Price, Quality, and Variety: Measuring the Gains
from Trade in Differentiated Products
Gloria Sheu∗
US Department of Justice
September 2011
Abstract
The empirical trade literature has found that the ability to import differentiated products has significant positive welfare effects. These gains have been established using
price indices that measure the value to consumers of changes in the set of goods available over time. In this paper, I explore how these price indices are shaped by their
underlying structural assumptions. I draw parallels with methods used in industrial
organization, where a number of researchers have also studied differentiated products,
albeit in domestic markets. I show that a standard trade model, the nested constant
elasticity of substitution (NCES) framework, produces the same market demand system and price index as a standard industrial organization model, the nested logit (NL).
This finding allows me to connect commonly used NCES and NL variants into one
coherent family. Furthermore, I show how standard NCES empirical techniques, which
rely on data that aggregates over individual products, relate to the product-level data
methods more commonly used in logit settings. I then apply these methods to a data
set on Indian imports of computer printers, highlighting how these approaches differ in
a concrete example. In this application, I find that using aggregated data understates
the gains in the price index by 31 to 43 percent relative to using product-level data.
Furthermore, loosening the assumed substitution structure between goods raises the
price index by over 60 percent.
∗
The views expressed here are not purported to reflect those of the US Department of Justice. I
would like to thank Pol Antràs, Elhanan Helpman, Julie Mortimer, and Ariel Pakes for their guidance
and support on this project. This paper has also benefitted from discussions with Deepa Dhume,
Oleg Itskhoki, Greg Lewis, Marc Melitz, David Mericle, Nathan Miller, Eduardo Morales, and Marc
Remer. I am greatly indebted to George Gibson of the Xerox Corporation for giving me access to
the printer data set and for helping me understand the Indian printer market. Mary Carlin at the
Xerox Corporate Library also provided key assistance in obtaining the printer data. Petia Topalova
graciously made the Indian tariff data available. All errors are my own. First version: November 2009.
Email: [email protected]
1
Introduction
As emphasized in the seminal work of Krugman (1979), an important channel by which
countries can gain from trade is through increased access to differentiated products.
Imported goods widen the choice set available to consumers by providing a different
combination of price, quality, and variety than domestic goods alone. Although the
benefits of cheaper imports have long been recognized, consumers also place value on
the varying qualities (that is, the unique mix of non-price characteristics) provided by
foreign differentiated goods. Furthermore, access to imported products may increase the
number of goods available for a given distribution of price and quality, thus increasing
variety. All three of these forces contribute to the gains from trade.
After establishing these effects theoretically, the next step has been to measure them
empirically. Feenstra (1994) facilitated these efforts by introducing a simple procedure
for computing the price index from a differentiated products demand system. This
price index measures how much prices on one set of products would have to fall (or
rise) in order to give consumers the same welfare as that from a different set. The
Feenstra (1994) method has been widely adopted, and much of the resulting literature
underscores the importance of accounting for differentiated products when measuring
the gains from trade.
Now that these papers have confirmed the existence of welfare gains, what more
can be learned? Can the standard theoretical and empirical techniques be refined in
order to better understand the causes of these welfare effects? In considering these
questions, it is important to examine the empirical industrial organization literature
on differentiated products. Like the aforementioned trade literature, there is a rich
industrial organization tradition studying how consumers are affected by changes in
the price, quality, and variety of differentiated products. The basic research question
is the same, just applied to domestic empirical examples instead of international ones.
Therefore, examining the relationship between the methods used in these literatures
shows how the results in trade are shaped by the techniques used to construct them.
The purpose of this paper is to reach a more fundamental understanding of the
international trade approach towards differentiated products by comparing it to techniques that are usually confined to industrial organization. My analysis has two key
components. First I show that the seemingly disparate theoretical frameworks used
in trade and industrial organization are actually tightly linked. More specifically, the
workhorse models of international trade, the constant elasticity of substitution (CES)
1
and the nested constant elasticity of substitution (NCES) setups, produce the same
market demand functions and price indices as two of the most common models in
industrial organization, the multinomial logit (MNL) and the nested logit (NL), respectively. As a consequence, the differences between trade and industrial organization
empirical findings based on these models are driven more by differences in data and
empirical techniques than by differences in theory. Furthermore, this result means that
the random coefficients framework, another common model in industrial organization,
is also connected to the NCES as an extension of the NL that I call the nested random
coefficients logit (NRCL). Therefore, the extra impact of random coefficients can be
assessed through a comparison between the NL and the NRCL.
Second, I present an empirical application that shows how the trade and industrial
organization approaches can differ in practice. Using a product-level data set on imports of computer printers into India, I estimate several industrial-organization-style
logit models. Furthermore, by aggregating this data, I am also able to implement standard trade methods. This exercise produces three main findings. First, by obscuring
improvements in quality and variety amongst the underlying goods, I find that the
aggregated data commonly used in trade understate the gains in the price index by 31
to 43 percent. Second, the MNL, with its restrictive substitution structure, overstates
gains in the price index by 65 to 68 percent relative to the NL and NRCL. Third, the
addition of random coefficients reveals important heterogeneity across types of consumers. The NRCL price index for certain subgroups of consumers is 53 percent lower
than the market-level NL index.
There are two main distinctions between how trade and industrial organization approach the study of differentiated products. First, there is a difference in terms of data.
The standard in the trade literature is to use data collected from customs authorities.
Customs information is often the only data available that exhaustively covers the imports of an entire nation. As a result, these data are the preferred choice for trade
papers, where the emphasis is on studying the economy-wide effects of international
trade. However, a drawback of this data is that it aggregates individual goods into
“Harmonized System” (HS) codes. A product is defined as an HS code/supplier country pair. When reporting imports of computer printers, for instance, a good could be
defined as broadly as “inkjet printers from the United States.”
In contrast, the industrial organization literature usually relies on detailed productlevel data. Continuing with the printer example, a typical data set would report the
quantities sold and prices of individual models. The “HP Deskjet 630C” and the “HP
2
Deskjet 1220C” would be separate observations, recognizing the fact that the latter
model prints at twice the speed as the former. Not only does this level of analysis
match the level of differentiation relevant to consumers, it also allows the researcher
to supplement the sales data with product characteristics information. For instance,
one could obtain proxies for the quality of each printer model by incorporating data on
features like print speed or paper capacity. As a result, this data provide more direct
information on price, quality, and variety when compared to customs data. However,
the downside is that such detailed data are only available for selected sectors and
countries.
The second difference between the trade and industrial organization approaches is
in terms of structural modeling. In order to assess the effects on consumers of changes
in products, the researcher assumes a demand system. A number of theoretical trade
papers use the CES demand system, which is derived from the utility maximization
problem of a representative consumer.1 Because of its simplicity, the CES model is
both algebraically elegant and easy to implement empirically. However, the CES also
severely restricts the substitution structure between products. In order to address this
problem, many empirical researchers have adopted an NCES specification, which allows
the substitution parameter within a sector to differ from that between sectors.
Meanwhile, the industrial organization literature has largely relied on the MNL
demand system.2 Unlike the CES, this framework assumes a distribution of heterogeneous consumers, each purchasing one type of good. But like the CES, the MNL places
strong restrictions on substitution patterns. In response, researchers have developed a
number of modifications, the most common being nesting (as in the NL) and random
coefficients.3 I combine these two extensions into a unified model, the NRCL.
My results build upon the aforementioned empirical trade and industrial organization literatures studying the welfare effects of changes in differentiated products.
Although the many contributions in these literatures are too numerous to fully summarize here, key papers in trade include Broda and Weinstein (2006), Broda et al. (2006),
and Goldberg et al. (2010), along with the aforementioned work in Feenstra (1994).
On the industrial organization side, significant developments include Berry, Levinsohn,
1
This functional form is sometimes referred to as the Spence-Dixit-Stiglitz demand system after
the work in Spence (1976) and Dixit and Stiglitz (1977).
2
This trend follows from the influential work in McFadden (1974).
3
The latter type of model is sometimes referred to as a mixed logit. Train (2009) defines the mixed
logit model based on the form of the resulting demand system. He then notes that one way of deriving
a mixed logit demand system is through a random coefficients specification.
3
and Pakes (1995) (“BLP”), Goldberg (1995), Berry et al. (1999), Petrin (2002), and
Berry et al. (2004). Khandelwal (2010) is one of the few hybrid papers that uses an
industrial organization model (the NL) with a trade data set. Here I show that the
theory behind this approach is equivalent to the NCES setup.
The closest paper to this one is Blonigen and Soderbery (2010), which uses productlevel data on the US automobile market to study how aggregated HS trade data biases
the NCES price index. They find that using aggregated trade data can greatly understate improvements in the price index. I find a parallel result in my data and then
expand upon this analysis by exploring how CES-style models behave relative to logit
models.
In the next section, I describe the CES-based models and the Feenstra (1994) method
for estimating their price indices. Section 3 lays out the basics of the logit models and
relates them back to the CES-based frameworks, followed by a description of empirical
industrial organization techniques for dealing with product-level data. I present results
from the computer printers example in Section 4, including a discussion of the differences
between the CES-based and logit results. Section 5 concludes.
2
CES-Based Frameworks
The NCES model is popular in empirical trade applications because it yields a price
index that combines changes in price, quality, and variety into one easily interpretable
number. Furthermore, the NCES includes the basic CES framework, the workhorse
model of international trade theory, as a special case.
In order to calculate the NCES price index, Feenstra (1994) provides a simple procedure designed for the typical trade data set. This methodology has become the standard
for measuring the gains from imports of differentiated products. These techniques contrast with those favored in industrial organization, where estimation using product-level
data is more common.
2.1
The Consumer’s Problem
Assume there is a representative consumer that has a utility function given by
Ut =
X
γ−1
γ
γ
! γ−1
,
Mgt
g∈G
4
where γ > 1.
(1)
Here g indexes different groups of products from the set G. The time period is indexed
by t. The quantity consumed of each group is denoted by Mgt , and γ is the elasticity
of substitution between these groups.
Within each product group g the consumer has an inner nested utility function of
the form
σ
 σ−1

