Export Variety and Country Productivity
by
Robert Feenstra
Department of Economics
University of California, Davis
and NBER
Hiau Looi Kee
The World Bank
* The authors thank Russell Davidson, Jonathan Eaton, Marcelo Olarreaga and David Weinstein
for helpful comments. Research funding from the World Bank is cordially acknowledge. The
findings, interpretations, and conclusions expressed in this paper are entirely those of the authors,
and do not necessarily represent the view of the World Bank, its Executive Directors, or the
countries they represent.
Export Variety and Country Productivity
Robert Feenstra
Hiau Looi Kee
Abstract
This paper provides evidence on monopolistic competition models with endogenous technology
by studying the effects of sectoral export variety on country productivity. The effects are
estimated in a translog GDP function system based on data for 34 countries from 1982 to 1997.
Country productivity is constructed and export variety is shown to be significant. Instruments
such as tariffs, transport costs, and distance are shown to affect country productivity through
export variety, and only through this channel. Overall, while export variety accounts for only
2% of cross-country productivity differences, it explains 13% of within-country productivity
growth. A 10% increase in the export variety of all industries leads to a 1.3% increase in country
productivity, while a 10 percentage point increase in tariffs facing an exporting country leads to a
2% fall in country productivity.
Non-technical Summary
This paper studies the link between export product variety and country productivity, based on
data of 34 developed and developing countries, from 1982 to 1997. Export product variety is
measured by the share of US imports on the set of goods exported by each sampled country
relative to the world. It is a theoretically sound index which is consistent with within-country
GDP maximization as well as cross-country comparison. Country productivity is constructed
based on relative endowments and product variety. Increases in output product variety improve
country productivity as the new mix of output may better utilize resources of the economy and
improve allocative efficiency. Such effects depend on the elasticity of substitution in production
between the different varieties. The more different the varieties are in terms of production, the
more efficient it is to use the endowments of the economy when a new variety is available, which
leads to productivity gains. In addition, as suggested in the literature, export product variety
depends on trade costs, such as tariffs, distance and transport costs. Such trade cost variables are
used as instruments to help us identify the effects of export variety on country productivity.
Empirical evidence supports our hypothesis. Overall, while export variety accounts for only 2%
of cross-country productivity differences, it explains 13% of within-country productivity growth.
A 10% increase in the export variety of all industries leads to a 1.3% increase in country
productivity, while a 10 percentage point increase in tariffs facing an exporting country leads to a
2% fall in country productivity.
2
1. Introduction
Recent models of monopolistic competition and trade have emphasized that productivity
levels are endogenous. For example, Eaton and Kortum (2002) allow for stochastic differences in
technologies across countries, with the lowest cost country becoming the exporter of a product
variety to each location. In that case, the technologies utilized in a country will depend on its
distance and trade barriers with other countries. Melitz (2003) allows for stochastic draws of
technology for each firm, and only those firms with productivities above a certain cutoff level
will operate. A subset of these firms the most productive also become exporters. Melitz
shows how the average productivity in a country is determined by the cutoff productivity level,
which in turn depends on trade barriers faced by the exporters and other features of the world
market. In Melitz's model and that of Eaton and Kortum, trade volume and variety are
endogenous and are jointly determined with average productivity.
Empirical testing of this class of models can proceed by utilizing firm-level data and
inferring the productivity levels of firms. That approach is taken by Bernard et al (2003) for
U.S. firms; Eaton, Kortum and Kramarz (2003, 2004) for French firms; and Helpman, Melitz and
Yeaple (2004) for U.S. multinationals operating abroad. When firm level data are available, it is
highly desirable to make use of them like these authors do. But for many countries such data are
not available, and in those cases, we are still interested in estimating the joint relationship
between the productivity of countries and their trade volume and variety. The objective of this
paper is to examine the effects of export variety on productivity at the country level, using a
broad cross-section of advanced and developing nations and disaggregating across sectors.
Rather than modeling heterogeneity across firms, as in above-cited papers, we rely
instead on product differentiation across firms to generate productivity gains. This idea is
3
familiar from the earlier, endogenous growth models (e.g. Romer 1990, Grossman and Helpman,
1991) where greater variety of inputs leads to higher productivity. Similarly, we argue that a
greater variety of outputs also leads to higher productivity, provided the outputs are
differentiated from each other in production (i.e. use different factor intensities). Like many
monopolistic competition models we will rely on a constant elasticity of substitution (CES)
framework, but applied to the outputs of a country rather than its inputs. Empirically, we
measure output variety by the export variety of each country. Our goal is to see how export
variety (which is endogenous) affects aggregate productivity across countries.
Our work is complementary to other research estimating the gains from new varieties in a
CES framework. Feenstra (1994) showed how the gains from new product varieties could be
measured, and applied it to a handful of U.S. import goods. Broda and Weinstein (2003) have
recently extended this to all U.S. imports, and find that increased import variety contributes to a
1.2% per year fall in the "true" import price index. On the output side, a direct link between
export variety and productivity has been found by Feenstra et al (1999) for South Korea and
Taiwan, and by Funke and Ruhwedel (2001a,b, 2002) for the OECD and East Asian countries.1
Finally, Hummels and Klenow (2002) investigate the extent to which increased trade between
countries consists a larger set of goods, or higher quantity of existing goods what they call the
"extensive" versus "intensive" margin.
We begin by constructing export variety indexes at the sectoral level in sections 2 and 3,
as in Feenstra and Kee (2004). The variety indexes are incorporated into a translog GDP
function for the economy in section 4. The effects of export variety on country productivity are
shown to depend on the elasticities of substitution in production of different varieties in each
1 Funke and Ruhwedel (2003) use export variety measures to calculate the welfare gains from trade liberalization in
Central and Eastern Europe.
4
sector. Analogous to Harrigan (1997), the differences in export variety across countries play the
role of "price differences" in the GDP function, and therefore influence the shares of value added
devoted to each sector. An empirical specification based on the translog GDP function is
developed in section 5. The export variety indexes are regressors in the share equations, which
are estimated along with a productivity equation for each country. The estimates are then used to
construct country productivity based on data for 34 countries from 1982 to 1997.
In section 6, we report estimates of the system of the share equations and the productivity
equation. Export variety is treated as an endogenous variable, and the instrumental variables
used to determine export variety are those suggested by the work of Eaton and Kortum (2002)
and Melitz (2003): tariffs, transport costs and distance. There is also an important exclusion
restriction suggested by these models: tariffs and transport costs should not have an impact on
aggregate productivity except through export (and import) variety. This exclusion restriction
amounts to a test for overidentification in our system, as we describe. We formally test this
overidentifying restriction in section 7, as well as hypothesis tests based on other restrictions
imposed on the system of equations. Most importantly, the over-identifying restriction test is not
rejected and confirms the importance of export variety as the mechanism (Hallak and Levinsohn,
2004) by which trade affects productivity.
We discuss the empirical importance of tariffs, transport costs, and distance on export
variety in section 8. The results also show that a 10 percentage point increase in U.S. tariffs
would lead to a 2% fall in exporting countries' productivity, which indicates that tariffs are
statistically and economically important in affecting productivity via export variety. Increases in
distance and transport costs are also significant in reducing export variety of the industries. In
section 9, we decompose productivity differences across countries into that part explained by
5
export variety and the remaining explained by other determinants, such as fixed effects and
regression errors. We find that while export variety only accounts for 2% of the variation in
country productivity differences in level (though if country fixed effects are not included in
productivity differences, then export variety accounts for 60% of the variation), it can explain
more than 13% of within-country productivity growth. Overall, at the sample mean, a 10%
increase in export varieties of all industries leads to a 1.3% increase in country productivity.
Additional conclusions are given in section 10.
2. Effect of New Varieties
Consider a world economy with many c=1,...,C countries, each of which produce many
types of goods. For simplicity in this section we aggregate these goods into a single sector, but
the extension to multiple sectors will be immediate. For each period t, let the set of goods
produced in country c be denoted by Ict {1,2,3,....}. Then the quantity vector of each type of
good produced in country c in period t is denoted by qct > 0 . The aggregate output of each
country c, Qct , is characterized by a CES function of the output of each good in the country, qit :
c
Qct = f(qct ,Ict ) =iIt
ai (q )
c (-1) /
(1)
it
c /(-1)
,ai > 0, c =1,...,C,
where the elasticity of substitution between goods is . We assume that total output obtained
from the economy is constrained by the transformation curve:
F[f(qct ,Ict ),Vt ] = 0,
c (2)
where Vt = v1 , vc2 ,...,vcMt > 0 is the endowment vector for country c in year t.
c ( c )
t t
6
For outputs, we suppose that < 0 in (1), which means that the set of feasible varieties
qit in any country will lie along a strictly concave transformation curve defined by (2). This is
c
shown in Figure 1, where we draw the transformation frontier between two product varieties q1t
and q2t, within a country. For a given transformation curve, and given prices, an increase in the
number of output varieties will raise revenue. For example, if only output variety 1 is available,
then the economy would be producing at the corner A, with output revenue shown by the line
AB. Then if variety 2 becomes available, the new equilibrium will be at point C, with an
increase in revenue. This illustrates the benefits of output variety.
