Rivalry in Price and Location by
Di¤erentiated Product Manufacturers
Timothy J. Richards, William Allender, and Stephen F. Hamilton
Paper presented at 3rd GAEL Conference, June 20-21, 2013. Grenoble, FR.
May 23, 2013
Abstract
In this paper, we estimate a model of strategic rivalry between food manufacturers
in product design and pricing. We derive a spatial structural model in which food manufacturers jointly select prices and the optimal attribute composition of their product
lines. We …nd that manufacturers have an incentive to locate yogurt products nearby
others in attribute space and that products with the most similar attribute compositions enjoy the widest price-cost margins. Our …ndings explain the obsevation that
most consumer package goods tend to be very similar, and yet manufacturers appear
to earn above normal pro…ts.
Running Title: Rivalry in Price and Location
JEL Classi…cation: L13, C21, M31, Q13.
Keywords: di¤erentiated products, discrete choice, distance metric, yogurt, pricing, product
design.
Richards is Morrison Professor of Agribusiness, and Allender is Ph.D. student in the Morrison School
of Management and Agribusiness, Arizona State University. Hamilton is Professor in the Department of
Economics, Orfalea College of Business, California Polytechnic State University, San Luis Obispo. Contact
author: Richards, 7231 E. Sonoran Arroyo Mall, San Tan 230B, Mesa, AZ. 85212. (480) 727-1488, Fax: (480)
727-1961, email: [email protected]. Support from AFRI-NIFA (USDA) grant no. 2009-04140 is gratefully
acknowledged.
Introduction
Manufacturers of consumer packaged goods (CPGs) face an important trade-o¤ when
pricing and designing food products. When marketing a line of food products, introducing
products that have attributes signi…cantly di¤erent from other products in the category
increases product di¤erentiation, which can facilitate wider price-cost margins by softening
price competition. On the other hand clustering products more closely around the attributes
contained in the top-selling variety can raise total sales volume.
In light of this trade-
o¤, Anderson, de Palma and Thisse (ADT, 1992) show that …rms do not necessarily have
an incentive to di¤erentiate their products from rivals in settings where individual tastes
di¤er. Rather, if consumers exhibit su¢ cient heterogeneity in their tastes, then “...product
/ taste heterogeneity softens price competition, locating together is no longer ruinous, and
‘central’locations allow …rms to better serve consumers over the whole market (ADT, 1992,
p. 10).” Indeed, when multiple manufacturers compete in product lines, collusive strategies
may involve segmenting the attribute space served by each manufacturer into distinct submarkets. Understanding the linkages between heterogeneity in consumer tastes for attributes
and the attribute space spanned by food manufacturers’existing product lines is essential
for evaluating both the marketing and welfare implications of product design.
Existing empirical research on product design tends to de…ne the product space as
linear in a single, de…ning attribute (Mazzeo, 2002; Seim, 2006; Thomadsen 2007). While
reducing the dimensionality of the attribute space has the advantage of simplicity, it may
not fully capture the strategic considerations facing food manufacturers in practice. In this
paper, we extend the empirical literature on product design and pricing to multi-dimensional
attribute space and assess the role of product di¤erentiation in food manufacturers’ equilibrium product design and pricing strategies. In so doing, we are able to decompose the
manufacturer margins that result from typical mark-up practices from those that come from
the nature of the attribute pro…le of the product.
We frame our study around an explicitly spatial, discrete-choice model of consumer
demand and apply it directly to yogurt products.
Discrete choice models have become
a popular tool for the analysis of complex strategic problems, including retailers’strategic
choice of geographic location (Mazzeo, 2002; Thomadsen, 2005, 2007; Seim, 2006; Zhu and
Singh, 2006; Orhun, 2006), retail pricing format (Ellickson and Misra, 2007) and the design
of a product assortment (Draganska, Mazzeo and Seim, 2006).
We extend the discrete
choice framework here to examine more general forms of strategic interaction among food
manufacturers in selecting the relative attribute composition of products in a food category
1
where manufacturers are widely known to maintain long product lines.
Speci…cally, our
approach conceives product design in a complex, discrete / continuous attribute space as
arising jointly from manufacturers’selection of prices and the relative attribute composition
of products in their product lines.
It is common in spatial models to specify the dependent variable in a cross-section
of data as being functionally related to the dependent variable at other locations in space.
For example, the prices of homes that are located near each other are likely to be more
highly correlated than the prices of homes that are farther away.
In our product design
application, we similarly consider the utility a consumer receives from one product as being
more closely-related to the utility received from consuming a product with a comparable
attribute composition than from consuming a product located at a greater distance away in
attribute space. Similar to the use of a lagged dependent variable in a time-series model, we
account for unobserved factors that explain the utility available from a particular attribute
composition in a di¤erentiated-product market using spatially-lagged values of consumer
utility.
There are several advantages to de…ning consumer utility as coming from a product’s
attributes in an explicitly spatial framework. First, our spatial model of product di¤erentiation provides a new interpretation of product variety. Both theoretical models of product
variety (ADP, Hamilton, 2009; Hamilton and Richards, 2009) and empirical models of product line decisions (Bayus and Putsis, 1999; Draganska and Jain, 2005) rely on product counts
or line-length as a measure of product variety in a category. In contrast, our spatial econometric framework allows us to describe the extent of variety available in a product category in
terms of the size of the multi-dimensional attribute space spanned by the set of products sold
in the market. From a purely methodological perspective, de…ning variety in terms of the
size of the attribute space spanned by a collection of objects provides a way of articulating
di¤erences in variety among sets of objects with similar counts, for instance how a rainbow
contains “greater variety”of color than seven shades of blue. Second, our approach provides
an analytically rich framework for examining the strategic role of product variety decisions
in consumer goods markets. Calculating the distance between each product and all other
products in attribute space permits us to examine a broader range of strategic behavior by
food manufacturers. For a given domain of consumer preferences, manufacturers that seek
to extend their product lines can “crowd the attribute space”around top-selling products or
expand the attribute space by selecting highly di¤erentiated attribute compositions relative
to existing brands, which can serve to attract consumers to the product category who would
2
otherwise have fallen into the “outside option”and not made a purchase at all.
We consider product design to be the outcome of a two-stage game in which food
manufacturers …rst select the attribute composition of their product lines and then select
prices. To limit the number of strategic variables involved in de…ning the …rst-stage choice
of attribute location over a large number of products, we conceive manufacturers’choice of
attribute composition in terms of selecting the relative distance between each product and
other products in the category to maximize pro…t resulting from the second-stage pricing
decision. This approach results in a stylized choice problem where manufacturers select the
entire constellation of products based on the relative distance between the location of each
product and the location of all other products in attribute space. Our resulting measure
of equilibrium product design, which responds to the willingness-to-pay of consumers at
the category level for product variety, can be interpreted as the optimal degree of attribute
clustering among manufacturer’s o¤erings in the product category.
We apply our model to a data set that combines detailed data on product attributes
with retail scanner data on sales volume, shelf prices and promotional activity for a large
number of US yogurt brands.1 Similar to Feenstra and Levinsohn (1995) and Seim (2006),
our econometric model is structural in nature as it includes components for di¤erentiated
product demand, and strategic choice of product location and pricing; however, we depart
from these studies by using a distance metric / multinomial logit (DM-MNL) approach for
the demand model.
Conditional on this spatial demand model, the …rst-order-conditions
for …rm pro…t maximization convey this spatial structure into yogurt manufacturer’s price
and product location choices.
Our major …ndings for product design and pricing in the yogurt category are as
follows.
First, in the demand-side model we …nd that consumer preferences for yogurt
attributes exhibit a positive spatial lag in the utility structure, which suggests consumers
prefer to consume yogurt products with a similar attribute composition.
That is, when
switching between one yogurt product and another, utility rises with greater proximity between the products in attribute space. Second, after accounting for the e¤ect of product
di¤erentiation on softening price competition, we …nd that yogurt manufacturers have an
incentive to locate products nearby others in attribute space. Third, we …nd that yogurt
products with the most similar attribute compositions enjoy the widest price-cost margins,
suggesting that yogurt manufacturers are able to raise prices by introducing products in the
most congested portions of the attribute space. This raises the interesting possibility that
co-locating products in attribute space can crowd out the products of rival manufacturers,
3
thereby providing a measure of local market power as …rms enjoy hegemony over consumers
on each side of a “Hotelling beach.” Our results in this sense are broadly consistent with
the observation that food manufacturers exert considerable research and development e¤ort
to identify the most popular product formulation as opposed to the most unique product
design.
