Globalization and the Gains from Variety
Author(s): Christian Broda and David E. Weinstein
Source: The Quarterly Journal of Economics, Vol. 121, No. 2 (May, 2006), pp. 541-585
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/25098800
Accessed: 24-08-2017 11:18 UTC
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide
range of content in a trusted digital archive. We use information technology and tools to increase productivity and
facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at
http://about.jstor.org/terms
Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access
to The Quarterly Journal of Economics
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND THE GAINS FROM VARIETY*
Christian Broda and David E. Weinstein
Since the seminal work of Krugman, product variety has played a central role
in models of trade and growth. In spite of the general use of love-of-variety models,
there has been no systematic study of how the import of new varieties has
contributed to national welfare gains in the United States. In this paper we show
that the unmeasured growth in product variety from U. S. imports has been an
important source of gains from trade over the last three decades (1972-2001).
Using extremely disaggregated data, we show that the number of imported
product varieties has increased by a factor of three. We also estimate the elastic
ities of substitution for each available category at the same level of aggregation,
and describe their behavior across time and SITC industries. Using these esti
mates, we develop an exact aggregate price index and find that the upward bias
in the conventional import price index over this time period was 28 percent or 1.2
percentage points per year. We estimate the value to U. S. consumers of the
expanded import varieties between 1972 and 2001 to be 2.6 percent of GDP.
I. Introduction
It is striking that in the quarter-century since Krugman
[1979] revolutionized international trade theory by modeling how
countries could gain from trade through the import of new vari
eties, no one has structurally estimated the impact of increased
variety on aggregate welfare. As a result, our understanding of
the importance of new trade theory for national welfare rests on
conjecture, calibration, and case studies. While Feenstra [1992],
Klenow and Rodriguez-Clare [1997], Bils and Klenow [2001], and
Yi [2003] made important inroads into our understanding of the
role played by new varieties and differentiated trade, this paper
represents the first attempt to answer the question of how much
increases in traded varieties matter for the United States. Ana
lyzing the most disaggregated U. S. import data available for the
period between 1972 and 2001, we find that consumers have low
elasticities of substitution across similar goods produced in dif
* We would like to thank Fernando Alvarez, Alan Deardorff, Robert Feenstra,
Jonathan Eaton, Amartya Lahiri, Mary Amiti, and Kei-Mu Yi for excellent com
ments and suggestions. Rachel Polimeni provided us with outstanding research
assistance. We are grateful to the National Science Foundation for its support of
this research (NSF grant No. 0214378). David Weinstein was at the Federal
Reserve Bank of New York when most of this research was done. In addition, he
would like to thank the Center for Japanese Economy and Business for research
support. The views expressed here are those of the authors, and do not necessarily
reflect the position of the Federal Reserve Bank of New York, the Federal Reserve
System, or any other institution with which the authors are affiliated.
? 2006 by the President and Fellows of Harvard College and the Massachusetts Institute of
Technology.
The Quarterly Journal of Economics, May 2006
541
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
542 QUARTERLY JOURNAL OF ECONOMICS
ferent countries. Moreover, we show that the threefold increase in
available varieties arising in the last 30 years has produced a
large welfare gain for the United States. We find that consumers
are willing to pay 2.6 percent of their income to access the wider
set of varieties available in 2001 rather than the set of varieties
in 1972. In short, our results provide confirmation of the impor
tance of thinking about international trade within a framework of
differentiated goods.
The starting point for our analysis is the seminal work of
Feenstra [1994]. In this paper Feenstra develops a robust and
easily implementable methodology for measuring the impact of
new varieties on an exact price index of a single imported good
using only the data available in a typical trade database. Unfor
tunately, his approach has two drawbacks that have prevented
researchers from adopting it more widely. First, it cannot be used
to assess the value of the introduction of completely new product
categories. Second, Feenstra's methodology tends to generate a
large number of elasticities that take on imaginary values, which
are hard to interpret. This paper solves both problems and dem
onstrates the relative ease with which the Feenstra subindexes
can be used to compute an aggregate price index.
To calculate an aggregate import price index, we first have to
estimate a number of parameters. This constitutes our second
contribution. In particular, we estimate elasticities of substitu
tion among goods at various levels of aggregation. At the lowest
level of aggregation available for trade data (Tariff System ofthe
U.S.A. (TSUSA) seven-digit for 1972-1988 and Harmonized Tar
iff System (HTS) ten-digit for 1990-2001) we estimate almost
30,000 elasticities. This enables us to directly test a number of
stylized facts. For example, we directly demonstrate the validity
of Rauch's [1999] conjecture that goods traded on organized ex
changes are more substitutable than those that are not. We are
able to document that varieties appear to be closer substitutes in
more disaggregate product categories. We also find that the me
dian elasticity of substitution has fallen over time indicating that
traded goods have become more differentiated.
We then use these estimated parameters to construct a U. S.
import price index hewing very closely to theory. Starting with
the constant elasticity of substitution utility function which un
derlies the Spence-Dixit-Stiglitz (henceforth SDS) framework, we
compute an exact aggregate price index that allows for changes in
varieties. Since this is the same assumption that is used in much
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 543
of the new trade theory, economic geography, and growth litera
tures [Helpman and Krugman 1985; Grossman and Helpman
1991; Fujita, Krugman, and Venables 1999], our estimates can be
directly applied to these models. Our results suggest that the
impact of increased choice on the exact import price index is both
statistically and economically significant. Between 1972 and
2001, if one adjusts for new varieties, import prices have been
falling 1.2 percentage points per year faster than one would
surmise from a conventional price index. If we aggregate across
all the years, this means that the variety-adjusted import price
index has fallen by 28.0 percent relative to a conventionally
measured import price index.
Finally, we are able to use this price decline to obtain an
estimate ofthe gains from new imported varieties under the same
structural assumptions as Krugman [1980]. We calculate the
compensating variation required for consumers to be indifferent
between the set of varieties available in 2001 and that in 1972.
We find that consumers are willing to pay 2.6 percent of their
income to access the expanded set of varieties available in 2001
rather than the set in 1972. On a per-year basis, this suggests
that consumers would pay up to 0.1 percent of their income each
year to have access to the net new varieties created that year. We
show that the stronger assumptions that are commonly used in
the macro literature (e.g., Feenstra [1992], Romer [1994], and
Klenow and Rodriguez-Clare [1997]) would lead to welfare gains
from variety up to three times larger. Moreover, our results are
qualitatively unaffected when we use a Fisher ideal price index or
make adjustments for changes in domestic varieties. In sum, our
results show that, when measured correctly, increases in im
ported varieties have had a large positive impact on U. S. welfare.
II. Prior Work
What is a variety? Previous work has not answered this
question with a unified voice. In terms of theory, a variety is
commonly defined as a brand produced by a firm, the total output
of a firm, the output of a country, or the output within an industry
in a country.1 As a result ofthe variety of definitions of variety,
empirical papers are often not strictly comparable. The choices
1. Representative papers would include Hausman [1981], Feenstra [1994],
and Roberts and Tybout [1997].
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
544 QUARTERLY JOURNAL OF ECONOMICS
are often driven by data availability and the types of theories that
the researchers are examining. While we will make precise our
definition of variety later, we want to emphasize that as we
discuss prior work, the definition of variety will vary across
papers.
Several studies have attempted to measure the impact of new
varieties on welfare for individual goods and at the aggregate
level. Hausman [1981] pioneered an approach to estimating the
gains from new varieties (product line) of an individual good
using micro data. He develops a closed-form solution to estimat
ing linear and log-linear demands and calculates the new prod
uct's "virtual price," the price that sets its demand to zero. Based
on this estimate and on the current price, he calculates the
welfare change that results from the price drop of the new prod
uct. The advantage of this approach is that by taking enormous
care to model, for example, the market for Apple Cinnamon
Cheerios, one can obtain extremely precise estimates that can
take into account rich demand and supply interactions. However,
the data requirements to implement this approach for the tens of
thousands of goods that comprise an aggregate price index are
simply insurmountable. For this reason, it is not surprising that
no one has attempted to estimate aggregate gains from new
products using this method.
At the aggregate level, all existing studies rely on calibration
or simulation exercises to measure the effect of variety growth.
These studies typically define a variety as the imports from a
given country or the imports from a given country in a particular
industry. They also typically do not focus on how varieties affect
prices but rather provide some interesting calculations about
potential welfare effects. Feenstra [1992] and Romer [1994], for
example, provide numerical exercises showing that the gains
from new varieties from small tariff changes can be substantial.
Klenow and Rodriguez-Clare [1997] calibrate a model of the im
pact of trade liberalization on Costa Rica and find only modest
gains. They suggest that the low elasticity of substitution and
large import shares used in Romer [1994] account for the differ
ence in welfare gains.2
These papers have provided an invaluable first step in un
2. Rutherford and Tarr [2002] simulate a growth model with intermediate
input varieties that magnifies the effect of trade liberalization on welfare, and
suggest that a 10 percent tariff cut can lead, in the long run, to welfare gains of
roughly 10 percent.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 545
derstanding how to move from theory to data, but they require a
large number of restrictive simplifying assumptions in order to
obtain the estimates. For example, this prior work uses one or at
most two elasticities of substitution in order to value varieties.
This creates three types of problems. The first arises from assum
ing that all elasticities of substitution are the same for varieties
of different goods. Since presumably consumers care more about
varieties of computers than crude oil, it is not clear that all
increases in imports correspond to the same gains from increased
variety. The second problem arises from assuming that the elas
ticity of substitution across goods equals that across varieties of a
given good. Presumably we care more about the different variet
ies of fruits than about varieties of apples. The final and perhaps
largest problem arises from assuming that all varieties enter into
the utility function with a common elasticity. When one is esti
mating a parameter that is averaging together, say, the impact of
an increase of Saudi Arabian oil prices on Mexican oil imports
and Japanese car imports, it is hard to interpret the meaning of
the elasticity or have intuition for its magnitude.
A different class of problem with calibration exercises stems
from the choice ofthe parameter values and the use of symmetric
utility functions (e.g., Romer [1994] and Broda and Weinstein
[2004]). Parameter values, such as elasticities of substitution, are
often chosen arbitrarily or are estimated from one data set and
applied to another data set. An important feature of our study is
that all parameters are estimated directly from the relevant data
and not chosen in order to obtain sensible values for some other
stage ofthe analysis. Moreover, in the case of a symmetric utility
function, since all varieties are valued alike, a count of the num
ber of imported varieties is sufficient to perform welfare calcula
tions. This approach is only valid under the extreme symmetry
assumptions underlying the particular utility function used. In
deed, this paper shows that the use of count data, rather than the
changes in import volumes as suggested by Feenstra [1994], can
be highly misleading as a measure of variety growth if one allows
for a more general utility function.
The third problem is related to the way in which previous
studies have estimated the single elasticity of substitution. By far
the simplest of these approaches is to follow the pioneering work
of Anderson [1979] and estimate the elasticity of substitution by
regressing bilateral trade flows on various control variables and a
measure of trade costs. The coefficient on trade costs is used as
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
546 QUARTERLY JOURNAL OF ECONOMICS
the elasticity of substitution among varieties. The major problem
with this approach is that one needs to make extreme identifying
assumptions in order to ignore simultaneity problems. Chief
among these is the assumption that trade costs are completely
passed through to consumers. This assumption is almost surely
inappropriate for the United States and the other large importers
who together account for the majority of world trade. A second
problematic identifying assumption is that movements in trade
costs are unaffected by movements in import demand. Unfortu
nately, this assumption will be violated whenever per unit trans
port costs are a function of import volumes, countries care about
import responses when cutting bilateral tariffs, or movements in
nontariff barriers are correlated with movements in tariffs. Since
all of these conditions are likely to be violated in reality, the
estimated elasticities are problematic. Ignoring the simultaneity
problem would result in lower estimates of the elasticities of
substitution.