X 1 σ−1
, where σ > 1.
(2)
Mgt = 
bjtσ mjtσ 
j∈Jgt
Individual products are indexed by j from the set Jgt . The bjt denotes the quality of
good j, and mjt denotes the quantity consumed of good j. The elasticity of substitution
between products within a group is σ.4 Assuming the nesting structure is reasonable,
one would expect σ > γ, meaning that products within a group are closer substitutes
than those in separate groups.
Each time period the consumer’s problem is to maximize current period utility
subject to a budget constraint. This is an entirely static model, with no borrowing or
saving. The consumer can solve the utility maximization problem in two stages. First,
P
the consumer maximizes Mgt subject to the constraint j∈Jgt pjt mjt = Ygt , where Ygt
is the total money spent on group g. Then the consumer decides on the allocation
of expenditure across groups. This exercise results in the expression for the share of
expenditure allocated to product j within Ygt ,
bjt p1−σ
jt
1−σ .
j∈Jgt bjt pjt
sjt|g = P
(3)
In turn, the share of expenditure devoted to group g out of total expenditure is
1−γ
1−σ 1−σ
b
p
j∈Jgt jt jt
sgt =
1−γ .
P
P
1−σ 1−σ
g∈G
j∈Jgt bjt pjt
P
(4)
Multiplying these two expressions gives the share of expenditure allocated to product
4
An extension of this model is to allow the elasticity of substitution to vary by group, giving σg . I
do not pursue this variant for simplicity, but its mechanics are similar to those discussed in the main
text.
5
j out of the money spent on all product groups,
bjt p1−σ
jt
P
γ−σ
P
1−σ
1−σ
sjt = P
j∈Jgt bjt pjt
j∈Jgt
g∈G
1−σ
bjt pjt
1−γ .
1−σ
(5)
In the special case where σ = γ, the NCES reduces to a simpler framework known
as the CES model. Once the elasticities of substitution in the outer and inner utility
functions are equal, the nesting ceases to have any effect. It is as if all the products are
located in a single group.5 The resulting expenditure shares are given by
sjt = P
1−γ
bjt pjt
1−γ
j∈Jt bjt pjt
.
(6)
The CES is one of the most popular differentiated products demand systems in the
theoretical trade literature.6
2.2
The IIA Problem
When quantifying the gains from changes in differentiated products, it is extremely
important to accurately measure the substitutability between goods. For instance, if
one incorrectly finds that a new product is a poor substitute for existing products,
one will mistakenly conclude that this new product greatly increased welfare. The
CES, although useful in a number of theoretical applications, has a highly restrictive
substitution structure. The industrial organization literature commonly refers to this
issue as the “independence of irrelevant alternatives” problem. It is the struggle to solve
this problem that led to the adoption of the NCES in the empirical trade literature.
In order to illustrate the IIA property, note that according to the CES expenditure
share equation (6) the ratio of the quantity demanded for a pair of products 1 and 2 is
b1t p−γ
m1t
1t
=
,
m2t
b2t p−γ
2t
which does not depend on the other products available. Thus, if a third good is in5
That is, utility reduces to Ut =
P
1
γ
γ−1
γ
j∈Jt bjt mjt
γ
γ−1
.
6
The CES and Cobb-Douglas (which the CES reduces to when γ = 1) models have been featured
in standard trade textbooks such as Helpman and Krugman (1985) and in key theoretical papers such
as Dornbusch et al. (1977), Eaton and Kortum (2002), and Melitz (2003).
6
troduced that is identical to good 1 and very different from good 2, the demand ratio
between 1 and 2 will remain constant. One would expect sales of good 1 to fall relative
to good 2, but the CES model does not allow this to occur.
Another way of expressing this problem is using cross-price elasticities, which in the
case of the CES have the following form:
∂mjt pkt
= (γ − 1)skt
∂pkt mjt
∀j 6= k.7
(7)
∀j, k, l such that j, l 6= k.
(8)
These elasticities have the property that
∂mjt pkt
∂mlt pkt
=
∂pkt mjt
∂pkt mlt
Hausman (1997) argues that because of this property, the CES will overvalue new goods.
If one thinks of a new good being introduced as its price falling from the reservation
level, expression (8) says that demand must flow symmetrically towards the new product
from all other products. This may not be a realistic assumption for many sectors. For
instance, it is unlikely that expenditure will flow equally from an old laser printer and
from an old injet printer to a newly introduced laser printer.
If σ 6= γ, the NCES model can partially alleviate the IIA problem. This effect is
apparent in the NCES cross-price elasticities,
∂mjt pkt
=
∂pkt mjt
(
(γ − 1)skt + (σ − γ)skt|g
(γ − 1)skt
if j and k are in the same group
otherwise
(9)
for all j 6= k. Since it is likely that σ > γ, the (σ − γ)skt|g term should be positive and
thus increase the cross-price elasticity between goods of the same type. This adds a level
of realism compared to the CES. However, the IIA problem remains when comparing
goods within the same group.
2.3
The Price Index
A key reason for the popularity of CES-based models is that they yield a simple price
index for measuring the relative benefits of two sets of goods. In order to understand
this index, imagine that the representative consumer is comparing two possible bundles
7
This elasticity can be derived by noting that mjt =
7
sjt Y
pjt
, where Y denotes income.
of goods, the bundle available in time t and that available in time t + 1. These bundles
may vary in terms of the combination of price, quality, and variety they offer. How
could one derive a metric that reflects the difference in value the consumer assigns to
these bundles?
N CES
One common way to build this metric is to look for a factor, τt+1
, by which the
prices of all goods in period t would have to fall (or rise) in order to give the same
utility as the set of goods available in t + 1. This exercise results in the expression
P
N CES
=
τt+1
g∈G
P
P
g∈G
j∈Jgt+1
P
bjt+1 p1−σ
jt+1
1−σ
j∈Jgt bjt pjt
1
1−γ 1−γ
1−σ
1
1−γ 1−γ
1−σ
,
(10)
which is the standard measure of the gains from imports of differentiated products in
the trade literature.8 In the special case of the CES model, this index reduces to
1
1−γ 1−γ
b
p
j∈Jt+1 jt+1 jt+1
.
1
P
1−γ 1−γ
j∈Jt bjt pjt
P
CES
τt+1
=
(11)
N CES
is actually just a geThe nested structure of the NCES model means that τt+1
ometric average of CES price indices calculated within each group of products.9 That
is,
Y
N CES
CES ωgt+1
τt+1
=
τgt+1
,
(12)
g∈G
where
1
1−σ 1−σ
b
p
j∈Jgt+1 jt+1 jt+1
P
1
1−σ 1−σ
b
p
j∈Jgt jt jt
P
CES
τgt+1
=
8
Y/
This
P
g∈G
9
result
P
and ωgt+1 = P
follows
(sgt+1 − sgt )/(ln(sgt+1 ) − ln(sgt ))
.
g∈G (sgt+1 − sgt )/(ln(sgt+1 ) − ln(sgt ))
from the form of the indirect
1
1−γ 1−γ
1−σ
1−σ
. Here Y denotes income.
j∈Jgt bjt pjt
utility
This result follows from the proof in the appendix of Feenstra (1994).
8
function,
which
is
2.4
Estimation
The next task is to estimate this price index. Most empirical trade papers analyze
welfare effects at an economy-wide level. Given this focus, these authors need a method
that can be applied to customs data and requires as few parameters as possible. The
procedure pioneered by Feenstra (1994) satisfies both of these criteria.
In this section I replace the product subscript j with c for “category.” This is
because the standard method uses trade data, where a good is actually an HS category
imported from a certain country. This aggregates over individual products.
Note that once I switch to defining a product using these categories, the bct parameters no longer have a pure quality interpretation. Feenstra (1994) shows that these
terms not only reflect the quality but also the number of underlying products in each
category. If the number of sub-products in a product category increases, this in turn
increases its associated bct . Thus, bct captures both quality and variety.
Define Cg = (Cgt+1 ∩ Cgt ) as the “common goods” set available for a group in two
different time periods. As shown by Feenstra (1994), so long as one assumes that the
products in Cg have constant bct parameters between t and t + 1, the following holds:
ωgt+1
ωgt+1
Y λgt+1 σ−1
Y pct+1 ωcgt+1