The remainder of the paper is organized as follows. In the next section, we present
the econometric model used to estimate yogurt manufacturers’ strategic behavior in price
and product design.
Section 3 provides a brief overview and description of the U.S. yo-
gurt market. Section 4 describes the data and estimation methods used to implement our
econometric approach. In Section 5 we present and interpret our estimation results and provide a numerical simulation to demonstrate the role of spatial trends in consumer attribute
preferences on product design, pricing, and welfare. We conclude in Section 6 by identifying implications of our results for product design and highlighting some general directions
for further study on strategic behavior by manufacturers in the attribute composition and
pricing of product lines.
Econometric Model of Product Pricing and Design
We model demand using a random utility model of choices among di¤erentiated products
(Berry, 1994; Nevo, 2001). Within this general modeling structure, we account for consumer
heterogeneity and product di¤erentiation by directly measuring the distance between choices
made by individuals in attribute space and we estimate the resulting model of product
di¤erentiation using spatial econometric methods following Pinkse and Slade (2004) and
Slade (2004).
The supply-side of the model consists of a set of food manufacturers who choose
the degree of product di¤erentiation between a new product and existing products when
designing and pricing new products.
The …rms anticipate rivals’ optimal design choices
and choose attribute distances between products in a continuous, spatial framework. The
econometric model therefore consists of demand, pricing and product design components that
are grounded in theoretical frameworks of consumer behavior. We discuss each element of
the model in detail below and then simulate our equilibrium results in the …nal section of
the paper to highlight the importance of key parameters on predicting the price and product
design choices of food manufacturers.
Consumer Demand
When making a purchasing decision in the yogurt category, we model each consumer as
making a discrete choice of a single brand and ‡avor.
4
In our discrete choice framework,
consumers choose the one product from all alternatives that provides the highest level of
utility, where utility is assumed to be made up of the utility the consumer gets from consuming the product as well as a random term that re‡ects heterogeneity among consumer
tastes. Yogurt products in the choice set are di¤erentiated by brand, nutrient and marketing attributes, where the composition of attributes in a particular product e¤ects utility by
de…ning a product’s location relative to others. Our spatial modeling structure allows us
to account for di¤erences in the perceived location of each yogurt in attribute space, which
allows the extent to which a particular brand of yogurt is di¤erentiated from others (based
on its distance in attribute space) to enter consumer utility.
We model the distance between products in attribute space as a primitive of the consumer choice process. Slade (2004) applies a similar notion of product di¤erentiation to the
discrete choice model by assuming the price-coe¢ cient to be a function of attributes; however, a disadvantage of this approach is that a consumer’s price-response in a discrete-choice
model of demand is determined by the marginal utility of income, which is a characteristic
of the individual that cannot logically vary over choices. To circumvent this problem, we
introduce the attribute distance between products directly into the utility function in a parsimonious manner that re‡ects the role of product di¤erentiation in determining the relative
utility level available from each product.
To understand our framework of consumer demand, suppose the relative utility level
available to consumer i from choosing product j depends on how di¤erent the set of attributes
contained in the product is from the attributes contained in other products. For example, the
utility from consuming a product such as mocha Greek yogurt relative to the utility from
consuming another yogurt product would be di¤erent if all other yogurts are traditional,
vanilla ‡avors than if all other yogurts are cappuccino ‡avors.
In aggregate data, our conceptual interpretation of spatial dependent utility is that
utility of the representative consumer is context-dependent, and this need only be true for
the representative consumer. For example, consider a convenience store that o¤ers only skim
milk and whole milk and a supermarket that o¤ers 2% milk, skim milk, whole milk (4%),
and 1% milk (set goat’s milk and soy milk aside for the moment). If half the consumers in
the convenience store purchase whole milk and half purchase skim milk, then we can think of
a representative consumer in the convenience store that prefers 2% milkfat. But there is no
reason why the utility level of this representative consumer must be the same as the utility
level of a representative consumer in a supermarket where 20% of the customers purchase
skim milk, 20% purchase 1% milk, 30% purchase 2% milk and 30% purchase whole milk, even
5
though the average product purchased in the latter case is also 2% milkfat. Utility from
the choice of the representative consumer is inherently state-dependent, where the state
characterizes the “amount of product variety” as measured by the span of the attribute
space.
Our approach re‡ects a similar mechanism to that described by the address models
developed by ADT (1992) and Feenstra and Levinsohn (1995). Speci…cally, the utility from
each choice depends upon the distance between the attributes contained in that choice and
the consumer’s “ideal” set of product attributes, where the ideal product reduces, in this
case, to the product chosen by a representative consumer. We account for the utility-loss
associated with distance in by introducing a spatial autoregression parameter to measure
the extent to which di¤erentiation from other products raises (or lowers) the utility from
choosing product j according to the relative distances between products and the ideal attribute mix of a given consumer. In this way, we model the spatial state-dependence of
demand.2 The resulting estimation framework nests a general model of di¤erentiation in the
utility structure that is grounded in theory and capable of accommodating di¤erentiation in
multiple attributes.3
We begin by developing a model of mean utility and then incorporate unobserved
heterogeneity to motivate the empirical model. We follow ADT (1992) and Feenstra and
Levinsohn (1995) by adopting a non-linear utility-loss function, where mean utility from
product j falls (or rises) in the distance from all other products, measured by the distance
matrix W. Each element of W measures the distance between each pair of product, so the
element wjl measures the distance between product j and product l in the multi-attribute
space described below. Our approach di¤ers from previous studies in that we project the
utility-loss from product matches into utility space using a spatial auto-regressive framework
instead of measuring it directly in attribute space.
We write the mean utility for product j = 1; 2; :::; J in week t = 1; 2; :::; T in vector
notation (with bold notation indicating a vector) as:
=
where
is a JT
0
x+ W
(1)
p+ ;
1 vector of mean utility, x is a JT
K matrix of demand shifters (brand
indicators, discount and discount-price interaction), p is a JT
1 vector of prices, and
is a random error unobserved by the econometrician that re‡ects variables known to the
manufacturer to in‡uence price, for instance the quality of ingredients, marketing inputs, and
anticipated surpluses (shortages). The vector
6
and scalar parameters
and
are to be
estimated. The matrix W measures the e¤ect of product di¤erentiation on utility according
to attribute distance, which de…nes
The interpretation of
as a spatial autoregression parameter (Anselin, 2002).4
is the marginal impact on mean utility from the observed
choice according to the attribute distance between the product and all other products in the
choice set. This re‡ects the notion that consumers evaluate the utility attainable from each
product relative to the utility that can be attained from consuming other available products
in the choice set. We follow convention in de…ning W as a measure of inverse-distance, or
proximity, so that greater product di¤erentiation in the yogurt category reduces utility when
> 0 (i.e., utility rises with attribute proximity) and increases utility when
< 0.
Solving equation (1) for mean utility gives
= (I
where (I
W)
1
W) 1 ( 0 x
(2)
p + );
is the Leontief inverse, or spatial multiplier matrix (Anselin, 2002) de-
scribes the utility of each choice relative to the utility available from all other choices in the
product category.
We measure proximity in terms of the inverse Euclidean distance between products
in terms of nutritional and ‡avor attributes.
Inverse Euclidean distance is represented
continuously using a general spatial weight matrix, W, with typical element wjl between the
nutritional pro…le of item j and item l de…ned as
v
uM
uX
wjl = @1 + 2t (njk
0
k=1
1
nlk )2 A
1
;
(3)
where njk is the value of attribute k associated with product j and similarly for item l. For
our application to yogurt products, the set of nutrient attributes contains fat, protein, sugar,
sodium and total calories. Recall that equation (3) is de…ned it terms of inverse-distance,
so that larger values of wjl represent items that are closer together in attribute space.5 We
then de…ne the J
J spatial weight matrix that includes all of the wjl as elements and thus
describes the distance between all pairs of products that are compared in the sample. The
distance between each product and itself is normalized to 0, which in terms of equation (3)
implies that own-proximity is normalized to 1. Notice by construction that W is symmetric,
that is the distance between items j and l is the same as the distance between items l and
j; however, recall that mean utility in equation (2) re‡ects only observed heterogeneity and
not unobserved heterogeneity.
