Import Demand Elasticities and Trade Distortions
Hiau Looi Kee
Alessandro Nicita
Marcelo Olarreaga§
Abstract
To study the effects of tariffs on gross domestic product (GDP) one needs import demand
elasticities at the tariff line level that are consistent with GDP maximization. These do not exist.
We modify Kohli's (1991) GDP function approach to estimate demand elasticities for 4,625
imported goods in 117 countries. Following Anderson and Neary (1992, 1994) and Feenstra
(1995), we use these estimates to construct theoretically sound trade restrictiveness indices
(TRIs) and GDP losses associated with existing tariff structures. Countries are revealed to be
30 percent more restrictive than their simple or import-weighted average tariffs would suggest.
Thus, distortion is nontrivial. GDP losses are largest in the United States, China, India, Mexico
and Germany.
JEL classification numbers: F1, F10, F13
Keywords: Import demand elasticities, GDP function, trade restrictiveness, deadweight loss
We are grateful to James Anderson, Paul Brenton, Hadi Esfahani, Rob Feenstra, Joe Francois, Kishore Gawande,
Catherine Mann, William Martin, Jaime de Melo, Christine McDaniel, Peter Neary, Guido Porto, Claudio Sfreddo,
Clinton Shiells, David Tarr, Dominique Van Der Mensbrugghe, L. Alan Winters, and participants at seminars at the
Center of Global Development, the Econometric Society Meetings at Brown University, the Empirical Trade Analysis
Conference at the Woodrow Wilson International Center, PREM week, University of West Virginia, and the World
Bank for helpful comments and discussions. The views expressed here are those of the authors and do not necessarily
reflect those of the institutions to which they are affiliated.
Development Research Group, The World Bank, Washington, DC 20433, USA; Tel. (202)473-4155; Fax:
(202)522-1159; e-mail: hlkee@worldbank.org
Development Research Group, The World Bank, Washington DC, 20433, USA; Tel. (202)473-4066; Fax: (202)522-
1159; e-mail: anicita@worldbank.org
§Development Research Group, The World Bank, Washington, DC 20433, USA, and CEPR, London, UK; Tel.
(202)458-8021; Fax: (202)522-1159; e-mail: molarreaga@worldbank.org
Non-Technical Summary
This paper proposes a methodology that is consistent with GDP maximization in estimating
import demand elasticities for more than 4,000 goods in 117 countries. Import demand is a function
of prices of all goods and aggregate endowments as in Kohli's (1991) GDP function approach. We
found that homogeneous goods have higher elasticites, and point estimates increase as we increase
the level of disaggregation at which elasticities are estimated. Import demand is also more elastic
in large and rich countries. Using the estimated import demand elasticities, we compute the effect
of tariffs on GDP using the theoretically sound trade restrictiveness index (TRI) developed by
Anderson and Neary (1992, 1994) and Feenstra (1995). TRI values are on average 30 percent
higher than simple or import-weigthed average tariffs. GDP losses are largest in the United States,
China, India, Mexico and Germany.
1 Introduction
Import demand elasticities are crucial inputs into many ex-ante analyses of trade reform. To
evaluate the impact of regional trade agreements on trade flows or customs revenue, one needs to
first answer the question of how trade volumes would adjust. To estimate ad-valorem equivalents
of quotas or other non-tariff barriers one often needs to transform quantity impacts into their price
equivalent, for which import elasticities are necessary. Moreover, trade policy is often determined
at much higher levels of disaggregation than existing import demand elasticities.1 This mismatch
can lead to serious aggregation biases when calculating the impact of trade interventions that have
become more of a surgical procedure. Finally, to compare trade restrictiveness and its associated
welfare losses across different countries and time, one would need to have a consistent set of trade
elasticities, estimated using the same data and methodology that, ideally, would be consistent with
trade theory. These do not exist. The closest substitute and the one often used by trade economists
is the survey of the empirical literature put together by Stern et al. (1976). More recent attempts
to provide disaggregate estimates of import demand elasticities (although not necessarily price
elasticities, but Armington or income elasticities) have been country specific and have mainly
focused on the United States. These include Shiells, Stern and Deardorff (1986), Shiells, Roland-
Holst and Reinert (1993), Blonigen and Wilson (1999), Marquez (1999, 2002, 2003), Broda and
Weinstein (2003) and Gallaway, McDaniel and Rivera (2003).
The primary objective of this paper is to fill in this gap by estimating import demand elasticities
for over 4,625 goods (at the six digit of the Harmonized System (HS)) in 117 countries. We use
a methodology that is consistent with trade theory (i.e., imports are a function of prices and
factor endowments), and data sources are identical for all countries and goods. We then use these
estimates to construct theoretically sound measures of trade restrictiveness for 88 countries, based
on Feenstra's (1995) simplification of Anderson and Neary's (1992, 1994, 2003) trade restrictiveness
index (TRI).2 The TRI is the uniform tariff that would maintain welfare at the current level
under the observed tariff structure. Finally, we used the constructed TRI to calculate the overall
1 Trade policy is (almost by definition) often determined at the tariff line level. To our knowledge the only set
of estimates of import demand elasticities at the six digit level of the Harmonized System (HS) that exist in the
literature are the one provides by Panagariya et al. (2001) for the import demand elasticity faced by Bangladesh
exporters of apparel and the elasticities of substitution across exporters to the US by Broda and Weinstein (2003).
2 For the other 29 countries, we had no tariff schedules available.
2
deadweight loss associated with the current tariff structure in each of the 88 countries.
The basic theoretical setup is the production based GDP function approach as in Kohli (1991)
and Harrigan (1997). This GDP function approach takes into account general equilibrium effects
associated with the reallocation of resources due to exogenous changes in prices or endowments,
and has close links to trade theory. Imports are considered as inputs of domestic production, for
given exogenous world prices, productivity and endowments. In a world where a significant share
of growth in world trade is explained by vertical specialization (Yi, 2003), the fact that imports
are treated as inputs into the GDP function -- rather than as final consumption goods as in most
of the previous literature -- seems an attractive feature of this approach.3
While Kohli (1991) focuses mainly on aggregate import demand and export supply functions and
Harrigan (1997) on industry level export supply functions, this paper modifies the GDP function
approach to estimate import price elasticities at the tariff line level (HS six digit). When estimating
elasticities at the tariff line level, dealing with cross-price effects can become insurmountable. In
order to avoid running out of degrees of freedom in the estimation of the structural parameters of the
GDP function, we first re-express each N-good economy into N sets of two-good economies using
properties associated with price indices in translog GDP functions. This transformation allows us
to go from a system of n equations with n price related structural parameters to be estimated in
each equation to a system of n equations with 2 price related parameters to be estimated. Another
practical problem we are facing is that the Harmonized System of trade classification was only
introduced in the late 1980s, so even if we solve the n-good problem, we may still run out of
degrees of freedom if we were to estimate the different parameters using only the time variation in
the data. Thus, assuming that the structural parameters of the GDP function are common across
countries (up to a constant) as in Harrigan (1997), we take advantage of the panel dimension of
the data set by applying within estimators. Finally, as in Kohli (1991), to ensure that second-order
conditions of the GDP maximization program are satisfied we impose the necessary curvature
conditions which ensure that all estimated import demand elasticities are negative. This requires
estimating the parameters of the import share equation using non-linear least squares.
More than 300,000 import demand elasticities have been estimated. The simple average across
3Kohli (1991) argues that most imported products when sold in the domestic market have some domestic value
added embedded, i.e., marketing and transport costs, which justifies the assumption that they are inputs into the
GDP function.
3
all countries and goods is about -1.67 and the median is -1.08. They are generally estimated with
great precision. The median t-statistics (obtained through bootstrapping) is 11.96 (91 percent of
the estimates are significant at the 5 percent level). We also found some interesting patterns in
our estimated import demand elasticities that are consistent with some simple hypothesis. First,
homogenous goods are shown to be more elastic than heterogenous goods. Second, import demand
is more elastic when estimated at the tariff line, rather than at the more aggregate industry level.
Third, large countries tend to have more elastic import demands, due probability to a larger
availability of domestic substitutes. Fourth, more developed countries tend to have less elastic
import demands, mainly driven by a higher share of heterogenous goods in developed countries
import demand. In sum, the estimated import demand elasticities exhibit significant variation
across countries and products that is consistent with some basic hypothesis.
Using the estimated import demand elasticities, we construct the TRI for 88 countries for which
tariff schedules are available. Results suggest that both simple and import-weighted average tariffs
tend to underestimate the restrictiveness of a country's tariff regime by an average of 30 percent.
Thus, GDP losses can be much larger than suggested by average tariffs. In particular, large losses
are found in the United States, China, India, Mexico and Germany.