For inputs, we would instead use that > 1 in (1), which is then the formula for a CES
production function. Given output Qct = Qt , the inputs would lie along an iso-quant like that
c
illustrated in Figure 2. If only input 1 is available, then the costs of producing Qt would be
c
minimized at point A, with the budget line AB. But if input 2 is also available, then the costs are
instead minimized at point C, with a fall in costs. This illustrates the benefits of input variety.
We will use the output case to illustrate the effects of export variety, whereas the input case
would apply to import variety (as in Feenstra, 1994, and Broda and Weinstein, 2003).
3. Measuring Output Variety
Considering maximizing the value of output obtained in each industry, as in Figure 1.
Under the assumption of perfect competition, and given equation (1), the value of output
obtained in each country will be Pt Qct , where Pt is a CES function of the prices of all output
c c
varieties produced in the country:
7
Pt c(pct ,Ict ) =
c (pit)1-
c 1/(1-)
iItbi ,bi = ai > 0, c = 1,...,C, (3)
c
and pct > 0is the domestic price vector for each country.
The right-hand side of expression (3) is a CES cost function, with potentially differing
sets of product varieties across countries and over time. These cannot be evaluated with
knowledge of the parameters bi. But a standard result from index number theory is that the ratio
of cost function can be evaluated, using data on price and quantities in the two periods or two
countries. Feenstra (1994) shows how this result applies even when the number of goods is
changing. In particular, the ratio of the CES cost functions over two countries a and b, equals to
the product of the Sato-Vartia price index of goods that are common, I Iat Ibt ,
( )
multiplied by terms reflecting the revenue share of "unique" goods:
a
Pt = pit pait , a,b = 1,...,C, (4)
b
Pt b
iI wi(I)bt
at(I) 1/(-1)
(I)
where the weights wi(I) are constructed from the revenue shares in the two countries:
wi(I) ln sait(I)- sit(I)
b
sait(I)- lnsit(I) iI lnsait(I)- lnsit(I)
/
b sait(I)- sit(I)
b , (5)
b
scit(I) pcitqcit /pcitqcit, for c = a,b, (6)
iI
pcitqcit pcitqcit
ct(I) = iI =1- iIct ,iI , for c = a,b. (7)
pcitqcit pcitqcit
iIct iIct
8
Notice that the output shares in (6), for each country, are measured relative to the common set of
goods I. Then the weights in (5) are the logarithmic mean of the shares sait(I) and sit(I) , and b
sum to unity over the set of goods i I .2
To interpret (7), notice that ct (I) 1 due to the differing summations in the numerator
and denominator. This term will be strictly less than one if there are goods in the set Ict that are
not found in the common set I. In other words, if country a is selling some goods in period t that
are not sold by country b, this will make at(I) < 1.
We can re-express equation (4) in logs as:
Pta
ln = wi pait 1 at(I) a,b,= 1,...,C. (8)
b
Pt iI (I)ln pit + ln bt(I),
b -1
The first term on the right of (8) is the Sato (1976)-Vartia (1976) price index, which is simply a
weighted average of the price ratios, using the values wi(I) as weights. What is new about
equation (8) is the second term on the right, which reflect changes in product variety. If country
a in period t has new, unique outputs (not in the common set I), we will have at <1. From (8),
when < 0 this will raise the price index of outputs, Pt / Pt . In other words, the introduction of
a b
new output varieties will act in the same way as an increase in prices in a sector: it will draw
resources towards that sector.3
2 More precisely, the numerator of (5) is the logarithmic mean of the output shares of the two countries, and lies in-
between these shares. The denominator of (5) is introduced so that the weights wi(I) sum to unity,
3 If instead we consider the case of input variety, then > 1 in (8). Then the introduction of new inputs will lower
their price index. Thus, new input varieties would have the same positive efficiency effect as would a drop in input
prices.
9
In practice, we will measure the ratio at / bt using exports of countries to the United
States. While it would be preferable to use their worldwide exports, our data for the U.S. are
more disaggregate, and allows for a finer measurement of "unique" products sold by one country
and not another. Specifically, for 1972 1988 we will use the 7-digit Tariff Schedule of the U.S.
Annotated (TSUSA) classification of U.S. imports, and for 1989 1997 we shall use the 10-digit
Harmonized System (HS) classification of imports.
To measure the ratio at / bt , we need to decide on a consistent "comparison country."
For this purpose, we shall use the worldwide exports from all countries to the U.S. as the
comparison. Denote this comparison country by *, so that the set I*t = UCc=1 Ict is the complete
set of varieties imported by the United States in year t, and p*itq*it is the total value of imports for
good i. Then comparing country c to country * in year t, it is immediate that the common set of
goods exported is Ict I*t = Ict , or simply the set of goods exported by country c. Therefore, from
(7) we have that ct(Ict ) = 1, and:
p*itq*it p*itq*it
ct *t(Ict ) =
* iIct =1- iI*t ,iIct . (9)
p*itq*it p*itq*it
iI*t iI*t
Noting from (8) that product variety in country c relative to the comparison is measured
as ct(Ict ) / *t(Ict ) , but this has a negative coefficient when < 0, let us instead invert it and
measure product variety of country c relative to the world by *t(Ict ) / ct(Ict ) = *t(Ict ) , which
enters (8) with a positive coefficient 1/(1 ). For brevity we denote this by ct in (9). It is
*
interpreted as the share of total U.S. imports from products that are exported by country c.
10
Equivalently, it is one minus the share of total U.S. imports from products that are not exported
by country c. Note that this measure depends on the set of exports by country c, Ict , but not on its
value of exports, except insofar as they affect the value of worldwide exports.
4. GDP Function with Export Variety
To study the effects of export variety on productivity, we need to model the allocation of
factors among the production of goods in all industries. The effects of export varieties on
productivity depend on the elasticities of substitution in production between different variety
within the industries for a two good case, the elasticity of substitution in production captures
the curvature of the PPF of an economy given fixed endowments, as in Figure 1. In this section,
we develop a general equilibrium based GDP function approach which links export variety to
country productivity. Such a model will allow us to develop an empirical model for the
estimation of the elasticities of substitution in production of various industries, and will also
allow us to infer the contribution of export variety in explaining country productivity.
Suppose there are M kinds of factor endowments in the economy, denoted by the
endowment vector Vt = (v1 ,..., vcMt) > 0. There are N differentiated traded good sectors in the
c c
t
economy, with output denoted by (Q1 ,...,QcNt ), each of which is a CES aggregate as in (1) with
c
t
n < 0.4 In addition to the N traded goods, each country has one homogeneous nontraded good
sector produces output QcN+1 . The aggregate output vector of the economy is denoted by
t
Qct = Q1 ,...,QcNt ,QcN+1 > 0. Likewise, the aggregate price vector is Pt = (P1 ,...,PNt ,PN+1 ) > 0,
( c ) c c c c
t t t t
which consists of N traded good prices as defined by the CES unit-costs in (3) , and one
4 In the case that some of these sectors are imported rather than exported, we would denote Qnt < 0 as the negative
c
of the CES aggregate (1), with n > 1.
11
nontraded good price, PN+1 . Given the assumption of perfect competition, total revenue or GDP
c
t
of the economy in period t is:
Gct Pt ,Vt max Pt Qct : Ft Qct ,Vt = 0 ,
( c c) { c c( c) } (10)
where Ft (Qct ,Vt ) = 0 is the transformation curve in period t that generalizes (2) when there are
c c
many sectors. Gct Pt ,Vt
( c c) is homogeneous of degree one with respect to prices and, with the
assumption that F is homogeneous of degree one, then Gct Pt ,Vt ( c c) isalso homogeneous of
degree one with respect to endowments. As usual, the derivative of the GDP function with
respect to Pt equals the sectoral outputs Qct , and the derivative with respect to endowments Vt
c c
can be interpreted as the factor prices wct .
To implement the above GDP function empirically, we will assume that it follows a
translog functional form:
lnGct Pt ,Vt = c0 + c0t +
( c c) N+1 M N+1 N+1
1 c c
n ln Pnt +
c
k ln vckt + ln Pmt ln Pnt
2 mn
n=1 k=1 m=1 n=1 (11)
M M N+1 M
+ 1 c ln Pnt ln vckt.
c
2 kl ln vckt ln vlt + nk
k=1 l=1 n=1 k=1
Notice that we allow this function to differ across countries based on the constant c0 and also
the exogenous time trend c0t . To satisfy the properties of homogeneity in prices and
endowments as well as symmetry, we impose the following restrictions:
N+1 N+1 N+1
mn = nm, =1, = = 0,
n mn nk
n=1 n=1 n=1 (12)
M M M
kl = lk, =1, = = 0.
k kl nk
k=1 k=1 k=1
12
The share of factor k in the GDP of the economy in period t equals to the derivative of
lnGct Pt ,Vt with respect to ln vckt :
( c c )
M N+1
skt = k + (13)
kl ln vclt +
knln Pnt , k =1,...,M.
c
l=1 n=1
Similarly, the share of sector n in GDP of period t equals to the derivative of lnGct Pt ,Vt with
( c c)
respect to ln Pnt :
c
N+1 M
snt = n + mn ln Pmt +
c nk ln vckt , n =1,..., N +1. (14)
m=1 k=1
To introduce export variety into the GDP function, we assume that the prices of goods
sold by each country are the same across countries, but that they differ in the variety of products
sold by each. Denote the set of varieties produced by industry n as Icnt , so the aggregate price
Pnt is a CES function of the prices of these varieties:
k
Pnt c(pct ,Ict ) =
c (pit )1-
c 1/(1-)
iIcnt
bi ,bi = ai > 0, c =1,...,C, n =1,...,N.