Assuming utility varies among consumers in a random way, we write utility as
7
ui =
(4)
+ "i ;
where "i is an iid random error that accounts for unobserved consumer heterogeneity. This
leads to our description of behavior - consumer i chooses item j if the utility from this choice
is greater than the utility from all other alternatives: Pr(j = 1) = Pr[
where
j
j
l
"il
"ij ]
is the jth element of .
The probability that consumer i chooses product j over all others is governed by the
distribution of "ij . As in the non-spatial case, if "ij is extreme value distributed, then the
random utility model in (4) implies a market share expression for item j given by:
Sj = exp( j )=(1 +
J
X
exp( l ));
(5)
l=1
where Sj is the volume-share of product j. Thus, our model is closely-related to the distancemetric multinomial logit (DM-MNL) model of discrete choice among di¤erentiated products
developed by Slade (2004). Given the evident non-linearity of the system, we follow Berry
(1994) and Cardell (1997) and linearize equation (5) by taking logs of both sides and write
the resulting expression in vector notation as
ln S
where
ln S0 = (I
W) 1 ( 0 x
is the error term described in equation (3).
p + );
(6)
By explicitly recognizing the extent
of di¤erentiation among the products in our yogurt sample, the resulting demand model is
more ‡exible than simple discrete-choice models in that the cross-price elasticities of demand
are not restricted to be equal for all products.
Our approach is similar to Slade (2004) and Pinkse and Slade (2004) in that we
explicitly incorporate a distance-metric component in the demand model; however, attribute
distance enters in a structural way in equation (6) through the utility function.
Given that yogurt manufacturers price and locate products to maximize pro…ts for
a given demand structure, the parameters from the demand system condition the pricing
and positioning (attribute) decisions made by food manufacturers. When a …rm considers
introducing a new yogurt product, the optimal product design takes into account the set
of consumers who prefer a given combination of attributes, for instance the demand for
vanilla-‡avored yogurt with standard fat, sugar and sodium content relative to the demand
for low-sodium, non-fat, key lime-‡avored yogurt. The manufacturer can produce a highly
di¤erentiated line of yogurt products or “cluster” yogurt products more closely around a
8
popular attribute composition, and the strategy the …rm pursues in equilibrium depends
on the expected price-cost margins and sales volumes that can be attained under various
product compositions. We derive the equilibrium choice of price and location in attribute
space in the next section.
Pricing and Product Location
Now consider the supply side of the model.
Each manufacturer sells multiple brands
and ‡avors j 2 M and engages in Bertrand-Nash competition with rivals in prices and
product location. To simplify the interpretation of our model, we assume cooperative vertical
relationships exist between manufacturers and retailers, so that manufacturers’ choice of
optimal price and location is conditioned directly by retail demand conditions.6
Following Thomadsen (2007) and Stavins (1997), manufacturers play a two-stage
game in selecting attribute locations and prices for their products. Firms choose location
in the …rst stage, and then compete in prices in a second stage.
We solve the game by
backward induction, solving the pricing sub-game …rst and then the location game.7
When designing a new product, manufacturers must choose a speci…c location for
the product. In the product-design literature, Stavins (1997), and Draganska, Mazzeo and
Seim (2009) take the direct approach of de…ning the location of all products in attribute
space, much like one would consider the position of individual retailers in geographic space
(Thomadsen, 2007); however, such an approach is only practical when the attribute space
is highly simpli…ed. In our model, we accommodate the multidimensional attribute space
of yogurt products by looking at the entire constellation of products in terms of the relative di¤erence in attribute composition between individual products in the category. This
provides a measure of the degree of product di¤erentiation in the category that is embodied
implicitly in a scaled, perceptual, Euclidean-distance sense of the relationship between all
products sold in the category. Put di¤erently, product designers span the attribute space
with an equilibrium composition of products, and the resulting pricing and market share
implications of locating products at particular locations in attribute space depend on the
entire composition of the product line in terms of the relative distance between products in
equilibrium.
It is helpful to consider the analogy between product design and the choice of geographic location. When retailers contemplate store location, they typically apply algorithms
that involve drawing concentric circles of one mile and 1.5 miles in radius and then analyze
the trading area therein (Berman and Evans, 2009). Selecting a location at the center of
this two-dimensional circle amounts to choosing an average distance between the store and
9
all other stores that lie within the two circles.8 We adopt a similar heuristic to simplify
the description of equilibrium attribute location in multi-dimensional space by measuring
market share and prices in terms of the average distance between a product and all other
products in the category.
Each element of the spatial weight matrix, W, above describes how far each product
j lies from each other product l in a multi-dimensional attribute space.
To assume that
the manufacturer chooses each row-element of this matrix uniquely is neither tractable nor
interesting, and we consequently follow Feenstra and Levinsohn (1995) and Stavins (1995,
1997) in assuming manufacturers consider the pro…t implications of locating products at
di¤erent average-distances from all other products using an arithmetic-mean de…nition of
distance.9 To operationalize our measure, we de…ne a J
J matrix b with each element
[bjk ] = 1=J and post-multiply the spatial weight matrix to create a diagonal matrix of
average distances, w = Wb I, with typical element wj where
element multiplication and I is a J
indicates element-by-
J identity matrix.
We write the pro…t maximization problem for a yogurt manufacturer as
j
= max
pj ;wj
X
Q(pj
cj )Sj (wj )
Fj
(7)
g(wj );
j2J
where cj is the marginal cost of production, Q is the size of the total market, Fj is the …xed
cost of manufacturer j, and g(wj ) is a cost function that re‡ects the cost of producing items
that are either similar to, or di¤erentiated from, others in the market and is assumed to be
separable from cj .10 We specify the marginal cost of production as arising from a normalized
P
quadratic cost function, Cj , so that marginal cost is cj = @Cj =@qj = 'j0 + 'k vk ; where vk
k
are input prices in the manufacturing process and qj is the quantity of product j purchased.
Finally, for expedience, we subsume both production and marketing inputs, which consist
of the price of class III milk, sweeteners, packaging, and dairy-product manufacturing labor,
utilities and transportation costs, into the marginal cost function.
The …rst order necessary condition for the …rm’s optimal choice of price for product
j is
@ j
= QSj (wj ) + Q(pj
@pj
cj )
@Sj (wj ) X
+
Q(pl
@pj
l6=j
cl )
@Sl (wl )
= 0:
@pj
(8)
Solving equation (8) for the optimal price-cost markup provides an expression for the rela-
10
tionship between the margin and degree of di¤erentiation for product j; namely,
!
1
X
@Sj (wj )
@Sl (wl )
(pj cj ) =
Sj (wj ) +
:
(pl cl )
@pj
@pj
l6=j
(9)
Equation (9) allows us to form hypotheses on the expected e¤ect of greater distance
among products on pricing behavior. To see this more clearly, rewrite equation (9) in matrix
notation and de…ne Sp as the logit share-derivative matrix in prices so that the …rst-ordercondition for all products becomes:
p
c=
(Wb I))(Sp 1 )S =
(I
(Sp 1 )S+ (Wb I)(Sp 1 )S:
(10)
The second expression on the right decomposes the markup term into the conventional
markup
(Sp 1 )S and the part due to spatial di¤erentiation
(Wb I)(Sp 1 )S .
Notice that the markup term in equation (10) di¤ers from the markup in the nondi¤erentiated case according to the value of the spatial auto-regressive parameter,
.
If
> 0, consumers prefer products that are more like existing products in the market, so
that rival …rms can be expected to raise prices if the manufacturer selects a more similar
composition of products.
The collusive or minimum di¤erentiation e¤ect of ADT (1992)
dominates product design decisions, leading …rms to increase wj , thereby gravitating products toward the center of the attribute space to obtain local monopoly power over consumers
who prefer the attribute composition of their products and higher margins. Conversely, if
< 0, consumers prefer products that are more di¤erentiated, and a maximum di¤erentiation (d’Aspremont, Gabszewicz and Thisse, 1979) e¤ect dominates product design decisions,
leading …rms to reduce wj to increase margins. If utility does indeed rise in the extent to
which a product is di¤erentiated from others, then the softening price competition outcome
prevails and …rms reduce margins on mass-market products in order to compensate for low
margins through high volume.