Section 2 provides the theoretical framework to estimate import demand elasticities, whereas
section 3 describes the empirical strategy. Section 4 discusses data sources. Section 5 presents
the results and explores patterns across goods and countries. Section 6 applies the estimated
import demand elasticities to construct TRIs and deadweight losses associated with existing tariff
structures. Section 7 concludes.
2 Theoretical Model -- GDP Function Approach
The theoretical model follows Kohli's (1991) GDP function approach for the estimation of trade
elasticities. We also draw on Harrigan's (1997) treatment of productivity terms in GDP functions.
We will first derive the GDP and import demand functions for one country. However, assuming
that the GDP function is common across all countries up to a country specific term --which controls
for country productivity differences-- it is then easily generalized to a multi-country setting in the
next section.
4
Consider a small open economy in period t.4 Let St RN+M be the strictly convex pro-
duction set in t of its net output vector qt = q1,q2,...,qN and factor endowment vector vt =
t t t
v1,v2,...,vM 0. For the elements in the net output vector qt, we adopt the convention that
t t t
positive numbers denote outputs, which include exports, and negative numbers denote inputs,
which include imported goods. We consider imported goods and competing domestically produced
goods as differentiated products. Similarly domestic products sold in the domestic market are
differentiated from products sold in foreign markets (i.e., exported).
Given the exogenous world price vector p~t = p~t1,p~t2,...,p~tN > 0, the country specific endow-
ments, vt, and N-dimensional diagonal Hicks-neutral productivity matrix At = diag At1,At2,...,AtN ,
perfect competition leads firms to choose a mixed of goods that maximizes GDP in each period t :
Gt p~t,At,vt max p~t · Atqt : qt,vt St (1)
qt
Gt p~tAt,vt max p~tAt · qt : qt,vt St , (2)
qt
where Gt p~tAt,vt , is the maximum value of goods the economy can produce given prices, Hicks-
neutral productivity and factor endowments in period t. It equals to the total value of output for
exports and final domestic consumption minus the total value of imports (qn < 0 for imports).
t
In other words, the optimal net output vector is chosen to maximize GDP in equilibrium, given
prices, productivity and endowments. We shall refer to the optimal net output vector as the GDP
maximizing net output vector, which includes GDP maximizing import demands.
As shown in Harrigan (1997), Equation (2) highlights that price and productivity enter mul-
tiplicatively in the GDP function, Gt p~tAt,vt . This property allows us to re-express the GDP
function, by defining the productivity inclusive price vector, pt = pt1,pt2,...,ptN > 0 :
Gt pt,vt = max pt · qt : qt,vt St , with (3)
qt
pt p~tAt, and ptn p~tnAtn,n. (4)
Notice that the productivity inclusive price vector, pt, is no longer common across country even
though the world price vector, p~t, is identical across countries. This allows the model to better fit
4 For a discussion of the relevance of the small country assumption when estimating trade elasticities, see Riedel
(1988), Athukorala and Riedel (1994) and Panagariya et al. (2001).
5
the data where different world prices are observed for the same good in different countries. In a
recent study, Schott (2004) successfully explains variation in unit values for goods in the same tariff
line but in different countries with GDP per capita levels. To the extent that GDP per capita is a
proxy for labor productivity, Schott's finding provides support for our productivity inclusive price
level, pt.
For Gt pt,vt to be a well defined GDP function, it is assumed to be homogeneous of degree
one with respect to prices. Moreover, strict convexity of St also ensures that the second order
sufficient conditions are satisfied, such that Gt pt,vt is twice differentiable and it is convex in pt
and concave in vt. To derive import demand function, we apply the Envelope Theorem, which
shows that the gradient of Gt pt,vt with respect to pt is the GDP maximizing net output vector,
qt pt,vt :
Gt pt,vt
t (5)
ptn = qn pt,vt , n = 1,...,N.
Thus if good n is an imported good, Equation (5) would be the GDP maximizing import demand
function of good n, which is a function of prices and endowments. It also implies that an increase
in import prices would reduce GDP (i.e., qn < 0 if n is an imported good). Given that Gt pt,vt is
t
continuous and twice differentiable, and is convex and homogeneous of degree one with respect to
prices, the Euler Theorem implies that qn is homogenous of degree zero in prices, has non-negative
t
own price effects and has symmetric cross price effects:5
qn(pt,vt)
t
2Gt pt,vt
= 0,tn = k . (6)
ptnptk ptn
qn(pt,vt)
t qk(pt,vt)
=
ptk ptn , n = k
In other words, for every final good, including exports, a price increase raises output supply; for
every input, including imports, an increase in prices decreases input demand. In addition, if an
increase in the price of an imported input causes supply of an exported output to decrease, then
an increase in the price of the exported output would increase the demand of the imported input
in the same magnitude.
Equation (5) shows that the GDP maximizing import demand function of good n is a function
5The latter by Young's Theorem.
6
of prices and factor endowments. Thus, the implied own price effects of imports, and the import
demand elasticities, are therefore conditioned on prices of other goods and aggregate endowments
being fixed. Thus, the GDP maximizing import demand functions do not depend on income or util-
ity, unlike the expenditure minimizing Hicksian import demand functions or the utility maximizing
Marshallian import demand functions. This is because, aggregate factor income and welfare are in
fact endogenous to prices and endowments. Such a set up is more relevant for general equilibrium
trade models, but may not be relevant for partial equilibrium micro models which often take aggre-
gate income as exogenous. As a result, comparing the GDP maximizing import demand elasticities
to the existing Hicksian or Marshallian import demand elasticities in the literature may not be
appropriate. Finally, we will not be able to derive income elasticities from the GDP maximizing
import demand functions, but instead, we would be able to estimate the Rybczynski elasticities
from Equation (5) , which shows how import demand reacts to changes in factor endowments.6
To implement the above GDP function empirically, let's assume, without loss of generality, that
Gt pt,vt follows a flexible translog functional form with respect to prices and endowments, where
n and k index goods, and m and l index factor endowments:
N N N
1
ln Gt pt,vt = at00 + at0n lnptn + atnk lnptn lnptk
2
n=1 n=1 k=1
M M M
1
+ bt0m lnvm +
t btml lnvm lnvl
t t
2
m=1 m=1 l=1
N M
+ ctnm lnptn lnvm,
t (7)
n=1 m=1
where all the translog parameters a, b and c s are indexed by t to allow for changes over time. In
order to make sure that Equation (7) satisfies the homogeneity and symmetry properties of a GDP
function, we impose the following restrictions:
N N N
at0n = 1, atnk = ctnm = 0, atnk = atkn, n,k = 1,...,N, m = 1,...,M. (8)
n=1 k=1 n=1
Furthermore, if we assume that the GDP function is homogeneous of degree one in factor endow-
6 See Section 5.3 of Kohli (1991) for a thorough discussion on the various import demand specifications.
7
ments, then we also need to impose the following restrictions:
N N M
bt0n = 1, btnk = ctnm = 0, btnk = btkn, n,k = 1,...,N, m = 1,...,M. (9)
n=1 k=1 m=1
Given the translog functional form and the symmetry and homogeneity restrictions, the deriva-
tive of lnGt pt,vt with respect to lnptn gives us the equilibrium share of good n in GDP at period
t :
stn pt,vt ptnqn pt,vt
t N M
t
Gt (pt,vt) = at0n + atnk lnptk + ctnm lnvm
k=1 m=1
M
= at0n + atnn ln ptn + atnk lnptk + ctnm lnvm, n = 1,...,N,
t (10)
k=n m=1
where stn is the share of imports of good n in GDP (stn < 0 if good n is an input as in the case
of imports). From Equation (10) it can be shown that, if good n is an imported good, then the
import demand elasticity of good n derived from its GDP maximizing demand function is:7
tnn qn pt,vt ptn
t atnn
= (11)
ptn qn
t stn + stn - 1 0, stn < 0.
Thus we can infer the import demand elasticities once ann is properly estimated based on Equation
(10). Note that the size of the import elasticity, tnn, depends on the sign of atnn, which captures
the changes in the share of good n in GDP when price of good n increases by 1 percent:
tnn < -1 if atnn > 0,
= -1 if atnn = 0,
> -1 if atnn < 0.
The rationale is straightforward. If the share of imports in GDP does not vary with import prices
atnn = 0 , then the implied import demand is unitary elastic such that an increase in import
price induces an equi-proportional decrease in import quantities and leaves the value of imports
unchanged. If the share of imports in GDP, which is negative by construction, decreases with
7Cross-price elasticities of import demand are given by:tnk qn pt,vt
t( )ptk= atnk
ptk qn
t stn + stk, n = k.
