P1−

[ωHτja]1−(3.5)

The exporting profits for a firm with labour requirement ausing distribution

technology Xj, j ∈ {1,2}with associated fixed cost fjand variable cost τjare:

π(a, Xj) = 1

−1EF

P1−

[ωHτja]1−−ωHfj(3.6)

Productivity thresholds

To export via either distribution method, exporting profits must be non-negative:

π(a, Xj)≥0. Re-arranging the profit function yields a productivity threshold

¯a1, that satisfies:

1

¯a1=(ωH)f1τ−1

DF

−1

(3.7)

where DFis a constant with respect to a.14 This implies that firms must be

sufficiently productive to cover at least the lower fixed cost of exporting, f1, to

make exporting profitable.15

There is also a threshold that determines which firms will choose to export

via method X2rather than method X1, where π(a, X2)> π(a, X1). Solving this

inequality yields the productivity threshold 1

¯a2, that satisfies:

1

¯a2=ωH

(f2−f1)

(ωHτ2)1−−(ωHτ1)1−

−1

(3.8)

14DF=h1

−1iEF

P1−

15It is assumed that (f1, τ1)and (f2, τ2)are such that 1

¯a1is lower for method X1than method

X2. Thus, by assumption, f1

f2<τ2

τ1−1.

Firms with sufficiently high productivity will choose to export via the higher-

fixed cost method, X2, while firms with lower productivity will choose to export

via method X1, as long as their productivity is such that paying the lower-fixed

cost of exporting still yields positive exporting profits.16

Figure 3.4: Initial level of export sales

Figure 3.4 demonstrates the stratification of export sales across goods, by

productivity. Firms with low productivity draws do not export. Firms with suf-

ficiently high productivity find exporting profitable after paying the fixed cost,

with sales increasing in productivity. The less productive of these firms will ex-

port via method X1, while the more productive firms will export via method X2.

There is a discontinuous jump in export sales at the upper productivity thresh-

old 1

¯a2, with the more productive firms benefiting from the lower variable cost,

leading to higher export sales.

16It is assumed that 1

¯a2>1

¯a1, which further disciplines the relationship of the fixed and

variable costs: f2> f1h1−τ1

ωH−1τ1−

2−τ1−

1i.

3.4.3 Comparative Statics: Tariff and Productivity Changes

To analyze trade growth in the static model, I solve the model twice — for

an “Initial” period and for a “Final” period. I calculate the difference in pre-

dicted export sales across the two cases to represent trade growth for each

good. To determine the Initial period’s export sales, I solve the model with a

random productivity draw from a Pareto distribution for each firm producing

good variety aand solve for each firm’s profit maximization export decision and

distribution method choice. To determine the Final period’s export sales, I re-

solve the model while incorporating heterogeneous changes in productivity and

tariffs across goods, imputed from bilateral trade data. I impute the changes

in productivity from U.S. production data between 1989–1991 and 1997–1999,

and apply the corresponding change directly to the productivity of each good,

afrom the Initial period. Similarly, I impute changes in AVE tariff rates for

each good from U.S. export destination tariff rates, which takes the form of a

proportional reduction in the variable costs of exporting, τ1or τ2, relative to the

Initial period’s values.

Across goods, an increase in productivity or a decrease in tariffs lowers the

price offered in the foreign market, as given in Equation 3.4. The direct ef-

fect is a proportional increase in exports, as given by Equation 3.5 due to the

heterogeneous changes in productivity and tariff rates across goods.

Changes in productivity and tariff rates also have an indirect effect on ex-

port sales by altering the productivity thresholds that dictate the optimal dis-

tribution choice for each good. Equations 3.7 and 3.8 show that a reduction

in tariffs which decreases the variable costs of exporting, τ1and τ2, lowers the

productivity thresholds, 1

¯a1and 1

¯a2. This allows some goods that were below the

exporting threshold, 1

¯a1, to become exported, and some goods that were below

the upper threshold, 1

¯a2, to switch from exporting via method X1to X2. The for-

mer is categorized as extensive margin growth— previously not-traded goods

become exported. For the latter, firms that switch from X1to X2also benefit

from the reduction in variable costs by moving from τ1to τ2, bringing a sec-

ondary increase in export sales, as in Equation 3.5.17

Figure 3.5: Final level of export sales

With three distribution possibilities, {0, X1, X2}in each period, there are 9

potential combinations for distribution method choice across the two periods.

