Estimating the
International Transport Cost Elasticity
Ahmad Lashkaripour
Indiana University
May 2017
Abstract
The iceberg assumption, which underlies most quantitative trade models,
imposes that the transport cost elasticity (i.e., the elasticity of unit transport
cost with respect to unit price) equals “one.” Employing micro-level data and
accounting for previously-overlooked variations, I provide a first estimate of
the transport cost elasticity for a wide range of industries. The estimated
transport cost elasticity varies across industries, displaying an average value of
0.9, which is suggestive of quasi-iceberg transport costs. While these estimated
variations have sharp implications for quality specialization and industrial
policy, quantitative analysis suggests that the iceberg assumption is relatively
innocuous to counterfactual welfare predictions.
1
Introduction
Quantitative trade models impose strong parametric restrictions on international
transport costs. Most notably, the elasticity of unit transport cost with respect to
unit price (i.e., the transport cost elasticity) is often set to “one,” resulting in the
well-known iceberg cost formulation. While this standard restriction brings along
parsimony, it may also undermine the credibility of counterfactual predictions within
1
canonical trade models. Therefore, not surprisingly, while the iceberg assumption remains a central feature of standard trade models, it is often regarded with
considerable skepticism.
In recent years, the skepticism surrounding the iceberg assumption has amplified.
Multiple studies have estimated the transport cost elasticity to be closer to “zero,”
suggesting that international transport costs are best described by the additive rather
than the iceberg specification (Hummels and Skiba (2004); Clark, Dollar, and Micco
(2004); Hummels, Lugovskyy, and Skiba (2009)). These estimates, however, hinge
on a strong assumption that unit weight is uniform within product categories. This
assumption, which is imposed to overcome data limitations, enables researchers to
infer import quantities from the weight of imported shipments.1
Using transaction level data on actual import quantities and shipment weights, I
show that import unit weights vary widely even within narrowly-defined categories.
Furthermore, I find that the variation in import unit weights are systematic. Within
narrowly defined categories, import unit weights increase systematically with (i)
unit price (i.e., expensive items are systematically heavier), and (ii) distance from
supplier, (i.e., heavier items are shipped relatively more to faraway markets).
I show that overlooking the systematic variation in import unit weights leads to
an omitted variable bias when estimating the transport cost function. As a result of
this bias, traditional estimates systematically understate the transport cost elasticity.
To illustrate this point formally, I estimate the transport cost elasticity across a wide
range of industries, while accounting for the systematic variation in import unit
weights. The estimated elasticities vary considerably across industries, with the
average industry displaying a transport cost elasticity of 0.9. Overall, these improved
elasticity estimates are systematically higher than traditional estimates, and suggest
1
Note that the main finding of Hummels and Skiba (2004) that Alchian-Allen effects are quantitatively important is not driven by this assumption. Instead, the byproduct of their analysis that
transport costs are quasi-additive is an artifact of assuming uniform unit weights. This assumption is
adopted to overcome data limitations and is carefully spelled out on page 1391 of their paper: “The
use of weight, instead of count, data as a quantity measure is not problematic. In our empirical
analysis, we shall express data relative to commodity k means, which subsumes differences in units
across categories. That is, one can think of all categories in terms of a common unit (weight) or in
terms of a category-specific unit (e.g., number of shoes) multiplied by weight per category unit.” In
fact, inferring quantity from weight has been common practice and dates back to Moneta (1959).
2
that transport costs are quasi-iceberg.2
There is a simple intuition for why overlooking the variation in import unit
weights attenuates the estimated transport cost elasticity. High-price items are
costlier to transport due to (i) being heavier and (ii) the greater insurance, packaging
and handling requirements associated with high-value goods. By treating unit
weight as uniform, traditional estimates overlook the former channel, and understate
the elasticity of transport cost with respect to unit price. Accounting for both
channels, however, transport costs increase near proportionally with unit price,
thereby resembling iceberg melt costs.
As a natural next step, I plug the estimated transport cost elasticities into a
general equilibrium multi-industry trade model. I calibrate the model to aggregate
trade shares across 8 regions and 33 industries. I then compare the predictions of
this benchmark model to two alternative models calibrated to the same data: one
featuring standard iceberg transport costs (i.e., a uniform transport cost elasticity
equal to 1), and another featuring additive transport costs (a uniform transport cost
elasticity equal to 0).
The realized gains from trade are similar across all three models, which is
reminiscent of the well-know Arkolakis, Costinot, and Rodriguez (2012) result. The
prospective gains from free trade, however, are sensitive to the values assigned to
the transport cost elasticity. The model featuring additive transport costs predicts
considerably larger gains from free trade. This outcome fits with the conventional
wisdom that additive transport costs are more distortionary, so eliminating them is
more welfare-enhancing. Perhaps more notable is that the benchmark model and the
standard iceberg model predict gains from free trade that are starkly similar. That is
to say, the estimated deviations from the iceberg assumption or the cross-industry
variation in the transport cost elasticities have minimal impact on the predicted gains
from trade—for example, the prospective gains from free trade for the US economy
are 102.97% under the estimated transport cost elasticities versus 101.22% under
2
My analysis focuses primarily on international transport costs. Trade costs also include tariffs,
which are typically imposed as an ad valorem tax on imports. Hence, while tariffs are multiplicative
like iceberg transport costs, they generate revenue, making them inherently different from iceberg
melt costs—see Ossa (2014) and Beshkar and Lashkaripour (2017) for a formal analysis of revenue
generating tariffs in quantitative trade models.
3
the iceberg assumption. Hence, considering the trade-off between parsimony and
precision, the iceberg assumption appears to be a practical and innocuous choice.
The above results contribute to a vibrant empirical literature on inter- and intranational trade costs. The existing literature takes two distinct approaches when
analyzing trade costs. One approach is to infer trade cost magnitudes from price or
sales data (Limao and Venables (2001); Donaldson (2010); Novy (2013); Irarrazabal,
Moxnes, and Opromolla (2014); Atkin and Donaldson (2015)). The other approach
is model-free and directly uses data on tangible transport costs (Hummels and Skiba
(2004); Clark et al. (2004); Hummels et al. (2009); Blonigen and Wilson (2008);
Abe and Wilson (2009)). This paper falls under the latter category, and offers a
two-fold contribution to this literature. First, I account for the role of product weight,
which has been previously overlooked. Second, I estimate industry-level transport
cost elasticities using firm-level rather than aggregate-level variations in the data.
At a broader level, this paper relates to a literature providing micro-level estimates
for structural parameters that underly quantitative trade models. Currently, there is
a well-established literature on estimating industry-level trade elasticities (Broda
and Weinstein (2006); Simonovska and Waugh (2014); Caliendo and Parro (2015)).
More recently, several studies including Lashkaripour and Lugovskyy (2017) have
estimated the scale elasticity across various industries. This paper provides the first
industry-level estimates of the transport cost elasticity.
Altogether, this paper takes a preliminary step towards understanding the credibility and consequences of the iceberg assumption. Obviously, the present analysis
does not alleviate all concerns surrounding the iceberg assumption. Instead it highlights a caveat in the estimates that have triggered much of the existing skepticism.
Furthermore, this paper argues that empirical deviations from the iceberg assumption
seem moderate, and thereby have a small effect on the predicted gains from trade.
2
Theoretical Framework
In this section, I describe an economic environment that nests an important class
of trade models to highlight the role of the transport cost elasticity. There are N
countries, each populated by a continuum of firms indexed by ω. Preferences in
4
country i are described by a nested CES aggregator across firm-specific varieties,
and a Cobb-Douglas aggregator across product categories:
σ

! σσh · ηhη−1 γi,h · σh h−1
N Z
X
σh −1
h−1
h 

Ui = Πh 
qωih σh dω

ω∈Ω jih
j=1
∗
Demand for variety ω is thus x ji,h (ω) = p∗ji,h (ω)1−σ Pσ−1
i,h γi,h Yi , where p ji,h (ω) denotes
the final price (inclusive of transport costs) charged by firm ω from origin country
j in market i. Pi,h and Yi denote the product-wide price index and total income in
country i. Each firm is characterized by productivity ϕ, and faces the following
non-linear cost function (in units of labor), which includes both production and
transportation costs:
!
1 d ji
c ji,h (q; ϕ) =
+
q + f ji ,
ϕ ϕ βh
where q denotes quantity produced and delivered from country j to market i, with
d ji /φβh reflecting the cost of transportation. The above transport cost specification
has deep root in the literature. It acknowledges the argument in Alchian and Allen
(1964) that transport costs distort relative prices in favor of high-price product
varieties; it is analogous to the transport cost function introduced by Hummels and
Skiba (2004) (see Section 3.3); and when the transport cost elasticity, βh , is set to
“one” it encompasses the transport cost specification employed in canonical trade
models (see below).
Letting w j denote wage in country j, a firm from country j with productivity ϕ
charges the following price:
p∗ji,h (ϕ) =
σh w j 1 + d ji ϕ1−βh ,
σh − 1 ϕ
(1)
j
h
in the above equation, p ji,h (ϕ) ≡ σσh −1
is the f.o.b. component of the final price,
ϕ
d ji
σh
and τ ji,h (ϕ) ≡ σh −1 w j ϕβh corresponds to the cost of transportation. Importantly, the
above price equation identifies two polar specifications:
w
i. Iceberg transport costs, β h = 1: in this case, defining τ̃ ji ≡ 1 + d ji , the price
5
equation reduces to the familiar equation described below:
p∗ji,h (ϕ) = τ̃ ji
σh w j
,
σh − 1 ϕ
ii. Additive transport costs, β h = 0: in this polar case, defining τ̂ ji ≡
the price equation becomes:
p∗ji,h (ϕ) =
σ
wd ,
σ−1 j ji
σh w j
+ τ̂ ji ,
σh − 1 ϕ
Importantly, the choice of β directly affects the estimated gains from economic
integration—if a quantitative model assigns a higher-than-factual value to β it will
systematically understate the gains from trade (Irarrazabal et al. (2014); Martin
(2012)). Hence, given that quantitative trade models often adopt the iceberg specification, the credibility of counterfactual predictions within these models hinges on
the credibility of this specification.
In the following section, I use micro-level data to estimate β across a wide range
of industries. Then, in Section 4, I plug the estimated elasticities in to a quantitative
multi-country trade model calibrated to aggregate industry-level trade data. This
exercise allows me to asses the credibility of counterfactual predictions attained
based on the standard iceberg specification.
3
Estimating the Transport Cost Elasticity
In this section, I first describe the data used in my empirical analysis. I then highlight
the systematic variation in import unit weights (i.e., weight per imported item) within
narrowly defined categories. The prior literature has overlooked these variations,
but they play a central role in international transportation. Finally, I estimate the
transport cost elasticity, β, using firm-level variation in transport costs, unit prices
and unit weights.
6
Table 1: The composition of imports by unit of measurement.
The unit in which quantity is reported in
Sample
Count of items
Kilograms and its dervatives
Other Units
Colombia Imports
51.60%
38.57%
9.83%
U.S. Imports
45.2%
18.9%
35.9%
Note: This table reports the f.o.b. value-weighted share of imports based on units of measurement.