8
import price atnn < 0 , then the implied import demand is inelastic, so that an increase in import
price induces a less than proportionate decrease in import quantities. Finally, if the share of import
in GDP increases with import prices atnn > 0 , then the implied import demand must be elastic
such that an increase in the price of import induces a more than proportionate decrease in import
quantity.8
3 Empirical Strategy
With data on output shares, unit values and factor endowments, Equation (10) is the basis of our
estimation of import elasticities. In principle, we could first estimate the own price effects, atnn, for
every good according to Equation (10) , and apply Equation (11) to derive the implied estimated
elasticities, since the own price elasticity is a linear function of own partial effects. There are,
however, at least three problems with the estimation of the elasticities using (10). First, there
are literally thousands of goods traded among the countries in any given year. Moreover, there
is also a large number of non-traded commodities that compete for scarce factor endowments and
contribute to GDP in each country. Thus the number of explanatory variables in Equation (10)
could easily exhausts our degrees of freedom or introduce serious collinearity problems. Second,
even after solving this first problem, we could also run out of degrees of freedom given the short
time span of trade data available at the six digit of the HS --which only started being used in the
late 1980s. Finally, there is nothing so far to ensure that the estimated elasticities satisfy second
order conditions of GDP maximization, i.e., there are negative. We tackle these three problems in
turn.
3.1 From an N good economy to N sets of two-good economies
Given that our objective is to estimate the own price effect, atnn, for every good n, we re-express
the N-good GDP function into N "two-good economies"producing goods n and -n :
Gt ptn,pt-n,vt max ptnqn + pt-nq-n : qt,vt St ,
t t (12)
qt
8Kohli (1991) found an inelastic demand for the aggregate US imports with ann < 0, while highly elastic demand
for the durables and services imports of the US, with the corresponding ann > 0, when the aggregate import is broken
down into 3 disaggregate groups.
9
where for every good n, we construct a price index, pt-n, and a quantity index, q-n, such that their
t
product equals the sum of the value of all other goods in GDP,
N
pt-nq-n =
t ptkqk.
t
k=n,k=1
With the appropriate price and quantity indexes of good -n, the translog specification of Equation
(12) and the implied share equations for good n could then be use to estimate the own price effect
of every good n in this two good economy:
ln Gt ptn,pt-n,vt = at00 + at0n ln ptn + at0
-n ln pt-n
1
+ atnn lnptn + at-n-n ln pt-n + atn-n lnptn lnpt-n
2 1 2
2 2
M M M
1
+ bt0m lnvm +
t btml lnvm lnvl
t t
2
m=1 m=1 l=1
M M
+ ctnm lnptn lnvm +
t ct-nm lnpt-n lnvm,
t (13)
m=1 m=1
M
stn ptn,pt-n,vt = at0n + atnn ln ptn + atn-n lnpt-n + ctnm lnvm, n.
t (14)
m=1
For the above two good economy to be equivalent to the N good economy, it is necessary
for Equations (13) and (14) to be equivalent to Equations (7) and (10). This could be true if
ln p-n is constructed in the following way.9 According to Caves, Christensen and Diewert (1982), if
Gt pt,vt follows a translog functional form and assuming that all the translog parameters are time
invariant, atnk = ank, n,k,t, then a Tornqvist price index is the exact price index of Gt pt,vt :
N 1
PT pt,pt-1,vt,vt-1 ptn (stn+stn-1)
2
, (15)
ptn-1
n=1
and is equal to the geometric mean of the theoretical GDP price index Pt pt,pt-1,vt-1
Gt-1(pt,vt )
-1 Gt(pt,vt) . Re-writing Equation (15) by separating price index
Gt-1(pt-1 t-1
,v )and Pt pt,pt-1,vt Gt(pt-1 t
,v )
of good n from the product term, and taking logarithm on both sides of the equations, we obtain
9For a more detailed description see Appendix A.
10
the price of good -n :
N
1 1
lnPT pt,pt-1,vt,vt-1 ptn ptk
= stn + stn-1 ln +
2 ptn-1 2 stk + stk-1 ln
k=n,k=1 ptk-1
1 ptn 1
= stn + stn-1 ln + 1 pt-n1with (16)
2 ptn-1 2 st-n + st--n ln pt--n
N
pt-n1 1 1 ptk
ln (17)
pt--n 1 1 2 stk + stk-1 ln
2 st-n + st--n k=n,k=1 ptk-1.
Thus, in a two-good economy, the overall GDP deflator is the weighted average between the price
changes of good n and the composite good -n. In addition, according to Equation (17) , with
information on the overall GDP deflator and the unit value of good n, the change in the price
index of the composite good -n is the difference between the change in the overall GDP deflator
at period t and the weighted change in the price of good n :
1 1
ln pt-n = lnpt--n +
1 ptn
. (18)
1 1 ln PT pt,pt-1,vt,vt-1 - stn + stn-1 ln
2 ptn-1
2 st-n + st--n
By normalizing prices of all goods, both n and -n, to 1 in the first year of our sample, we can then
construct price indexes for goods n and -n in each sample country.
Imposing the additional assumption that all parameters in the GDP functions are time invariant,
and substituting Equation (17) into Equation (14) and equating Equation (14) with Equation (10) ,
it is clear that the following is necessarily true for the two good economy to be equivalent to the
N good economy for every k = n :
1 stk + stk-1
an-n 2 (19)
1 1 ank, n, and k = n.
2 st-n + st--n
In order words, with the proper construction of lnpt-n according to Equation (18) for every good
n, we can reduce a N-good economy which has N share equations with N price parameters each
into N two good economies, with N share equations with 2 price parameters each. The parameters
between the N-good economy and the two-good economy are related as indicated by Equation (19).
A more detailed proof is provided in the Appendix.
Thus, with the properly constructed lnpt-n and the two good share equation, we reduce the
11
challenging problem of estimating n - 1 cross price effects for each good n into simply estimating
one own price effect, ann, and a cross price effect an-n. We further impose homogeneity constraints
M
to the two good share equation, so that ann + an-n = 0 and ctnm = 0, and express the
m=1
two good share equation in terms of price of good n relative to good -n and factor endowment m
relative to land, l :
M
stn ptn,pt-n,vt = a0n + ann ln ptn vm
t
+ cnm ln (20)
pt-n vl
t + µtn, n.
m=l,m=1
With an additive stochastic error term, µtn, to capture measurement errors, Equation (20) is the
basis used for the estimation of own price effect, ann, and hence own price import elasticity, nn.10
3.2 Using the panel variation in the data
Due to the limited time variation in the data and to take advantage of the panel nature of the
sample, Equation (20) is pooled across countries and years for each good n. We assume that the
structural parameters of the GDP function are time and country invariant (up to a constant) as in
Harrigan (1997). Notice that even though we assume that ann is common across all countries, the
implied own price elasticities will still vary across countries, given that stnc is country specific (see
Equation (11)).
Pooling the data across countries and years and introducing country subscript c in Equation
(20), we further assume that the stochastic term, µtn, has a two way error: one is country specific,
anc, and the other one is year specific, atn:
M
stnc ptnc,pt-nc,vc t ptnc vmc
t
= a0n + ann ln + cnm ln
pt-nc vlc
t + µtnc, n,c, with
m=l,m=1
µtnc = anc + atn + utnc, utnc N (0,n),
M
stnc ptnc,pt-nc,vc t = a0n + anc + atn + ann ln ptnc vmc
t
+ cnm ln (21)
pt-nc vlc
t + utnc, n.
m=l,m=1
Equation (21) allows for country and year fixed-effects, which enable us to capture any system-
10Note that in this two good economy set up, there is a system of two equations for each good, one for n and one
for -n. To avoid singularity in the estimation, we drop the equation for -n such that no cross equation restrictions
are necessary, and the estimation procedure is reduced to a single equation estimation.
12
atic shift in the share equation that is country or year specific. We apply the within estimator to
estimate Equation (21), by appropriately removing the country means and year means from each
variable (and adding back the overall mean), and express all variables in deviation form (with suffix
d) :
M
dstnc = a0n + anndln ptnc vmc
t
+ cnmdln (22)
pt-nc vlc
t + utnc, n.
m=l,m=1
3.3 Ensuring second order conditions
For Equation (22) to be the solution to the GDP maximization program, second order necessary
conditions need to be satisfied (the Hessian matrix needs to be negative semi-definite). Such
conditions are also known as the curvature conditions which ensure that the GDP function is
smooth, differentiable, and convex with respect to output prices and concave with respect to input
prices and endowments. This implies that the estimated import elasticities are not positive (see
Equation (6)), i.e.:
ann stnc 1 - stnc ,c,t,n.