Using the union of all exporting countries as the comparison country, then from (8) and (9),
Pnt
c c 1
ln = 1 ln Pt lncnt ,
* (15)
*
Pnt iIntwi(I)ln p*it + n
pcit -1 lncnt*
cnt *
Pt = 1- n
where the latter equality comes from assuming that pcit = p*it for every tradable good. Thus, the
ratio of CES price indexes depends only on the relative export variety of country c. A similar
approach was used by Harrigan (1997) to model the effective price differences across countries
13
as reflecting total factor productivity in the exporting sectors, whereas we are modeling the price
differences as reflecting product variety of exports.
If we difference (14) with respect to the share equation of the comparison country, we
obtain an expression that relates the industry share in country c in period t to cnt : *
M
scnt = s*nt +kn (ln vckt - ln v*kt +
) N
mn ln cmt +N
*
+1,n (ln c
PN +1,t - ln PN *
+1t) , (16)
k=1 m=1(1- m)
where the last term captures the effect of a nontraded good on the industry shares. We measure
the endowments of the hypothetical country by the sum of endowments of all sample countries,
v*kt = Cc=1 vckt , while the nontraded goods price for the comparison country is a weighted
average of the country nontraded good price indexes.5
Equation (16) allows us to estimate 1/(1- m ) , which depends on m, the elasticity of
substitution between output varieties in industry m. However, given that 1/(1- m ) and mn enter
multiplicatively, it is not possible to separately identify the parameters based on (16). Thus, in
addition to the share equations (16), a country productivity equation is derived from the GDP
function is added to the estimation system. This will also allow us to estimate how the expansion
of product varieties contributes to GDP and therefore to country productivity.
To derive the country productivity equation, we assume that the hypothetical country also
has the translog function shown in (11), where without loss of generality we can normalize
*0 = *0 = 0. Then using the share equations in (13)-(14), it can be confirmed that the difference
between GDP of country c and the comparison country is:
5 The nontraded good price indexes of the sample countries are obtained by netting the prices of traded goods, both
export and import, from the country GDP deflators.
14
lnG Pt ,Vt - lnG Pt ,Vt
( c c) ( * * )
(s )( ) (s )( )
N+1 M (17)
= c0 +c0t + 1 c + s*nt lnPnt - lnPnt +
c * 1 c + s*kt lnvckt - ln v*kt .
2 nt 2 kt
n=1 k=1
The right-hand side of (17) equals a time trend, plus a Törnqvist index of relative prices, plus a
Törnqvist index of relative endowments. These indexes provide a decomposition of relative
GDP into its price and factor-endowment components.6
In our case, the price differences of the traded goods industries are due entirely to export
variety, so using (15) we can re-express (17) initially as:
lnG Pt ,Vt - lnG Pt ,Vt -
( c c) ( * *) (s )( )
M
1 c + s*kt lnvckt - lnv*kt
2 kt
k=1
*
- scN+1 + s*N+1 lnPN+1 - lnPN+1 = c0 +c0t + lncnt
1 c * 1 (sc + s*nt) , (17')
2( )( ) N
t t t t 2 nt
n=1 (1- n )
where the differences in factor endowments between country c and the hypothetical country are
moved to the left-hand side. Also listed as the last term on the left is the difference in the
nontraded good's price between the countries. Thus, the left-hand side of this equation is
interpreted as the country productivity differences between country c and the hypothetical
country it is the GDP of country c relative to that of the hypothetical country, net of the
differences in factor endowments and prices due to nontraded goods. The remaining difference
between the two countries GDP is the productivity differences due to export variety, on the right.
Equation (17') is not immediately useful since the GDP level of the hypothetical country,
and its factor shares, are not observable. For the unobserved factor shares, given that we use the
sum of sampled countries endowments to proxy for the endowments of the hypothetical country,
6 The decomposition in (17) is a special case of results in Diewert and Morrison (1986), which are summarized by
Feenstra (2004, Appendix A, Theorem 5).
15
it is reasonable to assume that its factor shares are the average of the sampled countries factor
shares. As for the unobserved GDP level, given that it is common across all countries in any
year, it is possible to be controlled by year fixed-effects in a panel regression setting, i.e.
*t = lnG Pt ,Vt , and moving it to the right-hand side of the equation,
( * * )
(s )(ln )
N
ln G Pt ,Vt -
( c c) (s )(ln )
M
1 c + s*kt vckt - ln v*kt - 1 c + s*nt c *
2 kt 2 nt PN+1 - ln PN+1 =
t t
k=1 n=1
(s ) (ln )
N *
*t + c0 + ln cnt
1 c + s*nt + PN+1 - ln PN+1 + ct
c * (18)
2 nt t t
n=1 (1- n )
where 1 c 1 (sc + s*nt is used in order to leave the differences in nontraded
)
2 (s N
N+1t+ s*N+1 =1-
)
t 2 nt
n=1
good's prices on the right-hand side, and therefore test for the violation of homogeneity
constraint in prices (due to measurement error in the nontraded price, for example).
Notice that the year fixed-effects completely absorb the explanatory power of time trend
appearing in (17'), which makes the latter redundant. In addition, a classical error term ct is
introduced in (18) to capture the productivity difference between country c and the hypothetical
country. Equation (18) shows that the difference in country c productivity relative the
hypothetical country can be estimated by a year fixed effect, a country fixed effect, its relative
export variety, and the relative nontraded good price index.
5. Data and Estimating Equations
With data on GDP, factor endowments, nontraded good prices, and industry shares, we
can estimate (18) with the sample data set together with the system of share equations. Most
importantly, such a system of equations enables us to estimate the elasticity of substitution
16
between different output varieties within an industry, n , which is not sufficiently identified by
the share equations alone. The output shares of the hypothetical country, appearing as s*nt , are
measured using sample averages in (18), but will be fully absorbed by year fixed effects, nt in
the share equations (16). Then the equality of n can be imposed between (16) and (18) to
identify these elasticities.
Our data set covers 34 countries from 1982 to 1997, a total of 342 observations. GDP is
measured in constant 1995 U.S. dollars to make cross country and time series comparisons
appropriate. We will use (9) to measure export variety from country c to the U.S. in every years
1972 1988 (using the TSUSA data), and 1989 1997 (using the HS data). This gives a
consistent comparison of export variety in each country relative to the hypothetical country
producing all varieties.
There are three kind of primary factor endowments: labor, capital and agriculture land.
Labor is defined as the number of persons in the labor force of each country. Capital is
constructed using perpetual inventory method using real investment of the countries. Real
investment is obtained by deflating the gross domestic capital formation of the countries with the
respective GDP deflator on domestic capital formation. In addition, we construct the base year
capital stock using an infinite sum series of investment prior to the first year, assuming that the
growth rate of investment of the first five years are good proxy for investment prior to the first
year. All these data, together with price deflators of GDP, exports and imports are available in
World Development Indicators (World Bank, 2003).
We aggregate up all export goods into N = 7 sectors: agriculture, textiles & garments,
woods & papers, petroleum & plastics, mining & basic metals, machinery & transport
equipment, and the electronics. The value added of these sectors are available in the UNIDO
17
data set, which we compare to the GDP values to construct the value added share of each sector
in GDP. We also need information on factor shares in national income for the estimation. A
United Nations national account data set is obtained which has information on labor share in
GDP.7 One minus the labor share gives us the sum of capital share and land share, which we are
not be able to separately identify. To overcome this shortcoming, we chose to estimate the land
share in the productivity equation as follows. It can be shown from (18) that the log of GDP is
the sum of the log of overall prices (denoted Pt for brevity), productivity (At), and the weighted
log of endowments:
ln(GDPt) = ln At + ln Pt + sLt ln Lt + sKt ln Kt + (1- sLt - sKt)ln Tt .
Then we can estimate the share of land (Tt) by moving those terms for which we have data to the
left-hand side:
ln(GDPt ) - sLt (lnLt - lnTt ) - (1- sLt )(lnKt - lnTt )- lnTt =
ln At + ln Pt - (1- sLt - sKt )(ln Kt - lnTt ). (19)
Thus, when we use the labor share and one minus the labor share to weight lnlt ln(Lt /Tt )
and ln(Kt / Tt ), respectively, we should also include capital per unit of land lnkt ln(Kt / Tt )
on the right-hand side of the equation, as shown in (19). The estimated coefficient associated
with capital per unit of land is interpreted as the negative value of the average share of land in
GDP.