Our paper proceeds as follows. In Section III we provide an
overview of the basic theoretical contributions on the literature of
variety growth and the reasons behind the structure we use in
this paper. In Section IV we provide descriptive statistics on the
growth in varieties in U. S. imports since 1972. Section V is
devoted to the methodology used to compute an exact aggregate
price index and to estimate elasticities of substitution that correct
for endogeneity bias, measurement error, and that allow for
changes in taste and quality parameters. Section VI presents the
main results of the paper. We present our conclusions in Section
VII.
III. Theory: Why Do Varieties Matter?
All studies that seek to quantify the potential gains from
variety are forced to impose some structure on how varieties
might affect welfare. Theorists have proposed many ways of mod
eling this (see, for example, Hotelling [1929], Lancaster [1975],
Spence [1976], and Dixit and Stiglitz [1977]), and the assump
tions underlying these models are not innocuous. As empirical
researchers, we are forced to choose from a number of plausible
theories. Our choice of the SDS framework is based on three
criteria: prominence, tractability, and empirical feasibility.
There is little question that in international trade, economic
geography, and macroeconomics, the SDS framework is the pre
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 547
ferred way of specifying how consumers value variety. A major
reason for this stems from the tractability of the constant elas
ticity of substitution (CES) utility function and its close cousin,
the Cobb-Douglas. In addition to the work of Krugman, the Dorn
busch, Fisher, and Samuelson models are more recent work by
Eaton and Kortum [2002] all use CES or Cobb-Douglas functions.
Hence, it is quite natural to use this preference structure as the
basis of our empirical work. At the very least, our work provides
a useful benchmark for thinking about the potential gains from
imported varieties within this framework.
A second reason to base our work on the SDS framework is
theoretical tractability. As Helpman and Krugman [1985, pp.
124-129] note, preference systems based on the Hotelling and
Lancaster models do not easily lend themselves to the creation of
aggregate price indexes or utility functions when there is more
than one market in the economy. Since one of the main objectives
of this study is to build an aggregate price index, we need to use
a theoretical structure that will let us aggregate price changes
across markets.
Finally, the CES satisfies another important characteristic?
empirical feasibility. Demand systems based on CES utility func
tions are relatively easy to estimate. This is of paramount impor
tance since we need to be able to aggregate estimates of the gains
from variety in tens of thousands of markets. Moreover, since we
know next to nothing about demand and supply conditions in
virtually all of the markets we examine, it is simply not feasible
to implement a more complex supply and demand structure.3
Thus, although one would ideally like to control for all of the
complexities present in international markets, the data and time
limitations required to perform a careful analysis of all of these
markets make this impossible in practice.
Given the way we model how consumers value variety, we
now need to be precise about what we mean by a variety. Our
reliance on the Krugman [1980] structure might suggest that we
adopt a definition of variety that is based on firm-level exports.
Unfortunately, there are a number of problems with taking this
literal approach to the data. First, by treating all imports from a
given firm as a single variety, one may understate the gains from
3. One property of the CES is that, by assumption, consumers care about
varieties to some extent. In practice, this assumption does not bias our results
because an increase in variety will have a trivial impact on prices and welfare if
the estimated elasticity of substitution is large.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
548 QUARTERLY JOURNAL OF ECONOMICS
variety that occur when a firm starts exporting in more than one
product line. Second, it is difficult to obtain bilateral firm-level
export data for more than a handful of countries. We therefore opt
to use the same definition of variety as in Feenstra [1994]?
namely, a seven- or ten-digit good produced in a particular coun
try. To give a concrete example, a good constitutes a particular
product, e.g., red wine. A variety, however, constitutes the pro
duction of a particular good in a particular country, just as in
Armington [1969], e.g., French red wine.
Being clear about this distinction highlights an important
difference between monopolistic competition models and compara
tive advantage models that feature a continuum of goods. Both
models share the feature that output of tradables is perfectly
specialized in equilibrium. However, they differ in terms of how
individual varieties are treated. In the comparative-advantage,
continuum-of-goods models, consumers are indifferent about
where a good is produced as long as the price does not vary. In
other words, these models assume that holding the good fixed, the
elasticity of substitution among varieties is infinite. This is in
sharp contrast to the Krugman model that hypothesizes that all
firms produce differentiated products and hence the elasticity of
substitution should be finite.
Despite the sharp theoretical difference, our ability to do
precise hypothesis testing is limited. The point estimate for the
elasticity of substitution will always be finite, and thus we cannot
formally reject this hypothesis. However, by examining the elas
ticities of substitution at the seven- or ten-digit level, we can
obtain a sense ofthe degree of substitutability among varieties. If
the elasticities of substitution tend to be high, say above 10 or 20,
then this suggests that the potential for gains from variety, a key
theoretical result ofthe monopolistic competition framework, are
small. If they are low, then this suggests that even when we use
the most disaggregated trade data in existence, goods are highly
differentiated by country. Of course, we cannot rule out that if we
had even more disaggregated data, we might find a higher esti
mate of the elasticity of substitution. Yet even so, we do learn
something about the world?at the seven- or ten-digit level of
aggregation, it is reasonable to think of goods from different
countries as far from perfect substitutes. More importantly for
our purposes, low elasticities of substitution across varieties are
a necessary condition for increases in the number of varieties to
be a source of potential gain.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 549
Turning to welfare, the monopolistic competition model de
scribed in Krugman [1979, 1980] suggests two clear channels for
the gains from trade arising from variety growth. The first is
through reductions in trade costs. If trade costs fall, countries will
gain through the import of new varieties.4 The second is through
growth of the foreign country. As the size of the foreign country
rises (which in the Krugman framework is equivalent to a rise in
its labor force), it will produce more varieties, and this will also be
a source of gain for the home country. These gains are in sharp
contrast to the gains postulated by comparative advantage mod
els. In these models, all goods are consumed in equilibrium re
gardless of the level of trade costs or the size of the foreign
country. Hence, in comparative advantage models, all gains from
reductions in trade costs or increases in the size of a foreign
country are achieved through conventional movements in prices
and not through changes in the number of goods. One of the
distinguishing features of the Krugman model is that a country
may gain from trade even though there are no price changes of
existing goods.
In sum, although theorists have developed a number of mod
els of variety, our choice of the Dixit-Stiglitz structure stems from
that model's prominence, tractability, and empirical implement
ability. Moreover, since this model can easily explain key stylized
facts of how the growth of foreign countries and the reduction of
international barriers have contributed to an increase in. U. S.
imports of varieties, we believe it is a particularly appropriate
structure to use in order to obtain estimates of the gains from
variety.
IV. Data: The Growth of Varieties
It is well-known that trade has been growing faster than
GDP for many decades. This process, which is a part of what some
term "globalization," has had a profound impact on the depen
dence of the U. S. economy on foreign goods. Over the last 30
years, the share of imports of goods in U. S. GDP has more than
4. The basic Krugman model predicts that a change in tariffs within nonpro
hibitive values will not change the number of available varieties, although con
sumers will gain from the falling prices of imported varieties. Romer [1994],
however, presents a simple extension of this model to allow for fixed costs of
accessing foreign markets so that the number of available varieties rises with a
fall in tariffs.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
550 QUARTERLY JOURNAL OF ECONOMICS
doubled: rising from 4.8 percent in 1972 to 11.7 percent in 2001.5
The causes for this explosion in trade stem from a number of
sources that have been explored in a vast literature. Most studies
attribute the source of the rise to three interrelated causes: re
ductions in trade costs, relaxations of capital controls (e.g., bar
riers to foreign direct investment), and the relative growth of
many East Asian and other economies outside of the United
States.
This rise in U. S. imports has been accompanied by a rise in
another phenomenon that has received much less attention?a
dramatic rise in imported varieties. Table I gives a preliminary
overview ofthe extent of this increase. Between 1972 and 1988 we
rely on the TSUSA seven-digit data and in later years on the
ten-digit HTS data [Feenstra 1996; Feenstra, Hanson, and Lin
2004]. We define a good to be a seven- or ten-digit category, and,
as mentioned in the previous section, a variety is defined as the
import of a particular good from a particular country.6 We do not
report numbers for 1989 because the unification of Germany
means that data for that year are not comparable with later HTS
data.7
Using our definition of varieties, Table I reports that in 1972
the United States imported 71,420 varieties (i.e., 7731 goods from
an average of 9.2 countries) and in 2001 there were 259,215
varieties (16,390 goods from an average of 15.8 countries). Ulti
mately, we will want to make comparisons across years, and to do
that properly we will need to formally deal with a host of issues
relating to whether the data for two different years are truly
comparable. For now, we put these issues aside and focus on the
crude measure of variety that we can glean from the sample
statistics.
The second column of Table I reports the number of goods for
which imports exceeded one dollar in a given year. There are two
features of this column that are important to note here. First,
comparing the values for 1988 and 1990, there appears to be little
5. Data are from the World Bank World Development Indicators unless
otherwise stated.
6. This definition matters less than one might suppose for our later empirical
work since we will estimate elasticities of substitution across varieties of a good
and let the data tell us how important differences among varieties are. For the
time being, however, we will leave aside the question of how substitutable goods
produced in different countries are, and simply focus on the number of varieties.
7. All the countries in the former Soviet Union are aggregated together
throughout our analysis.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 551
TABLE I
Variety in U. S. Imports (1972-2001)
U. S. Imports 1972-1988
Median Average Share of
number number Total number total
Number of of of varieties U. S.
ofTSUSA exporting exporting (country
Year categories countries countries p
(1) (2) (3) (4) (5) (6)
All 1972 goods 1972 7731 6 9.2 71420 1.00
All 1988 goods 1988 12822 9 12.2 156669 1.00
Common
1972-1988 1972 4167 6 8.4 35060 0.41
Common
1972-1988 1988 4167 10 12.2 50969 0.33
1972 not in
1988 1972 3553 7 10.2 36355 0.59
1988 not in
1972 1988 8640 8 12.7 105696 0.67
U. S. Imports 1990-2001
Median Average Share of
number number Total number total
Number of of of varieties U. S.
ofHTS exporting exporting (country-g
Year categories countries countries p
(1) (2) (3) (4) (5) (6)
All 1990 goods 1990 14572 10 12.5 182375 1.00
All 2001 goods 2001 16390 12 15.8 259215 1.00
Common
1990-2001 1990 10636 10 12.4 132417 0.73
Common
1990-2001 2001 10636 13 16.3 173776 0.67
1990 not in
2001 1990 3936 10 12.7 49958 0.27
2001 not in
1990 2001 5754 11 14.8 85439 0.33
Source: NBER CD-ROM and http://data.econ.ucdavis.ed\i
difference in the number of categor
TSUSA and HTS systems. Second t
increase in the number of U. S. im
periods. Combining the increases o
1990-2001, it appears that the num
doubled. This establishes the impor
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
552 QUARTERLY JOURNAL OF ECONOMICS
apparent new goods or categories when calculating changes in
import structure and the price of imports.