.
=
p
λgt
ct
g∈G
g∈G
c∈C

N CES
τt+1
Y
(13)
g
where
P
c∈Cg
pct mct
c∈Cgt
pct mct
λgt = P
and
(sct+1 (Cg ) − sct (Cg ))/(ln(sct+1 (Cg )) − ln(sct (Cg )))
c∈Cg (sct+1 (Cg ) − sct (Cg ))/(ln(sct+1 (Cg )) − ln(sct (Cg )))
ωcgt+1 = P
Here sct (Cg ) denotes the share of expenditure accounted for by category c out of the
categories in the set Cg .
In the special case of the CES model, this index is calculated without regards to
any groups. There is one common goods set C = (Ct+1 ∩ Ct ), giving
1
CES
τt+1
=
Y pct+1 ωct+1 λt+1 γ−1
c∈C
pct
λt
9
(14)
where
P
pct mct
λt = P c∈C
c∈Ct pct mct
and ωct+1 = P
(sct+1 (C) − sct (C))/(ln(sct+1 (C)) − ln(sct (C)))
.
c∈C (sct+1 (C) − sct (C))/(ln(sct+1 (C)) − ln(sct (C)))
Note that sct (C) denotes the expenditure share of product c in time t amongst the
goods in C.
The advantage of this methodology is that the price index can be computed using
only one parameter, the within-group elasticity of substitution, and widely available
trade data. Feenstra (1994) and Broda and Weinstein (2006) show how to estimate
this elasticity of substitution for different industries. Many other authors assume an
elasticity based on estimates in the literature.
Although this procedure is useful, it depends on the assumption that the common
goods do not experience any change in their bct terms. Therefore, both the quality and
variety of the underlying goods in each product category are assumed to be constant.
If quality or variety improve within the common goods, this will not be reflected in the
price index.
In order to solve this problem, one could switch to product-level data and compute
the price index over short enough time periods so that the common goods set is nonempty. This is the approach studied by Blonigen and Soderbery (2010). Of course, this
method is not feasible for most industries in most countries, where only aggregated trade
data is available. As a result, in practice most researchers assume that HS code/country
pairs appearing in both periods have constant bct parameters.10
2.5
The Price Index Decomposition
A key advantage of the Feenstra
approach
is that it decomposes the price index
ωcgt+1 ωgt+1
Q (1994)
Q
pct+1
(which I call the common goods
into two parts. The g∈G
c∈Cg
pct
gt+1
ωσ−1
Q
λgt+1
term) captures gains from price amongst common products, while the g∈G λgt
(which I call the changing goods term) captures gains from new and disappearing
products. If there has been a large relative increase in spending on new products
in period t + 1, the changing goods term will fall, indicating that the price index has
decreased. If however, these new products are highly substitutable with common goods,
the elasticity of substitution σ will be large, and this term will approach 1.
10
An exception is the original Feenstra (1994) paper, where he reports sensitivity results for several
different common goods sets.
10
There are two differences in the NCES decomposition compared to the CES one.
First, in the NCES case, both the common goods and the changing goods terms are
calculated within each group before being aggregated. This reflects the fact that, assuming the chosen grouping is sensible, a change in a product should affect the competing
products in the same group more than those in other groups.
Second, the NCES decomposition uses σ instead of γ for the elasticity of substitution
in the changing goods term. Note that σ is likely to be greater than γ because it
reflects substitution within groups of similar products instead of substitution across all
products. Therefore, the changing goods term is less likely to find large gains from
new products or large losses from disappearing products. Taken together, these two
differences tend to dampen movements in the NCES index relative to those in the CES
index.
Unfortunately, this method does not decompose the distribution of gains into those
due to price, quality, and variety. The common goods term calculates the gain from
price holding quality and variety constant in an artificial set of goods. Because the
common goods set excludes products in time t that did not appear in time t + 1 and
products in time t + 1 that did not appear in time t, this set is not equal to the actual
choice set in either period.
Furthermore, the changing goods term embeds price, quality, and variety effects,
making it difficult to distinguish them. A new product, for example, may have a large
expenditure share because it is cheap or because it is of high quality.
3
Logit-Based Frameworks
In measuring the gains from trade in differentiated products, the trade literature has
struggled with two issues: (1) how to allow for realistic substitution patterns and (2)
how to estimate price indices without product-level data. The industrial organization
literature on differentiated products has faced these same challenges. In tackling the
substitution problem, industrial organization has turned to two strategies, the first being nesting products, the second being random coefficients. These methods can be combined in a unified framework that I call the “nested random coefficients logit” (NRCL).
In addressing the data aggregation problem, industrial organization has bypassed this
issue by focusing on sectors for which product-level data is available. Because these
trade and industrial organization approaches are aimed at solving the same basic prob-
11
lems, comparing them highlights the costs and benefits of each.
At first glance this comparison appears difficult because of the stark differences in
the standard trade and industrial organization modeling frameworks. The empirical
industrial organization literature favors demand systems based on the MNL discrete
choice setup. Unlike in the CES framework, here there is a population of heterogeneous
consumers, each with unique preferences. Each buyer only purchases a quantity of one
product instead of consuming some of every product.
Nevertheless, Anderson et al. (1992) show that the MNL model produces the same
market demand system and price index as the CES. Building upon this insight, I show
that the NCES and NRCL are also tightly linked. In fact, I find that a special case of the
NRCL model, the NL, generates the exact same price index as the NCES. This result
allows me to separate the comparison based on structural theory differences (which arise
between the MNL, NL, and NRCL) from that based on data aggregation differences
(which arise between the CES and MNL or the NCES and NL).
3.1
The Consumers’ Problem
Assume that there are different types of consumers, with each type indexed by r.
Further assume, as in the NCES model, that goods are separated into groups indexed
r 11
by g ∈ G. In addition, each good within a group g is indexed by j in the set Jgt
. The
utility for consumer i of type r buying good j in group g is
r
urijt = ln(arjt mrijt ) + ζigt
+ rijt .
(15)
Here arjt is a good-specific measure of quality similar to bjt . The mrijt is the quantity of
good j that consumer i chooses to buy.12
r
Meanwhile the ζigt
is a random draw from a logit distribution with scale parameter
r
r
µ1 , and the ijt is a random draw from a logit distribution with scale parameter µr2 .13
11
r
The set of goods available Jgt
may vary by consumer, meaning that some goods can be consumed in
zero quantities by all consumers of a certain type. For example, a home office buyer would not consider
purchasing a large enterprize printer, so it should not be in that consumer’s choice set. Another way
r
to think of this is to assume that the utility from goods outside of Jgt
is zero.
12
In most applications of logit models, a consumer can only buy discrete units (usually one unit) of
a good. However, I change this assumption in order to match the CES model, where consumers can
buy a continuous amount of a good.
13
variable
x is distributed logit if it has a cumulative distribution function of
i
hA random
x
exp − exp − µ + % where µ is the scale parameter and % is Euler’s constant (≈ 0.577). This is
often referred to as a “Type I Extreme Value” distribution.
12
Thus, each consumer has a series of independently and identically distributed (iid)
r
and one for each group g ∈ G.
random draws, one for each product j ∈ Jgt
This utility specification combines two common industrial organization methods for
dealing with the IIA problem. First, products are divided into groups, which allows the
substitution between goods in the same group to differ from that for goods in separate
groups. This method is known as nesting, as in the NCES model. Second, there are
some parameters (arjt , µr1 , and µr2 ) that vary according to a probability distribution
across consumers. As a result, aggregate substitution patterns depend on the mix
of substitution responses found in the population. This method is known as random
coefficients.
Each time period consumer i’s problem is to maximize current period utility subject
to a budget constraint. As with the NCES framework, this is an entirely static problem,
with no borrowing or saving. The budget constraint is given by pjt mrijt = y r where y r
is the consumer’s income. Substituting this constraint into the utility function gives an
indirect utility of
r
r
vijt
= ln(arjt ) − ln(pjt ) + ln(y r ) + ζigt
+ rijt .
(16)
As in the NCES model, the consumers’ problem can be tackled in steps, starting
with the demand for goods conditional on being within a certain product group. When
r
term drops out, reducing the choice problem to
focusing on one group, the ζigt
n
o
max ln(ar1t ) − ln(p1t ) + ri1t , . . . , ln(arJgtr t ) − ln(pJgtr t ) + riJgtr t ,
(17)
r
to refer to both the goods set and
where, in a slight abuse of notation, I have used Jgt
its cardinality. Integrating over the logit random shocks gives,
1
−1
r
µ
r
arjt µ2 pjt2
probrjt|g =
1
P
r
j∈Jgt
−1
r
,
µ
r
arjt µ2 pjt2
which is the conditional probability that any type r consumer will choose good j.14
Turning to the choice of which product group to buy from, the consumer chooses
14
This expression follows from the form of the logit distribution. Specifically, when given the
problem max{d1 + 1 , . . . , dJ + J }, the probability that option j will be the maximum is given by
PJ
exp(dj /µ)/ j=1 exp(dj /µ). Here the j are iid logit random variables with scale parameter µ.
13
the group with the maximum expected indirect utility,
max




µr2 ln 
X
1
−1
µr
2


r
r
arjt µ2 pjt  + ζi1t
, . . . , µr2 ln 
r
j∈J1t
X
1
−1
µr
2

r
r
arjt µ2 pjt  + ζiGt
r
j∈JGt


.
(18)

Again I have used G to refer both to the set and to its cardinality.15 Maximization
results in a group probability of
P
probrgt =
r
j∈Jgt
arjt
1
µr
2
g∈G
P
j∈Jtr
µµr2r
1
pjt
P
−1
µr
2
arjt
−1
µr
2
1
µr
2
µµr2r
pjt
.
1
I now derive the connection between this model and the CES-based frameworks.
This is an extension of the proof in Anderson et al. (1992), which shows the relationship
1
r
= 1−σ r , and µ1r = γ r −1. Then convert
between the CES and MNL. Let arjt µ2 = brjt , −1
µr2
1
probrjt|g and probrgt to (expected) expenditure shares by multiplying and dividing by the
consumer’s income. The resulting expenditure shares are
srjt|g
=P
brjt p1−σ
jt
r
and
P
r
j∈Jgt
srgt =
P
g∈G
(19)
r 1−σ r
r bjt pjt
j∈Jgt
1−σ r
brjt pjt
P
r
j∈Jgt
1−γ r
1−σ
r
1−σ r
brjt pjt
1−γ r .
1−σ
r
(20)
Multiplying these two shares gives
r
srjt = P
r
j∈Jgt
1−σ
brjt pjt
γ r −σrr P
P
1−σ r 1−σ
brjt pjt
g∈G
r
j∈Jgt
1−σ r
brjt pjt
1−γ r .
1−σ
r
(21)
Note that if all types of consumers have identical preferences, meaning that brjt = bjt ,
σ r = σ, and γ r = γ for all r, these formulas collapse down to those in the NCES model.
15
Expression (18) follows from the form of the expected maximum of a series of iid logit random
PJ
variables. That is, E[max{d1 + 1 , . . . , dJ + J }] = µ ln( j=1 exp(dj /µ)), where the j are iid logit
random variables with scale parameter µ.
14
In industrial organization terminology, this case is known as the NL model. Therefore,
the nested method is the same in both trade and industrial organization. If additionally
σ = γ, the model collapses to the basic MNL framework. In that case the expenditure
shares are identical to those in the CES model. Therefore, the difference between the
NCES and the NL or between the CES and the MNL is due to the empirical techniques
usually chosen to estimate them as opposed to differences in the underlying theory.
The market-level share is found by integrating srjt across the distribution of consumer
types. For example, if the distribution is discrete the share is then
sjt =
X
ftr srjt ,
(22)
r∈R
where ftr is the fraction of expenditure accounted for by type r consumers in time t,
and R is the set of all consumer types.16
3.2
Addressing the IIA Problem
The NRCL tackles the IIA problem in two ways. First, this model takes the nesting
approach just as in the NCES framework. Second, this model averages across the
heterogeneous preferences of different types of consumers. The latter method breaks
the IIA property between products in the same nest.
The effect of these two approaches can be seen in the cross-price elasticities, which
have the following form:




∂mjt pkt
=
∂pkt mjt 


1
sjt
P
r∈R
ftr [(γ r − 1)srjt srkt + (σ r − γ r )srjt srkt|g ]
if j and k are
in the same group
−
otherwise
(23)
r
r
for all j 6= k. One would expect σ > γ for all r ∈ R because the nests gather together
similar products. Therefore, just as in the NCES model, the (σ r − γ r ) term should
increase the cross-price elasticity between goods in the same groups.
1
sjt
r
r
r∈R ft (γ
P
1)srjt srkt
16
I focus on the discrete distribution case because this allows me to express the NRCL results as
weighted averages of the NL formulas. This makes the relationship between the NRCL and the other
models particularly transparent. The discrete specification is familiar in the marketing literature (see
Kamakura and Russell (1989) for example), while the specification using a normal distribution has been
popularized by Berry, Levinsohn, and Pakes (1995). The normal distribution does not give closed-form
expressions for market demand (because the gaussian integral must be computed numerically), which
makes it cumbersome for my purposes here.
15
The random coefficients have an added effect. If, for example, type a consumers
have high preferences for laser printers, and both goods j and k are laser printers,
the expenditure shares for type a consumers will be large. In turn, this will place
more weight on type a’s elasticities of substitution, γ a and σ a , in the aggregate crossprice elasticity. Similarly, those types that dislike goods j and k will tend to have less
influence on the cross-price elasticity because their expenditure shares are smaller.
3.3
The Price Index
Although the basic logic of the price index remains the same as in the NCES, in this
model one needs to integrate welfare across consumer types. In the case of a discrete
distribution for consumer types, this aggregation weights each type’s utility by their
share in expenditure in time t + 1. Then imagine taking away the set of goods available
to these consumers in period t + 1 and replacing it with the set from time t. The price
index is the factor by which the prices on the time t goods would have to fall to equalize
the weighted sum of indirect utilities.
The expected indirect utility for a consumer of type r can be calculated by finding
the expected maximum of the choice problem in equation (18). The condition for the
price index is then
1−γ r 
 1−σ
r
X  X r N RCL

1−σ r σ r −1 
bjt (τt+1 pjt )
ln 
y


r
X ft+1
γr − 1
r∈R

g∈G
r
j∈Jgt
1−γ r 
 1−σ
r
r
r

X  X r
1−σ σ −1 
ln 
bjt+1 pjt+1
y
.

=
r
X ft+1
γr − 1
r∈R

g∈G
r
j∈Jgt+1
Solving for the price index itself gives

P
N RCL
τt+1

g∈G
Y

=
 
P
r∈R 
P
g∈G
1−γ r
1−σ
r
r
r
ft+1
1
! 1−γ
r
1−σ
brjt+1 pjt+1
r
j∈Jgt+1
P
1−σ r
r
r bjt pjt
j∈Jgt
1
1−γ r 1−γ r
1−σ
r






.
(24)
Note that this expression is the geometric average of individual NL (or NCES) price
16
rN L
, for each type of consumer, where
indices, τt+1
P
g∈G
rN L
τt+1
=
P
brjt+1 pjt+1
r
j∈Jgt+1
P
1−σ r
g∈G
P
1−σ r
r
r bjt pjt
j∈Jgt
1−γ r
1−σ
r
1
! 1−γ
r
1
1−γ r 1−γ r
1−σ
r
.
(25)
rN L
In turn, as in the NCES model, each τt+1
is a geometric average of individual MNL
(or CES) price indices,
Y
r
rM N L ωgt+1
rN L
)
(26)
=
(τgt+1
τt+1
g∈G
where
1r
1−σ r 1−σ
r
b
p
r
jt+1 jt+1
j∈Jgt+1
1r
P
r 1−σ r 1−σ
r bjt pjt
j∈Jgt
P
rM N L
τgt+1
=
and
r
ωgt+1
3.4
(srgt+1 − srgt /(ln(srgt+1 ) − ln(srgt ))
.
=P
r
r
r
r
g∈G (sgt+1 − sgt )/(ln(sgt+1 ) − ln(sgt ))
Estimation
Given the strong theoretical similarities between the trade and industrial organization methods, much of the difference between these literatures stems from the use of
different empirical techniques. Industrial organization usually focuses on industries for
which detailed product-level data, including information on product characteristics, are
available. As a result, quality parameters for each product can be estimated and the
“common goods assumption” can be dispensed with.
Choose one good that appears in every time period to be the “outside good.” Assign
this product the zero index and assume that br0t = 1 for all consumer types and time
periods.17 This gives
r
p1−γ
0t
r
s0t =
P
1−γ rr .
P
r 1−σ r 1−σ
r bjt pjt
g∈G
j∈Jgt
Then take logs of this equation and subtract it from the log of srjt in equation (21).
17
This can be thought of as re-scaling the qualities of all other goods to be in units relative to the
quality of good 0.
17
After some minor algebraic manipulations following Berry (1994), this results in
ln(srjt ) − ln(sr0t ) =
γr − 1
σr − γ r
r
r
)
−
(γ
−
1)[ln(p
)
−
ln(p
)]
+
ln(b
ln(srjt|g ). (27)
jt
0t
jt
σr − 1
σr − 1
This equation is the basis for estimating the model.
Standard product-level data sets will report expenditure shares and prices. The
only question is how to capture quality in equation (27). This is where product characteristics information is useful. In industries commonly studied in empirical industrial
organization, such as automobiles and electronics, product characteristics are a reasonable proxy for quality. In the case of printers, characteristics such as print speed,
color capability, or paper capacity are easily observed and closely related to quality.
Therefore, the standard practice has been to use data on such features to parameterize
quality in the demand model.
Collect the characteristics for each printer j in a vector denoted by xjt . Then assume
the following:
γr − 1
ln(brjt ) = (xjt − x0t )β r + erjt .
(28)
σr − 1
The β r is a vector of parameters to be estimated and erjt is an error term that allows
for quality unobserved by the econometrician. This gives
ln(srjt ) − ln(sr0t ) = (xjt − x0t )β r − (γ r − 1)[ln(pjt ) − ln(p0t )] +
σr − γ r
ln(srjt|g ) + erjt . (29)
r
σ −1
Equation (29) is an estimating equation that can be run on product-level purchase data
that is categorized by consumer types. Once the parameters have been estimated for
each consumer type, one can calculate the price index by plugging directly into equation
(24), bypassing the common goods assumption entirely. Note that if β r = β, γ r = γ,
and σ r = σ for all r ∈ R, this equation then reduces to the NL model. If in addition
the ln(srjt|g ) term is dropped, this equation then reduces to the MNL model.
Estimation of equation (29) could proceed by ordinary least squares, but this is not
the usual practice. One would expect the coefficient on price to have a positive bias
(making it smaller in absolute value) because printer vendors will tend to set higher
prices for models that have high unobserved quality. In addition, it is likely that ln(sjt|g )
is endogenous, as increased unobserved quality can drive higher within group sales. This
would also induce a positive bias on the ln(sjt|g ) coefficient. Therefore, instruments are
18
found for both the log price and the log share variables.18
One could take a different approach if data broken up by consumer type is unavailable. That is, one could specify a distribution for consumer types, be it discrete
or continuous, and estimate its parameters by matching the market-level expenditure
shares (as in equation (22)) with those observed in the data. Because I have access
to data by consumer type for the computer printers example, I have elected to avoid
wading into these econometric intricacies.19 Introducing this level of complexity into
the model would make the estimation routine less transparent and hamper comparisons
between the NRCL and other logit models.20
3.5
Price Index Decompositions
Another advantage of the product-level estimation approach is that it allows for the
decomposition of changes in the price index into their price, quality, and variety components. That is, here one can step beyond the “common goods” and “changing goods”
breakdown by incorporating the estimated qualities into the Feenstra (1994) methodology. The resulting decomposition is useful in exploring the mechanisms at work behind
movements in the overall price index.
Imagine that there are Jgr goods in consumer type r’s group g choice set in period
t. Order these goods by some metric such as increasing quality, and then assign each
an index 1, . . . , Jgr .21 Next choose a size Jgr group of goods from time period t + 1 that
is representative of the t + 1 distribution of price and quality.22 Order these goods
similarly, and again assign each an index 1, . . . , Jgr .23 Because this set is scaled to be of
size Jgr , it captures the price and quality distribution present in t + 1 but holds variety
18
Treating other product characteristics besides price as endogenous is much less common because
finding an instrument that is uncorrelated with unobserved quality but correlated with observed quality
is difficult.
19
For certain distributions, this procedure can be computationally intensive. In the case of the
normal distribution, integrating up to the market-level shares has to be done numerically, and then
the parameters have to be fitted using a non-linear search. See Knittel and Metaxoglou (2008) and
Dubé et al. (2009) for discussions on the challenges involved in this type of estimation.
20
Readers who are interested in these other estimation methods should consult Berry, Levinsohn,
and Pakes (1995), Nevo (2000), and Train (2009).
21
In theory, the ordering of these goods does not matter, so long as one keeps track of which price
and quality goes with which good. However, the resulting decomposition can be sensitive to which
goods are matched in periods t and t + 1, so it is best to establish a consistent procedure.
22
I discuss one method for choosing such a set in Section 4.
23
This procedure assumes that there are at least as many products available in time t + 1 as in t.
Otherwise, the size of the set Jgr would be defined as the number of goods in time t + 1 and the price
r
r
index would be interpreted as measuring the change relative to the set Jgt+1
instead of relative to Jgt
.
19
constant at the period t level. Repeat this process for each g ∈ G and r ∈ R.
Then the price index decomposition is

N RCL
=
τt+1

Y Y


r∈R
g∈G
Jgr
Y
j=1
pjt+1
pjt
Jgr r
ωjgt+1
Y
j=1
r
brjt
ωjgt+1
σ−1
brjt+1
Jgr
λt+1
Jr
λt g
r
1 ωgt+1
! σ−1
r
ft+1