In the Colombia sample the vast majority of shipments that report quantity in counts, report the
number of items (“UNIDADES O ARTÍCULOS”) with a few shipments reporting pairs (“PAR”)
and thousands (“MILLAR”). In the U.S. data, various units correspond to item count (e.g. “N”,
“NO”, “DOZ”, “DPC”, “DPR”, “PCS”, “PRS”, “PK”, “HUN”, “THS”). Similarly, the U.S. data
contains various derivatives of kilograms: “K”, “KG”, “TON”, “T”, “kg”, “GRS”, “GM”, “GKG”,
“G”, “CYK”, “GTN”.
3.1
Data
I use proprietary transaction-level data on Colombian imports in the 2007–2013
period. The data has been collected and made available by the National Tax Agency.
For each import transaction the data identifies the exporting firm’s id, the Colombian
importing firm’s tax id, the corresponding 10-digit Harmonized System (HS10)
product category, plus the f.o.b. value, freight cost, insurance charge (all in U.S.
dollars), quantity and net weight of the imported goods.3 The detailed structure the
Colombia data set enables me to conduct my estimation with an extensive set of
fixed effects. Nonetheless, I show that all estimation outcomes hold equally in the
publicly available but more aggregate US import data. A detailed description of the
US sample is provided in Appendix A. I also use export data from Colombia and the
US to complement the import data. The export data for each country has a similar
format to that of the import sample, but does not report freight, insurance, and tariff
charges. The Colombia data reports the imported quantities in 1 of 10 different units
of measurement. Count is the most frequent unit of measurement (see Table 1). In
total, there are 17,281,272 data entries with 12,258,450 entries reporting quantity in
counts—I restrict my main analysis to these observations.
3
Colombian imports from 2007 to 2013 include 7,296 distinct HS10 product categories.
7
3.2
Systematic Variation in Product Weights
Traditionally, information on product weight have played a key role in estimating
the transport cost elasticity. Specifically, estimating the transport cost elasticity
requires information on import quantities, which were absent in earlier data sets. By
assuming that unit weight is uniform within HS10 categories, traditional estimates
have inferred import quantities from import weights. To give an example, suppose
all TV units weigh the same. Consider two import shipments consisting of TVs:
shipment 1 weighing WGT 1 kilograms and shipment 2 weighing WGT 2 = N ×WGT 1
kilograms. Knowing this information alone, one can conclude that the quantity of
TVs in shipment 2 is N times the quantity in shipment 1—i.e., Q2 = N × Q1 . This
assertion, however, will fall apart if unit weights (i.e., weight per TV unit) vary
across shipments.
In view of the above practice, this section uncovers three stylized facts about
the variation in import unit weights. As noted above, the Colombia sample reports
the total net weight (WGT s,ωht ) and quantity (Q s,ωht ) of each individual shipment
s sourced from firm ω, in a given HS10 product h, in year t. The U.S. sample
reports similar variables, but shipments from the same country are aggregated up to
a given country of origin–US district–product–year.4 The analysis on the US sample
therefore requires a different notation and utilizes different variations in the data.
Throughout the paper, I present the empirical strategy based on the transaction-level
Colombia data. Appendix A presents the estimating equations and the identification
strategies corresponding to the US sample.
Given the information on total weight and quantity, one could calculate the unit
weight associated with shipment s, ωht as:
wgt s,ωht =
WGT s,ωht
Q s,ωht
A first-order analysis of import unit weights unveils three basic facts that are common
4
The U.S. sample reports the quantity (Q s,ωht ) and weight (WGT s,ωht ) of aggregate imports from
country s to U.S. district ω, in a given HS10 product h, in year t. Therefore, while s indexes
individual shipments in the benchmark analysis (conducted on the Colombia sample) it denotes
exporting country in the U.S. data. Similarly, ω indexes an exporting firm in the benchmark analysis,
whereas it indexes the port-of-entry in the U.S. data.
8
to both samples. Additionally, while my analysis of unit weight is confined to
observations reporting quantity in counts, these three facts apply equally to other
observations with one exception: those that report quantity in some derivative of
kilograms. For these observations (which, for example, constitute less than 19% of
US imports) unit weight is by definition “one” and import quantity is exactly equal to
import weight: Q s,ωht ≡ WGT s,ωht . For the remaining majority of import transactions,
however, the variation in unit weights are both substantial and systematic. Overall,
the three facts outlined below, cast doubt on the traditional practice of inferring
import quantities from import weights.
Fact 1. Unit weight is not uniform even within narrowly defined categories.
The unit weight of imported tradables vary tremendously even across shipments from the same country in a given product-year. Within the median country–product–year cell, the heaviest (95 percentile) item imported by Colombia is
18-times heavier than the lightest (5 percentile) item. Furthermore, unit weight is
far from uniform even across shipments from the same firm, of the same product, in
the same year. Similarly, there is tremendous variation in the unit weight of items
imported by the U.S. within 10-digit product categories in a given year. Take for
example the median product-year cell in the U.S. sample that reports quantity in
counts. Within this narrowly defined category, the heaviest (95 percentile) imported
item weighs 112-times more than the lightest (5th percentile) item (see Table 2).5
These observations leave little doubt that the variation in import unit weights
are considerable, even within narrowly defined categories. However, as noted
earlier, these variations have been traditionally overlooked by the trade literature. In
particular, by assuming that unit weight is uniform within product categories, many
studies use weight, WGT , as a substitute for quantity, Q, with unit prices calculated
as e
p = VALUE
rather than p = VALUE
. Later, I will argue that in face of the systematic
WGT
Q
within-category variation in unit weights (facts 2 and 3) this practice can lead to
systematic bias when estimating the international transport cost elasticity.
5
Two clarifications about this and others statistic reported in Table 2 with relation to the U.S.
Sample: (i) this statistic describes the median category, not the median observation, and (ii) it is
calculated for the sample of 1,667,243 observations, which report quantity in numbers (“N” and
“NO”) and provide full information on total weight, value, freight charge, and quantity (see Section
3.1)
9
Table 2: The variation in unit weight within narrowly-defined categories
Mean
Median 1st quartile
3rd quartile
Colombia sample (within country-HS10-year)
unit weight95pct
unit weight5pct
Coeff. Var. of unit weight
5276.3
18.3
3.4
144.2
130%
98%
50%
161%
Colombia sample (within firm-HS10-year)
unit weight95pct
unit weight5pct
Coeff. Var. of unit weight
407.3
3.1
1.5
11.4
64%
52%
22%
93%
U.S. sample (within HS10-year)
unit weight95pct
unit weight5pct
Coeff. Var. of unit weight
5776.9
111.7
19.7
770.1
240%
180%
108%
303%
Note: The U.S. sample includes 1,667,243 observations and the Colombia sample includes 12,258,450
observations—See Appendix A for a description of the US sample.
Presumably, the variation in unit weights reflect variation in the quantity and
quality of inputs; whereby higher quality varieties that involve more or higher quality
inputs, are systematically heavier. The following pattern accentuates this proposition.
Fact 2. Unit weight increases systematically with (f.o.b.) unit price.
Fact 2 states that in addition to being sizable, the variation in unit weights are
systematic. To demonstrate this, I can calculate the f.o.b. unit price of each imported
shipment as:
V s,ωht
p s,ωht =
,
Q s,ωht
where V s,ωht and Q s,ωht , respectively, denote the f.o.b. value and quantity pertaining
to shipment s from firm ω in product category h in year t. I establish Fact 2 by
adopting the following estimating equation6
ln wgt s,ωht = α · ln p s,ωht + δωht + s,ωht ,
6
(2)
I would like to emphasize that the estimated wight-price relationship should not be treated as
behavioral/structural. We can only interpret the sign of α as the sign of a conditional correlation that
does not necessarily reflect causality.
10
Table 3: The relationship between unit weight and f.o.b. unit price.
Dependent variable: (log) unit weight
Colombia sample
Regressor
(log) f.o.b. unit price
Observations
FE groups
Within-R2
U.S. sample
firm-product-year FE
country-product-year FE
product-year FE
product-year-district FE
0.90***
(0.008)
0.73***
(0.008)
0.75***
(0.005)
0.75***
(0.005)
12,254,253
2,907,770
0.68
12,254,253
293,288
0.59
1,667,243
20,083
0.62
1,667,243
316,254
0.63
Note: The standard errors are clustered by HS10 product and reported in parentheses (*** denotes
significance at the 1% level). See Appendix A for a description of the US sample.
where δωht denotes provider-product-year fixed effects. The extensive set of fixed
effects control for provider-product-year characteristics that are invariant across
shipments. Elasticity α is thus identified by exploiting across shipment variation
with provider-HS10 product-year cells. The above equation presents the benchmark
estimation. Alternatively, I also estimate α ≡ ∂ ln wgt/∂ ln p conditioning on country
of origin-product-year effects. In this alternative specification, α is identified by
exploiting the across-firm variation in unit price and weight within country-productyear cells. The first two columns in Table 3 report estimation results corresponding to
the Colombia sample. The results point to a strong, significant and tight relationship
between weight and price that is robust across both specifications. Roughly speaking,
a 10% increase in f.o.b. unit price is associated with an 8% increase in unit weight.
Remarkably, unit price alone can explain up to 70% of the variation in unit weight
across shipments within narrowly-defined categories.
Importantly, the strong relationship between weight and price is not driven by
outlier categories. To illustrate this, I run Regression 2 separately for 2836 HS10 categories in the Colombia sample. Table 4 summarizes the product-specific estimation
results, and Figure 1 displays a histogram of the estimated HS10-specific weightprice elasticities. The results indicate that the weight-price relationship is significant
and positive for more than 90% of the products in the sample. The relationship
is relatively stronger for “HS72” (pearls, precious stones, metals, and imitation
jewelry), and relatively weaker for “HS61” and “HS62” (apparel and clothing accessories). To dig deeper, I plot the weight-price relationship for two suspect HS10
11
Table 4: The weight-price relationship by HS10 product.
Colombia sample
Statistic
α≡
∂ ln unit weight
∂ ln p
F-test p-value
Variation
No. of HS10 codes in the sample
Positive relationship (α > 0)
Stat. Sig. at the 95% level
U.S. sample
Median
1st quartile
3rd quartile
Median
1st quartile
3rd quartile
0.86
0.72
0.94
0.75
0.59
0.90
0.000
0.000
0.000
0.000
0.000
0.000
Within firm-product-year
Cross national
2836
2676
2590
4259
4119
3951
Note: This table estimates Equation 2 separately for various HS10 products (that report quantity
in units of count). The standard errors are clustered by HS10 product and reported in parentheses
(*** denotes significance at the 1% level). The estimation performed on the US sample includes
product-year fixed effects (see Appendix A).
categories: “HS8712000000” (bicycles and other cycles) plus “HS9102190000”
(quartz, metal-base wrist watches). For both products I find a strong, positive relationship between unit weight and f.o.b. unit price (Figure 2). Finally, I look closer
at an HS10 category in which imports are sourced from well-know international
providers: “HS8703239000” (compact passenger vehicle with 1500-2500cc engine).
For each provider, I plot the average unit weight of imports against the average f.o.b.
unit price (Figure 3). The results indicate that luxury brands (Audi, Volvo, Jaguar)
are systematically heavier than economy brands (Daewoo, Skoda, Renault). The
positive relationship persists even across varieties sold by the same brand in category
“HS8703239000” (Figure 4).
One might wonder wether the weight-price relationship is a peculiar feature
of the Colombia data. To address this concern, I estimate the same relationship
with the publicly-available U.S. data. As noted earlier, the U.S. sample is more
aggregated with limited within-provider variation. The different structure of the
data requires a slightly different notation. Specifically, as described in Appendix
A, each observation in the U.S. sample correspond to total annual imports from a
given country, through a specific port-of-entry, in an HS10 product category. I can
thus estimate Equation 2 by exploiting the cross-national variation within either (i)
12
Figure 1: The weight-price relationship across HS10 product categories.
