Price, Quality, and Variety: Measuring the Gainsfrom 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 prod-ucts has significant positive welfare effects. These gains have been established usingprice indices that measure the value to consumers of changes in the set of goods avail-able over time. In this paper, I explore how these price indices are shaped by theirunderlying structural assumptions. I draw parallels with methods used in industrialorganization, where a number of researchers have also studied differentiated products,albeit in domestic markets. I show that a standard trade model, the nested constantelasticity of substitution (NCES) framework, produces the same market demand sys-tem 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 onecoherent family. Furthermore, I show how standard NCES empirical techniques, whichrely on data that aggregates over individual products, relate to the product-level datamethods more commonly used in logit settings. I then apply these methods to a dataset on Indian imports of computer printers, highlighting how these approaches differ ina concrete example. In this application, I find that using aggregated data understatesthe 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 theprice index by over 60 percent.

∗The views expressed here are not purported to reflect those of the US Department of Justice. Iwould like to thank Pol Antras, Elhanan Helpman, Julie Mortimer, and Ariel Pakes for their guidanceand 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 MarcRemer. I am greatly indebted to George Gibson of the Xerox Corporation for giving me access tothe printer data set and for helping me understand the Indian printer market. Mary Carlin at theXerox Corporate Library also provided key assistance in obtaining the printer data. Petia Topalovagraciously made the Indian tariff data available. All errors are my own. First version: November 2009.Email: gloria.sheu@usdoj.gov

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 tech-

niques 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), re-

spectively. 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 im-

ports of computer printers into India, I estimate several industrial-organization-style

logit models. Furthermore, by aggregating this data, I am also able to implement stan-

dard 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 con-

sumers. 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 ap-

proach 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 im-

ports 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 coun-

try 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 product-

level 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 heteroge-

neous 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 organi-

zation literatures studying the welfare effects of changes in differentiated products.

Although the many contributions in these literatures are too numerous to fully summa-

rize 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,

1This functional form is sometimes referred to as the Spence-Dixit-Stiglitz demand system afterthe work in Spence (1976) and Dixit and Stiglitz (1977).

2This trend follows from the influential work in McFadden (1974).3The 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 derivinga 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 product-

level 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 under-

state 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 proce-

dure designed for the typical trade data set. This methodology has become the standard

for measuring the gains from imports of differentiated products. These techniques con-

trast 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 =

(∑g∈G

Mγ−1γ

gt

) γγ−1

, where γ > 1. (1)

4

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

Mgt =

∑j∈Jgt

b1σjtm

σ−1σ

jt

σσ−1

, where σ > 1. (2)

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,

the consumer maximizes Mgt subject to the constraint∑

j∈Jgt pjtmjt = 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,

sjt|g =bjtp

1−σjt∑

j∈Jgt bjtp1−σjt

. (3)

In turn, the share of expenditure devoted to group g out of total expenditure is

sgt =

(∑j∈Jgt bjtp

1−σjt

) 1−γ1−σ

∑g∈G

(∑j∈Jgt bjtp

1−σjt

) 1−γ1−σ

. (4)

Multiplying these two expressions gives the share of expenditure allocated to product

4An extension of this model is to allow the elasticity of substitution to vary by group, giving σg. Ido not pursue this variant for simplicity, but its mechanics are similar to those discussed in the maintext.

5

j out of the money spent on all product groups,

sjt =bjtp

1−σjt(∑

j∈Jgt bjtp1−σjt

) γ−σ1−σ ∑

g∈G

(∑j∈Jgt bjtp

1−σjt

) 1−γ1−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 =bjtp

1−γjt∑

j∈Jt bjtp1−γjt

. (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

m1t

m2t

=b1tp

−γ1t

b2tp−γ2t

,

which does not depend on the other products available. Thus, if a third good is in-

5That is, utility reduces to Ut =

(∑j∈Jt b

1γ

jtmγ−1γ

jt

) γγ−1

.

6The CES and Cobb-Douglas (which the CES reduces to when γ = 1) models have been featuredin standard trade textbooks such as Helpman and Krugman (1985) and in key theoretical papers suchas 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

pktmjt

= (γ − 1)skt ∀j 6= k.7 (7)

These elasticities have the property that

∂mjt

∂pkt

pktmjt

=∂mlt

∂pkt

pktmlt

∀j, k, l such that j, l 6= k. (8)

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

pktmjt

=

{(γ − 1)skt + (σ − γ)skt|g if j and k are in the same group

(γ − 1)skt 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

7This elasticity can be derived by noting that mjt =sjtYpjt

, where Y denotes income.