Figure 3.5 shows the stratification of these possibilities. With a reduction in

the variable costs of exporting from a decrease in tariffs, export sales will in-

crease proportionally across the productivity distribution for each method. Ad-

ditionally, the productivity thresholds will shift, as represented by the shaded

regions in Figure 3.5. Trade growth can be decomposed as follows: Goods that

17It should be noted that if productivity decreases or tariffs increase, the converse is true—

the productivity thresholds increase and sales decrease, with firms potentially “switching

down” in their distribution choices.

begin with and retain the lowest productivities will remain not-traded. Some

previously traded goods will increase export sales proportionally to the reduc-

tion in tariffs, while continuing to use the same distribution method, either X1

or X2. However, some previously not-traded goods may now cross the lower

productivity threshold and become exported via method X1.18 Similarly, with

the reduction in variable costs of exporting, some goods that were previously

traded via method X1now find it profitable to switch to method X2(as shown

in the blue shaded region). This increase in export sales is disproportionately

larger than it would be at similar productivity levels where the choice of distri-

bution method does not change (as in the white shaded regions to the left and

right).

Adding changes in productivity moves firms across the productivity distri-

bution, which potentially generates more granularity in trade growth. Firms

with a sufficiently large increase in productivity may “jump” across a produc-

tivity threshold in Figure 3.5. For example, a firm with low productivity may

choose not to export in the initial period, but an increase in productivity may

move them into a region of the distribution where exporting becomes profitable

via X1, or via X2if the increase in productivity is sufficiently large. Similarly,

goods initially exported via X1may receive a sufficient increase in productiv-

ity to move to a portion of the distribution where switching to X2is profitable,

bringing a disproportionately larger growth in trade than the direct effect of

the productivity increase.19

The model now provides three channels for generating heterogeneity in

18While not shown explicitly in 3.5, it is theoretically possible for goods to jump from not-

traded to exported via method X2if the tariff reductions are sufficiently large.

19Again, it should be noted that although the cases presented here deals with tariff decreases

and productivity increases, the converse holds for cases of tariff increases and productivity

decreases and the resultant decreases in export sales across goods.

trade growth across goods. First, heterogeneous tariff changes, represented

as changes in the variable cost of exporting for both distribution technologies,

changes the price offered in the foreign market and results in proportionally

larger export sales for the goods exhibiting the largest tariff reductions. Sec-

ond, heterogeneous productivity changes, represented as changes to the vari-

able cost of domestic production, similarly result in heterogeneous changes in

the price offered in the foreign market and proportionally larger export sales

for the goods exhibiting the largest productivity increases. Third, these first

two channels may lead to certain goods crossing the productivity thresholds,

resulting in disproportionately larger growth for these “switchers” — goods

that switch from not-traded to traded via either technology, or switching from

method X1to X2. This occurs due to the combined effect of these goods ex-

hibiting increases in export sales proportional to the growth in the first two

channels being magnified by a switch to a lower-variable cost method, ampli-

fying the growth in trade. The larger growth exhibited by this subset of goods

increases the granularity of trade growth predicted by the model, compared to

the model with a singular distribution technology.

3.5 Quantitative Analysis

To quantitatively assess the model’s ability to match the granularity in the

data, I calibrate and simulate the model with multiple distribution technolo-

gies to match bilateral trade flows. I first simulate the model and calibrate the

fixed and variable costs of exporting to match U.S. exports to Canada, Mex-

ico and Japan, for the 3-year average from 1989–1991, representing the “Ini-

tial period”. I re-simulate the model, adding heterogeneous productivity and

tariff changes imputed from U.S. data, to match bilateral trade data for each

country-pair over a three-year average from 1997–1999, representing the “Fi-

nal period”. I calibrate the distribution of tariff reductions for the Final period

to match the overall growth in trade for each country-pair between 1989–1991

and 1997–1999 averages.

One key issue in simulating the model is how to implement the fixed and

variable costs (f1, τ1;f2, τ2) associated with the different distribution methods

available to exporters. Since direct data on variations in shipping rates across

goods is highly limited at this level of disaggregation, I calibrate these pa-

rameters to match the granularity of cross-sectional trade flows. Specifically,

I calibrate the relative fixed and variable costs for the two methods, X1and

X2, to match the shares of total trade accounted for by the top 2, 5 and 10%

of goods categories in the Initial period. I then take these costs as given when

re-simulating the model for the Final period.

