Trade Elasticities, Heterogeneity, and Optimal Tariffs
Anson Soderbery
Purdue University
October 29, 2014
Abstract
Empirical evaluations of international trade with cross country heterogeneity are limited
by restrictive assumptions. Specifically, identification of import demand and export
supply elasticities has relied on the implausible assumption that exporters face identical
supply elasticities and market power in a given destination. This paper develops a
tractable structural estimator that relies solely on readily available bilateral trade data
in order to estimate heterogeneous export supply and import demand elasticities. The
estimates of heterogeneous elasticities are shown to follow intuitive patterns of importer
and exporter market power and produce believable distributions and magnitudes. The
aim of the estimator is to be parsimonious enough to be applied to any study where
pairwise heterogeneity in trade is expected. To highlight the desirable properties of
the estimator, we extend the cornerstone theory from Grossman and Helpman (1994)
to a setting where exporters have heterogeneous supply elasticities. We demonstrate
that heterogeneous export supply elasticities provide valuable insight into how countries
apply tariffs over time in response to compositional changes in trade patterns.
1
1
Introduction
Modern advancements in international trade have been geared toward describing the heterogeneous micro level responses by countries and their trading partners to globalization.
Flexible estimation techniques that capture the implied heterogeneity of supply and demand
elasticities within varieties of goods by country pairs have unfortunately lagged behind.
Practitioners have consequently been subject to relying on incompatible estimates of core
parameters to evaluate modern trade theory.
This paper develops a tractable estimator that can be applied to readily available trade
data in order to identify pairwise export supply and import demand elasticities for varieties at
the finest disaggregation of product codes. To do so, we structurally estimate a parsimonious
model of international trade that incorporates the core assumptions of new trade theory with
heterogeneity. The model is compatible with the predominant theories of firm, consumer,
and factor market heterogeneity in trade. Yet, it is flexible enough to be readily applied to
prominent modifications of these models. To illustrate the estimator’s flexibility, we develop
a model of optimal trade policy with heterogeneity and apply our estimates to evaluate its
efficacy in explaining applied tariffs.
Studies of optimal trade policy have assumed that every exporter of a particular good
into a given destination faces an identical export supply elasticity. Without lobbying, this
assumption implies the optimal tariff that balances terms of trade gains and efficiency losses
is the inverse of this common export supply elasticity. While this assumption is generally
made out of necessity due to the nonexistence of a strategy to estimate heterogeneous export
supply elasticities, it is difficult to come to grips with. We know countries are heterogenous,
and that their trade patterns are unique. This realization makes it extremely difficult to
continue to accept the assumption that, for instance, exported automobiles from Sweden
to the US have the same export supply elasticity as automobiles originating from Japan.1
1
Using ComTrade data, HS code 8703 represents automobiles. Swedish cars are sold extensively in the
US and EU by Volvo. Japanese automakers include Honda and Toyota. Both exporters are reliant on the US
market – 39% of all Swedish and 46% of all Japanese auto exports are destined for the US. The key difference
between the two is Swedish exports comprise only 2% of the US market, while Japanese exports capture
32%. This disparity suggests that the US should have a higher degree of market power over Swedish autos
2
We should expect differences in not only the production processes associated with these two
varieties, but also the degree of market power that the US can impose on each variety. Both
of these channels would suggest recognizable differences in export supply elasticities.
With heterogeneity in export supply elasticities, the optimal tariff set by an importer
is no longer simply the inverse of a single elasticity.2 We demonstrate that when exported
varieties come from distinct supply curves, the optimal tariff weights the relative contribution
of each variety to terms of trade gains and efficiency losses. The difficulty of applying this
theory to data is reliably estimating trade elasticities with heterogeneity.
The estimator developed here is tasked with identifying pairwise trade elasticities for
thousands of goods traded by hundreds of countries. This amounts to estimating millions
of elasticities without a single reliable instrument. Our predecessors are Feenstra (1994)
and Broda, Limao and Weinstein (2008), which rely on time series variation in prices and
market shares of imported varieties of goods to identify trade elasticities. Given that they
focus solely on import data from various countries, they are forced to assume that the
import supply and demand elasticities are identical across varieties to ensure identification.
Soderbery (2014) argues that the assumption of a singular import demand elasticity seems to
be reasonable, but imposing a common export supply elasticity is not. This is fairly intuitive
as the demand elasticity describes how consumers substitute across varieties while the supply
elasticity characterizes many tradeoffs within the production and export of a variety.
This paper demonstrates that overcoming the identification issue of allowing for heterogeneous elasticities requires incorporating export data with matched import data. Here we
argue that the time series of prices and shares produced across export destinations from a
given origin differ from the prices and shares generated within an import destination. Since
(i.e., face a larger inverse export supply elasticity), as the US market for autos has a stronger reaction to
price fluctuations by Japanese imports. We estimate an inverse export supply elasticity of 0.821 for Swedish
exports to the US and 0.317 for Japanese exports, suggesting precisely the expected pattern of US market
power. Additionally, the pattern is exactly the reverse when we consider Swedish versus Japanese exports of
the same good to the UK. The UK is a more vital destination for Sweden and we see an inverse elasticity of
0.737 compared to 2.226 for Japan, suggesting greater market power for the UK over Japanese auto imports.
2
We focus on the case where an importer sets a single tariff across all varieties. It can be shown that
if an importer could perfectly discriminate across all varieties, they would set a tariff that is the inverse of
each exporter’s supply elasticity. However, we never see perfect discrimination in tariff rates in the data.
3
these data series are generated from the same underlying supply process, their statistical
differences will allow us to identify a unique pairwise export supply elasticity.
To understand the intuition of the estimator, we need to acknowledge the data generating process in our trade data. Independent supply and demand shocks fluctuate supply
and demand curves. Shocks combine with equilibrium conditions to form the observed data.
Leamer (1981) demonstrates that we can use the variation in shocks to bound the parameters that produce our observed equilibria. Feenstra (1994) argues that assuming multiple
varieties follow the same equilibrium generating process (i.e., elasticity parameters) allows
us to estimate supply and demand elasticities. Here we are unwilling to assume different
varieties follow identical equilibrium conditions. Consequently, we cannot look solely within
a market for identification. In essence, we will combine the differences in shock processes
across markets with related equilibrium concepts to identify our elasticities. Leveraging
the heteroskedastic differences in outcomes across versus within markets will be shown to
produce consistent estimates of heterogeneous elasticities.
Applying the structural estimator to the universe of trade flows at the HS4 level using
ComTrade data uncovers significant heterogeneity both between and across countries and
goods. Evaluating the “reasonableness” of the estimates produced here exploits the heterogeneity of the estimates and the interpretation of the inverse export supply elasticity as a
measure of market power. We begin by establishing intuitive relationships between product
differentiation and market power. Importers are expected to possess more market power for
highly differentiated goods on average. Our estimates suggest that the average inverse export
supply elasticity (i.e., market power) for differentiated goods is around two times larger than
for homogenous goods. Additionally, we expect differentiated goods to be less substitutable
than homogeneous goods. We confirm this expectation as our estimated import demand
elasticities are roughly 20% larger for homogeneous goods than differentiated goods.
Additionally, importers should have varying degrees of market power across types of
goods that depends on their composition of imports. To investigate, we regress inverse
export supply elasticities on importer by good characteristic fixed effects. The estimated
4
fixed effects allow us to rank the relative degree of market power across importer good pairs.
As we would expect, the largest importers in the data (Germany, US and China) possess
the highest degree of market power on average, while the smaller less developed importers
(India, Brazil and Northern European Countries) have the least.
Interestingly, these market power rankings vary across types of goods. China for instance ranks second in market power across differentiated goods, and near the bottom for
non-differentiated goods. China is notably reliant on foreign suppliers of raw materials, supporting the result that they possess relatively weak market power over non differentiated
goods. An identical story also holds for other Asian countries, including Taiwan and Korea.
Conversely, India ranks near last in differentiated goods, but first in market power for nondifferentiated goods. India’s imports of non-differentiated goods are predominantly supplied
by regional trade partners, of which India is an important export destination. Our estimates
thus support the idea that market power varies across types of goods and the composition
of imports. These patterns taken together suggest the heterogeneity of our estimates both
across and within goods and countries are important for uncovering the relationships shaping
market power in the data.
Finally, we show that country pair relationships also relate to the export supply elasticity.
First, large countries (in terms of GDP and world trade) have greater market power. Second,
countries that rely on one another to sustain trade (e.g., the share of a destination’s imports
fulfilled by an origin) have weaker market power. These heterogeneous pairwise patterns
in market power have significant implications for the construction of optimal trade policy.
This is the first study to show how the terms of trade motives for optimal tariffs depend on
the composition of an importer’s trade. Optimal tariffs with heterogeneity thus respond to
compositional changes in trade over time. This avenue of variation is used to demonstrate a
much stronger connection between applied and optimal tariffs than previous studies.
The estimation strategy developed in this paper fits with a small but growing set of
structural estimators in trade. Feenstra and Weinstein (2010) propose a structural estimator
based on translog preferences to estimate markup distributions. Their model is stylized and
5
not easily mapped into the foundations of new trade theory. Feenstra and Romalis (2012)
estimate an importer specific quality distribution parameter. In contrast to this paper, their
estimators are not tasked with uncovering pairwise heterogeneity between importers and
specific exporters, but rather potential distributional differences across countries. Here we
are interested in heterogeneous relationships both within and across countries and goods.
Hottman, Redding and Weinstein (2014) use proprietary scanner data to uncover quality,
costs and markups at the firm level.
Potentially the most important difference between our estimator and the preceding are
the data required for estimation. Our technique requires only readily available data on
trade flows. Feenstra and Weinstein (2010) requires measure of product specific Herfindahl
indexes that were specially constructed in the US for their study, and do not exist for most
(if not all) other countries. Feenstra and Romalis (2012) relies on highly detailed tariff and
wage data across countries that are not readily available. Hottman, Redding and Weinstein
(2014) leverage proprietary scanner data as they require highly detailed transaction level
data, which presents significant hurdles to extend their estimator beyond the US.
Our analysis of optimal trade policy is related in spirit to Ossa (2011), which calibrates a
model where countries with heterogeneous firms strategically set tariffs. While his theoretical
contribution is based on firm heterogeneity, his empirical work relies on homogenous elasticity
estimates (i.e., Feenstra (1994)) that are fundamentally incompatible with the theory. Here
we estimate the model based on heterogeneity and then evaluate an adapted version of
optimal trade policy. The estimation strategy and evaluation of the theoretical results are
perfectly compatible, and are shown to have unique explanatory power when estimating the
relationship between applied and optimal tariffs in the data.
This paper proceeds as follows. Section 2 presents a general model of trade that we
structurally estimate in Section 3. Section 4 evaluates the patterns of the resulting estimates
of heterogeneous supply and demand elasticities. Section 5.1 adapts the prevailing model
of optimal trade policy to allow for heterogeneity. Section 5.2 evaluates the relationship
between the model’s optimal tariffs and applied tariffs. Section 6 concludes.
6
2
A General Model of Trade
Here we specify a general model of trade that incorporates the key assumptions of new trade
theory. The model is flexible enough to accommodate structural estimation yet parsimonious
enough to highlight the strategic channels of optimal trade policy and lend itself to a wide
range of studies. Much of the following will be an exercise in notation, so it is useful to
clarify the context. We are faced with many importers and exporters trading a host of goods
and varieties. In the following empirics, we define an imported variety of a good utilizing the
Armington (1969) assumption. Denote goods imported by a country g ∈ Gm and varieties
of these goods v. Specifically, goods will be defined by their HS4 product category, and
varieties of these goods in a given country will be given by the origin of the exporter.
The following will borrow heavily from Broda, Limao and Weinstein (2008) and Grossman
and Helpman (1995). A representative consumer will maximize her utility by choosing
imports and domestic consumption. We will assume a Cobb-Douglas aggregation over the
composite domestic (D) and imported (X) goods. The subutility derived from the composite
imported good will be given by a CES aggregation with a good-importer specific elasticity of
substitution (σgI ), where I denotes the importing country. Individuals obtain utility through
their consumption of a numeraire good c0 and imported and domestic varieties of goods,
X
generally denoted as chg , such that U = ch0 +
ug (chg ). This quasilinear structure rules out
g
income effects in the model so that we can focus on trade flows and trade policy. Imports of
a particular variety (v) of good (g) are denoted by xgv . Also allow demand to be augmented
by a variety specific taste parameter bgv . Under these assumptions, we can write the utility
obtained by a consumer in any importing country as,3

I
I
0
I
X
U =c +ξ
X
g∈GI
m

 X σ1gI

φ log 
bgv x

I
g
v
3
I −1
σg
I
σg
gv


I
σg
I
σg −1


 + ξDI log(DI ).