In this study, we test which e¤ect prevails in a sample of
di¤erentiated yogurt brands.
Following Villas-Boas and Zhao (2005), Draganska and Klapper (2007), and others,
we recognize that manufacturers are unlikely to adhere to the Bertrand-Nash solution concept
exactly. Therefore, we parameterize deviations from the maintained solution by adding a
parameter, , to the markup term in (10) that measures any deviation from the hypothesized
Bertrand-Nash outcome:
p
c=
(I
(Wb I))(Sp 1 )S =
11
( Sp 1 )S+ (Wb I)(Sp 1 )S:
(11)
In empirical studies of market power,
is commonly referred to as a conduct parameter.
The conduct parameter measures the exercise of market power either below or above that
implied by the elasticity of product demand.11 Speci…cally, a value of
behavior consistent with Bertrand-Nash rivalry, while
competitive than Bertrand, and
= 1 implies pricing
< 1 implies pricing that is more
> 1 suggests behavior that is less competitive.
In the pricing model, two parameters ( and ) describe possible sources of valueadded for new yogurts.
To asses the pricing power of a yogurt at a particular point in
attribute space we test the null hypothesis H0 :
= 0. If this parameter is not signi…cantly
di¤erent from zero, then the …rm sets competitive prices for attributes; however, if
>0
the manufacturer earns positive margins between the retail price and production costs, so
the new product is value-adding. If
> 1, the yogurt adds more value than one priced in
a manner consistent with Bertrand-Nash rivalry, and if
< 1, then it is more competitive
than Bertrand.
We now turn to the …rst-stage problem of choosing a product’s location in attribute
space. This problem is conceptually more di¢ cult than price choices, because the decision
is potentially multi-valued. The typical strategy among market researchers is to reduce this
problem to a tractable form by either assuming a simple one-dimensional location problem
(Seim, 2006) or by assuming consumers always value more of each attribute (Horsky and
Nelson, 1992), where the problem is reduced by the later approach to one of …nding how to
incorporate the most of each attribute at the lowest cost. Our spatial framework de…ned over
relative distances is a relatively parsimonious solution. Rather than choosing the speci…c
attributes of each product, we follow Stavins (1995, 1997) in modeling …rms as choosing the
relative distance between each product and all other products in the category.
As in the pricing decision, we assume the location decision is a Nash equilibrium
among manufacturers, in the average distance of their product from all others. For simplicity,
we again assume one product per manufacturer, but it is a simple matter to accommodate
multiple-item production through the addition of an “ownership matrix”(Nevo, 2001). We
do so in the empirical model below. Using scalar notation for clarity, the …rst order condition
with respect to distance is given by
@ j
= Q(pj
@ wj
where g(wj ) =
gw =
1 wj .
0
cj )
@Sj (wj ) X
+
Q(pl
@ wj
l6=j
cl )
@Sl (wj )
@ wj
@g(wj )
= 0:
@ wj
(12)
+ 1=2 1 wj2 is the cost of di¤erentiation function, so the marginal cost is
Again focusing on the solution for product j, the share derivatives are given by
12
@Sj (wj )
= (1
@ wj
wj ) 2 (Sj (1
(13)
Sj ));
and:
@Sl (wj )
= (1
@ wj
wj ) 2 (Sj Sl );
(14)
for the cross-location term. Substituting these expressions into (12) and simplifying yields
the estimating equation:
Q(pj
cj )Sj (1
Sj ) + Q
X
(pl
cl )Sj Sl = (1= )( 1 wj )(1
wj )2 ;
(15)
l6=j
which is then estimated along with equation (11) after substituting in the share expressions,
adding an error term, allowing for a set of brand-speci…c indicator variables to identify the
cost parameters,
j0 ,
and de…ning the marginal cost function, cl ; as a linear function of input
prices as de…ned above.
Our model is therefore completely speci…ed by equations (8), (11), and (15), which we
estimate simultaneously to incorporate the cross-equation restrictions implied by the spatial
demand model. We compare this fully spatial model to a non-spatial alternative to assess
the relative …t of each model and discuss the pricing implications of ignoring the endogeneity
of product location.
Several testable hypotheses on the relationship between pricing and product location
arise from equation (15). Applying the implicit function theorem to (15), we …nd that the
conventional result from Hotelling (1929), namely that the optimal distance from other products rises in the price of product j is a special case in this model. Namely, @ wj =@pj > 0 holds
only under the condition that
< 1=wj ; which is immediately satis…ed if
prefer di¤erentiated products), or if
< 0 (consumers
> 0 and products are su¢ ciently highly di¤erentiated
(i.e., wj is su¢ ciently large).12 Note that this hypothesis is qualitatively similar to Thomadsen (2007), although our framework is more general. We test these hypotheses using the
spatial empirical model described below. We then simulate the resulting equilibrium to show
in a more concrete way the e¤ect of varying
on equilibrium price and location choices.
Data Description
Our data describe weekly sales of all adult brands of yogurt in 18 U.S. markets during
2005 from the two major national manufacturers: Dannon and Yoplait.
The data are
from IRI and are widely available to academic researchers (Bronnenberg, Kruger and Mela,
2008). As a category, yogurt represents an excellent opportunity to explain strategic product
13
location. First, the two major manufacturers constitute a near duopoly in most markets so
each must necessarily consider the position of rival products in designing their own. Private
labels represent a considerable share of many markets (see table 1), but retailers tend to
locate store brands near to existing national brands in attribute space (Mills, 1995) so do
not represent unique spatial in‡uences. Moreover, detailed nutritional data are not available
for the private labels used during the sample period, so form part of the outside option, which
includes all other brands not represented in our model. For example, other, relatively minor
brands such as Stoney…eld Farms and YoFarm are also assumed to represent choices in the
outside option. Second, yogurts are di¤erentiated in a number of dimensions, from brand
identity and nutritional pro…le to ‡avor and package size. Therefore, we are con…dent that
we observe su¢ cient variation among the items in our data set to identify the incentive to
locate at di¤erent points in attribute space, and to set prices accordingly.
Third, yogurt
input prices also exhibit signi…cant variation over time, input proportions vary according to
the brand and product type, and retailers in di¤erent geographic markets follow markedly
di¤erent pricing strategies so there is easily enough exogenous variation in the market to
identify demand.
The data presented in table 1, which summarizes the brand / ‡avor data for the
top 10 yogurt brands in our data set for …ve representative markets, documents the extent
of inter-brand and inter-market price variability. The contribution to the variability of not
only prices, but volume sales and promotion activity are documented in table 2. Clearly,
variation in product attributes explains much of the di¤erence in promotion activity between
products, but market-driven variation in demand explains more of the variation in volume
sales.
[table 1 in here]
[table 2 in here]
In any multi-dimensional, distance-based model, the units of measure for each element of the distance calculation are clearly important. For example, we measure the protein
content of yogurt in terms of grams per ounce and energy content in calories per 100 grams,
so the relative weight of each attribute in the distance metric will re‡ect the absolute value
of each measure. We need a method of determining weights for each attribute that re‡ect
their underlying economic importance. For this purpose, we use a hedonic pricing model
(Rosen, 1974) in which the market price of a product is interpreted as a weighted sum of the
marginal values of each attribute. We estimate the marginal value, or willingness-to-pay,
for each attribute by estimating a linear-hedonic regression model over all markets and spec-
14
ifying price per ounce as a function of yogurt attributes: total calories per ounce, grams of
protein, fat and sugars per ounce, milligrams of sodium per ounce, and a set of brand-speci…c
dummy variables. The units of measure are thus standardized in monetary terms, meaning
that distance is expressed in terms of dollars per 100 grams of yogurt. We estimate this
model with a random-e¤ects approach using simulated maximum likelihood. Measured this
way, our yogurt brands are arrayed across a relatively large attribute space. For example,
the fourth brand, Dannon La Creme, is only $0:76 away from the other brands, on average,
while Yoplait Thick & Creamy is fully $1.66 apart from the others.
