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Essays in retail management
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Content
ESSAYS IN RETAIL MANAGEMENT
by
Tae-kyun Kim
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BUSINESS ADMINISTRATION)
August 2010
Copyright 2010 Tae-kyun Kim
Acknowledgements
I would like to express my deepest gratitude to my dissertation committee, S.
Siddarth, Anthony Dukes, Shantanu Dutta, and Cheng Hsiao for their guidance
and advice. I am especially grateful to my chair, S. Siddarth, for encouraging,
assisting and caring for me throughout my Ph.d. life. Last, but not least, I
acknowledge the unyielding support from my Father, Mother, and two sisters,
which was crucial to getting me through the program.
ii
Table of Contents
Acknowledgements ii
List of Tables vii
List of Figures ix
Abstract x
Chapter 1: Overview 1
1.1 Retail Assortment and Consumer Purchase Decisions . . . . . . . 1
1.2 Structural Models of Manufacturer and Retailer Competition in
the U.S. Automobile Industry . . . . . . . . . . . . . . . . . . . . 3
Chapter 2: The Impact of Category- and Brand-level Assortment
on Consumer Purchase Incidence and SKU Choice Decisions 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Assortment Dimensions . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Measures of Assortment Structure . . . . . . . . . . . . . . 12
2.2.2 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.3 Category and Brand Level Assortment . . . . . . . . . . . 16
2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 SKU Choice Model . . . . . . . . . . . . . . . . . . . . . . 17
2.3.2 Purchase Incidence Model . . . . . . . . . . . . . . . . . . 19
2.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.2 Assortment Summary . . . . . . . . . . . . . . . . . . . . . 20
2.4.2.1 Category-level Assortment Variation . . . . . . . 21
2.4.2.2 Brand-level Assortment Variation . . . . . . . . . 22
2.5 Estimation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 25
iii
2.5.1 Calibration Sample Selection . . . . . . . . . . . . . . . . . 25
2.5.2 Prior Specication . . . . . . . . . . . . . . . . . . . . . . 25
2.5.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6.1 Calibration Sample Comparisons . . . . . . . . . . . . . . 27
2.6.1.1 SKU Choice Model . . . . . . . . . . . . . . . . . 27
2.6.1.2 Purchase Incidence Model . . . . . . . . . . . . . 28
2.6.2 Holdout Sample Comparisons . . . . . . . . . . . . . . . . 28
2.6.3 Parameter Estimates . . . . . . . . . . . . . . . . . . . . . 30
2.6.3.1 SKU Choice Model . . . . . . . . . . . . . . . . . 30
2.6.3.2 Purchase Incidence Model . . . . . . . . . . . . . 32
2.7 Managerial Implications . . . . . . . . . . . . . . . . . . . . . . . 33
2.7.1 Simulating SKU Deletion Decisions . . . . . . . . . . . . . 33
2.7.1.1 Manufacturer's Perspective . . . . . . . . . . . . 34
2.7.1.2 Retailer's Perspective . . . . . . . . . . . . . . . 35
2.7.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.7.2.1 Manufacturer's Perspective . . . . . . . . . . . . 35
2.7.2.2 Retailer's Perspective . . . . . . . . . . . . . . . 36
2.7.2.3 Dierence in Perspectives . . . . . . . . . . . . . 37
2.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Chapter 3: Structural Models of Manufacturer and Retailer Com-
petition in the U.S. Automobile Industry 40
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Study 1: Manufacturer Competition in the Presence of Exclusive
Dealers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2.1 Modeling Framework . . . . . . . . . . . . . . . . . . . . . 48
3.2.1.1 Glossary . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.1.2 Consumer Demand . . . . . . . . . . . . . . . . . 50
3.2.1.3 Retailer Behavior . . . . . . . . . . . . . . . . . . 51
3.2.1.4 Alternative Models of Retailer Interaction . . . . 52
3.2.1.5 Manufacturer Behavior . . . . . . . . . . . . . . . 53
3.2.1.6 Model 1: Strategic Retailer Interacting Flexibly . 56
3.2.1.7 Model 2: Retailers Pricing in a Bertrand-Nash
Fashion . . . . . . . . . . . . . . . . . . . . . . . 59
3.2.1.8 Model 3: Retailers Pricing With a Fixed Margin 59
3.2.1.9 Model 4: Manufacturers Competing Without Re-
tailers . . . . . . . . . . . . . . . . . . . . . . . . 61
iv
3.2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2.3 Model Estimation . . . . . . . . . . . . . . . . . . . . . . . 63
3.2.3.1 Price Construction by Hedonic Regression . . . . 64
3.2.3.2 Demand Side Estimation . . . . . . . . . . . . . . 64
3.2.3.3 Supply Side Estimation . . . . . . . . . . . . . . 66
3.2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2.4.1 Dealer Cost Variable . . . . . . . . . . . . . . . . 67
3.2.4.2 Price Construction by Hedonic Regression . . . . 67
3.2.4.3 Consumer Demand . . . . . . . . . . . . . . . . . 70
3.2.4.4 Supply Side . . . . . . . . . . . . . . . . . . . . . 71
3.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3 Study 2: An Empirical Investigation of Intra- and Inter-channel
Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3.1.1 Consumer Demand Model . . . . . . . . . . . . . 79
3.3.1.2 Supply Side: Retailer Behavior . . . . . . . . . . 81
3.3.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3.3.1 Demand Side Estimation . . . . . . . . . . . . . . 85
3.3.3.2 Supply Side Estimation . . . . . . . . . . . . . . 86
3.3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.4.1 Price Construction by Hedonic Regression . . . . 87
3.3.4.2 Demand Model . . . . . . . . . . . . . . . . . . . 89
3.3.4.3 Supply Model . . . . . . . . . . . . . . . . . . . . 91
3.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Bibliography 94
Appendices 97
A Assortment: Estimation Results for Other Categories . . . . . . . 98
A.1 Parameter Estimates of SKU Choice Model . . . . . . . . 98
A.2 Parameter Estimates of Purchase Incidence Model . . . . . 105
B Automobile: Deriving Estimation Equations for Supply Side Be-
havior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
B.1 Price Derivative of MNL . . . . . . . . . . . . . . . . . . . 107
B.2 Calculation of SW
t
. . . . . . . . . . . . . . . . . . . . . . 107
B.3 Calculation of PW . . . . . . . . . . . . . . . . . . . . . . 108
B.4 Derivation of PW . . . . . . . . . . . . . . . . . . . . . . . 109
B.4.1 Using FOC of retailer j . . . . . . . . . . . . . . 109
v
B.4.2 Using FOC of retailer k . . . . . . . . . . . . . . 110
B.4.3 Simultaneous Equation . . . . . . . . . . . . . . . 112
vi
List of Tables
2.1 Example of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Maximum Entropy and Assortment Size . . . . . . . . . . . . . . 15
2.3 SKU Attributes by Product Category . . . . . . . . . . . . . . . . 20
2.4 Assortment Variation at the Category Level . . . . . . . . . . . . 21
2.5 Number of SKUs for Skippy and Peter Pan . . . . . . . . . . . . . 23
2.6 Package Size Entropy Variation for Skippy and Peter Pan . . . . . 24
2.7 Flavor Entropy Variation for Skippy and Peter Pan . . . . . . . . 24
2.8 Log Marginal Density of SKU Choice Models . . . . . . . . . . . . 27
2.9 Log Marginal Density of Purchase Incidence Models . . . . . . . . 28
2.10 Mean Absolute Deviation (MAD) for SKU Choice Models . . . . 29
2.11 Mean Absolute Deviation (MAD) for Purchase Incidence Models . 29
2.12 Parameter Estimates of SKU Choice Model . . . . . . . . . . . . 31
2.13 Parameter Estimates of Purchase Incidence Model . . . . . . . . . 32
2.14 Recommendation of SKU to Drop . . . . . . . . . . . . . . . . . . 36
3.1 Transaction Summary by DMA . . . . . . . . . . . . . . . . . . . 62
3.2 Transaction Summary by Vehicle . . . . . . . . . . . . . . . . . . 63
3.3 Hedonic Regression Result of Retail Price . . . . . . . . . . . . . 69
vii
3.4 Hedonic Regression Result of Wholesale Price . . . . . . . . . . . 69
3.5 Summary of Demand Estimation . . . . . . . . . . . . . . . . . . 70
3.6 Supply Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.7 Vehicle Information Summary by Area . . . . . . . . . . . . . . . 83
3.8 Hedonic Regression Result of Retail Price . . . . . . . . . . . . . 88
3.9 Hedonic Regression Result of Wholesale Price . . . . . . . . . . . 89
3.10 Summary of Demand Estimation . . . . . . . . . . . . . . . . . . 90
3.11 Summary of Supply Estimation . . . . . . . . . . . . . . . . . . . 91
12 Parameter Estimates of SKU Choice Model: Bacon . . . . . . . . 99
13 Parameter Estimates of SKU Choice Model: Coee . . . . . . . . 100
14 Parameter Estimates of SKU Choice Model: Tissue . . . . . . . . 102
15 Parameter Estimates of SKU Choice Model: Towel . . . . . . . . 103
16 Parameter Estimates of PI Model: Bacon . . . . . . . . . . . . . . 105
17 Parameter Estimates of PI Model: Coee . . . . . . . . . . . . . . 105
18 Parameter Estimates of PI Model: Tissue . . . . . . . . . . . . . . 106
19 Parameter Estimates of PI Model: Towel . . . . . . . . . . . . . . 106
viii
List of Figures
3.1 Contributions of This Essay . . . . . . . . . . . . . . . . . . . . . 43
3.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3 Model Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4 Summary of Supply Side Estimation . . . . . . . . . . . . . . . . 75
3.5 Retail Price Variation Over Time . . . . . . . . . . . . . . . . . . 84
ix
Abstract
I study issues related to retail management in packaged goods and durable goods
markets. In the packaged goods context, I investigate how brand- and category-
level assortments impact consumers' purchase incidence and SKU choice deci-
sions. I also investigate retail competition in the U.S. automobile industry by
developing structural models and estimation approaches to (a) infer the nature
of competition between manufacturers in the presence of exclusive retailers and
(b) to identify how intra- and inter-channel competition varies by brands and
across dierent geographical markets.
x
Chapter 1
Overview
In my dissertation, I study issues related to retail management in packaged goods
and durable goods markets. In the rst part of my dissertation, I investigate how
product assortment at the brand- and category-level impacts consumers' purchase
incidence and SKU choice decisions. In the second part of my dissertation, I study
retail channel competition in the U.S. automobile industry.
1.1 Retail Assortment and Consumer Purchase
Decisions
Both academics and practitioners are interested in understanding how product
assortment impacts consumer choice behavior. Hoch, Bradlow, and Wansink
(1999) and van Herpen and Pieters (2002) conducted lab studies that show how
1
the structure of an assortment in
uences consumers' perception of variety. How-
ever, prior research has not examined whether and how assortment structure
aects actual choice behavior.
In this essay, I focus on how the assortment oered by a brand, as represented
by the individual SKUs that characterize its product line, in
uences a consumer's
probability of choosing that brand. Further, I also investigate how the assortment
of SKUs in a product category impacts consumers' purchase incidence decisions.
In contrast to previous eld studies that have examined the eect of one-time
changes in assortment (Borle, Boatwright, Kadane, Nunes, and Shmueli, 2005;
Zhang and Krishna, 2007), I leverage the cross-sectional variation in assortment
oered by dierent stores, and of the same store across time, to carry out my
analysis.
I propose a model that jointly incorporates a consumer's purchase incidence
and SKU choice decisions. The SKU choice model includes consumer preferences
for specic attribute levels, a la Fader and Hardie (1996), as well as the size and
structure of the assortment of the brand to which each SKU belongs. A novel
aspect of the purchase incidence model is that category purchase probabilities
are in
uenced by the assortment structure at the category-level, which provides
insights into how changes in assortment in
uence purchase incidence dierently
from SKU choice.
Model parameters are estimated with household purchases in ve frequently
purchased categories obtained from an IRI scanner panel. A hierarchical Bayes
approach is used to account for unobserved heterogeneity. The model provides
2
insights into the relative importance of dierent attributes on assortment, and
counterfactuals are used to assess the consequences of SKU deletion. These as-
pects of the model can guide managers seeking to rationalize their product oer-
ings.
1.2 Structural Models of Manufacturer and
Retailer Competition in the U.S. Automobile
Industry
Marketers and economists are often interested in the degree of price competition
among rms within an industry and the factors that aect its intensity. While
considerable attention has been paid to understanding the nature of competition
between manufacturers, relatively little is known about (1) how manufacturers'
use of exclusive retailers aects competitive intensity, or (2) how automobile
dealers actually compete with each other, which is the focus of my dissertation.
Recent empirical research has attempted to directly infer the degree of com-
petitive interaction between market players based on market data on sales and
prices. Two key features of this work are: (a) that it either completely ignores the
presence of retailers, e.g. Sudhir (2001a), or only studies cases in which there is a
single common retailer, e.g. Villas-Boas and Zhao (2005), and (b) that it focuses
on identifying the Horizontal Strategic Interaction (HSI) between manufacturers,
not between retailers.
3
In contrast, I am interested in studying markets characterized by exclusive re-
tailers, whose presence, the theoretical channels literature suggests, can alter the
competitive intensity between manufacturers (Coughlan, 1985). Because strate-
gic manufacturers will set wholesale prices after taking into account the response
of retailers, and because this response is inextricably linked to the nature of com-
petition between retailers, I argue that manufacturer HSI must be examined in
a model that also includes the competitive interaction among retailers.
I propose a structural model of competition between multiple manufactures,
each represented by an exclusive retailer in each of several geographic markets. A
key feature of the model is that both retailer and manufacturer competition are
captured in a
exible manner, i.e, not restricted to be Bertrand Nash. I analyze
a dataset of new car purchases in the premium compact sedan category that were
made at dealerships located in ve major markets from October 2003 to Septem-
ber 2004. I use a sequential estimation approach to obtain model parameters:
demand parameters are rst estimated using Hierarchical Bayes methods after
which supply side parameters for both retailers and manufacturers are estimated
using a Generalized Methods of Moments (GMM) approach.
The results show that the HSI between manufacturers is dierent from that
between retailers. Thus manufacturers in this particular segment of the market
interact cooperatively while the competition among retailers is aggressive. I also
demonstrate that alternative models which either a) ignore retailer presence, b)
4
assume non-strategic retailers, or c) assume retailer interaction to be Bertrand-
Nash, provide dramatically dierent inferences about the nature of competition
between manufacturers.