We proceed with a system of eight equations, consists of the seven sectoral share (16)
equations and the country productivity equation. According to (18) and (19), let the dependent
variable of the country productivity equation be TFP adjusted for capital-land ratio and prices of
nontraded goods:
7 We thank Ann Harrison for providing this data.
18
Adj. TFPt lnG Pt ,Vt - scLt + s*Lt lnlct - lnl*t - 1- scLt + s*Lt ln kct - ln k*t
c ( c c) 1( )( ) ( 1( ))( )
2 2
(20)
- lnTt - lnTt -
( c * ) (s )( )
7
1 c + s*nt lnP8 - lnP8 .
c *
2 nt t t
n=1
Making use of the homogeneity restriction 8
m=1mn = 0 in the share equations, and introducing
land and capital per unit of land onto the right of the productivity equation, our estimating
system becomes:
scnt = nt + Ln lnlct - lnl*t + Kn lnkct - ln k*t
( ) ( )
(
7 (21a)
+ c * )
mn
m=1 (lncmt *
1- m ) - lnP8 - lnP8 + cnt , n =1,...,7,
t t
Adj. TFPt = *t + K lnkct - ln k*t +8 lnP8 - ln P8
c ( ) ( c *)
t t
(s )
7 *
+c0 + lncnt
1 c + s*nt + ct . (21b)
2 nt
n=1 (1- n )
If the homogeneity constraint in prices are not violated we expect 8 to equal to one, whereas K
represents the negative value of the share of land in GDP. The constraints will be tested in the
regressions. With the estimated parameters, we will be able to construct country productivity
differences according (22):
Estimated TFPt Adj. TFPt - ^ - ^ K ln kct - ln k*t -^8 lnP8 - ln P8
c c * ( ) ( c *)
t t t
(s )
7 *
= ^ +
c lncnt
1 c (22)
0 + s*nt + ^ct .
2 nt
n=1 (1- ^ )
n
Due to cross equation restrictions on 1/(1- m) and mn, and the multiplicative nature of
these parameters, we need to use nonlinear system estimation to estimate equations (21a) and
(21b). This involves minimizing the criterion function of the full system with a consistently
estimated variance-covariance matrix. In addition, endogeneity and measurement errors of some
19
right-hand side variables need to be addressed. First, export variety could be endogenous.
Countries that have higher productivity may be able to produce more export varieties, which
leads to correlation between export variety and the regression errors. To correct for such
endogeneity, appropriate instrumental variables that are correlated to export variety but not
country productivity would be necessary. Eaton and Kortum (2002) and Melitz (2003) provide
us with such variables. In their models, export variety depends on various trade costs variables
such as tariffs, transport costs and distance. More importantly these trade costs variables only
affect country productivity through export variety. Thus, by using these variables as instruments
we can obtain estimates that are consistent. A subsequent over-identifying restrictions test will
then allow us to test for the validity of these instruments.
Second, due to the lack of available data, prices of nontraded goods are constructed using
the GDP deflator net of price of tradable goods. This may introduce serious measurement errors
and cloud correlation between the variables. In this case we can also treat the price of nontraded
goods as correlated with the error, and IV estimation would allow us to have more precise
estimates.
In the next section, we proceed by first estimating the system of equations without
correcting for endogeneity of export variety and measurement errors of nontraded good prices.
A full nonlinear 3SLS estimation with trade cost variables as instruments will then be presented.
Based on the nonlinear 3SLS estimation, a series of specification tests are performed: on the
homogeneity constraints on prices and endowments, symmetry constraints on cross price effects,
as well as the over-identifying restrictions of the instruments will be implemented. Finally, since
the first-stage regression of the nonlinear 3SLS system involves regressing the derivatives of the
20
criterion function with respect to all parameters on all instruments and exogenous variables, we
present some descriptive linear estimation linking export variety to all the instruments.
6. Estimation Results
Table 1 presents the result of the nonlinear system of share equations (21a) with the
country TFP equation (21b), estimated using iterative seemingly-unrelated regressions (ISUR).
All the homogeneity constraints on prices and endowments, as well as the symmetric constraints
are imposed in the share equations. Columns (1) to (7) of the table show the estimated
coefficients of each of the industry share equations, and the last column shows the estimated
coefficients of the country productivity equation.
In the top part of Table 1 in columns (1) to (7) we report mn, which are the partial price
effects due to export variety changes of the industry in the rows on the share of industries in the
columns. All the own-price effects nn are estimated to be positive and most are highly
significant.8 In other words, the underlying supply curves of these industries are positively
sloped. The bottom part of Table 1 in columns (1) to (7) presents the Rybczynksi effects of
endowments on the share of each industry. Positive point estimates indicate industry expansions
due to the increases in certain endowments. For example, an increase in the labor endowment
relative to that of land hurts agriculture, wood & paper, and the machinery & transport industry.
On the other hand, an increase in the labor endowment relative to land benefits textiles &
garments, petroleum & plastics, mining & metals, and the electronics industry. Similarly, while
an increase in capital relative to land hurts textiles & garments, petroleum & plastics, and mining
8Due to convergence problem, the nn coefficient of the petroleum & plastics industry (industry 4), is estimated
separately, by fixing all the rest of the parameters in the optimal values. We repeated the process a few rounds, and
the estimation results are very stable, as presented in Table 1.
21
& metals, such an increase benefits woods & paper, machinery & transport, and the electronics
industry. These finding are reasonable and broadly similar to those of Harrigan (1997).
The top half of column (8) in Table 1 presents the ISUR estimates of 1/(1- n ) for each
industry in the row. All the point estimates are positive, and most are smaller than one. This
implies that the underlying elasticities of substitution are negative, as suggested by theory. The
industry that is the most heterogeneous in production is electronics, for which an increase in
export variety contributes the most to country productivity. Furthermore, from the coefficient of
capital-land ratio in the lower part of column (8) in Table 1, we can infer that the average
estimated land share in GDP is about 10 percent. Finally, the coefficient on the price of
nontraded goods is significantly less than one, which violates the homogeneity constraint on
prices when we do not use instruments.
Table 2 presents the estimated coefficients using nonlinear 3SLS with a set of
instruments consisting of U.S. tariffs by industry, exporting country and year (seven industry
effective tariffs), indicator variables for various trade agreements between the U.S. and the
exporting countries (CANFTA, NAFTA, CBI, ANDEAN), distance between exporting countries
and US (in kilometers), average transport costs interact with two distance dummies, and relative
endowments. The nonlinear 3SLS estimates of the own-price effects reported in Table 2 are
significantly larger than the ISUR estimates from Table 1. This is not surprising since apart from
endogeneity problems, the export variety indexes and relative price of the nontraded sector may
have measurement errors which bias the estimates toward zero. Point estimates of the own price
effects range from 0.004 in machinery & transport to 0.133 in the wood & paper industry. The
Rybczynski effects of endowments presented in the bottom of this table are very similar to that
of the ISUR estimates, both in terms of magnitude and statistical significance.
22
The nonlinear 3SLS estimates of 1/(1- n ) presented in column (8) of Table 2 are larger
than the ISUR estimates in general. They range from 0.324 in the agriculture industry to 0.977
in the electronics industry. Thus agriculture industry is revealed to be most homogeneous in
production while the electronics is the least homogeneous: an increase in export variety in the
electronics industry would contribute most to country productivity, while export variety in
agriculture contributes the least. The ranking of industries according to their implied elasticities
of substitution are: electronics (-0.024), machinery & transport (-0.575), mining & basic metals
(-0.637), woods & paper (-0.669), textiles & garments (-0.698), the petroleum & plastics
industry (-1.976), and agriculture (-2.086).
The lower part of Table 2 presents the control variables in the country TFP equation. As
mentioned above, the estimated coefficient associated with the log capital-land ratio has the
interpretation of the negative of the average share of land in GDP. However, while this land
share is about 10 percent in the previous ISUR estimation, it is not precisely estimated in the
current nonlinear 3SLS estimation. The estimated coefficient on the log-difference in the
nontraded goods price is about 0.26. Similar to the previous ISUR finding, this estimate is
significantly less than one which indicates that the price of nontraded goods is poorly measured.
However, with the country and year fixed effects, and the inclusion of these two variables as
controls, as long as the measurement error in nontraded goods is not systematically related to the
country productivity or the export variety indexes, our estimation results should remain robust.
Overall, the results presented in Table 2 show that export variety is significant in determining
industry shares in GDP and aggregate country productivity.
23
7. Specification Tests
Given that the above nonlinear 3SLS estimation involves minimizing the criterion
function, the minimized value provides a test statistic for hypothesis testing. The difference
between the values of the criterion functions of the restricted and unrestricted models is
asymptotically chi-squared distributed with degree of freedom equal to the number of
restrictions. According to Davidson and MacKinnon (1993, p. 665), it is important that the same
estimate of variance-covariance matrix be used for both the restricted and unrestricted
estimations, in order to ensure that the test statistic is positive.
The nonlinear 3SLS estimation has the following restrictions. For each of the share
equation, the homogeneity constraints on prices and endowments are imposed. The homogeneity
constraint on endowments is imposed in the GDP function but not the homogeneity constraint on
prices due to the possible measurement errors in nontraded good prices. The twenty-one
symmetry constraints on the cross-price effects are also imposed on the whole system of
equations, as well as the over-identifying restrictions due to the extra instruments. We first test
for all the homogeneity constraints one at a time. In each case, we constrain the variance-
covariance matrix to be that of the unrestricted model. We further test for the overall
specification of the system by jointly testing the symmetry constraints (12) and over-identifying
restrictions, conditional on all the accepted homogeneity constraints. This is done by comparing
the value of criterion function of the restricted model to a just-identified model with no
symmetry constraints and no extra instruments.