Columns (3) and (4) report the median and average number
of countries exporting a good to the United States. These data
also reveal a substantial increase in the number of countries
supplying each individual good. Between 1972 and 2001 the me
dian number of countries doubled, rising from six countries in
1972 to twelve countries today. Similarly, the average number of
countries rose 30 percent between 1972 and 1988 and another 30
percent in between 1990 and 2001, resulting in an aggregate
increase of 67 percent. In other words, even if we leave aside the
issue of why the number of imported categories has increased
over time, the data reveal that there has been a dramatic increase
in the number of countries supplying each individual good.
This effect can also be seen if we restrict ourselves to the set
of goods that were imported at the start and end of each sample
period. In rows 3 and 4 of Table I, we present data on the set of
common goods within each sample. The data reveal that the
increase in countries supplying these goods was, if anything, even
more pronounced than the increase for the sample as a whole.
The aggregate increase in the median number of countries sup
plying common goods was 117 percent, and the average rose 91
percent.
The last two lines provide sample statistics for the set of
categories that ceased to exist or appeared during this time pe
riod. Roughly a third to a half of the categories in which the
United States recorded positive imports at the start of either
period did not contain positive imports at the end of the period.
Similarly, somewhere between a third and two-thirds ofthe prod
ucts imported at the end of each period were not imported at the
start of the sample. Once again, we will have to return to the
question of whether this represents the actual birth and death of
products or simply product categories, but the table underscores
that there are substantial changes in the measured composition
of imports across both time periods.
Taken together, the data in Table I suggest that the number
of varieties rose 119 percent in the first period and 42 percent in
the second period?a total increase of 212 percent. This increase
constitutes more than a threefold increase in the number of
varieties over the last three decades. Roughly half of this increase
appears to have been driven by an increase in the number of
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 553
goods and half by an increase in the number of countries supply
ing each good.
The fact that the number of countries supplying each good
almost doubled serves as prima facie evidence of a startling
increase in the number of varieties. The most plausible explana
tions for this rise involve some story of the globalization process
coupled with an assumption that goods are differentiated by
country (as in Krugman [1980], Romer [1994], and Rutherford
and Tarr [2002]). For example, reductions of trade costs may have
made it cheaper to source new varieties from different countries.
Alternatively, the growth of economies like China, Korea, and
India has meant that they now produce more varieties that the
United States would like to import. But, of course, if these goods
are differentiated by country, then this implies that there must be
some gain from the increase in variety?a point that we will
address in the next section.
One can obtain a better sense of the forces that have been
driving the increase in variety if we break the data up by export
ing country. Table II presents data on the numbers of goods
exported to the United States by country. The first column ranks
them from highest to lowest for 1972, and the following columns
rank them for subsequent years. Not surprisingly, the countries
that export the most varieties to the United States tend to be
large, high-income, proximate economies. Looking at what has
happened to the relative rankings over time, however, reveals a
number of interesting stylized facts. First, Canada and Mexico
have risen sharply in the rankings. Canada moved from being the
fourth largest source of varieties to first place, while Mexico
moved from thirteenth to eighth place. This may reflect free trade
areas and other trade liberalizations between the United States
and these countries over the last several decades.
Growth, perhaps coupled with liberalization, also appears to
have played some role. Fast growing economies like China and
Korea rose dramatically in the rankings. For example, in 1972
China only exported 710 different goods to the United States as
opposed to 10,315 in 2001. This fourteen-fold increase in the
number of varieties produced a dramatic change in China's rela
tive position: moving from the twenty-eighth most important
source of varieties in 1972 to the fourth most important today.
Similarly, after India began its period of liberalization in the last
decade, its growth rate rose sharply as did the number of goods it
began exporting. At the other extreme, economies like Japan and
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
554 QUARTERLY JOURNAL OF ECONOMICS
TABLE II
Ranking in Terms of Number of Goods Imported by the United States
Ranking in year:
Country 1972 1988 1990 2001
Japan 113 7
United Kingdom 2 4 4 3
Germany 3 3 2 2
Canada 4 2 11
France 5 6 5 6
Italy 6 5 6 5
Switzerland 7 11 11 11
Hong Kong 8 9 12 16
Netherlands 9 13 13 14
Taiwan 10 7 7 9
Spain 11 14 15 12
Belgium-Luxemburg 12 15 14 15
Mexico 13 12 10 8
Sweden 14 17 16 19
Denmark 15 22 21 23
Austria 16 18 18 21
India 17 19 23 13
Rep. of Korea 18 8 9 10
Brazil 19 16 17 18
Australia 20 20 20 20
Israel 21 21 22 22
Portugal 22 26 28 32
Norway 23 31 31 37
Ireland 24 27 26 28
Finland 25 28 30 31
Colombia 26 33 34 35
Philippines 27 25 25 26
China 28 10 8 4
Argentina 29 29 29 39
Greece 30 38 44 47
Top 30 countries in 1972 included. Same notes as in Table I apply.
Argentina have seen fairly substantial drops in t
ber of varieties they export.
The importance of these countries for the growt
U. S. varieties can be seen in Table III. The first c
the ratio of the net change in varieties between
from a given country to the change in varietie
United States as a whole. The second column rep
share of imports from that country in the first ti
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 555
TABLE III
Country Contribution to Growth in U. S. Varieties (1972-1988/1990-2001)
Average Average
share of share of
Contribution U. S. Contribution U. S.
Country 1972-1988 imports (*) Country 1990China
4.8% 1.0% China 5.7% 6.0%
Taiwan 4.4% 4.0% India 4.4% 0.7%
Rep. of Korea 4.4% 2.9% Mexico 3.7% 8.8%
Canada 4.2% 22.7% Spain 2.9% 0.6%
Italy 4.0% 2.9% South Africa 2.6% 0.4%
Germany 3.8% 6.9% Italy 2.6% 2.3%
France 3.8% 2.6% Indonesia 2.5% 0.8%
Japan 3.6% 18.4% Canada 2.5% 18.7%
United Kingdom 3.5% 4.7% Turkey 2.3% 0.3%
Hong Kong 3.1% 2.3% Thailand 2.3% 1.2%
Mexico 3.0% 4.0% Australia 2.1% 0.7%
Switzerland 2.6% 1.1% France 2.1% 2.7%
Brazil 2.6% 1.9% Rep. of Korea 2.0% 3.4
Netherlands 2.2% 1.1% Belgium-Luxemburg 1.9% 0.9%
Thailand 2.2% 0.5% Poland 1.8% 0.1%
Singapore 1.9% 1.1% Malaysia 1.8% 1.5%
A U. S. variety is defined as a TSUSA-exporting country pair in 1972-1988 and HTS-exporting c
pair in 1990?2001. (*) Log ideal weights used as average shares (see text for a definition).
third and fourth columns repeat this exercise for the second
period. The table highlights the importance that industr
Asia has played in the creation of new varieties. Partic
prominent is the role played by China. In the first period
accounted for almost 5 percent of aggregate U. S. variety gro
even though China only accounted for an average of 1 per
U. S. imports. Other rapidly growing or liberalizing coun
such as Taiwan, Korea, India, and Mexico, also contri
heavily to the increase in available varieties.
One simple way of numerically exploring the assoc
between growth, trade, and the number of varieties expo
the United States is to use a strategy similar to that in E
Kortum, and Kramarz [2004]. Let Met be the total import
exporting country e to the United States in time t, and V
number of varieties of goods imported by exporting country
can use the following identity, Met = Vetfhet, where met
average exports per variety, to describe the relationship b
the two variables. Moreover, it is standard to model bilat
trade using the gravity model, where bilateral import
function of the market sizes of the United States and the
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
556 QUARTERLY JOURNAL OF ECONOMICS
ing country, and measures of geographic barriers between the two
countries. That is, Met = iQeQus^us^, where Qe is the output of
country e, ? is a constant, and dus e a. measure of the distance
between countries.
From these two relationships we can derive and estimate the
following regression,
ln Ve>0i " In Ve,72 = a + P(ln Qeoi ~ In Qe72)
+ 7(ln fte01 - In ftc72) + ee,
where ftet = lQuslduse = Met/Qe measures exports of country e
to the United States as a share of its GDP and a, 0, and 7 are
parameters to be estimated. This is the time-series analog of the
regression in Eaton, Kortum, and Kramarz [2004]. This regres
sion yields the following coefficients: 0 = 0.32 (0.04), 7 = 0.35
(0.04), where robust standard errors appear in brackets, and
R2 = 0.55.8 These results suggest that holding fixed a country's
share of exports to the United States, a 1 percent increase in
trading partner's size is associated with a 32 percent increase in
the number of varieties exported to the United States. Similarly,
a 1 percent increase in imports by the United States from a
country is associated with 35 percent more varieties exported
from that country. These results further suggest that the increase
in varieties was not random. Rather, foreign countries that ex
ported and grew more tended to disproportionately increase the
number of varieties they exported to the United States.
We will now formally deal with how to correctly measure and
value these increases in product varieties. In particular, we dis
cuss how the methodology used is robust to a host of issues that
have been ignored in this descriptive section.
V. Empirical Strategy
V.A. The Feenstra Price Index
In this subsection we extend Feenstra's [1994] derivation of
the exact price index of a single CES aggregate good that allows
for both new varieties and taste or quality changes in existing
8. When a similar regression is run on the cross section for the year 2001, we
obtain the following parameters, (3 = 0.69 (0.03), 7 = 0.42 (0.05), andi.2 = 0.83.
Eaton, Kortum, and Kramarz [2004] using export firm data from France to the
rest of the world, get the following coefficients: f_ = 0.62 (0.02), 7 = 0.88 (0.03), and
R2 = 0.90.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 557
varieties, to the case of several CES aggregate goods. Our objec
tive in this subsection is to build an exact aggregate price index
corresponding to a CES utility function that can be used to
evaluate the impact of variety changes on prices and welfare. The
first step toward deriving an aggregate exact price index is to
define the utility function. Suppose that the preferences of a
representative agent can be denoted by a three-level utility func
tion (similar to Helpman and Krugman [1985, Ch. 6]) that aggre
gates imported varieties into composite imported goods, then
aggregates these imported goods into a composite import good,
and finally combines this imported good with the domestic good to
produce utility. For expositional purposes, we begin by specifying
the upper level utility function as
(1) Ut = (Dt~1)lK + j|f Jc-iyK)K/(K-1); k > 1,
where Mt is the composite imported good to be defined below, Dt
is the domestic good, and k is the elasticity of substitution be
tween both goods. While this functional form allows the share of
imports to vary over time, it creates a certain degree of separa
bility between imports and domestic goods that will prove useful
as we develop our price index. This assumption will be important
for calculating an aggregate import price index.
Moving to the second tier, we define the composite imported
good as
/ \V(r-i)
(2) ^=E<iyv ; 7>i,
where Mgt is the subutility derived from the consumption of
imported goodg in time t, 7 denotes the elasticity of substitution
among imported goods, and G is the set of all imported goods.