Given that by construction stnc < 0, the above is true if
ann s¯n (1 - s¯n), (23)
where s¯n is the maximum (negative) share in the sample for good n. For all variables we denote
such an observation (the s¯n maximum) with an over-bar. To ensure that the curvature conditions
are satisfied, we first need to difference all observations with respect to the observation where the
curvature condition is most likely to be violated, and add back s¯n, so that the expected value of
the intercept equals the maximum share:
dstnc - ds¯n + s¯n = a0n + ann dln ptnc pn
~
pt-nc - dln p-n
M
vmc
t v¯m
+ cnm dln (24)
vlc
t - dln v¯l + utnc - u,
¯ n.
m=l,m=1
Such a procedure ensure that the expected value of the intercept is equal to the maximum share,
s¯n, without affecting the slope coefficients, ann and cnm. We then impose the constraint provided
13
by Equation (23) , by reparameterizing ann in Equation (24) as follows:
ann = 2nn + a0n (1 - a0n
~ ~ ) ,
where a0n and nn are parameters to be estimated nonlinearly. Thus, the final version of the share
~
equation is
dstnc - ds¯n + s¯n = a ~0n + 2nn + a0n - a20n ptnc pn
~ ~ dln
pt-nc- dln p-n
M
vmc
t v¯m
+ cnm dln ~ (25)
vlc
t - dln + utnc,
v¯l
m=1
where regression error term, utnc, has a normal distribution with expected value of zero and variance
~
2. Given that a0n and is nonlinear with respect to unc
~ ~ ~t , nonlinear estimation techniques are
necessary.
Note that this may not be enough to ensure that all import demand elasticities are negative.
Indeed, if the estimated a0n turns out to be smaller than s¯n, then some of the elasticities may still
~
turn out to be non-negative. In other words, this is not a deterministic setup and s¯n is only the
E(~0n). Thus, when estimating the import share equation prior to differencing with respect to
a
the observation where the second order condition is more likely to be violated, if the error term of
a particular observation is positive, then the estimated elasticity for this observation will also be
positive. In those cases we impose a0n s¯n in the estimation procedure, which ensures that all
~
elasticities are negative. This occurs in less than 3 percent of the sample.
Finally, given that the import demand elasticity is non-linear in the estimated parameters we
estimate the standard errors of the import demand elasticities through bootstrapping (50 random
draws for each six digit HS good).
4 Data
The data consist of import values and quantities reported by different countries to the UN Comtrade
system at the six digit of the HS (around 4,600 products).11 The HS was introduced in 1988, but
11It is available at the World Bank through the World Integrated Trade System (WITS).
14
a wide use of this classification system only started in the mid 1990s. The basic data set consists
of an unbalanced panel of imports for 117 countries at the six digit level of the HS for the period
1988-2002. The number of countries obviously varies across products depending on the presence of
import flows and on the availability of trade statistics at the HS level.
There are three factor endowments included in the regression: labor, capital stock and agricul-
ture land. Data on labor force and agriculture land are from the World Development Indicators
(WDI, 2003). Data on capital endowments are constructed using the perpetual inventory method
based on real investment data in WDI (2003).
The estimation sample did not include tariff lines where the recorded trade value at the at
the six digit level of the HS was below $50,000 per year. This eliminated less than 0.1 percent of
imports in the sample, and it is necessary in order to avoid biasing our results with economically
meaningless imports. The elasticities are constructed following Equation (11), where the import
share is the sample average (i.e., we constrained the elasticities to be time invariant). We also
purged the reported results from extreme values by dropping from the sample the top and bottom
0.5 percent of the estimates.
5 Empirical Results
To be precise, we estimate a total of 315,451 import demand elasticities at the six digit level of the
HS for 117 countries. The simple average across all countries and goods is -1.67 and the standard
deviation is 2.47 suggesting quite a bit of variance in the estimates. Figure 1 shows the Kernel
density estimate of the distribution of all estimated elasticities. The vertical line to the left denotes
the sample mean (-1.67), and the line to the right the sample median (-1.08).
All import demand elasticities are quite precisely estimated. The median t-statistics is around
-11.96. Around 89 percent of the elasticities are significant at the 1 percent level; 91 percent at the
5 percent level and 93 percent at the 10 percent level.
The estimates vary substantially across countries. The top three countries with the highest
average elasticity are Japan, United States and Brazil (-4.05, -3.39 and -3.38, respectively). The
three countries with the lowest average import demand elasticities are Surinam, Belize and Guyana
(-1.02, -1.03 and -1.03, respectively). Table 1 summarizes the elasticities by country providing the
15
simple average, the standard deviation, the median and the import-weighted average elasticity.
The estimate also show some variation across products. Goods with the more elastic import
demands (on average across countries) at the six digit level of the HS include HS 520635 (Cotton
yarn), 854290 (Electronic integrated circuits), and 100810 (Buckwheat), with average elasticities of
-16.29, -12.89 and -11.72, respectively. Similarly, the least elastic import demands are found in HS
140291 (Vegetable residuals for stuffing), HS 420232 (Articles for pocket, plastic/textile materials)
and HS 290521 (Allyl Alcohol), with average elasticities of -0.52, -0.65 and -0.66.
Given the lack of existing estimates at the tariff line level, we need some guidelines to judge our
results. Below we enumerate some predictions we expect to find in the estimated import demand
elasticities:
1. The import demand for homogenous goods is more elastic than for heterogenous goods. Rauch
(1999) classifies goods into these categories, which we can use to test the hypothesis.
2. Import demand is more elastic at the disaggregate level -- the substitution effect between
cotton shirts and wool shirts is larger than the substitution effect between shirts and pants,
or garment and electronics. Thus, we expect the HS six digit estimates to be larger in
magnitude (more negative) than estimates at a more aggregate level, i.e., three digit level
ISIC classification, which is formed of 29 industries, respectively. Broda and Weinstein (2004)
uses a similar guideline for their elasticities of substitution estimates.
3. Import demand is more elastic in large countries. The rationale is that in large countries
there is a larger range of domestically produced goods and therefore the sensitivity of import
demand to import prices is expected to be larger. In other words, it is easier to substitute
away from imports into domestically produced goods in large economies.
4. Import demand is less elastic in more developed countries. The relative demand for het-
erogenous goods is probably higher in rich countries. Given that heterogenous goods are less
elastic, we expect the import demand to be less elastic in rich countries.
As a preview of the first prior that homogenous goods are more elastic, we compare the estimated
import demand elasticities for Metal (HS 72-83) with those of Machinery (HS 84-89), where the
former are expected to be more homogenous. The average import demand elasticity of Metal is
16
-1.62 while it is -1.39 for Machinery. A simple mean test supported the hypothesis that Metal
import demand is more elastic than that of the Machinery, with a t-statistics of -13.02. Figure 2
presents the two Kernel density distribution of the estimated import demand elasticities for Metal
and Machineries tariff lines across all countries.
To properly test the homogenous vs heterogenous goods hypotheses, we use Rauch's (1999)
classification. Rauch groups four digit SITC goods into three categories: differentiated, reference
priced and homogenous goods. By matching our HS six digit products to the SITC schedule,
we are able to classify our products according to Rauch's schedule. Table 2 provides the sample
averages, medians and standard deviations of the estimated import demand elasticities according
to the three categories of goods. It is clear that the average elasticity is larger in magnitude
for homogenous goods, follows by the reference priced and differentiated goods. Simple mean tests
supported the hypotheses that homogenous goods are more elastic than reference priced goods, and
reference priced goods are more elastic than differentiated goods. The t-statistics of the two tests
are 7.23 and 19.50 respectively. Similarly, the median elasticity for differentiated goods is smaller
in magnitude than both reference priced and homogeneous goods. A simple rank test shows that
the median elasticity of differentiated goods is statistically smaller in magnitude than the rest, with
a p-value close to 0, while the difference between the median elasticities of reference price goods
and homogenous goods is not statistically significant. All this suggests that differentiated goods
are less elastic than reference priced and homogeneous goods, which confirms our first a priori.
To test the second hypothesis, we reestimated import demand elasticities at the industry level,
through a concordance linking HS six digit classification to ISIC three digit industry classification.
Table 3 provides the average elasticity by country at the different levels of aggregation. It confirms
that elasticities are smaller in magnitude when estimated at the industry level than at the tariff
line level. On average elasticities estimated at the six digit level of the HS are 39 percent higher
than those estimated at the three digit level of the ISIC.