Table 3 presents the test statistics and the associated p-values of all the hypothesis tests.
None of the homogeneity constraints for endowments are rejected, and all industry share
equations satisfy the homogeneity constraints in prices. The only violation of homogeneity
24
constraint in prices is for the TFP equation, which we did not impose in the previous estimation.
Thus, the results supported our previous specification in terms of the imposed homogeneity
constraints.
Conditional on all the satisfied homogeneity constraints, the total number of parameters
estimated (excluding country fixed effects) is 178 and the total number of instruments is 264 (33
per each equation). This implies that the number of over-identifying restrictions is 86. This
jointly tests the 21 symmetry constraints, as well as 65 over-identifying constraints if the system
was just-identified. The minimized value of criterion function of the restricted system with the
fixed variance-covariance matrix is 89.4, and given that the value of criterion function of a just-
identified system is 0 (see Davidson and MacKinnon, 1993, p. 234), the overall specification of
the model is not rejected. The p-value of the test statistics is 0.38. Thus the data support the
joint hypotheses of symmetry constraints and over-identifying restrictions. Table 4 also provide
separate test statistics for the 21 symmetry constraints and the 65 over-identifying restrictions.
In both cases, the individual hypotheses are not rejected.
In summary, not only is the overall specification of the nonlinear 3SLS model not
rejected by the data, all the instruments included are also shown to be not related with the
regression errors (given that they jointly passed the over-identifying restriction test). Thus, the
results presented in Table 2 provide evidence that trade cost variables such as tariffs, distance
and transport costs affect country productivity only through export variety, so that variety is the
mechanism (Hallak and Levinsohn, 2004) through which trade affects country productivity. In
the next section, we will further present some direct evidence linking these trade costs variables
to export varieties of the industries.
25
8. Effects of Tariffs and Transport Costs on Export Variety
Table 4 presents least squares (LS) estimation linking export variety to all instruments
and exogenous variables of the nonlinear 3SLS system presented in Table 2. This is similar but
not identical to the first-stage estimation of the nonlinear system, which involves regressing the
derivatives of each equation with respect to the parameters of the system on all the instruments
and exogenous variables. For example, differentiating (21b) with respect to 1/(1- n ) we obtain
1 (sc ) *
2 nt + s*nt lncnt, which is the export variety index for country c and sector n, times the average
share of that industry. In comparison, the regressions we present in Table 4 just use the export
variety index lncnt as a dependent variable, which allows us to see the partial relationships
*
between export variety and the trade cost variables.
The top part of Table 4 shows the effects of a one percentage point increase in the U.S.
tariff on the export variety of the industry in the columns. Tariffs are constructed from detailed
U.S. custom data by taking the ratio of duties paid over imports. They vary by industries,
countries and years. We expect industry export variety to decrease with the own tariff of the
industry, while there may exist some positive effects due to reallocation of resources among
industries when there is a tariff increase in other industries.
All industry export variety indexes are negatively correlated with own tariffs except for
the textiles & garments and the electronics industry. For textiles & garments, MFA quotas are
known to be more restrictive and binding than tariffs, which may explain the insignificant effect
of tariffs on export variety. For the electronics industry, it could be the case that non-tariff
barriers, transport costs and skilled labor endowments are more important in explaining
expansion in export variety than tariffs. For the rest of the industries, the own tariff effects are
all negative and statistically significant. A one percentage point increase in U.S. tariffs lowers
26
export variety by 16.7 percent in the petroleum & plastics industry, at the highest, and 3.7
percent in the mining & basic metals industry, at the lowest. Finally, most industries benefit
from tariffs imposed on other industries due to reallocation of productive resources. For
example, the textiles & garments industry expands its export variety due to tariffs imposed on
agriculture industry and basic metals industry. Tariffs imposed on the basic metals industry also
benefits the machinery & transport industry, and the electronics industry. Using these tariff
impact estimates, along with the estimates of 1/(1- n) in Table 2 and the sample average
industry shares, we calculate that a 10 percentage point increase in all U.S. tariffs would reduce
the exporting country productivity by 2 percent due to the decreases in export variety of the
industries. This implies that tariffs are both statistical and economically important in explaining
export variety and country productivity.
The next section of Table 4 shows the marginal effects of four trade agreement dummies
(CANFTA, NAFTA, CBI and ANDEAN) on export variety. Given that we already control for
tariffs, these variables capture the effect of the reduction in non-tariff barriers due to the signing
of such agreements on export variety. CANFTA is shown to have positive and significant
impact on export variety in textiles & garments, wood & paper, machinery & transport and the
electronics industry, while NAFTA is shown to have no significant additional effects on variety.
On the other hand, the CBI increases the export variety in agriculture, textiles & garments,
machinery & transport, and the electronics industry, while ANDEAN provides for variety
expansion in textiles & garments and the petroleum & plastics industry.
The third section of Table 4 focuses on the effects of geography related trade costs
variables such as distance (in log of kilometers) and transport costs.9 In order to allow for
9Distance from US is the geographical distance in kilometers between the capitol cities, as obtained from Nicita and
Olarreaga (2004).
27
transport costs to have different effects on countries that are in different location, we interact
transport costs with nearby and far-away country dummies, defined as countries that are less or
more than median distance (7,037km) to the U.S. An increase in distance between an export
country and the U.S. diminishes the export variety in agriculture, petroleum & plastics and the
mining & basic metals industry, while distance does not seem to matter to the export variety in
the electronics industry. On the other hand, increases in transport costs reduce export variety in
all industries except agriculture. Transport costs are particularly important for the nearby
countries exporting textiles & garments, and far-away countries exporting petroleum & plastics
products. Transport costs are significant in reducing export variety in the machinery & transport
and electronics industries for countries in all locations.
The last section of Table 4 presents the effects of endowment differences in explaining
export variety in different industries. These variables are the exogenous variables from the
system of share equations and the country productivity equations. All the endowment variables
are positive and highly significant. The R2 values of these regressions range from 0.62 in the
agriculture industry to 0.83 in the mining & basic metals industry. Overall, the results presented
in Table 4 suggest that all the trade costs variables are important in explaining export variety of
the various industries, as well as the endowment variables. This provide empirical support to
models such as Eaton and Kortum (2002) and Melitz (2003), where trade costs are shown to
determine export variety.
9. Productivity Decomposition
To gain additional insight into the links between export variety and country productivity,
we performed a post-regression decomposition of estimated productivity based on the results in
Table 2. Using (22), we compute the variance of estimated country TFP as:
28
*
var(Estimated TFPt ) = var(^ ) + varn (s )
7
c c lncnt
1 c
0 + s*nt
2 nt
=1 (1- ^ )n
7 *
+ 2cov^ ,n=1 scnt + s*nt
c t (23)
0 12 ( ) lncnt
(1- ^ ) + var(^c).
n
The first term on the right is the variance of country fixed effects, the second is the contribution
of export variety constructed as a weighted average across industries, the third is the covariance
between these, and the fourth is the error variance. If we remove the country fixed effects and
the regression error, then the "variety-induced" country TFP is defined as:
(s )
N *
Variety-induced TFPt c lncnt
1 c + s*nt , (24)
2 nt
n=1 (1- ^ )
n
Taking the first difference of (23) within a country across two years, we can derive the
growth decomposition of country productivity into two terms, which is the growth of variety
induced country TFP and the change in regression errors:
( ) ln (^ )
* c*
Growth of TFPt c (s )
N lncnt
1 c + s^*nt 1 nt-1+ c
2 nt - scnt-1 + s^*nt-1
2 t- ^ct-1 . (26)
n=1 (1- ^ )
n (1- ^ )
n
The variance in the growth rate of country TFP is therefore the sum of the variance of the growth
rate of variety-induced country TFP, and the variance of the difference in error terms, along with
the covariance between the two terms.
Table 5 shows the variance decomposition of country TFP in levels and growth rates.
Not surprisingly, most of the cross-country differences in the TFP levels are explained by
country fixed effects which is not unusual for this type of cross-country study. Controlling for
country fixed effects, variety-induced country TFP can only account for about 2% of the country
productivity levels. However, variety-induced TFP and country fixed effects are correlated,
which jointly contribute nearly 14% of the cross-country variation in TFP levels. If we set aside
29
country fixed effects, and only focus on variety-induced TFP and regression error terms, then
variety-induced TFP can explain 60% of country productivity in levels.
The second column of Table 5 shows the growth decomposition of country productivity.
About 13% of the within-country growth in TFP can be explained by the year-to-year growth in
export variety, while the remaining part is explained by the change in regression errors and the
correlation between the two terms.10 This suggests that while the overall productivity differences
across countries are mainly explained by country fixed effects, export variety nonetheless is
important in explaining within country productivity differences in levels and growth rates.
To further illustrate the effects of export variety on country productivity, according to
(24) a 1% increase in the export variety of each industry n would increase country productivity
1
by 1 (sc + s*nt) percent. Thus, we can compute that at the sample mean, a 10% increase
2 nt (1- ^ )
n
in export varieties of all industries could lead to 1.3% increase in country productivity. This
effect is significant both statistically and economically.