7

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?

One common way to build this metric is to look for a factor, τNCESt+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

τNCESt+1 =

(∑g∈G

(∑j∈Jgt+1

bjt+1p1−σjt+1

) 1−γ1−σ) 1

1−γ

(∑g∈G

(∑j∈Jgt bjtp

1−σjt

) 1−γ1−σ) 1

1−γ, (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

τCESt+1 =

(∑j∈Jt+1

bjt+1p1−γjt+1

) 11−γ

(∑j∈Jt bjtp

1−γjt

) 11−γ

. (11)

The nested structure of the NCES model means that τNCESt+1 is actually just a ge-

ometric average of CES price indices calculated within each group of products.9 That

is,

τNCESt+1 =∏g∈G

(τCESgt+1

)ωgt+1, (12)

where

τCESgt+1 =

(∑j∈Jgt+1

bjt+1p1−σjt+1

) 11−σ

(∑j∈Jgt bjtp

1−σjt

) 11−σ

and ωgt+1 =(sgt+1 − sgt)/(ln(sgt+1)− ln(sgt))∑g∈G(sgt+1 − sgt)/(ln(sgt+1)− ln(sgt))

.

8This result follows from the form of the indirect utility function, which is

Y/

(∑g∈G

(∑j∈Jgt bjtp

1−σjt

) 1−γ1−σ) 1

1−γ

. Here Y denotes income.

9This result follows from the proof in the appendix of Feenstra (1994).

8

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 param-

eters 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:

τNCESt+1 =∏g∈G

∏c∈Cg

(pct+1

pct

)ωcgt+1

ωgt+1 ∏g∈G

(λgt+1

λgt

)ωgt+1σ−1

. (13)

where

λgt =

∑c∈Cg pctmct∑c∈Cgt pctmct

and

ωcgt+1 =(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)))

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

τCESt+1 =∏c∈C

(pct+1

pct

)ωct+1(λt+1

λt

) 1γ−1

(14)

9

where

λt =

∑c∈C pctmct∑c∈Ct pctmct

and ωct+1 =(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 non-

empty. 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 (1994) approach is that it decomposes the price index

into two parts. The∏

g∈G

(∏c∈Cg

(pct+1

pct

)ωcgt+1)ωgt+1

(which I call the common goods

term) captures gains from price amongst common products, while the∏

g∈G

(λgt+1

λgt

)ωgt+1σ−1

(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.

10An exception is the original Feenstra (1994) paper, where he reports sensitivity results for severaldifferent 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, assum-

ing 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 be-

ing nesting products, the second being random coefficients. These methods can be com-

bined 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

by g ∈ G. In addition, each good within a group g is indexed by j in the set Jrgt.11 The

utility for consumer i of type r buying good j in group g is

urijt = ln(arjtmrijt) + ζrigt + εrijt. (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

Meanwhile the ζrigt is a random draw from a logit distribution with scale parameter

µr1, and the εrijt is a random draw from a logit distribution with scale parameter µr2.13

11The set of goods available Jrgt may vary by consumer, meaning that some goods can be consumed inzero quantities by all consumers of a certain type. For example, a home office buyer would not considerpurchasing a large enterprize printer, so it should not be in that consumer’s choice set. Another wayto think of this is to assume that the utility from goods outside of Jrgt is zero.

12In most applications of logit models, a consumer can only buy discrete units (usually one unit) ofa good. However, I change this assumption in order to match the CES model, where consumers canbuy a continuous amount of a good.

13A random variable x is distributed logit if it has a cumulative distribution function of

exp[− exp

(− xµ + %

)]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)

random draws, one for each product j ∈ Jrgt and one for each group g ∈ G.