In order to test the last two hypothesis we run the average elasticity at the country level on log
of GDP and GDP per capita. The conditional plots of these relationships are provided in Figures
3 and 4, as well as the estimated coefficient and its standard error. They confirm that import
demand is more elastic in large and less developed countries. Thus, the last two hypotheses cannot
17
be rejected.12
6 Calculating TRIs and Deadweight Losses
The estimated import demand elasticities allow us to examine the trade restrictiveness and welfare
losses associated with the existing tariff structure in 88 countries in our sample for which tariff
schedules are available.13 More importantly, this can be done within a theoretically-sound frame-
work. The literature has traditionally measure trade restrictiveness using a-theoretical measures
such as simple and import-weigthed tariffs.14 As argued by Anderson and Neary (1992, 1994, 2003)
these have little theoretical foundations. Import-weighted averages tend to be downward bias, as
for example, they put zero weight on prohibitive tariffs and simple average tariffs put identical
weights on tariffs that may have very different economic significance. Anderson and Neary (1992,
1994) propose a trade restrictiveness index (TRI), which has a theoretically sound averaging proce-
dure. TRI is defined as the uniform tariff that yields the same real income, and therefore national
welfare, as the existing tariff structure. Deadweight loss measures can also be constructed using
TRIs and theoretically consistent estimates of import demand elasticities, which in turn allows for
comparisons of welfare distortions associated with each country's tariff structure.
To calculate the TRI, one would ideally need to solve a full-fledged general equilibrium model
for the uniform tariff that could keep welfare constant given the observed tariff structure. Feenstra
(1995) provides a simplification of TRI, which only requires information on import demand elastic-
ities, share of imports and the current tariff schedule. The major drawback of such simplification
is that it ignores the general equilibrium of cross price effects. Nonetheless, as an illustration of the
first order effect of trade distortions, the simplified TRI is informative:15
12We found similar patterns when regressing on the median elasticity by country. The coefficient on GDP is 0.03
and on GDP per capita - 0.02 and both are statistically significant at the 1 percent leve.
13Data sources for tariff data are United Nations' Comtrade and the Integrated Database of the WTO. In this paper,
we abstract from measuring the trade restrictiveness of non-tariff barriers, as well as the role of tariff preferences in
eroding trade restrictiveness. For an attempt to do so, see Kee, Nicita and Olarreaga (2004b).
14If NTB measures are to be considered, trade economist often use simple or import-weigthed coverage ratios of
NTBs.
15See Equation (3.5) in Feenstra (1995). Note that given our setup, the derivation in Feenstra (1995) is equivalent
to deriving the TRI that would keep GDP at its maximum level given the existing tariff structure.
18
1 1/2 1/2
1
2 n(dqn,c/dpn,c)t2n,c 2 nsnnnt2nc
TRIc = = (26)
1 1
(dqn,c/dpn,c) snnn
2 n 2 n
where tnc is the tariff on good n in country c. Thus, the simplified TRI is the squared root of a
weighted average of squared tariffs, where weights are determined by the import demand elasticities
in each country. Given that tariffs are squared in Equation (26), TRIc depends not only on the
weighted average level of tariffs, but also its variance. In other words, high dispersion of tnc increases
TRIc, for a given weighted average; see Anderson and Neary (2004) for a thorough discussion of
the importance of tariff dispersion when measuring trade restrictiveness.
Note that the numerator in Equation (26) is equal to the share in GDP of the deadweight loss
(DWL) associated with the existing tariff structure:
DWLc 1 1
= snnnt2nc = (TRIc)2 snnn, or
GDPc 2 2
n n
1
DWLc = (TRIc)2 GDPc snnn. (27)
2
n
Thus, with information on the current tariff schedule, import shares and import demand elasticities,
we can construct both TRIc and DWLc. Given that we are using GDP maximizing import demand
elasticities instead of Hicksian elasticities as in Feenstra (1995), our measures of TRI and DWL are
consistent with GDP maximization.16
Results using Equations (26) and (27) are provided in Table 4. Table 4 also shows simple and
import-weighted average tariffs, as well as the variance of tariffs for 88 countries. The sample mean
average tariffs, import-weighted tariffs and TRI are 10.04, 8.95 and 13.15. The three indicators of
trade restrictiveness are highly correlated: the correlation coefficient between TRI and the two other
measures is 0.91, and the correlation between the simple average tariff and the import-weighted
tariff is 0.96. Figure 5 provides a plot of TRIs versus simple average tariffs for the 88 countries in
our sample. Observations tend to be above the 45 degree dotted line, which suggests that average
tariffs tend to underestimate the degree of trade restrictiveness as defined by the TRI. Overall,
both simple and weighted average tariffs tend to underestimate TRI by about 30 percent. The
countries where underestimation is the largest are Estonia (EST), Norway (NOR), Sudan (SDN),
16See Kohli (1991), Equations 18.27 to 18.31.
19
Oman (OMN), and the United States (USA). The magnitude of underestimation in these countries
is more than 70 percent. Among these countries, Norway, Sudan and the United States also have
very high variances as shown in Table 4 which explains the relatively large TRIs. Countries that
have the largest TRIs include India (IND), Morocco (MAR) and Tunisia (TUN).
To facilitate cross country comparison of trade distortion, Table 4 also provides DWL estimates
in millions of US dollars. United States, China, Mexico, India and Germany are the countries in
the sample with the largest losses associated with their existing tariff structure. In particular, at
$7 billion per year, the DWL of the United States is more than a quarter of the sum of welfare
losses in our sample. Moreover, given that the TRI of the US presented in Table 4 is significantly
higher than the average tariff, the US deadweight loss estimate is larger then Feenstra's (1992),
who found that the welfare loss in the US associated with an average tariff of 3.7 percent was in
the range of $1.2 to 3.4 billion in 1985.
A few caveats. First, this version of TRI and DWL calculations only take into account the direct
own price effects of tariffs. They ignore the cross price effects of other tariffs on import demand.
Thus, at best, it represents the first order impact of import demand and welfare due to tariffs.
Second, the calculation of TRI and DWL ignore the existence of non-tariff barriers, such as quotas.
To the extent that non-tariff barriers are the more binding constraints in distorting imports, TRI
and DWL presented here may only capture the lower bound of the nature of trade protections and
welfare distortions. Third, we have focused on most favored nation's tariffs, ignoring the numerous
preferential agreements that may erode trade restrictiveness. Fourth, given the static nature of
our analysis, dynamics effects associated with tariffs are ignored. Finally, we only include positive
import in the calculation of TRI and DWL. This ignores prohibitive tariffs. To correct for this, we
re-calculated TRI and DWL according to the following specification, where we assume the demand
for goods that have zero import has a slope of ann :
1/2
TRIc = n(ann + s2n,c - sn,c)t2n,c .
n (ann + s2n,c - sn,c)
This out of sample prediction does not change our results. While TRIc tend to be slightly smaller
than TRIc, the two TRI's series have a correlation coefficient of 0.99. This suggests that if the
restrictiveness of prohibitive tariffs on a particular good is (by definition) infinite, their impact on
20
the overall trade restrictiveness is marginal in our sample.
7 Concluding Remarks
A set of consistently estimated import demand elasticities at the tariff line level is critical to
understand the consequences of trade liberalization. This paper is the first attempt to provide a
theoretically consistent methodology to estimate import demand elasticities for a wide variety of
countries at the six digit level of the HS (4,625 tariff lines). Moreover, the methodology can be
easily implemented with existing trade data.
We find that the sample average import demand elasticities is -1.67, while the sample median
is -1.08. There is wide variation in import demand elasticities across countries and tariff lines,
and the estimates exhibit some interesting patterns. First, homogeneous goods have more elastic
import demand than differentiated goods. Second, the average estimated elasticities decrease as we
increase the level of aggregation at which they are estimated. Third, large countries tend to have
more elastic import demands. Fourth, more developed countries tend to have less elastic import
demand.
In addition, we calculate trade restrictiveness indices (TRIs) and welfare losses associated with
the existing tariff structures for 88 countries. We use a methodology that is both theoretically
sound, and more importantly consistent with our estimated elasticities. Results show that both
simple and weighted average tariffs tend to underestimate the distortion imposed by the tariff
regime by 30 percent on average. Because of the large variance in the United States tariff schedule,
underestimation of trade restrictiveness is among the largest. The simple and import-weighted
tariffs in the United States are around 4 percent, whereas the TRI is close to 15 percent. With
welfare losses at around $7 billion per year, the United States is the country in our sample whose
tariff structure imposes the largest welfare costs on its nationals. It is followed by China, Mexico,
India and Germany. Finally, given the high TRI of the US, the $7 billion per year deadweight loss
estimate is also larger then previous findings of the literature which mainly use average tariffs.
