On the Measurement of
Product Variety in Trade
by
Robert Feenstra
Department of Economics
University of California, Davis
and NBER
Hiau Looi Kee
Development Research Group - Trade
The World Bank
February 2003
Address for correspondence: Robert Feenstra, Dept. of Economics, University of California,
Davis, CA 95616; Phone (530)752-7022; Fax (530)752-9382; rcfeenstra@ucdavis.edu
Prepared for the session "Dissecting International Trade: The Dimensions of National Market
Penetration," American Economics Association, January 4, 2004. The authors thank the World
Bank for providing research funding and support. 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.
Non-Technical Summary
Product variety plays an important role in the theoretical work on monopolistic competition and
trade, and recent empirical work has begun to quantify this for aggregate and disaggregate
import demands. The objective of this paper is to discuss the measurement of product variety in
trade, using a broad cross-section of advanced and developing countries and disaggregating
across sectors. We calculate the export variety of countries in their sales to the United States,
and relate the export variety indexes to country productivities. We confirm that countries with
greater product variety in exports also have higher productivity. This may be due to their own
development of, and access to, these products.
2
1. Introduction
The theoretical work on monopolistic competition and trade has emphasized the
important role of product variety, and recent empirical work has begun on quantify this. For
example, David Hummels and Peter Klenow (2002) and Peter Schott (2004) have investigated
the extent to which trade between countries consists of a common set of goods, or a larger set of
goods from bigger countries, or different quality goods. These authors identify an important role
for product variety and quality in explaining trade between countries. Christian Broda and David
Weinstein (2003) have recently analyzed the product variety in U.S. imports, and find that
increased variety contributes to a 1.2 percent per year fall in the "true" import price index. On
the other side of the coin, a direct link between export variety and productivity have been found
by Robert Feenstra et al (1999) for South Korea and Taiwan, and by Michael Funke and Ralf
Ruhwedel (2001a, 2001b, 2002) for the OECD and the East Asian countries.
The objective of this paper is to discuss the measurement of product variety in trade,
using a broad cross-section of advanced and developing countries and disaggregating across
sectors. We calculate the export variety of countries in their sales to the United States. In a
companion paper (Feenstra and Hiau Looi Kee, 2004), we also compute the total factor
productivity across countries, using a translog GDP function. Here we make use of those results
to illustrate the correlation between export variety and productivity.
2. Measuring Product Variety across Countries
Consider a world economy with many c=1,...,C countries, each of which produces many
types of goods. For each period t, let the set of goods produced in country c be denoted by
Ict {1,2,3,....}. For iIct the quantity of good i is qit > 0, and the vector of each type of good
c
3
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 outputs of each good in the country:
Qct = f (qct ,Ict ) = c (-1)/ /(-1)
iIt
ai (q ) (1)
it ,an > 0, c =1,...,C ,
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
For outputs we suppose that - < < 0 in (1), which means that the feasible varieties
qcit in any country lie along a strictly concave transformation curve, satisfying Qct = Qt . Given c
resources, < 0 captures the production trade-off between different outputs according to the
underlying rate of technical transformation. This is shown in Figure 1, where we draw the
transformation frontier between two product varieties q1t and q2t. As rises toward zero, the
transformation curve is more concave. For a given transformation curve and 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.1
1 For inputs we would instead use that > 1 in (1), which is then the formula for a CES production function. For
given output, the inputs would lie along a convex isoquant. If only one input is available, then costs would be
minimized at a corner, but with two inputs costs would be minimized at an interior point, with a fall in costs. This
illustrates the benefits of input variety. We 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).
4
Consider maximizing the value of output, 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 product varieties produced in the country:
c c
Pt c(pct ,Ict ) =
c c 1- 1/(1-)
iIt
bi (p ) (3)
it ,bi = ai > 0, c = 1,...,C,
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 without
knowledge of the parameters bi. But a result from index number theory is that the ratio of cost
functions can be evaluated, using data on prices 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 the
product of a price index of goods that are common, It Iat Ibt , multiplied by terms
( )
reflecting the revenue share of "unique" goods:
a
Pt =
Ptb
iIt
pit a
pit wit (It ) at(It ) 1/(-1)
b bt (It ) , a,b = 1,...,C, (4)
where the weights wit(It) are constructed from the revenue shares in the two countries:
wit (It ) ln sit (It )- sit (It )
a b a b
sit (It )- lnsit (It )/ , (5)
a b
iIt
ln sit (It )- sit (It )
sit (It )- lnsit (It )
a b
sit (It ) pitqit /
c c c pitqit,
c c for c = a, b, (6)
iIt
and the terms at (It ) and bt (It ) are:
5
pitqit
c c pitqitc c
ct(It ) = iIt =1- iIct ,iIt , for c = a, b. (7)
pitqit
c c pitqitc c
iIct iIct
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 sit (It ) and sit (It ) , and
a b
sum to unity over the set of goods i It .2
The first term on the right of (4) is the price index due to Kazuo Sato (1976) and Y.O.