After establishing the importance of considering retailer competition when
studying manufacturer interaction, in the second half of this essay, I focus on
retailer competition itself. There is considerable evidence that retailers directly
compete with each other at a local level. For example, packaged goods retailers
make strategic choices about the overall pricing formats that they will follow, for
example, positioning themselves as Every Day Low Pricing (EDLP) or High Low
stores that dier in their relative ability to attract dierent kinds of shoppers to
the store (Lal and Rao, 1997; Bell and Lattin, 1998). Also, retail competition
has been shown to be one of the most important drivers of price variations across
stores (Shankar and Bolton, 2004). In the automobile market, recent research by
Bucklin, Siddarth, and Silva-Risso (2008) show that a brand's distribution inten-
sity is a critical determinant of consumer demand. Similarly, Albuquerque and
Bronnenberg (2006) nd that dealer location relative to a consumer is an impor-
tant in
uence on consumer's vehicle choice decisions. Because there is signicant
heterogeneity in the intensity of distribution among dierent brands and, across
dierent geographical areas of the same brand, it stands to reason that that the
nature of competition among retailers will also depend upon local conditions.
Recent actions by auto manufacturers like GM and Chrysler to selectively reduce
the number of dealers in certain markets also support this view.
5
To gain further insights into local competitive intensity, I extend my model to
examine the variation in the nature of intra- and inter-channel competition across
dierent markets. Thus, in Study 2, I propose a structural model of competition
between multiple manufactures, each represented by dierent numbers of exclu-
sive retailers in dierent geographic markets. I estimate model parameters using
consumer purchases in the premium compact sedan category during the period
Oct 2005 to September 2007 at dealerships in two dierent DMAs: Houston and
Minneapolis. The results show (i) that inter- and intra-channel competition is
very dierent in the same market, and (ii) that intra-channel competition for
retailers of the same manufacturer also varies from one market to the other. I
discuss the relevance of my comprehensive modeling framework to the ongoing
upheaval in the U.S. automobile industry, particularly the drastic elimination of
dealers by GM and Chrysler.
6
Chapter 2
The Impact of Category- and Brand-level
Assortment on Consumer Purchase Incidence
and SKU Choice Decisions
2.1 Introduction
Product assortment is one of the top concerns for both retailers and manufac-
turers. Oering a larger assortment of items increases the likelihood that con-
sumers will nd a product that meets their needs (Draganska and Jain, 2005;
Kuksov and Villas-Boas, 2007). Specically, a larger assortment can a) sat-
isfy the heterogenous preferences of a larger number of consumers, b) cater to
the changing needs of individual consumers with time-varying preferences (Kahn
and Lehmann, 1991), and c) fulll consumers' need for variety (Hoch, Bradlow,
and Wansink, 1999). However, maintaining a larger assortment is not costless.
Consumers may be overwhelmed or confused when faced with a large number of
7
alternatives (Iyengar and Lepper, 2000; Kuksov and Villas-Boas, 2007) and man-
ufacturers and retailers have to incur the higher economic costs associated with
providing greater shelf-space and carrying higher inventories (Hoch et al., 1999).
Thus, managing product assortment requires a good understanding of the impact
of assortment on consumer choices and the benets and the costs of assortment
changes.
The signicant amount of academic research on assortment also attests to the
importance of this topic. Broadly speaking, the existing assortment research in
marketing can be usefully classied into two categories: a) lab-based studies that
examine how the size and structure of product assortment in
uence consumers
perception of variety, and b) eld studies that investigate the impact of assortment
changes on a sales or share metric. An example of the rst type of study is Hoch,
Bradlow, and Wansink (1999), that proposes a pairwise comparison measure of
assortment structure and shows that systematic changes in information structure
can impact consumers' variety perception. Another study by van Herpen and
Pieters (2002) also nds similar eects using the information-based measures
of entropy and disassociation to represent assortment structure. In a follow-
up paper, Hoch, Bradlow, and Wansink (2002) show that these measures are
closely related to the pairwise comparison measure. Recognizing the limitations
of directly applying the lab-ndings to actual choice contexts, Hoch et al. (1999)
state that they \do not want to oversell the in
uence of perceived variety on
actual shopping behavior." I advance research in this area by using purchase
8
data to examine whether, and by how much, assortment structure impacts the
actual choices of consumers.
Another stream of research in marketing has investigated the impact of a
one time reduction in assortment on sales. Boatwright and Nunes (2001) show
that assortment reduction can actually increase category level sales while Sloot,
Fok, and Verhoef (2006) identify negative short-term and long-term eect of
assortment reduction using the same metric. More recently, Zhang and Krishna
(2007) examine the same impact at a more disaggregate level with a model of
consumer's purchase incidence and brand choice decisions. They nd that the
impact of assortment reduction depends on various brand characteristics such
as price level and promotion frequency. In contrast to this work, my research
focuses on examining the impact of whether and/or how the small-scale, but
continuous, changes in assortment that result from variations in stocking policies
across stores, and of the same store across time, impacts choice behavior and
store performance.
Another important aspect of the current research is that it uses individual
stock-keeping units (SKU) as the unit of analysis. In contrast, previous research
has focused on more aggregate constructs such as brand share, product category
sales, or store sales. However, the SKU may be a more appropriate unit of anal-
ysis for several reasons. First, from a demand perspective, a SKU represents the
most fundamental choice unit that can satisfy a consumer's needs. Second, from
the manufacturer or retailer's point of view, changes in assortment must be im-
plemented by adding or deleting specic SKUs. Third, aggregate-level analysis
9
ignoring SKU utility cannot identify the values provided by changes to the size
and structure of the assortment. This research remedies the problem by account-
ing for the direct benets to the consumer of the attribute levels that each SKU
provides as well as its contribution to the assortment structure.
Because retailers oer the consumer multiple brands in a product category,
the assortment structure at the category level maybe even more important than
brand-level assortment. A nal, unique, aspect of the current research is that it
explicitly examines the impact of category-level assortment on consumer purchase
behavior, which has has been ignored in previous assortment research. Speci-
cally, the research proposes assortment structure measures at the category level
and quanties how much the addition or deletion of a specic SKU impacts con-
sumer's purchase incidence decisions.
I propose a model of SKU choice behavior that includes consumer preferences
for specic attribute levels (Fader and Hardie, 1996) also also incorporates several
aspects of the brand-level assortment to which each SKU belongs. These include
basic dimensions of assortment such as its size as well as assortment structure.
Specically, I operationalize product assortment with an entropy measure that
is constructed at the individual attribute level (van Herpen and Pieters, 2002).
I also create similar measures of category assortment. My model includes a
purchase incidence component in which category purchase probabilities are in
u-
enced by these category assortment dimensions and by household characteristics,
such as inventory and purchase frequency. Model parameters are estimated using
household purchases, in ve dierent product categories, obtained from an IRI
10
scanner panel. A hierarchical Bayes approach is used to account for unobserved
heterogeneity.
This essay addresses the following questions.
1. How does brand-level assortment impact consumers' SKU choice decisions?
2. How does category-level assortment impact consumer purchase incidence
behavior?
3. What is the impact of deleting SKUs on brand sales and store level sales?
How can manufacturers and retailers make better decisions about dropping
or adding SKUs from the product line?
This research makes several contributions to the literature. First, it extends
the lab-based ndings of previous research on variety perception eects of assort-
ment to actual purchase behavior. Second, it introduces the notion of category-
wide assortment and studies its impact on consumer purchase decisions. Finally,
by investigating SKU choices it provides direct insights into the consequences of
the SKU deletion decision.
The remainder of the paper is laid out as follows. In Section 2.2, I review dier-
ent measures of assortment structure and describe the category- and brand- level
measures that are used in my study. Section 2.3 describes the proposed incidence
and SKU choice model that incorporates brand-level assortment dimensions such
as size and structure. Section 2.4 presents the empirical application and discusses
the data, Sections 2.5 and 2.6 describe the estimation procedure and discuss the
results. Section 2.7 discusses the counterfactual study I use to gain insights into
11
the consequences of SKU deletion. Section 2.8 provides a summary of my con-
clusions, discusses the limitations of my study and provides some directions for
future research.
2.2 Assortment Dimensions
Two major assortment dimensions have been identied in the literature: size and
structure. As implied by the name, size indicates how large an assortment is,
and is typically measured by the number of alternatives in the assortment (Hoch
et al., 1999; Boatwright and Nunes, 2001). Assortment structure is derived from
the multiattribute structure of objects and their spatial co-location (Hoch et al.,
1999). To date, this construct has been used and operationalized exclusively in
experimental settings. In this section, I discuss these measures further and also
provide details on how they are operationalized in my study.
2.2.1 Measures of Assortment Structure
Two notable assortment structure measures have been proposed in the liter-
ature: The pairwise comparison measures of Hoch et al. (1999) and the en-
tropy/dissociation measures of van Herpen and Pieters (2002). The pairwise
comparison measure is based on attribute level dierences between objects and
the level of organizations of the objects (Hoch et al., 1999). Thus, it simultane-
ously captures both the attribute structure and spatial location. However, the
12
increased
exibility of this measure comes with the added cost of requiring many
more parameters to be estimated.
An alternative approach to capturing the information structure of an as-
sortment is via the entropy and dissociation measures proposed by van Her-
pen and Pieters (2002). Hoch, Bradlow, and Wansink (2002) show that the en-
tropy/disassociation measures and the pairwise comparison measures are math-
ematically equivalent, and both sets of measures have been validated by exper-
imental studies demonstrating their impact on consumers' variety perceptions.
Given the mathematical equivalence of the two measures, a major advantage of
entropy is its parsimony, requiring a much fewer number of parameters to be
estimated. van Herpen and Pieters (2002) include both entropy and dissociation
measures in their study, with the dissociation measure capturing the association
between attributes. In this essay, to reduce the number of estimated parameters,
I rely exclusively on the entropy measure to measure assortment structure.
2.2.2 Entropy
Entropy is derived from the literature on information theory and has been used in
various research disciplines to measure dispersion in industrial activity (Jacquemin
and Berry, 1979), prices (Chellappa, Sin, and Siddarth, 2011), and variety seeking
in consumer choices (Mitchell, Kahn, and Knasko, 1995). Young and Wasserman
(2001) showed that this measure can capture human perception of variety and van
Herpen and Pieters (2002) used the measure to represent assortment structure.
13
Table 2.1: Example of Entropy
Brand Assortment Entropy Normalized Entropy
1 R, R, R, R 0 0
2 R, R, R, B 0.56 0.40
3 R, R, B, B 0.69 0.50
4 R, R, B, G 1.04 0.75
5 R, B, G, C 1.39 1.00
Consider a set of multi-attribute choice alternatives, taking specic levels on
each of M common attributes. The raw entropy of a specic attribute m can be
calculated as
E
m
=
X
l2L
p
l
lnp
l
(2.1)
where p
l
is the proportion of alternatives with attribute level l. To see how this
measure works, consider a product category in which SKUs dier along a single
avor dimension. Specically, SKUs come in four dierent
avors: raspberry (R),
blueberry (B), grape (G), and cream(C).
Table 2.1 shows ve brands, each oering identically-sized assortments con-
sisting of exactly four items, that nevertheless vary in their composition. The en-
tropy measure captures the variations in assortment structure stemming from the
dierent items in each set. In the rst assortment, all alternatives share the same
attribute level, Red, which implies p
R
= 1 and E
m
=p
R
lnp
R
=1 0 = 0.
The variability of each assortment increases gradually and the fth assortment,
14
with each alternative having a unique
avor, has the highest entropy. For this
fth assortment, the attribute level proportions are
p
R
=p
B
=p
G
=p
C
= 1=4;
and the associated entropy can be calculated as:
4
1
4
ln
1
4
= ln
1
4
= 1:39:
It is important to note that, as dened, entropy is not independent of the size
of the assortment and increases with the number of alternatives n or assortment
size. For example, Table 2.2 shows how maximum entropy ln(1=n) increases as
the size of the assortment goes from 2 to 7.
Table 2.2: Maximum Entropy and Assortment Size
n Max entropy
2 0:69
3 1:10
4 1:39
5 1:61
6 1:79
7 1:95
In order to make entropy comparable across dierent assortment sizes, I
scale the raw entropy measure in Equation 2.1 by the maximum possible en-
tropy given the size of the assortment. It is interesting to note that van Herpen
15
and Pieters (2002) found that consumers' assortment perceptions did not depend
upon whether raw or normalized entropy was used to operationalize it.
The corresponding normalized entropy measure can be calculated as
E
0
m
=
P
l2L
p
l
lnp
l
ln(1=n)
; (2.2)
where n is the number of items in the set. For example, the normalized entropy
of Assortment 2 can be calculated as the raw entropy (0.56) divided by the
maximum possible entropy from an assortment of size 4 (1.39).
0:56
1:39
= 0:40
The last column of Table 2.1 shows normalized entropy values for each of the
assortments in the example.
2.2.3 Category and Brand Level Assortment
In this research, I seek to study how the natural variation in the assortment oered
by dierent stores, and the same store over time, impacts consumer purchase
decisions. The most disaggregate unit of analysis in my work is the SKU, which
is a bundle of attributes (Fader and Hardie, 1996). The assortment oered by
a brand in a product category depends upon the included SKUs. Adding or
removing SKUs, therefore, changes the size of the assortment oered by the
brand and also its assortment structure. At a higher level of aggregation, these
changes can also impact the size and structure of the assortment of the whole
16
product category, which could potentially in
uence consumer's category purchase
decision.
In my empirical application, therefore, I construct assortment size and struc-
ture measures at both category- and brand-levels. Assortment size for a brand
(category) is simply the number of unique SKUs oered by each brand (all
brands). Assortment structure is captured by calculating the normalized en-
tropy of each attribute for each brand, and for the category as a whole. For
example, in the peanut butter category, entropy is separately calculated for each
of the attributes such as
avor (creamy, crunchy, and so on) and package size (12
oz, 16 oz, and etc). Similarly, assortment structure at the product category level
uses the entropy for each attribute over all of the SKUs available in that product
category.
2.3 Model
2.3.1 SKU Choice Model
The deterministic component of utility of an SKU is typically modeled as an
additive sum of the utility for each of the dierent attribute levels that comprise
that SKU (Fader and Hardie, 1996). Thus, the utility of SKU j of brand i at
shopping occasion t for household h can be expressed as
U
hijt
=
hi
+W
ij
h
+X
ijt
h
+
hijt
: (2.3)
17
hi
is a brand-specic intercept, W
ij
includes all SKU attributes other than the
brand attribute, such as, for example, size,
avor and function. X
ijt
is a vector of
marketing mix variables for SKUj, belonging to brandi, on purchase occasiont
(e.g. price, promotion, display).
hijt
is the random component of utility, assumed
to have a Type-I extreme value distribution.