21
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24
A From N to 2 good-economies
This section constructs N two good economies from a N good economy. Consider a small economy
producing N goods. The share equation of industry n is given by:
N M
stn pt,vt = at0n + atnn lnptn + atnk lnptk + ctnm lnvm.
t (28)
k=n,k=1 m=1
Given the translog GDP function, if all the translog parameters are time invariant, then the exact
price index of the GDP function is a Tornqvist index (Caves, Christensen and Diewert, 1983):
N
lnPt = s¯tk lnptk, (29)
k=1
= s¯tn lnptn + 1 - s¯tn ln pt-n, with (30)
1
s¯tk = (31)
2 stk + stk-1 , k, and
N
1
lnpt-n = (32)
1 - s¯tn s¯tk lnptk, n,
k=n,k=1
where lnpt-n is the non-good-n price index, which is the aggregate Tornqvist price index of all goods
excluding good n. Notice that in Equation (32) we imposed the restriction that N s¯t = 1.
n=1 n
Substituting Equation (32) into Equation (28), and further assuming that all the parameters of
the GDP function are time invariant yields:
M
stn pt,vt = a0n + ann lnptn + an-n lnpt-n + cnm lnvm,
t
m=1
This requires
N
an-n lnpt-n atnk lnptk
k=n,k=1
N N
1
an-n1 - s¯tn s¯tk lnptk atnk lnptk
k=n,k=1 k=n,k=1
s¯tk
an-n1 (33)
- s¯tn ank, n,k.
Homogeneity of degree zero in prices implies N
k=1 ank = 0, n. Equation (33) implies the following
25
is necessary true:
an-n -ann, or
M
stn pt,vt ptn
= a0n + ann ln + t
pt-n cnm lnvm.
m=1
which completes the illustration of how we can reduce an N-good economy into a two-good economy,
with the appropriate construction of the price index lnpt-n.
B Aggregating elasticities to the industry level
Our estimation procedure in Section 3 could be applied to goods at any level of aggregation, provided
the adequate price indices have been constructed. This section provides an aggregation procedure
from six digit HS estimates to any higher level of aggregation for a translog GDP function.
Let good n A belong to industry A and good n B belong to industry B, and A B =
{1,...,N} , A,B = . Then, the shares of good n and industry A in GDP are given by:
N M
stn pt,vt = at0n + atnk lnptk + ctnm lnvm,
t
k=1 m=1
stA stn pt,vt
nA
M
= at0n + atnk lnptk + atnk lnptk + ctnm lnvm.
t (34)
nA kA kB kA m=1
As shown in Equation (29), the Tornqvist price index at the industry level is the weighted
average of goods' price indices within each industry:
1
ln ptA = (35)
1 - s¯tA s¯tn lnptn,
nA
1
ln ptB = 1 - s¯tB s¯tn lnptn,
nB
where s¯t denotes the average share between two consecutive periods. To apply the above Tornqvist
price index, we need to assume that all the translog parameters atnk are time invariant.
If we were to estimate our parameters at the industry level instead of the good level, the share
equation of industry A would be given by:
M
stA = a0A + aAA lnptA + aAB lnptB + ctAm lnvm.
t (36)
m=1
26
Equating Equations (34) and (36) imply that
a0A a0n, and,
nA
aAA lnptA ank lnptk
aAA kA
1 - s¯tAs¯tn = ank n,k A,
aAA = ank = 0, B = .
kA
From Section 2, we know that
tAA = aAA
stA + stA - 1
ank
= kA
stA + stA - 1.
We also know from Equation (33) that
stk
ank = -ann1 - stn
ank = ann 1 - stA.
kA 1 - stn
Thus the industry elasticity is given by:
tAA = 1 - stA ann
(37)
stA + stA - 1.
nA 1 - stn
It can be further shown that the price elasticity of an industry is the weighted average of the own
and cross price elasticities of all goods within the industry:
1
tAA = stA stntnk.
nA kA
27
Table 1: Estimated elasticities: sample moments by country
Country Simple Standard M edian Import Country Simple Standard Median Import
Average Deviation weighted Average Deviation weighted
average average
Albania (ALB) -1.12 -1.04 -1.04 -1.06 Italy (ITA) -2.1 -1.06 -1.07 -1.14
United Arab Em . (ARE) -1.38 -1.16 -1.11 -1.07 Jam aica (JAM ) -1.16 -1.1 -1.08 -1.05
Argentina (ARG) -2.52 -1.13 -1.15 -1.26 Jordan (JOR) -1.16 -1.05 -1.07 -1.04
Arm enia (ARM ) -1.09 -1.06 -1.06 -1.05 Japan (JPN) -4.05 -1.23 -1.4 -1.37
Australia (AUS) -2.49 -1.1 -1.1 -1.19 Kenya (KEN) -1.26 -1.14 -1.1 -1.07
Austria (AUT) -1.8 -1.05 -1.04 -1.08 Korea (KOR) -2.08 -1.1 -1.1 -1.1
Azerbaijan (AZE) -1.18 -1.11 -1.1 -1.07 Lebanon (LBN) -1.26 -1.03 -1.02 -1.06
Burundi (BDI) -1.07 -1.19 -1.12 -1.05 Sri Lanka (LKA) -1.2 -1.1 -1.04 -1.06
Belgium (BEL) -1.51 -1.04 -1.05 -1.05 Lithuania (LTU) -1.2 -1.03 -1.02 -1.06
Benin (BEN) -1.11 -1.11 -1.11 -1.05 Latvia (LVA) -1.16 -1.03 -1.02 -1.05
Burkina Faso (BFA) -1.1 -1.12 -1.08 -1.05 Morocco (M AR) -1.45 -1.1 -1.05 -1.09
Bangladesh (BGD) -1.65 -1.2 -1.19 -1.15 Madagascar (M DG) -1.17 -1.12 -1.18 -1.09
Bulguria (BGR) -1.18 -1.05 -1.04 -1.06 Maldives (MDV) -1.04 -1.04 -1.03 -1.02
Belarus (BLR) -1.17 -1.04 -1.05 -1.05 Mexico (M EX) -2.08 -1.06 -1.07 -1.11
Belize (BLZ) -1.03 -1.05 -1.03 -1.03 Macedonia (MKD) -1.12 -1.04 -1.05 -1.05
Bolivia (BOL) -1.23 -1.07 -1.1 -1.08 Mali (M LI) -1.15 -1.19 -1.09 -1.06
Brazil (BRA) -3.38 -1.3 -1.22 -1.34 Malta (M LT) -1.09 -1.04 -1.02 -1.04
Barbados (BRB) -1.08 -1.04 -1.08 -1.04 Mongolia (M NG) -1.05 -1.06 -1.07 -1.03
Central Afr. Rep. (CAF) -1.08 -1.15 -1.11 -1.05 Mauritius (MUS) -1.11 -1.05 -1.02 -1.05
Canada (CAN) -2.29 -1.05 -1.05 -1.13 Malawi (MW I) -1.07 -1.11 -1.13 -1.04
Switzerland (CHE) -1.99 -1.07 -1.06 -1.1 Malaysia (MYS) -1.45 -1.07 -1.06 -1.05
Chile (CHL) -1.61 -1.05 -1.08 -1.1 Niger (NER) -1.12 -1.1 -1.18 -1.06
China (CHN) -2.54 -1.12 -1.14 -1.13 Nigeria (NGA) -1.59 -1.29 -1.15 -1.11