A particularly useful form of Mgt is the nonsymmetric CES
function, which can be represented by
(3) Mgt=t2 dvg??(mgJ?^A g S ; <rg > 1 Vg G G,
where ug is the elasticity of substitution among varieties of good
g, which is assumed to exceed unity; for each good, imports are
treated as differentiated across countries of supply, c (as in Arm
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
558 QUARTERLY JOURNAL OF ECONOMICS
ington [1969] ).9 That is, we identify varieties of import good g
with their countries of origin. C is the set of all countries; dgct
denotes a taste or quality parameter for good g from country c.
Let Igt C C be the subset of all varieties of good g consumed
in period t. The minimum unit-cost function of subutility function
in (3) is given by the following expression:
/ \l/(l-o-^)
(4) 4#(/*,d*) = I d^ft*)1-*'
w* /
where pgct is the price of variety c
the vector of taste or quality para
that (4) can be used to illustrate th
approach and the source of defi
indices. Suppose that Vg varieti
consumers and that dgc = 1 Vc E
in a standard monopolistic compet
equally priced atp^. In this case, th
becomes $^f = V^/(1_<r^)p^. For
implies that the minimum cost re
utility falls. However, a conventi
only on common varieties will no
unit-costs, or equivalently, the ris
The minimum unit-cost functio
noted by
/ \ 1/(1-7)
(5) 4>F= 2 (4#</*,d*))H
And the overall price index is given by
(6) pt = [(pf)1"* + to*)1-]1*1-0,
where the price of the domestic good is given by pf. Equations
(4)-(6) constitute the main building blocks for the calculation of
exact aggregate price indices.
We turn next to the derivation of the aggregate bias gener
ated by ignoring new varieties. We proceed in three steps: first,
9. One of the features and limitations of the CES functional form is that the
elasticity of substitution plays a dual role as a measure of substitution across
varieties and a key factor in evaluating new varieties. This functional form
assumption makes the CES attractive for theoretical and empirical researchers,
but one can contemplate more complex relationships. Brown, Deardorff, and Stern
[1996] calibrate a model with variety growth using a more general CES function.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 559
we review Feenstra's [1994] contribution, namely, to generalize
the exact price index of a single good to the case of new and
disappearing product varieties; second, we derive the aggregate
exact import price index for (2); and last, we provide a description
of the useful properties of this aggregate index.
Diewert [1976] defines an exact price index for good g over a
constant set of varieties as
(7) PM(r> n x x 7)- ^"^
where Ig = Igt D Igt-i is the set of varieties consumed in periods
t and t ? 1, and taste parameters are constant over time, dgct =
dgct-i = dgc for c ? Ig. Since in this case varieties are constant
over time, Ig = Igt = Igt~\> x^ and xgt-i are the cost-minimizing
quantity vectors of good g's varieties given the prices of all vari
eties, pgt and p^^-i- This means that an exact price index has the
salient feature that a change in the index exactly matches the
change in minimum unit-costs.10 As noted by Diewert, a remark
able feature of (7) is that the price index does not depend on the
unknown quality parameters dgc. The intuition for this result is
that all ofthe information contained in the quality parameters is
captured by the levels of consumption.
In the case of the CES unit-cost function, Sato [1976] and
Vartia [1976] have derived its exact price index to be
T-r / Pgct \Wgct
(8) Pgipgt,pgt^,-Kgt,-Kgt^,Ig) = 11 I-- .
cez, Wgct-il
This is the geometric mean of the individual variety price
changes, where the weights are ideal log-change weights.11 These
weights are computed using cost shares sgc in the two periods, as
follows:
(9) s ct = PgctXgct
^C&Ig PgctXgct
10. Diewert [1976] also presents the dual of (7), where the exact quantity
index has to match the change in utility from one period to the other.
11. As explained in Sato [1976], a price index P that is dual to a quantum
index, Q, in the sense that PQ = E and shares an identical weighting formula
with Q is defined as "ideal." Fisher [1922] was the first to use the term ideal to
characterize a price index. He noted that the geometric mean of the Paasche and
Laspeyres indices is ideal.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
560 QUARTERLY JOURNAL OF ECONOMICS
( = (sgct ~ Sgq-J/Qn sgct - In sgct^)
2cG/_ ((sgct ? Sgct-xj/iln sgct ? ln s^c^-i))
The numerator of (10) is the difference in cost shares over time
divided by the difference in logarithmic cost shares over time.
The exact price index of good g in (7), Pg9 requires that all
varieties be available in the two periods. Feenstra [1994] showed
how to modify this exact price index for the case of different, but
overlapping, sets of varieties in the two periods. Proposition 1
states Feenstra's main theoretical contribution, the relationship
between the conventional price index and the exact price index
that incorporates changes in variety for a single good.
Proposition l.12 For g G G, if dgct = dgct_1 for c G Ig =
(Igt n Igt-i), Ig =? 0, then the exact price index for good g
with change in varieties is given by
tygt-vJ-gt-l&g)
( X- t \1/(ff*_1)
= Pg \Pgt>Pgt -1 >x#. >x#. -1 ilg) I ^ 1 ?
where
_ ^c^Ig Pgcftgct _ ^cGlg Pgct-lXgct-l
gt = y n r a ^_1 = y n r *^C&Igt Pget*"get ^C <=Igt-l Pgct - lxgct -1
This result states that the exact price index with var
(i.e., Ttgilg) for short) is equal to the "conventional" p
P^dg) (i.e., the exact price index of the common vari
time), multiplied by an additional term, (X^/X^^)17^
captures the role of the new and disappearing variet
that \gt equals the fraction of expenditure in the va
are available in both periods (i.e., c G Ig = (Igt n /^_
to the entire set of varieties available in period t (i.e.
Thus, this additional term implies that the higher t
ture share of new varieties, the lower is \gt, and the sm
exact price index relative to the conventional price in
12. The appendix of Feenstra [1994] provides the proof of a m
proposition, where c?/gC (Igt n Igt-\)
13. All ofthe index numbers used in this paper suffer from the
number problem." In particular, results are dependent on the base
used. Since we are examining long-run changes, we use two base
1990.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 561
symmetric case, (11) simply becomes Ttgilg) = Pg*(Jg)(ygt_1l
V^)1/(o*-1), where Vgt_1 and V^ are the number of varieties of
goodg consumed in periods t and t ? 1, respectively. It is easy to
see that, in this case, an increase in the number of varieties leads
directly to a fall in the exact price index relative to the conven
tional price index.
The Feenstra price index also depends on the good-specific
elasticity of substitution, <jg. As <jg grows, the term l/(o"^ - 1)
approaches zero, and the bias term (A^/X^_i)1/(a*~1) becomes
unity. That is, when existing varieties are close substitutes to
new or disappearing varieties, changes in variety will not have a
large effect on the exact price index. By contrast, when ag is close
to unity, varieties are not close substitutes, l/icrg ? 1) is high,
and therefore new varieties are very valuable, and disappearing
varieties are very costly.
Having derived the exact price index with variety change for
the subutility function in (3), we can now obtain the aggregate
exact import price index for (2) which is summarized in the
following proposition.14
Proposition 2. If Ig # 0 Vg G G and dgct = dgct_1 for c G Ig
\/g G G, then the exact aggregate import price index with
variety change is given by
(12) n^p^p^x^x^!,/) = m (TU A.
= ciPiii) n h^H
where CIPIil) = TLg(EG PgUg)Wgt and wgt are log-change ideal
weights.
The second equality follows from applying (8) to the CES bundle
of imported goods, and Samuelson [1965]. By replacing (7) and
(11) in (12), we obtain the relationship between the aggregate
conventional import price index iCIPI) and the aggregate exact
import price index. For future reference, we will refer to the
geometric weighted average ofthe X ratios in (12) as the aggregate
import bias that results from ignoring new varieties in all product
categories. The empirical measurement of this aggregate bias is
14. As will be clear in the empirical section, the number of goods, G, is
assumed constant over time.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
562 QUARTERLY JOURNAL OF ECONOMICS
the focus of the empirical section that follows and represents the
main contribution of this paper. The overall price index Ft is then
given by
/ DD \ W?
as) n= 5H (nM)^
where the exponents are the log-change ideal weights.
Basing an aggregate import price index on (12) corrects a
host of problems that plagued prior work. First, this framework
allows varieties to account for different shares of expenditures
due to quality or taste differences. This contrasts with prior work
measuring variety growth, which replace our lambda ratio, \gtl
X^.-i, with the ratio of the number of varieties in each period,
Vgt-i'Vgt (e-g-> Romer [1994] and Broda and Weinstein [2004]).
As equation (11) suggests, replacing the lambda ratio with the
ratio of the number of varieties in the two periods can yield
substantial biases. These "quality biases" can be quite large. For
example, if new varieties represent only a small (large) share of
the total expenditure in a good, then a simple count of varieties
will grossly overestimate (underestimate) the true impact of new
varieties.
Second, this framework eliminates the "symmetry bias" that
arises from assuming that all varieties are interchangeable. As
equation (12) indicates, the correct price index should allow for
elasticities of substitution among varieties of different goods to
vary. This implies that the same increase in price of a variety of
two different goods may be valued differently by consumers.
Thus, measuring the aggregate bias requires that these elastici
ties of substitution be estimated (this is the focus of the next
section). In other words, we do not require that wgt(G) or vg be
the same for all goods. Moreover, since we have a three-tiered
CES utility function, we do not require that the elasticity of
substitution among varieties be the same as that across goods.15
Third, the aggregate price index in (12) is robust to a wide
variety of data problems arising from the creation and destruc
tion of product categories g. For example, if goods are randomly
15. Proposition 2 still holds if the existing goods are bundled into CES
aggregates with different elasticities between them rather than using a common
elasticity 7 as in (2).
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 563
split or merged, then the index remains unchanged.16 By con
trast, a measure based on the number of varieties would errone
ously register a fall or rise in the price level. Similarly, it can be
shown that if categories are split when a product category be
comes large and merged when it becomes small, then the index
also will remain unchanged.17 Finally our index is also robust to
the possibility that there may be more than one variety contained
in the imports from a given country of a seven- or ten-digit good.18
V.B. Identification and Estimation ofthe Elasticity of
Substitution
In order to estimate the impact of new imported varieties on
the price index, we first need to obtain estimates of the elasticity
of substitution between varieties of each good. In this subsection
we present a simple model of import demand and supply equa
tions to estimate this elasticity of substitution. Our estimation
procedure closely resembles the approach in Feenstra [1994],
except that we supplement it by allowing for a more general
estimation technique and extend his treatment of measurement
error. We depart from the usual gravity equation model to esti
mate elasticities of substitution in that we allow for an upward
sloping export supply curve. The estimation procedure we use
allows for random changes in the taste parameters of imports by
country and is robust to measurement error from using unit
values that are not proper price indices.
The import demand equation for each variety of good g can be
derived from the utility function in (3). Expressed in terms of
16. A simple example can help understand the intuition of this result. As
sume that there are two varieties (1 and 2) of good g in period t ? 1, and
Pgit-iQgt-i - Pg2t-iQg2t-i = 5. In period t the consumption of variety 1 remains
unchanged, but variety 2 splits into varieties 3 and 4, and consumption is given by
pg2tQg2t = 0, PgstQgzt = 2, Pg4tQg4t = 3. It is easy to show that our measure of
the price movement arising from new varieties, i^gt/kgt_1)1/i<Tg~1), is unaffected
(as it should be). Similarly, we can show that if the number of goods categories
increases, our index will not change. Note also that if the number of varieties were
used instead of the shares, the index would fall from 1 to 2/3.