Estimation Method
We estimate the entire structural model in one stage because the spatial lag parameter
appears in all three equations. We consider both prices and product attributes to be endogenous and accordingly estimate the entire system using generalized method of moments
(GMM) by applying an identi…cation strategy similar to Pinkse, Slade and Brett (2002) and
Kelejian and Prucha (1998, 1999).13
For the demand model, we construct two sets of instruments, one for prices and
another for product attributes. The …rst set consists of yogurt manufacturing prices (raw
milk, sweetener, plastic for packaging, milk manufacturing wages, transport costs and utilities) interacted with individual brand indicator variables. This is a standard approach in
estimating structural models of di¤erentiated product demand (Berto Villas Boas, 2007) in
which retail prices are likely to be endogenous.
Input prices vary over time, and input-
contents vary by brand, so the interaction between the two exhibits su¢ cient variation to
identify the demand parameters. Further, because the demand model includes brand …xede¤ects, the instruments will not be correlated with the unobservable errors for each demand
equation because the brand-e¤ects have been removed (Berto Villas-Boas, 2007).
Our second set of demand-instruments accounts for the attributes of brands and
‡avors sold in other markets. Speci…cally, we apply spatially-weighted averages of the nutritional attributes of all other products in other markets, which are calculated by multiplying
each variable by the inverse Euclidean distance weight matrix described above. This procedure is used by Pinkse and Slade (2004) and Slade (2004) and is also suggested by Kelejian
and Prucha (1998) who include non-linear spatial-interaction terms in developing their spatial GMM estimator. Weighted average yogurt attributes from other brands and markets
are likely to be valid instruments because the remaining unobservables in the demand equation include such things as shelf-placement, in-store advertising and display activity – all
of which are independent of either pricing or design decisions. Moreover, rival product at-
15
tributes vary due to di¤erences in the portfolio of products sold by retailers in each market
(Berry, Levinsohn and Pakes, 1995; Draganska, Mazzeo and Seim, 2009). Regressing this
set of instruments – the weighted attributes of other yogurts and the input-price / brand
interactions – on the endogenous prices produces an F-statistic of 971.241.
Each of the
spatial-interaction terms are highly signi…cant so, combined with this F-statistic, we are
con…dent that our instruments are not “weak”in the sense of Staiger and Stock (1997).14
In the pricing and product design equations, we seek a set of instruments that are
correlated with share and location measures that appear on the right-side of those equations,
but are mean independent of the speci…c price and location of each product. For this purpose,
we again use two sets of instruments: one consistent with well-accepted practices taken in
the extant literature and the other exploiting the spatial nature of the model and data.
Intuitively, we seek a set of instruments that shift demand and, hence, markup terms in a way
that is exogenous to the pricing and location decisions of the two manufacturers considered
here. Factors that are pre-determined to the pricing and design decisions in a panel data
set, and vary both over time and across markets, include demographic measures unique to
each market.
Income, age, education and racial composition are all valid instruments in
this regard. We interact these variables with binary brand indicators to separately measure
the variation in demand for each brand.
Our second set of supply-instruments includes spatially-weighted values of demand
shifters in other markets. While others use the attributes of rival products as instruments,
the attributes of rival products are not valid instruments in our framework of endogenous
product design. Consequently, we rely only on exogenous variation in demand and supply
to identify the conduct parameters in our model. The summary statistics in Tables 1 and 2
document the inherent time-series and cross sectional variation in both the observed retail
price and share data. This variation is more than su¢ cient to identify di¤erences in pricing
and design behavior among manufacturers.
F-statistics from regressing average distance
and price on this set of instruments are 145.93 and 92.01, respectively, suggesting that these
instruments are suitable for the purpose at hand.
In each of the demand, pricing and location models we also test for spatial autocorrelation in the data. Analogous to serial correlation in time-series data, if spatial autocorrelation is present and not explicitly taken into account, the resulting parameter estimates
remain unbiased and consistent, but are ine¢ cient. To the extent that neighboring product characteristics are important omitted variables, we expect some bias in the non-spatial
estimates. LeSage (1998) presents a number of tests for spatial autocorrelation, the most
16
straightforward of which involves a Wald test for the signi…cance of the spatial autocorrelation parameter, . Because a non-spatial model is nested within a spatial alternative, we
also use a quasi-likelihood ratio (QLR) test to determine whether a spatial speci…cation is
necessary.
Results and Discussion
In this section, we …rst present the results from a series of speci…cation tests for the
spatial model, relative to non-spatial alternatives, and then tests of the central hypotheses
of the paper. We begin with the demand model and then move to the pricing and spatial
location models, which are the focus of this study.
Although the demand, pricing and
location equations are estimated as a system, we present the demand estimates in tables 3
and 4 and the pricing and location estimates in table 5. The results from the simulation
exercise are shown in table 6.
In table 3, we present the results for three di¤erent demand models: (1) a nonspatial model estimated with instrumental variables, (2) a spatial model estimated with
least squares, and (3) a spatial model estimated with instrumental variables.15 Both IV
models are estimated with GMM, but we include the non-IV estimates in this table in order
to show the extent of bias present if endogeneity is not properly accounted for. Comparing
the spatial and non-spatial models using a quasi-likelihood ratio test, we …nd a chi-square
test statistic value of 582.2, rejecting the restricted, non-spatial model in favor of the spatial
alternative. Similarly, applying t-test to the spatial lag coe¢ cient also indicates rejection of
the null hypothesis that there is no spatial autocorrelation in the data. The implication of
this …nding is that the demand for a product at one location in attribute space depends on
the demand for products at other locations. Because the di¤erence in location is measured as
inverse Euclidean distance, a higher value indicates greater proximity between products. A
positive spatial lag parameter therefore suggests that two yogurt products that are located
near each other have reinforcing, or complementary e¤ects on demand.
Consumers who
prefer a certain product design are more likely to try similar products than they are entirely
dissimilar ones, much like a BMW driver is more likely to test drive an Audi convertable
than a minivan. Our …nding of a positive e¤ect of proximity suggests that the Hotelling’s
minimum di¤erentiation result is an important element of new product design in the yogurt
category.
[table 3 in here]
The extent of the omitted-variables bias inherent in the non-spatial estimator is also
apparent from the results in Table 3. While the average own-price elasticity implied by the
17
spatial estimates is -7.043, the same measure for the non-spatial estimates is nearly three
times as large. Clearly, inferences made regarding the price sensitivity of brands from the
non-spatial model will lead to dramatically incorrect pricing decisions.
Spatial estimates
of promotion sensitivity, however, are stronger than the non-spatial alternatives. Finding
that demand shifts inward during promotional periods is likely due to the fact that we
control for both shift- and rotation of the demand curve. Accounting for these interaction
e¤ects, we …nd that demand rotates clockwise, or becomes more inelastic while promoted,
a …nding that is consistent with previous research in the retail price-promotion literature
(Chintagunta, 2002).
One of the primary advantages of estimating a DM-MNL model of demand is that
we avoid the IIA property inherent in the simple logit model in a straightforward, intuitive
way (Richards, Hamilton and Patterson 2010). With this approach, we allow cross-product
substitution e¤ects to depend on the relative distance in attribute space directly, rather
than through correlation with unobserved components of consumer utility as in a mixed
logit model (see, e.g. Nevo, 2001). The elasticity matrix in Table 4 illustrates the ‡exibility
of the DM-MNL model.16 In a simple logit model, the cross-product elasticities would be the
same in each column, but with the DM-MNL approach, they depend on the relative distance
in attribute space.
Low-fat yogurts, in general, substitute more readily for other low-fat
yogurts, and less so with more indulgent brands. This feature is critically important in the
optimal price and attribute location choice decision considered next.
[table 4 in here]
We estimate the demand, pricing and location models jointly to recognize their
fundamental interdependence, particularly in a model of strategic interaction. We also allow
for a departure from the maintained Bertrand-Nash assumption in order to allow for market
power e¤ects to vary by distance. The results from estimating the …nal two components of
the joint model appear in table 5 below. In terms of the pricing model, we compare two
alternative models to our maintained spatial / GMM: (1) one that ignores the endogeneity of
the markup and di¤erentiation terms (OLS), and (2) another that ignores the spatial element
of demand and rivalry in the pricing equation. In terms of the GMM / OLS comparison,
we …nd that the results are not qualitatively di¤erent between models, but the extent of the
bias in the OLS estimates is apparent.