In Chapter 2 I found that including heterogeneous productivity and tar-

iff changes in the Melitz-style model accounted for roughly 70% of the ob-

served granularity of trade growth in bilateral trade data. Adding a choice

among multiple distribution technologies to this model framework, I find that

the model now captures roughly 90–95% of the granularity in the data. Fur-

ther, I find evidence of switching behaviour in the model simulations, which

increases the level of granularity in predicted trade growth. Although a rel-

atively small number firms choose to switch technologies, with the majority

of overall trade growth occurring from goods retaining their distribution choice

across periods, I find evidence that on average, each switching firm accounts for

a greater share of trade growth (0.5–1.0% per good) than each non-switching

firm (0–0.5% per good), increasing the granularity of trade growth across goods.

3.5.1 Parameterization and Calibration

The calibration strategy in this chapter is similar to that of Chapter 2, with one

notable exception — I now have two additional free parameters to calibrate: f2

and τ2, the costs associated with the second distribution option X2. As in Chap-

ter 2, I first parameterize and calibrate the model to match bilateral trade

data on U.S. exports to Canada, Mexico and Japan for the 3-year average from

1989–1991, which I classify as the Initial period. To analyze changes in trade

flows across goods, I re-simulate the model, adding heterogeneous productivity

and tariff changes imputed from U.S. data, and calibrating the model to match

bilateral flows for U.S. exports to Canada, Mexico and Japan for 1997–1999,

which I classify as the Final period. To incorporate these heterogeneous pro-

ductivity and tariff changes, I calibrate the model to match data at the 6-digit

North American Industry Classification System (NAICS) level, resulting in 473

distinct goods classifications.

For the Initial period, I draw each firm’s initial productivity from a Pareto

distribution, G(1

a), mapping each firm to a single good category, and set the

elasticity of substitution, , at 6.0.20 Since my variable of interest is the share

of growth accounted for by each good category (not the absolute level of trade

flows for each category), I begin with τ1, the higher variable cost, as a free

parameter, as in Chapter 2. For a given τ1, the lower fixed cost, f1, which de-

termines the lower productivity threshold for exporting, is calibrated to match

the number of not-traded goods in the data. I then simultaneously calibrate

the higher fixed cost f2, and lower variable cost, τ2, to match the cross-sectional

trade flows accounted for by the top 2, 5 and 10% of goods in the Initial period

20Refer to Chapter 2, Section 5.2.1 for a discussion on these parameter choices and

implications.

(1989-1991 average for each destination country in the data).21

Similar to Chapter 2, I use U.S. manufacturing data to impute changes

in productivity across goods between the Initial and Final periods, and apply

these changes to the productivity distribution from the Initial period simu-

lation.22 I use 8-digit Harmonized Tariff Schedule (HTS) data, which I con-

cord to 6-digit NAICS classifications, to determine the changes in ad valorem

equivalent (AVE) tariff changes for Canada, Mexico and Japan between the

1989–1991 and 1997–1999 periods.23 I scale the distribution of tariff changes

to match total trade growth for each U.S. export destination for the Final pe-

riod, 1997–1999, retaining the same set of fixed and variable cost options cali-

brated in the Initial period, to determine exports, distribution choice, and share

of total trade growth accounted for by each good category.24

3.5.2 Initial Period

Table 3.2 presents the results of the model calibration for each destination

country. For the top 2, 5, and 10% of goods categories, the model captures

93–95% of the overall granularity in cross-sectional trade, on average across

21Specifically I grid search over a range of all plausible values of f2and τ2consistent with

the literature, to determine the parameter values that minimize the loss function over various

quantiles of trade, k~rdata −~rmodelk, where the ~r’s are vectors of the proportion of total trade ac-

counted for by the top 2, 5 and 10% of goods. Therefore, in keeping with the focus on matching

the share of trade growth accounted for across goods in the data, the calibration determines

the ratio of fixed and variable costs between methods X1and X2.

22Figure B.3 shows the distribution of Initial productivities along with the applied produc-

tivity changes.

23Figures B.4–B.6 show the distribution of tariff changes across goods classifications. Of

note, the mean tariff decreases are larger in Canada and Mexico, due to the formal trade

liberalization of NAFTA, as opposed to Japan. However, while there are many more goods

exhibiting large AVE decreases for Canada and Mexico, there are still large AVE reductions

for some goods categories in Japan, in the absence of formal trade liberalization agreements.