17. The proof is available from the authors. It is possible to have a bias if
statistical agencies split categories that grow but never destroy old categories.
However, if this were true, we should observe the average imports per category
falling over time rather than the relatively constant size of categories that we
actually see.
18. Feenstra [1994] shows that the effects of multi-variety per product
country pair acts in the same way as a change in the taste parameter or quality
parameter for that country's imports.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
564 QUARTERLY JOURNAL OF ECONOMICS
shares and changes over time, the equation for the import de
mand of a particular variety is the following:19
(14) A ln sgct = <pgt - iag - 1)A ln pgct + zgct,
where <pgt = ivg - l)ln[(()^(d^)/c|)^_1(d^_1)] is a random effect as
bt is random and egct = A ln dgct. As opposed to most of the
empirical literature that uses a gravity model to estimate the
elasticity of substitution which implicitly assumes a horizontal
supply curve (and therefore, no simultaneity bias), we allow the
export supply equation of variety c to vary with the amount of
exports. The export supply equation is given by the following
expression:
(Og
(15) A lnp^, - \\fgt + 1 + o) A ln sgct + bgct,
where <pgt = -&gA ln Egt/H + u>g), wg > 0 is the inverse supply
elasticity (assumed to be the same across countries) and 8^ = A
ln vgct/il + u>g) captures any random changes in a technology
factor vgct. Note that u>g = 0 is a special case of (15), where the
supply curve is horizontal and there is no simultaneity bias. More
importantly for the identification strategy is that we assume that
Eiegctbgct) = 0. That is, once good-time specific effects are con
trolled for, demand and supply errors at the variety level are
assumed to be uncorrelated.
As in Feenstra, it is convenient to write (14) and (15) in a way
that <pgt and tygt are eliminated so that we can use the assumption
that error terms are independent across equations. For this rea
son, we choose a reference country k and differences demand and
supply equations denoted in equations (14) and (15) relative to
country &:
(16) Ak ln sgct = -i<rg- l)A*ln pgct + ekgct
(17) Ak \npgct = y^ A*ln sgct + 8*c?
where &kxgct = Axgct - Axgkt, zkgct = egct - egkt and b*ct = bgct bgkt.
To take advantage of E(egctbgct) = 0, we multiply (16) and
(17) to obtain
(18) (A*In Pgctf = e1(A^ln sgct)2 + 02(A^ln PgctAkln sgct) + ugct,
19. We use shares (sgct) rather than quantities because shares should not be
influenced by the measurement error unit values [Kemp 1962].
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 565
where
u>g 1 ? <og(crg ? 2)
6l = (1 + og)(<rg ~ 1) ' 62=(l + co,)(a,-l)
and
W?c. = Zgcfigcf
Unfortunately, $g = (?*) cannot be consistently estimated from
(18) as the error term ugct is correlated with the regressands that
depend on prices and expenditure shares. However, it is still
possible to obtain consistency by exploiting the panel nature of
the data set combined with the assumption that demand and
supply elasticities are constant over varieties of the same good. In
particular, we can define a set of moment conditions for each good
g9 by using the independence of the unobserved demand and
supply disturbances for each country over time; that is,
(19) G($g) = Et(UgCt(Vg)) = 0 Vc.
As long as all countries, exporting good g satisfy the following
condition:
2 / 2 ___ 2/2
xe*/xe* * x8*/x0*>V V ?gc ?gc
where \x is the variance of x, equation (19) im
independent moment conditions for each good to
parameters of interest.20 This condition effec
the regressands between the two countries
collinear which would not let us solve the iden
faced in equation (18). This condition is formal
stra [1994].
For each good g9 all the moment conditions that enter the
GMM objective function can be combined to obtain Hansen's
[1982] estimator:
(20) $g = arg min G*(?gyWG*($g)9pes
where G*((_0 is the sample analog of G((3), W is a positive defin
20. Rigobon [2003] shows that by using the heteroskedasticity of one of
endogenous variables he can achieve full identification. In particular, he iden
the desired coefficients by dividing the sample into periods of high an
volatility and constraining the parameters and variances that are allowe
change across periods. Our approach is analogous in that we require tha
relative variances must differ across countries for a given time period.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
566 QUARTERLY JOURNAL OF ECONOMICS
weighting matrix to be defined below, and B is the set of econom
ically feasible 0 (i.e., vg > 1; u>g > 0). We implement this
estimator by first estimating the between estimates of 6X and 62
and then solving for fig as in Feenstra [1994]. If this produces
imaginary estimates or estimates of the wrong sign, we use a grid
search of p's over the space defined by B. In particular, we
evaluate the GMM objective function for values of <rg G
[1.05,131.5] at intervals that are 5 percent apart.21 Standard
errors for each parameter were obtained by bootstrapping the
grid-searched parameters.
The problem of measurement error in unit values motivates
our weighting scheme. In particular, there is good reason to
believe that unit values calculated based on large volumes are
much better measured than those based on small volumes of
imports. In the appendix we show that this requires us to add one
additional term inversely related to the quantity of imports from
the country and weight the data so that the variances are more
sensitive to price movements based on large shipments than
small ones. The use of the between estimate coupled with our
need to estimate <r^,(o^, and a constant means that we need data
from at least three countries to identify p.
VI. Results
Our estimation strategy involves four stages. First, we need
to obtain estimates of the elasticity of substitution, ug9 by esti
mating (20). Second, we obtain estimates of how much variety
21. To make sure that we were using a sufficiently tight grid, we cross
checked these grid-searched parameters with estimates obtained by nonlinear
least squares as well as those obtained through Feenstra's original methodology.
Using our grid spacing, the difference between the parameters estimated using
Feenstra's methodology and those obtained using the grid search differed only by
a few percent for the 65 percent of sigmas for which we could apply Feenstra's
approach.
One concern that one might have with this approach is that our grid search
sets a maximum ag of 131.5. While this potentially could bias our results because
we do not allow for infinite elasticities of substitution, in practice the bias is likely
to be quite small. To see this, consider the following example. If ag is 3, a 50
percent decline in the lambda ratio (i.e., a doubling in level of varieties) corre
sponds to a 29 percent decline in the price index; if crg is 20, it corresponds to a 4
percent decline; and if ug is 131.5, a 0.5 percent decline. In other words, constrain
ing the elasticity of substitution to lie below 131.5 will not cause us to identify
substantial variety gains or losses when none are present.
For technical reasons, rather than performing the grid search over parame
ters ((dg,cjg), it was easier to grid search over (pg,o-g) where pg = u>g(o-g - 1)/(1 +
o-gixig) and is restricted to the following interval 0 < pg < (crg ? 1)1 vg (see
Feenstra [1994] for the derivation of this restriction).
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 567
changed by calculating the X^ ratio for every good g (see equation
(11)). Third, by combining our estimates of the elasticity of sub
stitution with the measures of variety for each good, we obtain an
estimate of how much the exact price index for good g moved as
a result of the change variety growth. Finally, we can apply the
ideal log weights to the price movements of each good in order to
obtain an estimate of the movement of the aggregate price of
imports using equation (12). Once we know how much import
prices have changed, it is simple to apply equation (13) to calcu
late the welfare gain or loss from these price movements.
VI.A. Elasticities of Substitution
We now turn to our estimation of the elasticities of substitu
tion. Given the tens of thousands of elasticities we estimate, it is
impossible to report all of the results here. However, we can
provide some sample statistics that can shed light on the plausi
bility of our estimates. There are three main priors that we have
about these parameters. The first is that as we disaggregate,
varieties are increasingly substitutable. In other words, to give a
concrete example, varieties of the three-digit category of fruit and
vegetables are likely to be less substitutable than varieties of the
five-digit subcategory that only contains fresh, dried, or preserved
apples. Similarly, varieties within this five-digit sector are likely
to be still less substitutable than varieties in the seven-digit
subcategory containing just fresh apples. Second, we would like
the goods with high elasticities of substitution to correspond to
goods that we think of as less differentiated. Finally, we would
like to see that goods traded on organized exchanges have higher
elasticities than those that are not.
Equation (20) can be estimated with g fixed at various levels
of aggregation, and we report sample statistics for our elasticity
estimates in Table IV.22 The results reveal that for both time
periods, as we disaggregate product categories, varieties appear
to be closer substitutes. For instance, the simple average of the
elasticities of substitution is 17 for seven-digit (TSUSA) goods
during 1972-1988, while only 7 at the three-digit level. For the
22. A clarification can be handy to understand notation. When we estimate
(jg at the SITC-5 level, then c actually stands for the pair country-TSUSA goods.
For instance, if two different TSUSA categories (e.g., Apples and Kiwis) belong to
a given SITC-5 category (Fresh Fruit), then if the same country (Argentina)
exports in the two TSUSA categories, the two pairs (Apples from Argentina and
Kiwis from Argentina) will be treated as two different varieties of the same
SITC-5 category (Fresh Fruit).
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
568 QUARTERLY JOURNAL OF ECONOMICS
TABLE IV
Sigmas for Different Aggregation Levels and Time Periods
Period Statistic TSUSA/HTS SITC-5 SITC-3
1972-1988 Mean* 17.3 7.5 6.8
Standard error* 0.5 0.5 1.2
Median 3.7 2.8 2.5
Standard error 0.03 0.04 0.11
Median varieties per 15 54 327
category**
Nobs of categories 11040 1457 246
1990-2001 Mean* 12.6 13.1(6.6) 4.0
Standard error* 0.5 5.9(0.3) 0.5
Median 3.1 2.7 2.2
Standard error 0.04 0.06 0.13
Median varieties per 18 52 664
category**
Nobs of categories 13972 2716(2715) 256
(*) Estimates of the mean and standard error are adjusted for parameter censoring. The numbers in
brackets in the SITC-5 1990-2001 were calculated dropping the one outlier elasticity of 16049.
(**) As in Table III, a variety is defined as a TSUSA/HTS-country pair.
For the TSUSA/HTS column: number of observations is equivalent to the median number of countries.
For SITC-5 (SITC-3) column, it is the median number of TSUSA/HTS-good/country pairs in a given
SITC-5 (SITC-3) level.
period between 1990 and 2001, the average elasticity was around
12 for ten-digit (HTS) goods and 4 among three-digit goods. These
differences are not only large economically, but we can statisti
cally reject the hypothesis that the mean coefficient for disaggre
gated goods is the same as that for more aggregated goods.23 In
terms of medians, the elasticity falls less dramatically, from 3.7
and 3.1 at the lowest levels of disaggregation in the first and
second period, respectively, to 2.5 and 2.2. However, in both
periods we can statistically reject that the medians at different
levels of aggregation are the same. In sum, depending on the
statistic being used, the elasticities of substitution fall by 33 to 67
percent at we move from highest to lowest level of disaggregation
in Table IV. Note also that the median elasticities of substitution
for a given disaggregation level tend to slightly fall over time and
23. We performed this test two ways. First, we tested the difference between
the means of the estimated ct^'s, and second we recomputed the means and
standard errors after accounting for the censoring of the crgs due to the grid
search. In both cases, we can reject the hypothesis that the means are the same.