.
(30)
where
Jr
λt g
PJgr
r
j=1 pjt mjt
,
=P
r
r pjt mjt
j∈Jgt
(srjt+1 (Jgr ) − srjt (Jgr ))/(ln(srjt+1 (Jgr )) − ln(srjt (Jgr )))
r
.
= PJ r
ωjgt+1
g
r
r ) − sr (J r ))/(ln(sr
r )) − ln(sr (J r )))
(s
(J
(J
j=1 jt+1 g
jt g
jt+1 g
jt g
and
r
ωgt+1
=P
(srgt+1 − srgt /(ln(srgt+1 ) − ln(srgt ))
.
r
r
r
r
g∈G (sgt+1 − sgt )/(ln(sgt+1 ) − ln(sgt ))
Here srjt (Jgr ) is the share of expenditure by type r consumers accounted for by good
j out of the goods indexed by 1, . . . , Jgr . Equation (30) has three components. The
first part is a geometric average of price ratios, pjt+1 /pjt , which captures the changes
in price in the set {1, . . . , Jgr }. The second part is a geometric average of quality ratios,
brjt /brjt+1 , which captures changes in quality in the set {1, . . . , Jgr }. The third part is an
expenditure share adjustment, which reflects how much expenditure has shifted to the
greater number of goods that are available outside of the set {1, . . . , Jgr }. This term
captures variety.
It is important to note how this full decomposition compares with the MNL and NL
special cases. In the case of the NL model,
NL
τt+1
=
Y
g∈G
ω
Jg Y
pjt+1 jgt+1
j=1
!ωgt+1
Y
pjt
g∈G
Jg Y
bjt
bjt+1
j=1
ωjgt+1
σ−1
!ωgt+1
Y
g∈G
Jg
λt+1
J
λt g
gt+1
! ωσ−1
.
(31)
where
J
λt g
and
PJg
j=1 pjt mjt
=P
j∈Jgt pjt mjt
(sjt+1 (Jg ) − sjt (Jg ))/(ln(sjt+1 (Jg )) − ln(sjt (Jg )))
ωjgt+1 = PJg
.
(s
(J
)
−
s
(J
))/(ln(s
(J
))
−
ln(s
(J
)))
jt+1
g
jt
g
jt+1
g
jt
g
j=1
Note that sjt (Jg ) is the share of expenditure accounted for by good j amongst expen20
diture on the goods 1, . . . , Jg . In the case of the MNL model,
MNL
τt+1
ω
J J Y
pjt+1 jt+1 Y bjt
=
pjt
bjt+1
j=1
j=1
ωjt+1
γ−1
λJt+1
λJt
1
γ−1
(32)
where
λJt
PJ
j=1 pjt mjt
=P
j∈Jt pjt mjt
(sjt+1 (J) − sjt (J))/(ln(sjt+1 (J)) − ln(sjt (J)))
and ωjt+1 = PJ
.
j=1 (sjt+1 (J) − sjt (J))/(ln(sjt+1 (J)) − ln(sjt (J)))
Here sjt (J) denotes the expenditure share of good j out of the goods 1, . . . , J, in time
t.
The comparison between the NL decomposition and the MNL analog is similar
to the comparison between the CES and NCES decompositions. The price, quality,
and variety terms are calculated first within each group instead of immediately across
all products. This reflects the fact that according to the NL model, changes in all
three forces should have the strongest effect amongst goods that are in the same nest.
Furthermore, the NL uses σ instead of γ in the variety term. Since we expect that
σ > γ, this will tend to lower the variety term relative to that in the MNL.24
In moving from the NL to the NRCL, the random coefficients mean that there are
multiple consumer types that must be averaged over. Therefore the NRCL index allows
the effects of a change in price, quality, or variety to be asymmetric across consumers.
Whether this index is larger or smaller than the NL one depends on how the preferences
of individual consumer types compare to the average preferences of all consumers. The
NRCL may pick up gains (or losses) to minority groups of consumers that wash out in
the market-level data.
4
Empirical Example: Computer Printers
Given the similarities and differences between the models discussed above, it is important to see how they compare in practice. To this end, I apply these methods to the
Indian import market for computer printers over the period 1996 to 2005.
24
The quality term also includes σ, but this difference actually does not have an effect on the
relationship between the NL and MNL indices. This is because the definition of bjt in the estimation
equation causes the σ to cancel out.
21
4.1
Market Background
The information technology sector is one of the fastest growing import markets in India.
The quantity imported of computers and associated peripherals as classified in HS 8471
increased from 0.48 percent of the value of imports in 1996 to 1.40 percent in 2005.
Growth was extraordinarily strong in computer peripherals, HS 847160, rising from
0.08 percent of value in 1996 to 0.32 percent in 2005, a roughly 4 times increase in
share.25
Some of this growth has been spurred on by a liberalization of India’s import policies.
In 1997, India signed the WTO’s Information Technology Agreement. By doing so,
India agreed to lower tariffs on printers from 20 percent ad valorem to 0 percent by
2005. This goal was successfully achieved in the middle of 2005.
There are few local printer producers in India, and those firms that do operate almost
exclusively make dot matrix machines. The Department of Scientific and Industrial
Research, a government agency tasked with promoting technology development in India,
released a report in 1996 on the state of the Indian printer sector. They concluded that
India was unlikely to expand into laser printer manufacturing, even with the help of
foreign direct investment (DSIR (1996)). The report pointed to small local demand
and a poor technology infrastructure as major hurdles. This situation has only slightly
improved today. The firm WeP Peripherals announced the first Indian laser printer
factory in 2003, but their line remains small. No other Indian firm has established a
plant.
Instead of sourcing printers locally, most of the market is served by imports from a
number of multinational brands (such as Canon, Epson, HP, or Xerox). These foreign
companies prefer to do their manufacturing in China and Southeast Asia and then ship
into India. I do not know of any multinational brand or electronics outsourcing firm
which has a printer manufacturing facility in India.26 India, although a growing market,
is still too small to warrant major horizontal foreign direct investment.
Therefore, the Indian computer printer sector is a dynamic differentiated products
market that has seen a lot of growth fueled by imports. This makes it an ideal candidate
in which to study the effects on consumers of changes in differentiated goods.
25
These numbers are computed using the UN Comtrade database.
HP has had plants in India since the late 1990s, but they mostly produce computers. Xerox has a
facility in Rampur, but it makes single-function copiers. There are some plants that make components.
26
22
4.2
Data Description
My data is based upon an extract from the IDC Hardcopy Peripherals Database (IDC
(2008)). This data set tracks sales of individual printer models, listing their name,
quantity sold, and average price for every quarter from the beginning of 1996 to the
second quarter of 2006.27 Average price includes the purchase price and shipping costs,
but not taxes. I have converted these prices into real figures using the Indian consumer
price index.28 Only new sales are reported, not sales of used or refurbished models.
IDC, a market research firm that focuses on technology products, collects this information from retailers, distributors, and online vendors. They claim to track all models
of A2 through A4 size laser and inkjet printers.29 Some observations aggregate a base
configuration and other optional configurations into one model. However, this is not
a major occurrence amongst the machines offered in India because they are mostly
low-end models with few extra options.
I define a printer as a device that can print output from a computer, excluding
portable machines meant for travel. I focus on two technologies: inkjet and laser. These
machines may perform other functions, such as copying or scanning (“multi-function
peripherals” or MFPs). I exclude printers that use impact technologies, which are based
on older typewriter-like designs.30 The IDC data has limited coverage of impact models
and does not report purchases of these categorized by consumer types for most of the
models that are included. Furthermore, I am not able to collect characteristics data for
all of these printers because many were sold by small local firms that do not have their
back catalogs available in print or online. Regardless, laser and inkjet models account
for the vast majority of sales, particularly amongst imported models.31 It is also in
the laser and inkjet categories where most of the improvements in terms of quality and
variety have appeared, as impact is a dying technology. Note also that I limit my data
to non-Indian brands.
27
I also have data through the first quarter of 2008, but these observations have to be dropped
because there is no product that appears in all of these years to serve as the outside good in the logit
models.
28
The CPI is from http://labourbureau.nic.in/ and was downloaded in October 2009.
29
IDC does aggregate some models into an “other” category, but this never accounts for more than
2.4 percent of sales revenues in any quarter. I discard this category because it is not clear exactly
how it is constructed. Prior to 2001, MFPs are not recorded in the database. However, when MFP
tracking begins in 2001 Q1, these machines only comprise 4.5 percent of sales revenue, so it is unlikely
that they formed a large part of the market in the prior period.
30
The main impact technology is dot matrix.
31
When the Indian customs authority began reporting printer import quantities by inkjet and laser
versus dot matrix in the spring of 2003, inkjet and laser accounted for over 90 percent.
23
Importantly for my purposes, IDC also separates the units sold of each inkjet and
laser model into those purchased by different subsets of consumers. These divisions
are home office, 1 to 9 employee establishments, 10 to 99 employee establishments,
100 to 499 employee establishments, and 500 or more employee establishments. Note
that home office buyers may include family businesses. In order to form the set R
of consumer types for the NRCL model, I aggregate this data into two categories:
home office or 1 to 9 employee establishments (which I call “small” consumers) and
10 or more employee establishments (which I call “large” consumers). I choose to
use only two consumer types in order to keep the comparisons between the random
and non-random coefficients specifications simple. One would expect that this group
of home office and small firms would exhibit distinct buying patterns relative to the
average behavior in the data. Although larger establishments would consider using a
department-sized laser printer, for example, most small buyers would not because of
the set-up costs, technological expertise, and physical space required. Those costs are
not justified for a small establishment that will not print high volumes.
In order to accurately measure the quality of these printers, I need to know something about their characteristics. IDC provides some basic information, categorizing
models into different bins based on technology (laser, inkjet), function (single, MFP),
color versus monotone printing, and page per minute (PPM) speed (1-10 PPM, 11-20
PPM, etc.). In order to enrich my analysis, I supplement this data with characteristics
collected from manufacturer’s websites and from printer specification sheets published
by the firm Buyers Laboratory.32
I can not find data for all the models reported in the IDC dataset, meaning that
some observations are dropped. After these exclusions, I am left with data for about
96 percent of sales revenue and 97 percent of laser and inkjet units sold in the original
IDC data set. This data cover 1198 unique models. Summary statistics are presented
in Table 1.