Colombia Sample (within−firm variation)
400
Frequency
300
200
100
0
0
.5
1
1.5
α (elasticity of unit weight w.r.t. unit price)
2
.;
U.S. Sample (cross−national variation)
Frequency
300
200
100
0
0
.5
1
α (elasticity of unit weight w.r.t. unit price)
1.5
Note: This figure describes the estimated α = lnlnweight
price across various HS10 categories in the U.S and
Colombia Samples. The estimation is preformed across 4259 and 2836 HS10 categories in the U.S.
and Colombia sample, respectively. For illustration, I drop outlier categories with an estimated α
that falls above or below the 1st and 99th percentile. Also, note that both samples include only HS10
categories that report quantity in units of count.
13
product–year or (ii) port of entry–product–year cells. The estimation results under
both specifications are qualitatively similar to the benchmark estimation conducted
on the Colombian sample. In particular, a 10% increase in f.o.b. unit price is
associated with an 7.5% increase in unit weight (see Table 3).7 To further verify the
weight–price relationship, I estimate it separately for the 4259 HS10 categories in
the US sample. The weight–price relationship is positive and statistically significant
for 3951 of the 4295 product categories (Table 4).
V
A direct implication of fact 2 is that value-to-weight ratios (e
p ≡ WGT
) are a weak
p ×wgt, the strong relation between
proxy for unit prices. Specifically, given that p = e
unit price (p) and unit weight (wgt) entails a weak relationship between value-toweight and unit price. For example, within a firm-product-year cell, variations in unit
price are passed onto value-to-weight ratios with an elasticity of only 0.1, accounting
for only 3% of the total variation in value-to-weight ratios:8
ln e
p s,ωht = 0.11 · ln p s,ωht + δωht + s,ωht , within-R2 = 0.03
(0.002)
In comparison, note that variations in unit price are passed on to unit weight with an
e
p
elasticity of ∂∂ ln
= 1 − ∂∂lnlnwgt
= 0.89, accounting for 66% of of the total variation in
ln p
p
unit weights—see Table 3. If anything, these findings suggest that unit weight is a
better proxy for f.o.b. unit price. Nevertheless, dating back to Moneta (1959), the
value-to-weight ratio has been used extensively as a proxy for unit price or quality
in the literature.
Fact 3. Heavier items are exported relatively more to distant markets.
7
The weight-price relationship is no confined to goods reporting quantity in units of count.
Estimating the relation across all goods in the U.S. import data (except only those that report quantity
in units of kilograms) yields:
ln wgt jiht = 0.68 ln p jiht + δ jt + jiht , R2 = 0.68
(0.005)
where j denotes the exporting country; i denotes the US importing district; h denotes the HS10
product category; and t is the corresponding year. The above regression is conducted on 3,003,725
observations and includes HS10×year fixed effects. The standard error reported in parenthesis is
clustered by HS10 product.
8
The above regression is estimated with firm-product-year fixed effects on 12,254,237 observations
in the Colombia sample.
14
Table 5: The spatial variation in export unit weights.
Dependent variable: (log) unit weight
(log) Distance
Observations
HS10×years
R2
Colombia Exports
US Exports
0.015***
0.278***
(0.001)
(0.005)
3,371,272
17,689
0.80
1,855,621
14,871
0.76
Note: This table estimates the effect of distance on export unit weights. Both regressions include
HS10-year fixed effects, and cluster errors (reported in parentheses) by HS10 product (*** denotes
significance at the 1% level). The Colombia data spans from 2007 to 2011, while the U.S. export data
spans across years 1990 to 1996. Both samples include only entries that report quantity in units of
count.
Fact 3 states that the spatial variation in export unit weights are also systematic.
To demonstrate this, I run the following regression using Colombia and U.S. export
data:9
ln wgt s,iht = θ · ln DISTi + δht + s,iht ,
where wgt s,iht denotes the unit weight of shipment s, exported to market i in HS10
product category h, in year t. DISTi denotes geographical distance (in kilometers) to
market i, the fixed effect δht absorbs the product-year invariant determinants of export
unit weight. The results, displayed in Table 5, suggest that exporters selectively ship
heavier items to faraway markets.10
9
The usage of export rather than import data is motivated by the fact the variation in unit weights
are reflective of quality differences. Hence, when analyzing these variation one should preferably
include export fixed effects. When the above equation is estimated on import data, the effect of
distance will be absorbed by the exporter fixed effect. However, the coefficient on distance can be
identified by analyzing the variation in export unit weights from Colombia across different destination
markets.
10
In the online Appendix D, I argue that this rather surprising effect reflects the fact that heavy,
high-price product varieties exhibit higher markups and profit-margins and are more likely to prnetrate
difficult markets.
15
3.3
Estimating β
Considering Equation 1 in Section 2, and amending the notation to accommodate
transaction-level data, the shipment s-specific unit transport cost faced by firm ω
(from country of origin j) in product category h, in year t, can be written as:
τ s,ωht =
σh w jt d s,ωht
σh − 1 ϕβ
s,ωht
jt
h
Noting that the f.o.b. unit price is p s,ωht = σσh −1
, and manipulating the above
β
ϕ s,ωht
equation leads to the following formulation for the transport cost function:
w
τ s,ωht = T s,ωht p s,ωht β ,
1−β
h
w jt
d s,ωht . Transaction-level customs data report the total
where T s,ωht ≡ σσh −1
transportation cost (freight plus insurance), value, and quantity pertaining to each
shipment s, ωht. One can, therefore, calculate the unit transport cost, τ s,ωht , plus the
f.o.b. unit price, p s,ωht , per shipment, and estimate β using the above equation.
To arrive at an estimating equation, one can decompose the non-price cost
shifter, T s,ωht , into three components: (i) a provider-product-year fixed effect, δωht ,
(ii) controls for shipment scale, κ · ln S s,ωht , which account for scale economies in
international transportation, and (iii) an idiosyncratic error term ε s,ωht that reflects
measurement error plus non-systematic cost-shifters specific to shipment s, ωht.
Decomposing T s,ωht and taking logs, the transport cost function can be presented as
ln τ s,ωht = β · ln p s,ωht + κ · ln S s,ωht + δωht + ε s,ωht
(3)
Parametrically, the above transport cost function is identical to the aggregate cost
function estimated in Hummels and Skiba (2004)—which is labeled as “Equation
10” in their paper. Compared to the prior literature, my goal is to estimate the
above equation with firm-level data while accounting for the variation in import unit
weights.
Before outlining my estimation strategy, I briefly describe the traditional approach to estimating β and its underlying limitation. The traditional approach, which
16
has been adopted by Hummels and Skiba (2004) and Hummels et al. (2009), assumes
that unit weight is uniform within categories. This assumption is imposed in face
of data limitations, and allows the researchers to infer import quantity, Q s,ωht , from
total weight, WGT s,ωht . Put differently, under this assumption, one can estimate β
τ
τ ≡ wgt
as the elasticity of transport cost per kg, e
with respect to value-to-weight,
p
p
τ
e
p = wgt . To demonstrate this, notice that plugging e
τ ≡ wgt
and e
p = wgt
into Equation
β
β−1
τ s,ωht = T s,ωht e
3 implies that e
p s,ωht wgt s,ωht . Taking logs, the transportation cost
function in terms of e
τ and e
p becomes:
lne
τ s,ωht = β · ln e
p s,ωht + κ · ln S s,ωht + δωht + (β − 1) ln wgt s,ωht +ε s,ωht
|
{z
}
omitted variable
The traditional approach estimates the above equation, omitting the term (β − 1) ln wgt s,ωht .
When unit weight is uniform within firm-product-year cells (i.e., wgt s,ωht = wgtωht ),
the omitted term is absorbed by the fixed effect, δωht , and the traditional approach
delivers an unbiased estimate of β. Factually, however, unit weight is non-uniform,
and the omitted term is negatively correlated with value-to-weight, e
p. That being the
case, the traditional approach suffers from a classical case of omitted variable bias
that attenuates β.
To elaborate further on the role of product weight, one could decompose the
transport cost elasticity into two distinct components. In particular, given that
τ =e
τ × wgt, the transport cost elasticity can be expressed as
β=
∂ ln τ ∂ lne
τ ∂ ln e
p ∂ ln wgt
=
·
+
∂ ln p ∂ ln e
p ∂ ln p
∂ ln p
The term e
β ≡ ∂∂ lnlneeτp is the elasticity identified by the traditional approach (e.g.,
Hummels and Skiba (2004); Hummels et al. (2009)). Given that, by construction,
∂ ln e
p
= 1 − α and ∂∂lnlnwgt
= α, the above expression can be written as
∂ ln p
p
β=e
β (1 − α) + α
(4)
The transport cost elasticity, β, has two distinct components:
i. The weight-driven component α: this component accounts for the fact that
17
high-priced items are heavier, and thus costlier to transport.
ii. The value-driven component β̃(1 − α): this component reflects the rate at
which insurance, packaging and handling requirements increase with shipment
value.
Given the above decomposition, if unit weight is uniform within firm-product-year
categories (i.e., α = 0), then e
β, the elasticity estimated under the traditional approach,
equals the actual transport cost elasticity, β. However, in practice given that α ≈ 0.9,
the traditional elasticity estimate is attenuated: e
β = β−α
< β.
1−α
In what follows, I conduct an assumption-free estimation of the transport cost
function characterized by Equation 3. The benchmark estimation conducted on
the Colombia Sample, uses within firm-product-year variation to identify β. For
comparison, I also estimate β with US import data, which has been used extensively
by the previous literature for this exact purpose. Given the highly aggregated
structure of the US data, the estimation relies on cross-national variation within
HS10 product categories, the details of which are provided in Appendix A.
To control for shipment scale, I use the number of packages in shipment s, ωht.
Intuitively, shipping out ten boxes at once is more cost-efficient than sending out
ten single-box shipments throughout the year. When analyzing the U.S. sample, I
subscribe to the estimation strategy proposed by Hummels and Skiba (2004), which
is reflective of the limited information available in the data set. In particular, I control
for scale with the total weight of all shipments aggregated into a given data entry,
and employ bilateral distance (DIST s ) and the GDP per capita of the origin country
as additional controls—see Appendix A for a thorough description.
3.3.1
Identification
The within firm-product-year variation in transport costs (across shipments) are
driven by the variation in unit prices and shipment scales, plus an idiosyncratic
cost shifter denoted by ε s,ωht . The identification challenge is that unit price and
shipment scale are endogenous to idiosyncratic movements in transport costs. In
fact, the effect of transport costs on import price levels constitute the celebrated
“Washington apples” effect. To handle reverse causality, one needs to construct
18
instruments that are correlated with f.o.b. unit prices but unrelated to idiosyncratic
movements in transport costs. To guide the choice of instruments, I identify two
plausibly exogenous sources that trigger variation in price and shipment scale within
firm-product-year cells: (i) across shipment variation in trade taxes, and (ii) across
shipment variation the characteristics of the Colombian importing partner.