We reported only the latter.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 569
that these differences are statistically significant for the most and
least disaggregated data. This finding is robust at all product
levels, and may represent increasing differentiation among trad
able goods in the latter period.24
Table V shows the elasticities of substitution for the twenty
largest SITC-3 sectors in U. S. imports in each of the periods. For
the period between 1972 and 1988, the sector with the highest
elasticity of substitution among this group was that of crude oil.
The estimated sigma for this sector was 17.1, fourteen times
larger than the sigma for Footwear (oy00^ear = 1.2), the sector
with the smallest elasticity in the table. In the latter period, we
also find that sectors related to petroleum have the highest elas
ticities. More generally, a comparison of elasticities of substitu
tion across categories shows an intuitive pattern that by and
large seems reasonable.
Another way to establish the reasonableness of the estimates
is to examine how well they correspond to other measures of
homogeneous and differentiated goods. Rauch [1999] divided
goods into three categories?commodities, reference priced goods,
and differentiated goods?based on whether they were traded on
organized exchanges, were listed as having a reference price, or
could not be priced by either of these means. Commodities are
probably correlated with more substitutable goods, but one
should be cautious in interpreting commodities as perfect substi
tutes or the classification scheme as a strict ordering of the
substitutability of goods. For example, although tea is classified
by Rauch as a commodity, it is surely quite differentiated. Simi
larly, it is hard to see why a commodity like "dried, salted, or
smoked fish" would be more homogeneous than a reference priced
good like "fresh fish" or a differentiated good like "frozen fish."
That said, it would be disturbing if we found that goods traded on
exchanges are not more substitutable than those that are not.
In order to test this directly, we reestimated sigmas at the
four-digit level to make them directly comparable with Rauch's
classification and report the results in Table VI. The most strik
ing feature of the table is that in both time periods, the average
elasticities of substitution are much higher for commodities than
24. The total number of elasticities being estimated at the TSUSA/HTS level
is smaller than the total number of TSUSA/HTS available within each period.
This responds to the fact that the United States imports in a number of categories
from a small number of countries, and we require at least three countries per
category to identify parameters.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
570 QUARTERLY JOURNAL OF ECONOMICS
TABLE V
slgmas for the ten sitc-3 sectors with the largest import share by
Period
Period 1972-1988
Average
share
SITC-3 Sigma (in %) Descriptions
333 17.1 29.6 CRUDE OIL FROM PETROLEUM OR
BITUMINOUS MINERALS
781 1.6 8.3 MOTOR CARS & OTHER MOTOR VEHICLES
334 9.0 5.4 OIL (NOT CRUDE) FROM PETROL &
BITUMINOUS MINERALS, ETC.
341 5.7 2.4 LIQUIFIED PROPANE AND BUTANE
71 2.5 2.0 COFFEE AND COFFEE SUBSTITUTES
776 1.6 1.6 THERMIONIC, COLD CATHODE,
PHOTOCATHODE VALVES, ETC.
641 6.7 1.6 PAPER AND PAPERBOARD
851 1.2 1.4 FOOTWEAR
681 1.4 1.2 SILVER, PLATINUM & OTHER PL
GROUP METALS
674 11.8 1.2 IRON & NA STEEL FLAT-ROLLE
CLAD, ETC.
Period 1990-2001
Average
share
SITC-3 Sigma (in %) Descriptions
781 3.0 10.6 MOTOR CARS & OTHER MOTOR VEHICLES
333 22.1 7.0 CRUDE OIL FROM PETROLEUM OR
BITUMINOUS MINERALS
776 1.2 6.4 THERMIONIC, COLD CATHODE,
PHOTOCATHODE VALVES, ETC.
752 2.2 5.7 AUTOMATIC DATA PROCESS MACHS AND
UNITS THEREOF
784 2.8 3.4 PARTS AND ACCESSORIES OF MOTOR
VEHICLES, ETC.
851 2.4 2.0 FOOTWEAR
764 1.3 1.9 TELECOMMUNICATIONS EQUIPME
AND PTS, N.E.S.
713 2.7 1.8 INTERNAL COMBUSTION PISTON
AND PTS, N.E.S.
845 6.7 1.8 ARTICLES OF APPAREL OF TEXTILE
FABRICS N.E.S.
641 2.1 1.7 PAPER AND PAPERBOARD
Shares are simple averages calculated over the entire period. Descriptions for SITC-3 codes are
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 571
TABLE VI
Estimated Sigmas and Rauch Liberal Classification
Rauch's classification of goods:
Reference
Commodity priced Differentiated
1972-1988 (four-digit)
Mean 15.3 7.8 5.2
Standard error 3.0 1.5 0.8
Test if different than commodity
(jo-value) 0.01 0.00
Median 4.8 3.4 2.5
Standard error 0.4 0.3 0.1
Test if different than commodity
(p-value) 0.01 0.00
1990-2001 (fou
Mean 11.6 4.9 4.7
Standard error 3.0 0.6 1.0
Test if different than commodity
(p-value) 0.01 0.01
Median 3.5 2.9 2.1
Standard error 0.6 0.2 0.1
Test if different than commodity
{p -value) 0.14 0.00
p-values for one-sided ?-test reported.
for differentiated or reference
ticities of substitution for refe
those of differentiated. The s
at medians. In all but one cas
pothesis that commodities h
elasticity as reference priced
both periods, and we can alwa
modities have the same elastici
priced and differentiated goo
Rauch classifies as commodi
elasticities of substitution tha
ence priced or differentiated.
VLB. Growth in Varieties
Now that we have establis
elasticities of substitution app
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
572 QUARTERLY JOURNAL OF ECONOMICS
criteria, we turn to the task of correctly evaluating changes in
variety. One of the major obstacles we face in implementing this
procedure is in the calculation of the X^ ratio. Evaluating the
impact on price of a new variety is straightforward to do in cases
in which the United States imports other varieties of the same
TSUSA/HTS category. Unfortunately, the X^ ratio is undefined in
cases where there are no common varieties of the TSUSA/HTS
category between the start and end period (i.e., Ig = 0 in Propo
sition 1). The reason why the X^ ratio is undefined is that we
cannot value the creation or destruction of a variety without
knowing something about how this affects the consumption of
other varieties. To give an example drawn from our data, we
cannot value the invention of CD players for car radios without
knowing how these new goods affected other goods, say, simple
car radios. Our solution to this problem is to assume that when
ever a new variety is created within a seven- or ten-digit category
for which Ig = 0 then all seven- or ten-digit categories within the
same five-digit category have a common elasticity of substitution.
In other words, in these special cases, the elasticity we use to
evaluate the impact of a new variety being imported on the price
level is a weighted average of the substitutability of other goods
and varieties within the same five-digit category. Similarly, in
cases where the entire five-digit category is new, we assume a
common elasticity at the three-digit level.25
There are two important implications of this procedure for
our results. The first is that the restriction on the set of goods for
which we can calculate X ratios means that for some product
categories we need to define goods at the five-digit or three-digit
level rather than at the TSUSA/HTS level. Because of this nec
essary restriction, instead of defining 12,347 goods in the earlier
period and 14,549 goods for 1990-2001 (i.e., all TSUSA/HTS
categories for which we have cr's),26 we can only use 408 and 926
goods (a combination of TSUSA/HTS, SITC-5, and SITC-3), re
spectively. Note, however, that this forces some of the elasticities
between different TSUSA/HTS categories to be the same, but the
total number of varieties being used remains unchanged at over
150,000 and 250,000 in the period 1972-1988 and 1990-2001,
25. Note also that this approach also eliminates the bias arising from arbi
trary recategorization of goods since new goods simply appear as new varieties of
existing goods.
26. These are the numbers of available elasticities of substitution at the
TSUSA and HTS level, respectively.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 573
respectively. Moreover, we need to stress that this represents
vastly more disaggregated data than has been used in the past.
Whether this data limitation introduces a bias into our estimates
is harder to assess.
Table VII shows descriptive statistics for the X ratios of all
the 1334 goods used in the calculation of the aggregate price
index, and hence our sample statistics correspond to the complete
set of imported varieties. As the table indicates, even when using
X ratios to measure variety growth, the typical sector saw the
number of imported varieties increase. This table highlights the
importance of using X ratios rather than relying on count data to
measure variety growth. As shown in Table I, the total number of
varieties per TSUSA more than doubled in the period between
1972 and 1988 (i.e., V72/V88 = 0.46). In turn, the number of HTS
varieties rose by over 40 percent during 1990-2001. However,
when we correctly account for the fact that varieties are not
symmetric in the data, we find that the appropriate magnitudes
of variety growth are substantially smaller. We find that the
median measure of variety growth is approximately 25 percent (X
ratio = 0.81) in the period between 1972-1988 and 5 percent (X
ratio = 0.95) in the latter period. Although the count data suggest
a 211 percent increase in the number of varieties, our X ratios
suggest that a 30 percent increase is more appropriate due to the
large number of new varieties with small market shares. This
underscores the importance of carefully measuring variety
growth when making price and welfare calculations.
TABLE VII
Descriptive Statistic of Lambda Ratios
Combination of
TSUSA/HTS - Implied by count
Period Statistic SITC5 - SITC3 used data in Table I
1972-1988 Percentile 5 0.06
Median 0.81 0.46
Percentile 95 2.00
Nobs 408
1990-2001 Percentile 5 0.34
Median 0.95 0.70
Percentile 95 1.80
Nobs 926
See text for definitions.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
574 QUARTERLY JOURNAL OF ECONOMICS
TABLE VIII
The Impact of Variety in U. S. Import Prices
Ratio between aggregate exact price index including
Years variety and the aggregate conventional price index
End-point ratio Average per-annum ratio
1972-1988 0.803 0.986
[0.790,0.835]
1990-2001 0.917 0.992
[0.907,0.941]
1972-2001 (*) 0.720 0.988
[0.705,0.771]
This table shows the estimated values of equation (12) by period. (*) For the period between 1988 and
1990 the average per-annum rate was applied. Bootstrapped ninetieth percent confidence intervals are in
brackets.
VI.C. Import Prices and Welfare
We are now ready to use the elasticities of substitution to
evaluate the price effects of changes in varieties. Aggregating
together our X ratios according to equation (12) yields estimates of
the impact of variety growth on the exact aggregate import price
index. The results from this exercise are reported in Table VIII.
Standard errors on the bias were computed by bootstrapping each
estimate of ag 50 times and recalculating the bias for each set of
parameters. Overall, variety growth implies that the variety ad
justed unit price for imports fell a precisely estimated 19.7 per
cent faster than the unadjusted price between 1972 and 1988 or
about 1.4 percentage points per year. Interestingly, the impact of
variety growth was much smaller during the 1990s. Between
1990 and 2001 the growth of varieties meant that the exact price
index fell 8.3 percent faster than the unadjusted index over this
time period or about 0.8 percentage points per annum. The lower
rate of decline in the later period may reflect the fact that much
of the gains from globalization arising from rise in importance of
East Asian trade may have been realized prior to 1990. If we
assume that prices declined in the missing year at the average
rate across the entire sample, we find that throughout the entire
period, the growth of varieties reduces the exact price relative to
conventionally measured import price index by 28.0 percent.