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 pjtmrijt = yr where yr

is the consumer’s income. Substituting this constraint into the utility function gives an

indirect utility of

vrijt = ln(arjt)− ln(pjt) + ln(yr) + ζrigt + εrijt. (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

focusing on one group, the ζrigt term drops out, reducing the choice problem to

max{

ln(ar1t)− ln(p1t) + εri1t, . . . , ln(arJrgtt)− ln(pJrgtt) + εriJrgtt

}, (17)

where, in a slight abuse of notation, I have used Jrgt to refer to both the goods set and

its cardinality. Integrating over the logit random shocks gives,

probrjt|g =arjt

1µr2 p

−1µr2jt∑

j∈Jrgtarjt

1µr2 p

−1µr2jt

,

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

14This expression follows from the form of the logit distribution. Specifically, when given theproblem max{d1 + ε1, . . . , dJ + εJ}, the probability that option j will be the maximum is given by

exp(dj/µ)/∑Jj=1 exp(dj/µ). Here the εj are iid logit random variables with scale parameter µ.

13

the group with the maximum expected indirect utility,

max

µr2 ln

∑j∈Jr1t

arjt1µr2 p

−1µr2jt

+ ζri1t, . . . , µr2 ln

∑j∈JrGt

arjt1µr2 p

−1µr2jt

+ ζriGt

. (18)

Again I have used G to refer both to the set and to its cardinality.15 Maximization

results in a group probability of

probrgt =

(∑j∈Jrgt

arjt1µr2 p

−1µr2jt

)µr2µr1

∑g∈G

(∑j∈Jrt

arjt1µr2 p

−1µr2jt

)µr2µr1

.

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

between the CES and MNL. Let arjt1µr2 = brjt,

−1µr2

= 1−σr, and 1µr1

= γr−1. Then convert

probrjt|g and probrgt to (expected) expenditure shares by multiplying and dividing by the

consumer’s income. The resulting expenditure shares are

srjt|g =brjtp

1−σrjt∑

j∈Jrgtbrjtp

1−σrjt

(19)

and

srgt =

(∑j∈Jrgt

brjtp1−σrjt

) 1−γr1−σr

∑g∈G

(∑j∈Jrgt

brjtp1−σrjt

) 1−γr1−σr

. (20)

Multiplying these two shares gives

srjt =brjtp

1−σrjt(∑

j∈Jrgtbrjtp

1−σrjt

) γr−σr1−σr ∑

g∈G

(∑j∈Jrgt

brjtp1−σrjt

) 1−γr1−σr

. (21)

Note that if all types of consumers have identical preferences, meaning that brjt = bjt,

σr = σ, and γr = γ for all r, these formulas collapse down to those in the NCES model.

15Expression (18) follows from the form of the expected maximum of a series of iid logit random

variables. That is, E[max{d1 + ε1, . . . , dJ + εJ}] = µ ln(∑Jj=1 exp(dj/µ)), where the εj 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 =∑r∈R

f rt srjt, (22)

where f rt 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

pktmjt

=

1sjt

∑r∈R f

rt [(γr − 1)srjts

rkt + (σr − γr)srjtsrkt|g] if j and k are

in the same group1sjt

∑r∈R f

rt (γr − 1)srjts

rkt otherwise

(23)

for all j 6= k. One would expect σr > γr for all r ∈ R because the nests gather together

similar products. Therefore, just as in the NCES model, the (σr − γr) term should

increase the cross-price elasticity between goods in the same groups.

16I focus on the discrete distribution case because this allows me to express the NRCL results asweighted averages of the NL formulas. This makes the relationship between the NRCL and the othermodels particularly transparent. The discrete specification is familiar in the marketing literature (seeKamakura and Russell (1989) for example), while the specification using a normal distribution has beenpopularized by Berry, Levinsohn, and Pakes (1995). The normal distribution does not give closed-formexpressions for market demand (because the gaussian integral must be computed numerically), whichmakes 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, γa and σa, in the aggregate cross-

price 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

∑r∈R

f rt+1

γr − 1ln

∑g∈G

∑j∈Jrgt

brjt(τNRCLt+1 pjt)

1−σryσr−1

1−γr1−σr

=∑r∈R

f rt+1

γr − 1ln

∑g∈G

∑j∈Jrgt+1

brjt+1p1−σrjt+1 y

σr−1

1−γr1−σr

.