(1)
For the sake of notation, drop the consumer superscript. Also drop the importer superscript on variety
specific variables denoted by v .
7
The importer consumes fixed shares ξDI and ξXI of domestic and imported goods, respectively.
Additionally, the imported composite is formed by consumption of fixed shares of each
imported good given by Cobb-Douglas parameters φIg . Imports of each variety are denoted
by xgv , each of which are scaled by an importer specific random taste parameter bgv . The
separability of utility allows us to focus on the gains and losses from a tariff that work directly
through the prices and consumption of imported goods.4 Additionally, this specification
implies that policy affects goods independently, which later will allow us to evaluate the
efficacy of tariffs through their impact on consumption and strategic gains good by good.
XX
Consumers maximize (1) subject to the budget constraint cI0 +
pgv xgv ≤ Y I , which
g
v
yields demand for any variety of imported good as a function of its price pgv ,
I
I
σg −1
g
,
xgv = ξXI φIg bgv p−σ
gv Pg
!
where Pg =
X
I
1−σg
bgv pgv
(2)
1
I
1−σg
is the standard CES price index. All prices pgv thus far are
v
delivered prices in the importing country. While many factors may influence the relationship
between shipped and delivered prices (e.g., exchange rates), we will focus explicitly on the
role of tariffs.5 As such, we can write the delivered price as the shipped price scaled by the
tariff, pgv = (1 + τgI )p∗gv .6
Given the structure of demand, we now need to specify exporter supply. We want export
supply to be tractable enough to estimate, yet general and flexible enough to apply to many
studies. To do so, simply assume that exporter supply curves are upward sloping of the form,
I
p∗gv = exp(ηgv )(xgv )ωgv .
4
(3)
Consequently, we do not need to explicitly specify the form of the composite domestic good. Since
data coverage for production and consumption of domestic goods, it is impossible to respectably estimate
supply and demand elasticities (see Ardelean and Lugovskyy (2010) for a more thorough discussion) for the
domestic composite. More importantly, it is also unnecessary to evaluate the optimal tariff in this context.
5
The empirics will allow for, and exploit, other motives that enter through an unobservable error term.
6
To match the data and policy landscape, we assume τgv = τgI ∀ v.
8
Exporters thus have unique supply curves for their variety within and across countries.
I
. We also allow for
The destination-variety-specific inverse export supply elasticity is ωgv
unobservable variety specific supply shocks ηgv to facilitate estimation.
3
Empirical Strategy
In this section, we describe the methodology that will provide consistent estimates of the
heterogeneous export supply and import demand elasticities for every importer-exportergood pair in the data. The method will structurally estimate the preceding trade model,
and rely solely on commonly available trade data for identification.
3.1
Supply and Demand
The first step here is to be clear about notation and data. Trade flows between all countries
and goods come from ComTrade from 1991-2010. For tractability and consistent comparisons
with previous studies, we aggregate these data to the HS4 level.7 The survey is distributed
in two parts. First, the values and quantities of a good sold by an origin to a destination
as reported by the importer. Second, the values and quantities of trade of the same good
as reported by the exporter. We take advantage of both surveys in order to identify the
elasticities of interest. In the following, denote variables as reported by the importer with
I
, and those reported by the exporter with V . The direction of trade will be important in
what follows. Let
I←V
denote imports by
I
from V , and
V →I
are exports by
V
to I . Goods
and varieties will continue to be given by g and v, respectively. To remind the reader, gv
signifies a unique importer-exporter pair trading the good (i.e., a variety). We will also rely
on time series variation to identify our elasticities, and denote a given year in the data by t.
Identification will exploit time series variation and statistical differences between import
and export markets. To begin, take the perspective of the importer. The importer faces the
7
ComTrade data are generally available down to the more disaggregate HS6 product level. I have
estimated, and make available results, estimates from HS6 data. The themes of the paper are unaffected by
the level of aggregation. Therefore, I opt to present the HS4 estimates as they are directly comparable to
Broda, Limao and Weinstein (2008).
9
delivered price pI←V
for a given variety. In the data, prices are unit values and quantities are
gv
generally given in kilograms. The estimator will address measurement error in unit values
through optimal weighting, and as in Feenstra (1994), we follow Kemp (1962)’s suggestion
to convert the data into market shares in order to alleviate measurement error in quantities.
Call the market share of a variety within a destination in period t, sI←V
Following the
gvt .
preceding, we can write the exporter’s market share in the importing country as,
sI←V
≡
gvt
pI←V
gvt xgvt
P
I←V
v pgvt xgvt
=
pI←V
gvt
I
Pgt
σgI −1
bgvt .
We want to absorb as many unobservable fixed effects as possible. Begin by first differencing
to remove any time invariant importer specific effects.8 Then to absorb good by time specific
effects, select a reference variety k and difference. This yields,
I
k
I←V
I
∆k log(sI←V
gvt ) = −(σg − 1)∆ log(pgvt ) + gvt ,
(4)
where ∆k denote first then referenced differenced variables. Igvt are first and reference differenced unobservable variety specific taste shocks. Equation (4) is the demand curve of the
importer country for the exported variety v.
Estimating the system also requires a supply curve for the variety delivered to I . Taking
the same approach as above, we can write export supply in logs. After first and reference
differencing we are left with,
∆k log(sI←V
gvt ) =
I
1+ωgv
I
ωgv
∆log(pI←V
gvt ) −
I
1+ωgk
ωI
gk
I
∆log(pI←K
gkt ) + ρgvt ,
(5)
where ρIgv are unobservable differenced supply shocks. Notice that the export supply curve
from any country is determined by the exporter’s elasticity relative to its competitors.
With demand and supply in the importing country specified, we can begin discussing
estimation. Feenstra (1994) developed a methodology to consistently estimate the above
8
Appendix B details precisely how the following equations are constructed, and how error terms are
defined structurally.
10
I
system if we are willing to assume homogeneous export elasticities (i.e., ωgv
= ωgI ∀ v).
The estimator is based on Leamer (1981).9 Briefly, Leamer (1981) asserts that with time
series variation in a variety’s prices and shares, we can construct a hyperbola that given the
data contains the true elasticities. He demonstrates if we knew one elasticity for certain we
could uniquely solve for the other as a point on the hyperbola. Feenstra (1994) shows that
if a country imports at least two varieties, the intersection of the hyperbolae can be used
to uniquely determine supply and demand elasticities. The intuition for the estimator is
best seen in a picture. Figure 1 plots a hypothetical importer of two varieties supposing we
know the true import demand and export supply elasticities. The true demand elasticity is
Figure 1: Importer Hyperbolae
ω
ωIgv
ωIgk
Imports I !"V
Imports I !"K
σ Ig
σ
indicated by σgI , and the true export supply elasticity of the variety from country
for country
I
V
destined
I 10
is ωgv
. Assuming that import and export elasticities are homogenous across
varieties implies that the intersection of the hyperbolae Figure 1 uniquely identifies each
elasticity. With heterogeneous export supply elasticities the intersection of hyperbolae no
longer characterizes the solution, and the system of Equations (4) and (5) cannot solely
identify the elasticities.
9
10
Soderbery (2014) provides a thorough discussion of the methodology.
Equivalently, the true export supply elasticity of the good from country
11
K
destined for country
I
I
is ωgk
To provide additional variation to the problem, take the exporter’s perspective. An
exporter faces the same demand curve and supply curve in I . However, the decisions made
by an exporter
V
regarding goods shipped across destinations are substantively different
than the outcomes within a destination. The share of total export supply from country
represented by country
I
V
is given by,
sVgvt→I =
→I
pV
gvt xgvt
P
V →I
p
I gvt xgvt
=
I
ωgv
I
1+ωgv
V →I
exp
pgvt
I
ωgv
I
1+ωgv
P
V →I
exp
I pgvt
−ηgvt
I
ωgv
!
−ηgvt
I
ωgv
.
!
Again we want to eliminate time and country (here the exporter) specific effects. To do so,
take logs, first difference, then choose a reference destination (j) and difference. This yields,
∆j log(pVgvt→I ) =
I
ωgv
I
1+ωgv
∆log(sVgvt→I ) −
J
ωgv
J
1+ωgv
∆log(sVgvt→J ) + ρVgvt ,
(6)
where ρVgvt are the unobserved supply shocks. Equation (6) is a supply curve for the exported
variety across destinations. The supply curve again depends upon the export supply elasticity in
I
relative to the reference. However, the reference is now defined as the same variety
shipped to a different destination. Statistical differences between market shares within versus
across destinations are key to identification as they are derived from the same fundamental
elasticities but are generated by different relative shock processes.
Next we define the demand curve across the exporter’s destinations. In logs and first and
reference differences, demand is given by,
∆j log(sVgvt→I ) = (1 − σgI )∆log(pVgvt→I ) − (1 − σgJ )∆log(pVgvt→J ) + Vgvt ,
(7)
where Vgvt are the relative taste parameters. Prices and shares are driven by differences
in the elasticity of substitution in each of the exporter’s destination markets. Figure 2
presents hypothetical exporter hyperbolae implied by Equations (6) and (7), assuming we
know the true elasticities. We could apply the intuition of Feenstra (1994) discussed above,
12
Figure 2: Exporter Hyperbolae
ω
Exports
V
!"J
ωIgv
Exports
V
!"I
ωJgv
σ Jg
σ Ig
σ
but we would end with an analogous conclusion. Export flows by themselves cannot uniquely
identify heterogeneous elasticities.
Here it is worth spelling out the intuition of the estimator, so that the following explicit
formulation of the estimator is clear. First we need to acknowledge the data generating
process in our trade data. Independent supply and demand shocks fluctuate our curves.
Shocks combine with equilibrium conditions to form the observed data. Leamer (1981)
demonstrates that we can use the variation in shocks to bound the parameters that produce
our observed equilibria. Feenstra (1994) argues that multiple varieties following the same
equilibrium generating process (i.e., elasticity parameters) allows us to estimate supply and
demand elasticities. Here we are unwilling to assume different varieties follow identical equilibrium conditions. Consequently, we cannot look solely within a market for identification.
The following shows how to use variation across markets to achieve identification. In essence
we are combining different sources of shock processes with related equilibrium concepts to
identify our elasticities.
13
3.2
Identification and Estimation
Notice that while market outcomes for exporters and importers are related, they are not
identical. The share of a destination market captured by a particular exporter depends on
price and quantity fluctuations in that particular market. These can be driven by random
taste and supply shocks. Taste shocks are destination specific to the particular variety and
uncorrelated with shocks to the supply of that product. A given destination also has its own
particular market composition, such that the shares and prices of an imported variety in that
market are driven by the makeup of the destination. What we need to identify heterogeneous
supply elasticities, are differential relationships between the outcomes of an exporter within
markets and across markets. Specifically, the hyperbolae generated by looking at fluctuations
in prices and shares across markets must differ from the hyperbolae generated by looking
at fluctuations in prices and shares within markets.11 In practice, market shares realized
across export destinations look considerably different than market shares captured within a
destination.
To provide a specific example, Korea exported $6.7Bill of HS 8703 (automobiles) to
the US in 2010. The share of the import market captured by Korea in the US was 6%.
However, the share represented by the US for the Korean export market was four times the
size at 24%. Additionally, the raw correlation of these market shares from 1991-2010 was