Vartia (1976), which is simply a weighted average of the price ratios, using the values wit(It) as
weights. What is new about equation (4) is the second term on the right, which reflect changes
in product variety. If country c in period t has new, unique outputs (not in the common set It),
we will have ct <1. From (4), when < 0 this will raise the price index of outputs, Pt / Pt . In a b
other words, the introduction of new output varieties will act in the same way as an increase in
prices in a sector: it will draw resources toward that sector.3
In practice, we measure the ratio at / bt using exports of 34 countries to the United
States. While it would be preferable to use their worldwide exports, our data for the U.S. are
more disaggregated, and allows for a finer measurement of "unique" products sold by one
country and not another. Specifically, for 198288 we use the 7-digit Tariff Schedule of the U.S.
Annotated (TSUSA) classification of U.S. imports, and for 198997 we use the 10-digit
Harmonized System (HS) classification of imports.
2 More precisely, the numerator of (5) is the logarithmic mean of the output shares of the two countries, and lies
between these shares. The denominator of (5) is introduced so that the weights wit(It) sum to unity.
3 If instead we consider the case of input variety, then > 1 in (4). 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.
6
To measure the ratio at / bt , we need to decide on a consistent "comparison country."
For this purpose, we 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
*t(Ict ) =iIct =1- iI*t ,iIct . (8)
pitqit
* * pitqit* *
iI*t iI*t
Noting from (4) 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 (4) with a positive coefficient 1/(1 ). It is interpreted as the share of total U.S. imports
from products that are exported by country c. 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.
3. Export Variety and Country Productivity
Figure 2 presents a scatter plot of the export variety in 1991 for the sales of 34 countries
to the United States, against their country productivities. Both variables are shown in deviation
7
from their sample means in the figure. There is a clear positive relationship between the product
variety of a country and its productivity, which is highlighted by the positive sloping regression
line. Canada has the most product variety, and Canada produces nearly twice as much variety as
the sample mean. In terms of the productivity differences, Canada is 7 percent higher than the
sample mean. Japan has the highest productivity which is 12 percent higher than the sample
mean. In terms of export variety, Japan produces 80 percent more export products than the
sample mean. Other countries that have higher than sample productivity and export variety
include South Korea, Singapore, and some other OECD countries such as France 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 Kenya, Greece,
the Philippines, Turkey and Uruguay. For example, exporting industries in Uruguay produce
less than half of the variety relative to the sample mean in 1991, and productivity is 10 percent
less than the sample average. Similarly, Turkey produces 73 percent less export variety than the
sample mean, and its productivity is 9 percent lower. We can also compare country pairs from
the figure. For instance, in 1991, Singapore produces nearly 65 percent more export products
than the Philippines, and the country productivity advantage of Singapore over the Philippines is
about 12 percent. This is consistent with Kee (2002) where the growth of Singapore's major
exporting industry is shown to be mainly driven by productivity.
We can also explore the movement of export variety and productivity within a country
over time. Figure 3 compares Canada to the sample mean in terms of productivity, variety-
induced productivity differences, and the weighted-average export variety, from 1983 to 1997.4
The two productivity series are presented in bars relative to the left-hand scale. The export
4 The variety-induced productivity differences are that portion of total country productivities that can be explained
by export variety; see Feenstra and Kee (2004).
8
variety index is shown in line in the figure, measured relative to the vertical right hand scale. In
1983, Canada's productivity is 8.2 percent higher than the sample mean, while it produces 86
percent more exports products relative to the sample mean. In 1997, the productivity gap
reduces to 6.7 percent while the export variety difference is about 61 percent. Thus over the
years, we see a gradual decline of export variety in Canada, especially since the early 1990s, and
it is reflected in the productivity series.