Solving for the price index itself gives

τNRCLt+1 =∏r∈R

(∑

g∈G

(∑j∈Jrgt+1

brjt+1p1−σrjt+1

) 1−γr1−σr

) 11−γr

(∑g∈G

(∑j∈Jrgt

brjtp1−σrjt

) 1−γr1−σr

) 11−γr

frt+1

. (24)

Note that this expression is the geometric average of individual NL (or NCES) price

16

indices, τ rNLt+1 , for each type of consumer, where

τ rNLt+1 =

(∑g∈G

(∑j∈Jrgt+1

brjt+1p1−σrjt+1

) 1−γr1−σr

) 11−γr

(∑g∈G

(∑j∈Jrgt

brjtp1−σrjt

) 1−γr1−σr

) 11−γr

. (25)

In turn, as in the NCES model, each τ rNLt+1 is a geometric average of individual MNL

(or CES) price indices,

τ rNLt+1 =∏g∈G

(τ rMNLgt+1 )ω

rgt+1 (26)

where

τ rMNLgt+1 =

(∑j∈Jrgt+1

brjt+1p1−σrjt+1

) 11−σr

(∑j∈Jrgt

brjtp1−σrjt

) 11−σr

and

ωrgt+1 =(srgt+1 − srgt/(ln(srgt+1)− ln(srgt))∑g∈G(srgt+1 − srgt)/(ln(srgt+1)− ln(srgt))

.

3.4 Estimation

Given the strong theoretical similarities between the trade and industrial organiza-

tion 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

sr0t =p1−γr

0t∑g∈G

(∑j∈Jrgt

brjtp1−σrjt

) 1−γr1−σr

.

Then take logs of this equation and subtract it from the log of srjt in equation (21).

17This can be thought of as re-scaling the qualities of all other goods to be in units relative to thequality of good 0.

17

After some minor algebraic manipulations following Berry (1994), this results in

ln(srjt)− ln(sr0t) =γr − 1

σr − 1ln(brjt)− (γr − 1)[ln(pjt)− ln(p0t)] +

σr − γr

σr − 1ln(srjt|g). (27)

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 charac-

teristics information is useful. In industries commonly studied in empirical industrial

organization, such as automobiles and electronics, product characteristics are a rea-

sonable 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

σr − 1ln(brjt) = (xjt − x0t)β

r + erjt. (28)

The βr 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)βr− (γr−1)[ln(pjt)− ln(p0t)]+

σr − γr

σr − 1ln(srjt|g)+erjt. (29)

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 βr = β, γr = γ,

and σr = 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 un-

available. 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 com-

ponents. That is, here one can step beyond the “common goods” and “changing goods”

breakdown by incorporating the estimated qualities into the Feenstra (1994) methodol-

ogy. The resulting decomposition is useful in exploring the mechanisms at work behind

movements in the overall price index.

Imagine that there are Jrg 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, . . . , Jrg .21 Next choose a size Jrg 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, . . . , Jrg .23 Because this set is scaled to be of

size Jrg , it captures the price and quality distribution present in t+ 1 but holds variety

18Treating other product characteristics besides price as endogenous is much less common becausefinding an instrument that is uncorrelated with unobserved quality but correlated with observed qualityis difficult.

19For certain distributions, this procedure can be computationally intensive. In the case of thenormal distribution, integrating up to the market-level shares has to be done numerically, and thenthe parameters have to be fitted using a non-linear search. See Knittel and Metaxoglou (2008) andDube et al. (2009) for discussions on the challenges involved in this type of estimation.

20Readers who are interested in these other estimation methods should consult Berry, Levinsohn,and Pakes (1995), Nevo (2000), and Train (2009).

21In theory, the ordering of these goods does not matter, so long as one keeps track of which priceand quality goes with which good. However, the resulting decomposition can be sensitive to whichgoods are matched in periods t and t+ 1, so it is best to establish a consistent procedure.

22I discuss one method for choosing such a set in Section 4.23This procedure assumes that there are at least as many products available in time t + 1 as in t.

Otherwise, the size of the set Jrg would be defined as the number of goods in time t+ 1 and the priceindex would be interpreted as measuring the change relative to the set Jrgt+1 instead of relative to Jrgt.

19

constant at the period t level. Repeat this process for each g ∈ G and r ∈ R.

Then the price index decomposition is

τNRCLt+1 =∏r∈R

∏g∈G

Jrg∏j=1

(pjt+1

pjt

)ωrjgt+1Jrg∏j=1

(brjtbrjt+1

)ωrjgt+1σ−1

(λJrgt+1

λJrgt

) 1σ−1

ωrgt+1

frt+1

.