-0.04. This near zero correlation is actually representative of the entire sample. To add
to the argument we also utilize the differences in reported shipped and delivered prices to
capture differences in prices received by exporters versus those faced by importers. The raw
correlation between shipped and delivered prices is also quite low – for the case of Korean
autos it is 0.11. Variation of this sort is exactly what is required by the estimator. As long
as the fluctuations in prices and shares are not asymptotically identical the identification
strategy is sound.
Figures 1 through 3 present this intuition graphically. Figure 3 combines the importer
11
Precisely, we require that the export and import hyperbolae for any origin destination pair are not
asymptotically identical.
14
and exporter hyperbolae from Figures 1 and 2. We can see that the intersections of importer
and exporter hyperbolae for multiple varieties can identify heterogeneous export supply
elasticities since all exporters to
I
face the same import demand elasticity. Figure 3 is the
Figure 3: Combining Importer and Exporter Hyperbolae
σ
Exports
K
#"I
Imports I !"K
σIg
Exports
V #"I
Imports I !"V
ω
ωIgk
ωIgv
ideal situation where all of the hyperbolae cross and line up directly at the import demand
elasticity. The reality of the data is that this clean result will be rare – hyperbolae in general
may cross many times at different values in the feasible region or not at all. This necessitates
an estimation strategy where we jointly estimate the demand elasticity and use it to identify
the heterogeneous export supply elasticities.
First we need to assume, as each of our predecessors have done, that supply and demand
shocks realized by a variety are uncorrelated over time. Specifically, E[Igvt ρIgvt ] = 0 and
E[Vgvt ρVgvt ] = 0.12 Under this assumption, we can multiply the residuals from supply and
demand for the exporter and importer to generate consistent estimating equations. For the
Notably, it need not be the case that E[Igvt Vgvt ] = 0 and E[ρIgvt ρVgvt ] = 0, which is violated by the
construction of the model.
12
15
importer this yields,
ωI
2
k
I←V 2
gv
∆k log(pI←V
I )(σ I −1) ∆ log(sgvt ) +
gvt ) = (1+ωgv
g
+
+
1
I −1
σg
I
ωgv
I
1+ωgv
k
I←V
∆k log(sI←V
gvt )∆ log(pgvt )
I←V
∆k log(sI←V
gkt )∆log(pgvt ) +
I −ω I
ωgv
gk
I )
ω I (1+ωgv
gk
where the error term uIgvt =
I (1+ω I )
ωgv
gk
I
I )(σ I −1)
ω (1+ωgv
g
gk
I←K
∆k log(sI←K
gkt )∆log(pgkt )
I←K
I
∆k log(pI←V
gvt )∆log(pgkt ) + ugvt ,
I ρI I
ωgv
gvt gvt
I )(σ I −1)
(1+ωgv
g
(8)
is zero in expectation.13 To estimate the model we
apply the 2SLS methodology proposed by Feenstra (1994).14 This will transform Equation
(8) into a linear regression of price variances on share and price covariances and variances.
In other words, we map hyperbolae into data. Running this regression could consistently
estimate the import demand elasticity, but as we have seen it cannot identify heterogeneous
supply elasticities.
To overcome the identification problem, we produce a similar estimating equation from
the exporter’s perspective. Multiplying our error terms together yields,
ωI
V →I 2
gv
∆j log(pVgvt→I )2 = (1+ωgv
I )(σ I −1) ∆log(sgvt ) +
g
+
+
J
ωgv
J
I −1)
(1+ωgv )(σg
J (σ J −2)
1−ωgv
g
J )(σ I −1)
(1+ωgv
g
I (σ I −2)−1
ωgv
g
I )(σ I −1)
(1+ωgv
g
∆log(sVgjt→J )2 +
∆log(sVgvt→I )∆log(pVgvt→I )
J (σ I −2)
1−ωgv
g
J
I −1)
(1+ωgv )(σg
∆log(sVgvt→J )∆log(pVgvt→J ) +
+
I )+(1+ω J )
(1+ωgv
gv
I
J )(σ I −1)
(1+ωgv )(1+ωgv
g
+
J −σ I
σg
g
I −1
σg
V
ρV
gvt gvt
I −1
σg
I (σ J −2)−1
ωgv
g
I )(σ I −1)
(1+ωgv
g
∆log(sVgvt→I )∆log(sVgvt→J ) +
∆log(pVgjt→J )∆log(pVgvt→I ) + uVgvt ,
where the error term uVgvt =
∆log(sVgjt→J )∆log(pVgvt→I )
I −σ J
σg
g
I −1
σg
∆log(sVgvt→I )∆log(pVgvt→J )
∆log(pVgvt→J )2
(9)
is zero in expectation. Combining Equations (8) and
(9) provides us the necessary variation to identify heterogeneous elasticities. To estimate
the full model, we apply the 2SLS methodology using importer and exporter indicators as
instruments to each equation. Our estimation thus chooses the elasticities which minimize
13
Note that Equation (8) is identical to Feenstra (1994) if export supply elasticities are homogeneous.
Feenstra (1994) demonstrates that applying 2SLS to the above with country indicators as instruments
yields consistent estimates of the supply and demand elasticities when both are homogeneous.
14
16
the distance between hyperbolae across markets. We apply the estimator looking within
an importer-good pair across exporters over time. Exporters jointly identify the import
demand elasticity. Variation from export flows and import flows then pin down the pairwise
export supply elasticities. To jointly estimate Equations (8) and (9), we apply a nonlinear
seemingly unrelated regression constrained to the feasible region where σ > 1 and ω > 0.15
Estimates of the elasticities are consistent provided the import and export hyperbolae are
not asymptotically proportional.
4
Elasticity Estimates
All we need for estimation are trade flows associated with country pairs across goods – here
we rely on Comtrade data from 1991-2010. The data contain 1243 goods at the HS4 level
and 192 importing and exporting countries.
Not all countries trade all goods with one another, but we are still tasked with estimating
approximately 3 million export supply elasticities and 200,000 import demand elasticities.
Simply, this is computationally infeasible.16 To reduce the parameter space, assume small
countries in the same region have identical supply technologies. This is a restrictive assumption for these countries. However, it is necessary for econometric tractability, and still
considerably more disaggregate than any preceding study. Table 1 lists the regions designated
15
With raw trade data we worry about measurement error in prices (unit values) and quantities (product
weight). As mentioned above, the use of market shares alleviates much of our concern regarding the measurement of quantities. Unit values necessitate a weighting scheme. Given the use of both import and export data
and the context of the problem, we adopt the weights proposed by Broda and Weinstein (2006) and include
3
−1/2
an importer-exporter specific constant. Specifically, the data are weighted by Tgv/2 (1/xgvt + 1/xgvt−1 )
, as
we expect greater accuracy in the recorded data between large (↑ xgvt ) and persistent (↑ Tgv ) trading partners. Broda and Weinstein (2006) demonstrate that these weights accompanied by a constant in estimation
correct for random measurement error in prices along with measurement error that may be decreasing in the
amount of total trade. Additionally, this weighting scheme matches our intuition derived from hyperbolae
– we will give more weight to hyperbolae generated by large trading partners in the estimation. Soderbery
(2014) discusses the appropriate weighting of hyperbolae in great detail. In the case of Feenstra (1994) LIML
is the superior scheme. Here the problem is exponentially more computationally intensive and not amenable
to LIML, thus we adopt the intuitive weighting scheme.
16
The following makes some assumptions to reduce the parameter space. After these assumptions, we still
estimate over 1.2Mill export supply and 25,000 import demand elasticities. The estimation routine requires
two full weeks to complete running concurrently on three computers with 4 processors using StataMP (the
routine takes a month using a single processor on each machine).
17
along with their total imports and exports.17
Table 1: Regions and Trade
Country
Australia
Brazil
Canada
China & Hong Kong
Germany
France
Great Britain
India
Italy
Japan
Mexico
Russia
United States
Country
Code
Country
Count
Total Imports
($Billion)
Total Exports
($Billion)
AUS
BRA
CAN
CHN
DEU
FRA
GBR
IND
ITA
JPN
MEX
RUS
USA
1
1
1
2
1
1
1
1
1
1
1
1
1
147.92
153.93
340.25
1356.41
863.56
516.12
469.18
178.42
393.47
494.70
273.89
184.18
1644.87
156.82
186.45
344.19
1742.35
1035.62
442.38
303.24
168.24
367.91
715.76
288.55
285.18
1047.54
AFR
ASA
CAR
NWU
OCE
SAM
SEU
43
38
16
18
11
20
22
253.13
1414.52
21.37
1361.41
27.91
254.59
924.79
279.05
1463.69
17.10
1378.70
27.41
260.85
763.58
Region
Africa
Asia
Caribbean
Northern/Western Europe
Oceania
South American
Southern/Eastern Europe
Note: Imports and exports are in US dollars from 2010.
Applying the estimator requires imports from at least two countries that both export to
at least one other destination for a minimum of three periods. These are relatively weak
requirements conceptually, but practically the intersection of trade data and the estimator
meeting its minimum requirements reduces the sample of trade flows from around 1.25Mill
observations per year to 0.8Mill. Reassuringly, the remaining data account for 94% of all
trade globally.18 Table 2 summarizes our estimates across importer regions. Our estimated
trade elasticities vary considerably across and within goods and countries. Variation in our
estimated inverse export supply elasticities explained by importer product fixed effects is
17
We have tried to follow the United Nations Statistical Division’s definitions of country regions, which
can be found here https://unstats.un.org/unsd/methods/m49/m49regin.htm. The full listing
of countries and their assigned regions is given by Table A1.
18
Section 5.2.1 is devoted to comparing my estimates to those of Broda, Limao and Weinstein (2008),
but it is worth noting that their analysis covers data with 250,000 observations over 15 importers that only
accounts for 8% of trade.
18
only 33%, suggesting much of the variation in our estimates are a result of heterogeneity
across exporters within an imported good.19 Considering the median absolute deviation
(MAD) demonstrates that around 75% of these export supply elasticities lie between 0.025
and 1.375 with a long right tail. Our demand elasticities have a similar long right tail and
an interquartile range of 1.63–3.82, which is very much in line with previous studies.
Table 2: Summary Statistics: Elasticities and Country Size
σgI
GDP ($Bill)
I
ωgv
Obs
Mean
Total
Mean
Median
MAD†
Mean
Median
MAD†
AUS
BRA
CAN
CHN
DEU
FRA
GBR
IND
ITA
JPN
MEX
RUS
USA
16984
14827
16811
39111
34877
29303
30187
15044
29670
20852
14849
19278
33144
768.18
1067.96
1251.46
1574.23
2906.68
2230.72
2345.02
906.27
1844.75
4340.13
839.18
986.94
13201.82
768.18
1067.96
1251.46
2872.15
2906.68
2230.72
2345.02
906.27
1844.75
4340.13
839.18
986.94
13201.82
3.881
3.134
4.275
4.373
3.698
3.189
2.663
4.501
3.334
3.582
3.261
4.501
3.065
2.377
1.937
2.580
2.769
2.948
2.115
2.036
2.315
2.475
2.626
1.746
2.880
2.196
0.939
0.595
0.999
1.083
1.176
0.708
0.665
0.850
0.953
0.991
0.444
1.079
0.822
97.70
136.10
121.31
316.01
81.37
56.18
43.25
75.25
36.39
153.14
138.65
136.55
32.27
0.652
0.659
0.631
0.734
0.730
0.676
0.655
0.605
0.663
0.744
0.682
0.704
0.698
0.939
0.595
0.999
1.083
1.176
0.708
0.665
0.850
0.953
0.991
0.444
1.079
0.822
AFR
ASA
CAR
NWU
OCE
SAM
SEU
105691
241106
16930
207265
15374
98932
200747
83.39
248.54
17.68
328.79
90.15
98.64
292.89
941.65
2994.04
64.67
3278.56
113.45
962.40
2716.01
3.343
4.673
5.554
4.185
4.081
3.619
4.059
2.496
3.916
2.462
3.259
2.411
2.814
3.478
1.059
1.159
1.126
1.293
0.906
1.082
1.356
321.08
120.68
141.23
33.17
325.24
61.85
10.06
0.824
0.917
0.535
0.670
0.758
0.461
0.653
1.059
1.159
1.126
1.293
0.906
1.082
1.356
World
1200982
1190.68
35561.27
4.008
3.006
1.127
100.31
0.700
0.675
Importer
Notes: GDP are total gross domestic products reported by CEPII in billions of US dollars for 2006.
I
For exposition, σgI is truncated at 131.05, and the top and bottom 1% of ωgv
are dropped. † MAD
stands for the median absolute deviation.
The summary statistics of our estimates follow intuitive patterns. China and other Asian
countries have been importing the lion’s share of capital goods in recent years. These goods
19
Notably, variation in homogeneous export supply elasticity estimates, such as estimated by Broda,
Limao and Weinstein (2008), is fully explained by importer product fixed effects. Suggesting, the degree of
heterogeneity across country pairs masked by the assumption of homogeneity is a significant deficiency of
previous studies.
19
are likely more substitutable than many differentiated goods, and we see that on average
these countries import goods with higher average demand elasticities. China also imports
many differentiated goods, and thus faces a relatively wide range of demand elasticities for
its imports as its MAD is the second largest of the high GDP countries. Conversely, the
US imports predominantly differentiated goods, and faces a relatively low average demand
elasticity and low deviation.
I
Importer market power in trade is represented by the inverse export supply elasticity ωgv
.
I
High ωgv
corresponds with a high degree of importer market power. We can see that our