It is difficult to find a benchmark with which to compare our
results. We are not aware of any study that measures the impact
of variety on aggregate prices, and the papers that study a single
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 575
good at the micro-level (or at most a few goods) are not suitable
for this comparison. Given the lack of aggregate effects of variety
in the literature, we will use as a reference the effects that other
sources of bias (quality change, outlet substitution, etc.) have on
the overall consumer price index. In mid-1995 a commission was
appointed to study the potential biases in the existing measure
ment of the Consumer Price Index. This CPI Commission con
cluded that the change in the consumer price index overstates the
change in the cost of living by about 1.2 percentage points per
year [Boskin et al. 1996]. Several sources of bias are considered,
but the main source is the incorrect measurement of quality
change of products. The effect of quality change alone can account
for about 0.6 percentage points in the overall index. These num
bers suggest that the bias that we find in the import price index
only as a result of the unaccounted variety growth is very large.
That is, the bias due to variety growth in the import price index
is almost twice as large as the bias induced by quality change in
the overall price index and as large as the total bias from all
sources.
We now turn to calculating the welfare effect ofthe fall in
U. S. exact import price. Not surprisingly, the magnitude
welfare gain from this fall hinges on the functional forms
lying the Dixit-Stiglitz structure and cannot be general (an
we will return to in the next section). If elasticities of substit
are not constant or if marginal costs are not fixed, theory su
that one can obtain higher or lower estimates of the gain
variety. Although our estimate ofthe impact of imported vari
on import prices is correct for any domestic production struc
we cannot translate this into a welfare gain without m
explicit assumptions about the structure of domestic produ
Our choice is to assume the same structure ofthe U. S. ec
as in Krugman [1980]. We do this for two reasons. First, since
is the dominant model of varieties, it provides a useful b
mark for understanding the potential welfare gains. Seco
lack the necessary data and model of the economy's inputlinkages
to estimate variants of the monopolistic compet
model in which there are more complex interactions be
imported and domestic varieties.
The compensating variation that results from chan
varieties in imported goods can be calculated using the inve
the product of the weighted X ratios raised to the fracti
imported goods in total consumption goods, as shown in eq
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
576 QUARTERLY JOURNAL OF ECONOMICS
(12). In particular, given equation (13), we use the ideal import
share in each period, 6.7 percent for 1972-1988 and 10.3 percent
for 1990^2001, respectively, together with the information in
Table VIII to obtain the gains in welfare due to variety.27 We find
that consumers are willing to pay 2.6 percent of their income to
access the wider set of varieties available in 2001 rather than the
set available in 1972. Around 1.8 percentage points accrue to the
earlier period. On a per-year basis, consumers are willing to pay
on average 0.1 percent of their income to access each year's new
set of varieties rather than staying with the set of the previous
year.
VI.D. Robustness of Results to Alternative Assumptions
In the previous subsection we computed the impact of variety
growth of U. S. imports on aggregate welfare. Our computation
required several weaker assumptions than those present in pre
vious numerical exercises. First, we do not require that varieties
or goods have equal shares in consumption. Second, we allow for
different elasticities of substitution for each of the goods used.
Third, we obtain our elasticities of substitution by allowing each
of our 1334 markets to have a different elasticity of supply rather
than assuming that these supply elasticities are always equal to
zero. Table IX underscores the importance of using this weaker
set of assumptions. As mentioned in Section V, when import
shares are assumed equal for all varieties, the aggregate import
bias in equation (12) becomes
/V \Wgt(G)/(<Tg-l)
n ^7
where Vgt-ilVgt is the ratio of the actual number of varieties in
each period. Column (2) of Table IX shows how the impact of
variety on welfare is affected by using a simple count of varieties
(i.e., the V ratios) rather than the appropriate X ratios. By using
V ratios, the welfare gains from variety growth become 6.28
percent, more than twice as big as the true estimate using X
ratios. This suggests that in the case of U. S. imports, using a
simple count of varieties to measure the impact of variety growth
grossly overestimates the true impact.
27. We assume that welfare rose at the geometric average of the rates in the
two periods between 1988 and 1990.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 577
TABLE LX
Welfare Comparisons
Equality of Single Smaller
Benchmark import gravity median
estimate shares sigma sigma
(1) (2) (3) (4)
Number of sigmas used 1334 1334 1 1
Median sigma 2.9 2.9 2.9 2.0
Median [percentile 5,percentile
95] [2.1,5.2]
Average sigma 6.5 6.5 2.9 2.0
Lambda ratio (L) or count data
(N) L N N N
Average share (in percent) (*) 8.5 8.5 8.5 8.5
Welfare impact 2.59 6.28 5.09 8.62
[2.01,2.84]
(*) For expositional purposes, we present the weighted average share of imports between the periods
1972-1988 and 1990-2001. Calculations are based on each period's average share and not on this weighted
average.
Column (3) shows the additional impact of using a single
elasticity of substitution for all varieties. For comparison pur
poses with column (2), we choose our median elasticity 2.9 as a
benchmark. The impact of variety on welfare using the single
elasticity of 2.9 is 5.09 percent, smaller than that of column (2)
but still almost twice as large as our benchmark estimate. This
underscores the importance of using the full distribution of sig
mas to value variety. Despite using a smaller point estimate of
the average elasticity (relative to columns (1) and (2)), we find
that the impact of variety on welfare is reduced.28 Finally, column
(4) shows the effect of a reduction in the average elasticity of
substitution on welfare. By reducing the average from 2.9 to 2.0
(as used in Romer [1994]), the impact on welfare significantly
rises to 8.62 percent. In sum, columns (2)-(4) quantify the impor
tance of using X ratios and a complete distribution of sigmas to
calculate the impact of variety growth on welfare.
The previous discussion illustrates that within the CES
framework our estimated a's and X ratios tend to result in smaller
price and welfare movements than one would obtain if count data
28. This reveals that sectors with high variety growth seem to be associated
with low elasticity of substitutions.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
578 QUARTERLY JOURNAL OF ECONOMICS
or a common elasticity were used. However, what happens if we
relax the maintained assumption of a CES utility function? We
can address this by recomputing our main results using an exact
aggregate price index based on a quadratic utility function
instead.
The benefit of using a quadratic utility function is that its
exact price index is the Fisher ideal price index, which is the
geometric average of the Paasche and Laspeyres indices. Specif
ically, we assume that utility can be written as
U=(D* + (m'Am)T,
where m is column vector whose elements are the imported
quantities of varieties (including varieties whose quantity is
zero), \\t is a parameter between zero and one, and A is a sym
metric matrix indicating how the varieties enter into utility. The
import price index will then be the Fisher ideal price index given
by
(21) /^(pV^m1) = [p1 m1 X p?'m1/(p1'm? X p0'm?)]1/2,
where the superscript zeros and ones correspond to the initial and
final periods, respectively. The exact price index will then be a
weighted average of the domestic and imported goods price in
dexes, where we rely on Sato and Vartia for the formulas for the
weights.
The only remaining issue is how to measure the reservation
prices of varieties. To do this, we use the fact that our elasticity of
substitution corresponds to our estimate of the local demand
elasticity or
roo, dM^ pgct _
{ZZ) dpgcMgcr~ **'
If we assume that each variety constitutes a small component of
consumption so that we can ignore the effect of the consumption
of one variety on the aggregate price index, then the demand
curve will be linear in the price of any variety. Without loss of
generality, for a variety with positive imports in period t but not
in period r, we can express the implied price in period r as
dMgc ( 1 \(23) Mgct = -?- ipgct - pgcr) orpgc
where pgcr corresponds to the reserv
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 579
TABLE X
Impact of Variety Change under Alternative Assumptions
Price bias (1972-2001) with exact price indices (*)
CES utility function 0.72
Quadratic utility (Fisher ideal price index) 0.67
Welfare gain (1972-2001) as a percent of GDP
Utility-based approaches
Benchmark CES utility 2.59
Quadratic utility 2.65
(*) Price biases are expressed as ratios between aggregate exact price index and the conventional price
index (as in Table VI).
Using equation (23), we can compute the reservation prices for all
appearing and disappearing goods and then plug these into equa
tion (21).29 By taking the ratio of the Fisher ideal price index
computed using all varieties (i.e., including the new and disap
pearing varieties) relative to the index computed using only com
mon goods, we obtain an estimate of the gain or loss in utility
arising from prices of disappearing and created varieties moving
to and from their reservation levels.
The result from this exercise is reported in Table X. The
Fisher ideal price index that incorporates the virtual price move
ments for the disappearing and created goods is 33 percent lower
than the Fisher index that is based solely on the common goods.
Using the Sato-Vartia weights, we find that consumers would be
willing to pay 2.65 percent of GDP for the expanded set of vari
eties. These numbers (33 percent and 2.65 percent) are startlingly
close to the numbers we obtain with the Feenstra price index (28
percent and 2.59 percent). In other words, shifting between CES
preferences and quadratic preferences that imply a finite reser
vation price has a very small impact on our results.
Finally, we assess the sensitivity of our estimates to two key
assumptions of our framework. First, in our analysis all imported
goods are assumed to be for final consumption. This is not the
case in the data, as almost two-thirds of imports are intermediate
29. We wish to make two clarifying points about this calculation. First, we
are computing the reservation prices assuming that the sector is small and all of
the other prices are fixed. We therefore are not taking into account how the
reservation prices might change when the prices of other goods move. Doing so
would substantially complicate the calculation. Second, in order not to undervalue
the welfare losses in the earlier time period, we first converted historical prices
into current prices using the import price deflator before doing the calculation.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
580 QUARTERLY JOURNAL OF ECONOMICS
or capital goods and not final consumption goods. As noted by
Romer [1994], however, the Dixit-Stiglitz structure allows for
new varieties to be modeled either as consumption goods, as in
Grossman and Helpman [1991], or as intermediate inputs in
production, as in Romer [1990], with no fundamental change in
the underlying economic analysis. In other words, treating the
share of imported intermediate goods as final consumption does
not necessarily bias our estimates. The case of capital goods is
different. While consumption varieties only offer a static gain, the
potential gains from variety growth in capital goods can have
persistent effects in time. This has the potential of magnifying
the effects of variety growth on welfare relative to our "static"
results. Therefore, treating capital goods as final consumption
seems to imply that we are understating the true gains from
variety.
The second assumption that is important for our results is
that of Krugman's [1980] production structure. This structure
assumes that the number of domestic varieties is unaffected by
new foreign varieties (as in Feenstra [1992], Romer [1994], and
Klenow and Rodriguez-Clare [1997]). However, if domestic vari
eties were affected by imported varieties, then our welfare calcu
lations would change. One way to assess the impact of this change
is to calibrate the model of Helpman and Krugman [1985, pp.
197-209]. This model of the monopolistic competition framework
postulates that each country produces both traded and nontraded
goods. The entry of foreign varieties will cause the domestic
differentiated sector to shrink as firms move into the nontraded
sector. In the interest of brevity, we will not rederive the key
equations. In this model, the demand of foreign goods relative to
domestic goods can be written as
(24) n*Df/nD = 7i*t"7ti,
where n and n* are the number of domestic and foreign firms, D
and Df are the quantity of each domestic and foreign variety
purchased by the home country, t > 1 is the iceberg transporta
tion cost, and a is the elasticity of substitution. One can also show
that if one holds fixed the domestic labor force and assumes both
countries produce differentiated goods, then
(25) dn = -Tx~?dn*.