(30)

where

λJrgt =

∑Jrgj=1 pjtm

rjt∑

j∈Jrgtpjtmr

jt

, ωrjgt+1 =(srjt+1(Jrg )− srjt(Jrg ))/(ln(srjt+1(Jrg ))− ln(srjt(J

rg )))∑Jrg

j=1(srjt+1(Jrg )− srjt(Jrg ))/(ln(srjt+1(Jrg ))− ln(srjt(Jrg )))

.

and

ωrgt+1 =(srgt+1 − srgt/(ln(srgt+1)− ln(srgt))∑g∈G(srgt+1 − srgt)/(ln(srgt+1)− ln(srgt))

.

Here srjt(Jrg ) is the share of expenditure by type r consumers accounted for by good

j out of the goods indexed by 1, . . . , Jrg . 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, . . . , Jrg}. The second part is a geometric average of quality ratios,

brjt/brjt+1, which captures changes in quality in the set {1, . . . , Jrg}. 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, . . . , Jrg}. 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,

τNLt+1 =∏g∈G

(Jg∏j=1

(pjt+1

pjt

)ωjgt+1

)ωgt+1 ∏g∈G

(Jg∏j=1

(bjtbjt+1

)ωjgt+1σ−1

)ωgt+1 ∏g∈G

(λJgt+1

λJgt

)ωgt+1σ−1

.

(31)

where

λJgt =

∑Jgj=1 pjtmjt∑j∈Jgt pjtmjt

and

ωjgt+1 =(sjt+1(Jg)− sjt(Jg))/(ln(sjt+1(Jg))− ln(sjt(Jg)))∑Jgj=1(sjt+1(Jg)− sjt(Jg))/(ln(sjt+1(Jg))− ln(sjt(Jg)))

.

Note that sjt(Jg) is the share of expenditure accounted for by good j amongst expen-

20

diture on the goods 1, . . . , Jg. In the case of the MNL model,

τMNLt+1 =

J∏j=1

(pjt+1

pjt

)ωjt+1 J∏j=1

(bjtbjt+1

)ωjt+1γ−1

(λJt+1

λJt

) 1γ−1

(32)

where

λJt =

∑Jj=1 pjtmjt∑j∈Jt pjtmjt

and ωjt+1 =(sjt+1(J)− sjt(J))/(ln(sjt+1(J))− ln(sjt(J)))∑Jj=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 impor-

tant 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.

24The quality term also includes σ, but this difference actually does not have an effect on therelationship between the NL and MNL indices. This is because the definition of bjt in the estimationequation 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.

25These numbers are computed using the UN Comtrade database.26HP 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.

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 infor-

mation 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.

27I also have data through the first quarter of 2008, but these observations have to be droppedbecause there is no product that appears in all of these years to serve as the outside good in the logitmodels.

28The CPI is from http://labourbureau.nic.in/ and was downloaded in October 2009.29IDC 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 exactlyhow it is constructed. Prior to 2001, MFPs are not recorded in the database. However, when MFPtracking begins in 2001 Q1, these machines only comprise 4.5 percent of sales revenue, so it is unlikelythat they formed a large part of the market in the prior period.

30The main impact technology is dot matrix.31When 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 some-

thing 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

32If one or two characteristics for a model can not be found, they are imputed from similar modelsof the same brand, or, if those are not available, from similar models across all brands in a givenquarter. This affects 10 percent of observations in the final sample. I convert printing speeds listed incharacters 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 ex-

change 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 re-

searchers 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 (Oce). Therefore, any rev-

enues 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

33A related concern is that upfront printer prices may be uninformative if printer vendors are pursu-ing a strategy of lowering the prices of printers in order to make money on printer cartridges. Althoughsuch a strategy has been used in the US, it is much less prevalent in India because of the high pene-tration of third party and counterfeit cartridges. IDC estimates that over 50 percent of the cartridgessold in India are made by third parties.

34These 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). Sim-

ply 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

35There are some drawbacks to this approach. Most prices for printers are probably set initially inIndian rupees, not set in foreign currencies and converted. If there are menu costs, this may mean thatprices 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 inturn related to local demand factors. Nevertheless, the exchange rate is one of the few variables thatexhibits strong variation across time periods while also having a reasonable probability of satisfyingthe exogeneity requirement.

