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 authors discuss the measurement of product variety in trade, using a broad cross-section of industrial and developing countries and disaggregating across sectors. The authors calculate the export variety of countries in their sales to the United States, and relate the export variety indexes to country productivities. They confirm that countries with greater product variety in exports also have higher productivity. This may be due to their development of and access to these products.Economic Theory&Research,Environmental Economics&Policies,Labor Policies,Banks&Banking Reform,Biodiversity,Economic Theory&Research,Environmental Economics&Policies,Biodiversity,Poverty and Trade,Banks&Banking Reform

Feenstra, Robert

Hiau Looi Kee

English

Research Papers in Economics

 
 
 
 
 
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.
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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 
,....}. 3 , 2 , 1 { I
c
t ⊂   For 
c
t I i∈  the quantity of good i is 
c
it q > 0, and the vector of each type of good  3
produced in country c in period t is denoted by  0 q
c
t > .  The aggregate output of each country c, 
c
t Q , is characterized by a CES function of the outputs of each good in the country: 
()
()
C ,..., 1 c , 0 a , q a ) I , q ( f Q n
1 /
I i
/ ) 1 ( c
it i
c
t
c
t
c
t
c
t
= > 







= =
− σ σ
∈
σ − σ
∑ ,   (1) 
 
where the elasticity of substitution between goods is σ .  We assume that total output obtained 
from the economy is constrained by the transformation curve: 
   ] V ), I , q ( f [ F
c
t
c
t
c
t  = 0,  (2) 
where  ( ) 0 v ,..., v , v V c
Mt
c
t 2
c
t 1
c
t > =  is the endowment vector for country c in year t. 
For outputs we suppose that  0 < σ < ∞ −  in (1), which means that the feasible varieties 
c
it q  in any country lie along a strictly concave transformation curve, satisfying  c
t
c
t Q Q = .  Given 
resources, σ  < 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 σ  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 σ  > 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  
c
t
c
t Q P , where  c
t P  is a CES function of the prices of all product varieties produced in the country:   
()
()
, C ,..., 1 c , 0 a b , p b ) I , p ( c P i i
1 / 1
I i
1 c
it i
c
t
c
t
c
t
c
t
= > = 







= ≡
σ
σ −
∈
σ −
∑    (3) 
and 0 pc
t > is 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,  ( ) ∅ ≠ ∩ ≡ b
t
a
t t I I I , multiplied by terms 
reflecting the revenue share of “unique” goods: 
()
()
()
()
, C ,..., 1 b , a ,
I
I
p
p
P
P
1 / 1
t
b
t
t
a
t
I w
I i
b
it
a
it
b
t
a
t
t it
t
= 







λ
λ








=
− σ
∈
∏     (4) 
where the weights wit(It) are constructed from the revenue shares in the two countries: 
 
() () ()
() ()
() ()
() ()
,
I s ln I s ln
I s I s
/
I s ln I s ln
I s I s
I w
t I i t
b
it t
a
it
t
b
it t
a
it
t
b
it t
a
it
t
b
it t
a
it
t it ∑
∈ 







−
−








−
−
≡  (5) 
() , q p / q p I s
t I i
c
it
c
it
c
it
c
it t
c
it ∑
∈
≡  for c = a, b,        (6) 
and the terms  ) I ( t
a
t λ  and  ) I ( t
b
t λ  are:  5
() ,
q p
q p
1
q p
q p
I
c
t
t
c
t
c
t
t
I i
c
it
c
it
I i , I i
c
it
c
it
I i
c
it
c
it
I i
c
it
c
it
t
c
t
∑
∑
∑
∑
∈
∉ ∈
∈
∈
− = = λ  for c = a, b.            (7) 
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  ) I ( s t
a
it  and  ) I ( s t
b
it , and 
sum to unity over the set of goods  t I i∈ .
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  1
c
t < λ .  From (4), when σ  < 0 this will raise the price index of outputs,  b
t
a
t P / P.   I n  
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 
b
t
a
t /λ λ  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 1982–88 we use the 7-digit Tariff Schedule of the U.S. 
Annotated (TSUSA) classification of U.S. imports, and for 1989–97 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 σ  > 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 
b
t
a
t /λ λ , 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 
c
t
C
1 c
*
t I I U = =  is the complete set of varieties 
imported by the United States in year t, and 
*
it
*
itq p  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 
c
t
*
t
c
t I I I = ∩ , or simply the set of goods exported by country c.  Therefore, from (7) 
we have that  1 ) I ( c
t
c
t = λ , and: 
.
q p
q p
1
q p
q p
) I (
*
t
c
t
*
t
*
t
c
t
I i
*
it
*
it
I i , I i
*
it
*
it
I i
*
it
*
it
I i
*
it
*
it
c
t
*
t
∑
∑
∑
∑
∈
∉ ∈
∈
∈ − = = λ      (8) 
Noting from (4) that product variety in country c relative to the comparison is measured 
as ) I ( / ) I (
c
t
*
t
c
t
c
t λ λ , but this has a negative coefficient when σ  < 0, let us instead invert it and 
measure product variety of country c relative to the world by  ) I ( ) I ( / ) I (
c
t
*
t
c
t
c
t
c
t
*
t λ = λ λ , which 
enters (4) with a positive coefficient 1/(1– σ ).  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, 
c
t I , 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
 
 
 
 
 
 
 
 
 
 
coef = .08634144, se = .01611587, t = 5.36
e
(
 
p
r
o
d
u
c
t
i
v
i
t
y
 
|
 
X
)
e( variety | X )
-2 -1 0 1
-.2
-.1
0
.1
URY
KEN
TUR
GRC
ZAF
CRI
FIN
IRL
PHL
PRT
DNKISR
IDN COL
AUT
ESP
VEN SGP
KOR
AUS
FRA
ITA
JPN
GBRCAN
 
Figure 2:  Productivity Differences without Country Fixed Effects 
versus Product Variety Differences, 1991 
 
 
q2t 
q1t 
C 
Figure 1:  Output Varieties 
A 
 
B  11
0
0.02
0.04
0.06
0.08
0.1
0.12
1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
0
0.2
0.4
0.6
0.8
1
1.2
Country Productivity Differences Variety Induced Productivity Differences
Product Variety Differences (right scale)
 
 
Figure 3:  Canada Compared to Sample Mean 
 
 
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995
0
0.1
0.2
0.3
0.4
0.5
0.6
Country Productivity Differences Variety Induced Productivity Differences
Product Variety Differences (right scale)
 
 
Figure 4: Japan Compared to South Korea 

Across-Product versus Within-Product Specialization in

Export Variety and Export Performance: Empirical Evidence for the OECD Countries.” Weltwirtschaftliche Archiv,

Export Variety and Export Performance: Evidence from East Asia.”

Globalization and the Gains from Variety.” Federal Reserve Bank,

Ideal Log-Change Index Numbers.” Scandinavian Journal of Statistics,

New Product Varieties and the Measurement of

Product Variety and Economic Growth: Empirical Evidence from

Productivity versus Endowments: A Study of Singapore’s Sectoral Growth.” The World Bank,

Testing Endogenous Growth

The Ideal Log-Change Index Number.”

The Variety and Quality of a Nation’s Trade.” NBER paper 8712,

On the measurement of product variety in trade

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