If we assume that the left-hand side of equation (
share of imports to domestic demand (= GDP - exp
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 581
(i.e., 0.13), n*ln equals the ratio of GDP in the rest ofthe world to
U. S. GDP (i.e., 2.13), and a equals our median sigma of 2.9, then
after a little algebra one can show that -t1_<t = -0.16. This
suggests that every incoming variety displaces 0.16 domestic
varieties, and hence one might want to reduce our welfare esti
mate by 16 percent, i.e., from 2.6 percent of GDP to 2.2 percent of
GDP. In this context, making the number of domestic firms en
dogenous reduces our point estimate, but it does not dramatically
alter our main result.
VII. Conclusion
Understanding the impact of new products and the growth in
varieties on economies has been one of the central questions in
international economics, regional economics, and macroeconom
ics. Until now, attempts to estimate magnitude of these effects
have been limited to extremely careful econometric studies of
particular goods and attempts to calibrate standard models. The
failure to obtain credible estimates ofthe impact of new goods and
varieties on prices and welfare at the national level has stemmed
from the difficulty of implementing careful econometric studies of
particular markets more broadly and from the implausibility of
many assumptions underlying calibration exercises.
This paper provides a methodology that estimates all of the
parameters necessary to calculate an exact aggregate price index
and perform welfare calculations at the national level. This, of
course, does not obviate the need for careful econometric studies
of entry in particular markets. Indeed, we see this work as com
plementary to ours. In markets where sufficient data exist to
obtain better estimates of price effects due to entry, one should do
so. Indeed, one could imagine more precise estimates of the im
pact of new goods and varieties arising from a hybrid technique in
which certain markets are modeled in detail and others are
modeled according to our implementation of the Feenstra index.
Whether that would substantially alter our results is impossible
to say, but our results are robust to a wide range of model
specifications and assumptions.
Our results indicate that the effect of new goods and varieties
on the U. S. economy is large. By ignoring these effects, a con
ventional import price index overstates import price inflation by
1.2 percentage points per year. If the bias in the CPI is compa
rable to the bias in the import price index, then this suggest that
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
582 QUARTERLY JOURNAL OF ECONOMICS
the biases identified in this paper are not only more important
than quality adjustments, they are more important than all other
biases combined. Obviously, more work needs to be done to un
derstand whether the biases in the import price index are similar
in magnitude to those in the CPI, but the results suggest that
there is potential for very large effects.
Finally, our results suggest that globalization had had sub
stantial impacts on welfare through the import of new varieties.
U. S. welfare is 2.6 percent higher due to gains accruing from the
import of new varieties. An important qualification is that our
estimates are obtained by assuming the U. S. economy can be
modeled as in Krugman [1980]. While this is a sensible bench
mark, there clearly is a need for better modeling and estimation
of dynamic and input-output effects arising from increases in the
number of imported varieties. Even so, our estimation indicates
that the gains from trade first suggested by Krugman a genera
tion ago are quite important in reality.
Appendix: Biases and Weighting in the Presence of
Measurement Error
Let pgct be the unit value of a variety that we have in our
data set (i.e., French red wine) andp^c^ is the price of product i
contained in variety gc (i.e., the price of a particular bottle of
French red wine). Hence qgcti will always equal one. If we assume
that the log of the geometric mean price of a variety is approxi
mately equal to the log of the arithmetic mean, we have
(26) lnp,c( - W^M - \J^PaS^\
where qgct = 2; qgcti is the quantity of imported variety gc in
time t.
Assume that product prices are measured with an i.i.d. error
such thatpgcti = pgctAgcti, where pgcti is the true price andp^
is the measured price. In this case
varQn igcti) = \2
cov(ln igcti9\n Igc'sj) = 0 Vc =? c'9t ?= s9i ?j
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 583
(27) XlPgct = vaJlnp^Ml - varL^P J^'V
= iVar(?ln^)=^^x2=^x2
Now
(28) E(\nPgct - Xnp^-tf = h2gct + x2(^~ + -^?1Yd get Hgct-lf
where bgct is the variance ofthe true price change. Averaging this
across all periods produces
(29)
EyJ, ilnpgct - lnpgct^)2 = yS^ + X2yS (? +-).t t t ^Sct Hgct 1/
This implies that we should add a term equal to
<30) *r2(9- + ^)
to the right-hand side of equation (18) where x2 is a parameter to
be estimated. It is worth noting that if qgct = qgct-1 and the
importance of measurement error does not decline with the num
ber of periods used in the between estimate, the terms in paren
theses in equation (30) become a constant. This is the specifica
tion estimated in Feenstra [1994]. Our algebra can thus be seen
as a generalization of Feenstra's approach that allows for mea
surement error to depend on the quantity of varieties and the
number of periods over which the average is taken.
A related but distinct issue concerns heteroskedasticity in
the data. Every data point comprising the left-hand side of equa
tion (18) is an estimate ofthe variance. However, if the prices are
measured with error, then so are our sample variances. Using
equation (28), we can correct for this heteroskedasticity by real
izing that the variance of the average of the sample variance can
be written as
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
584 QUARTERLY JOURNAL OF ECONOMICS
(31) varj^ 2 dnPgct ~ Inpgct-i? - j> E (Inpgct - lnPg^-O2 1
1 [ r 1 ]2i
= ^2 var _? (ln/^c, - lnp^_x)2 The
term in curly brackets is likely t
quantity of goods used in order to co
inversely related to the number of peri
the average variance. We correct for
assuming that the variance of the
proportional to
and we therefore weight the data by
/ 1 1 \'y2
T3/2[? +\Qgct Qgct-v
University of Chicago, Graduate School of Business, and Federal Reser
Bank of New York
Columbia University and National Bureau of Economic Research
References
Anderson, James, "A Theoretical Foundation for the Gravity Equation," American
Economic Review, LXJX (1979), 106-116.
Armington, Paul, "A Theory of Demand for Products Distinguished by Place of
Production," International Monetary Fund Staff Papers, XVI (1969), 159-178.
Bils, Mark, and Peter Klenow, "The Acceleration of Variety Growth," American
Economic Review, XCI (2001), 274-280.
Boskin, Michael, Ellen Dulberger, Robert Gordon, Zvi Griliches, and Dale Jorgen
son, Toward a More Accurate Measure ofthe Cost of Living: Final Report to
the Senate Finance Committee (Washington, DC: U. S. Government Printing
Office for the U. S. Senate Committee on Finance, December 1996).
Broda, Christian, and David Weinstein, "Variety Growth and World Welfare,"
American Economic Review Papers and Proceedings, XCIV (2004), 139-145.
Brown, Drusilla, Alan V. Deardorff, and Robert Stern, "Modeling Multilateral
Trade Liberalization in Services," Asia-Pacific Economic Review, II (1996),
21-34.
Diewert, W. Erwin, "Exact and Superlative Index Numbers," Journal of Econo
metrics, TV (1976), 115-145.
Dixit, Avinash, and Joseph Stiglitz, "Monopolistic Competition and Optimum
Product Diversity," American Economic Review, LXVII (1977), 97-308.
Eaton, Jonathan, and Samuel Kortum, "Technology, Geography, and Trade,"
Econometrica, LXX (2002), 1741-1779.
Eaton, Jonathan, Samuel Kortum, and Francis Kramarz, "Dissecting Trade:
Firms, Industries, and Export Destinations," American Economic Review
Papers and Proceedings, XCIV (May 2004), 150-154.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms
GLOBALIZATION AND GAINS FROM VARIETY 585
Feenstra, Robert, "How Costly Is Protectionism?" Journal of Economic Perspec
tives, VI (1992), 159T178.
-, "New Product Varieties and the Measurement of International Prices,"
American Economic Review, LXXXTV (1994), 157-177.
-, "U. S. Imports, 1972-1994: Data and Concordances," National Bureau of
Economic Research Working Paper No. 5515, 1996.
Feenstra, Robert, Gordon Hanson, and Songhua Lin, "The Value of Information in
International Trade: Gains to Outsourcing through Hong Kong," Advances in
Economic Analysis & Policy, IV (2004), 1-35.
Fisher, Irving, The Making of Index Numbers (Boston, MA: Houghton-Mifflin,
1922).
Fujita, Masahisa, Paul Krugman, and Anthony Venables, The Spatial Economy:
Cities, Regions, and International Trade (Cambridge, MA, and London, UK:
MIT Press, 1999).
Grossman, Gene, and Elhanan Helpman, Innovation and Growth in the Global
Economy (Cambridge, MA, and London, UK: MIT Press, 1991).
Hansen, Lars, "Large Sample Properties of Generalized Method of Moments
Estimators," Econometrica, L (1982), 1029-1054.
Hausman, Jerry, "Exact Consumer's Surplus and Deadweight Loss," American
Economic Review, LXXI (1981), 662-676.
Helpman, Elhanan, and Paul Krugman, Market Structure and Foreign Trade:
Increasing Returns, Imperfect Competition, and the International Economy
(Cambridge, MA, and London, UK: MIT Press, 1985).
Hotelling, H., "Stability in Competition," Economic Journal, XXXIX (1929), 41-57.
Kemp, Murray, "Errors of Measurement and Bias in Estimates of Import Demand
Parameters," Economic Record, XXXVIII (1962), 369-372.
Klenow, Peter, and Andres Rodriguez-Clare, "Quantifying Variety Gains from
Trade Liberalization," September 1997.
Krugman, Paul, "Increasing Returns, Monopolistic Competition, and Interna
tional Trade," Journal of International Economics, IX (1979), 469-479.
-, "Scale Economies, Product Differentiation, and the Pattern of Trade," Ameri
can Economic Review, LXX (1980), 950-959.
Lancaster, Kelvin, "Socially Optimal Product Differentiation," American Eco
nomic Review, LXV (1975), 567-585.
Rauch, James, "Networks versus Markets in International Trade," Journal of
International Economics, XLVIII (1999), 7-35.
Rigobon, Roberto, "Identification Through Heteroskedasticity," Review of Econom
ics and Statistics, LXXXI (2003), 777-792.
Roberts, Mark, and James R. Tybout, "The Decision to Export in Colombia: An
Empirical Model of Entry with Sunk Costs," American Economic Review,
LXXXVII (1997), 545-563.
Romer, Paul, "Capital, Labor, and Productivity," Brookings Papers on Economic
Activity, Special Issue (1990), 337-367.
-, "New Goods, Old Theory, and the Welfare Costs of Trade Restrictions,"
Journal of Development Economics, XLIII (1994), 5-38.
Rutherford, Thomas, and David Tarr, "Trade Liberalization, Product Variety and
Growth in a Small Open Economy: A Quantitative Assessment," Journal of
International Economics, LVI (2002), 247-272.
Samuelson, Paul, "Using Full Duality to Show that Simultaneously Additive
Direct and Indirect Utilities Implies Unitary Price Elasticity of Demand,"
Econometrica, XXXIII (1965), 781-796.
Sato, Kazuo, "The Ideal Log-Change Index Number," Review of Economics and
Statistics, LVIII (1976), 223-228.
Spence, Michael, "Product Differentiation and Welfare," American Economic Re
view, LXVI (1976), 407-414.
Vartia, Yrjo, "Ideal Log-Change Index Numbers," Scandinavian Journal of Sta
tistics, III (1976), 121-126.
Yi, Kei-Mu, "Can Vertical Specialization Explain the Growth of World Trade?"
Journal of Political Economy, CXI (2003), 52-102.
This content downloaded from 147.251.185.127 on Thu, 24 Aug 2017 11:18:01 UTC
All use subject to http://about.jstor.org/terms