36See 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

37I do not have consumer-level data for this model, so I assume that 5 percent of reported salesare made up of small consumers. This estimate is based on IDC sales data for two other dot matrixmodels sold from 1998 to 2003.

38I use both the homoskedastic and heteroskedasticity robust overidentification tests suggested byWooldridge (2002). These F test and overidentification test results hold regardless of whether the threeequations (no consumer types, small consumers, and large consumers) are estimated stacked togetheror 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

39These 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.

40The common goods effects do not have confidence intervals because those terms do not use esti-mated 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 re-

sult 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

41In order to build these confidence intervals, I sample from the estimated asymptotic distributionof the regression parameters in Table 3 to form 100 simulated parameter sets. Then I calculate theindices for each sample and take the difference between the MNL and CES indices and the NL andNCES 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 con-

structed 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 signifi-

cant.

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 hetero-

geneity 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. How-

ever, 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.

42The differences across these models for the price and quality terms are also significant, thoughthey 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 less-

obvious 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 meth-

ods 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 be-

cause 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 prod-

ucts. 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 struc-

ture 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 innova-

tions 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. Feen-

stra (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 ad-

vancements 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 of1996, 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 of1996, 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 of1996, 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 of1996, for example), and then averaged over all four quarters. The index for each year takes 1996 as the base year.

40

Table 1: Summary StatisticsVariable Mean Standard DeviationPrice (USD) 604.996 1084.060Units Sold 1059.538 4763.041Color Dummy 0.468 0.499BW PPM Speed 20.806 13.430RAM (MB) 49.764 98.272Resolution (DPI) 1336.798 771.611A3 Capable Dummy 0.355 0.478Footprint (in2) 416.175 381.911Ethernet Interface Dummy 0.343 0.475MFP Dummy 0.356 0.479Laser Dummy 0.663 0.473Number of Model-Quarters 6413Number of Unique Models 1189Notes: Data sources are in the text, Section 4. Price is in real 2001 IndianRs, then converted to USD at 1 Rs=47.12 USD. “BW PPM Speed” is themaximum number of pages per minute that can be printed in black and white.

41

Table 2: Product CategoriesProduct Type Japan US Korea EUMFP Color Inkjet 1-10 PPM X X XMFP Color Inkjet 11-20 PPM X X XMFP Color Inkjet 21 PPM or more X XMFP Color Laser 1-10 PPM X XMFP Color Laser 11-20 PPM X XMFP Color Laser 21-30 PPM X XMFP Color Laser 31-44 PPM X X XMFP Mono Inkjet All Speeds XMFP Mono Laser 1-20 PPM X X XMFP Mono Laser 21-30 PPM X X XMFP Mono Laser 31-44 PPM X XMFP Mono Laser 45-69 PPM X X XMFP Mono Laser 70-90 PPM X XPrinter Color Inkjet 1-10 PPM X XPrinter Color Inkjet 11-20 PPM X XPrinter Color Inkjet 21 PPM or more X XPrinter Color Laser 1-10 PPM X X XPrinter Color Laser 11-20 PPM X XPrinter Color Laser 21-30 PPM X XPrinter Color Laser 31-44 PPM XPrinter Mono Inkjet All Speeds X XPrinter Mono Laser 1-20 PPM X X XPrinter Mono Laser 21-30 PPM X X XPrinter Mono Laser 31-44 PPM X XPrinter Mono Laser 45-69 PPM X XPrinter Mono Laser 70-90 PPM XNotes: Product types are from the IDC taxonomy. “PPM” stands for pagesper minute.

42

Tab

le3:

Log

itR

egre

ssio

nR

esult

sN

oT

yp

esS

mall

Larg

eV

aria

ble

OL

SC

oeffi

cien

tIV

Coeffi

cien

tO

LS

Coeffi

cien

tIV

Coeffi

cien

tO

LS

Coeffi

cien

tIV

Coeffi

cien

tL

n(P

rice

)-0

.594

***

-1.5

21***

-0.6

55***

-1.4

20***

-0.5

41***

-1.4

80***

(0.0

19)

(0.0

68)

(0.0

30)

(0.0

85)

(0.0

19)

(0.0

72)

Ln

(Gro

up

Sh

are)

0.87

9***

0.8

10***

0.8

54***

0.7

38***

0.8

87***

0.8

30***

(0.0

06)

(0.0

35)

(0.0

09)

(0.0

48)

(0.0

06)

(0.0

38)

Col

orD

um

my

0.46

5***

1.4

13***

0.6

53***

1.1

53***

0.4

46***

1.4

13***

(0.0

44)

(0.0

88)

(0.0

97)

(0.1

31)

(0.0

44)

(0.0

95)

BW

PP

MS

pee

d0.