Figure 4 compares Japan to South Korea. Similar to the previous figure, the two
productivity series are presented in bars relative to the left-hand scale. The product variety index
is shown by the line in the figure, relative to the right-hand scale. The line series shows that, in
1982, Japan produced 53 percent more export variety than South Korea. The Japanese advantage
over Korea deteriorates over time such that in 1995, Japan only produced 18 percent more
variety than Korea. On the other hand, the first bar series shows that, over the same period of
time, the underlying productivity advantage of Japan declines from 18 percent to less than 2
percent. Thus with Korea catching up in export variety, the underlying productivity gap between
Korea and Japan is also narrowing.
In summary, Figure 2 clearly shows a cross-sectional correlation between export variety
and country productivity, while Figures 3 and 4 show the same result over time. This illustrates
that countries with greater product variety in exports also have higher productivity, which may
be due to their own development of, and access to, these products. Of course, this logic can also
work in reverse, whereby countries with higher productivity will export more varieties, as occurs
in the model of Jonathan Eaton and Samuel Kortum (2002), for example. Regardless of the
causation, the close link between export variety and productivity neatly confirms our theoretical
expectation, and deserves to be explored further empirically.
9
References
Broda, Christian and David Weinstein. "Globalization and the Gains from Variety." Federal
Reserve Bank, New York and Columbia University, 2003.
Eaton, Jonathan and Samuel Kortum. "Technology, Geography and Trade." Econometrica,
September 2002, 70(5), 1741-1780.
Feenstra, Robert C. "New Product Varieties and the Measurement of International Prices."
American Economic Review, March 1994, 84(1), 157-177.
Feenstra, Robert C., Dorsati Madani, Tzu-Han Yang, and Chi Yuan Liang. "Testing Endogenous
Growth in South Korea and Taiwan." Journal of Development Economics, 1999, 60, 317-
341.
Feenstra, Robert C. and Hiau Looi Kee. "Export Variety and Country Productivity." University
of California, Davis and the World Bank, 2004.
Funke, Michael and Ralf Ruhwedel. "Product Variety and Economic Growth: Empirical
Evidence from the OECD Countries." IMF Staff Papers, 2001a, 48(2), 225-242.
Funke, Michael and Ralf Ruhwedel. "Export Variety and Export Performance: Evidence from
East Asia." Journal of Asian Economics, 2001b, 12, 493-505.
Funke, Michael and Ralf Ruhwedel. "Export Variety and Export Performance: Empirical
Evidence for the OECD Countries." Weltwirtschaftliche Archiv, 2002, 138(1), 97-114.
Hummels, David and Peter Klenow. "The Variety and Quality of a Nation's Trade." NBER
paper 8712, 2002.
Kee, Hiau Looi. "Productivity versus Endowments: A Study of Singapore's Sectoral Growth."
The World Bank, 2002.
Sato, Kazuo. "The Ideal Log-Change Index Number." Review of Economics and Statistics 58,
May 1976, 223-228.
Schott, Peter. "Across-Product versus Within-Product Specialization in International Trade."
Quarterly Journal of Economics, 2004, forthcoming.
Vartia, Y. O. "Ideal Log-Change Index Numbers." Scandinavian Journal of Statistics, 1976, 3,
121-126.
10
q2t
B
C
q1t
A
Figure 1: Output Varieties
coef = .08634144, se = .01611587, t = 5.36
JPN
.1
FRA
AUS
GBRCAN
ESP ITA
AUT KOR
VENSGP
ZAF
X)| DNKISR
0
y
viti GRC IDN
PRT COL
KEN
FIN
oduct
PHL
pr
e( TUR CRI
-.1 URY
-.2 IRL
-2 -1 0 1
e( variety | X )
Figure 2: Productivity Differences without Country Fixed Effects
versus Product Variety Differences, 1991
11
0.12 1.2
0.1 1
0.08 0.8
0.06 0.6
0.04 0.4
0.02 0.2
0 0
1983 1984 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 3: Canada Compared to Sample Mean
0.2 0.6
0.18
0.5
0.16
0.14
0.4
0.12
0.1 0.3
0.08
0.2
0.06
0.04
0.1
0.02
0 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 4: Japan Compared to South Korea