Figures 3 and 4 plot the partial scatter graph of the country TFP against the export variety
in level and in growth respectively (conditional on country fixed effects and regression errors).
It is evident that holding all else constant, export variety has significant explanatory power for
the variation of the country productivity differences, both in level across countries and in growth
within countries.
Figure 5 presents a cross country scatter plot of the country TFP against export variety in
1991. Both variables are shown in deviation from their sample means. There is a clear positive
relationship between the export variety of a country and its productivity, which is highlighted by
10Similar results are obtained when we express the productivity growth decomposition using Tornqvist
approximation, rather than first different as in (26). Contribution of variety growth to the growth country TFP is
around 10%.
30
the positive sloping regression line. Canada has the most export variety which is twice as much
as the sample mean. In terms of the productivity differences, Canada is 42% higher than the
sample mean. Japan has the highest productivity which is 77% higher than the sample mean. In
terms of export variety, an industry in Japan produces 83% more export products than the sample
mean.
Other countries that have higher than productivity and export variety in Figure 5 include
South Korea, Singapore, and some other OECD countries such as Britain, France, Italy and
Australia. These countries appear on the first quadrant. Countries that perform poorly in terms
of the country productivity and export variety are in the third quadrant. They include Uruguay,
Kenya, Turkey, and the Philippines. For example, export industries in Uruguay produces 179%
less variety than the sample mean, and its productivity is 84% lower. We can also compare
country pairs from the figure. For instance, in 1991, Singapore produces 60% more export
products than the Philippines, and the productivity of Singapore is about twice as high as that of
the Philippines.
We further explore the movement of export variety and productivity within a country
over time. Figure 6 compares Canada to the sample mean in terms of productivity, variety-
induced productivity differences, and the weighted-average export variety, from 1985 to 1997.
The two productivity series are presented in bars relative to the left-hand scale. The export
variety index is shown as a line in the figure, measured relative to the vertical right-hand scale.
In 1985, Canada's productivity is 14% higher than the sample mean, while it produces 93% more
export products relative to the sample mean. In 1997, the productivity gap reduces to 7% while
the export variety difference is about 62%. Thus over the years, we see a gradual decline of
31
export variety in Canada relative to the rest of the world and this is reflected in the productivity
series.
Figure 7 compares Japan to South Korea. Similar to the previous figure, the two
productivity series are presented in bars relative to on left-hand scale. The export variety index
is shown as a line in the figure, relative to the right-hand scale. The line series shows that, in
1982, industries in Japan produced 50% more export variety than South Korea. The Japanese
advantage over Korea deteriorates over time such that in 1995, an industry in Japan produced
only 20% more variety than Korea. On the other hand, the first bar series shows that, over the
same period of time, the underlying TFP advantage of Japan declines from 20% to near zero.
Thus, with Korea catching up in export variety, the underlying productivity gap between Korea
and Japan is also narrowing.
A similar comparison can be done for Israel and Greece, as shown in Figure 8. In 1985,
Israel produced 30% more export variety than in Greece, and by 1995, the advantage of Israel
over Greece widens to nearly 90%. On the other hand, with a negative 4% TFP difference, in
1982 Israel was less productive than Greece, but by 1995, Israel had became about 10% more
productive than Greece. Thus, there is a positive correlation between the observed export variety
difference and the country productivity difference, as predicted by the variety-induced
productivity difference, the second bar series in the figure.
10. Conclusions
Existing analyses of export variety and growth have been restricted to a limited range of
countries (e.g. Feenstra et al, 1999), or a single aggregate measure of export variety correlated
with GDP (Funke and Ruhwedel, 2001a,b, 2002). In this paper we have attempted to improve
the estimation of product variety on country productivity by allowing for multiple sectors, and
32
introducing export varieties into the GDP function. In exploiting the translog GDP function we
are following Harrigan (1997), who hypothesized that export prices would differ across countries
due to total factor productivity in exports. We have used the industry CES price indexes that
differ across countries due to export variety, and enter as "price effects" into the GDP function
and sectoral share equations. Estimating the share equations simultaneously with the GDP
equation (transformed to become relative country productivity) allows us to identify and estimate
the elasticity of substitution n between export varieties in each sector, and then infer the
contribution of export variety to country productivity.
The resulting elasticity estimates range from a low of -0.02 in the electronics industry, to
a high of 2 in the agriculture industry and the petroleum & plastics industry. Because these are
the elasticity of substitution between outputs (measuring the curvature of the concave production
possibilities frontier), we have less intuition about the magnitude of the expected estimates than
for inputs. But the ranking we have obtained seems reasonable, since there is the least
substitution between export varieties in electronics, and the greatest substitution between
varieties within agriculture and petroleum & plastics. In electronics, the estimate of -0.02
indicates that a 10% expansion of product varieties has the same effect as a 10/1.02 = 9.8%
increase in prices, in terms of drawing resources into that sector. For agriculture and petroleum,
however, a 10% increase in product variety has the same effect as a 10/3 = 3.3% rise in prices,
since these products are more highly substitutable in terms of production.
We have treated export variety as an endogenous variable, and as instruments use those
suggested by the work of Eaton and Kortum (2002) and Melitz (2003): tariffs, transport costs
and distance. By using an over-identifying restriction test on the nonlinear system estimation,
we have also been able to test the important exclusion restriction suggested by these models, that
33
tariffs and transport costs should not have an impact on productivity except through export
variety. This restriction cannot be rejected, and confirms the importance of export variety as the
mechanism (Hallak and Levinsohn, 2004) by which trade affects productivity. Our results also
show that a 10 percentage point increase in U.S. tariffs would lead to a 2% fall in exporting
countries' productivity, which indicates that tariffs are statistically and economically important
in affecting productivity via export variety.
Finally, we have also calculated the impact of export variety differences across countries
on their respective productivities. Not surprisingly, country fixed effects in a panel regression
still account for the vast majority of country productivity differences, so that export variety
explains only 2% of the total variation in country productivity. But setting aside country fixed
effects, export variety can explain 60% of the residual productivity differences, as well as 13%
of the within-country productivity growth. Moreover, at the sample mean, a 10% increase in
export varieties of all industries leads to 1.3% increase in country productivity. By considering
specific pairs of countries over time, we have also traced out quite plausible patterns between
changes in export varieties and changes in country productivities. These patterns confirm the
importance of export variety in explaining county productivity.
34
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from East Asia," Journal of Asian Economics, 12, 493-505.
Funke, Michael and Ralf Ruhwedel (2002) "Export Variety and Export Performance: Empirical
Evidence for the OECD Countries," Weltwirtschaftliche Archiv,138(1), 97-114.
35
Funke, Michael and Ralf Ruhwedel (2003) "Trade, Product Variety and Welfare: A Quantitative
Assessment for the Transition Economies in Central and Eastern Europe," BOFIT
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Grossman, Gene M. and Elhanan Helpman (1991) Innovation and Growth in the Global
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Hallak, Juan Carlos and James Levinsohn (2004) "Fooling Ourselves: Evaluating the
Globalization and Growth Debate," NBER working paper no. 10244.
Harrigan, James (1997) "Technology, Factor Supplies, and International Specialization:
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Hausman, J. (1983) "Specification and Estimation of Simultaneous Equation Models," in Z.
Griliches and M. Intriligator, eds., Handbook of Econometrics, Amsterdam: North
Holland.
Helpman, Elhanan, Marc Melitz and Stephen Yeaple (2004) "Exports vs. FDI with
Heterogeneous Firms," American Economic Review, March, 300-316.
Hummels, David and Peter Klenow (2002) "The Variety and Quality of a Nation's Trade,"
NBER working paper no. 8712.
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Industry Productivity," Econometrica, 71(6),1695-1725.
Nicita, Alessandro and Marcelo Olarreaga (2004) "Exports and Information Spillovers," the
World bank.
Romer, Paul (1990) "Endogenous Technological Change," Journal of Political Economy 98(5),
pt. 2, October, S71-S102.
Sato, Kazuo (1976) "The Ideal Log-Change Index Number," Review of Economics and
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Vartia, Y.O. (1976) "Ideal Log-Change Index Numbers", Scandinavian Journal of Statistics 3,
121-126.