There is an important omitted variable from the characteristics listed in Table 1. In
particular, I do not have information on the maintenance costs of each printer model.
These are largely due to printer cartridges (though they also include other factors
like paper and electricity). However, upon examining the industry literature, I have
32
If one or two characteristics for a model can not be found, they are imputed from similar models
of the same brand, or, if those are not available, from similar models across all brands in a given
quarter. This affects 10 percent of observations in the final sample. I convert printing speeds listed in
characters per second to PPM by assuming a rate of 4000 characters per page.
24
found that few estimates of these costs are available. The statistics that do exist
indicate that running costs vary strongly with the technology of the printer (laser or
inkjet) and with whether or not the machine prints in color. Therefore, in estimating
the demand models, I use dummies for these characteristics to proxy for this omitted
variable. Unfortunately, this means that I cannot separately identify tastes for these
technologies from preferences for their maintenance costs.33
I supplement this printer data with information on Indian printer tariffs and exchange rates. Tariff data covering 1996 to 2001 are from Khandelwal and Topalova
(2010) for HS category 847160. I extend this data to 2006 using announcements of
changes to the tariff schedule published by the Indian Central Board of Excise and
Customs.34 I obtain information on the quarterly exchange rate between India and
the US, Japan, South Korean, China, and the European Union from Global Financial
Data.
4.3
Identification
In order to estimate the logit-based models, I need instruments for the log price and
log group share variables. When faced with this situation, industrial organization researchers often struggle to find plausibly exogenous instruments that exhibit enough
time-series and cross-sectional variation to be useful. In my empirical application, I can
leverage the international trade aspect of my data to solve this problem.
As discussed above, the vast majority of sales in the Indian printer market (and all
sales in my data) are accounted for by foreign brands. These brands’ parent companies
are located in the US (such as Xerox and HP), Japan (such as Canon and Ricoh), South
Korea (Samsung), China (Lenovo), and the European Union (Océ). Therefore, any revenues these corporations make by selling printers in India must ultimately be converted
from Indian rupees into their home currency in order to become part of their bottom
lines. As such, the exchange rate between their home currency and the Indian rupee
should affect the prices that are set and in turn affect expenditure shares. However,
given that the buyers of printers in this market are largely small Indian firms that only
33
A related concern is that upfront printer prices may be uninformative if printer vendors are pursuing a strategy of lowering the prices of printers in order to make money on printer cartridges. Although
such a strategy has been used in the US, it is much less prevalent in India because of the high penetration of third party and counterfeit cartridges. IDC estimates that over 50 percent of the cartridges
sold in India are made by third parties.
34
These announcements are available at http://www.cbec.gov.in/ and were accessed in July 2010.
25
operate domestically, the exchange rate should not affect demand independently.35
Thus, I use these exchange rates to build two instrumental variables. First, I take
the exchange rate for the headquarters currency of each brand. Second, I form the
average exchange rate of each model’s rival products in the same IDC product type.36
For example, imagine that there are three models in a certain category, one from Japan
and two from the US. Then the instrument for the Japanese model would be the US
exchange rate, while the instrument for each of the US models would be the average of
the US exchange rate and the Japanese exchange rate. This second instrument helps
me capture the variation in pricing competition across types of printers.
I also construct a third instrumental variable based on tariffs. As mentioned above,
India pursued a dramatic liberalization in the computer printer sector over the time
period I study, zeroing out most printer tariffs. This fall in taxes was mandated by a
WTO agreement covering a number of information technology products, and hence is
probably unrelated to unobservables in printer demand. Furthermore, tariffs are likely
to be correlated with printer prices and in turn with within group expenditure shares,
while not entering into demand separate from their effect on price.
4.4
Overview of Results
I begin by discussing how I estimate the logit-based models. Recall that I have three
logit variants: the MNL, the NL, and the NRCL. In the interest of simplicity, I choose
to define just two product groups in the nested models, one for inkjet and the other for
laser.
The estimating equations for all three models are combined in equation (29). Simply drop the consumer type distinction in order to reduce the NRCL to the NL and
further drop the log group share term in order to reduce the NL to the MNL model.
Because there are two types of consumers in the NRCL model, I have three equations to
estimate: one equation without consumer types, one equation for small consumers, and
one equation for large consumers. I merge all of these equations into one by stacking
35
There are some drawbacks to this approach. Most prices for printers are probably set initially in
Indian rupees, not set in foreign currencies and converted. If there are menu costs, this may mean that
prices are sticky in Indian rupees and hence less sensitive to exchange rate movements. In addition,
the exchange rate may be affected by domestic policy controls or general equilibrium effects that are in
turn related to local demand factors. Nevertheless, the exchange rate is one of the few variables that
exhibits strong variation across time periods while also having a reasonable probability of satisfying
the exogeneity requirement.
36
See the first column of Table 2 for a list of these categories.
26
the observations for all three and interacting the independent variables with a constant
and with dummies for whether an observation is for small buyers and for whether an
observation is for large buyers. I estimate this equation using both least squares and
instrumental variables methods.
I need to difference the data with respect to one printer model, the outside good.
The natural choice is a dot matrix printer, since that is the most common alternative
to the laser and inkjet models included in my main dataset. As previously mentioned, I
only have data on selected dot matrix models, but there is one candidate that appears
in all the years from 1996 to 2005, the Panasonic KX-P1150. This is the product that
I take as my outside good.37
The parameter estimates appear in Table 3. Although I estimate all the models
stacked into one equation, I separate the results into their three component equations
(MNL/NL, NRCL small, and NRCL large) to make the numbers easier to interpret.
In all regressions, instrumenting appears to remove a positive bias on the log price
and log group share coefficients. The price estimate becomes more negative and the
share coefficient becomes less positive. This result accords with the hypothesis that
the log price and the log share variables are positively correlated with unobserved
quality. Note also that instrumenting tends to raise the resulting estimates of σ and
γ, the elasticities of substitution. The first-stage F statistics are all above 50, and the
overidentification test statistics are not significant at conventional levels for any of the
models.38 In what follows, I use the IV results as my preferred specification.
The coefficients indicate that nearly all characteristics increase quality relative to
that for the Panasonic KX-P1150, which has relatively low characteristics. The only
exceptions is resolution, which may result from the fact that a unless they print photos
regularly, many buyers have little use for ultra-high resolution machines. The latter
point reveals a potential heterogeneity between consumer types that I return to in
discussing random coefficients.
The coefficient on the log group share is always highly significant, indicating that
a nested model is appropriate for this data set. This result is to be expected, because
37
I do not have consumer-level data for this model, so I assume that 5 percent of reported sales
are made up of small consumers. This estimate is based on IDC sales data for two other dot matrix
models sold from 1998 to 2003.
38
I use both the homoskedastic and heteroskedasticity robust overidentification tests suggested by
Wooldridge (2002). These F test and overidentification test results hold regardless of whether the three
equations (no consumer types, small consumers, and large consumers) are estimated stacked together
or separately.
27
there is a natural dichotomy in printers between laser and inkjet models.
As for the random coefficients, F tests on the interactions between dummies for
consumer type and the independent variables indicate that these are jointly significant.
Therefore, the NRCL model is the best fit. Focusing on individual coefficients, I find
that small consumers’ coefficients on the color dummy, laser dummy, and network
interface dummy are significantly lower and the coefficient on resolution is significantly
higher compared to those in the non-random coefficient models. Meanwhile, the large
consumers’ coefficient on resolution is significantly lower and the coefficient on the laser
dummy is significantly higher.39 These results indicate that there is some variation in
preferences that the MNL and NL models mask.
A selection of own- and cross-price elasticities appear in Table 4. Each entry is
the percentage change in quantity sold of the row good in response to a percentage
change in price of the column good. In the top panel, which contains the results for the
MNL model, I find that the cross-price elasticity is identical down each column, which
occurs because of the IIA property. Once I shift to the NL model, these elasticities vary
depending on which group (inkjet or laser) the row good is in. Models that are in the
same group as the column good have much larger elasticities compared to those that
are in different groups. Finally, the NRCL elasticities also vary within groups, due to
the random coefficients.
The results for the 1996 versus 2005 price indices are presented in Table 5. These
annual figures average over the results for the first quarter of 1996 versus the first
quarter of 2005, the second quarter of 1996 versus the second quarter of 2005, and so on.
Following Broda and Weinstein (2006), I construct bootstrapped 95 percent confidence
intervals by sampling 100 times from the estimated joint normal distribution of the
regression parameters in Table 3 and calculating the price index for each sample.
In order to facilitate comparisons between the CES-based and logit-based models,
I set the elasticities of substitution in the CES and NCES calculations to the numbers