As previously discussed, one of my objectives is to test and quantify the impact
of brand-level assortment on choice behavior. Kalyanam, Borle, and Boatwright
(2007) show that an item aects the sales of the product category beyond its
own sales. Adopting this idea, I postulate that an item can aect the sales of
all of the other alternatives belonging to its brand. To incorporate the impact of
brand-level assortment impact on brand value, I augment the utility of the brand
attribute with the assortment size and structure of the SKUs that belong to that
brand.
hi
)
hi
+
h
BA
it
: (2.4)
Thus, in addition to the time-invariant brand value
hi
, the brand level assort-
ment BA
it
also aects the value of the brand. Substituting Equation 2.4 into
Equation 2.3, the utility of SKU j on shopping trip t of household h can be
specied as:
U
hijt
=
hi
+
h
BA
it
+
h
W
ij
+
h
X
ijt
+
hijt
: (2.5)
The brand assortment variable BA
it
includes attribute size and structure
measures. Specically, the total number of available SKUs oered by brand i in
18
each store in each week represents the size of its assortment while the normalized
entropy for each attribute captures assortment structure.
2.3.2 Purchase Incidence Model
I model the utility of the category purchase incidence decision as:
v
ht
=
h
CA
t
+
h
Q
ht
+
h
T
ht
+
h0t
: (2.6)
Thus, the decision to purchase in a certain category depends upon the charac-
teristics of the category-level assortment, CA
t
, and household-specic shopping
variables such as last purchased quantity, Q
ht
, and time since last purchase, T
ht
,
with
h
,
h
,
h
being the corresponding parameters. The vector CA
t
includes
the number of SKUs in the category as well as the entropy of each attribute
calculated over all oerings in the category as a whole.
2.4 Data
In this section, I brie
y discuss the data used in the study and illustrate the
variations in assortment size and structure observed in the data.
2.4.1 Overview
The data set come from an IRI database containing the shopping trip history of
548 participating panelists in two separate metro markets in a large U.S. city,
19
one urban, the other suburban, during the period June 1991 to June 1993. The
shopping history contains information on the chosen alternative and quantity for
24 categories as well as weekly store level marketing activity information. In this
study, I analyze purchases in ve product categories: bacon, coee, peanut butter,
paper tissue, and paper towels from the suburban market. In each category, I
selected for further analysis those SKUs with at least 0.5% of total category share.
2.4.2 Assortment Summary
Table 2.3 provides a brief summary of some important characteristics of the
assortment in each of the selected categories, after aggregating the data across
stores and time. For example, across all stores in the sample, the peanut butter
category had 9 unique brands, 8 dierent package sizes, 5
avors, and a total
of 39 unique SKUs. Table 2.3 also reports the corresponding numbers from the
other product categories.
Table 2.3: SKU Attributes by Product Category
Number Bacon Coee Peanut butter Paper tissue Paper towl
Brands 11 11 9 11 14
SKUs 18 45 39 19 40
Package sizes 4 13 8 5 3
Flavors 3 10 5
Product types 2
Functions 14
20
Table 2.4: Assortment Variation at the Category Level
Store Mean Median Min Max SD
Number of SKUs
1419 28:560 29:000 25:000 33:000 1:696
1420 31:871 32:000 29:000 34:000 1:474
1422 27:345 27:000 23:000 30:000 1:546
1423 23:500 23:000 21:000 26:000 1:295
1424 23:474 24:000 19:000 26:000 1:270
Brand Entropy
1419 0:508 0:504 0:407 0:558 0:029
1420 0:531 0:537 0:511 0:544 0:011
1422 0:581 0:578 0:552 0:623 0:014
1423 0:540 0:543 0:494 0:596 0:027
1424 0:536 0:543 0:481 0:585 0:026
Package Size Entropy
1419 0:557 0:563 0:522 0:604 0:019
1420 0:539 0:542 0:522 0:558 0:008
1422 0:502 0:502 0:462 0:530 0:016
1423 0:521 0:513 0:476 0:563 0:020
1424 0:528 0:521 0:499 0:562 0:016
Flavor Entropy
1419 0:346 0:347 0:297 0:375 0:014
1420 0:343 0:343 0:325 0:364 0:010
1422 0:348 0:348 0:326 0:377 0:010
1423 0:336 0:334 0:284 0:365 0:012
1424 0:337 0:334 0:284 0:365 0:014
2.4.2.1 Category-level Assortment Variation
Table 2.4 reports variations in category assortment over time. It consists of four
sections, each reporting summary statistics for a single assortment measure over
time. The rst segment of the table represents the total number of unique SKUs
21
for each store, i.e. the category assortment size. Thus, the number of SKUs
oered in the peanut butter category in store 1419 varied from 25 to 33, with a
median (mean) value of 29 (28.56) and a standard deviation of 1.7. Overall, store
1420 stocked the largest number of unique SKUs while store 1424 had the fewest.
The remaining sections of the table report summary statistics for the normalized
entropy of each attribute taken across the the category as a whole. For example,
in store 1422,
avor entropy is about 0.35, while the values for brand and package
size are much higher, indicating that many more brand and package size variants
are oered in this category than are
avors.
2.4.2.2 Brand-level Assortment Variation
I illustrate the variation in assortment size and structure at the category- and
brand-levels using the peanut butter category as an example. I select two brands
(Skippy and Peter Pan) to illustrate the variation in brand level assortment
and present summary statistics for three assortment related variables, number
of SKUs, package size, and
avor in Table 2.5, 2.6, and 2.7, respectively.
Table 2.5 shows the variation in the number of SKUs oered during the ob-
servation period. In store 1419 Skippy consisted of an average of about 7.4 SKUs
while Peter Pan had about 2.5 SKUs. This dierence in product line lengths was
found in the other stores as well. However, despite the lower number of SKUs, the
maximum value of both package size and
avor entropy is greater for Peter Pan
than for Skippy. Table 2.6 shows that, package size entropy for Skippy in store
1419 varied between 0.69 and 0.8 (mean value 0.77, median value 0.8) while that
22
for Peter Pan varied between 0 and 1. The standard deviation in the measure
is 0.01 for Skippy and 0.33 for Peter Pan. A similar pattern is also observed for
avor entropy in Table 2.7.
Table 2.5: Number of SKUs for Skippy and Peter Pan
Mean Median Min Max SD
Skippy
Store 1419 7:37 7 6 8 0:53
Store 1420 8:04 8 8 9 0:20
Store 1422 6:63 7 5 8 0:53
Store 1423 7:58 8 6 8 0:55
Store 1424 7:63 8 5 8 0:61
Peter Pan
Store 1419 2:49 3 1 3 0:63
Store 1420 2:33 2 2 3 0:47
Store 1422 2:44 2 2 3 0:50
Store 1423 2:77 3 2 3 0:42
Store 1424 2:71 3 2 3 0:46
23
Table 2.6: Package Size Entropy Variation for Skippy and Peter Pan
Mean Median Min Max SD
Skippy
Store 1419 0:77 0:80 0:69 0:80 0:03
Store 1420 0:67 0:67 0:67 0:72 0:01
Store 1422 0:67 0:69 0:61 0:74 0:04
Store 1423 0:68 0:67 0:61 0:69 0:02
Store 1424 0:68 0:67 0:66 0:74 0:02
Peter Pan
Store 1419 0:43 0:58 0:00 1:00 0:33
Store 1420 0:86 1:00 0:58 1:00 0:20
Store 1422 0:25 0:00 0:00 0:58 0:29
Store 1423 0:47 0:58 0:00 1:00 0:25
Store 1424 0:41 0:58 0:00 0:58 0:26
Table 2.7: Flavor Entropy Variation for Skippy and Peter Pan
Mean Median Min Max SD
Skippy
Store 1419 0:34 0:35 0:33 0:39 0:01
Store 1420 0:33 0:33 0:31 0:33 0:00
Store 1422 0:36 0:35 0:33 0:42 0:02
Store 1423 0:34 0:33 0:33 0:39 0:01
Store 1424 0:34 0:33 0:33 0:42 0:01
Peter Pan
Store 1419 0:58 0:58 0:00 1:00 0:33
Store 1420 0:19 0:00 0:00 0:58 0:27
Store 1422 0:82 1:00 0:58 1:00 0:21
Store 1423 0:65 0:58 0:00 1:00 0:20
Store 1424 0:70 0:58 0:58 1:00 0:19
24
2.5 Estimation Procedure
2.5.1 Calibration Sample Selection
I use systematic random sampling to select 84% of the purchase occasions used to
calibrate the model parameters. Estimation proceeds in two stages. In the rst
stage, a heterogenous MNL SKU choice model is estimated using a Hierarchical
Bayes (HB) approach. The estimated posterior means of the parameters of this
rst stage model are used to calculate the inclusive value of category alternatives
for each household's shopping trip, which are then used to estimate binary logit
model of purchase incidence, also using a HB approach.
In both stages, I draw from the full conditional distribution of each param-
eter using Gibbs or Metropolis Hastings steps, as appropriate. In each stage of
estimation, 50000 MCMC draws were made, with every 50th draw retained for
posterior inference.
2.5.2 Prior Specication
I collect all of the household level parameters for the SKU choice models in the
vectore
h
, i.e,
h
= (
h1
;
h2
;:::;
h
;
h
): (2.7)
Priors for the parameters in the SKU choice model are specied as:
25
h
N(D
h
;V
); (2.8)
vec() N(vec(
);V
A
1
); (2.9)
V
IW (;V ); (2.10)
whereA
= 0:1I, = number of variables+3, andV is set to the identity ma-
trix multiplied by; adapting the default setup for the MCMC routine described
in Rossi, Allenby, and McCulloch (2005). D
h
includes household specic vari-
ables such as household size and income level. Priors for the purchase incidence
models are specied in a similar manner.
2.5.3 Estimation
Since the number of SKUs changes over time across stores, the number of alter-
natives varies constantly. I used R to write functions (or routines) to perform
hierarchical Bayesian estimation of multinomial logit choice models adapting the
codes developed by Rossi, Allenby, and McCulloch (2005) to account for the
varying number of alternatives.
2.6 Results
The model was estimated for ve categories: bacon, coee, peanut butter, tissue,
and paper towels.
26
2.6.1 Calibration Sample Comparisons
2.6.1.1 SKU Choice Model
In total, I estimate three dierent SKU choice models for each category. The
baseline model, which corresponds to the model of Fader and Hardie (1996),
includes intercepts for each attribute-level and the marketing mix variables. The
second model adds assortment size measures to the baseline model while the third
model adds in the assortment structure measures as well. Table 2.8 reports the
log marginal density for each model that measures how well it ts the calibration
data (Newton and Raftery, 1994).
Table 2.8: Log Marginal Density of SKU Choice Models
Baseline Assortment Size Assortment Size & Structure
Bacon 2021:68 2015:49 1966:69
Coee 3913:33 3867:75 3835:51
Peanut Butter 1220:08 1205:47 1192:28
Tissue 9273:87 9214:14 9196:07
Towel 10969:83 10964:17 10923:82
The table shows that adding assortment dimension measures improves the t
of the SKU choice model in all ve product categories and that the full model,
which includes both assortment size and structure dimensions, performs the best
in each category.
27
Table 2.9: Log Marginal Density of Purchase Incidence Models
Baseline Assortment Size Assortment Size & Structure
Bacon 6975:14 6804:21 6700:44
Coee 10546:12 10323:19 10192:58
Peanut Butter 3159:91 3110:12 3102:10
Tissue 17579:52 17049:24 16571:57
Paper Towel 16020:60 15442:37 15371:75
2.6.1.2 Purchase Incidence Model
Table 2.9 reports the corresponding log marginal densities for three purchase
incidence models in each category : a baseline model without variables related to
category assortment, an intermediate model that includes a category assortment
size measure, and the full model that also adds in the category entropy terms.
The pattern of log marginal densities matches that of the SKU choice model:
the baseline model has the worst t while the model with assortment size and
structure dimensions provides the best t to the data.
2.6.2 Holdout Sample Comparisons
In order to validate these results, I also compared the performance of these mod-
els on the holdout sample. My approach follows earlier research by using the
predicted probabilities from the dierent models to calculate the Mean Absolute
Deviation (MAD) in the holdout sample.
Table 2.10 reports these values for all categories and reveals that, except for
the bacon category, the pattern of model t follows that seen in the calibration
28
Table 2.10: Mean Absolute Deviation (MAD) for SKU Choice Models
Baseline Assortment Size Assortment Size & Structure
Bacon 0:4475 0:4494 0:4487
Coee 0:5082 0:5062 0:5030
Peanut Butter 0:5291 0:5254 0:5224
Tissue 0:4552 0:4536 0:4525
Paper Towel 0:5861 0:5844 0:5820
sample. Thus the full model has the smallest, and the basline model the largest,
MAD values, while the model that includes assortment size alone provides an
intermediate level of t.
Table 2.11: Mean Absolute Deviation (MAD) for Purchase Incidence Models
Baseline Assortment Size Assortment Size & Structure
Bacon 0:1719 0:1668 0:1628
Coee 0:1890 0:1842 0:1826
Peanut Butter 0:1530 0:1490 0:1476
Tissue 0:3252 0:3129 0:3046
Paper Towel 0:2890 0:2741 0:2724
Table 2.11 reports the MAD for the dierent purchase incidence models and
once again the results are consistent with the results from the calibration sample.
29
2.6.3 Parameter Estimates
Overall, results from both the calibration and holdout samples conrm that as-
sortment size and structure, at the SKU- and category-levels, respectively, signi-
cantly impact SKU choice and purchase incidence behavior. Parameter estimates
from the full model are reported in Table 2.12. To conserve space, I conne my
discussion to the estimates from the peanut butter category and provide results
for the other categories in the Appendix.
2.6.3.1 SKU Choice Model
Table 2.12 reports the mean coecients with the signicant coecients displayed
in bold face. Table 2.12 shows that marketing mix variables such as price, feature,
and display have the expected signs and a statistically signicant impact on SKU
choice. Dierent SKU attributes are also seen to impact SKU choice dierently.
My main interest is in the impact of assortment size and structure aect on
SKU choice. First, we see that assortment size has negative impact on choice
though its impact is statistically insignicant. Second, assortment structure ef-
fects are much greater for some attributes than for others. Specically, the results
show that, while
avor entropy does not aect SKU choice, variability in package
size does have a positive and signicant impact on SKU choice. This shows that
that some attributes are more important to the assortment than others. Third,
responsiveness to assortment structure varies across households and larger house-
holds are less responsive to
avor assortment structure. .