36
Table 1: Dependent Variables - Industry Shares in Columns (1) to (7), and Adjusted TFP in Column (8)
Estimation method: Iterative Seemingly Unrelated Regressions
Total system observations: 2736
Observations per equation: 342
(1) (2) (3) (4) (5) (6) (7) (8)
Textiles & Petroleum & Mining & Machinery &
Independent Variables: Agriculture Garments Wood & Paper Plastics Basic Metals Transports Electronics Adj. TFP
Agriculture 0.038*** -0.005 -0.017*** 0.010** -0.019*** -0.005* -0.001 0.303***
(0.010) (0.004) (0.006) (0.004) (0.005) (0.003) (0.001) (0.076)
Textiles & -0.005 0.068*** -0.039*** -0.018*** 0.007*** -0.009*** -0.004** 0.282***
Garments (0.004) (0.010) (0.008) (0.005) (0.002) (0.003) (0.002) (0.043)
:
in
ytei Wood & -0.017*** -0.039*** 0.102*** -0.042*** -0.004* 0.005 -0.004* 0.233***
Paper (0.006) (0.008) (0.013) (0.006) (0.002) (0.003) (0.002) (0.031)
Var
tropx Petroleum & 0.010** -0.018*** -0.042*** 0.051 0.005*** 0.002 -0.005** 0.091***
E
Plastics (0.004) (0.005) (0.006) - (0.002) (0.003) (0.002) (0.015)
vei
lat
Mining & -0.019*** 0.007*** -0.004* 0.005*** 0.015*** -0.006*** 0.001 0.788***
Re
of Basic Metals (0.005) (0.002) (0.002) (0.002) (0.004) (0.002) (0.001) (0.217)
og
L
Machinery & -0.005* -0.009*** 0.005 0.002 -0.006*** 0.005 0.009*** 0.516***
Transports (0.003) (0.003) (0.003) (0.003) (0.002) (0.003) (0.003) (0.130)
Electronics -0.001 -0.004** -0.004* -0.005** 0.001 0.009*** 0.005*** 1.030***
(0.001) (0.002) (0.002) (0.002) (0.001) (0.003) (0.002) (0.359)
Labor-Land -0.004*** 0.004*** -0.004*** 0.007*** 0.006*** -0.003*** 0.005***
: Ratio (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
vei
lat
Capital-Land 0.002 -0.002** 0.004*** -0.004*** -0.005*** 0.007*** 0.002** -0.107***
Re
Ratio (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.023)
of
og
L
Non-Traded 0.214***
Goods Prices (0.006)
Year Fixed-Effects Yes Yes Yes Yes Yes Yes Yes Yes
Country Fixed-Effects Yes
R-squared 0.3396 0.3804 0.4614 0.1916 0.4217 0.5897 0.5976 0.9980
Note: For columns (1) to (7), each log of relative export variety coefficient is the partial price effect of the industry in that row on
the share of the industry in the column. These are the point estimates of the gamma's. Own price effects are in bold.
For column (8), each log of relative export variety coefficient is the point estimate of 1/(1-sigma) of the industry in that row.
*, **, and *** indicate significance at 90%, 95%, and 99% confidence levels respectively, and White-robust standard errors are in parentheses.
37
Table 2: Dependent Variables - Industry Shares in Columns (1) to (7), and Adjusted TFP in Column (8)
Estimation method: Three Stage Least Squares Regressions
Total system observations: 2736
Observations per equation: 342
(1) (2) (3) (4) (5) (6) (7) (8)
Textiles & Petroleum & Mining & Machinery &
Independent Variables: Agriculture Garments Wood & Paper Plastics Basic Metals Transports Electronics Adj. TFP
Agriculture 0.062** -0.015** -0.008 -0.013* -0.016* -0.002 0.002 0.324**
(0.026) (0.008) (0.013) (0.007) (0.009) (0.006) (0.005) (0.143)
Textiles & -0.015** 0.051** -0.054* 0.005 0.019* -0.015* 0.012* 0.589**
Garments (0.008) (0.023) (0.029) (0.005) (0.011) (0.009) (0.007) (0.264)
:ni
yteira Wood & -0.008 -0.054* 0.133** -0.018 -0.039** 0.038* -0.048** 0.599**
Paper (0.013) (0.029) (0.065) (0.013) (0.019) (0.022) (0.024) (0.267)
V
tro
Petroleum & -0.013* 0.005 -0.018 0.040** 0.002 -0.010 0.004 0.336**
Exp
Plastics (0.007) (0.005) (0.013) (0.017) (0.004) (0.007) (0.005) (0.145)
ve
tiale Mining & -0.016* 0.019* -0.039** 0.002 0.035** -0.016* 0.012 0.611**
R
of Basic Metals (0.009) (0.011) (0.019) (0.004) (0.016) (0.010) (0.008) (0.273)
og
L
Machinery & -0.002 -0.015* 0.038* -0.010 -0.016* 0.004 0.009 0.635**
Transports (0.006) (0.009) (0.022) (0.007) (0.010) (0.010) (0.008) (0.249)
Electronics 0.002 0.012* -0.048** 0.004 0.012 0.009 0.018* 0.977**
(0.005) (0.007) (0.024) (0.005) (0.008) (0.008) (0.010) (0.448)
Labor-Land -0.002 0.004*** -0.004 0.005*** 0.006*** -0.002 0.007***
: Ratio (0.002) (0.001) (0.002) (0.002) (0.001) (0.002) (0.001)
ve
tiale Capital-Land 0.000 -0.003** 0.004** -0.004** -0.004*** 0.005*** 0.000 0.000
R
Ratio (0.002) (0.001) (0.002) (0.002) (0.001) (0.001) (0.001) (0.110)
of
Log
Non-Traded 0.262***
Goods Prices (0.022)
Year Fixed-Effects Yes Yes Yes Yes Yes Yes Yes Yes
Country Fixed-Effects Yes
R-squared 0.2760 0.2710 0.2397 0.1072 0.2221 0.4779 0.4999 0.9562
Note: For (1) to (7), each coefficient of the log of relative export variety in the row industry is the partial price effect of that industry on
the share of the column industry. These are the point estimates of gamma's. Own price effects are in bold.
For (8), each coefficient of the log of relative export variety in the row industry is the point estimate of 1/(1-sigma) of that industry.
*, **, and *** indicate significance at 90%, 95%, and 99% confidence levels respectively, and White-robust standard errors are in parentheses.
Instruments: effective tariffs, trade agreement dummies (CANFTA, NAFTA, CBI, ANDEAN), distance, average transport cost interacts
with distance dummies, relative land, labor and capital endowments.
38
Table 3: Hypothesis Testing
Null Homogeneity in Symmetry in Over-identifying Overall
Hypothesis Endowments Prices Cross Price Effects Restrictions Specification
Degree of Freedom 1 1 21 65 86
Critical Value at 95% 3.841 3.841 32.671 84.821 108.648
Overall System 28.179 58.202 89.432
(0.135) (0.712) (0.379)
Agriculture 0.367 0.427
(0.544) (0.514)
Textiles & 0.888 0.011
Garments (0.346) (0.916)
Wood & 0.548 0.552
Paper (0.459) (0.458)
Petroleum & 0.571 0.612
Plastics (0.450) (0.434)
Mining & 0.435 0.440
Basic Metals (0.510) (0.507)
Machinery & 0.519 0.516
Transports (0.471) (0.473)
Electronics 0.391 0.422
(0.532) (0.516)
GDP Function 2.140 554.986***
(0.144) (0.000)
Notes: All test statistics are asymptotically Chi-squared distributed with degree of freedom equals number of restrictions.
Numbers in parentheses denote p-value of the test statistics.
39
Table 4: Dependent Variables - Export Variety Index
Estimation method: Ordinary Least Squares
Observations per equation: 342
Eq (1) Eq(2) Eq(3) Eq(4) Eq(5) Eq(6) Eq(7)
Textiles & Petroleum & Mining & Machinery &
Independent Variables: Agriculture Garments Wood & Paper Plastics Basic Metals Transports Electronics
Agriculture -7.901*** 4.362*** -3.790*** -7.426*** -2.153* -0.747 -2.878*
(1.269) (1.007) (1.309) (2.319) (1.292) (1.795) (1.675)
Textiles & -0.899 0.088 -2.318*** -1.947 -0.750 -3.321*** -3.645***
: Garments (0.662) (0.525) (0.683) (1.210) (0.674) (0.937) (0.874)
of
ffira Wood & 1.336 0.534 -5.053*** 3.198 -4.919*** -2.629 -1.334
Paper (1.709) (1.356) (1.763) (3.123) (1.740) (2.417) (2.255)
T
ivetceff Petroleum & -7.938*** 1.066 0.652 -16.707*** 0.977 3.659* 0.836
Plastics (1.551) (1.231) (1.600) (2.835) (1.579) (2.195) (2.047)
E
1+ Mining & 3.048** 4.248*** 3.742** -0.236 -3.678** 7.713*** 7.774***
of Basic Metals (1.494) (1.186) (1.541) (2.730) (1.521) (2.114) (1.972)
og
L
Machinery & 0.968 -1.885 -3.507* -0.650 -6.680*** -14.716*** -9.127***
Transports (1.904) (1.510) (1.964) (3.478) (1.938) (2.693) (2.512)
Electronics 1.085 -1.869 9.095*** 4.396 9.690*** 12.928*** 12.279***
(2.067) (1.640) (2.132) (3.777) (2.104) (2.924) (2.728)
Canada-US 0.233 0.346** 0.445** -0.423 0.228 0.542** 0.842***
Trade Agreement (0.174) (0.138) (0.179) (0.318) (0.177) (0.246) (0.230)
r:
fo
elba North America Free 0.131 0.073 -0.024 -0.132 -0.026 0.021 -0.104
Trade Agreement (0.194) (0.154) (0.200) (0.355) (0.198) (0.275) (0.256)
ri
Va
y Caribbean Basin 0.731*** 0.613*** 0.078 -0.356 -0.405*** 0.366* 0.329*
m Initiative (0.136) (0.108) (0.140) (0.248) (0.138) (0.192) (0.179)
m
Du
ANDEAN 0.256 0.383*** -0.027 0.662** -0.395** -0.227 -0.209
(0.181) (0.144) (0.187) (0.331) (0.185) (0.256) (0.239)
Log of Distance -0.219*** -0.031 -0.049 -0.348*** -0.101** -0.072 0.140**
(0.050) (0.040) (0.051) (0.091) (0.051) (0.070) (0.066)
Transport Cost of 2.088** -2.283*** -0.911 -2.462 -1.413 -6.591*** -5.455***
Close-by Country (0.998) (0.792) (1.030) (1.824) (1.016) (1.412) (1.318)
Transport Cost of 2.868** -1.174 -1.573 -6.116*** -1.576 -5.560*** -6.592***
Far-away Country (1.155) (0.917) (1.192) (2.111) (1.176) (1.634) (1.525)
Labor-Land 0.191*** 0.136*** 0.216*** 0.256*** 0.049 0.163*** 0.224***
Ratio (0.036) (0.028) (0.037) (0.065) (0.036) (0.050) (0.047)
:
of Capital-Land 0.125*** 0.064** 0.140*** 0.302*** 0.426*** 0.306*** 0.071*
og Ratio (0.032) (0.026) (0.033) (0.059) (0.033) (0.045) (0.042)
L
Difference in Land 0.278*** 0.179*** 0.273*** 0.489*** 0.489*** 0.397*** 0.175***
(0.022) (0.018) (0.023) (0.041) (0.023) (0.031) (0.029)
Years Yes Yes Yes Yes Yes Yes Yes
R-squared 0.6193 0.6195 0.6480 0.6502 0.8268 0.7628 0.6264
Note: All figures in bold are the own partial effects of effective tariffs. Standard errors are in parentheses.