286*

**0.5

02***

0.4

22***

0.4

54***

0.2

76***

0.5

06***

(0.0

14)

(0.0

31)

(0.0

41)

(0.0

51)

(0.0

14)

(0.0

33)

RA

M0.

170*

**0.2

32***

0.1

62***

0.2

80***

0.1

77***

0.2

37***

(0.0

15)

(0.0

18)

(0.0

30)

(0.0

36)

(0.0

16)

(0.0

19)

Res

olu

tion

2.02

5***

-0.5

84**

2.8

40***

0.4

69

1.3

45***

-1.3

10***

(0.1

77)

(0.2

39)

(0.3

46)

(0.4

25)

(0.1

84)

(0.2

56)

A3

Du

mm

y0.

506*

**1.4

62***

0.6

84***

1.4

10***

0.4

30***

1.4

14***

(0.0

33)

(0.0

75)

(0.0

56)

(0.1

29)

(0.0

34)

(0.0

76)

Foot

pri

nt

0.08

90**

0.4

52***

0.1

19

0.7

17***

0.0

78*

0.4

36***

(0.0

40)

(0.0

76)

(0.0

91)

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(0.0

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77)

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31)

(0.0

43)

(0.0

61)

(0.0

83)

(0.0

33)

(0.0

43)

MF

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0.6

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39***

0.8

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26)

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39)

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56)

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28)

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43

Tab

le4:

ASam

ple

ofO

wn-

and

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ss-P

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Gro

up

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ther

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ther

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0.0

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0.0

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314

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son

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Lase

r0.0

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0.1

199

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332

-8.7

924

0.0

063

0.2

627

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Des

kje

t16

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t0.2

259

0.0

143

0.3

665

0.0

237

-8.9

208

0.0

314

Xer

ox45

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ase

r0.0

205

0.1

199

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CL

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pp

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olor

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rite

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0.0

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0.0

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ther

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r0.0

176

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0.0

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onB

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0.0

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570

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son

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500

Lase

r0.0

154

0.1

098

0.0

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-7.3

321

0.0

046

0.2

242

HP

Des

kje

t16

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t0.1

995

0.0

118

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-7.3

328

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241

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ox45

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ase

r0.0

163

0.1

163

0.0

244

0.1

694

0.0

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-7.6

992

Note

s:T

hes

ecr

oss

-pri

ceel

ast

icit

ies

are

calc

ula

ted

usi

ng

the

form

ula

sd

iscu

ssed

inS

ecti

on

3.

Each

entr

yis

the

per

centa

ge

chan

ge

inqu

anti

tyso

ldof

the

row

good

inre

spon

seto

ap

erce

nta

ge

chan

ge

inp

rice

of

the

colu

mn

good

.

44

Table 5: Price Index Results, 1996 vs. 2005Model IndexCES 0.061

[0.056, 0.065]NCES 0.160

[0.148, 0.178]MNL 0.035

[0.028, 0.040]NL 0.110

[0.094, 0.123]NRCL 0.100

[0.090, 0.111]NRCL Small 0.051

[0.038, 0.062]NRCL Large 0.122

[0.105, 0.140]Notes: These price indices are calculated at the quar-terly level (comparing the first quarter of 2005 to thefirst quarter of 1996, for example), and then averagedover all four quarters. Bootstrapped 95 percent confi-dence intervals are in brackets.

Table 6: Price Index Decompositions, 1996 vs. 2005Model Common Goods Changing GoodsCES 0.137 0.446

[0.408, 0.475]NCES 0.201 0.800

[0.743, 0.888]Model Price Quality VarietyMNL 0.386 0.376 0.247

[0.376, 0.387] [0.347, 0.413] [0.210, 0.275]NL 0.411 0.352 0.757

[0.398, 0.413] [0.326, 0.388] [0.646, 0.863]NRCL 0.374 0.352 0.783

[0.356, 0.380] [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, forexample), and then averaged over all four quarters. Bootstrapped 95percent confidence intervals are in brackets.

45