Cote d'Ivoire (CIV) -1.32 -1.16 -1.13 -1.08 Nicaragua (NIC) -1.06 -1.06 -1.07 -1.03
Cameroon (CMR) -1.36 -1.21 -1.15 -1.12 Netherlands (NLD) -1.66 -1.04 -1.04 -1.07
Congo (COG) -1.13 -1.11 -1.09 -1.04 Norway (NOR) -1.93 -1.06 -1.08 -1.11
Colombia (COL) -1.81 -1.13 -1.08 -1.16 New Zealand (NZL) -1.56 -1.11 -1.07 -1.1
Comorros (COM) -1.04 -1.17 -1.08 -1.03 Oman (OMN) -1.23 -1.05 -1.06 -1.05
Costa Rica (CRI) -1.23 -1.03 -1.04 -1.06 Panama (PAN) -1.24 -1.05 -1.09 -1.07
Cyprus (CYP) -1.17 -1.03 -1.02 -1.05 Peru (PER) -1.74 -1.18 -1.11 -1.16
Czech Rep. (CZE) -1.36 -1.03 -1.04 -1.05 Philippines (PHL) -1.61 -1.08 -1.06 -1.07
Germ any (DEU) -2.01 -1.06 -1.07 -1.14 Poland (POL) -1.51 -1.08 -1.04 -1.09
Denm ark (DNK) -1.69 -1.09 -1.07 -1.11 Portugal (PRT) -1.47 -1.05 -1.03 -1.09
Algeria (DZA) -1.59 -1.13 -1.14 -1.1 Paraguay (PRY) -1.19 -1.06 -1.02 -1.07
Egypt (EGY) -1.78 -1.14 -1.13 -1.12 Rom ania (ROM) -1.37 -1.04 -1.06 -1.09
Spain (ESP) -1.95 -1.06 -1.05 -1.14 Rwanda (RWA) -1.12 -1.13 -1.14 -1.07
Estonia (EST) -1.09 -1.03 -1.02 -1.03 Saudi Arabia (SAU) -1.86 -1.04 -1.06 -1.13
Ethiopia (ETH) -1.17 -1.09 -1.06 -1.07 Sudan (SDN) -1.32 -1.15 -1.14 -1.08
Finland (FIN) -1.84 -1.07 -1.06 -1.12 Senegal (SEN) -1.16 -1.08 -1.11 -1.05
France (FRA) -1.93 -1.05 -1.07 -1.14 Singapore (SGP) -1.3 -1.06 -1.02 -1.04
Gabon (GAB) -1.15 -1.11 -1.12 -1.08 El Salvador (SLV) -1.25 -1.06 -1.08 -1.07
United Kingdom (GBR) -1.91 -1.07 -1.06 -1.13 Surinam (SUR) -1.02 -1.05 -1.04 -1.02
Georgia (GEO) -1.15 -1.13 -1.09 -1.05 Slovakia (SVK) -1.22 -1.03 -1.02 -1.05
Ghana (GHA) -1.15 -1.05 -1.07 -1.05 Slovenia (SVN) -1.24 -1.03 -1.03 -1.05
Guinea (GIN) -1.19 -1.12 -1.1 -1.08 Sweden (SW E) -2.01 -1.06 -1.07 -1.11
Gambia (GMB) -1.04 -1.05 -1.06 -1.04 Togo (TGO) -1.08 -1.05 -1.06 -1.04
Greece (GRC) -1.71 -1.04 -1.03 -1.12 Thailand (THA) -1.83 -1.15 -1.08 -1.08
Guatem ala (GTM) -1.38 -1.09 -1.14 -1.09 Trinidad T. (TTO) -1.15 -1.07 -1.07 -1.06
Guyana (GUY) -1.03 -1.04 -1.04 -1.02 Tunisia (TUN) -1.24 -1.04 -1.06 -1.06
Hong Kong (HKG) -1.57 -1.04 -1.02 -1.04 Turkey (TUR) -1.97 -1.11 -1.09 -1.14
Honduras (HND) -1.11 -1.05 -1.09 -1.04 Tanzania (TZA) -1.28 -1.09 -1.09 -1.11
Croatia (HRV) -1.22 -1.04 -1.02 -1.07 Uganda (UGA) -1.22 -1.08 -1.17 -1.09
Hungary (HUN) -1.32 -1.06 -1.05 -1.06 Ukraine (UKR) -1.46 -1.05 -1.06 -1.1
Indonesia (IDN) -2.09 -1.12 -1.13 -1.14 Uruguay (URY) -1.4 -1.08 -1.1 -1.12
India (IND) -3.26 -1.31 -1.38 -1.33 United States (USA) -3.39 -1.1 -1.16 -1.3
Ireland (IRL) -1.51 -1.04 -1.05 -1.07 Venezuela (VEN) -1.85 -1.09 -1.12 -1.15
Iran (IRN) -1.87 -1.13 -1.15 -1.11 South Africa (ZAF) -2.04 -1.14 -1.1 -1.16
Iceland (ISL) -1.2 -1.04 -1.07 -1.07 Zambia (ZMB) -1.12 -1.06 -1.09 -1.05
Israel (ISR) -1.13 -1.06 -1.03 -1.06
28
Table 2: Sample moments of the estimated import demand elasticity by Rauch
classificationa
Mean Median Standard Deviation
Differentiated goods -1.59 -1.07 2.25
Referenced price -1.84 -1.09 2.84
Homogeneous goods -1.98 -1.09 3.32
aThe HS six digit schedule is first filtered into the four digit SITC schedule which Rauch (1999) used to classify
goods. Homogenous goods are those traded on organized exchanges. Reference priced goods are those listed as having
a reference price, and differentiated goods are goods that cannot not be priced by either of these two means.
29
Table 3: Average Estimated elasticities at different levels of aggregationa
Country HS six digit ISIC three digit Country HS six digit ISIC three digit
ALB -1.12 -1.04 ITA -2.10 -1.06
ARE -1.38 -1.16 JAM -1.16 -1.10
ARG -2.52 -1.13 JOR -1.16 -1.05
ARM -1.09 -1.06 JPN -4.05 -1.23
AUS -2.49 -1.10 KEN -1.26 -1.14
AUT -1.80 -1.05 KOR -2.08 -1.10
AZE -1.18 -1.11 LBN -1.26 -1.03
BDI -1.07 -1.19 LKA -1.20 -1.10
BEL -1.51 -1.04 LTU -1.20 -1.03
BEN -1.11 -1.11 LVA -1.16 -1.03
BFA -1.10 -1.12 MAR -1.45 -1.10
BGD -1.65 -1.20 MDG -1.17 -1.12
BGR -1.18 -1.05 MDV -1.04 -1.04
BLR -1.17 -1.04 MEX -2.08 -1.06
BLZ -1.03 -1.05 MKD -1.12 -1.04
BOL -1.23 -1.07 MLI -1.15 -1.19
BRA -3.38 -1.30 MLT -1.09 -1.04
BRB -1.08 -1.04 MNG -1.05 -1.06
CAF -1.08 -1.15 MUS -1.11 -1.05
CAN -2.29 -1.05 MW I -1.07 -1.11
CHE -1.99 -1.07 MYS -1.45 -1.07
CHL -1.61 -1.05 NER -1.12 -1.10
CHN -2.54 -1.12 NGA -1.59 -1.29
CIV -1.32 -1.16 NIC -1.06 -1.06
CMR -1.36 -1.21 NLD -1.66 -1.04
COG -1.13 -1.11 NOR -1.93 -1.06
COL -1.81 -1.13 NZL -1.56 -1.11
COM -1.04 -1.17 OM N -1.23 -1.05
CRI -1.23 -1.03 PAN -1.24 -1.05
CYP -1.17 -1.03 PER -1.74 -1.18
CZE -1.36 -1.03 PHL -1.61 -1.08
DEU -2.01 -1.06 POL -1.51 -1.08
DNK -1.69 -1.09 PRT -1.47 -1.05
DZA -1.59 -1.13 PRY -1.19 -1.06
EGY -1.78 -1.14 ROM -1.37 -1.04
ESP -1.95 -1.06 RWA -1.12 -1.13
EST -1.09 -1.03 SAU -1.86 -1.04
ETH -1.17 -1.09 SDN -1.32 -1.15
FIN -1.84 -1.07 SEN -1.16 -1.08
FRA -1.93 -1.05 SGP -1.30 -1.06
GAB -1.15 -1.11 SLV -1.25 -1.06
GBR -1.91 -1.07 SUR -1.02 -1.05
GEO -1.15 -1.13 SVK -1.22 -1.03
GHA -1.15 -1.05 SVN -1.24 -1.03
GIN -1.19 -1.12 SW E -2.01 -1.06
GMB -1.04 -1.05 TGO -1.08 -1.05
GRC -1.71 -1.04 THA -1.83 -1.15
GTM -1.38 -1.09 TTO -1.15 -1.07
GUY -1.03 -1.04 TUN -1.24 -1.04
HKG -1.57 -1.04 TUR -1.97 -1.11
HND -1.11 -1.05 TZA -1.28 -1.09
HRV -1.22 -1.04 UGA -1.22 -1.08
HUN -1.32 -1.06 UKR -1.46 -1.05
IDN -2.09 -1.12 URY -1.40 -1.08
IND -3.26 -1.31 USA -3.39 -1.10
IRL -1.51 -1.04 VEN -1.85 -1.09
IRN -1.87 -1.13 ZAF -2.04 -1.14
ISL -1.20 -1.04 ZMB -1.12 -1.06
ISR -1.13 -1.06
aThe same pattern is obtained with the median elasticities by country.