30
Table 2.12: Parameter Estimates of SKU Choice Model
Intercept Family Size Income
Price -2.359 0:278 0:103
Feature 0.909 0:002 0:014
Display 1.207 0:042 0:076
Brand.HOLSUM 1:269 0:052 0:233
Brand.JIF 2.888 0:146 0:337
Brand.PETER.PAN 0:732 0:828 0.586
Brand.PRIVATE.LABEL 1:135 0:159 0:087
Brand.REAL 1:107 -3.959 0:529
Brand.REESES 1.916 0:580 0.546
Brand.SKIPPY 3.785 0:009 0:391
Brand.SMUCKERS 2.688 0:346 0:333
Size.16 0:856 0:391 0:212
Size.17.3 1.962 0:040 0:203
Size.18 2.981 0:273 0:032
Size.27 0:164 1.819 1.614
Size.28 4.315 0.852 0.464
Size.40 4.524 1.358 0:537
Size.64 2.242 0:155 1.209
Flavor.CRMY 2.107 1.477 0:221
Flavor.CRNC 0:345 1.140 0:297
Flavor.SCHKY 0:650 0.855 0:174
Flavor.XCRNC 1:026 1.626 0:279
Assortment Size 0:001 0:006 0:033
Entropy Package Size 2.142 -0.920 0:405
Entropy Flavor 1:333 -0.861 0.347
31
2.6.3.2 Purchase Incidence Model
Table 2.13 shows the estimation results for the peanut butter category. In this
table, the bold faced numbers denote coecients that have are statistically sig-
nicant based on their 95% posterior interval.
Table 2.13: Parameter Estimates of Purchase Incidence Model
Intercept Family Size Income
Assortment Size 0:059 0:003 0:009
Entropy Brand -5.446 0:177 0:464
Entropy Package Size -3.825 0:408 0:269
Entropy Flavor 1:057 0.783 0:240
Last Purchased Quantity 0:343 0:006 0:005
Inclusive Value 0.145 0:007 0:022
The table shows that consumers are not in
uenced by the number of SKUs
in the category (Assortment Size) or the variety of
avors oered (Entropy Fla-
vor). On the other hand, they are less likely to purchase in the category if the
store oers a large number of brands (Entropy Brand) or package sizes (Entropy
Package Size). Also the category inclusive value (Inclusive Value) aects pur-
chase incidence positively. In this category, household specic variables such as
last purchased quantity (Last Purchased Quantity) do not seem to impact pur-
chase incidence decisions. Overall, household characteristics such as family size
or income level play a relatively small role in the peanut butter category. One
exception is that high income households tend to be in
uenced more by higher
avor entropy (second column in Entropy Flavor).
32
2.7 Managerial Implications
Having established that brand- and category-level assortment structures do have
an important in
uence on consumer's SKU choice and category purchase deci-
sions, respectively, and that it is possible to identify these eects using the cross-
sectional and over-time variation in oered assortment, I now turn to examining
the implications of my model for manufacturers and retailers.
2.7.1 Simulating SKU Deletion Decisions
From both a manufacturer's and a retailer's perspective, a critical aspect of man-
aging a product line comes down to deciding which individual SKUs to oer.
This decision requires a good understanding of the impact of how product assort-
ment impacts demand, which is the objective of the next analysis. My modeling
framework permits me to directly examine how the presence or absence of certain
SKUs, and the corresponding product attributes that they represent, directly im-
pact consumers' choice decisions. It is important to recognize that analyzing this
eect is complicated by the fact that adding or deleting an SKU has a direct
impact not only on the brand to which it belongs, but that it can also change
the assortment structure of the category as well via changes in entropy. More
specically, for example, introducing a new
avor variant of a brand by adding
a new SKU, will increase the brand's assortment size by one unit, change the
entropy of its
avor attribute, and also impact entropy at the product category
level.
33
One thing to note is that retailers and manufacturers may view assortment
decisions dierently. . For example, if the manufacturer of JIF plans to reduce
the product line length by removing one SKU, they will be concerned about the
impact of this decision on brand share. In contrast, retailers considering dropping
an SKU from the JIF brand will be more interested in its impact on category-
level sales. I perform two simulations to address both manufacturer and retailer
perspectives.
2.7.1.1 Manufacturer's Perspective
Taking a manufacturer's perspective, I examine the impact of deleting a single
SKU on the share of the brand to which it belongs. Repeating this exercise for
each SKU in a brand's line, enables me to rank each SKUs in according to its
relative impact on the brand's assortment. I compare these SKU rankings to
those obtained from a similar analysis based on the parameters of the baseline
model.
This simulation seeks to answer the following manufacturers' questions: (1)
\How much will brand share change if I drop a particular SKU from the product
line?", (2) \Which SKU should I drop if it has to have the smallest impact on
brand share?"
The procedure for the counterfactual is illustrated for the JIF brand in store
1420. In the counterfactual SKU choice probabilities are recalculated for each
34
household and store visit, after deleting the target SKU. Summing these proba-
bilities across the sample yields the shares of of the remaining SKUs and of the
brand.
2.7.1.2 Retailer's Perspective
The second simulation is performed to address the following questions taking a
retailer's perspective. Thus, I ask \What will total category sales be if a certain
SKU is dropped?" and \Which SKU deletion has the least impact on sales?"
This counterfactual follows the logic of the rst one, except that both purchase
incidence and SKU choice models are used to predict store sales instead of brand-
share.
2.7.2 Results
I select one store (1420) and one brand (JIF) with 11 SKUs for the two coun-
terfactuals. Results are summarized in Table 2.14, which ranks each SKU in the
order of the impact of its deletion on share. Thus a small number indicates that
deleting an SKU has the least impact on share, while large number indicates
SKUs whose deletion causes the greatest impact on shares.
2.7.2.1 Manufacturer's Perspective
The rst column in Table 2.14, shows the rankings based on the baseline model
while the second column represent the rank order obtained from the proposed
model. It is notable that both models identify SKU 13700000409 as the best
35
Table 2.14: Recommendation of SKU to Drop
SKU Manufacturer Retailer
Baseline Full Baseline Full
13700000406 6 6 5 5
13700000407 11 10 10 10
13700000408 9 7 8 4
13700000409 1 1 3 8
13700000410 3 3 11 11
13700000411 8 9 6 6
13700048007 7 8 4 3
13700048008 2 2 7 9
13700048014 4 5 2 1
3 10 11 1 7
13700048009 5 4 9 2
candidate for deletion. However, the two models dier in their recommendations
for the other SKUs. For example, 13700048014 ranks fourth in the baseline
model analysis, while SKU 13700048009 is the fourth best candidate based on
the proposed model. Since two models can produce quite dierent predictions
in some cases, this result shows us the importance of incorporating assortment
measures to gain a better insight.
2.7.2.2 Retailer's Perspective
I also compare recommendations from the following models:
Proposed model of SKU choice and incidence model in which assortment
size and structure in
uence both decisions. (Full SKU-PI model)
36
Baseline model of SKU choice and purchase incidence, with no assortment
eects. (Baseline SKU-PI model)
The third and fourth column of Table 2.14 shows how the recommendations of
the full model dier from those from the baseline model. The full model predicts
that removing SKU 13700048014 has the least impact on category sales, while
the baseline model identies SKU 3 as having the smallest decrease in category
sales. Such dierence in prediction emphasizes the importance of using the full
model incorporating category level assortment measures as well as brand-level
assortment measures to help retailers make better decisions.
2.7.2.3 Dierence in Perspectives
In this simulation, both manufacturer and retailer have the same question, \Which
SKU to drop from JIF brand?". Nevertheless, they do not share the same objec-
tive since retailers are interested in category or store level sales while manufactur-
ers are more concerned about its brand share. This simulation shows that such
dierence may lead to potential con
ict of interest between retailers and manu-
facturers. For example, the second and fourth column of table 2.14 illustrates the
dierence. For JIF manufacturer, it is best to remove SKU 13700000409 to keep
the brand share as high as possible. For retailer 1420 planning to drop an SKU,
it is best to remove 13700048014 to achieve the maximum category sales. There-
fore, if a retailer is planning to reduce one SKU from JIF brand, the retailer's
optimal decision may not be optimal for JIF manufacturer.
37
2.8 Discussion
Many researchers have investigated diverse aspects of assortment but, to my
knowledge, no one has examined how assortment structure aects actual brand
choice behavior or its in
uence on purchase incidence behavior. To address these
gaps, I propose an SKU choice model incorporating both brand-level assortment
size and structure and a purchase incidence model that includes the eect of
category assortment.
The result shows that including both assortment dimensions improves the
model. In addition, I identied how assortment structure varies across attributes.
It turns out that providing assortment variability in some attributes aects SKU
choice signicantly but not in the other attributes.
I also found that assortment responsiveness diers across households. Bigger
households tend to value variability in
avor more than smaller households. The
nding implies that retailers can improve protability by adapting their assort-
ment decision to their customer demographics.
In addition, I illustrate the importance of considering assortment dimensions
in SKU level decision by calculating expected brand share using the full model
with assortment measures and baseline model without assortment measures. The
model with assortment measures produces quite dierent prediction of brand
share and store purchase incidence compared to the model without assortment
measures. This shows that models without assortment dimensions may lead to
suboptimal SKU level decisions.
38
The study can be extended in several ways. First, Chintagunta, Dube, and
Goh (2005) showed that the price estimates will be biased if the unobserved
brand-time characteristics are not accounted for. My research is an attempt to
study the impact of observable part of brand-time specic variation out of unob-
servable variation in their study. Since the current study does not control unob-
served impact, the coecient for brand-level entropy measures may be picking up
the variation from the unobservable brand-time specic shock. Thus, to clearly
quantify the impact of assortment variation, the model needs to incorporate the
unobservable part as well.
Second, by estimating the model on multiple categories of products, and link-
ing the parameters together, researchers should be able to directly study how
household response to assortment sensitivity is correlated across categories simi-
lar to Ainslie and Rossi (1998) and Iyengar, Ansari, and Gupta (2003).
Third, a store choice model can be incorporated in addition to the SKU
choice and purchase incidence models. Estimating this integrated model can
help identify how assortment impacts dierent consumer purchase decisions, and
particularly to examine whether assortment is more in
uential in one decision
stage than others.
39
Chapter 3
Structural Models of Manufacturer and Retailer
Competition in the U.S. Automobile Industry
3.1 Introduction
As an important element of the marketing mix, the distribution channel has been
a focus of extensive research in marketing both theoretical and empirical. Theo-
retical analysis has focused on issues such as how to design an optimal channel
structure (McGuire and Staelin, 1983; Coughlan, 1985) and the impact of dier-
ent channel structures on channel prot (Choi, 1991). Marketers and economists
are often also interested in the degree of price competition among rms within an
industry and the factors that aect its intensity. In the channels context, while
considerable attention has been paid to understanding the nature of competition
between manufacturers, relatively little is known about how manufacturers' use
of exclusive retailers aects competitive intensity.
40
Recent empirical research has attempted to directly infer the degree of com-
petitive interaction between market players based on market data on sales and
prices. Kadiyali, Chintagunta, and Vilcassim (2000) gain insights into channel
power by empirically estimating the nature of the Vertical Strategic Interaction
(VSI) between a manufacturer and retailer in the refrigerated orange juice and
tuna categories. A key feature of their modeling approach is a conduct param-
eter that captures a continuum of possible VSIs, in contrast to the traditional
menu approach with a pre-specied number of interactions such as Vertical Nash,
Manufacturer Stackelberg and Retailer Stackelberg.
Research on Horizontal Strategic Interaction (HSI) meanwhile has been con-
ned to the interaction between manufacturers, not between retailers. For exam-
ple, Sudhir (2001a) contributes to the literature on automobile competition by
proposing an approach to identify the degree of competitive interaction among
manufacturers, but his analysis ignores the role of retailers. Because the theo-
retical channels literature has suggested that using exclusive retailers can alter
the competitive intensity between manufacturers (Coughlan, 1985), models that
exclude retailers could result in incorrect inferences about the nature of manu-
facturer competition. In summary, two key features of previous work are : (a)
that it either completely ignores the presence of retailers, e.g. Sudhir (2001a),
or only studies cases in which there is a single common retailer, e.g. Villas-Boas
and Zhao (2005), and (b) that it focuses on identifying the Horizontal Strategic
Interaction (HSI) between manufacturers, and not between retailers.
41
However, there is considerable evidence that retailers directly compete with
each other at strategic and tactical levels. For example, retailers make strategic
choices about the overall pricing formats that they will follow, positioning them-
selves as Every Day Low Pricing (EDLP) or High Low stores that dier in their
relative ability to attract dierent kinds of shoppers (Lal and Rao, 1997; Bell and
Lattin, 1998). At a more tactical level, Shankar and Bolton (2004) show that
that competitor factors explain most of the variance in weekly brand prices of
multiple retailers in six CPG categories in ve U.S. markets. Similarly, automo-
bile dealers devote signicant resources to TV and newspaper advertising that
emphasizes low prices and attractive terms for nancing and leasing contracts in
order to attract car buyers to their dealerships.
In the face of this evidence, the paucity of research examining the HSI between
retailers represents a signicant gap in the literature. Because strategic manufac-
turers will set wholesale prices after taking into account the response of retailers,
and because this response is inextricably linked to the nature of competition be-
tween retailers, it raises the question of how retailer actions impact inferences
about manufacturer competition. Also, because automobile dealers have been
either overlooked in the empirical literature (Sudhir, 2001a) or assumed to com-
pete in a Bertrand-Nash fashion in the theoretical literature (Coughlan, 1985),
the true nature of dealer competition is still left unexplored. I attempt to ll this
gap via two studies of the automobile market, which is characterized by multiple
manufacturers selling through exclusive retailers.
42
Figure 3.1: Contributions of This Essay
(a) Literature
(b) Study 1
(c) Study 2
43
Consider a simple example in which two manufacturers, GM and Toyota, say,
compete in a particular geographic market. Figure 3.1(a) is a stylized representa-
tion of the models used in previous work, which ignore the presence of retailers.
In contrast, I propose a structural model of competition between multiple manu-
factures, each represented by exclusive retailers. The model identies the nature
of the competition between retailers (and manufacturers) as well as the impact
of demand and costs on wholesale and retail prices. A key feature of the model
is that the HSI between retailers is captured in a
exible manner: i.e. it is not
restricted to be Bertrand-Nash. The HSI between manufacturers is also cap-
tured in a similarly
exible manner, permitting it to be more aggressive or more
cooperative than that implied by Bertrand-Nash.
In Study 1, as illustrated in Figure 3.1(b), I abstract away from competi-
tion among dealers of the same make (intra-channel HI) and focus only on the
competition among dealers carrying dierent nameplates (inter-channel HI). In
this study, I explicitly examine how including retailer competition in the model
alters conclusions about the nature of the HSI between manufacturers in this
market. I analyze a dataset of new car purchases in the premium compact sedan
category made at dealerships located in ve major markets in the US. I use a
sequential estimation approach to obtain model parameters. Demand parameters
are rst estimated using Hierarchical Bayes methods; supply side parameters for
both retailers and manufacturers are then estimated using Generalized Methods
of Moments (GMM).