estimates suggest countries with the highest GDPs tend to have the most market power, as
their imports have the largest median inverse supply elasticities. Of these large countries,
Japan (JPN), China (CHN) and Germany (DEU) impose the highest degree of market power
on their median import. As we may expect, regions with the least market power are the
small Caribbean (CAR) and South American (SAM) countries. One surprising feature of
the summary statistics is the relatively high estimated market power for African (AFR) and
Asian (ASA) countries on average. Subsequently we will explain these moments in the data
by controlling for intuitive patterns of market power. Yet it is worth noting here that these
surprising results are a direct consequence of compositional heterogeneity in the goods and
partners that comprise importers’ trade. This heterogeneity is precisely the feature of the
data the estimator was tasked with uncovering.
4.1
Product Differentiation and Market Power
Here we consider some tests of our intuition regarding various relationships between importerexporter and country-good characteristics that we would expect to impact market power.
First we explore the relationship between product differentiation and market power and the
substitutability of goods. Then we examine the role of shares of countries’ trade on forming
market power across goods.
Generally, we believe importers to have more market power in differentiated goods since
the equilibrium price of a differentiated good may be more affected by a single importer. For
20
instance, if US demand for Japanese autos falls and the price of Japanese auto exports decrease globally, there will be relatively weak substitution by other countries toward Japanese
autos. Conversely, we would expect strong substitution by other countries with price fluctuations if the good is more homogenous (e.g., steel sheet). A more direct comparison can be
made with the demand elasticity. We expect homogenous goods to be more substitutable,
and thus have higher estimated demand elasticities.
To analyze whether product differentiation is related to the estimates of demand and supply elasticities, Table 3 presents various reduced form regressions of our inverse export supply
and import demand elasticities on indicators of product differentiation defined according to
Rauch (1999).
Table 3: Trade Elasticities and Product Differentiation
I
log(ωgv
)
(1)
Reference Good
Homogeneous Good
Importer FEs
Importer × Non-Differentiated Good FEs
R2
F stat
N
(2)
∗∗∗
−1.091
(0.013)
−2.120∗∗∗
(0.028)
log(σgI )
(3)
∗∗∗
−1.109
(0.013)
−2.160∗∗∗
(0.028)
(4)
∗∗∗
(5)
∗∗∗
(6)
∗∗∗
−0.391
0.046
0.044
0.040∗∗∗
(0.065)
(0.001)
(0.001)
(0.007)
−1.443∗∗∗ 0.187∗∗∗ 0.186∗∗∗ 0.181∗∗∗
(0.069)
(0.003)
(0.003)
(0.007)
No
No
Yes
No
Yes
Yes
No
No
Yes
No
Yes
Yes
0.011
5688.76
1144288
0.018
942.76
1144288
0.019
517.57
1144288
0.003
2025.48
1144288
0.032
2388.52
1144288
0.035
1343.04
1144288
Notes: Rauch (1999)’s conservative classification is used to indicate differentiated, reference priced, and
homogeneous goods (the liberal classification yields identical results). Robust standard errors are in parentheses where, * p<0.10, ** p<0.05, *** p<0.01 indicate significance.
Considering the long right tail of the distributions of our elasticity estimates, our regressions are run in logs. Regardless of specification, Table 3 demonstrates that importers have
monotonically decreasing market power in markets for less differentiated goods. Column (1)
suggests that the average differentiated good is supplied with an inverse export supply elasticity that is twice the size of the average homogenous good. The degree of heterogeneity in
our estimates allows us to analyze whether certain countries have different degrees of market
power across types of goods.
21
The preceding regressions include importer fixed effects to examine whether the relationship between product differentiation and trade elasticities varies across countries. Column
(2) begins by adding importer fixed effects. Column (3) pushes the data further by exploring
whether countries have differential market power across types of goods by including importer
fixed effects interacted with a dummy indicating whether a good is classified as differentiated
or not. In all of these regressions countries have higher market power for differentiated goods
on average. Columns (4)-(6) extend the exercise to the import demand elasticity estimates.
We can see that our estimates of σgI are highly correlated with product differentiation. As
we would expect, differentiated goods have the lowest elasticities of substitution, and in increasing order, reference and homogenous goods have higher elasticities. Columns (5) and
(6) include importer fixed effects to examine the mix of goods countries tend to import, with
no change to the preceding result.
The fixed effects in the preceding regression can be used to rank countries by their average
market power across goods. Table 4 presents the implied ordering of each region’s market
power by these estimated fixed effects. We can see that the Germany, the US and China
have the highest degree of market power on average. Outside of the US, North American
countries have noticeably low market power. This feature is likely due to their strong ties
with and inability to exert market power on US imports.
For differentiated goods, market power rankings at the top have a similar ordering to
that of all goods. One noticeable departure is market power in Asian (ASN) countries over
differentiated goods. Overall, Asian countries rank eighth, but in terms of differentiated
goods they have the fourth highest degree of market power. This is quite intuitive as this
region contains countries such as Taiwan and Korea which are significant importers of hightech electronics. Additionally, this region’s reliance on imported commodities leads to one
of the lowest levels of market power across non-differentiated goods. The exact opposite
story is true for India. They have one of the lowest levels of market power for differentiated
goods, and the highest degree of market power for non-differentiated goods. India’s imports
of non-differentiated goods are predominantly supplied by regional trade partners, of which
22
India is an important export destination. These ranking thus support the idea that market
power varies across types of goods and the composition of imports.
Table 4: Rankings of Average Market Power
Market Power Ranking
Importer
DEU
USA
CHN
JPN
GBR
FRA
ITA
ASA
CAN
AUS
OCE
RUS
AFR
MEX
BRA
IND
SEU
NWU
CAR
SAM
All
Goods
Differentiated
Goods
Non-Differ
Goods
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
3
2
5
6
8
9
4
13
12
10
11
7
14
16
18
17
15
19
20
9
4
12
8
2
7
10
17
5
6
13
13
19
11
3
1
18
20
15
16
Notes: Rankings are determined by sorting the
fixed effects in Table 3. All Goods sorts the fixed
effects from Column (2), while Differentiated and
Non-Differ sort the fixed effects from Column (3).
Table 5 ranks the average estimated demand elasticities for each country. China and
other Asian countries have oriented their imports toward more homogeneous goods. Table 5
bears this result. On average Asian countries have the most substitutable imports followed
by Southern (SEU) and Northern European (NWU) then China. Developed countries tend to
yield the opposite patterns. The UK, France, and US import some of the least substitutable
goods. Save for France, which imports the second most substitutable homogeneous goods,
these developed countries tend to import less substitutable differentiated and homogeneous
goods. Notably, these fruitful comparisons are a product of the degree of heterogeneity in
our estimates, which allows us unprecedented insight into the composition of types of goods
traded across and within countries.
23
Table 5: Rankings of Average Substitutability of Goods
Substitutability Ranking
Importer
ASA
SEU
NWU
CHN
RUS
DEU
CAR
SAM
CAN
JPN
OCE
IND
AUS
AFR
ITA
USA
FRA
BRA
GBR
MEX
All
Goods
Differentiated
Goods
Non-Differ
Goods
1
2
3
4
5
6
7
7
9
10
11
12
13
14
15
16
17
18
19
20
1
3
2
4
5
7
13
8
6
9
11
14
12
10
15
16
17
18
19
20
20
14
18
10
11
6
1
9
19
8
7
4
15
16
3
17
2
12
5
13
Notes: Rankings are determined by sorting the
fixed effects in Table 3. All Goods sorts the fixed
effects from Column (5), while Differentiated and
Non-Differ sort the fixed effects from Column (6).
The preceding looks across products to make cross country comparisons. Table 6 looks
within products by including product fixed effects in order to compare our market power
estimates across country pair relationships. Column (1) begins with the assertion that country size, measured by GDP in $US, correlates with estimated market power.20 We see that
large importers have higher degrees of market power. Conditional on country size, we might
expect that importers in remote regions to possess added market power over their network of
trade partners. Column (2) thus adds a measure of importer remoteness to capture regional
market power. We see a stronger correlation between country size and our inverse elasticity,
as well as a strong positive relationship with importer remoteness.
Next Table 6 investigates whether pairwise relationships between countries within and
across goods influences market power. Columns (3) and (4) consider covariates that capture
various measures of the share of the imports. We expect that large importers of a particular
20
Importer specific measures such as GDP are extracted from CEPII, and averaged over 1984-2006.
24
good possess greater influence on the world market for that good. Column (3) supports this
expectation. Our estimates suggest that going from China’s average share of a product’s
imports (5%) to the US share (16%) implies on average 53% larger inverse export supply
elasticities for a given good. Column (4) demonstrates that importers which are important
for a particular exporter (i.e., they are a large share of an exporter’s trade activity) have
greater market power. Lastly, the heterogeneity of our estimates allow us to look at the
finest level of the importer-exporter relationship. Column (5) highlights that even at the
most disaggregate level, the share of exporter’s exports of the particular product, we find
intuitive patterns. Exporter’s that send a greater share of a particular product to a particular
destination have strong responses to fluctuations in that market as seen by large inverse
export supply elasticities.
Table 6: Inverse Export Supply Elasticities and Market Size and Share
I
log(ωgv
)
Controls
(1)
(2)
∗∗∗
0.038
(0.003)
log(Importer GDP)
log(Importer Remoteness)
(3)
(4)
(5)
∗∗∗
0.280
(0.008)
0.183∗∗∗
(0.006)
4.709∗∗∗
(0.134)
Importer’s Share of Global Imports of the Product
2.768∗∗∗
(0.081)
Importer’s Share of Total Exporter’s Exports Across Products
0.245∗∗∗
(0.038)
Importer’s Share of Exporter’s Exports within Product
R2
F stat
N
0.074
157.51
949559
0.076
662.27
933068
0.078
1237.73
1001144
0.078
1171.77
1001144
0.077
41.45
1001144
Notes: All regressions include industry, defined at the HS4 level, fixed effects. Robust standard errors are in parentheses where, * p<0.10, ** p<0.05, *** p<0.01 indicate significance.
5
Optimal Tariffs
Here we will add to the preceding structural model of trade with heterogeneity a theory of
optimal tariffs following the literature. The incorporation of heterogeneity yields a new form
for the optimal tariff that depends on the composition of trade and distribution of estimated
25
export supply elasticities with an importer good pair. We then evaluate the propensity of
importers’ applied tariffs to follow the theoretical optimal tariff, and how these optimal tariffs
follow our notions of market power uncovered by our heterogeneous elasticity estimates.
5.1
Theory
A benevolent social planner will weigh the efficiency losses against the terms of trade gains
when setting tariffs. Generally, the!planner will maximize the sum of household income and
X
X
surplus, or W =
Yh+
ψg . Here we follow the assumptions laid out by Grossman
h
g
and Helpman (1994) to focus the analysis. The numeraire is freely traded in a perfectly
competitive market, produced according to constant returns to scale using only labor as an
input, and its price is normalized to unity. These assumptions taken together imply wages
equal unity. Additionally, domestic varieties are produced under constant returns to scale
using labor and a specific factor earning quasi-rent πdI . Lastly, revenues from the tariff placed
on a good are redistributed uniformly as rgI . Individuals own a unit of labor and a subset of
them own at most one unit of specific capital.
Normalizing the population to one in conjunction with our assumptions behind the numeraire yields the social welfare problem,