estimated for the NL and MNL models (Table 3, second column). Remember that
these parameters are the only ones needed in the CES and NCES calculations. The
other input is the aggregated price and expenditure share data. I form this data by
taking the share-weighted average price and the total expenditure for each product
category/country combination reported in Table 2.
In interpreting the numbers in Table 5, note that the index is calculated between
39
These results are based on separate 5 percent t tests for each coefficient.
28
1996 and 2005. Therefore, the index is the factor by which one would have to multiply
the prices of all goods in 1996 in order to give the same welfare as the goods available in
2005. For instance, the 0.061 CES index means that 1996 prices would have to fall by
93.9 percent in order to make consumers as well off as in 2005. All five indices estimate
dramatic falls in the 1996 prices, ranging from about 84 percent to 96 percent. However,
there are some subtle differences. The aggregated indices tend to be higher than their
logit counterparts (compare the CES and MNL or the NCES and NL). Nesting tends to
raise the index (compare the CES and NCES or the MNL and NL). Including random
coefficients appears to slightly lower the index (compare the NL and NRCL).
Figure 1 shows how the 1996 versus 2005 price index developed over the intervening
years. For each year from 1997 to 2005, I calculate the price index with respect to
1996, thus showing how much of the 1996 to 2005 change had occurred by that year.
Broadly speaking, all of the indices for the five models move together. The descent in
the indices over the years is reasonably smooth, except for a large drop between 1997
and 1998. This occurs because 1997 was a year where the price indices exhibited losses
(particularly in the second quarter) when some firms withdrew products.
The decompositions into common and changing goods effects (for the CES models)
or price, quality, and variety effects (for the logit models) appear in Table 6.40 In
constructing the logit-based decompositions, I need to choose a subset of goods from
the 2005 set of products available that is the same size as the set available in 1996.
Keeping with the spirit of the price, quality, and variety breakdown, I build a subset
that approximates the joint distribution of price and quality available in 2005, but
scales it to have the same variety (number of products) as in 1996. In this way, the
price and quality terms in the decomposition will give a good approximation of the
relative changes in price and quality between 1996 and 2005.
For example, suppose that there are X products available in 1996 and Y > X
products available in 2005. I split the 2005 ranges of price and quality into 5 different
percentile bands, giving 25 price/quality bins. I then randomly choose models at a rate
of X/Y from each bin. This procedure gives me a set of 2005 goods that is the same
size as the set of 1996 goods, and then I calculate the decomposition using these sets.
In order to ensure that my findings are not driven by a particular sample, I repeat this
procedure 100 times for different samples, and average across the resulting terms to get
my final numbers.
40
The common goods effects do not have confidence intervals because those terms do not use estimated parameters. They are constructed using only average price data.
29
In comparing the CES and NCES decompositions, the largest difference comes in
the changing goods term, which rises noticeably in the NCES case. As for the logit
decompositions, the price and quality terms are broadly similar across models, while
the variety term rises markedly in the NL and NRCL models. These differences hint at
the importance of the nested elasticity of substitution, σ.
Therefore, an initial scan of the results suggests some important differences between
the five price indices. I discuss these trends in more detail in the following sections.
4.5
Disaggregated Data: CES/NCES vs. MNL/NL
I begin by examining the effect that using product-level data has on the resulting price
indices by comparing the CES with the MNL and the NCES with the NL. Because the
price index formulas in these models are identical, any actual differences in the results
are due entirely to divergent empirical techniques. I find that the CES and NCES
methods cannot distinguish developments within product categories because of these
models’ reliance on aggregated data. As a consequence, the CES and NCES indices
tend to understate gains (or losses) from changes in products.
This pattern is already somewhat apparent in Figure 1. The CES-based indices
fall steadily while the logit indices bounce around. This difference occurs because the
product-level data allow the logit indices to capture subtle changes in the products
offered that the aggregated data miss.
On net, the MNL and NL indices find a larger gain over 1996 to 2005 when compared
to the CES and NCES indices, respectively. This distinction is statistically significant,
as bootstrapped 95 percent confidence intervals for the difference between the 1996/2005
MNL and CES indices and the 1996/2005 NL and NCES indices do not include zero.41
In terms of economic significance, the MNL index is about 42 percent lower than the
CES index, and the NL index is about 31 percent lower than the NCES index. This result is similar to that in Blonigen and Soderbery (2010), who find that using aggregated
trade data understates the improvements in the price index from increased variety in
the US automobile market.
Thus, it appears that using aggregated data tends to understate improvements in
the price index. One way to explore this point is to take a closer look at the common
41
In order to build these confidence intervals, I sample from the estimated asymptotic distribution
of the regression parameters in Table 3 to form 100 simulated parameter sets. Then I calculate the
indices for each sample and take the difference between the MNL and CES indices and the NL and
NCES indices.
30
goods terms. These terms are the price indices calculated using only goods categories
that appear in both time periods. By assumption, these categories are supposed to have
constant quality and variety. However, because printer firms are constantly tweaking
their offerings, this assumption is unlikely to hold. I can assess the effect this has on
the common goods term by calculating the price index for the common goods using
the product-level data underlying these categories. That is, I apply equation (11)
and equation (10) to the individual printer models that are within the common goods
categories.
I graph the resulting “common goods terms” in Figures 2 and 3. The terms constructed using product-level data are lower than those using aggregated data in all years
except 1997. Hence, the product-level data reveal that there were significant increases
in quality and variety (or decreases in the second quarter of 1997) within the common
goods. By assuming these changes away, the standard CES and NCES indices have
missed these movements in the price index.
4.6
Nesting Products: CES/MNL vs. NCES/NL
Another important point of comparison is between the nested and non-nested models.
Nesting allows the elasticity of substitution to be larger within groups (where goods
tend to be more similar) than between groups. As a result, I find that improvements
in the price index tend to be dampened in the nested frameworks.
Comparing the overall 1996/2005 indices in Table 5, the CES is about 62 percent
lower than the NCES and the MNL is about 68 percent lower than the NL. Based on
bootstrapped 95 percent confidence intervals, these differences are statistically significant.
Nesting also has a noticable effect on the price index decompositions in Table 6. As
the elasticity of substitution within groups rises between the CES and NCES models, the
changing goods term becomes larger. Indeed, the CES term is about 44 percent lower
than the NCES one, and the bootstrapped 95 percent confidence interval indicates that
the difference is statistically significant. This reflects the fact that new and disappearing
goods have a smaller effect on utility when they are more substitutable with some
existing common goods.
Similarly, the variety terms in Table 6 also rise when nesting is implemented. The
MNL variety term is about 67 percent lower than that for the NL. The bootstrapped
31
95 percent confidence interval indicates that this difference is significant.42 The change
occurs because increasing variety has less of an effect on utility when the elasticity of
substitution between some goods increases due to nesting. Therefore, it is the variety
channel that is most affected by nesting.
Some of the most dramatic results from nesting appear in the cross-price elasticities.
As Table 4 shows, the NL cross-price elasticities between printers in the same product
group are on the order of 10 times larger than those in different groups. Meanwhile
the elasticities are exactly constant across printers in the MNL case. As a result,
improvements in the printers available are not as highly valued in the NL model, since
this framework recognizes that there are some good substitutes already on the market.
4.7
Random Coefficients: NL vs. NRCL
The final comparison is between the NL and the NRCL, which highlights the effect of
random coefficients. These coefficients allow the model to better reflect the spread of
tastes across consumers, which can be obscured in market-level data. Here I find that
small consumers experience larger gains than average due to improvements in printers.
Although the overall NRCL index is similar to the NL, this similarity masks heterogeneity between consumer types. See Figure 4, which graphs the indices for small and
large types (according to equation (25)) alongside the overall NRCL and NL indices.
The price index for small consumers is always lower than that for large consumers. However, large consumers account for about 80 percent of expenditures. As a result, the
NL model tracks the large index more closely, whereas the NRCL is pulled downwards
because it incorporates small buyer preferences.
In turn, the NRCL price index for 1996 versus 2005 is lower than the NL index,
although the effect is statistically insignificant. The statistically significant distinction
comes in examining the price index for small buyers, which is 53 percent lower than the
NL index. The NL only distinguishes average sales patterns, so it does not recognize
that certain new goods may have a greater effect on some buyers compared to others.
In this case the NL is influenced mainly by the behavior of large consumers and fails
to pick up improvements for small consumers. This difference has a small effect on the
overall price indices, but it is important when assessing the distributional consequences
of improvements in differentiated products.
42
The differences across these models for the price and quality terms are also significant, though
they are much smaller in economic terms.
32
When compared to the results from disaggregating data and nesting products, the
effects of introducing heterogeneity in preference coefficients are less pronounced in the
market-level index. This is related to the nature of the computer printer example,
where products clearly vary a great deal at the model level and where there is an