44
The results show that the HSI between manufacturers is dierent from that
between retailers. Manufacturers in this market interact cooperatively while their
retailers interact aggressively. I also demonstrate that alternative models that a)
ignore the presence of retailers, b) assume retailers set prices non-strategically,
or c) assume interactions between retailers are Bertrand-Nash, all produce mis-
leading inferences about the nature of manufacturer interaction in the channel.
In Study 2, as illustrated in Figure 3.1(c), I extend the model to examine how
intra- and inter-channel competition varies across dierent markets. I propose a
structural model of competition between multiple manufactures, each of whom
is represented by dierent numbers of exclusive retailers in each geographic mar-
ket. I analyze consumer purchases for the premium compact sedan segment for
the period Oct 2005 to September 2007 in two dierent DMAs: Houston and
Minneapolis. The results show that (i) inter- and intra-channel competition can
be very dierent from each other even in the same market, and (ii) intra-channel
competition among same brand retailers varies from one market to another. I
discuss the relevance of my comprehensive modeling framework to the ongoing
upheaval in the U.S. automobile industry, particularly the drastic elimination of
dealers by GM and Chrysler.
45
3.2 Study 1: Manufacturer Competition in the
Presence of Exclusive Dealers
In this study, I propose a model of demand and supply that accounts for both
manufacturer and retailer interaction to address the following research questions.
First, can the nature of competition between retailers in a market be dierent
from that between manufacturers? Second, how do dierent assumptions made
about the presence or absence of dealers, and about their pricing behavior, impact
inferences about the horizontal strategic interaction (HSI) between manufactur-
ers?
Previous research in the automobile industry has typically ignored retailers
(Berry et al., 1995, 2004; Petrin, 2002; Sudhir, 2001a) or included non-strategic
retailers charging a xed margin over the wholesale price (Albuquerque and Bron-
nenberg, 2008). On the other hand, the theoretical literature on exclusive retailers
assume that these retailers compete in a Bertrand-Nash fashion (Coughlan, 1985;
Moorthy, 1988). I test how these dierent assumptions about the retailer impact
our inferences about the nature of competition between manufacturers.
My empirical analysis shows that, indeed, the HSI between manufacturers is
dierent from that between retailers. Thus, the major manufacturers in this mar-
ket interact cooperatively while the interaction between retailers in the channel
is aggressive. I also demonstrate that alternative models that a) ignore retailer
presence, b) assume retailers are non-strategic in setting prices, or c) assume in-
teraction between retailers to be Bertrand-Nash, produce misleading inferences
46
about the nature of manufacturer interaction in the channel. Specically, these
models conclude that competition between manufacturers is aggressive, not co-
operative.
From a managerial perspective, the importance of assessing the nature of
manufacturer and dealer competition is signicant because of the recent turmoil
in the nancial markets, the global recession and the resulting upheavals in the
U.S. automobile industry. Several rms have had to try extraordinary measures
to survive the fallout. For instance, GM had to declare bankruptcy, sell or shut-
down several divisions and terminate the contracts for about 2600 dealers in their
distribution network. During the same period, Chrysler terminated the contracts
of almost 800 dealers. Because only some manufactures have been able to prune
their dealer network, this raises the possibility that competition among dealers
has been impacted dierently vis- a-vis competition among manufacturers, which
calls for a modeling approach that can separately identify the nature of interaction
among retailers from that among manufacturers.
The remainder of the study is laid out as follows. First, I discuss the primitives
of the demand and supply model and derive the optimal prices charged by retailers
and manufacturers. The following section describes the data used in the empirical
analysis and discusses the estimation strategy. After discussing the estimation
results, I summarize the conclusions, discuss the limitations of my study and
provide some directions for future research.
47
3.2.1 Modeling Framework
I propose a structural model of demand and supply for a particular vehicle prod-
uct segment in the automobile industry (e.g., mid-sized sedans or minivans),
characterized by multiple manufacturers who sell through an exclusive retailer
network in each of several geographic markets. The model makes the following
assumptions:
Each manufacturer sells through one, and only one, representative retailer
in each DMA. Thus, even though the empirical analysis uses sales data
from several dealers in a DMA, optimal prices are derived as if all these
purchases were made at a single representative dealership. In other words,
the proposed model ignores competition among dealers for the same make
(intra-channel competition) and focuses exclusively on competition between
dealers of dierent manufacturers (inter-channel competition). Thus, with
J manufacturers, each DMA has J representative dealers, one for each
manufacturer.
Because I focus on understanding the HSI between manufacturers and re-
tailers, I assume that the VSI between each pair of manufacturers and
retailer is Manufacturer Stackelberg (Sudhir, 2001b). Thus, manufacturers
set prot-maximizing wholesale prices rst, before retailers follow by setting
retail prices.
I do not make a priori assumptions about the nature of the competitive in-
teraction between the dierent retailers in a DMA: the parameter describing
48
competition is estimated from the data and it can be Bertrand-Nash, more
aggressive than Bertrand-Nash, or more cooperative than Bertrand-Nash
(Sudhir, 2001a).
I follow the same approach to describe competition between manufactur-
ers in the market: aggressive, Bertrand-Nash competitive, or cooperative
(Sudhir, 2001a).
The unit of analysis is the DMA-week. Thus both manufacturers and re-
tailers set vehicle prices in each DMA and time period in order to maxi-
mize prots from this region and time period. This is consistent with the
time frame for promotion-planning practices in the industry as discussed
by Silva-Risso and Ionova (2008).
Prices of both retailers and manufacturers are chosen to maximize prots
for a specic product category, e.g., entry level sedans, and not jointly
across multiple automobile segments such as SUV's, minivans etc.
Retailer competition is assumed to be restricted to dealers within a DMA;
Because the markets in my analysis are geographically very dispersed, com-
petition between retailers in dierent DMAs is ignored.
3.2.1.1 Glossary
The subscripts used in the model are as follows.
i: household,
49
j;k;l: vehicle model of manufacturer j, k, & l, respectively
J: the total number of manufacturers (retailers),
d: geographic area (DMA),
t: time (week or month depending on the unit of analysis).
3.2.1.2 Consumer Demand
The utility of vehicle j for consumer i in geographic area d at time t is specied
as:
U
ijdt
=
jd
+
d
p
jdt
+
jdt
+
ijdt
; (3.1)
where,
jd
is the intrinsic preference for vehicle j,
p
jdt
is the net retail price
1
for vehicle j in DMA d at time t,
jdt
the unobserved demand shock for vehicle j in area d at time t,
and
ijdt
are individual-specic demand shocks with a type I extreme value
distribution.
1
I will dene \net" retail(wholesale) price as the retail(wholesale) price less manufacturer
rebate, which is equivalent to assuming that 100% of the rebate is passed through to the
consumer.
50
To account for heterogeneity, preference coecients,
jd
, and price coecient,
d
, are region specic.
The utility of the outside good is specied as
U
i0dt
=
i0dt
; (3.2)
with
i0dt
having an extreme value type 1 distribution.
Assuming no residual preference heterogeneity within a DMA, the choice prob-
ability of vehicle j can be expressed as
s
jdt
=
exp(V
jdt
)
1 +
P
k
exp(V
kdt
)
(3.3)
where V
jdt
=
jd
+
d
p
jdt
+
jdt
.
3.2.1.3 Retailer Behavior
I assume that a retailer sets net retail prices,p
jdt
, for vehiclej in geographic area
d at time t, in order to maximize the following objective function:
max
p
jdt
(p
jdt
w
jdt
)s
jdt
+
X
k6=j
jk
(p
kdt
w
kdt
)s
kdt
: (3.4)
In the above equation, w
jdt
represents the manufacturer's net wholesale price.
Suppressing the common subscripts d and t, permits this equation to be re-
written as:
max
p
j
(p
j
w
j
)s
j
+
X
k6=j
jk
(p
k
w
k
)s
k
: (3.5)
51
Thus, in setting retail prices net of rebate (or net retail prices), retailer j not
only considers his own prots (rst term in Equations (3.4) and (3.5)) but may
also consider the prot levels of the other competing retailers in the same DMA
(second term in the equations) through the interaction parameter
jk
. Values
of
jk
> 0 indicate cooperative behavior, values of
jk
< 0 represent aggressive
competition among retailers and
jk
= 0 for all j6= k represents the standard
assumption of Bertrand-Nash competition among retailers (Sudhir, 2001a).
3.2.1.4 Alternative Models of Retailer Interaction
Figure 3.2: Models
BLP (1995,2004)
Sudhir (2001)
Albuequerque &
Bronnenberg (2008)
McGuire & Staelin (1983)
Coughlan (1985)
This Research
No Retailer
With Retailer
Non-Strategic Retailer
Strategic Retailer
BN Competition Flexible Competition
52
As previously discussed, previous theoretical and empirical research has adopted
dierent approaches to modeling market competition, yielding several competi-
tive scenarios that are summarized in the hierarchical tree shown in Figure 3.2.
The top node of the tree distinguishes between the cases in which the retailer is
ignored and those in which retailer behavior is considered. The second level of
the tree pertains to the type of pricing behavior assumed for the retailer: non-
strategic or strategic. Under strategic pricing, the nal node pertains to the type
of retailer interaction being modeled: Bertrand-Nash or
exible. The relevant
citations pertaining to these scenarios are also shown in the gure.
The resulting nodes at the bottom of the tree thus yield four alternative
scenarios: 1) the No Retailer model, 2) non-strategic retailers charging a xed
margin, termed the Non-strategic Retailer model, 3) strategic price setting retail-
ers whose interaction is Bertrand Nash, termed the Strategic Retailer-BN model
and 4) the proposed model in which retailer price setting is strategic and their
interaction is general, termed the Strategic Retailer-Flexible model.
The Strategic Retailer-BN model is a special case of the Strategic Retailer-
Flexible model in which
jk
= 0 for j6= k. The proposed Strategic Retailer-
Flexible Interaction Model generalizes the interaction by allowing retailer inter-
action to be more aggressive (
jk
< 0) or more cooperative (
jk
> 0).
3.2.1.5 Manufacturer Behavior
Vehicle manufacturers vary wholesale price and manufacturer rebate, charging
retailers the net wholesale price,w
j
, (wholesale price net of manufacturer rebate)
53
that maximizes their own prots. Thus the manufacturer objective function can
be written as:
max
w
j
(w
j
c
j
)s
j
+
X
k6=j
jk
(w
k
c
k
)s
k
;
2
(3.6)
where, c
j
is the manufacturing cost.
As in the retailer case, the interaction parameter,
jk
, represents the impact of
competing manufacturerk's prot on manufacturerj's pricing decision. Dierent
values for the estimated parameters reveal whether this interaction is aggressive,
Bertrand-Nash, or cooperative (Sudhir, 2001a).
The model set-up and the parameters estimated in the dierent models are
summarized in Figure 3.3. The dotted lines in the gure represent the interac-
tions that are estimated from the data while the solid lines stand for interactions
that are assumed. For example, in Figure 3.3(a), both manufacturer and retailer
interactions are estimated from the data. However, retailer interaction in Figure
3.3(b) is assumed to be Bertrand-Nash, while manufacturer interaction is esti-
mated. Similarly, Figure 3.3(c) also assumes non-strategic retailers charging a
xed margin, and only estimates manufacturer interaction. Finally, the baseline
model in Figure 3.3(d) completely ignores retailers and only infers manufacturer
HSI from the data. I rst discuss the most general model, in which both types of
HSI are estimated, and then discuss the other scenarios, which are special cases
of the general model.
2
Time and area subscripts have been suppressed to aid exposition.
54
Figure 3.3: Model Summary
M
1
M
2
R
1
R
2
C
Estimated
Estimated
(a) Model 1: Strategic Retailer Flexible
M
1
M
2
R
1
R
2
C
Estimated
BN Assumed
(b) Model 2: Strategic Retailer BN
M
1
M
2
R
1
R
2
C
Estimated
(c) Model 3: Non-strategic Retailer
M
1
M
2
C
Estimated
(d) Model 4: No Retailer
55
3.2.1.6 Model 1: Strategic Retailer Interacting Flexibly
In this model, each manufacturer-retailer pair plays a manufacturer Stackelberg
game. To derive the optimal prices, I rst solve for the optimal retailer prices
in any DMA/week, taking manufacturer wholesale prices as given. Then opti-
mal manufacturer prices are obtained taking into account the retailer's optimal
response function.
Retailer Price
Retailer j sets retail price net of manufacturer rebate, p
j
, to maximize prot
(Equation 3.5) given manufacturers' net wholesale prices (w
j
and w
k
) and net
prices at the competing retailers, p
k
. The optimal net retailer price p
j
can be
shown to satisfy the following rst order condition.
"
s
j
+ (p
j
w
j
)
@s
j
@p
j
+
X
k6=j
jk
(p
k
w
k
)
@s
k
@p
j
#
= 0: (3.7)
Equation 3.7 can be further expanded by using the price derivative of the MNL
model and vertically stacking the resulting equations to yield
p
t
=w
t
[
(SP
t
)
0
]
1
s
t
(p
t
): (3.8)
In equation 3.8, elements of the matrix , i.e.,
[j;k] =
jk
; (3.9)
56
represent the type of interaction betweenj andk. The vectors of net retail prices,
net wholesale prices, and market shares are denoted byp
t
,w
t
, ands
t
, respectively.
The matrix SP contains the market share derivatives with respect to net retail
price, i.e.,
SP [j;k] =
@s
j
@p
k
: (3.10)
Solving equation 3.8 yields the optimal net retailer prices, p
t
as a function of net
wholesale prices, w
t
, and the retailer conduct parameters, .
Manufacturer Price
The optimal wholesale price net of rebate can be shown to satisfy the following
rst order condition:
s
j
(p
t
(w
t
; )) + (w
j
c
j
)
@s
j
(p
t
(w
t
; ))
@w
j
+
X
k6=j
jk
(w
k
c
k
)
@s
k
(p
t
(w
t
; ))
@w
j
= 0:
(3.11)
Stacking the J equations vertically, these supply side equations can be written
in matrix form as:
w
t
=c
t
[
(SW
t
)
0
]
1
s
t
(p
t
(w
t
; )); (3.12)
where c
t
is the vector of manufacturing costs and SW
t
and are JJ square
matrices that are specied as:
SW
t
[j;k] =
@s
j
(p
t
(w
t
; ))
@w
k
; (3.13)
57
and
[j;k] =
jk
: (3.14)
The matrix contains the manufacturer conduct parameters, with diagonal el-
ements equal to unity, i.e,
jj
= 1 for all j: Manufacturers take retailer price
setting behavior and potential share changes into account in setting net wholesale
prices. Suppressing the t subscript, SW can be calculated as
SW =SPPW; (3.15)
where each square matrix is dened as:
SW [j;k] =
@s
j
@w
k
; (3.16)
SP [j;k] =
@s
j
@p
k
; (3.17)
PW [j;k] =
@p
j
@w
k
: (3.18)
Assuming MNL demand, SP can be calculated analytically. PW can be calcu-
lated as
PW =C
1
D; (3.19)
where
C = (
S
v
) + ( (M
h
SP ))I; (3.20)
D =
(S
v
I): (3.21)
58
In the above equation,
denotes element-wise multiplication and represents
matrix multiplication. The square matrix, , contains the retailer conduct pa-
rameters and S
v
is a square matrix in which each row contains the vector of
market share s = (s
1
;s
2
;:::;s
J
). M
h
is a square matrix in which each column is
equal to the vector of retailer margins m = ((p
1
w
1
); (p
2
w
2
);:::; (p
J
w
J
)),
and I denotes an identity matrix of dimension of JJ.