The first instrument exploits the exogenous variation in (ad valorem) import tax
rates, which include import tariffs and the Colombian value added tax. The validity
of this instrument is based on the well-known fact that import taxes lower import
price levels. The price-reducing (or terms-of-trade improving) effects of import taxes
have deep roots in the trade policy literature, and are at the core of classical optimum
tariff arguments (Graaff (1949); Johnson (1953)). The within firm-product-year
variation in import taxes stem from the fact that (i) a different value added tax rate
may apply to different shipments pertaining to the same firm-product-year category,
and (ii) import tariff rates vary over time—these variations are generally triggered
by trade agreements or WTO disputes and settlements (see Eaton, Eslava, Kugler,
and Tybout (2010)). Altogether, the within-category variation in import taxes are
empirically significant: the standard deviation of the import tax rate applied to
shipments from the same firm in the same HS10 product code is 1.7%.
The second instrument is motivated by the observation that Colombian importing firms source their imports from various exporters in a given year—each
entry/shipment in the data identifies a unique provider, ω, and importing firm, m.
Presumably, for any Colombian importing firm, the quality of imported inputs from
different providers are systematically correlated. In other words, if importing firm
m imports high quality (high price) inputs from provider ω, it most likely imports
high quality inputs from other providers. That being the case, if shipment s, ωht is
imported by Colombian firm m, the unit price of that shipment can be instrumented
with the average unit price of firm m’s imports from other providers; namely, p̄ms,ωht .
Altogether, for 9,830,046 observations in the Colombia sample, I can construct
the needed instruments for the following first-stage regression
ln p s,ωht = 0.365 · ln p̄ms,ωht − 0.015 · ln t s,ωht + ψωht + ε s,ωht ,
(0.0008)
(0.0006)
19
where ψωht denotes firm-product-year fixed effects; robust standard errors are reported in parenthesis; and the R2 is 0.78. Importantly, the first-stage regression
delivers the expected coefficient signs, and displays an F-statistic on the excluded
instruments with a p-value well below 1%. The equation expressed above, describes
the first stage of the benchmark 2SLS estimation. Later, to conduct sensitivity
analysis, I construct additional instruments that exploit auxiliary variations in the
data.
3.4
Estimation Results
The benchmark estimation results are displayed in Table 6. The top panel reports
estimates corresponding to the full Colombia sample. The middle panel corresponds
to a trimmed sample of Colombian imports, which excludes transactions reporting an
import value below 1000 US dollars—this sample is presumably less contaminated
with measurement errors. Finally, the bottom panel reports estimates conducted with
the US import data. Expectedly, the two-stage least square (2SLS) estimator delivers
lower estimates of β than the ordinary least square (OLS) estimator. Altogether, the
estimates point to a transport cost elasticity of β ≈ 0.8 − 0.9, which corresponds
to quasi-iceberg transport costs. To be more specific, across all specifications and
samples, a 10% increase in f.o.b. unit price increases the unit transport cost by
around 8 to 9%.
While these results resemble the widely-used iceberg specification, they contrast
traditional estimates. As noted earlier, traditional estimates of the transport cost
elasticity are attenuated due to an omitted variable bias.11 To illustrate the strength
of this bias, I estimate the transport cost function under the traditional presumption
11
The results reported in Table 7 suggest that across all samples and specifications, scale effects
are significant. Specifically, the within-firm estimation (which is the most reliable) indicates that A
10% increase in shipment scale reduces the shipping rate by 1.3%. Further, the estimation conducted
on the U.S. sample (which exploits across country variations) confirms two well-established results:
(i) Distance matters. A 10% increase in geographical distance to the US increases the transport
cost by more than 2.4%, and (ii) High-income countries face systematically lower transport costs.
Specifically, high-income countries are significantly more efficient in transportation, and face lower
costs despite paying higher wages.
20
that unit weight is uniform, which amounts to estimating the following Equation:
lne
τ s,ωht = e
β · ln e
p s,ωht + κ · ln S s,ωht + δωht + ε s,ωht ,
(5)
where e
τ s,ωht and e
p s,ωht denote transport cost per kg and the value-to-weight ratio,
respectively. The estimated transport cost elasticities (displayed in Table 7) are
attenuated, and resemble traditional estimates in the literature. Relatedly, note that
under the traditional approach the OLS estimated elasticity is slightly higher than
the elasticity estimated under the 2SLS specification. This result is not surprising
given the weak relationship between unit prices and value-to-weight ratios. More
specifically, even though transport costs increase import price levels (through the
Alchian-Allen effects) they may lower the value-to-weight ratio. Hence, the error
term ε s,ωht may be negatively correlated with value-to-weight, e
p s,ωht .
To dig deeper, the difference between the traditional estimation and my benchmark estimation is that the former overlooks the role of product weight in transportation. In fact, one could decompose the transport cost elasticity to isolate the role
of product weight. Following Equation 4, the transport cost elasticity β ≡ dd lnln τp is
composed of a weight-driven component, α ≈ 0.8, and a value-driven component,
e
β (1 − α). The standard approach (reported in Table 7) estimates e
β ≈ 0.5. Using
Equation 4, and knowing that α ≈ 0.8, we can thus decompose the transport cost
elasticity as12
d ln τ
≈ |{z}
0.8 + 0.5(1 − 0.8) = 0.9
β≡
| {z }
d ln p
weight-driven
value-driven
The above decomposition indicates that more than 80% of the relationship between
unit transport cost and unit price is driven by the within-category variation in unit
weights. Overlooking these variations therefore attenuate the transport cost elasticity;
to the extent that international transport costs appear quasi-additive.
Industry-Level Estimates. I also estimate an industry-level transport cost elasticity for 33 industries, based on the GTAP industry classification. The industry-level
Alternatively, we can use the estimated β and e
β to cross-check the estimated weight-price
elasticity, α, from the previous section. Doing so, the estimated β ≈ 0.9 and e
β = 0.5 imply an α ≈ 0.8,
which is consistent with direct estimates in Section 3.2.
12
21
Table 6: Benchmark Estimation
Dependent Variable: (log) Unit Transport Cost
Variables (in logs)
Unit Price
Shipment Scale
Distance
GDP per capita
R2
Observations
Colombia full sample (firm-product-year FE)
OLS
0.92
(0.0003)
-0.13
(0.0002)
...
...
0.64
9,830,046
2SLS
0.81
(0.0017)
-0.14
(0.0002)
...
...
...
9,830,046
Colombia trimmed sample (firm-product-year FE)
OLS
0.93
(0.0003)
-0.08
(0.0002)
...
...
0.64
4,725,704
2SLS
0.86
(0.0023)
-0.05
(0.0003)
...
...
...
4,725,704
U.S. sample (product-year FE)
OLS
0.91
(0.000)
-0.04
(0.000)
0.28
(0.002)
-0.08
(0.001)
0.72
1,607,858
2SLS
0.88
(0.002)
-0.02
(0.003)
0.23
(0.003)
-0.06
(0.001)
...
1,607,858
Note: The estimating equation is Equation 3. All 2SLS estimates pass the over-identifying restrictions
test and have low first-stage F-statistic p-values. All regressions cluster errors (reported in parentheses)
by HS10 product. All reported coefficient are significant at the 1% level.
22
Table 7: Traditional Estimation: treating unit weight as uniform
Dependent Variable: (log) Transport Charge/Weight
Variables (in logs)
Value/Weight
Shipment Scale
Distance
GDP per capita
R2
Observations
Colombia full sample (firm-product-year FE)
OLS
0.57
(0.000)
-0.17
(0.000)
...
...
0.31
9,830,046
2SLS
0.59
(0.006)
-0.17
(0.000)
...
...
...
9,830,046
OLS
0.61
(0.001)
-0.11
(0.000)
...
...
0.31
4,725,704
2SLS
0.69
(0.004)
-0.10
(0.000)
...
...
...
4,725,704
Colombia trimmed sample (firm-product-year FE)
U.S. sample (product-year FE)
OLS
0.55
(0.001)
-0.15
(0.000)
0.20
(0.002)
-0.03
(0.001)
0.44
1,607,858
2SLS
0.52
(0.006)
-0.15
(0.003)
0.23
(0.004)
-0.03
(0.001)
....
1,607,858
Note: The estimating equation is Equation 5—assuming that unit weight is uniform, unit price and
Transport charge
transport cost are calculated as Value
. All 2SLS estimates pass the over-identifying
WGT and
WGT
restrictions test and have low first-stage F-statistic p-values. All regressions cluster errors (reported in
parentheses) by HS10 product. All reported coefficient are significant at the 1% level.
23
estimation involves estimating Equation 3 independently for each of the 33 industries
in the Colombia sample, with results reported in Table 8. Overall, the estimated
transport cost elasticities display a considerable amount of cross-industry variation.
Most industries feature an elasticity greater than one-half (i.e., β > 0.5), with the
largest industries (e.g., Motor vehicles, Machinery, and Electronics) featuring a
transport cost elasticity close to unity (i.e., β ≈ 1). Later, in Section 4, I plug
these industry-wide elasticity estimates into a standard multi-industry trade model to
analyze the general equilibrium implications of these estimates.
3.5
Sensitivity Analysis
This section investigates the robustness of the estimation results to (i) the parameterization of the transport cost function, (ii) the choice of instruments, and (iii) the
inclusion of omitted observations.
(i) Parametric Specification. Given that ln p = ln e
p + ln wgt, the benchmark es∂ ln τ
∂ ln τ
timation implicitly restricts that ∂ ln ep = ∂ ln wgt . As noted earlier, ∂∂ lnln eτp captures the
τ
effect of insurance, handling and packaging requirements, whereas ∂∂lnlnwgt
reflects the
pure effect of physical weight on transportation. Considering this distinction, one
can allow for theses two elasticities to diverge. This amounts to including ln e
p and
ln wgt as separate explanatory variables in the transport cost function, which delivers
the following estimating equation:
ln τ s, jht = 0.96 ln e
p s,ωht + 0.54 ln wgt s,ωht − 0.17 ln S s,ωht + δωht + ε s, jht
(.0004)
(.0002)
(.0002)
In view of the above estimation result, and using the estimated values of ∂∂ lnln eτp = 0.54
e
p
τ
and ∂∂lnlnwgt
= 0.96 one can calculate β. In particular, noting that ∂∂ ln
= 1 − α and
ln p
∂ ln wgt
= α, it follows that
∂ ln p
β≡
∂ ln τ ∂ ln τ
∂ ln τ
=
· (1 − α) +
· α ≈ (0.54) (0.1) + (.96) (0.9) = 0.92
∂ ln p ∂ ln e
p
∂ ln wgt
The above approach, therefore, estimates an elasticity that is nearly identical to
the benchmark estimate. Alternatively, instead of the log-linear formulation, the
24
Table 8: Industry-wide estimates of the transport cost elasticity.
GTAP product description
PCR - Processed rice
WHT - Wheat
GRO - Cereal grains n.e.c.
V_F - Vegetables, fruit, nuts
OSD - Oil seeds
SGR - Sugar
OCR - Crops n.e.c.
CTL - Bovine cattle, sheep and goats, horses
OAP - Animal products n.e.c.
MIL - Dairy products
FRS - Forestry
CMT - Bovine meat prods
OMT - Meat products n.e.c.
VOL - Vegetable oils and fats
OFD - Food products n.e.c.
B_T - Beverages and tobacco products
TEX - Textiles
WAP - Wearing apparel
LEA - Leather products
LUM - Wood products
PPP - Paper products, publishing
CRP - Chemical, rubber, plastic products
OMN - Minerals n.e.c.
NMM - Mineral products n.e.c.