argmax W = 1 + πd +
τgI
XX
g
v
|

 X σ1gI

τ p xgv + log 
bgv x

I
g
∗
gv
I −1
σg
I
σg
gv
v
{z
I
rg
}
|


I
σg
I −1
σg


 − pgv xgv .

{z
(10)
}
ψg
Since worker rents are separable, the above problem amounts to choosing tariffs for each
good that weight tariff revenues from terms of trade gains with changes in consumer surplus.
Noting
∂ψg
∂τgI
gv
= −xgv ∂p
, by the envelope theorem, and
∂τgI
∂pgv
∂τgI
∂p∗
∗
= (1 + τgI ) ∂τgv
I + pgv , from the
g
relation between shipped and delivered prices, we can derive the first order condition in
26
general from (10) for each good,
X
gv
τgI p∗gv ∂x
− xgv
∂τgI
∂p∗
gv
∂τgI
= 0.
v
The first term above are the efficiency costs associated with the tariff as consumers decrease
their imports as exporters pass through the cost of the tariff. The second term represents
terms of trade gains as exporters partially absorb the tariff in their shipped price. It will be
helpful to rewrite the above in elasticities,
X ∂x
I
gv τg
∂τgI xgv
−
I
∂p∗
gv τg 1
I
∂τgI p∗
gv τg
= 0.
(11)
v
Next we simplify Equation (11). Clearing the import and export market implies,21
I
I
p∗gv = ϕgv (1 + τgI )−σg Pgσg −1
The term ϕgv ≡
I φI b
ξX
g gv
I )
exp(−ηgv/ωgv
I
ωgv
I σI
1+ωgv
g
.
(12)
is comprised of unobservable variety specific characteristics that
are independent of the tariff. Solving for the aggregate price level allows us to represent
individual prices as a function of tariffs. To do so, we aggregate the individual variety
prices given by the market clearing condition in (12) to match the CES price index.22 This
aggregation yields,
1
I
Pg = (1 + τgI ) 1+ωg Φg .
(13)
In order to aggregate prices, we must normalize prices relative to an “average” variety that
charges a price equal to the price index. Let this average variety be produced with technology
21
The market clearing condition equates import demand with export supply curves and is given by
I
I
I I −σg σg −1
ξX
φg pgv Pg
22
I
= (exp(−ηgv )p∗gv ) /ωgv .
Given that each variety responds differently as dictated by their supply elasticity, this is not a superficial
task. It is, however, key to the calculation of the optimal tariff. The details of the aggregation are relegated
to the appendix.
1
27
denoted ω g .23 The term Φg is an index of variety taste and technology parameters that is
tariff free.24
Combining the price index with the equilibrium condition for prices in (12) yields the
price charged by variety v in terms of the tariff,
p∗gv = (1 + τgI )
I (1+ω I σ I )
−ωgv
g g
I
I
(1+ω I
g )(1+ωgv σg )
I
ωgv
I −1
σg
g
ϕgv Φ
I σI
1+ωgv
g
.
Heterogeneity in supply elasticities highlight the differential responses of the prices of imports
to the tariff.25 Additionally, we can write imports as a function of the tariff and variety
specific characteristics,
I
g
xgv = (1 + τ )
I
−(1+ω I
g σg )
I
I
I)
(1+ω g )(1+ωgv σg
I −1
σg
g
exp(ηgv ) ϕgv Φ
1
I σI
1+ωgv
g
.
Again we can see the significance of heterogeneity in export supply elasticities on variety
level adjustments to trade in response to changes in tariffs.26 These heterogenous responses
will be key to a country’s determination of optimal trade policy, as it has to measure the
welfare contributions of each variety relative to one another when setting tariffs.
We can take the above derivations to Equation (11) to solve for the optimal tariff,
X
p∗gv xgv
I
τgI
−(1+ω I
g σg )
I σ I ) 1+τ I
(1+ω I
)(1+ω
g
gv g
g
+
I (1+ω I σ I )
ωgv
τgI
g g
1
I σ I ) 1+τ I τ I
(1+ω I
)(1+ω
g
gv g
g g
= 0.
v
∗
Then the optimal tariff (τgI ) is given by,
I∗
τg =
I
ωgv
∗
v pgv xgv 1+ω I σ I
gv g
1
P
∗
v pgv xgv 1+ω I σ I
gv g
P
.
(14)
23
The exact value of ω Ig is irrelevant to the calculation of the optimal tariff.
24
Specifically, Φg ≡ ϕg
25
The elasticity of a variety’s price with respect to the tariff is thus,
26
The elasticity of a variety’s exports with respect to the tariff is thus,
I
ωI
g/1+ω g
28
∂log(p∗
gv )
∂log(τgI )
I
−ωgv
(1+ω Ig σgI )
τgI
I σ I ) 1+τ I .
(1+ω Ig )(1+ωgv
g
g
−(1+ω Ig σgI )
τgI
∂log(xgv )
=
.
I
I
I
I
∂log(τg )
(1+ω g )(1+ωgv σg ) 1+τgI
=
In essence, the optimal tariff is a trade weighted average of variety level responses to policy.
The numerator represents the total terms of trade gains of the tariff, while the denominator
are the total efficiency losses in the industry. The planner thus chooses an optimal tariff that
weights the terms of trade gains relative to the efficiency losses by the importance of each
of their trading partners. In the canonical case where the inverse export supply elasticities
are homogenous, we can clearly see that the planner will set a tariff equal to the common
inverse supply elasticity. Here, the planner takes into account the full distribution of export
supply curves along with how they interact with the import demand curve as all varieties
shift in response to a tariff.
5.2
Empirical Evaluation
5.2.1
Evaluating the Impact of Heterogeneity
Here we investigate how incorporating heterogeneity in export supply into optimal trade
policy relates to applied tariffs. The most comparable empirical study to ours is Broda,
Limao and Weinstein (2008) (BLW henceforth). BLW demonstrates a strong relationship
between applied tariffs and terms of trade gains for select countries when export supply
elasticities are homogeneous. We begin our analysis with an apples to apples comparison of
our heterogeneous elasticities and the homogenous elasticities from BLW.27
First, start by narrowing the broader sample in this paper to the subset considered by
Broda, Limao and Weinstein (2008). Table 7 presents summary statistics of the BLW elasticity estimates alongside our heterogeneous elasticities for the subset of countries and years
in the narrowed sample. BLW strategically choose a set of countries at various years before
significant changes in trade policy regimes (i.e., WTO accession). Their sample was chosen in
order to avoid any trade policy effects from structural changes in the policy environment that
would convolute the relationship between optimal and applied tariffs. One noticeable fea27
The original code and estimates from BLW are available at: https://www.aeaweb.org/aer/data/
dec08/20060147_data.zip. Their data include inverse export supply elasticities and applied tariffs
across a subset of developing countries and their imported products.
29
ture of optimal tariff estimates under homogeneity is it is constant over time. Consequently,
being concerned that a regime change such as WTO accession would distort their results
is valid since their optimal tariff estimates cannot adjust to any compositional changes in
trade. Table 7 highlights this key difference between BLW and our heterogeneous estimates.
Notice that in BLW the optimal tariff is exactly the constant inverse export supply elasticity.
By taking into account the composition of trade, our heterogeneous optimal tariff estimates
are orders of magnitude smaller than BLW even though the average supply elasticities are
of similar magnitude.
Table 7: Summary Statistics: Homogeneous and Heterogeneous Export Supply
Inverse Export Supply Elasticity
Heterogeneous
th
Mean
Optimal Tariff
BLW
Mean
†
50
BLW
Mean
50
th
Mean
Corr†
HS4
50
Algeria
Belarus
Bolivia
China
Czech Republic
Ecuador
Latvia
Lebanon
Lithuania
Oman
Paraguay
Russia
Saudi Arabia
Taiwan
Ukraine
739
703
647
1125
1075
753
872
782
811
629
511
1029
1036
891
730
1.03
1.00
0.69
0.77
0.78
0.66
0.99
1.32
0.91
1.86
0.66
0.72
1.04
0.90
1.05
336.26
6.41
117.81
490.52
20.84
92.35
116.66
134.71
87.66
359.96
97.45
138.43
141.93
126.59
25.71
2.96
1.88
2.04
2.05
1.57
2.16
1.28
0.96
1.38
1.37
3.14
1.98
1.77
1.43
2.38
110.61
80.15
98.58
89.02
52.74
96.30
53.42
57.81
63.58
186.33
128.30
47.25
61.57
93.74
77.45
-0.03
0.00
-0.02
0.02
0.00
0.02
0.00
-0.01
0.02
0.01
-0.04
0.00
0.01
0.01
0.00
99%
79%
64%
73%
75%
73%
85%
111%
74%
154%
59%
58%
84%
104%
92%
952%
173%
158%
278%
165%
136%
225%
224%
184%
366%
126%
101%
196%
221%
197%
296%
188%
204%
205%
157%
216%
128%
96%
138%
137%
314%
198%
177%
143%
238%
11061%
8015%
9858%
8902%
5274%
9630%
5342%
5781%
6358%
18633%
12830%
4725%
6157%
9374%
7745%
-0.02
-0.02
0.06
-0.01
-0.03
0.08
-0.05
0.03
0.02
0.02
-0.02
-0.03
0.05
0.06
0.04
Full Sample
1207
0.86
163.98
1.78
75.69
0.00
77%
221%
178%
7569%
0.01
†
Corr
th
Importer
Notes:
50
Heterogeneous
th
Corr indicates the raw Pearson correlation between the Heterogeneous and BLW estimates.
Table 7 also illustrates a significant amount of heterogeneity in both optimal tariff and
elasticity estimates that BLW is unable to capture. These differences result in a near zero
correlation between the methods for both the inverse export supply elasticity and the optimal
tariff. The lack of correlation even extends to more disaggregate relationships including
within countries and within goods, which demonstrates that the heterogeneity absorbed by
BLW is substantial.
Differences in the distributions of the heterogeneous and homogeneous elasticity estimates
extend into our analysis of optimal trade policy. Using the actual data from BLW, Columns
30
(1), (3), (5) and (7) of Table 8 replicate some of the key results in Table 7 of Broda et al.
(2008).28
Table 8: Optimal Tariffs: Homogeneous versus Heterogeneous Export Supply
Dependent Variable
Average Tariff at Four-Digit HS (%)
Fixed Effects
Country
(1)
Optimal Tariff: BLW
I∗
(2)
Belarus
Bolivia
China
Czech Republic
Ecuador
Latvia
Lebanon
Lithuania
Oman
Paraguay
Russia
Saudi Arabia
Taiwan
Ukraine
AdjR
2
(5)
∗∗∗
(6)
(7)
(8)
∗∗∗
0.0004
(0.0000)
∗∗∗
∗∗∗
0.0071
(0.0022)
log(Optimal Tariff: BLW)
Algeria
(4)
0.0003
(0.0001)
Optimal Tariff: τg
log(Optimal Tariff:
Country and Industry
(3)
0.0076
(0.0020)
∗∗∗
0.1206
(0.0420)
I∗
τg )
∗∗∗
0.1687
(0.0407)
∗∗∗
23.8
(0.6)
∗∗∗
12.3
(0.2)
∗∗∗
9.7
(0.0)
∗∗∗
37.8
(0.7)
∗∗∗
9.4
(0.5)
∗∗∗
9.8
(0.1)
∗∗∗
7.2
(0.3)
∗∗∗
17.1
(0.5)
∗∗∗
3.6
(0.2)
∗∗∗
5.6
(0.3)
∗∗∗
16.0
(0.4)
∗∗∗
10.6
(0.3)
∗∗∗
12.1
(0.0)
∗∗∗
9.6
(0.2)
∗∗∗
7.3
(0.2)
19.6
(0.2)
∗∗∗
11.4
(0.1)
∗∗∗
9.5
(0.0)
∗∗∗
33.2
(0.2)
∗∗∗
10.0
(0.2)
∗∗∗
8.3
(0.1)
∗∗∗
5.9
(0.1)
∗∗∗
17.8
(0.1)
∗∗∗
3.4
(0.1)
∗∗∗
5.8
(0.1)
∗∗∗
14.5
(0.2)
∗∗∗
10.8
(0.0)
∗∗∗
12.2
(0.0)
∗∗∗
9.4
(0.0)
∗∗∗
6.3
(0.0)
23.6
(0.6)
∗∗∗
12.2
(0.2)
∗∗∗
9.6
(0.0)
∗∗∗
37.7
(0.7)
∗∗∗
9.3
(0.5)
∗∗∗
9.7
(0.2)
∗∗∗
7.2
(0.3)
∗∗∗
17.0
(0.5)
∗∗∗
3.5
(0.2)
∗∗∗
5.6
(0.3)
∗∗∗
15.9
(0.5)
∗∗∗
10.5
(0.3)
∗∗∗
12.0
(0.0)
∗∗∗
9.6
(0.2)
∗∗∗
7.2
(0.2)
0.1926
(0.0160)
∗∗∗
19.7
(0.2)
∗∗∗
11.6
(0.1)
∗∗∗
9.7
(0.0)
∗∗∗
33.3
(0.2)
∗∗∗
10.1
(0.2)
∗∗∗
8.4
(0.1)
∗∗∗
6.0
(0.1)
∗∗∗
17.9
(0.1)
∗∗∗
3.6
(0.1)
∗∗∗
5.8
(0.1)
∗∗∗
14.7
(0.2)
∗∗∗
10.9
(0.0)
∗∗∗
12.3
(0.0)
∗∗∗
9.4
(0.0)
∗∗∗
6.4
(0.0)
0.611
0.612
0.611
0.613
∗∗∗
∗∗∗
∗∗∗
∗∗∗
24.6
(0.9)
∗∗∗
12.6
(0.7)
∗∗∗
10.1
(0.7)
∗∗∗
38.2
(0.9)
∗∗∗
9.7
(0.8)
∗∗∗
10.3
(0.7)
∗∗∗
7.2
(0.7)
∗∗∗
17.1
(0.8)
∗∗∗
3.6
(0.7)
∗∗∗
5.6
(0.7)
∗∗∗
16.3
(0.8)
∗∗∗
10.8
(0.7)
∗∗∗
12.4
(0.7)
∗∗∗
10.3
(0.7)
∗∗∗
8.0
(0.7)
19.5
(0.3)
∗∗∗
10.2
(0.2)
∗∗∗
8.6
(0.2)
∗∗∗
32.5
(0.3)
∗∗∗
8.8
(0.3)
∗∗∗
7.9
(0.2)
∗∗∗
4.4
(0.2)
∗∗∗
15.9
(0.3)
∗∗∗
1.9
(0.2)
∗∗∗
4.1
(0.3)
∗∗∗
13.1
(0.3)
∗∗∗
9.0
(0.2)
∗∗∗
10.4
(0.2)
∗∗∗
8.3
(0.2)
∗∗∗
5.4
(0.2)
24.3
(0.9)
∗∗∗
12.5
(0.7)
∗∗∗
9.9
(0.7)
∗∗∗
38.0
(0.9)
∗∗∗
9.6
(0.8)
∗∗∗
10.2
(0.7)
∗∗∗
7.2
(0.7)
∗∗∗
17.0
(0.8)
∗∗∗
3.5
(0.7)
∗∗∗
5.6
(0.7)
∗∗∗
16.1
(0.8)
∗∗∗
10.7
(0.7)
∗∗∗
12.2
(0.7)
∗∗∗
10.1
(0.7)
∗∗∗
7.8
(0.7)
0.1943
(0.0159)
∗∗∗
19.6
(0.3)
∗∗∗
10.4
(0.2)
∗∗∗
8.8
(0.2)
∗∗∗
32.6
(0.3)
∗∗∗
9.0
(0.3)
∗∗∗
8.0
(0.2)
∗∗∗
4.6
(0.2)
∗∗∗
16.0
(0.3)
∗∗∗
2.1
(0.2)
∗∗∗
4.2
(0.3)
∗∗∗
13.4
(0.3)
∗∗∗
9.2
(0.2)
∗∗∗
10.5
(0.2)
∗∗∗
8.4
(0.2)
∗∗∗
5.5
(0.2)
0.660
0.655
0.661
0.655
∗∗∗
∗∗∗
∗∗∗
Notes: Industry dummies are defined by section according the HTS. Robust standard errors are in parentheses, where
* p<0.10, ** p<0.05, *** p<0.01 indicate significance.
Columns (2), (4), (6) and (8) repeat the study with our estimate of the optimal tariff under
heterogeneity. We can see that the relationship between the optimal tariff estimated with
heterogeneous elasticities and applied tariffs in this sample are an order of magnitude larger
than the relationship between the optimal tariff under BLW’s assumptions.
BLW selected this subsample of countries and years in order to isolate importers’ responses to terms of trade motives. They argue that since these countries were yet to joint
28
For a full list of years and countries the data are drawn from Table 3 in Broda et al. (2008).
31
the WTO at the time of their sample, they were more likely to target the optimal tariffs without the impediment of the GATT. Our estimates provide strong support for this argument.
In the BLW subset, we find that doubling the optimal tariff leads to a 15% increase.
To investigate whether trade policy regime changes (e.g., WTO accession) affect the
ability of countries to respond to terms of trade gains with applied tariffs, we add time series
variation to BLW’s data. Data on applied tariffs across country pairs over goods is drawn
from a combination of Trains, the International Customs Tariffs Bureau and the WTO.29
These data span 1984-2007. I combine the data with CEP II, which records when countries
joined the WTO by signing GATT. I then concord the data to the HS4 level and combine
them with Comtrade.
Now we can define the number of years since or until an importer joins the WTO. Table