Table 5 compares our spatial and non-spatial parameter estimates. Notice from the
entries in Table 5, it is clear that the non-spatial model does not …t the data as well as
the spatial model, although it does produce similar brand-level margin estimates. The key
18
di¤erence between the two formulations is in the estimated departure from Bertrand-Nash
pricing. In the maintained spatial model, our estimate is
= 1:4566, relative to
= 1:5337
in the non-spatial model.
[table 5 in here]
Our estimates of
are obtained by controlling for consumer preference for proximity.
By including a component of the markup that is due speci…cally to product di¤erentiation, we
are better able to isolate the extent of “unilateral”market power. Failing to account for the
e¤ect of spatial di¤erentiation on pricing overstates the degree of unilateral market power by
nearly 50%.17 Still, based on the spatial estimates it is clear that yogurt manufacturers enjoy
a signi…cant premium over both competitive pricing ( = 0), and that implied by BertrandNash equilibrium ( = 1). Given the small premium attached to proximity ( = 0:0073), it
is apparent that most of the margin earned by yogurt manufacturers derives from unilateral
sources of market power, for instance due to advertising e¤ort, brand loyalty, access to
distribution, or implicit collusion.
Estimated simultaneously with the pricing model, the location model allows us to
estimate the cost of di¤erentiation and the equilibrium extent to which each brand is differentiated from all others. Notice from the entries in Table 5 that the di¤erentiation-cost
function is convex.18 Taking into account consumers’preference for proximity, and the margins earned by each product, the estimates in this table therefore reveal the relative location
of products (on average) in the category. Comparing the results from the pricing and location models in Table 5, there is a close correspondence between the average proximity of
each product and the margin earned by each product (correlation = 0.710). For example,
Dannon Frusion (-0.0210), Dannon Sprinklins (-0.0164) and Yoplait Whips (-0.0124) are
among the least di¤erentiated yogurts. From table 5, the equilibrium margin for Frusion
is 3.2661 cents per oz, Sprinklins is 3.2905 cents and 3.2931 cents for Whips – the highest
margins observed for any three products. On the other hand, Dannon Light n’Fit, Dannon
Fat Free and Yoplait Light are among the most highly di¤erentiated (because of their low fat
content), and earn margins that are below average. While the correlation among brands is
not perfect, they do match closely with our hypothesis. Namely, because consumers prefer
yogurts that are more like others, manufacturers earn higher margins by locating near the
“center” of our multi-dimensional attribute space and implicitly colluding on prices in this
pro…table market segment. Because each manufacturer has market power over its segment
of the market, manufacturers do not have strong incentives to compete on price with their
rivals. One reason we observe products that are di¤erentiated may be because the mass of
19
consumers is always moving. Di¤erentiation may be costly, so experimentation by manufacturers results in lower pro…ts and provides pressure to gravitate product compositions back
to the center.
The practical importance of our …ndings can be illustrated by simulating comparative static e¤ects of varying
on price, location and welfare. We calculated …tted values
for the optimal pricing and location equations under a range of
0.025 increments. Our choice of this range of
from -0.25 to +0.25 in
values spans our empirical estimate, and
encompasses values likely to be estimated for other products. Table 6 shows simulated price
and location values for an hypothetical new product under
values that range from -0.25,
which is signi…cantly below our estimated value, and +0.25, which is signi…cantly higher.
The entries in Table 6 clearly show that when
> 0 (our estimated case), there is a positive
relationship between price and proximity. That is, the closer a new product is to existing
products, the higher the equilibrium price. Conversely, when
< 0 the entries in Table 6
indicate a negative relationship between proximity and price, providing manufacturers with
an incentive to market highly di¤erentiated products in the category.
[table 6 in here]
Notice that the relationship between prices and location is non-monotonic.
For
all values of , prices decrease with increases in ; however, products are located at greater
distances in attribute space for increases in
when
closely together in attribute space for increases in
> 0, whereas products are located more
when
< 0. Thus, our …ndings indicate
a positive relationship between equilibrium prices and the degree of product di¤erentiation
when
< 0 and a negative relationship between equilibrium prices and the degree of product
di¤erentiation when
> 0.
We then calculated the implied values for consumer surplus relative to the estimated
case, and change in pro…t earned by …rms. The change in consumer surplus is calculated
using the mean utility expression in (1) according to:
E(CS) =
where
value of
0
j
1
"
ln
J
X
!
exp( 1j )
j=1
is the initial value of mean utility, and
1
j
ln
J
X
j=1
!#
exp( 0j )
(16)
is the new value that results when the
is changed (Train 2003). Producer surplus is simply the change in pro…t relative
to the base case. The third and fourth columns in each panel of Table 5 show that as
consumers’preference for di¤erentiated products becomes stronger ( < 0), prices and the
degree of di¤erentiation rise, so consumer surplus falls and pro…t rises. In this case, consumer
20
surplus falls at a greater rate than pro…t rises, so the net e¤ect on welfare is negative. The
opposite occurs when consumers have a preference for similarity ( > 0). Namely, as the
preference for similarity rises, …rms earn lower price for products that are more di¤erentiated.
Consumer surplus rises, and pro…t falls at a lower rate, resulting in a net positive e¤ect on
welfare. Note, however, that the net increase in welfare is smaller in this case for similar
changes in ;suggesting that product di¤erentiation is excessive in both cases, but is of lesser
consequence when consumers prefer products that are more like each other. Recall that this
is an equilibrium result: When consumers prefer di¤erentiated products, …rms respond with
an excessive amount of di¤erentiation from society’s perspective, but when consumers prefer
similar products, society is less concerned with …rms’behavior.
Conclusions and Implications
Most of the existing research that seeks to resolve the joint pricing and design problem
faced by manufacturers of di¤erentiated products …nds that di¤erentiation tends to soften
price competition, so …rms tend to di¤erentiate their products from one another.
Never-
theless, casual observation of products in many categories of consumer goods reveals that
the products tend to fall into a very small part of a potentially very large attribute space,
and yet manufacturers remain pro…table. In this study, we consider the pricing and product location problem faced by yogurt manufacturers and contribute some new results to the
“minimum di¤erentiation versus maximum di¤erentiation”debate.
Our approach is explicitly spatial. We model the demand for yogurt using a distance
metric - multinomial logit (DM - MNL) model in which the utility obtained from one product
depends on its distance from all others.
If utility rises in the proximity of each product
to all others, then we expect a minimum-di¤erentiation result to obtain, but if utility rises
in the level of di¤erentiation, then we expect the opposite.
To determine which of these
outcomes is consistent with …rm behavior in the yogurt industry, we estimate a simultaneous,
spatial model of yogurt pricing and location within a multi-dimensional attribute space.
Equations describing equilibrium pricing and design decisions are derived from the …rstorder conditions for pro…t maximization under a Bertrand-Nash behavioral assumption in
both prices and product location. We estimate the pricing and location models using GMM
with an appropriate instrumentation strategy designed to account for the endogeneity of
market prices and attribute choices.
The estimation results show consumers have a small, but statistically signi…cant
preference for proximity in the attribute composition of yogurt. Our results are consistent
with …rms earning price premiums for locating products near other products in the attribute
21
space to de…ne local monopolies among consumers who prefer a particular set of attributes.
This minimum di¤erentiation outcome explains why we observe so many yogurts that are
fundamentally similar to others in attribute composition. Greater product di¤erentiation
in the yogurt category does not appear to soften price competition, perhaps because doing
so would cause manufacturers to venture into attribute sets that do not appeal to many
consumers.
Our numerical simulation reveals that product di¤erentiation increases equilibrium
prices in some cases ( < 0) and not in others (
0). This …nding may help explain why
food manufacturers proliferate products in some categories but not in others. Our results
indicate that excessive product di¤erentiation causes welfare losses whether consumers prefer
products that are di¤erent, or whether they are similar, but welfare losses are smaller when
consumers have a preference for similarity. Although advertising is not the focus of this
paper, our results suggest another reason for the oft-cited result that advertising is socially
excessive (Dixit and Norman 1978). Namely when consumers prefer similarity, attempting
to convince them otherwise can only be wasteful.
A potentially fruitful direction for future research in this area is to consider other
categories that involve greater levels of product di¤erentiated than yogurt.