I_S - Ferrous metals
NFM - Metals n.e.c.
FMP - Metal products
MVH - Motor vehicles and parts
OTN - Transport equipment n.e.c.
ELE - Electronic equipment
OME - Machinery and equipment n.e.c.
OMF - Manufactures n.e.c.
P_C - Petroleum, coal products
GAS - Gas
COA - Coal
FSH - Fishing
25
β
std. err.
No. of
obs.
.73
.20
.27
.17
.63
.58
.39
.84
.61
.74
.69
.45
.40
.57
.58
.71
.76
.82
.81
.93
.64
.75
.67
.86
.60
.44
.80
.97
.83
.86
.93
.88
.97
1.07
.69
.68
.037
.019
.011
.005
.017
.022
.006
.025
.021
.014
.024
.019
.009
.009
.003
.005
.002
.001
.002
.002
.002
.001
.006
.002
.002
.005
.001
.001
.002
.001
.000
.001
.002
.039
.070
.022
2,720
4,038
21,045
61,775
5,295
3,958
2,6811
1,425
3,192
7,487
2,600
6,840
23,630
38,406
207,808
5,3537
570,136
781,618
376,842
160,985
383,554
2,842,428
31,701
277,840
269,679
83,745
1,415,261
1,036,576
92,086
579,104
4,112,369
406,323
67,169
25
222
2,533
transport cost function may be specified as τ = τ̃p+t, where τ̃ and t denote the iceberg
and additive components of the transport cost. In Appendix C, I use Monte-Carlo
simulation to show that even when the true data generating process is τ = τ̃p + t, the
log-linear specification identifies the relative importance of the iceberg component,
τ̃, to the additive component, t. In particular, a β = 0.9 indicates that 98% of the cost
corresponds to the iceberg component τ̃p, with only 2% being driven by the specific
component, t.
(ii) Choice of Instruments. To verify the robustness of the benchmark results to
the choice of instruments, I construct two alternative instruments for f.o.b. unit price.
The first instrument builds on the observation that a considerable fraction of imports
are conducted by Colombian firms that concurrently engage in exports. Furthermore,
there is evidence that Colombian firms that import high-quality inputs, produce
and export higher quality outputs (Kugler and Verhoogen (2012)). Guided by this
regularity, I first match the Colombian import and export data sets by matching
importer and exporter ids. This leaves me with a subsample of import transactions
conducted by Colombian firms that engage in both importing and exporting in a
product category h. In this subsample, for every shipment s, ωht, I can calculate the
average f.o.b. unit price of exports ( p̄ xs,ωht ) performed by the Colombian firm that
imports shipment s, ωht. Then, I instrument for the f.o.b. unit price of shipment
s, ωht (i.e., p s, jht ) with the lagged export price of the Colombian importing firm
x
( p̄ωh,t−1
). This approach basically exploits across shipment variation in the quality
of the Colombian importing partner to estimate the transport cost elasticity. The
estimation results (presented in the Table 12) closely resemble the benchmark results,
and point to quasi-iceberg transport costs.
Additionally, I re-estimate the transport cost function with the “lagged price”
instrument suggested by Hummels and Skiba (2004). Specifically, the unit price of
shipment s, ωht is instrumented with the unit price of the prior shipment pertaining
to the same provider-product-year cell. Exploiting the across shipment variation
in lagged import price levels, I can then estimate the transport cost elasticity.This
approach inevitably excludes the first observation within each firm-product-year
cell, since there is no lagged price for this observation. The estimation results,
26
nevertheless, closely resemble the benchmark results (see Table 12).
(iii) Extended Sample. Complying with existing literature, the benchmark analysis
focuses on observations that report quantity in similar units (namely, in units of
“count,” which is by far the most common unit of measurement). This standard
approach excludes an important set of transactions that report quantity in kilograms
(e.g., transactions relating to commodities such as coal, metals, wheat, etc.). As noted
earlier, the import unit weight of these transaction equals “one” by definition. As a
result, the variations in unit weight levels are irrelevant to this smaller class of goods.
It is nonetheless interesting to estimate the transport cost function across all import
transactions, including those that report quantity in kilograms. The estimation result
corresponding to the extended sample are reported in Table 12. As expected, the
estimated transport cost elasticity (β) is marginally lower once we include products
that feature no variation in unit weight levels. Nevertheless, the estimated elasticity
still favors the iceberg specification.
4
General Equilibrium Implications
The iceberg transport cost assumption is at the core of modern quantitative trade
models. There is, however, a growing skepticism that the iceberg assumption hinders
the credibility of counterfactual predictions in canonical trade frameworks. The
previous section estimated that the iceberg formulation provides a close, but not
perfect, representation of factual transport costs. One may still wonder how the
predicted gains from trade are affected by adopting of the exact iceberg formulation
instead of the estimated transport cost elasticities. To address this question, I calibrate
a standard 33 industry trade model to bilateral trade values across 7 regions. Based
on the calibrated model and using the estimated transport cost elasticities, I determine
the sensitivity of counterfactual predictions to the iceberg assumption.
Data. My application focuses on 7 regions (namely, Brazil, China, the European
Union, India, Japan, the United States, and the Rest of the World) and 33 industries
in the year 2007. The regions are chosen to represent countries form different
27
income levels. The industries span the agricultural and manufacturing sectors of
the economy. My main data source is the Global Trade Analysis Project database
(GTAP 8) from which I take industry-level trade, production, and expenditure data.
Ossa (2014) eliminates trade imbalances for this data set, and estimates the trade
elasticity for each of the 33 industries—Hertel, Hummels, Ivanic, and Keeney (2007)
also provide trade elasticity estimates for each of the industries in the sample.
4.1
Model.
I adopt a basic competitive multi-industry trade model, where each region can be
treated as one representative firm. In this basic setting, preferences in region i can be
described as
 N
γ · σh
X σσh ·  i,h σh −1
h−1 

Wi = Πh  q ji,h
,
j=1
where q ji,h denotes the quantity of market i’s consumption of region j varieties
in product category or industry h. Labor is the only factor of production, and
(following Section 2) the labor cost of producing q units of industry h varieties in
d
region j and delivering them to market i is given by c ji,h (q) = ϕ1j,h + βjih , where ϕ j,h
ϕ j,h
denotes the efficiency of region j in industry h. Considering the aforementioned
cost function, industry h varieties exported from country j to market i display the
following competitive price:
p ji,h =
wj h
1 + d ji ϕ1−β
j,h
ϕ j,h
n
o
Given the vector of prices p ji,h , and total income in region i, Yi = wi Li , total
j,h
1−σh
industry-wide expenditure on region j varieties will be X ji,h = p ji,h /Pi,h
γi,h Yi ,
where Pi,h denotes the industry-wide CES price index. Substituting for prices in the
CES demand function, delivers the following gravity equation describing total sales
of region j to market i in industry h:
28
X ji,h
h wj i
1−βh 1−σh
1
+
d
ϕ
ji j,h
ϕ j,h
γi,h wi Li
=P h i
1−βh 1−σh
wk
k ϕk,h 1 + dki ϕk,h
(6)
n o
Considering the above gravity equation, equilibrium is a vector of wages, w j , that
j
P P
satisfy the balanced of payments condition: w j L j = h i X ji .
Calibration Strategy. The parameters necessary to conduct counterfactual analn o
yses are (i) regional industry-wide efficiency levels, ϕ j,h , (ii) trade elasticities,
j,h
{σh − 1}h , (iii) population size, {Li }i , (iv) industry-wide expenditure shares, γi,h i,h ,
n o
(v) transport cost elasticities, {βh }h , and (vi) bilateral transport cost parameters d ji
j,i
where dii = 0. I use the estimated transport cost elasticities from Section 3.3, and the
take the trade elasticities from Ossa (2014). Given these externally chosen structural
n o
n o
parameters and data on population size, I choose d ji and ϕ j,h to match the
j,i
j,h
8 × 8 × 33 matrix of inter-regional expenditure shares and regional wage levels—this
step employs the method of mathematical programming with equilibrium constraints
(MPEC) developed by Su and Judd (2012).
In addition to the benchmark model, I calibrate two alternative models that
feature two polar transport specifications: (i) a model with additive transport costs in
all industries (i.e., βh = 0 for all h), and (ii) a model with iceberg transport costs in
all industries (i.e., βh = 1 for all h). The iceberg case, where βh = 1, represents a
standard and widely-used class of quantitative trade models, and is governed by a
familiar log-linear gravity equation:
h τ ji w j i1−σh
ϕ j,h
βh = 1 =⇒ X ji,h = P h
γi,h wi Li .
i
τki wk 1−σh
k
ϕk,h
Comparing the benchmark model to the standard iceberg model allows me to assess
the harm, in terms of credibility, inflicted by the iceberg assumption.
29
4.2
Counterfactual Welfare Predictions
Using the calibrated model, I conduct two counterfactual analyses. The first analysis
computes the realized gains from trade—i.e., the gains associated with moving from
the counterfactual autarky equilibrium to the factual equilibrium. The computed
gains are reported in Table 9 under three different transport cost specifications
(namely, (i) factual or estimated βh ’s, (ii) iceberg transport costs, βh = 1, and
(iii) additive transport costs, βh = 0). Perhaps not surprisingly the realized gains
from trade are not sensitive to the transport cost specification. This outcome is
reminiscent of the celebrated Arkolakis et al. (2012) result. To gain intuition, note
that irrespective of the value assigned to βh , the following relationship follows from
setting dii = 0 in Equation 6:
where Pi,h
!1−σh
Xii,h
wi
1−σh
λii,h ≡
= ξi,h
= ξi Wi,h
,
γh wi Li
Pi,h
P h 1
i
1−βh 1−σh 1−σh
wk
=
denotes the price index of industry h
k ϕk,h 1 + dki ϕk,h
in market i, and ξi,h ≡ ϕσi,hh −1 is invariant to aggregate trade shocks. Given that total
γ
A
welfare in country i is given by Wi = Πh Wi,hi,h , and noting that λii,h
= 1 (where A
denotes autarky), the realized gains from trade can be calculated as
γ
i,h
Wi
1−σh
=
Π
λ
h
ii,h ,
WiA
where, for any region i, λii,h equals the factual domestic expenditure share and γi,h
equals total factual expenditure share on industry h. Clearly, the above expression
delivers the same predicted gains irrespective of the value assigned to βh . Hence, the
realized gains from trade are identical across all three models, despite the different
underlying transport cost elasticities.
The second counterfactual analysis, however, highlights the critical role played
by the transport cost elasticity. It calculates the prospective gains from economic
W FT
integration—i.e., Wi i where FT denotes free trade. The prospective gains are
calculated by counterfactually setting d ji to zero for all regional pairs. The results
reported in Table 9, highlight the critical role of the transport cost elasticity. The
30
Table 9: The predicted gains from trade under different transport cost elasticity values.
Factual β
Country Prospective Gains
Iceberg, β = 1
Additive, β = 0
Realized Gains
Prospective Gains
Realized Gains
Prospective Gains
Realized Gains
Brazil
218.98%
9.58%
157.62%
9.58%
561.42%
9.58%
China
107.44%
12.13%
105.18%
12.13%
325.14%
12.13%
99.64%
12.62%
90.00%
12.62%
247.24%
12.62%
India
187.02%
9.21%
170.01%
9.21%
620.09%
9.21%
Japan
129.43%
12.88%
117.54%
12.88%
266.32%
12.88%
ROW
81.37%
23.93%
85.21%
23.93%
365.94%
23.93%
102.97%
14.97%
101.22%
14.97%
277.01%
14.97%
EU
US
prospective gains from free trade are systematically larger under additive transport
costs. The intuition is that additive transport costs are more distortionary, and
eliminating them is therefore more beneficial.