3
3.2.1.7 Model 2: Retailers Pricing in a Bertrand-Nash Fashion
Setting the retailer conduct parameter in Model 1 to zero yields Model 2. Thus
the only dierence between Model 2 and Model 1 is that in equation 3.12 is an
identity matrix. Thus,
jk
= 1; for all j =k (3.22)
jk
= 0; for all j6=k: (3.23)
3.2.1.8 Model 3: Retailers Pricing With a Fixed Margin
In this model the VSI between manufacturers and retailers is still Manufacturer
Stackelberg, but retailers are non-strategic, simply charging a xed margin over
3
A detailed derivation of SW appears in Appendix B
59
the wholesale prices (Albuquerque and Bronnenberg, 2008). The net retail pricing
equation can therefore be written as:
p
j
=w
j
+m
j
; (3.24)
where m
j
is the xed margin for vehicle j. The net retail price derivatives with
respect to wholesale price become:
@p
j
@w
j
= 1; (3.25)
@p
k
@w
j
= 0: (3.26)
The share derivative with respect to net wholesale price can be simplied as
@s
j
@w
j
=
@s
j
@p
j
@p
j
@w
j
+
X
k6=j
@s
j
@p
k
@p
k
@w
j
=
@s
j
@p
j
; (3.27)
@s
k
@w
j
=
@s
k
@p
j
@p
j
@w
j
+
X
l6=j
@s
k
@p
l
@p
l
@w
j
=
@s
k
@p
j
: (3.28)
Using matrix notation, the manufacturer pricing equation can be written as fol-
lows:
w
t
=c
t
[
(SP
t
)
0
]
1
s
t
; (3.29)
where,
SP
t
[j;k] =
@s
jt
@p
kt
: (3.30)
60
3.2.1.9 Model 4: Manufacturers Competing Without Retailers
As a benchmark model, manufacturers are assumed to directly compete with
each other by setting retail price, a la Sudhir (2001a). The rst order condition
implies that manufacturers' optimal net retail prices,p
t
, must satisfy the following
equation:
p
t
=w
t
[
(SP
t
)
0
]
1
s
t
(p
t
): (3.31)
In this model, the decision variable is net retail price, p
t
, not net wholesale price
w
t
. Also, in order to provide a cleaner comparison to the other models, this
analysis diers from Sudhir (2001a) by setting list prices given manufacturing
costs.
3.2.2 Data
The empirical analysis uses automobile transaction data from the Power Informa-
tion Network (PIN), an aliate of J.D. Power and Associates. PIN collects sales
transaction data from a sample of dealerships in the major metropolitan areas
in the U.S. Currently, the PIN samples includes 26 U.S. markets accounting for
70% of total U.S. sales (Silva-Risso and Ionova, 2008).
PIN acquires information on all new and used car transactions from partici-
pating dealers and retains about 250 details for each transaction. The information
sent by dealers electronically to PIN is cleaned, decoded, and condential infor-
mation removed (Bucklin, Siddarth, and Silva-Risso, 2008). Each observation in
the PIN database contains the transaction date, the manufacturer, model year,
61
make, model, trim and other vehicle information, the transaction price, consumer
rebates, the interest rate, term, amount nanced (when the vehicle is nanced or
leased), and others.
I focus my attention on the premium compact sedan segment, which accounts
for 12.93% of all automobiles sales. My data cover the period October 2003 to
September 2004 and represent sales in the ve DMAs that have the highest sales
in this category, which taken together account for about 25% of total category
sales. The summary statistics in Table 3.1 show that during this time Los An-
geles was the largest market, followed by New York, Miami, San Francisco and
Philadelphia.
Table 3.1: Transaction Summary by DMA
DMA Freq Perc Cum.Freq Cum.Perc
Los Angeles 14091 34:19 14091 34:19
New York 11234 27:26 25325 61:45
Miami 5786 14:04 31111 75:49
San Francisco 5246 12:73 36357 88:22
Philadelphia 4856 11:78 41213 100:00
I select the three top-selling vehicles that together account for about 67%
of all transactions in this category. After deleting transactions that are missing
important vehicle information, such as MPG and vehicle size, which are required
to construct moment conditions in the GMM estimation procedure, I am left with
41213 transactions for further analysis. The average retail and wholesale prices,
and the shares of the shortlisted vehicles are summarized in Table 3.2.
62
Table 3.2: Transaction Summary by Vehicle
Vehicle Retail Price Wholesale Price Rebate Share (%)
Toyota Corolla 15746 13804 286 44:41
Honda Civic 15528 13636 0 33:35
Nissan Sentra 15867 13507 2070 22:25
The table shows that, in the ve selected DMAs, Toyota Corolla has the
largest market share, followed by the Honda Civic and Nissan Sentra, respectively.
The Sentra has the highest average retail price while the Civic has the lowest.
The wholesale prices of the Toyota Corolla are the highest while those for the
Nissan Sentra are the lowest. It is also notable that manufacturers dier in the
extent to which they use rebates to attract consumers. The Nissan Sentra was
supported by a signicant amount of price rebates while, in stark contrast, Honda
oered no consumer rebates for the Civic during the same time period.
3.2.3 Model Estimation
The rst step in our empirical analysis is constructing the prices and costs from
the transaction data. Next, demand model parameters are estimated using a Hi-
erarchical Bayes MCMC approach and, nally, the supply side model parameters
are estimated using a Generalized Method of Moments (GMM) approach.
63
3.2.3.1 Price Construction by Hedonic Regression
The unit of analysis is a specic vehicle model (e.g. Honda Accord). Each vehicle
model includes many congurations with various attributes, such as the trim level,
engine size, etc. Thus, variables like the wholesale price, retail price and market
share require us to aggregate over dierent vehicle congurations. Separate,
DMA-specic, hedonic regressions are used to relate wholesale and retail prices
to the dierent vehicle attributes and impute the retail and wholesale price used
in model estimation.
3.2.3.2 Demand Side Estimation
First, the demand side model is converted to a share regression using the method
of Berry (1994) and then DMA specic parameters are estimated via a Hierar-
chical Bayes approach. The share of vehicle j and the outside good is specied
as
s
jdt
=
exp(V
jdt
)
1 +
P
k
exp(V
kdt
)
; (3.32)
(3.33)
and
s
0dt
=
1
1 +
P
k
exp(V
kdt
)
; (3.34)
64
respectively. These equations can be simplied to yield:
ln(s
jdt
=s
0jdt
) =V
jdt
=
jd
+
d
p
jdt
+
jdt
: (3.35)
I make the standard assumption that
jdt
is normally distributed, i.e.,
djt
N(0;
d
). Heterogeneity across geographic regions is captured by specifying a
normal prior distribution for
d
= (
1d
;:::;
d
) as follows:
d
N(;V
):
Thus, DMA-specic parameters have a common mean,, and a variance-covariance
matrix, V
. I also make the standard assumption of an Inverse Wishart prior for
the variance covariance matrix V
,
V
IW (;V ):
Estimation proceeds by sequentially drawing from the full-conditional distribu-
tions of each parameter, discarding the initial `burn-in' draws, and using the
remaining draws to make inferences about the posterior distribution of parame-
ters.
65
3.2.3.3 Supply Side Estimation
Parameters for each of the four models, which correspond to dierent assumptions
about retailer presence and behavior, are estimated sequentially, i.e., after obtain-
ing the the demand side estimates. The estimation uses Generalized Methods of
Moments (GMM) to build moment conditions by assuming that the dierence
between observed price and expected price is independent of exogenous vehicle
attributes. The common moment condition for Models 1, 2 and 3 is:
E[w
jt
^ w
jt
jZ
jt
] = 0; (3.36)
where Z
jt
includes an intercept and vehicle characteristic such as vehicle size,
weight, miles per gallon (MPG), displacement, and engine size. For Model 4, the
corresponding moment condition is given as:
E[p
jt
^ p
jt
jZ
jt
] = 0: (3.37)
For identication, I further assume that the conduct parameters for every
pair of competitors at both levels of the channel, manufacturer and retailer, is
the same. Thus:
jk
=; (3.38)
jk
= (3.39)
66
for all j6= k. This yields one conduct parameter for retailers and another for
manufacturers.
3.2.4 Results
3.2.4.1 Dealer Cost Variable
In the data set, there are several variables that can be used to capture the dealer
cost and I measure the dealer cost or wholesale price mainly by VEHICLECOST
variable in the data set. If the variable is missing, then DEALERCOST is used.
When both are missing, then FICOST variable is used instead.
Once the dealer cost is determined, it needs to be adjusted since I do not
observe dealer discounts such as dealer cash in the transaction data. As a re-
sult, without adjustment, about 22% of all transactions end up having negative
margins, which is not reasonable. Thus, I adjust the observed wholesale price
by reducing by a xed percentage so that the most of transactions have positive
margins. When the wholesale price is multiplied by 0.9, about 97% of transac-
tions have positive margin and these are retained for the analysis. The vehicle
summary in Table 3.2 shows the wholesale price after adjustment.
3.2.4.2 Price Construction by Hedonic Regression
Retail Price
The hedonic regression for the retail price includes vehicle specic dummies,
model year dummies, displacement, transmission (auto/manual) dummy, and
67
dealer cost deviation for a specic conguration for dealers in the same DMA. The
dealer cost deviation is calculated by taking the dierence between the observed
dealer price for a certain car from the mean price of the same congurations
sold by all dealers in the DMA. The dealer cost deviation variable is included
to account for price variations due to factory- and dealer-installed options which
may vary within trim level but are not observable by researchers (Zettelmeyer,
Morton, and Silva-Risso, 2006). The t statistics and parameter estimates for the
hedonic regression of retail prices appear in Table 3.3. Overall, the explanatory
variables do a good job of explaining the variance in retail price, with R-squared
ranges between 0.534 and 0.614. The predicted retail price for a vehicle in a
specic area and a given week is calculated by adding the model specic intercept
to the mean of residuals from the hedonic regression.
Wholesale Price
Similarly, wholesale prices are regressed on vehicle attributes and retail cost
deviation to account for price variation due to factory- and dealer-installed op-
tions. Estimation results are reported in Table 3.4.
Once again the t of the models is reasonable, with R-square values ranging
from 0.544 to 0.625. The wholesale prices are imputed by adding the model
intercept from the hedonic regression to the mean value of the residuals.
68
Table 3.3: Hedonic Regression Result of Retail Price
LA MI NY PHIL SF
(Intercept) 0.844 0.829 0.896 0.929 0.840
Nissan Sentra 0:002 -0.036 -0.085 -0.075 -0.140
Toyota Corolla -0.020 0.008 -0.042 -0.030 -0.028
MODELYEAR2004 0.033 0.039 0:000 0.025 -0.042
MODELYEAR2005 0.036 0.054 0.035 0.047 -0.037
DISPLACEMENT.NUM 0.403 0.389 0.393 0.366 0.432
TRANSMISSIONManual -0.029 -0.061 -0.028 -0.033 -0.043
W.DIFF 1.149 1.052 1.033 0.965 1.111
R2 0:534 0:555 0:554 0:599 0:614
Adj.R2 0:533 0:555 0:553 0:599 0:613
N 14091 5786 11234 4856 5246
Table 3.4: Hedonic Regression Result of Wholesale Price
LA MI NY PHIL SF
(Intercept) 0.788 0.758 0.839 0.818 0.875
Nissan Sentra -0.045 -0.046 -0.116 -0.094 -0.097
Toyota Corolla -0.026 0.026 -0.034 0:003 -0.014
MODELYEAR2004 0:004 0.010 -0.019 0:015 -0.064
MODELYEAR2005 -0.016 0.022 0:001 0:018 -0.060
DISPLACEMENT.NUM 0.346 0.328 0.329 0.309 0.322
TRANSMISSIONManual -0.042 -0.048 -0.035 -0.038 -0.041
P.DIFF 0.432 0.489 0.487 0.565 0.537
R2 0:544 0:592 0:592 0:625 0:618
Adj.R2 0:544 0:591 0:592 0:625 0:618
N 14091 5786 11234 4856 5246
69
3.2.4.3 Consumer Demand
Based on the parameter estimates obtained in the previous analysis, retail and
wholesale prices for each vehicle model are constructed. The net retail price
term, which enters the utility function, is operationalized by subtracting the
median manufacturer rebate oered for the vehicles sold in a given week, from
the retail price constructed from hedonic regression. Similarly, I use constructed
wholesale price minus median rebate as the instrumental variable for the price
paid to account for endogeneity.
Model parameters are estimated by making 40,000 draws from the posterior
distribution and retaining every 40th draw is kept. After discarding the draws
corresponding to the burn-in period of 20,000 draws, I obtain 500 draws that
form the basis of the inferences.
Table 3.5: Summary of Demand Estimation
Prior Parmeters
All LA MI NY Phil SF
(Intercept) 0:85 0:19 -1.43 0:49 1:00 -1.55
Nissan Sentra -1.54 -1.02 -1.73 -1.50 -1.07 -2.33
Toyota Corolla 0:29 0:10 1.02 0:00 0.55 0:04
Price - Rebate -2.95 -2.95 -2.94 -3.48 -3.43 -1.83
Table 3.5 summarizes the posterior estimates with statistically signicant co-
ecients shown in bold. The rst column of the table reports the mean of the
posterior distribution of each parameter across DMAs. Based on the values for
the intercepts, the mean value for the Honda Accord (the baseline vehicle) is
70
higher than those of the other alternatives. The net price coecient is negative
and highly signicant.
The remaining columns in the table report the posterior mean of DMA-specic
coecients (
d
and
d
). All price coecients are statistically signicant and
negative with signicant heterogeneity in the price responsiveness of consumers,
which vary from1:83 to3:48 depending on the DMA.