30
Table 4: Trade restrictiveness indices and welfare losses
Country Simple Im port TRIa Variance DW L Country Sim ple Im port TRIa Variance DW L
Average Weighted of (M illion Average Weighted of (M illion
Tariff Tariff Tariff of US$) Tariff Tariff Tariff of US$)
ALB 11.96 11.92 13.56 44.06 6.3 KOR 8.52 5.41 8.12 41.87 273
ARG 14.49 13.93 15.06 31.13 303 LBN 6.37 6.94 11.99 91.82 38.9
AUS 4.8 4.88 7.19 42.43 95 LKA 7.72 7.77 14.86 71.02 23.6
AUT 4.58 4.32 6.52 18.9 132 LTU 3.8 3.13 7.71 62.44 11.9
BEL 4.6 4.74 7.17 19.28 312 LVA 3.32 2.6 6.48 45.85 4.52
BFA 12.42 10.78 13.01 46.26 4.8 MAR 28.82 24.54 31.99 514.29 390
BGD 20.07 18.82 23.91 180.55 106 MDG 4.43 3.93 5.86 16.65 0.84
BLR 10.76 9.62 11.52 35.65 29.4 MEX 17.55 16.18 21.29 143.42 1970
BOL 8.94 8.08 8.82 7.3 6.01 MLI 12.09 9.75 11.9 44.06 2.13
BRA 14.27 12.18 14.96 35.51 527 MUS 18.97 11.43 24.29 690.61 49.6
CAF 17.81 16.45 19.21 91.13 2.43 MW I 13.08 9.93 13.58 92.57 3.52
CAN 4.6 3.71 6.3 35.91 187 MYS 8.66 6.81 17.41 131.45 671
CHL 6.98 6.74 6.85 0.1 29.8 NGA 24.16 18.07 27.15 457.7 180
CHN 15.94 16.3 24.38 135.7 4070 NIC 4.98 7.33 14.12 41.88 7.69
CIV 12 9.82 11.73 46.92 14.7 NLD 4.59 4.44 6.86 19.31 279
CMR 16.35 13.37 16.06 80.48 16.4 NOR 2.21 1.63 9.46 157.49 144
COL 12.42 11.08 13.74 38.56 110 NZL 3.04 3.47 5.08 15.26 14.1
CRI 5.52 4.98 8.38 50.17 13.2 OMN 7.64 13.28 28.55 88.13 83.4
CZE 5.06 4.53 7.81 46.19 69.5 PER 13.59 13.27 13.7 13.05 67.5
DEU 4.56 4.69 7.22 19.84 912 PHL 5.43 3.9 8.51 29.79 101
DNK 4.6 4.4 6.86 19.29 81.4 POL 11.2 7.8 14.16 204.45 372
DZA 18.45 13.96 17.48 97.57 139 PRT 4.64 4.8 7.04 20.14 67.2
EGY 18.59 13.02 19.54 192.69 255 PRY 13.35 12.82 14.04 34.13 18.8
ESP 4.58 4.5 7.1 19.93 260 ROM 17.14 15.94 21.84 137.93 188
EST 0.07 0.54 2.37 0.88 0.9 RWA 9.66 9.28 11.91 47.49 1.48
ETH 17.88 14.1 18.64 159.17 17.4 SAU 11.3 9.95 11.04 12.6 162
FIN 4.61 4.02 6.58 19.04 49 SDN 4.98 5.1 20.1 125.3 24.5
FRA 4.57 4.65 7.51 19.91 737 SEN 12.36 10.62 12.4 47.42 9.44
GAB 18.4 14.87 17.77 90.55 13.6 SGP 0 0 0 0 0
GBR 4.58 4.56 7 20.01 602 SLV 7.35 7.26 11.02 79.44 15.5
GHA 12.95 9.91 13.65 103.3 16.8 SVN 10.22 10.88 12.98 39.78 69.7
GRC 4.69 4.41 7.15 20.18 58 SW E 4.6 3.99 6.36 19.22 103
GTM 6.69 6.39 9.57 62.39 15.5 THA 15.41 12.36 19.74 177.33 779
HKG 0 0 0 0 0 TTO 8.2 7.66 12.55 102.01 14.5
HND 7.12 7.53 11.04 50.44 10.7 TUN 28.86 27.47 30.42 175.13 302
HUN 9.24 8.11 12.65 95.5 134 TUR 9.25 6.41 15.99 345.43 396
IDN 6.76 5.02 10.02 99.35 140 TZA 16.39 14.53 16.97 75.97 17.1
IND 31.87 30.88 36.61 178.2 1740 UGA 7.95 7.53 9.46 32.44 3.63
IRL 4.64 4.02 6.89 20.27 57.4 UKR 6.57 4.16 8.43 47.86 40.3
ISL 4.15 3.71 8.03 51.86 5.35 URY 14.64 14.22 15.37 36.74 37
ITA 4.58 4.59 7.31 19.93 517 USA 4.17 3.93 15.18 134.81 7070
JOR 15.58 13.26 18.88 192.14 51.1 VEN 12.69 13.74 15.84 37.22 156
JPN 3.29 3.05 6.17 22.99 512 ZAF 8.02 6 11.92 127.64 146
KEN 17.96 17.07 23.05 176.69 49.9 ZMB 11.71 10.08 13.28 87.5 4.44
aThis is Feenstra's (1995) linear approximation of Anderson and Neary's (1992, 1994) trade restrictiveness index.
31
Figure 1: Distribution of the estimated import demand elasticities at HS six digit level
1
yit
ens
D
0
-4 0
elasticity
32
Figure 2: Distribution of import demand elasticities: Metal vs. Machinery
Metal Machinery
.52
0
-4 0
elasticity
33
Figure 3: Import demand elasticities and Log of GDP
coef = .23388554, se = .01648894, t = 14.18
2.14571 JPN
IND
BRA
USA
CHN
X)| ARG
yit IDN
ict AUS
MEX
CAN
ZAF IRN BGDNGA
TUR
EGY
VEN THA
KOR
COL
PER ITA
E(-elas SAU PHL
SWE SDNTZA
ESP
ETH DEU
NORCHE CMR DZAUKR
KEN FRA
GBR
MAR
BDI NER
FIN
RWABFAGTMUGA ROM
MLIAUT
MWIMDGCIV
GRCCHL POL
COM GMB MNGCAFTGOBENHNDBLR
GEOBOL
GINSEN
ZMBAZEGHA
LKA MYS
COGALBNZL
URYDNKTUN
SLV
ARE NLD
PRYLBNHKG
BGRCZE
PRT
GUY HUN
SUR
MDV NICGABMKDLVAPANHRVSVK
ARM JAM LTU
IRL
CRIJOR BEL
OMN
BLZ MUSTTOSVN
EST
SGP
BRB
MLT CYP
ISL ISR
-.867343
-3.70841 4.57085
Log of GDP | X
34
Figure 4: Import demand elasticities and Log of GDP per capita
coef = -.06671826, se = .02244586, t = -2.97
1.50838 JPN
IND BRA
USA
X)|
yit ARG
COM
ict AUS
GUY
CHN GMB
SUR MDV
BLZ
IDN BDI CAF MNG
ZAF
TGO
E(-elas RWA CAN
MWI
NER COG
BGD MDGBFA NIC SWE NOR
NGA BRB
TZA SDN UGA MEX THA
AZE ALB KOR
SAU CHE
FIN
CIV MKD GAB
MUS MLT
ETH EGYIRNZMBSENBOL
MLITUR
CMRGEOVEN
COLPER
BENGIN ARM
KEN DZA HNDGTM ISL
SLVPRY LVAURY
JORLTU
CHLJAM PAN
GRC EST
PHL
GHA TTONZL
UKR MAR
LKA CYP
ITAESP
LBN CRI OMNAUT
ROM BLR
BGRTUN ARE
SVKHRV SVNIRL
DNK
MYS CZE
HUN PRT HKG
POL
GBRFRA
DEU NLD SGP
BEL
-.673301 ISR
-3.06539 3.05794
Log of GDP per capita| X
35
Figure 5: TRI versus Simple Average Tariffs by Country
35.21 IND
MAR
TUN
NGA
OMN
MUS
BGD
CHN KEN
ROM
MEXEGY
THA CAF
ETH CAC
JOR GAB
I SDN TUR TZA DZA
TR CMR
MYS POL
VEN BRA
ARG
URY
USA LKA ALBMWI
COLPER
BFAPRY
GHA
NIC ZAF ZMB
TTOHUN
RWA
SVN MLI
SEN
LBN BLR CIV
SAU
IDN
HND
SLV
NOR
GTMUGA
KOR
CRIUKR BOL
LTU PHL
ISLCZE
LVASWE
ESP
NLD CHL
AUT
GRC
BEL
AUS
DEU
GBR
FRA
CAN
DNK
PRT
ITA
FIN
IRL
JPNMDG
NZL
EST
HKGSGP
0
0 31.87
tariff
36