Importantly, the prospective gains from trade attained under the estimated transport cost elasticities starkly resemble those attained under the standard iceberg
assumption. That is to say, neither the estimated deviations from the exact iceberg
specification nor the cross-industry variation in the transport cost elasticities have a
pivotal impact on the gains from trade. For example, the prospective gains for the
US are 102.97% under estimated transport cost elasticities versus 101.22% under the
iceberg assumption. Considering the trade-off between accuracy and tractability, the
above results suggest that the iceberg assumption maybe a practical and relatively
innocuous choice.
5
Conclusion
This paper analyzes the within-product variation in import unit weights, uncovering
several new stylized facts. I argue that the most natural way to account for these
systematic variations is to model transport costs as iceberg melt costs. To the best of
my knowledge, this is the first empirical argument in support of the classic iceberg
trade cost assumption posited by Samuelson (1954). Altogether, my analysis pro-
31
vides a glimpse into the role of product weight in international trade—an unexplored
avenue that warrants further research.
My finding that import weight is not an appropriate proxy for import quantity has
sharp implications for the empirical trade literature. In a tradition that dates back to
Moneta (1959), many studies on quality specialization use value-to-weight ratios as
a proxy for price or quality levels. Against the backdrop of this tradition, this paper
highlights the weak relationship between the value-to-weight ratio and unit price.
This result opens up an important avenue for future research. Namely, analyzing the
robustness of existing findings to the distinction between value-to-weight and price
or quality levels.
At broader level, my estimation of industry-level transport cost elasticities has
basic implications for economic development and trade policy. In view of the
Alchian and Allen (1964) conjecture, high-quality exports are less impeded by
distance in industries featuring lower transport cost elasticities. As a result, highquality suppliers have a comparative advantage in low-transport cost elasticity
industries. This observation has the potential to explain existing patterns of vertical
specialization and North-South trade. Furthermore, it has immediate implications
for industrial policies targeted at quality-upgrading.
The implications of my analysis for trade policy are more nuanced. Beshkar and
Lashkaripour (2017) demonstrate that non-linearities in production and delivery costs
are an important source of variation in optimal sectoral tariffs. The present paper
highlights and estimates a rather unexplored aspect of these non-linearities—namely,
the aspect relating to transport costs. The elasticity estimates presented in this paper
therefore, can shed new light on the sectoral structure of optimal trade policy.
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A
The US Sample: Data and Estimation
Data Description. I show that all the documented patterns hold equally in the
publicly-available U.S. import data compiled by Schott (2008). The U.S. import
data reports the f.o.b. value, freight and insurance charge (both in U.S. dollars), the
35
quantity of goods, and the gross weight of shipments aggregated at the HS10 level,
across all firms exporting from a given country to a given district in the U.S. in a given
year (1989-1994).13 The U.S. sample adopts a finer classification of units than the
Colombia sample. For example, while pairs (“PR”) or dozen (“DOZ”) correspond to
item-count, they are treated as distinct units of measurement. Combined, the entries
that report a derivative of item-count, constitute more than 45% of U.S. imports in the
1989-1994 period. As is common in the literature, I restrict attention throughout this
paper to products that report quantity directly in units of count (“N” and “NO”)—the
Sample includes 6,594,414 entries with 1,980,257 entries reporting quantity in terms
of of “N” or “NO”.14 The U.S. sample, moreover, does not directly report shipment
weight for all entries. Instead, each entry reports the weight of shipments transported
by air (under “air_val_yr”) and by vessel (under “ves_val_yr”).15 For 1,667,243
observations, (i) a non-zero quantity is reported in units of count (“N” and “NO”),
(ii) imports are exclusively shipped by air and vessel (i.e., “gen_val_yr = ves_val_yr
+ air_val_yr”), and (iii) the total weight reported, is non-zero. I, therefore, restrict
my analysis of U.S. imports to these 1,667,243 observations, which provide full
information on total weight, value, freight charge, and quantity. Note that while the
final samples do not exclude potential outliers, the estimation results presented in
the following sections are fairly robust to such exclusions.16
Estimating Equations. In the US sample observation s, ωht corresponds to aggregate export from country of origin s, to US district ω, in product category h, in year
13
Note that while the Colombia data reports insurance and freight charges separately, the U.S.
data lumps up freight, insurance, and other charges (excluding U.S. import duties) into one reported
variable.
14
This restriction is not critical. In fact, the results presented in this paper hold for all goods except
those that report quantity in kilograms or its derivatives. Excluding observations that report quantity
in kilograms, such as imports of wheat, apples and coal, is critical. For such goods unit weight is by
definition equal to “one” and uniform. Importantly, if not excluded, these observations might appear
as outliers to the results presented in this paper. I will come back to this point again later.
15
Note that the U.S. data reports only the gross weight (of airborne and seaborne imports) associated
with each observation. The Colombia data, by contrast, reports both the net weight and the gross
weight.
16
The estimation results presented in Sections 3.2-3.3 change by less than 2 decimal points when I
drop (i) entries reporting a quantity less than 2, (ii) entries reporting a value below $2500, and (iii)
entries with a unit price below or above the 95 and 5 percentiles of their HS10-year category.
36
t. The weight-price relationship is estimated using the following equation
ln wgt s,ωht = α · ln p s,ωht + δωht + s,ωht ,
The above equation includes district-product-year fixed effects, and exploits variation
across exporting countries within a district-product-year cell.
The transport cost elasticity is estimated using the following log-linear transport
cost function:
ln τ s,ωht = β · ln p s,ωht + κ · ln S s,ωht + δht + ε s,ωht
Parametrically, the above equation is identical to estimating equation –Equation
“10”– in Hummels and Skiba (2004). Furthermore, in line with the aforementioned
study, the estimation includes product-year fixed effects, controls for scale effects
with the total weight of all shipments aggregated into entry s, ωht, and also includes
bilateral distance (DIST s ) and the GDP per capita of the origin country as additional
controls The only distinction is that Hummels and Skiba (2004) assume a uniform
unit weight, wgtht , within product-year cells. Based on this assumption, they compute
the unit price and transport cost by inferring import quantity from weight: Q s,ωht =
WGT s,ωht /wgtht . Knowing that unit weight is non-uniform within cell ht, I instead
use actual data on import quantity to calculate the unit price and unit transport cost
per observation. Following Hummels and Skiba (2004), I instrument for unit price
and total weight with tariff rates plus lagged unit price and total weight levels.
B
The Weight-Price Relation in Export Data
Section 3.2 established a systematic relationship between the unit weight and unit
price of imports. Here, I demonstrate that this relationship extends to export data.
To this end, I run the following regression on the transaction-level Colombian export
data:
ln wgt s, jiht = α · ln p s, jiht + δ jht + s, jiht
37
Table 10: The weight-price relationship in export data.
Dependent variable: (log) unit weight
Colombia sample
Regressor
(log) f.o.b. unit price
Observations
FE groups
Within-R2
U.S. sample
firm-HS10-year FE
HS10-year-destination FE
HS10-year FE
0.72***
(0.013)
0.73***
(0.008)
0.88***
(0.002)
3,053,709
240,815
0.52
3,053,709
131,987
0.59
1,858,254
14,871
0.56
where observation s, jht corresponds to shipment s, exported by Colombian firm j, to
market i, in HS10 product h–year t. The fixed effect δ jht accounts for the determinants
of unit weight that are invariant across shipments from firm j in product category
h, year t. The above specification identifies α based on across shipment variation
within firm-product-year cells. Alternatively, I run the above regression conditioning
on product-destination-year fixed effects. Both specifications imply similar estimates
for α ( first two columns in Table 10), and closely resemble the import-side estimates.
I also identify the weight-price relationship using product-level US export data. In
particular, I identify α by exploiting across market variation in export unit prices and
weights within HS10 product-year cells. Again, the estimated elasticity (reported in
the last column of Table 10) closely resembles the import-side estimates.
C
Alternative Transport Cost Formulation
The benchmark estimation adopts a micro-founded log-linear transport cost function,
similar to one specified in Hummels and Skiba (2004).17 The previous appendix
illustrated that this specification has simple micro-foundation. Recently, Irarrazabal
et al. (2014) have estimated an alternative specification which would decompose
the transport cost into an additive component, t, and an iceberg component, τ̃:
17
Hummels and Skiba (2004) estimate a log-linear transport cost function described in “Equation
10” of their paper. Additionally, they assume that trade costs have an ad-valorem component (in
addition to the transportation cost), which is exclusively comprised of tariffs.
38
Table 11: The mapping between alternative cost formulations: Monte Carlo simulation
τ̃p
% share of the iceberg component ( τ̃p+t
)
Estimated transport cost elasticity β
99.5%
97%
79%
36%
0.95
0.89
0.71
0.47
Note: this table displays the link between β in the Hummels and Skiba (2004) specification and the
“share of the iceberg component” in the specification adopted by Irarrazabal et al. (2014).
τ s,ωht = t + τ̃p jht . The following argues that the specification adopted here and in
Hummels and Skiba (2004) maps easily into the specification adopted by Irarrazabal
et al. (2014). First, note that for any price p, there is a unique β that satisfies:
t + τ̃p = pβ
Further, β is increasing in τ̃t . In particular, β → 0 when the iceberg component
is negligible ( τ̃t → 0), whereas when β → 1 the additive component is negligible
( τ̃t → 0). Estimating a log-linear transport cost function is, therefore, an alternative
way of estimating the ratio of the iceberg component to the additive component. To
illustrate this numerically, suppose that the data generating process is τ s,ωht = t+ τ̃p jht .
I fix τ̃ = 0.5 and simulate a vector of transport costs τ̂ s,ωht for various values of t,
using the factual vector of US import prices in 1994. I then estimate the following
log-linear transport cost function:
τ̂ s,ωht = β ln p s,ωht + δht + ε s,ωht
The results are displayed in Table 11, indicating that the estimated β reflects the
τ̃p
(median) share of the iceberg component, τ̃p+t
. Further, these results roughly suggest
that the estimated β̂ ≈ 0.9 in Section 3.3 implies an additive transport cost component
that is smaller than 3%.
39
Additional Tables and Graphs
Table 12: Robustness check—dependent variable: (log) unit transport cost.
Alternative Instrument
Variables (in logs)
Unit Price
Shipment Scale
R2
Observations
Export price of Colombian importing firm
1.09
(0.049)
-0.18
(0.000)
0.62
2,185,419
Lagged price
0.80
(0.002)
-0.13
(0.000)
0.62
8,424,093
R2
Observations
Instrument
Extended Sample
Variables (in logs)
Estimator
Unit Price
Shipment Scale
within HS10-firm variation
OLS
0.85
(0.0002)
-0.13
(0.0002)
0.53
12,860,579
2SLS
0.62
(0.005)
-0.13
(0.0002)
0.49
12,860,579
40
Figure 2: The positive relationship between unit weight and f.o.b. unit price in two suspect
HS10 categories: bicycles and watches.