Ice cream,
beer and wine are examples of categories that tend to exhibit a high degree of product
di¤erentiation and it would be interesting to verify whether consumer demand in these
categories is characterized by negative spatial autocorrelation among attributes. It would
also be interesting to examine product categories that are served by a greater number of
manufacturers, as a large number of manufacturers may tend to crowd the core of the
attribute space, rewarding attempts to move towards more di¤erentiated product lines. A
logical extension of our work is to apply our method to problems such as horizontal merger
among manufacturers of di¤erentiated food products.
Notes
1. Our data describe speci…c ‡avor and package variants for a number of brands. To
avoid confusion, speci…c variants are referred to generically as products throughout.
2. Train (2003) makes an equivalent distinction between state dependence in demand,
where mean utility can indeed depend on observables from other periods such as lagged
dependent variables, lagged attributes (Erdem 1996) or future prices (Adamowicz 1994)
without violating the independence assumption of the logit model.
Likewise, we are not
saying that tastes change, but rather that they are state-dependent in a spatial sense.
3. Another option is to model the demand for attributes in a mixed-logit framework as
22
in Berry, Levinsohn and Pakes (BLP 1995). However, locational choice by …rms that face
demand for individual attribute levels in the BLP model is intractable for all but the simplest
models (Seim et al 2006).
4. Note that W is JxJ and does not vary by T , so we multiply W by
each period to
arrive at the JT x1 speci…cation of :
5. Inverse-distance is an abstract yet convenient de…nition of the relationship between
products, as products at the same location have an inverse-distance of 1, while the value for
more dissimilar products tends toward zero. Pinkse and Slade (2004) …nd little di¤erence
in the results generated by alternative distance metrics.
6. While introducing strategic retailers would be an interesting exercise, doing so adds
little to the primary question addressed here on how manufacturers price and locate differentiated products. Strategic retailer behavior may be relevant if retailers use attributedi¤erences between private labels and national brands to enhance their bargaining power
over manufacturers, and we implicitly suppress such behavior.
7. This assumption is not strictly necessary for an equilibrium to exist as Anderson,
de Palma and Thisse (1992) show that an equilibrium to a game of simultaneous choices
exists when products are di¤erentiated. Caplin and Nalebu¤ (2001) outline the conditions
necessary for an equilibrium in pure strategies for multi-product manufacturers.
8. Two circles are used to approximate the intensive and extensive margins of a store’s
expected market.
9. Feenstra and Levinsohn (1995) use a harmonic-mean de…nition of distance, while
Stavins (1997) uses an arithmetic mean.
As Stavins (1997) argues, harmonic means are
problematic for identical products.
10. We have no priors on the curvature of g(wj ) because if it proves to be more pro…table
to di¤erentiate new products, on the margin, then g should be convex in distance, but if
…rms have an incentive to make products that are more similar to others, then g should be
convex in proximity. There are examples that reveal both in industry –…rms often include
expensive ingredients as a means of di¤erentiating their products from others, but privatelabel manufacturers …nd it very costly to mimic national brand manufacturers. We leave the
sign of
1
as an empirical question.
11. The conduct parameter is identi…ed by demand curve rotations caused by exogenous
factors such as manufacturer promotions passed through by retailers.
12. Note that this condition applies only in the simpler case of linear di¤erentiation costs.
The sign of the derivative is indeterminate with more general, quadratic di¤erentiation costs.
23
13. All data and estimation code used to estimate the GMM model are posted on the
Journal website. The GMM estimates presented below were obtained using least-squares
estimates for starting values, and the estimates proved somewhat sensitive to the choice of
starting values.
14. Detailed …rst-stage instrumental variables regression results are available in an online
appendix on the Journal website.
15. Individual nutrient values were also included, but proved highly collinear with the
distance variable so were excluded from the …nal version.
16. The precise form of the own- and cross-price elasticities are available in an online
appenix on the Journal website.
17. Corts (1999) arguest that estimates of such conduct parameters are biased if they are
far di¤erent from the null ( = 0). We acknowledge this fact, but have no way of comparing
the estimated conduct parameter against a true value.
18. Recall that wj measures proximity, so rising costs of di¤erentiation implies gw < 0:
j
24
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28
Table 1: Average Prices and Market Share, by Brand and Market
Brand
1
2
3
4
5
6
7
8
9
10
11
1
2
3
4
5
6
7
8
9
10
11
Market 1
Price
Share
Mean Std Dev Mean Std Dev
0.093
0.007 0.024
0.003
0.109
0.014 0.005
0.004
0.119
0.013 0.009
0.004
0.136
0.006 0.013
0.003
0.107
0.012 0.017
0.010
0.153
0.010 0.006
0.001
0.110
0.008 0.012
0.003
0.110
0.011 0.013
0.006
0.110
0.008 0.012
0.003
0.164
0.011 0.007
0.002
0.121
0.010 0.401
0.028
Market 2
Price
Share
Mean Std Dev Mean Std Dev
0.085
0.005 0.039
0.004
0.097
0.008 0.015
0.004
0.125
0.015 0.007
0.003
0.132
0.011 0.007
0.002
0.102
0.013 0.023
0.011
0.149
0.009 0.005
0.001
0.103
0.008 0.018
0.008
0.100
0.008 0.015
0.006
0.104
0.008 0.012
0.002
0.151
0.013 0.005
0.002
0.115
0.010 0.164
0.024
Market 3
Market 4
Mean
0.077
0.086
0.114
0.117
0.098
0.132
0.093
0.092
0.094
0.136
0.104
Price
Std Dev
0.001
0.009
0.009
0.009
0.013
0.006
0.004
0.003
0.005
0.007
0.007
Share
Mean Std Dev
0.066
0.005
0.008
0.006
0.010
0.004
0.014
0.008
0.015
0.014
0.008
0.002
0.022
0.011
0.020
0.008
0.010
0.001
0.007
0.003
0.126
0.013
Market 5
1
2
3
4
5
6
7
8
9
10
11
Price
Mean Std Dev
0.100
0.004
0.110
0.016
0.137
0.026
0.137
0.011
0.115
0.017
0.178
0.006
0.116
0.014
0.114
0.011
0.115
0.017
0.173
0.020
0.130
0.014
Share
Mean Std Dev
0.011
0.002
0.004
0.003
0.008
0.005
0.012
0.003
0.012
0.007
0.004
0.001
0.017
0.009
0.017
0.008
0.008
0.002
0.006
0.002
0.305
0.025
29
Mean
0.086
0.096
0.131
0.131
0.100
0.159
0.101
0.102
0.102
0.152
0.116
Price
Std Dev
0.003
0.010
0.013
0.003
0.014
0.001
0.007
0.009
0.005
0.010
0.007
Share
Mean Std Dev
0.060
0.010
0.012
0.005
0.004
0.003
0.012
0.003
0.019
0.015
0.005
0.001
0.023
0.009
0.013
0.008
0.014
0.002
0.009
0.003
0.146
0.045
Table 2. Source of Price, Quantity and Promotion Variation
Retail Price Retail Quantity
Promotion
Variable
R2
R2
R2
Weekly E¤ects
0.075
0.012
0.010
Market E¤ects
0.165
0.297
0.025
Product Attributes
0.392
0.071
0.237
30
Table 3: Spatial Logit (DM-MNL) Demand Model: U.S. Yogurt Market
Non-Spatial
Spatial LS
Spatial IV
Variablea
Estimate
t-ratio
Estimate
t-ratio
Estimate t-ratio
Dannon Fat Free
1.9588*
25.0197
2.4082*
46.6607
2.0812* 36.3781
Dannon Fruit on the Bottom
2.8920*
59.8628
1.1893*
46.8428
1.0518
22.4552
Dannon Frusion
4.0944*
67.3092
1.2139*
33.6269
0.7801* 12.0146
Dannon La Creme
4.7426*
78.0541
1.4138*
29.2775
0.7912* 11.5339
Dannon Light N’Fit
3.4590*
68.8499
1.7346*
67.0236
1.5286* 31.7937
Dannon Sprinklins
5.7833*
77.6068
1.8717*
16.2772
1.2046* 14.8958
Yoplait Light
3.5903*
79.7676
1.9066*
68.6085
1.6064* 36.1162
Yoplait Original
3.5218*
74.0023
1.9128*
72.2910
1.5681* 34.1389
Yoplait Thick & Creamy
3.3377*
67.5240
1.8284*
41.0507
1.4227* 29.7881
Yoplait Whips
6.0333*
81.5760
2.1144*
39.5740
1.3239* 16.1283
P rice
-60.0810* -132.3170 -28.9887* -117.0600 -23.4427* -41.9624
Discount
-1.9568*
-4.3564 -0.7662*
-9.0599 -1.0975* -3.7433
Discount P rice
38.1272*
8.4276
5.0949*
5.8715
7.9096*
2.6839
Distance ( )
N.A.