3.2.4.4 Supply Side
Using the posterior mean of demand estimates, the parameters of the four alterna-
tive supply side models shown in Figure 3.3 are estimated. In Model 1, strategic
manufacturers compete with each other either aggressively or cooperatively, and
set prices after accounting for retailers who can also compete either aggressively
or cooperatively. Model 2 includes strategic manufacturers set wholesale prices
and strategic retailers that are assumed to compete in Bertrand Nash fashion. In
Model 3, strategic manufacturers have non-strategic retailers who charge a xed
margin; Model 4 assumes away the retailers so that manufacturers directly set
retail prices. Three types of parameters are estimated: manufacturer conduct
parameter, , retailer conduct parameter, , and vehicle costs.
Manufacturer Conduct
In the rst three models, the manufacturer conduct parameter,, is estimated
from the variations in observed net wholesale price. However, because Model 1
71
assumes that manufacturers set net retail prices directly, is estimated from the
net retail price variation instead.
Retailer conduct
In Model 1, the retailer conduct parameter,, is estimated from the variation
in retail price given wholesale prices. In Model 2, competition between retailers
is assumed to be Bertrand Nash,
jk
= 0 for all j6=k.
Vehicle Cost
Manufacturing costs are estimated in Models 1, 2, and 3, while Model 4
estimates the dealer cost (net wholesale price). I assume that the manufacturing
cost does not vary over time or region, which is reasonable given that the data
come from a one year time period during which vehicle manufacturing costs are
unlikely to have changed signicantly.
The supply side estimation results are summarized in Table 3.6. I discuss
the result starting from the simplest model, Model 4. The manufacturer conduct
parameter is estimated to be2:06, which implies that manufacturer competition
is more aggressive than Bertrand-Nash. Also, the cost estimates are slightly
higher than those of the other models since they are dealer costs, rather than the
manufacturing costs estimated in the other models.
In Model 3, the manufacturer conduct parameter is estimated to be0:60,
but is statistically insignicant. So, Model 3 leads to the conclusion that man-
ufacturers compete in a Bertrand-Nash fashion. Model 2 permits retailers to
be strategic but retailer HSI is assumed to be Bertrand-Nash. The manufacturer
72
Table 3.6: Supply Estimates
Estimate SE z.value
M1: Flexible Retailer Competition
3:04 0:09 32:84
10:00 0:14 70:89
Cost: Honda Civic 0:55 0:02 33:67
Cost: Nissan Sentra 0:25 0:01 40:40
Cost: Toyota Corolla 0:48 0:02 30:91
M2: Retailers competing in BN
0:73 0:59 1:25
Cost: Honda Civic 0:49 0:01 33:37
Cost: Nissan Sentra 0:20 0:02 12:38
Cost: Toyota Corolla 0:45 0:01 36:63
M3: Non-strategic Retailers
0:60 0:57 1:05
Cost: Honda Civic 0:49 0:01 33:53
Cost: Nissan Sentra 0:19 0:02 12:36
Cost: Toyota Corolla 0:45 0:01 36:77
M4: No Retailer
2:06 0:96 2:14
Cost: Honda Civic 0:59 0:02 30:76
Cost: Nissan Sentra 0:31 0:02 14:22
Cost: Toyota Corolla 0:53 0:01 36:05
73
conduct parameter is estimated as0:73, which leads to the same inference about
manufacturer completion as obtained from Model 3.
Finally, the full model provides a very dierent characterization of the nature
of competition. Specically, this suggests that the competition among manu-
facturers is more cooperative than BN ( = 3:04), but it is the retailers who
are competing aggressively ( =10). Strikingly, the manufacturer competition
turns out to be cooperative, and not aggressive as inferred from the the model
without retailers. This drastic change in conclusions underscores the importance
of incorporating retailer interaction in a
exible way, even if inferring the nature
of manufacturer interaction is the main objective of the analysis, for example, an
analysis by the FTC. The conduct parameters from the supply side models are
summarized in Figure 3.4.
In sum, the results show that ignoring retailers or assuming certain types of
retailer pricing behavior can change inferences about the nature of competition
between manufacturers. Ignoring retailers completely precludes the possibility
that retailer HSI is dierent from that between manufacturers.
Models acknowledging retailer presence provide improved estimates of man-
ufacturer competition. However, assuming retailer interactions to be either non-
strategic or Bertrand-Nash can still change inferences about manufacturer inter-
action.
Correctly identifying manufacturer interaction apart from retailer competition
can be very important since incorrectly attributing the interaction to manufac-
turers can lead to suboptimal policy decisions.
74
Figure 3.4: Summary of Supply Side Estimation
M
1
M
2
R
1
R
2
C
= 3:04
=10
(a) Model 1: Strategic Retailer Flexible
M
1
M
2
R
1
R
2
C
= 0
0
(b) Model 2: Strategic Retailer BN
M
1
M
2
R
1
R
2
C
= 0
(c) Model 3: Non-strategic Retailer
M
1
M
2
C
=2:06
(d) Model 4: No Retailer
75
3.2.5 Conclusion
The recent upheaval in U.S. automobile industry has forced several rms to re-
duce the number of automobile dealers they employ in their channel, potentially
changing the nature of competition at the local and national levels. This has
brought the issue of separately identifying the horizontal strategic interactions
(HSIs) between retailers to the fore. However, existing models cannot be used to
analyze channels in which manufacturers sell through exclusive retailers.
Therefore, I propose a structural model that incorporates retailer competing
in a
exible way. The model is estimated using automobile transaction data from
the Power Information Network, that captures purchases in the premium compact
sedan segment during the period October 2003 to September 2004. I nd that
the interaction between manufacturers is cooperative but that between retailers
is much more aggressive. In addition, I show that inferences about manufacturer
competition are biased if retailers are ignored or if incorrect assumptions are
made about the nature of their interaction.
One limitation of the current model is that it assumes each manufacturer
has only one single representative retailer in each DMA. Generalizing the model
to incorporate multiple dealers for each manufacturer in each DMA can provide
better insights into both intra- and inter-channel competition. Study 2, proposes
and estimates such a model.
76
3.3 Study 2: An Empirical Investigation of Intra-
and Inter-channel Competition
In Study 1, I showed that it is very important to account for retailer competition
when studying manufacturer interaction. In this study, I focus on empirically
investigating the nature of retailer interaction in depth.
There is considerable evidence that retailers directly compete with each other
at a local level. For example, retailers make strategic choices about the overall
pricing formats that they will follow, positioning themselves as Every Day Low
Pricing (EDLP) or High Low stores, diering in their relative ability to attract
dierent kinds of shoppers. (Lal and Rao, 1997; Bell and Lattin, 1998). Also,
retail competition is shown to be one of the most important factors in explaining
price variations across stores (Shankar and Bolton, 2004).
Recent research on the automobile market by Bucklin, Siddarth, and Silva-
Risso (2008) show the extent to which consumer demand depends on a brand's
local distribution intensity. Similarly, Albuquerque and Bronnenberg (2006) nd
that dealer location relative to a consumer plays an important role in a consumer's
vehicle choice decisions. Because there is signicant heterogeneity in the intensity
of distribution among dierent brands and, across dierent geographical areas of
the same brand, it stands to reason that that the nature of competition among
retailers will also depend upon local conditions. Automobile dealers also devote
signicant resources to TV and newspaper advertising that emphasizes low prices
and attractive terms for nancing and leasing contracts to attract car buyers to
77
their dealerships, further enhancing this local competition. Recent actions by
auto manufacturers like GM and Chrysler to selectively reduce the number of
dealers in specic areas also suggests that dealer competition is likely to vary by
market.
I dene two dierent types of horizontal interaction between dealers depending
upon whether or not these dealers sell the same make of car. Intra-channel HI
refers to the competition between dealers of the same nameplate (e.g. between
dierent Toyota dealers) and Inter-channel HI to the competition between dealers
selling cars of dierent nameplates (e.g. Toyota Dealers versus Honda Dealers).
To gain further insights into this issue, I extend the model in Study 1 to study
the nature of intra- and inter-channel competition. Specically, I am interested
in answering the following questions:
How aggressively do dealers of the same make compete with each other and
with dealers who sell cars of a dierent make? For example, is the compe-
tition among Honda dealers more or less aggressive than the competition
between Honda and Toyota dealers?
Does the nature of intra-channel competition vary across dierent makes of
cars? For example, is the competition among Toyota dealers dierent from
that among Honda dealers?
Finally, how does the nature of competition vary over geographic markets?
For example, is competition among Toyota dealers in Minneapolis more
aggressive than it is in Houston?
78
I propose a structural model of competition between multiple manufactures,
each represented by a set of exclusive retailers in dierent geographic markets.
This model set-up enables me to infer the nature of inter- and intra-channel
competition in multiple geographical markets. I estimate model parameters using
transaction data on consumer purchases in the premium compact sedan segment
during the period Oct 2005 to September 2007, in the Houston and Minneapolis
markets. I nd that (i) inter- and intra-channel competition in the same market
can be quite dierent, and (ii) the nature of intra-channel competition itself varies
from one market to the other.
This research extends our knowledge of retailer competition, an understudied
area of research. From an applied perspective, this approach could help managers
better target their scarce resources in decreasing distribution intensity by provid-
ing insights into the nature of competitive interaction among dealers in dierent
markets. The ongoing upheaval in the U.S. automobile industry, particularly the
drastic elimination of dealers by GM and Chrysler makes this benet particularly
relevant.
3.3.1 Model
3.3.1.1 Consumer Demand Model
In this study, the unit of analysis is a vehicle model sold by a retailer. To account
for factors aecting consumers' choice of dealer-model combination, the utility of
79
model j sold by dealer d at time t to consumer i living in geographic area g is
specied as:
U
ijdgt
=
jg
+
g
p
jdgt
+
g
X
id
+
g
jdgt
+
ijdgt
; (3.40)
where,
jg
is the intrinsic preference for vehicle modelj sold in geographic areag,
p
jdgt
is the retail price minus rebate of vehicle j sold by dealerd located in
DMA g at time t,
X
id
is the distance between household i and dealer d which is a measure
of the shopping cost incurred by the consumer (Albuquerque and Bronnen-
berg, 2009),
jdgt
is the impact of unobserved vehicle attributes that aect prices, e.g.,
car accessaries,
and
ijdgt
is an individual-specic demand shock with a type I extreme value
distribution.
To account for heterogeneity across geographic areas, all parameters (
jg
,
g
,
g
,
g
) are assumed to be region specic, as noted by g subscript. Price endogene-
ity is accounted for by including the term
jdgt
in the utility function, adopting
the control function approach proposed by Petrin and Train (2010). The control
function method is used to address price endogeneity problem coming from de-
mand shock or unobserved vehicle characteristics that are observable to dealer
80
but not to researchers. As the rst step, I specify the pricing equation to recover
unobserved factors aecting the price. Here I assume that the price is linear
in instruments Z
jdgt
in addition to a separable error
jdgt
and the equation is
specied as follows.
p
jdgt
=Z
jdgt
+
jdgt
; (3.41)
where Z
jdgt
is the instruments that are correlated with p
jdgt
but not with unob-
served market conditions aecting pricing decision. Using wholesale price, w
jdgt
,
as the instrument, retail price, p
jdgt
, is regressed on wholesale price, w
jdgt
, to re-
cover the residual,
jdgt
. An outside good is not included in the current analysis.
3.3.1.2 Supply Side: Retailer Behavior
I extend the model proposed in Study 1 to examine the competitive interactions
among dealers. I am interested in capturing two types of interactions, between
dealers who sell dierent car makes (inter-channel competition) and between
dealers who carry cars with the same nameplate (intra-channel competition).
Let be a matrix that contains the conduct parameters between any pair of
dealers in a market. In theory, we could specify a unique conduct parameter for
each pair of competitors, so that
jk
is unique for eachj andk pair. Because this
leads to an explosion in the number of parameters to estimated, I impose certain
reasonable restrictions on
jk
to avoid this curse of dimensionality.
First, I assume that the conduct parameters for any pair of dealers is sym-
metric, i.e.,
jk
=
kj
for all j6=k: (3.42)
81
Second, I assume that conduct parameters between dealers carrying the same
nameplate are equal. Thus, for example, conduct parameters among three dealers
j;k;l, all of whom carry the Honda brand, are the same. Thus,
jk
=
jl
=
kl
=
H
for j;k;l2H: (3.43)
In other words, only a single parameter,
H
, captures the intra-channel HI among
all Honda dealers in a market.
Third, I assume that the competition between dealers carrying dierent car
makes is the same. Thus, competition parameters between Honda (h), Toyota
(t), and Mazda (m) dealers are given as,
ht
=
hm
=
tm
=
0
: (3.44)
In other words, the inter-channel interaction between dierent makes in a market
is the same.
3.3.2 Data
I use transaction data from the premium compact sedan segment in two geo-
graphic markets to estimate intra- and inter-channel HI in each market. Specif-
ically, the data consist of consumer purchases in this category, made during the
period October 2005 to September 2007 in two DMAs: Houston and Minneapo-
lis. These two DMAs are selected because they have the same set of top-selling
vehicles: Toyota Corolla, Honda Civic and Mazda 3, which together account for
82
about 48% of all compact sedan sales in these markets. Table 3.7 provides some
summary statistics relating to the marketing variables and shares.
Table 3.7: Vehicle Information Summary by Area
Retail Price Rebate Wholesale Price Share
HOUSTON
Toyota Corolla 16528 451 16193 56:68
Honda Civic 18923 0 17749 32:08
Mazda 3 18047 19 17653 11:24
MINNEAPOLIS
Honda Civic 18712 0 17364 35:77
Toyota Corolla 16415 278 15768 33:77
Mazda 3 18360 59 18071 30:47
The table reveals both similarities and dissimilarities between the DMAs. For
instance, we see that while Honda's promotion policy does not include rebates,
the other manufacturers do oer rebates in both markets. Toyota Corolla has
the highest market share in Houston while Honda Civic is the top-selling car
in the Minneapolis market. The market shares of the three brands are more
equal in Minneapolis (from 31% to 36%) than in Houston (from 12% to 57%).
The average retail price, wholesale price, and rebates oered also vary by vehicle
model and market. For example, the average rebate amount for the Toyota
Corolla in Houston, $451, is higher than in Minneapolis. Prices for the Toyota
Corolla and the Honda Civic are lower in Minneapolis than in Houston, while
those for the Mazda 3 are higher in Minneapolis.