"HS8712000000"
(Bicycles or other Cycles)
Unit Weight (Kilograms)
50
10
100
F.O.B. Price (U.S. Dollars)
2100
"HS9102190000"
(Metal−Base, Quartz Wrist Watch)
Unit Weight (Kilograms)
1
.05
.5
F.O.B. Price (U.S. Dollars)
1000
Note: Each point in the scatter plot corresponds to a firm-specific shipment in “HS8712000000” (top
41
panel) or “HS9102190000” (bottom panel) arriving in Colombia in 2008.
Figure 3: The weight-price relationship across auto-producers within the same HS10
category.
"HS8703239000"
Unit Weight (Kilograms)
(Passenger Vehicle with 1500−2500cc engine)
1700
1400
1100
CHRYSLER
VW VEN JAGUAR
SUZUKI
DMG ALS
CHERY
FORD
OMNIBUS
AUDI
DAIMLER
VW
BMW
MAZDA
VOLVO
GM MEXICO
KIA PEUGEOT−CITROEN
ITOCHUCITROEN
BRA
SEAT
HYUNDAI
PEUGEOT
VW
MEX
NISSAN
MEX
HONDA
FORD
ARG
FORD
BRA
JONWAY
TOYOTA
BRA
RENAULT
SOJITZ GM
GM BRA
FIAT
PEUGEOT−CITROEN
ARG VEN
TOYOTA
ZOTYE
VW ARG
SKODA
LIFAN
RENAULT ROM
VW BRA
RENAULT
RENAULTBRA
TUR
800
SUMITOMO
DAEWOO
5000
15000
25000
35000
F.O.B. Price (U.S. Dollars)
Note: This figure plots the average f.o.b. price against the average unit weight for various autoproducers exporting to Colombia in “HS8703239000” in 2008.
42
Figure 4: The weight-price relationship across exports of the same firm within the same
HS10 product.
Volkswagen exports in "HS8703239000"
Unit Weight (Kilograms)
2500
2000
1500
1000
10000
15000
20000
F.O.B. Price (U.S. Dollars)
BMW exports in "HS8703239000"
Unit Weighr (Kilograms)
1800
1600
1400
1200
20000
30000
40000
50000
F.O.B. Price (U.S. Dollars)
Note: Each point in the scatter-plot corresponds to a shipment from Volkswagen (top panel) or BMW
(bottom panel) to Colombia in “HS8703239000” in 2008.
43
Figure 5: The relationship between unit weight and f.o.b. unit price in the pooled US
sample.
Note: This graph plots the relationship between unit weight and f.o.b. price (in terms of deviations
from HS10×year mean), for all the 1,667,243 observations in the U.S. sample that (i) report a
non-zero quantity in units of “N” or “NO”, (ii) are transported by air or vessel and thus provide full
information on shipment weight, and (iii) report a non-zero total weight.
44
D
Quasi-iceberg Transport Costs and Export Composition (For Online Publication)
The skepticism surrounding the iceberg assumption, is often rooted in the perception
that iceberg transport costs are incompatible with spatial variations in the pricemix of exports. In particular, it is well-documented that both greater distance and
higher transport costs induce firms to export higher price product varieties. This
regularity, known as the “Washington Apples” effect (W-A effect, hereafter), is
widely considered a symptom of non-iceberg transport costs. Against the backdrop
of these concerns, this section illustrates how quasi-iceberg transport costs could be
reconciled with spatial variations in export prices.
As a first step, I check wether the W-A effect diminishes once we account for
variations in unit weight . To this end, I run the following regression
ln p s,ωht = θ · ln τ s,ωht + δωh + δt + jht
(7)
where δωh and δt denote firm–product and year fixed effects, respectively. Following
the previous section, one has to address simultaneity between f.o.b. unit price and
unit transport cost when running the above estimation. To handle simultaneity, I
instrument for transport cost, τ s, jht , with other transportation fees paid for shipments
exported by provider j in the same year (in parallel product categories). As an
additional instrument, I also use the number of packages in shipment s (which is
strictly different from shipment quantity).
The estimation results reported in Table 13 indicate that, if anything, the W-A
is magnified once we account for variations in export unit weight. That is, the
estimated coefficient θ –which reflects the force of the W-A effect– increases once
we account for within firm-product variations in unit weight (see Table 13).18 This
outcome though is expected in light of fact 3 (from Section 3.2) that heavier goods
Assuming that unit weight is uniform within firm-product categories, it follows that e
p s,ωht = p s,ωht
and e
τ s,ωht = τ s,ωht . That being the case, we can simply estimate Equation 7 as:
18
ln e
p s,ωht = θ · lne
τ s,ωht + δωh + δt + s,ωht
45
Table 13: The effect of quasi-iceberg transport costs on the f.o.b. unit price of imports.
Dependent variable: (log) f.o.b. unit price
Regressor
Benchmark Estimation
Standard Estimation
accounting for variations in unit weight
treating unit weight as unifrom
IV
OLS
IV
OLS
(log) unit transport cost
0.506***
(0.0006)
0.619***
(0.0002)
0.333***
(0.0006)
0.332***
(0.0002)
Observations
FE groups (firm-HS10)
R2
9,055,699
776,376
0.55
9,055,699
776,376
0.80
9,055,722
2,301,249
0.19
9,055,722
293,288
0.51
Note: All regressions are conducted on the Colombia sample, include firm×HS10 fixed effects, year
dummies, and cluster errors (reported in parentheses) by HS10 product. The first two columns reports
cost
Value
the standard estimation that calculates unit price and transport cost as Quantity
and Transport
Quantity . The
second two columns correspond to an estimation that assume uniform weight (within categories) and
charge
Value
calculates unit price and transport cost on a per kilo basis as Weight
and Trnasport
. All IV estimates
Weight
pass the over-identifying restrictions test and have low first-stage F-statistic p-values. The estimated
coefficient significant at the 1% level, in all four regressions.
are shipped relatively more to distant markets.
So what drives the W-A effects? To take stock, note that traditionally the effect
is attributed to the classic Alchian and Allen (1964) conjecture that non-iceberg
(additive) transport costs distort relative price/demand in favor of high-price varieties.
Sections 3.2 and 3.3 established that transport costs are quasi-iceberg, implying that
the standard Alchian-Allen forces behind the W-A effect are smaller than previously
assumed. Meanwhile, accounting for variations in unit weight, the W-A effect itself
is estimated to be stronger than previous estimates suggest.19 To reconcile these
two seemingly conflicting observations, I first highlight two alternative factors that
contribute to the W-A effect; both of which are consistent with iceberg transport
costs. I then conduct a cross-industry analysis to show that while the W-A effect is
partly driven by standard Alchian-Allen forces, it is mostly driven by firms varying
their export markup-mix with transport costs.
19
Note that one might argue that transport cost per kg is quasi-specific and distorts the relative
value-to-weight ratio in favor of high-value goods. However, note that value-to-weight and unit price
are only weakly related (see Section 3.2 ). Hence, relative demand is not sensitive to distortions in
value-to-weight ratios across goods.
46
D.1
What drives the “Washington Apples” effects?
In general, the W-A effect could be driven by either (i) firms adjusting their price per
good with variations in transport costs (pricing-to-market) or (ii) firms adjusting their
export product-mix with variations in transport costs (composition effects). From
an empirical perspective, Hummels and Skiba (2004) argue that pricing-to-market
cannot be the dominant force. Relatedly, Harrigan, Ma, and Shlychkov (2015) show
that the W-A effect is driven primarily by composition effects.
The existing literature highlights three distinct forces that qualify as composition
effects: (i) firms varying their export quality-mix in the presence of non-iceberg
(additive) transport costs (Alchian and Allen (1964); Hummels and Skiba (2004)),
(ii) firms varying their export markup-mix with variations in iceberg transport costs
(Lashkaripour (2015)), and (iii) transport costs directly affecting the mix of exporting
firms (i.e., firm-sorting—Baldwin and Harrigan (2011); Crozet, Head, and Mayer
(2012)). Below, I formally review all three channels, deriving a testable hypothesis
corresponding to each one of them. These hypotheses relate the magnitude of the
(within-industry) W-A effect to an observable industry-wide characteristic. By analyzing cross-industry variations in the W-A effect, I can thus isolate the contribution
of each competing channel.
(i) Firms varying the quality-mix of exports. Alchian and Allen (1964) argue
that non-iceberg transport costs distort relative prices in favor of high-quality goods;
inducing firms to vary their export quality-mix across markets. Below, I present this
idea formally. Consider a Krugman (1980) model where firms (indexed by ω) are
multi-product and supply two types of goods (i) high-quality, H, and (ii) low-quality,
L. The utility of the representative consumer at home is given by:

ρ
X X

1
U = 
φω qω,z ρ 
ω z=H,L
where qω,z denotes the quantity of type z from firm ω, and φz denotes quality with
φH > φL . As a sensible assumption, suppose that the f.o.b. price of the high-quality
type is higher from each provider: pω.H > pω,L . Imports are also subject to a
47
value-dependent transport cost (dω pβω,z ) resulting in a final consumer price (p∗ω,z ) of
p∗ω,z = pω,z + dω pβω,z z = H, L
The relative demand for high-quality types from provider ω is given by
xω,H
φH
=
xω,L
φL
1−σ
!σ−1 
 pω,,H + dω pβω,H 


pω,L + dω pβω,L
1
where σ ≡ 1−ρ
denotes the elasticity of substitution across varieties. The elasticity of
relative demand for high-quality types from a given provider with respect to transport
cost, dω , is given by:
∂ ln
xω,H
xω,L
∂ ln dω
= (σ − 1)
pω,H · pβω,L − pβω,H · pω,L
p∗ω,H p∗ω,L
If β < 1 (provided that pω,H > pω,L ) the relative demand for high-quality types
increases with transport costs, and so does the unit price of imports from provider ω,
x pω,H+ xω,L pω,L
p̄ω = ω,H xω,H
:
+xω,L
!
xω,H
∂
∂ p̄ω
β < 1 =⇒
ln
> 0 =⇒
>0
∂ ln dω
xω,L
∂dω
(8)
Notice that ∂∂dp̄ωω basically captures the magnitude of the W-A effect, and depends
critically on the transport cost elasticity, β. Evidently, the W-A effect is weaker the
more ad-valorem or iceberg-like the transport costs:
!
∂ ∂ p̄ω
<0
∂β ∂dω
The W-A effect disappears altogether when transport costs are perfect icebergs:
β = 1. One could draw on these findings to evaluate the Alchian-Allen conjecture. In
particular, if the W-A effect were driven by non-iceberg transport costs it should be
more pronounced in low-β industries. An implication summarized in the following
proposition.
48
Proposition 1. Firms vary the quality-mix of their exports in response to variations
in non-iceberg transport costs (the Alchian-Allen conjecture). This behavior leads
to a W-A effect that is more pronounced in low-β industries.
(ii) Firms varying the markup-mix of exports. There is exhaustive evidence
pointing to within-industry dispersion in demand elasticity and hence markups.