9 regresses applied tariffs on the log of optimal tariffs across various subsamples of the data.
Each subsample is defined by years around importers’ joining of the WTO. For instance 0
indicates the year of membership, while −5+ indicates the importer will join in 5 or more
years, and 3 are importers that have been WTO members for exactly three years. The
BLW subsample is best approximated by observations where importers will join the WTO
in five or more years (i.e., −5+ ). This subsample presents the strongest relationship between
applied and optimal tariffs, and the coefficient estimates are nearly identical to Table 8.
The relationship between applied and BLW optimal tariffs decreases rapidly as importers
approach WTO accession. In the year that importers join, the estimated relationship is
more than halved when compared to BLW’s subset. This relationship continues to decline,
and disappears by the time the importer has been a member for more than two years. This
result confirms BLW trepidation regarding the effects of policy regime changes. This result is
driven by the fact that both applied tariffs and the composition of trade in countries joining
the WTO changes rapidly. Since BLW estimates of optimal tariffs are constant over time,
they are unable to respond to changes in the composition of terms of trade gains over time.
29
The data were generously furnished by Robert Feenstra and John Romalis. They are the same utilized
by Feenstra and Romalis (2012), which include a detailed description in their Appendix B.
32
Table 9: Optimal Tariffs: The Impact of WTO Membership
Years Since WTO Accession
-5+
BLW
R2
N
τgI
∗
R2
N
-4
∗∗∗
-3
∗∗∗
-2
∗∗∗
-1
∗∗∗
0
∗∗∗
1
∗∗∗
2
∗∗∗
3
∗∗∗
5+
4
∗
0.124
(0.010)
0.446
339520
0.109
(0.013)
0.436
64491
0.066
(0.013)
0.48
65637
0.066
(0.011)
0.491
74185
0.064
(0.010)
0.506
79571
0.050
(0.009)
0.482
84097
0.051
(0.009)
0.446
86697
0.036
(0.009)
0.386
90333
−0.009
(0.008)
0.42
69560
−0.012
(0.007)
0.424
72687
-5+
-4
-3
-2
-1
0
1
2
3
4
0.010∗∗∗
(0.003)
0.425
347404
5+
0.167∗∗∗ 0.119∗∗∗ 0.127∗∗∗ 0.113∗∗∗ 0.117∗∗∗ 0.142∗∗∗ 0.097∗∗∗ 0.097∗∗∗ 0.041∗∗∗ 0.040∗∗∗ 0.034∗∗∗
(0.006)
(0.009)
(0.009)
(0.009)
(0.008)
(0.008)
(0.007)
(0.007)
(0.007)
(0.007)
(0.003)
0.44
0.451
0.495
0.516
0.527
0.522
0.498
0.475
0.498
0.533
0.538
446311
95157
100024
117881
124954
137017
143383
150144
131739
138443
1120274
Notes: Each column regresses applied tariffs on optimal tariffs in the subsample defined by years since WTO accession
∗
(superscript + indicates years or more). BLW is the log of the homogeneous optimal tariff. τgI is the log of the homogeneous
optimal tariff. All regressions include importer and industry fixed effects. Robust standard errors are in parentheses, where
* p<0.10, ** p<0.05, *** p<0.01 indicate significance.
Conversely, our heterogeneous optimal tariffs adjust over time as the composition of trade
changes. The estimated relationship between applied and optimal tariffs with heterogeneity
in the years preceding WTO membership are strongly positive and nearly twice the size of the
homogeneous optimal tariffs estimates with much less variability. In the years following WTO
accession, there is a weakening of the estimated relationship, but our estimates maintain a
strong positive relationship between applied and optimal tariffs that is not present when
we rely on the homogeneous estimates. The adjustment of heterogenous optimal tariffs to
changes in the landscape of trade allows our estimates to identify importers responding to
terms of trade motives even as the composition of these motives have changed. However,
the weakening of this relationship does support the assertion that signing the GATT is an
impediment on the ability of importers to adjust tariffs in response to terms of trade gains.
5.2.2
Applied and Optimal Tariffs Globally
Preceding results warrant a fully inclusive analysis of the relationship between optimal and
applied tariffs. Here we expand the data to the full sample of tariffs and trade flows across
all countries over 1984-2007. We will leverage the ability of the heterogeneous estimates
to adjust to changes in the composition of trade over time to more extensively study trade
33
policy responses to the terms of trade gains described by our optimal tariff estimates.
Table 10: Summary Statistics: Optimal and Applied Tariffs
∗
Applied Tariff†
Importer
Optimal Tariff (τgI )
Mean
Median
Rank
Mean
Median
Rank
AUS
BRA
CAN
CHN
DEU
FRA
GBR
IND
ITA
JPN
MEX
RUS
USA
9.01%
24.30%
7.27%
24.30%
6.43%
6.60%
6.53%
47.14%
6.28%
5.81%
14.67%
11.54%
4.82%
5.83%
17.10%
6.52%
21.97%
6.17%
6.34%
6.33%
37.49%
6.13%
1.92%
13.12%
10.06%
3.79%
12
2
14
3
17
15
16
1
19
20
6
9
21
115.4%
112.2%
161.3%
1189.6%
91.8%
100.6%
93.4%
93.9%
95.2%
130.2%
207.2%
105.3%
100.4%
61.9%
67.5%
64.2%
73.6%
62.4%
62.8%
64.1%
59.5%
59.4%
68.6%
95.9%
61.9%
63.2%
13
14
11
4
21
16
20
19
18
12
8
15
17
AFR
ASA
CAR
NWU
OCE
SAM
SEU
17.93%
13.75%
14.67%
6.39%
7.86%
11.54%
9.77%
15.00%
8.00%
15.18%
6.04%
7.17%
10.61%
8.73%
4
7
5
18
13
8
11
3858.5%
870.2%
7186.6%
206.0%
7940.3%
232.7%
174.3%
112.4%
118.7%
69.0%
93.9%
74.6%
63.7%
84.4%
3
5
2
9
1
7
10
WLD
10.30%
7.33%
10
787.9%
78.1%
6
Notes: † Applied tariffs are from Feenstra and Romalis
(2012)
∗
over 1984-2007. For exposition, the top 1% of τgI are dropped.
Mean is the average within and then across years.
Table 10 presents summary statistics of the applied and optimal tariffs across regions in
the data. Within sample rankings of the average tariffs are also presented. Comparing the
applied and optimal tariff rankings in the sample supports the idea that the optimal tariffs
track applied tariffs quite well. Countries setting some of the largest tariffs include China
and other Asian countries along with African and Caribbean countries. These countries
also have some of the largest predicted optimal tariffs. More developed countries tend to set
much lower tariffs on average. The developed countries setting the lowest tariffs are Germany,
Japan and the US. Surprisingly, even though these countries have the strongest unconditional
34
market power in our estimates (i.e., large average inverse export supply elasticities), they
actually have some of the lowest estimated optimal tariffs. This result is unique in the
literature. Homogeneous estimates of optimal tariffs are unable to reconcile the low tariffs set
by developed countries with their large estimated average inverse export supply elasticities
without incorporating alternative trade policy motives. Here, this feature of the data is
readily explained by the marked heterogeneity across exported varieties mixed with the
composition of these varieties consumed by importers.
While these unconditional patterns in the data are supportive of the predicted link between applied and optimal tariffs, we can establish a causal link in the data through a series
of fixed effect regressions. Table 11 begins by examining whether the correlations between
applied and optimal tariffs established in the previous section is maintained in the full sample. Column (1) regresses applied tariffs on optimal tariffs with only importer and product
fixed effects.
Table 11: The Relationship Between Applied and Optimal Tariffs
Applied Tariff
Controls
log(Optimal Tariff)
(1)
(2)
∗∗∗
(3)
∗∗∗
(4)
∗∗∗
0.204
(0.006)
0.192
(0.006)
Yes
Yes
No
No
No
Yes
Yes
No
Yes
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
No
Yes
0.376
40165.8
11010717
0.717
1065.77
11010717
0.750
970.73
11010717
0.762
61760.52
10153149
Importer WTO
Exporter WTO
Regional Trade Agreement
Product FEs
Importer FEs
Exporter FEs
ProductXImporter FEs
ProductXImporterXExporter FEs
Adj. R2
F
N
0.149∗∗∗
(0.006)
−2.799∗∗∗
(0.018)
−3.433∗∗∗
(0.012)
−2.633∗∗∗
(0.010)
0.126
(0.002)
We see that even in the full sample there is a strong positive relationship between applied
and optimal tariffs. Column (2) pushes the data further by including importer by product
fixed effects. This specification absorbs any importer product specific effects that does not
35
vary over time (e.g., constant endogenous lobbying). The coefficient is identified within
importers across exporters over time. Including these interacted fixed effects strengthens the
relationship between applied and optimal tariffs. The coefficient is positive and significant at
the 1% level, and is nearly twice the magnitude when compared to Column (1). Additionally,
the adjusted R2 almost doubles to 0.715.
Our estimates are the first to produce variation over time in optimal tariffs. Columns
(3) and (4) exploit this variation by controlling for importer by exporter by product fixed
effects, such that our estimates are identified solely by variation over time. This strategy
has the benefit of absorbing any trade policy targeted at a particular exporter of a given
product.30 Column (3) yields nearly identical results to Column (2) suggesting applied tariffs
are mainly determined within importer product pairs. Still, isolating the variation of tariff
changes over time yields a strong positive relationship between applied and optimal tariffs.
Column (4) checks the robustness of Column (3) by including policy regime changes in the
form of importers or exporters signing GATT or a regional trade agreement. These regime
variables are identified by countries that switch status over time. As we should expect,
importers and exporters that sign the GATT or a regional trade agreement set lower tariffs.
Even after controlling for these regime driven motives of tariff setting there is still a strong
positive relationship with optimal tariffs. In contrast, BLW find that US market power
influences trade policy only for trade barriers not set cooperatively under the WTO. Here
we find that by appropriately measuring market power relative the composition of trade, we
are able to uncover the relationship between applied and optimal tariffs even when these
tariffs are set under the WTO.
Time series variation in our estimates allows us a new avenue of control unavailable under
homogeneity. Eliminating any importer by exporter by good motives driving applied tariffs,
identifies a strong causal relationship between market power as embodied by optimal tariffs
and applied tariffs even after controlling for structural changes in how policy is set.
30
A nice discussion of one such policy is presented by Feenstra and Taylor (2014). Page 233 discusses the
2009 tariffs applied by the US on tire imports that targeted Chinese exports.
36
6
Conclusion
After adapting a general model of trade and trade policy to incorporate exporter and importer heterogeneity, we construct a flexible structural estimator of the underlying heterogeneous export supply and import demand elasticities. The estimates produce intuitive
relationships with expected patterns of importer and exporter market power. Our estimates
and theory imply a new measure for the optimal tariff set by an importer. These optimal
tariffs are strongly correlated with applied tariffs across a plethora of dimensions of the data.
Additionally, the rich detail of the estimates and theory allow us to meaningfully decompose
the channels of tariff setting across countries and products. Amongst other things, the data
display intuitive patterns of importers targeting goods that generate pronounced terms of
trade gains with higher tariff rates.
Going forward, the unmatched level degree of heterogeneity in the trade elasticity estimates produced here opens doors to new understanding of a host of prominent theories.
Supply elasticities are fundamental to evaluating core channels of globalization such as the
degree of passthrough between countries (as in Goldberg and Knetter (1997)) and our estimates of trade indexes (restrictiveness as in Anderson and Neary (1996) and prices as
in Feenstra (1994)). The tractability of the estimator constructed in this paper lends itself naturally to extending these prevailing theories of inter-country relationships to include
heterogeneity.
37
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Studies .
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Economics 121(2), pp. 541–585.
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850.
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Role of Quality, Scope, Markups, and Cost’, nber.org .
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Record 38(83), pp. 369–72.
Leamer, E. (1981), ‘Is it a demand curve, or is it a supply curve? Partial identification through inequality
constraints’, The Review of Economics and Statistics 63(3), pp. 319–327.
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Mimeo .
38
Appendix
A
Price Index Derivation
Recall that Pg =
X
I
1−σg
!
bgv pgv
1
I
1−σg
is the standard CES price index. We need to transform then aggregate the individual variety prices given
v
by the market clearing condition. First transform the market clearing prices as,
I
I
I 1−σg
(1 + τg )
I
∗1−σg
bgv pgv
I
1−σg
= (1 + τg )
= (1 + τg
I σ I −1
−σg
g
Pg
bgv
I
I
1−σg
I σI
1+ωgv
g
)
I −1
σg
ϕgv Pg
bgv
I
! ωgv (1−σg )
ϕgv (1 + τg )
I σI
1+ωgv
g
I
! ωgv (1−σg )
I σI
1+ωgv
g
.
Aggregating to match the form of the CES price index yields,
I
I
1−σg