Effective tariffs are the ratios of duties paid over industry exports.
Transport costs are the ratios of freight and insurance in custom values.
*, **, and *** indicate significance at 90%, 95%, and 99% confidence levels respectively.
40
Table 5: Productivity Decompositions
Level Decomposition Growth Decomposition
(in % of TFP) (in % of TFP)
Variance of Estimated Country TFP 0.2592 (100) 0.0016 (100)
Variance of Country Fixed Effects 0.2157 (83.2) -
Variance of Variety Induced TFP 0.0047 (1.8) 0.0002 (13.1)
2*Covariance between Country Fixed Effects and Variety Induced TFP 0.0356 (13.8)
Source: Authors calculation based on regression results of Tables 2.
41
q2t B
C
q1t
A
Figure 1: Output Varieties
q2t
B
C
A q1t
Figure 2: Input Varieties
42
coef = .11104563, se = .00701725, t = 15.82
.4
PER
MEX
.2
KOR
TUR KOR IDN
) GBRCAN
KOR
KOR
X| URY ZAFPHL CAN IDN
GBRCAN
CAN
ZAF KOR
GBRCAN
KORCAN
CAN
ytivit ECUTURESPAUSCOLJPN ITAITAKOR
PRT VENJPNKORITA
JPN ITAGBR
KORTHA
GBRCAN
IRL PERSGP PHL PHLITAITA CAN
AUSFRA
FRAPHL
SWEAUSJPNVEN
VENNLDJPN
ZAF
FRAFRAJPNGBR
JPNFRAITAITA
VENFRAITAGBRCAN
PHLJPNVENGBR
ITAGBR
ITAGBR
ISRECUPRT
PRT
GRCKENCRI AUTAUTPRTISR
PRT
PRT ZAFVENBLXPHL VENITAITAITA CAN
JPNKOR KOR MEX
GRCURY COL PERCOLPHLFRAVEN KOR
PRT SGP COLVENITA GBR CAN
ESPESPFRAFRA GBR CAN
AUSNLDFRA
AUS
TUR
PRT COLESPESPFRA
ZAF AUS BLXESP
ZAFAUS
ESPZAFFRAJPN
ESPESP
JPN
AUS
AUSVENVENGBR
ESP
ESPJPN
0 NZL
URYGRC AUT
IRL GRCAUTAUT SWECOLESPESPFRA
ZAF SWEESPCOL JPN
PER
CRI
CRIFINIRL
GRCCRIDNKFINNZL AUTISR
DNKECUISR ESPSWEBLXVEN
SWE AUS JPN
KENNZLNZLFINTUR
URY ISRCRI SWE
SGP ZAF KOR
URYFINIRLFINECUCRI
IRLNZLDNK AUTPRT
DNKECUDNK
AUTGRC ISR
ZAF ECUISR
SWE SWECOLAUSVENKOR
DNKISR
TURAUTISR
CRIAUT ISRPRT ZAFCOL
IRLDNKGRCAUT
DNKCRIISR KOR
FINNZLZAF
FIN
GRC FINFIN
CHLTURFINAUTISR PRT
CRIFIN
PRTCRI
AUTAUT PRT
DNK ISR ZAF SGPZAFCOL
COLZAFVEN
FIN GRCISR ZAF
produc GRC SGP
GRC
FIN GRCIRL
CRIFIN
AUT PRT
PRT
GRC TURPRT
ECU
e( NZL KOR
GRC
URYFIN CRI
NZL IRL
IRL IRL TUR
CHLIRL
NZL IRL
IRL IRL
-.2 TURPER
URY
URY
URY
URY
PER
-.4
-2 -1 0 1
e( variety | X )
Figure 3: Country Productivity versus Average Variety
coef = .50028222, se = .00896564, t = 55.8
.1
ISR
) .05
X| URY
FIN
h PRT
COL KOR
FIN
CRI AUT
ZAF
IRLAUTISRCAN
AUSFINAUS
TURZAFBLXFIN
CHLCOLISRCOL
PRTPHL
AUTAUT
ZAFCRI
IRLJPNISR
COLTURGRCIRL
TURISRKORURY
VEN
GRCSWEZAF
URY
NZLNZL
VENVEN
IDNAUSFIN
PERAUT
GRCZAF
NZLISR
NZLIRL
AUSGRC
ZAFDNK
CRIKOR
KORDNK
PRT
NZLECU
VEN
FIN
GRCKOR
VENFRAJPN
JPNCRIFRA
SGPIRL
ESP
_growtytivit URY SWE
ESPITA
GRCPRTPHL
BLXGBRURY
AUTAUS
DNKPRT
IRLITADNKJPN
ECUESPPRT
GBRJPN
FRAFRAISR
ZAFPHLVEN
GRCSWE
PRTPRTTUR
FRAFRAITA
ITAJPN
GBR
ITAESPCRIISR
ITACAN
CAN
KORPHL
COLGBRIRL
GRCCANPRT
CAN
ITA
AUSGBR
IRLITACOL
GBRKORFRA
IRLESPAUT
FINSGP
CANAUT
ISRFINAUS
DNKPHLCRI
ESPSWE
ITAPRTJPN
AUSESP
DNK
VENFRA
ECUGBRGBR
KORVEN
ECUPRT
ESPKOR
ITAFRA
FINPRT
SWE
IRLDNK
VENFRA
GBRFRA
SGP
GRCAUT
TURESP
FINAUT
ESPESPZAF
SGP
PHLZAF
CANZAF
VENKOR
0 ZAF
KORECUECU
GRCCRIVEN
KORITA
VENGBRGRC
IRLCAN
SWE
GBRPRT
JPNAUT
ITACOL
FRAISRAUT
JPNAUSCRI
PRTCOL
CAN
KOR
JPN
SWE
ZAFJPNMEX
ESPPERAUTNZL
NZLFIN
JPNFRA
FINDNK
PRTESP
TURTUR
COL
VENGRC
NLDAUS
ZAFESP
KORURY
IRLISR AUT
FINIRLZAF
CRI
DNKCOL
VEN KEN
ISR
PERCRI
ISR
URY NZL
produc ZAFURY
TUR
GRC
e( -.05 PER
URY
PER
-.1
-.2 -.1 0 .1
e( variety_growth | X )
Figure 4: Productivity Growth versus Variety Growth
43
coef = .6038302, se = .14890149, t = 4.06
1
JPN
DNK
AUT FRA
FIN
IRL
ISR AUS ITAGBRCAN
ESP
SGP
GRC
)
X| 0 PRT KOR
ytivit ZAF
VEN
TURCRI COL
produc URY PHL
e( -1
KEN
IDN
-2
-2 -1 0 1
e( variety | X )
Figure 5: Productivity Differences versus Product Variety Differences, 1991
0.16 1.2
0.14
1
0.12
0.8
0.1
0.08 0.6
0.06
0.4
0.04
0.2
0.02
0 0
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
Country Productivity Differences Variety Induced Productivity Differences
Product Variety Differences (right scale)
Figure 6: Canada compared to Sample Mean
44
0.25 0.6
0.2 0.5
0.15 0.4
0.1 0.3
0.05 0.2
0 0.1
-0.05 0
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995
Country Productivity Differences Variety Induced Productivity Differences
Product Variety Differences (right scale)
Figure 7: Japan Compared to South Korea
0.12 1
0.1 0.9
0.08 0.8
0.7
0.06
0.6
0.04
0.5
0.02
0.4
0
0.3
-0.02 0.2
-0.04 0.1
-0.06 0
1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995
Country Productivity Differences Variety Induced Productivity Differences
Product Variety Differences (right scale)
Figure 8: Israel Compared to Greece