Broda and Weinstein (2006) estimate that HS10 products that belong to the same
industry could future systematically different demand elasticities, motivating firms
to charge different markups for these products. Their findings resonate with Berry,
Levinsohn, and Pakes (1995) who find that demand elasticities and the corresponding
markups are systematically different across different classes of cars. In particular,
high-price, luxury cars are subject to a lower demand elasticity and feature higher
markups. Within-industry dispersion in demand elasticity/markup, creates a scope
for firms to vary their export markup-mix across destination markets. To model
this type of behavior, I use the previous setting with one modification. Instead
of supplying different qualities, each firm supplies a highly-differentiated and a
less-differentiated type product. The utility of the representative consumer at home
is thus given by:

 ρ%z %
 X X
 qρz  
U = 
ω,z  


z=H,L
ω
in the above utility, various providers are indexed by ω; H denotes the highly1
differentiated type, and L denotes the less-differentiated type. ε ≡ 1−%
, is the
1
elasticity of substitution across the two types, and σz ≡ 1−ρz is the elasticity of
substitution across firm varieties of type z. Type H being more differentiated entails
that
σH < σL ⇐⇒ ρH > ρL
For simplicity, suppose that unit labor cost is uniform and wages are equalized
across all providers and normalized to one. Every provider will, therefore, charge a
monopolistically competitive type-specific f.o.b. price equal to:
p∗ω,z = ρz τ̃ω , z = H, L
49
where τ̃ω denotes the iceberg transport cost incurred by provider ω. Note that
due to its higher markup, the highly-differentiated type exhibits a higher price:
ρH > ρL =⇒ p∗ω,H > p∗ω,L . Moreover, the relative demand for high-markup products
from provider ω is given by:
xω,H
= R0 (τ̃ω )σL −σH
xω,L
(9)
x
ω,0
where R0 ≡ xω,0
denotes the relative demand for high-markup products from from
local providers that incur no transport cost: τ̃0 = 1. Provided that σL > σH , the
relative demand for the high-markup product increases with iceberg transport costs:
∂xω,H /xω,L
>0,
∂τ̃ω
(10)
which gives rise to the the W-A effect. To illustrate this, note that the f.o.b. unit price
of varieties imported from provider ω is
p̄ω = λω,H · ρω,H + λω,L · ρω,L
where λω,H ≡ xω,H / xω,H + xω,L = 1−λω,L denotes the share of highly-differentiated,
high-markup type in the export-mix of provider ω. Noting that ρH > ρL , inequality
10 implies
∂ p̄ω ∂λω,H =
ρH − ρL > 0
(11)
∂τ̃ω
∂τω
Note that –unlike the Alchian-Allen effects– firms vary their export markup-mix in
response to all types of transport costs, including perfect iceberg costs. Furthermore,
here, the magnitude of the W-A effect is determined by the length of the markup
ladder within industries. In particular, the W-A effect is stronger the longer the
industry-wide markup ladder:
!
∂
∂ p̄ω
>0
∂Markup Ladder ∂τ̃ω
where Markup Ladder ≡ ρH − ρL denotes the spread between the highest and lowest
category-specific markup in a given industry. These arguments are summarized in
50
the following proposition:
Proposition 2. Firms vary the markup-mix of their exports in response to variations in iceberg transport costs. This behavior leads to a W-A effect that is more
pronounced in industries with longer markup ladders.
(iii) Firm-Sorting. The Melitz (2003) model predicts that firms with the lowest
quality-adjusted price sort into distant, tougher markets. Baldwin and Harrigan
(2011) build on this idea to show that if quality increases more than proportionally
with price, firm-sorting will give rise to the W-A effect. Specifically, suppose that
the quality (φω ) and price (pω ) of a given firm variety ω covary according to the
following relationship:
φω = p1+η
ω ,
In the above equation, η > 0 corresponds to the case where quality increases more
than proportionally with price. Baldwin and Harrigan (2011) show that the unit price
of exports from country j (relative to local varieties indexed with 0) is given by:
p j /ϕ j
−γ
p̄ j γη
= τj
=⇒
= τ̃ j
p̄0
p0 /ϕ0
where γ denotes the industry-wide trade elasticity, and τ̃ j the iceberg transport cost
from country j to the market of interest. When η > 0, the industry is governed by
quality competition, with high-priced varieties being more competitive and more
∂ p̄
capable of penetrating distant markets: ∂τ̃ jj > 0. Conversely, when η < 0, the
industry is governed by price competition. In that case, low-priced items are more
∂ p̄
competitive and ∂τ̃ jj < 0. In both cases, the magnitude of the W-A effect is regulated
by the industry-wide trade elasticity, γ:

quality competition



η > 0 −−−−−−−−−−−−→

price competition


η < 0 −−−−−−−−−−−→
∂
∂γ
∂
∂γ
∂ p̄ j ∂τ̃
>0
∂τ̃ j
<0
∂ p̄ jj (12)
Inequality 12 implies that if quality-competition dominates (η > 0), the W-A effect
is stronger in industries with higher trade elasticities. However, if price-competition
51
dominates (η < 0), firm-sorting countervails the W-A effect, leading to a weaker W-A
effect in high-elasticity industries. Hence, if firm-sorting were the main driver of
the W-A effect, we should observe a strong cross-industry relation between the W-A
effect and the industry-wide trade elasticity. The following proposition summarizes
these arguments.
Proposition 3. Under quality-competition, high-quality firms sort into markets with
higher transport costs. This behavior leads to a W-A effect that is more pronounced
in industries featuring a higher trade elasticity.
The forces that govern quality-sorting underly a similar theory put forward by
Manova and Zhang (2012). In particular, they argue that firms vary the quality
of their exports with distance to a given market. Following Baldwin and Harrigan
(2011), this type of behavior gives rise to the W-A effect only if high-quality varieties
have a lower effective price.20 If high-quality varieties have a higher effective price,
firms would lower their quality in distant markets where competition is tougher.
The quality-adjusting behavior proposed by Manova and Zhang (2012) thus closely
resembles quality-sorting. Hence, based on proposition 3, the quality-adjusting
behavior should more pronounced in high-trade-elasticity industries.
D.2
Estimating the Relative Importance of Each Force
With the aid of propositions 1-3, this sections attempts to identify the relative
importance of the three contributing forces highlighted above. To this end, I first
estimate the magnitude of the W-A effect per industry. This is done by running the
following regression separately for 826, 5-digit SITC industries in the U.S. sample
(indexed by k):
ln p s,ωht = θk · ln τ s,ωht + controls st + s, jht , h ∈ Hk
where s, ωht is an observation corresponding to exporting country s, US district
ω, HS10 product category h (with Hk denoting the set of all HS10 products within
20
Alternatively, as Manova and Zhang (2012) point out, this type of behavior could arise when
transport costs are additive.
52
SITC5 industry k), and year t. The term controls st corresponds to two standard
controls: the GDP per capita and population of origin country s.21 Propositions
1-3 establish that depending on what drives the W-A effect, the estimated “W-A
effect elasticity” θk would covary with the industry-wide (i) transport cost elasticity
cost
(βk ≡ ∂transport
), (ii) markup-ladder, or (iii) trade elasticity. Hence, to isolate the
∂price
contribution of each channel, I construct an industry-specific measure of transport
cost elasticity, markup-ladder, and trade elasticity.
The industry-specific transport cost elasticity is attained by estimating the transport cost function (Equation 3) separately for each SITC5 industry. The estimation
yields an elasticity βk that takes a higher value the more ad-valorem (or iceberg-like)
the transport costs in industry k. I can infer the industry-wide markup ladder using
the HS10-specific price elasticities estimated by Broda and Weinstein (2006).22
h
Theoretically, firms charge an HS10-specific markup ρh = σσh −1
in HS10 product
category h, which reflects the elasticity of substitution (σh ) in that product category—this strategy of inferring markups from demand elasticities is reminiscent of
Berry et al. (1995). I can, therefore, calculate the within-industry markup ladder as
the spread between the highest and lowest HS10-specific markups in industry k:23
Markup Ladderk = ρmax|k − ρmin|k
(13)
Finally, for the industry-wide trade elasticity (γk ) I adopt the trade elasticity estimated by Broda and Weinstein (2006) at the SITC5 industry level of aggregation.
The original U.S. sample contains 826 industries (see Section 3.1 for a detailed
description). For 605 of the industries, I find statistically significant estimates for
θk and βk (at the 10% level). These estimates plus the trade elasticities and the
markup-ladders are summarized in Table 14.
To evaluate the contribution of (i) the Alchian-Allen effects, (ii) firms varying
their markup-mix, and (iii) quality-sorting, I regress the W-A effect elasticity (θk ) on
21
Similar to Hummels and Skiba (2004), I also instrument for transport costs with distance and
shipment scale in alternative product-years.
22
Broda and Weinstein (2006) estimate the elasticities for the period of 1990-2001, which overlaps
with the period for which I estimate θk and βk .
23
Alternatively, I can measure the markup ladder of industry k as Markup Ladderk =
S.D. (ρh | h ∈ Hk ). The results are, however, extremely robust to this alternative measure.
53
Table 14: Summary of estimated or adopted industry-specific statistics.
Sample
Median
1st quartile
3rd quartile
The W-A effect elasticity (θk )
1.10
0.93
1.25
Tansport cost elasticity (βk )
0.93
0.83
1.04
Markup ladder
1.9
1.5
2.8
Trade elasticity
1.24
0.13
2.78
Number of SITC5 Industries
605
Note: This table summarizes SITC5 industry-specific statistics for a sample of 605 industries used
in Regression 14. The transport cost elasticity the magnitude of the W-A effect are estimated using
U.S. import data from 1989 to 1994. The markup-ladder and trade elasticity are calculated using the
estimates in Broda and Weinstein (2006).
the industry-wide (i) transport cost elasticity, βk , (ii) markup-ladder, and (iii) trade
elasticity. In particular, the following regression is performed across 605 industries
in the final sample:
θk = a1 + a2 · transport cost elasticityk + a3 · markup ladderk + a4 · trade elasticityk + k
(14)
The results (displayed in Table 15) support the Alchian-Allen proposition that
the W-A effect is stronger in low transport cost elasticity (i.e., low-β) industries.
Hence the W-A effect to some extent reflects firms varying the quality-mix of their
exports with transport costs. The majority of W-A effect, however, is driven by
firms varying the markup-mix of their exports in response to variations in transport
costs, even when transport cost are perfect icebergs. In particular, when facing high
transport costs, firms export relatively more goods that belong to high-markup HS10
categories. A conclusion drawn from fact that cross-industry variations in the W-A
effect are explained primarily by variations in the industry-wide markup ladder (see
Proposition 2). Trade elasticity, meanwhile, does not have a statistically significant
effect on the W-A effect. This simply indicates that while both quality-sorting
and productivity-sorting are operating at the industry-level, neither force strictly
dominates the other at the aggregate level.
54
Together, these results suggest that variations in the price composition of U.S. imports can be reconciled with quasi-iceberg transport costs. Specifically, even though
quasi-iceberg transport costs distort relative prices minimally, they significantly shift
demand in favor of high-markup varieties, giving rise to the W-A effect. Finally, the
above findings have strong implications for studies that infer trade costs from spatial
variations in trade values and unit prices. In particular, the spatial variation in export
prices are driven by both specific trade costs and variations in the export markup-mix.
Overlooking the markup margin will attribute all the variation to specific trade costs;
thus over-estimating the specific trade cost component.
Table 15: The determinants of the W-A effect
Dependent variable: θk (The W-A effect elasticity)
Coefficient
Shapley decomposition of R2
Markup Ladder
Transport Cost Elasticity (βk )
Trade Elasticity
0.018***
(0.006)
-0.102*
(0.060)
-0.000
(0.000)
60.9%
27.5%
11.6%
2
Overall R
Observations
0.021
605
Note: This table examines the relative importance of various mechanisms driving the “Washington
Apples” effect effect. The robust standard errors are reported in parenthesis. *** and * denote
significance at the 1% and 10% level, respectively.
55