X
1+ωI σI

gv g b
Pg = 
1 + τg
gv
 v
I −1
σg
ϕgv Pg
I

I σI
1+ωgv
g




! ωgv (1−σg )
1
I
1−σg
I
Taking logs of both sides and isolating an arbitrary variety (denoted by o with export supply elasticity ω go ) yields,

I
I
! ωgo (1−σg )
I −1
I
σg
1+ω I
go σg
ϕgo Pg
I
I



I
1−σg




I
1
1+ω I
σg
go
log 
bgo
log(Pg ) =
(1
+
τ
)

g
I 

1 − σg



I
1−σg
! ωgv (1−σg )
I −1
P
I σI
I σI
σg
1+ωgv
 (1 + τ ) 1+ωgv
g
g b
ϕgv Pg
gv
g


 v


+
log


I
I
I

1−σg

! ωgo (1−σg )

I −1
I
I
σg

1+ω I
σg
1+ω I
σ
go
go g b
(1 + τg )
go ϕgo Pg











The goal is to solve for the price index solely as a function of the tariff and market characteristics. Separating the last term above and
applying the market clearing price condition for variety o produces,

1
1

I
I 1−σg
1+ω I

go σg b
log(Pg ) = log (1 + τg )
go

I −1
σg
ϕgo Pg
!
ωI
go
I
1+ω I
go σg








Pg


 + log 


1

 1−σI

g
bgo
(1 + τg )p∗
go
With a little algebra we can eliminate the unobservable component of demand for variety o, bgo . Additionally, we will assume there exists
a variety of import
! exactly the CES average price in the importing country and that this variety is variety o. Consequently,
! that charges
Pg
Pg
log
= 0 and,
= log
(1 + τg )p∗
pgo
go
log(Pg ) =
1
I
1 + ωI
go σg
log(1 + τg ) +
I
ωI
go (σg − 1)
I
1 + ωI
go σg
log(Pg ) +
ωI
go
I
1 + ωI
go σg
log(ϕgo )
Solving for the log of the price index yields,
log(Pg ) =
1
1+
ωI
go
I
log(1 + τg ) +
ωI
go
1 + ωI
go
log(ϕgo )
31
Now we can rewrite the price index solely as a function of the tariff, elasticities and variety unobservables,
1
I 1+ω I
g
Pg = (1 + τg )
31
Φg .
(15)
For those following Broda et al. (2006), the result in Equation (15) is similar to an index of unobservable variety specific
I I
1+σg
ω go
ωI
go
1+ω I
go
shocks as, Φg ≡ ϕgo

I
I
ωgv
(1−σg
)

I
(1+ω I
go )(1−σg )
X
1+ω I σ I 
'
bgv ϕgv gv g 


, which is how Broda et al. (2006) represent the price index.
v
39
B
Derivation of Estimating Equations
B.1
Importer Demand
Demand for any variety of imported good g in country I is given by,
pI←V
gvt
φI
g (bt )
xgvt =
!1−σI
g bgvt E I
gt
I←V
pgvt
,
which leads to within destination market shares of the form,

I←V
sgvt
=
pI←V
gvt xgvt
P
I←V
v pgvt xgvt

=
1−σ I
g
pI←V
gvt
I

bgvt Egt
φI
(b
)
t
g
pI←V
gvt
φI
g (bt )
=
I
Egt
!1−σI
g
bgvt
First we take logs to simplify the algebra. Then we first difference shares (denoted ∆) to eliminate time specific unobservables,
I←V
∆log(sgvt
I
I
I←V
) = ϕgt + 1 − σg ∆log(pgvt ) + ∆log(bgvt ),
I
I
I
σg − 1 ∆φg (bt ). Note that the above still contains good specific unobservables ϕgt . Thus, we select a reference variety k and
difference once more (denote reference differences by superscript k) which yields,
I
where ϕgt =
k
I←V
∆ log(sgvt
I
)=
I
k
I←V
I
1 − σg ∆ log(pgvt ) + gvt
(16)
k
where gvt = ∆ log(bgvt ) are first and reference differenced unobservable variety specific taste shocks.
B.2
Exporter Supply
Given monopolistically competitive exporters we can write exporter V ’s share of total export supply as,
I←V
sgvt
=
pI←V
gvt xgvt
P
I←V
v pgvt xgvt
pI←V
gvt
I +1
ωgv
I
ωgv
exp
=
P I←V v pgvt
I +1
ωgv
I
ωgv
exp
−ηgvt
I
ωgv
!
−ηgvt
I
ωgv
!
We follow the same approach as before and first difference to obtain,
I←V
∆log(sgvt
I +1
ωgv

where
I
ψgt
X ωI

I←V
gv
= ∆log 
pgvt
 v
I
) = ψgt +
I +1
ωgv
I←V
∆log(pgvt
I
ωgv
η
) + ∆ gvt
I ,
ωgv

exp
−ηgvt
I
ωgv
!


I
. Then, to eliminate good specific unobservables (ψgt ) we select the same variety k as

above and difference. This yields,
k
I←V
∆ log(sgvt
I
k ηgvt
I
ωgv
where ρgvt = ∆
B.3
)=
I +1
ωgv
I←V
∆log(pgvt
I
ωgv
)−
I +1
ωgk
ωI
gk
I←K
∆log(pgkt
I
) + ρgvt ,
(17)
are first and reference differenced unobservable supply shocks.
Estimating Equation: Importer Perspective
Assuming supply and demand shocks are uncorrelated, we can multiply the residuals from supply and demand for the importer to generate the
following estimating equation,
I
I
k
I←V 2
ρgvt gvt =∆ log(sgvt
I
k
I←V
) − (1 − σg )∆ log(sgvt
+
I +1
ωgk
k
I←V
∆ log(sgvt
ωI
gk
−
I +1)(1−σ I )
(ωgk
g
k
I←V
∆ log(pgvt
ωI
gk
I←K
)∆log(pgkt
)+
k
I←V
)∆ log(pgvt
)−
I +1
ωgv
k
I←V
∆ log(sgvt
I
ωgv
I +1)(1−σ I )
(ωgv
k
I←V
g
∆ log(pgvt
I
ωgv
I←K
)∆log(pgkt
40
).
I←V
)∆log(pgkt )
I←V
)∆log(pgvt
)
k
I←V 2
Simplifying and solving for ∆ log(pgvt
k
I←V 2
∆ log(pgvt
"
I
where E[ugvt ] ≡ E
)
=
I ρI
I
ωgv
gvt gvt
I )(σ I −1)
(1+ωgv
g
)
we obtain
I
ωgv
k
I←V 2
I )(σ I −1) ∆ log(sgvt )
(1+ωgv
g
+
k
I←V
1
I −1 ∆ log(sgkt
σg
+
I −ω I
ωgv
k
I←V
gk
∆ log(pgvt
I )
ω I (1+ωgv
gk
+
I
ωgv
I
1+ωgv
I←V
)∆log(pgvt
)+
k
I←V
∆ log(sgvt
k
I←V
)∆ log(pgvt
)
I (1+ω I )
ωgv
k
I←K
I←K
gk
∆ log(sgkt )∆log(pgkt )
I )(σ I −1)
ω I (1+ωgv
g
gk
I←K
)∆log(pgkt
I
) + ugvt ,
(18)
#
= 0. As described in the text, we consistently estimate Equation (18) using the 2SLS procedure describe
by Feenstra (1994), which maps the data into hyperbolae.
B.4
Exporter Demand
To achieve identification, we need to follow a similar procedure as above from the exporter’s perspective. For any good g and exporter V , demand
in destination I is given by,
→I
pV
gvt
φI
g (bt )
xgvt =
!1−σI
g bgvt E I
gt
V →I
pgvt
,
which leads to across destination market shares of the form,
1−σ I
→I
g
pV
gvt
I

bgvt Egt
I
φg (bt )