N.A.
0.0066*
13.5058
0.0073* 95.7989
2
R
0.3259
0.4654
0.4498
G
11,096.3
N.A.
10,805.2
a
In this table, a single asterisk indicates signi…cance at a 5% level. G is the value of the GMM objective function
for the entire demand, pricing and location system (demand and pricing for non-spatial model). R2 is between
observed and predicted.
31
32
Dannon 1
-5.7258
(0.0254)
0.0833
(0.0011)
0.0779
(0.0013)
0.0888
(0.0012)
0.1164
(0.0014)
0.1131
(0.0015)
0.1172
(0.0011)
0.1090
(0.0010)
0.1161
(0.0012)
0.0811
(0.0011)
Dannon 2
0.0833
(0.0011)
-6.9037
(0.0344)
0.0590
(0.0007)
0.0637
(0.0007)
0.0931
(0.0012)
0.0639
(0.0008)
0.0937
(0.0010)
0.0920
(0.0009)
0.0713
(0.0007)
0.0621
(0.0007)
Dannon 3
0.0779
(0.0013)
0.0590
(0.0007)
-7.2426
(0.0328)
0.0503
(0.0005)
0.0937
(0.0012)
0.0442
(0.0005)
0.0945
(0.0012)
0.0922
(0.0010)
0.0600
(0.0006)
0.0495
(0.0004)
Note: Values in parentheses are standard errors.
Yoplait 4
Yoplait 3
Yoplait 2
Yoplait 1
Dannon 6
Dannon 5
Dannon 4
Dannon 3
Dannon 2
Dannon 1
Dannon 4
0.0888
(0.0012)
0.0637
(0.0007)
0.0503
(0.0005)
-5.8239
(0.0190)
0.0972
(0.0012)
0.0545
(0.0004)
0.0980
(0.0009)
0.0950
(0.0009)
0.0684
(0.0005)
0.0557
(0.0004)
Dannon 5
0.1164
(0.0014)
0.0931
(0.0012)
0.0937
(0.0012)
0.0972
(0.0012)
-6.7553
(0.0322)
0.1033
(0.0013)
0.1100
(0.0012)
0.1060
(0.0011)
0.1050
(0.0012)
0.0939
(0.0012)
Dannon 6
0.1131
(0.0015)
0.0639
(0.0008)
0.0442
(0.0005)
0.0545
(0.0004)
0.1033
(0.0013)
-8.5668
(0.0320)
0.1042
(0.0010)
0.0993
(0.0009)
0.0716
(0.0006)
0.0528
(0.0004)
Yoplait 1
0.1172
(0.0011)
0.0937
(0.0010)
0.0945
(0.0010)
0.0980
(0.0009)
0.1100
(0.0012)
0.1042
(0.0010)
-6.6158
(0.0328)
0.1064
(0.0009)
0.1058
(0.0009)
0.0947
(0.0009)
Table 4: Own- and Cross-Price Elasticity Matrix for Ten Yogurt Brands
Yoplait 2
0.1090
(0.0010)
0.0920
(0.0009)
0.0922
(0.0009)
0.0950
(0.0009)
0.1060
(0.0011)
0.0993
(0.0009)
0.1064
(0.0009)
-7.2105
(0.0353)
0.1008
(0.0009)
0.0925
(0.0009)
Yoplait 3
0.1161
(0.0012)
0.0713
(0.0007)
0.0600
(0.0006)
0.0684
(0.0005)
0.1050
(0.0012)
0.0716
(0.0006)
0.1058
(0.0009)
0.1008
(0.0009)
-7.3444
(0.0348)
0.0650
(0.0005)
Yoplait 4
0.0811
(0.0011)
0.0621
(0.0007)
0.0495
(0.0004)
0.0557
(0.0004)
0.0939
(0.0012)
0.0528
(0.0004)
0.0947
(0.0009)
0.0925
(0.0009)
0.0650
(0.0005)
-8.2429
(0.0343)
33
In this table, a single asterisk indicates signi…cance at a 5% level. Among other parameters, is the pricing conduct parameter,
0j are the brand-speci…c cost intercepts, dj are brand-speci…c di¤erentiation parameters, and 1 is the cost-of-di¤erentiation
slope parameter. See table 3 for system GMM criterion function.
a
Table 5: Non-Spatial Pricing and Spatial Pricing and Location Model: U.S. Yogurt
Non-Spatial Pricing
Spatial Pricing
Spatial Location
a
Variable
Estimate t-ratio Estimate t-ratio
Estimate
t-ratio
Milk Price
0.0201
8.4268
0.0141 6.7692
1
Sweetener Price
0.0397
8.9954
0.0339 8.9081
2
Plastic Price
-0.0246
-3.9534
-0.0335 -6.2000
3
Manufacturing Wage
-0.0059
-8.5073
-0.0041 -6.9000
4
Conduct / Cost Parameter
1.4566 10.2391
1.5337 12.4531
0.0002
2.2373
1
Dannon Fat Free
1.8573
2.5225
3.2540 5.0901 d1
-0.0649
-29.7936
01
Dannon Fruit on the Bottom
1.8434
2.5033
3.2389
5.0658
d
-0.0400
-22.7273
2
02
Dannon Frusion
1.8736
2.5441
3.2663 5.1085 d3
-0.0210
-16.3984
03
Dannon La Creme
1.8713
2.5410
3.2661 5.1083 d4
-0.0072
-8.8642
04
Dannon Light N’Fit
1.8549
2.5189
3.2521
5.0866
d
-0.0420
-25.1437
5
05
Dannon Sprinklins
1.8952
2.5735
3.2905
5.1463
d
-0.0164
-13.6250
6
06
Yoplait Light
1.8518
2.5147
3.2480
5.0802
d
-0.0403
-24.3939
7
07
Yoplait Original
1.8486
2.5103
3.2446 5.0747 d8
-0.0429
-24.1011
08
Yoplait Thick & Creamy
1.8475
2.5087
3.2420 5.0707 d9
-0.0387
-21.9830
09
Yoplait Whips
1.8986
2.5780
3.2932
5.1504
d
-0.0124
-11.8286
10
010
34
on Price, Location, and Welfare
CS
PS
Welfare
Price Location
CS
PS
Welfare
-2.4692 0.7227 -1.7465 0.250 0.1195
1.0731 2.3287 -0.7550
1.5737
-2.2293 0.6492 -1.5801 0.225 0.1198
1.1272 2.0888 -0.6807
1.4081
-1.9894 0.5758 -1.4136 0.200 0.1200
1.1900 1.8489 -0.6063
1.2426
-1.7495 0.5025 -1.2470 0.175 0.1203
1.2641 1.6090 -0.5318
1.0772
-1.5096 0.4294 -1.0803 0.150 0.1207
1.3531 1.3691 -0.4572
0.9119
-1.2697 0.3564 -0.9133 0.125 0.1210
1.4620 1.1292 -0.3824
0.7468
-1.0298 0.2838 -0.7460 0.100 0.1214
1.5981 0.8893 -0.3073
0.5821
-0.7899 0.2117 -0.5782 0.075 0.1218
1.7661 0.6494 -0.2316
0.4179
-0.5500 0.1407 -0.4093 0.050 0.1224
1.9625 0.4096 -0.2548
0.2548
-0.3101 0.0725 -0.2377 0.025 0.1231
2.0036 0.1697 -0.0752
0.0944
_
Note: In this table, Location = w, CS = Consumer Surplus, PS = Producer Surplus and W = Total Welfare.
Table 6. Simulation of
Price Location
-0.250 0.1224
1.0001
-0.225 0.1222
1.0526
-0.200 0.1219
1.1143
-0.175 0.1216
1.1881
-0.150 0.1213
1.2784
-0.125 0.1210
1.3924
-0.100 0.1206
1.5421
-0.075 0.1202
1.7491
-0.050 0.1197
2.0514
-0.025 0.1190
2.4318