24As in Chapter 2, this is computationally equivalent to calibrating DFto match the overall

level of trade growth.

country-pairs. For all country-pairs, the ratio of the two calibrated variable

costs, τ2

τ1, is consistently between 0.55–0.65.25 There is more variation in the

ratio of calibrated fixed costs, f2

f1, across country-pairs. For U.S. exports to Mex-

ico, where the top quantiles of goods account for lower shares of Initial trade,

the ratio is lower, at 670. For U.S. exports to Canada and Japan, where the

trade shares accounted for by the upper quantiles of goods is higher, the ratio

of fixed costs is higher, at 1430 and 1840, respectively.26 These results suggest

that a higher fixed cost ratio creates a higher productivity threshold for firms

using method X2, which, combined with a lower variable cost τ2, concentrates

a larger share of Initial trade in a smaller proportion of goods categories at the

top end of the distribution.

3.5.3 Final Period

Table 3.3 reports the share of trade growth accounted for by quantiles of largest-

growth goods categories for each U.S. export destination. The share of trade

growth accounted for by the top 2, 5 and 10% of goods is roughly 90–95% as

high as that observed in the data, on average across country-pairs. This marks

an improvement from the roughly 70% of granularity generated by the model

with a single distribution technology, as in Chapter 2.

25With the higher variable cost, τ1, set as a free parameter at 2.0, this results in values for τ2

across countries of 1.12–1.32, consistent with the interpretation in the literature of the iceberg

costs shipping, where τrepresents the number of units necessary to ship to result in 1 unit

arriving at the destination country.

26Due to the scarcity of direct measures of the fixed costs of exporting, it is difficult to as-

sess the appropriateness of these fixed cost ratios — the vast majority of the relatively small

literature that seeks to directly measure distribution and transportation costs in international

trade goes no deeper than identifying total costs, without decomposing the shares of fixed vs.

variable costs, and virtually all assume a common distribution technology. However, Kropf

and Saure (2014) estimate variation across Swiss firms in fixed costs per shipment, and find

logged values that range from -3 to 9 — thus the fixed cost ratios I calibrate between 670 and

1840 correspond to logged differences of 6.5 to 7.5, which arguably fall within realistic ranges

of those imputed by Kropf and Saure.

100

Table 3.2: Cross-Sectional Granularity: Initial Period

Share of trade from top X%of goods

(6-digit NAICS codes)

USA-CAN USA-JPN USA-MEX

Model Data Model Data Model Data

2% 37 37 41 41 21 27

5% 57 53 63 59 49 45

10% 62 66 68 74 62 62

20% 71 81 75 88 71 79

40% 84 94 87 97 84 94

f11430 1840 670

τ2

τ10.59 0.56 0.66

Additionally, I track the distribution choice for each good across the two sim-

ulations to quantitatively assess the ability of the model’s “switching” mecha-

nism to account for trade growth granularity. Figure 3.6 plots the distribution

choice across goods, arranged by ascending initial productivity. Firms are ini-

tially stratified according to productivity, with the least productive firms not

exporting, the most productive firms exporting via method X2, and those in

between the productivity thresholds exporting via method X1, represented by

the starred levels. After including the productivity and tariff changes from the

data, and simulating the model, the bars represent the new distribution choice

for each good. Many previously not-traded goods remain not-traded, but some

now become traded via X1or X2(as reflected by the bars ascending to 1 or 2).

Similarly, a large proportion of goods previously traded via method X1remain

traded via X1; however, some now switch to method X2(as reflected by the bar

ascending above the starred line) while others no longer export (as reflected by

a blank space for that good). The same is true for goods initially traded via X2,

where the majority remain traded via X2, but some goods switch to either X1

101

Table 3.3: Trade Growth Granularity: Second Period

Share of growth from top X%of goods

(6-digit NAICS codes)

CAN-USA JPN-USA MEX-USA

Model Data Model Data Model Data

2% 33 38 59 56 37 36

5% 48 56 74 86 50 57

10% 75 71 97 102 70 74

20% 92 86 116 114 87 89

40% 111 99 138 123 104 101

f11430 1840 670

τ2

τ10.59 0.56 0.66

(a space down to level 1) or not-traded (a space down to 0).

Comparing across the two simulations, I find that firms switching from dis-

tribution technology 1 to 2 account for a larger shares of total trade growth

than the traditional extensive margin of firms switching from non-traded to

traded. Table 3.4 reports the shares of trade growth accounted for by each of

the 9 possible combinations of distribution choices across the two simulations.