1−σ I
g
pV →I
P
I
 gvt

bgvt Egt
I φI (b )
t
g

V →I
sgvt
=

→I
pV
gvt xgvt
P
V →I
p
I gvt xgvt
=
=
→I
pV
gvt
φI
(b
t)
g
!1−σI
I
g bI
gvt Egt
Xgvt
.
Taking logs and first differencing yields,
V →I
∆log(sgvt
I
Egt
Xgvt
) = ∆log
!
I
I
I
V →I
I
+ σg − 1 ∆log(φg (bt )) + 1 − σg ∆log(pgvt ) + ∆log(bgvt )
To eliminate exporter specific effects Xgvt , we choose a reference destination j and difference to obtain
V →I
j
∆ log(sgvt
)=
J
V →J
V
I
V →I
1 − σg ∆log(pgvt ) − 1 − σg ∆log(pgvt ) + gvt ,
(19)

I −1
σg
I
I
I
 bgvt Egt φg (bt )

= ∆log  J
 are first and reference differenced unobservable demand shocks.
σ J −1
b
EJ

where
B.5
V
gvt
gvt
gt φJ (bt ) g
g
Exporter Supply
The share of total export supply from country V to country I is given by,
V →I
sgvt
V →I
p
xgvt
= P gvt
=
V →I
I pgvt xgvt
I −w
ωgv

!
I
σ I −1
−ηgvt
ωgv
 g

I exp
I
σg
ωgv
I
ωgv −w 
!
I
σ I −1
−ηgvt
P V →I ωgv
 g

I pgvt
I exp
I
σg
ωgv
V →I
pgvt
.
Taking logs and first differencing yields
V →I
∆log(pgvt

X 
V
V →I
where ψgt = ∆log 
pgvt

I −w
ωgv
I
ωgv
V
) = ψgt +
I
ωgv
I +1
ωgv
V →I
∆log(sgvt
η
) + ∆ gvt
I ,
ωgv

I −1
σg
I exp
σg
I
−ηgvt
I
ωgv
!!


. To eliminate exporter specific effects, we choose a reference destination j and

difference to obtain,
j
V →I
∆ log(pgvt
)=
I
ωgv
V →I
I +1 ∆log(sgvt )
ωgv
41
−
J
ωgv
V →J
J +1 ∆log(sgvt )
ωgv
V
+ ρgvt ,
(20)
j ηgvt
I
ωgv
V
where ρgvt = ∆
B.6
are first and reference differenced unobserved supply shocks.
Estimating Equation: Exporter Perspective
Assuming supply and demand shocks are uncorrelated, we multiply the residuals from supply and demand for the exporter to generate the following
estimating equation
ωI
V →J 2
V →I 2
V
V
I
V →I 2
J
ρgvt gvt = σg − 1 ∆log(pgvt ) + σg − 1 ∆log(pgvt ) − I gv ∆log(sgvt )
ωgv −1
!
ωI
ωJ
V →J 2
I
V →I
V →I
gv
− J gv ∆log(sgvt ) + 1 − σg − 1
∆log(pgvt )∆log(sgvt )
I
ωgv +1
−
ωgv +1
I
1 − σg − 1
J
ωgv
J +1
ωgv
!
V →I
∆log(pgvt
V →J
)∆log(sgvt
)+
!
ωJ
V →J
V →J
J
gv
∆log(pgvt )∆log(sgvt ) +
1 − σg − 1
J +1
ωgv
I
J
V →I
V →J
−
σg − 1 + σg − 1
∆log(pgvt )∆log(pgvt )
−
I←V 2
Simplifying and solving for ∆log(pgvt
j
V →I 2
∆ log(pgvt
V
where E[ugvt ] ≡ E
)
=
)
J←V 2
then adding ∆log(pgvt
I
ωgv
V →I 2
I )(σ I −1) ∆log(sgvt )
(1+ωgv
g
)
+
ωI
J
gv
1 − σg − 1
I +1
ωgv
!
I
ωgv
I +1
ωgv
V →I
∆log(sgvt
V →I
)∆log(sgvt
V →J
)∆log(sgvt
)
)
I (σ I −2)−1
ωgv
V →I
V →I
g
I )(σ I −1) ∆log(sgvt )∆log(pgvt )
(1+ωgv
g
J (σ I −2)
1−ωgv
V →J
V →I
g
J )(σ I −1) ∆log(sgjt )∆log(pgvt )
(1+ωgv
g
J
ωgv
V →J 2
J )(σ I −1) ∆log(sgjt )
(1+ωgv
g
+
J (σ J −2)
1−ωgv
V →J
V →J
g
J )(σ I −1) ∆log(sgvt )∆log(pgvt )
(1+ωgv
g
+
I )+(1+ω J )
(1+ωgv
V →I
V →J
gv
I )(1+ω J )(σ I −1) ∆log(sgvt )∆log(sgvt )
(1+ωgv
gv
g
+
J −σ I
σg
g
I −1
σg
V →J
J
ωgv
J +1
ωgv
V →J
∆log(pgvt
to both sides, we obtain
+
∆log(pgjt
+
!
+
V →I
)∆log(pgvt
V
) + ugvt ,
#
" V
ρgvt V
gvt
+
I (σ J −2)−1
ωgv
V →I
V →J
g
I )(σ I −1) ∆log(sgvt )∆log(pgvt )
(1+ωgv
g
+
I −σ J
σg
g
I −1
σg
V →J 2
∆log(pgvt
)
(21)
= 0. Again, we consistently estimate Equation (21) using the 2SLS procedure describe by Feenstra (1994), which
I −1
σg
maps the data into hyperbolae. Now by combining Equations (18) and (21) we can consistently identify all supply and demand elasticities in the
data.
C
Region Classification
42
Table A1: Countries and Regions
ISO
New
ISO
Top GDPs:
AUS
AUS
BRA
BRA
CAN
CAN
CHN
CHN
HKG
CHN
DEU
DEU
FRA
FRA
GBR
GBR
IND
IND
ITA
ITA
JPN
JPN
MEX
MEX
RUS
RUS
USA
USA
African:
BDI
AFR
BEN
AFR
BFA
AFR
BWA
AFR
CAF
AFR
CIV
AFR
CMR
AFR
COG
AFR
COM
AFR
CPV
AFR
DZA
AFR
EGY
AFR
ETH
AFR
GAB
AFR
GHA
AFR
GIN
AFR
GMB
AFR
KEN
AFR
MAR
AFR
MDG
AFR
MLI
AFR
MOZ
AFR
MRT
AFR
MUS
AFR
MWI
AFR
MYT
AFR
NAM
AFR
NER
AFR
NGA
AFR
REU
AFR
RWA
AFR
SDN
AFR
SEN
AFR
STP
AFR
SWZ
AFR
SYC
AFR
TGO
AFR
TUN
AFR
TZA
AFR
UGA
AFR
ZAF
AFR
ZMB
AFR
ZWE
AFR
Asian:
AFG
ASA
ARE
ASA
ARM
ASA
AZE
ASA
BGD
ASA
BHR
ASA
BRN
ASA
BTN
ASA
CYP
ASA
GEO
ASA
IDN
ASA
IRN
ASA
ISR
ASA
JOR
ASA
KAZ
ASA
Country
Australia
Brazil
Canada
China
Hong Kong
Germany
France
UK
India
Italy
Japan
Mexico
Russia
USA
Burundi
Benin
Burkina Faso
Botswana
Central Afr
Cote d’Ivory
Cameroon
Congo
Comoros
Cape Verde
Algeria
Egypt
Ethiopia
Gabon
Ghana
Guinea
Gambia
Kenya
Morocco
Madagascar
Mali
Mozambique
Mauritania
Mauritius
Malawi
Mayotte
Namibia
Niger
Nigeria
Reunion
Rwanda
Sudan
Senegal
Sao Tome
Swaziland
Seychelles
Togo
Tunisia
Tanzania
Uganda
South Africa
Zambia
Zimbabwe
Afghanistan
Arab Emirates
Armenia
Azerbaijan
Bangladesh
Bahrain
Brunei
Bhutan
Cyprus
Georgia
Indonesia
Iran
Israel
Jordan
Kazakhstan
ISO
New
ISO
Country
Asian cont’d:
KGZ
ASA
Kyrgyzstan
KHM
ASA
Cambodia
KOR
ASA
Rep of Korea
KWT
ASA
Kuwait
LBN
ASA
Lebanon
LKA
ASA
Sri Lanka
MDV
ASA
Maldives
MMR
ASA
Myanmar
MNG
ASA
Mongolia
MYS
ASA
Malaysia
NPL
ASA
Nepal
OMN
ASA
Oman
PAK
ASA
Pakistan
PHL
ASA
Philippine
PSE
ASA
Occ. Pales
QAT
ASA
Qatar
SAU
ASA
Saudi Arabia
SGP
ASA
Singapore
SYR
ASA
Syria
THA
ASA
Thailand
TUR
ASA
Turkey
TWN
ASA
Taiwan
VNM
ASA
Viet Nam
YEM
ASA
Yemen
Caribbean:
ABW
CAR
Aruba
ATG
CAR
Antigua
BHS
CAR
Bahamas
CUB
CAR
Cuba
DMA
CAR
Dominica
DOM
CAR
Dominican Rep
GLP
CAR
Guadeloupe
GRD
CAR
Grenada
JAM
CAR
Jamaica
KNA
CAR
Saint Kitt
LCA
CAR
Saint Luci
MSR
CAR
Montserrat
MTQ
CAR
Martinique
TTO
CAR
Trinidad
VCT
CAR
Saint Vinc
Oceania:
COK
OCE
Cook Isds
FJI
OCE
Fiji
KIR
OCE
Kiribati
NCL
OCE
New Caledo
NZL
OCE
New Zealand
PNG
OCE
Papua New
PYF
OCE
French Pol
TON
OCE
Tonga
TUV
OCE
Tuvalu
VUT
OCE
Vanuatu
WSM
OCE
Samoa
South America:
ARG
SAM
Argentina
BLZ
SAM
Belize
BOL
SAM
Bolivia
BRB
SAM
Barbados
CHL
SAM
Chile
COL
SAM
Colombia
CRI
SAM
Costa Rica
ECU
SAM
Ecuador
GTM
SAM
Guatemala
GUF
SAM
French Gui
GUY
SAM
Guyana
HND
SAM
Honduras
NIC
SAM
Nicaragua
PAN
SAM
Panama
PER
SAM
Peru
PRY
SAM
Paraguay
SLV
SAM
El Salvador
SUR
SAM
Suriname
URY
SAM
Uruguay
VEN
SAM
Venezuela
43
ISO
New
ISO
Country
Northern & Western Europe:
ANT
NWU
Neth. Anti
AUT
NWU
Austria
BEL
NWU
Belgium
BLX
NWU
Belg-Lux
CHE
NWU
Switzerland
DNK
NWU
Denmark
EST
NWU
Estonia
FIN
NWU
Finland
FRO
NWU
Faeroe Isd
GRL
NWU
Greenland
IRL
NWU
Ireland
ISL
NWU
Iceland
LTU
NWU
Lithuania
LUX
NWU
Luxembourg
LVA
NWU
Latvia
NLD
NWU
Netherland
NOR
NWU
Norway
SWE
NWU
Sweden
Southern & Eastern Europe:
ALB
SEU
Albania
AND
SEU
Andorra
BGR
SEU
Bulgaria
BIH
SEU
Bosnia Herz
BLR
SEU
Belarus
CZE
SEU
Czech Rep.
ESP
SEU
Spain
GRC
SEU
Greece
HRV
SEU
Croatia
HUN
SEU
Hungary
MAC
SEU
Macedonia
MDA
SEU
Moldova
MKD
SEU
TFYR of Mace
MLT
SEU
Malta
MNE
SEU
Montenegro
POL
SEU
Poland
PRT
SEU
Portugal
ROM
SEU
Romania
SER
SEU
Senegal
SRB
SEU
Serbia
SVK
SEU
Slovakia
SVN
SEU
Slovenia
UKR
SEU
Ukraine