obvious nesting structure (inkjet versus laser). Heterogeneity in coefficients is a lessobvious concern. Indeed, Table 4 shows that nesting plays a far more important role
in addressing the IIA problem and as a result has the most dramatic effect on the
price indices. That being said, I do find that using random coefficients allows the
resulting price indices to better reflect the preferences of minority consumer types.
An NRCL specification with a richer distribution of consumer preferences (such as a
normal) may produce even more realistic results, although these would come at a higher
computational cost.
5
Conclusion
Although the approaches that international trade and industrial organization take with
regards to differentiated products appear quite different, I find that the underlying
theories are actually closely related. The CES and the MNL models yield the same
demand system and price index, and this fact greatly facilities the comparison between
a number of common variations on these frameworks. In effect, the NCES, NL, and
NRCL are all just ways of addressing the IIA problem. The only differences come in
how these models are used empirically (using aggregated versus product-level data) and
in how they tackle IIA (using nesting versus using random coefficients).
In the computer printers empirical application, I find that aggregated data methods understate the gains from differentiated products in the price index. This occurs
because these data mask product-level improvements in the goods available on the
market. Meanwhile, non-nested models exaggerate improvements in the price index because these frameworks underestimate the substitutability between products. Finally,
incorporating random coefficients improves the model’s ability to match the spread of
preferences in the population.
Although these results apply to this one empirical example, they also highlight two
general lessons that apply to all studies on the effects of changes in differentiated products. First, it is the nature of aggregated data to obscure some movements in quality
and variety at the underlying product level. This caveat must be kept in mind when
33
using the common goods assumption to calculate price indices. Second, the CES and
MNL models fall prey to the IIA problem, which greatly limits the substitution structure between goods and can distort the gains from differentiated products. It is the
constant search for ways in which to alleviate this problem that has produced innovations in demand modeling, such as nesting products and using random coefficients. One
should be sure to choose a flexible option, given the strictures imposed by the current
research question and the data available.
An interesting avenue for future research would be to examine the ramifications
of other demand models on the price index. Several authors have proposed different
frameworks in order to address issues with the CES and MNL beyond just IIA. Feenstra (2009), for example, suggests using a translog specification in order to avoid the
constant markups that obtain in the CES under monopolistic competition. Ackerberg
and Rysman (2005) modify the MNL in order to address the overvaluing of variety
caused by each good having its own logit shock. Gowrisankaran and Rysman (2009)
extend the random coefficients logit so as to deal with durable goods. Exploring advancements such as these would complement the findings in this paper and provide
further insight into the manner in which both trade and industrial organization should
approach differentiated products.
34
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37
Figure 1: All Price Indices, 1996-2005
Notes: These indices are calculated at the quarterly level (comparing the first quarter of 2005 to the first quarter of
1996, for example), and then averaged over all four quarters. The index for each year takes 1996 as the base year.
38
Figure 2: CES Common Goods Terms, 1996-2005
Notes: These indices are calculated at the quarterly level (comparing the first quarter of 2005 to the first quarter of
1996, for example), and then averaged over all four quarters. The index for each year takes 1996 as the base year.
Figure 3: NCES Common Goods Terms, 1996-2005
Notes: These indices are calculated at the quarterly level (comparing the first quarter of 2005 to the first quarter of
1996, for example), and then averaged over all four quarters. The index for each year takes 1996 as the base year.
39
Figure 4: NL and NRCL Indices, 1996-2005
Notes: These indices are calculated at the quarterly level (comparing the first quarter of 2005 to the first quarter of
1996, for example), and then averaged over all four quarters. The index for each year takes 1996 as the base year.
40
Table 1: Summary Statistics
Variable
Price (USD)
Units Sold
Color Dummy
BW PPM Speed
RAM (MB)
Resolution (DPI)
A3 Capable Dummy
Footprint (in2 )
Ethernet Interface Dummy
MFP Dummy
Laser Dummy
Number of Model-Quarters
Number of Unique Models
Mean
604.996
1059.538
0.468
20.806
49.764
1336.798
0.355
416.175
0.343
0.356
0.663
6413
1189
Standard Deviation
1084.060
4763.041
0.499
13.430
98.272
771.611
0.478
381.911
0.475
0.479
0.473
Notes: Data sources are in the text, Section 4. Price is in real 2001 Indian
Rs, then converted to USD at 1 Rs=47.12 USD. “BW PPM Speed” is the
maximum number of pages per minute that can be printed in black and white.
41
Table 2: Product Categories
Product Type
MFP Color Inkjet 1-10 PPM
MFP Color Inkjet 11-20 PPM
MFP Color Inkjet 21 PPM or more
MFP Color Laser 1-10 PPM
MFP Color Laser 11-20 PPM
MFP Color Laser 21-30 PPM
MFP Color Laser 31-44 PPM
MFP Mono Inkjet All Speeds
MFP Mono Laser 1-20 PPM
MFP Mono Laser 21-30 PPM
MFP Mono Laser 31-44 PPM
MFP Mono Laser 45-69 PPM
MFP Mono Laser 70-90 PPM
Printer Color Inkjet 1-10 PPM
Printer Color Inkjet 11-20 PPM
Printer Color Inkjet 21 PPM or more
Printer Color Laser 1-10 PPM
Printer Color Laser 11-20 PPM
Printer Color Laser 21-30 PPM
Printer Color Laser 31-44 PPM
Printer Mono Inkjet All Speeds
Printer Mono Laser 1-20 PPM
Printer Mono Laser 21-30 PPM
Printer Mono Laser 31-44 PPM
Printer Mono Laser 45-69 PPM
Printer Mono Laser 70-90 PPM
Japan
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
US
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Korea
X
X
EU
X
X
X
X
X
X
X
X
Notes: Product types are from the IDC taxonomy. “PPM” stands for pages
per minute.
42
43
Small
OLS Coefficient IV Coefficient
-0.655***
-1.420***
(0.030)
(0.085)
0.854***
0.738***
(0.009)
(0.048)
0.653***
1.153***
(0.097)
(0.131)
0.422***
0.454***
(0.041)
(0.051)
0.162***
0.280***
(0.030)
(0.036)
2.840***
0.469
(0.346)
(0.425)
0.684***
1.410***
(0.056)
(0.129)
0.119
0.717***
(0.091)
(0.250)
-0.094
0.316***
(0.061)
(0.083)
0.687***
0.853***
(0.042)
(0.056)
0.253**
1.414***
(0.102)
(0.152)
1.655***
2.420***
(0.030)
(0.085)
5.487***
6.419***
(0.299)
1.174
2852
2852
Large
OLS Coefficient IV Coefficient
-0.541***
-1.480***
(0.019)
(0.072)
0.887***
0.830***
(0.006)
(0.038)
0.446***
1.413***
(0.044)
(0.095)
0.276***
0.506***
(0.014)
(0.033)
0.177***
0.237***
(0.016)
(0.019)
1.345***
-1.310***
(0.184)
(0.256)
0.430***
1.414***
(0.034)
(0.076)
0.078*
0.436***
(0.040)
(0.077)
0.075**
0.466***
(0.033)
(0.043)
0.639***
0.807***
(0.028)
(0.045)
2.152***
3.783***
(0.054)
(0.156)
1.541***
2.480***
(0.019)
(0.072)
5.799***
9.702***
(0.325)
(2.294)
5944
5944
Notes: * indicates 10% significance, ** indicates 5% significance, and *** indicates 1% significance. Heteroskedasticity robust standard errors are in
parentheses. All regressions include a constant. All variables are differenced with respect to the Panasonic KX-P1150. Small consumers are home
office buyers or 1 to 9 employee establishments. Large consumers are 10 or more employee establishments. “BW PPM Speed” is the maximum number
of pages per minute that can be printed in black and white.
Number of Observations
Implied σ
Implied γ
Laser Dummy
MFP Dummy
Ethernet Dummy
Footprint
A3 Dummy
Resolution
RAM
BW PPM Speed
Color Dummy
Ln(Group Share)
Variable
Ln(Price)
Table 3: Logit Regression Results
No Types
OLS Coefficient IV Coefficient
-0.594***
-1.521***
(0.019)
(0.068)
0.879***
0.810***
(0.006)
(0.035)
0.465***
1.413***
(0.044)
(0.088)
0.286***
0.502***
(0.014)
(0.031)
0.170***
0.232***
(0.015)
(0.018)
2.025***
-0.584**
(0.177)
(0.239)
0.506***
1.462***
(0.033)
(0.075)
0.0890**
0.452***
(0.040)
(0.076)
0.0898***
0.484***
(0.031)
(0.043)
0.658***
0.852***
(0.026)
(0.039)
1.563***
3.169***
(0.053)
(0.136)
1.594***
2.521***
(0.019)
(0.068)
5.927***
8.991***
(0.286)
(1.754)
6413
6413
44
Inkjet
Laser
Inkjet
Laser
Inkjet
Laser
Inkjet
Laser
Inkjet
Laser
Inkjet
Laser
Inkjet
Laser
Inkjet
Laser
Inkjet
Laser
Apple Color StyleWriter 2400
Brother HL-631
Canon BJ-200ex
Epson EPL-5500
HP Deskjet 1600C
Xerox 4505
Apple Color StyleWriter 2400
Brother HL-631
Canon BJ-200ex
Epson EPL-5500
HP Deskjet 1600C
Xerox 4505
Apple Color StyleWriter 2400
Brother HL-631
Canon BJ-200ex
Epson EPL-5500
HP Deskjet 1600C
Xerox 4505
-7.4814
0.0176
0.1915
0.0154
0.1995
0.0163
-8.7649
0.0205
0.2259
0.0205
0.2259
0.0205
-2.5009
0.0205
0.0205
0.0205
0.0205
0.0205
Apple Color
StyleWriter 2400
0.0123
-8.4220
0.0113
0.1098
0.0118
0.1163
0.0143
-8.8709
0.0143
0.1199
0.0143
0.1199
0.0143
-2.5071
0.0143
0.0143
0.0143
0.0143
Brother
HL-631
Canon
Epson
BJ-200ex EPL-5500
MNL Model
0.0332
0.0237
0.0332
0.0237
-2.4882
0.0237
0.0332
-2.4977
0.0332
0.0237
0.0332
0.0237
NL Model
0.3665
0.0237
0.0332
0.1984
-8.6243
0.0237
0.0332
-8.7924
0.3665
0.0237
0.0332
0.1984
NRCL Model
0.3108
0.0179
0.0263
0.1825
-6.8084
0.0165
0.0231
-7.3321
0.2988
0.0172
0.0244
0.1694
0.0618
0.0052
0.0570
0.0046
-7.3328
0.0049
0.0699
0.0063
0.0699
0.0063
-8.9208
0.0063
0.0063
0.0063
0.0063
0.0063
-2.5150
0.0063
HP Deskjet
1600C
0.0251
0.2558
0.0232
0.2242
0.0241
-7.6992
0.0314
0.2627
0.0314
0.2627
0.0314
-8.7281
0.0314
0.0314
0.0314
0.0314
0.0314
-2.4900
Xerox
4505
Notes: These cross-price elasticities are calculated using the formulas discussed in Section 3. Each entry is the percentage change in
quantity sold of the row good in response to a percentage change in price of the column good.
Group
Table 4: A Sample of Own- and Cross-Price Elasticities
Product
Table 5: Price Index Results, 1996 vs. 2005
Model
CES
NCES
MNL
NL
NRCL
NRCL Small
NRCL Large
Index
0.061
[0.056, 0.065]
0.160
[0.148, 0.178]
0.035
[0.028, 0.040]
0.110
[0.094, 0.123]
0.100
[0.090, 0.111]
0.051
[0.038, 0.062]
0.122
[0.105, 0.140]
Notes: These price indices are calculated at the quarterly level (comparing the first quarter of 2005 to the
first quarter of 1996, for example), and then averaged
over all four quarters. Bootstrapped 95 percent confidence intervals are in brackets.
Table 6: Price Index Decompositions, 1996 vs. 2005
Model
CES
Common Goods
0.137
NCES
0.201
Model
MNL
Price
0.386
[0.376, 0.387]
0.411
[0.398, 0.413]
0.374
[0.356, 0.380]
NL
NRCL
Changing Goods
0.446
[0.408, 0.475]
0.800
[0.743, 0.888]
Quality
Variety
0.376
0.247
[0.347, 0.413]
[0.210, 0.275]
0.352
0.757
[0.326, 0.388]
[0.646, 0.863]
0.352
0.783
[0.319, 0.366]
[0.714, 0.852]
Notes: These decompositions are calculated at the quarterly level
(comparing the first quarter of 2005 to the first quarter of 1996, for
example), and then averaged over all four quarters. Bootstrapped 95
percent confidence intervals are in brackets.
45