While there are a smaller total number of firms switching from not-traded to

traded, or from method X1to X2than there are firms that retain the same

distribution choice, these switching firms account for relatively larger shares

of trade growth, on average. Firms switching from not-traded to traded ac-

count for an average of roughly 0.3–0.7% of total trade growth per good, while

firms switching from X1to X2account for an average of 0.5–1.0% of total trade

growth per good, across the various country pairs. Conversely, firms that re-

tain X1in both simulations account for virtually none of the total trade growth,

and while firms that retain X2account for 50–60% of the total trade growth,

the fact that there are relatively so many of these firms (140–150 per country)

102

Figure 3.6: Model Simulation: Optimal Distribution Choice

means that on average, they account for only 0.3–0.5% of total trade growth

per good.

Table 3.4: Optimal Distribution Method Choice

Proportion of total trade growth

U.S.-Canada U.S.-Japan U.S.-Mexico

Methods Tot. Share # goods Avg. Share Tot. Share # goods Avg. Share Tot. Share # goods Avg. Share

0→0 0% 74 0% 0% 78 0% 0% 74 0%

0→X10.03% 6 0.00% 0.03% 6 0.01% 0.05% 6 0.01%

0→X26.14% 10 0.61% 8.98% 7 1.28% 4.60% 10 0.46%

X1→0 -0.27% 77 0.00% -0.50% 81 -0.01% -0.36% 78 0.00%

X1→X10.08% 74 0.00% -0.08% 67 0.00% 0.32% 71 0.00%

X1→X239.61% 66 0.60% 61.41% 62 0.99% 32.22% 69 0.47%

X2→0 -3.31% 7 -0.47% -6.34% 5 -1.27% -1.99% 7 -0.28%

X2→X1-7.06% 17 -0.42% -15.88% 15 -1.06% -3.95% 16 -0.25%

X2→X264.78% 142 0.46% 52.39% 152 0.34% 69.11% 142 0.49%

It is also important to note that in Table 3.4 it is possible for firms to “switch

down” in the model — firms with decreases in productivity or increases in tar-

iffs may choose to switch from X2to X1following the inverse rationale of firms

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that “switch up”, or may even decide to stop exporting altogether. While there

are a smaller number of these types of down-switching firms than up-switching

firms, their presence in the model serves to amplify the granularity of trade

growth, as the up-switching firms account for an even larger share of total

trade growth when these decreases in exports from down-switching firms are

taken into consideration.

3.6 Conclusions

This chapter extends the literature by identifying a novel mechanism that

helps account for the high degree of granularity of trade growth observed in

bilateral trade data. I use data U.S. exports to Canada, Mexico and Japan,

between 1989 and 1999, at the 6-digit NAICS level, to determine the distribu-

tion of trade growth shares across goods. I find that trade growth is granular

— a small number of goods categories accounts for a majority of total bilateral

trade growth- specifically, the top 5% of goods accounts for roughly 66% of over-

all trade growth, on average across country-pairs. Further, I find that trade

growth is more granular than cross-sectional trade, and that trade growth is

uncorrelated with previous levels of trade.

To match this level of granularity in the data, I use a standard trade model

framework, and add a discrete choice among multiple distribution technologies

for firms in the exporting process. I introduce a low-fixed, high-variable cost

exporting technology, and a high-fixed, low-variable cost exporting technology,

and include heterogeneous productivity and tariff changes, imputed from trade

data, to analyze the predictions for trade growth across goods in the model. I

calibrate the fixed and variable costs, and the distribution of productivity and

tariff changes, to match overall bilateral trade flows, and simulate the model

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to determine the distribution of growth in export sales predicted by the model.

I find that the model simulation generates roughly 90–95% of the observed

granularity of trade growth in the bilateral trade data, as measured by the

share of total trade growth accounted for by the top quantiles of goods cate-

gories. The model with multiple distribution technologies increases the gran-

ularity of trade growth in the model, as compared to a standard model with a

single distribution technology, which generates only 60–70% as much granu-

larity as the data. In the model, I find evidence that goods that switch their

distribution technology in response to heterogeneous productivity changes and

tariff reductions account for a relatively larger share of total trade growth than

non-switching goods. This occurs as a result of the double effect of a direct re-

duction in variable costs of exporting from tariff reductions and productivity

increases, combined with an indirect effect of switching to a lower variable cost

method of exporting, resulting in disproportionately higher growth, accounting

for the observed granularity of trade growth.

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