83
Figure 3.5: Retail Price Variation Over Time
5 10 15 20
18500 19500
Honda Civic
Month
Retail Price
HOUSTON
MINNEAPOLIS
5 10 15 20
16200 16500 16800
Toyota Corolla
Month
Retail Price
HOUSTON
MINNEAPOLIS
5 10 15 20
17000 18000 19000
Mazda 3
Month
Retail Price
HOUSTON
MINNEAPOLIS
84
Figure 3.5 shows that the over-time variation in retail prices also diers by
market. Specically, Honda Civic price levels in the two markets move together
in earlier periods, but at dierent levels, but not in the later period. Prices for
the Toyota Corolla in Houston seem to move in the opposite direction to those in
in Minneapolis, a pattern that that also characterizes the prices for the Mazda 3
in both markets.
3.3.3 Estimation
Similar to Study 1, demand model parameters are rst estimated using a Hierar-
chical Bayes MCMC approach. These parameters are then used in estimating the
supply side model parameters using a Generalized Method of Moments (GMM)
approach. Before proceeding to the estimation stage, the price and costs are
constructed from the transaction data via a hedonic regression approach.
3.3.3.1 Demand Side Estimation
Collecting all the DMA-specic parameters in the utility equation in the vector
g
yields
g
= (
1g
;
2g
;:::;
g
;
g
;
g
): (3.45)
85
Priors for the parameters are specied .
g
N(
;V
); (3.46)
N(
;A
1
); (3.47)
V
IW (;V ): (3.48)
Thus, DMA-specic parameters are distributed around a common mean,
with
a variance-covariance matrix, V
. I make the standard assumption of an Inverse
Wishart prior for the variance covariance matrixV
and set the hyper-priorA
1
=
0:1I, = number of variables+3, andV to the identity matrix multiplied by
adapting the default setup for MCMC routine in Rossi, Allenby, and McCulloch
(2005).
Estimation proceeds by sequentially drawing from the full-conditional distri-
bution of each parameter, discarding the initial `burn-in' draws, and using the
remaining draws to make inferences about the posterior distribution of parame-
ters.
3.3.3.2 Supply Side Estimation
The Generalized Methods of Moments (GMM) approach is used to build moment
conditions by assuming that the dierence between observed and expected prices
is independent of exogenous vehicle attributes. Using equation 3.8, the moment
condition for the supply side model is:
E[p
jt
^ p
jt
jZ
jt
] = 0; (3.49)
86
where Z
jt
includes an intercept and vehicle characteristic such as vehicle size,
weight, miles per gallon (MPG), displacement, and engine size. These moment
conditions are used to recover the conduct parameters. As previously mentioned,
several restrictions were placed on the conduct parameters for identication pur-
poses, reducing the number of conduct parameters for the three-brand markets
analyzed in this research from six to four.
3.3.4 Results
3.3.4.1 Price Construction by Hedonic Regression
As in Study 1, hedonic regressions are used to construct retail and manufacturer
prices for each vehicle.
Retail Price
The hedonic regression equation for the retail price includes vehicle spe-
cic dummies, model year dummies, displacement, transmission (auto/manual)
dummy, and dealer cost deviation for a specic conguration for dealers in the
same DMA. The dealer cost deviation is calculated by taking the dierence be-
tween the observed dealer price for each car from the mean price of the same
congurations sold by all dealers in the DMA. The dealer cost deviation variable
is included to account for price variations due to factory- and dealer-installed
options, which may vary within trim level but is not observable to researchers
(Zettelmeyer, Morton, and Silva-Risso, 2006). The t statistics and parameter
estimates for the hedonic regression of retail prices appear in Table 3.8.
87
Table 3.8: Hedonic Regression Result of Retail Price
Houston Minneapolis
(Intercept) 1.57 1.56
Mazda 3 -0.46 -0.47
Toyota Corolla -0.20 -0.21
MODELYEAR2006 0.18 0.17
MODELYEAR2007 0.19 0.19
MODELYEAR2008 0.19 0.22
DISPLACEMENT.NUM 1.19 1.16
TRANSMISSIONManual -0.09 -0.08
W.DIFF 1.21 1.13
R2 0:74 0:82
Adj.R2 0:74 0:82
N 10259 5197
Overall, the explanatory variables do a good job of explaining the variance in
retail price, with R-squared ranges between 0.74 and 0.82. The predicted retail
price for a vehicle in a specic area and a given week is calculated by adding the
model specic intercept to the mean of residuals from the hedonic regression.
Wholesale Price
A similar hedonic regression is used to model the wholesale price (or dealer
cost), with wholesale prices regressed on vehicle attributes and retail cost devi-
ation to account for price variation due to factory- and dealer-installed options.
Estimation results are reported in Table 3.9. Once again, model ts are rea-
sonable, with R-square values ranging from 0.74 to 0.82. Wholesale prices are
88
Table 3.9: Hedonic Regression Result of Wholesale Price
Houston Minneapolis
(Intercept) 1.35 1.34
Mazda 3 -0.32 -0.30
Toyota Corolla -0.11 -0.14
MODELYEAR2006 0.10 0.10
MODELYEAR2007 0.13 0.15
MODELYEAR2008 0.14 0.16
DISPLACEMENT.NUM 1.00 0.96
TRANSMISSIONManual -0.08 -0.06
P.DIFF 0.53 0.61
R2 0:74 0:82
Adj.R2 0:74 0:82
N 10259 5197
imputed by adding the model intercept from the hedonic regression to the mean
value of the residuals for each model.
3.3.4.2 Demand Model
The consumer utility function is specied based on a vehicle specic intercept,
retail price paid, and distance to dealers. The retail price paid, or net retail
price, is operationalized by subtracting the median manufacturer rebate across
all transactions for a vehicle in a particular week from the retail price constructed
from hedonic regression. To account for price endogeneity, I adopt the control
function approach of Petrin and Train (2010), by including the term in the de-
mand model. Model parameters are estimated by making 30,000 draws from the
posterior distribution, discarding the rst 15,000 draws for burn-in, and retaining
89
every 10th draw, yielding 1500 draws for making posterior inferences. Table 3.10
summarizes the posterior estimates. Each signicant coecient whose posterior
interval does not include zero is marked in boldface.
The rst column of Table 3.10 reports the mean of the posterior distribution
for all elements of the prior mean
. The mean value for the Honda Civic (the
baseline vehicle) is seen to be higher than those of the other alternatives. The
price coecient is negative and highly signicant. The remaining columns in
the table report the posterior distribution of DMA-specic coecients
g
. The
estimates show that, in both markets, consumers have the highest preference
for the Honda Civic, as denoted by negative coecients for the other vehicle-
specic intercepts. All price coecients are statistically signicant and negative
but consumers in Minneapolis are seen to be more price sensitive than those in
Houston. The variable XI, included to control for endogeneity is insignicant in
both areas. Distance to dealers signicantly aects consumer choice negatively
and this result is consistent with Albuquerque and Bronnenberg (2009).
Table 3.10: Summary of Demand Estimation
g
All HOUSTON MINNEAPOLIS
Mazda3 -2.73 -2.45 -3.05
ToyotaCorolla 0:80 -0.20 -1.39
Price - Rebate -4.69 -4.11 -5.37
XI 0:08 0:39 0:52
Distance 0:08 -0.07 -0.05
90
Table 3.11: Summary of Supply Estimation
Houston Minneapolis
Intra-channel HI
Honda 2.53 0.83
Mazda 0:92 -10.51
Toyota -1.16 0:38
Inter-channel HI
Others -1.44 -0.42
3.3.4.3 Supply Model
Table 3.11 reports the conduct parameters for each brand's own dealer network
(intra-channel HI), as well as for the HI between dealers of dierent manufactur-
ers (inter-channel HI). As in previous tables, signicant coecient are shown in
boldface.
These numbers reveal that the interaction among same-brand dealers in Hous-
ton is more cooperative than their interaction with dealers carrying another brand
of car. Specically, intra-channel HI among Honda dealers (2.53), Mazda deal-
ers (0.92), and Toyota dealers (1.16) is more cooperative than inter-channel HI
(1.44). In Minneapolis also, intra-channel HI among Honda dealers (0.83) and
Toyota dealers (0.38) is more cooperative than inter-channel HI (0.42). How-
ever, Mazda provides the only exception to this pattern, with a very an aggressive
intra-channel parameter (10:51<0:42).
91
Second, intra-channel competition is also very dierent across in the two mar-
kets. In Houston, Honda dealers interact cooperatively, Toyota dealers aggres-
sively, while competition among Mazda dealers is Bertrand-Nash. In Minneapolis,
Honda dealers are cooperative, Mazda dealers compete aggressively and Toyota
dealers interact in a Bertrand-Nash fashion. These estimates show that the na-
ture of interaction varies substantially by market area.
3.3.5 Conclusion
Traditionally, researchers have studied retailer competition quite extensively in
frequently purchased goods market. However, retailer competition in markets
with exclusive dealers, such as the U.S. automobile industry, have been under-
studied. While researchers have investigated the role of dealers in consumer de-
mand (Bucklin et al., 2008; Albuquerque and Bronnenberg, 2006), the strategic
interaction among dealers remains unexplored.
In this study, I propose a model that captures two dierent types of channel
interaction at the dealer level: intra-channel HI and inter-channel HI. Using
the model, I investigate the pattern of dealer competition and nd interesting
patterns of interaction among dealers. For instance, intra-channel HI is found to
be more cooperative than inter-channel HI, which is counter-intuitive.
The recent turmoil in the nancial markets combined with the global reces-
sion has led to a major upheaval in the U.S. automobile industry, with several
rms taking extraordinary measures to survive. For instance, GM had to de-
clare bankruptcy, sell or shut down several divisions and terminate the contracts
92
for about 2600 dealers in their distribution network (LA Times, Apr 28, 2009);
during the same period, Chrysler terminated the contracts of almost 800 dealers
(NY Times, July 23, 2009).
Given that dealer reduction is an important decision that changes the struc-
ture of the distribution channel, careful analysis would be expected before making
the decision. Intuitively, the decision to reduce the number of dealers in a market
should depend upon its consequences on dealer and manufacturer prot. Since
retailer competition is one of many factors aecting the protability, providing a
measure of retail competition separately for intra-channel HI and inter-channel
HI is likely to be helpful to managers wrestling with dicult decisions on the
optimal level of channel intensity in a market.
Despite the contributions, this study has several limitations. First, the cur-
rent model does not explain the observed pattern of strategic interaction among
retailers. In future work, it may be useful to identify the factors that explain
the pattern of dealer competition. Once the factors aecting the nature of dealer
competition are identied, then the model may be used to predict changes in
dealer competition when some factors change (e.g. dealer addition and/or dele-
tion). Second, demand model is assumed to be captured by MNL reasonably well.
This assumption enables me to derive pricing behavior analytically but, if this
assumption is not met, this model may produce a biased inference on demand
side model.
93
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Appendices
A Assortment: Estimation Results for Other
Categories
In the main paper, the estimation result was reported for only one out of ve
categories: Peanut Butter. Here, the rest 4 categories are reported.
A.1 Parameter Estimates of SKU Choice Model
98
Table 12: Parameter Estimates of SKU Choice Model:
Bacon
Intercept Family Size Income
Price -1.525 0:022 0:028
Feature 0.985 0:104 0:041
Display 0.869 0:146 0:057
Brand Country Brand 1.767 1.401 0:000
Brand Dubuque -2.174 0:232 0.579
Brand Farmstead -2.353 0:453 0.382
Brand Frontier -4.338 0:016 0.651
Brand Hormel 0:063 0:661 0:310
Brand Hygrade West Virgini -3.329 0:350 0.454
Brand Oscar Mayer 1.522 0:962 0.521
Brand Private Label -2.717 0:105 0:218
Brand Thorn Apple Valley -2.700 0:035 0.366
Brand Wilson Corn King 0:485 0:218 0.480
Size 12 0:956 0:175 0.300
Size 16 4.953 1.321 0:075
Size 24 3.060 0:070 0:001
Flavor Reg -2.370 0:204 0:163
Flavor Smkd 0:437 0:196 0:104
Assortment Size 0:164 0:025 0:061
Entropy Package Size 1.201 -1.084 0:133
Entropy Flavor 0:243 0:007 0:148
99
Table 13: Parameter Estimates of SKU Choice Model:
Coee
Intercept Family Size Income
Price -0.521 0:053 0.058
Feature 1.462 0:112 0:061
Display 1.369 0:016 0:008
Brand Hills Brothers 0:203 0.518 -0.276
Brand Kava 1.456 0:504 0:327
Brand Maxwell -0.646 0:043 0:191
Brand Mjb 0:668 0:440 0:191
Brand Nescafe 0:117 0:358 0:024
Brand Private Label 2.435 -1.947 0.594
Brand S W 0:809 -1.354 0:162
Brand Sanka 1:427 0.873 0:024
Brand Stewarts 0:959 0:352 0.410
Brand Tasters Choice 3.502 0:260 0:006
Size 3 5 0:202 0:134 0:017
Size 4 0:654 0:268 0:258
Size 7 1.191 -1.527 0:261
Size 7 1 -3.121 1.489 0:260
Size 8 2.968 0:289 0:059
Size 10 1.617 -0.868 0:162
Size 12 0:134 0:333 0:043
Size 13 0:271 0:200 0:092
Size 24 2.788 0.614 0:022
Size 26 4.046 0.905 0:099
Size 36 1.840 0:485 0:044
Size 39 2.804 1.153 -0.302
Flavor Clmbn -1.115 0:297 0:078
Flavor Clmbs -3.029 0:277 0.303
Flavor Dkrst -1.799 0:205 0:039
Flavor Eurpn -1.261 -1.328 -0.438
Flavor Frchr 0:495 0:115 0:170
Flavor Mntn 0:544 0.777 0:141
Flavor Origb 1:007 0:365 0:143
Flavor Premm 1:037 0:011 0:258
100
Table 13: (continued)
Intercept Family Size Income
Flavor Reg 1.714 0:114 0:031
Prod Descsoluble -2.105 1.230 -0.485
Assortment Size 0:132 0:039 0:012
Entropy Package Size 1.286 0:023 0:189
Entropy Flavor 0:065 0:197 0:078
Entropy Prod Desc 4.205 2.859 -0.388
101
Table 14: Parameter Estimates of SKU Choice Model:
Tissue
Intercept Family Size Income
Price -2.710 0:010 0.121
Feature 0.773 0.178 0:006
Display 1.046 0:041 0:010
Brand Charmin 0:267 -0.403 0:098
Brand Cottonelle -0.480 -0.423 0.195
Brand Generic -5.239 0:249 -0.396
Brand Green Forest -3.633 0:423 0:070
Brand Kleenex 0:228 -0.176 0:062
Brand Northern 0:147 -0.471 0.138
Brand Private Label -2.927 0:097 -0.260
Brand Scott 0:743 0.505 0:033
Brand Soft Gentle -0.861 0:037 0:071
Brand White Cloud -1.196 -0.597 0:079
Size 4 2.004 0:065 0:006
Size 6 1.749 0:025 0:102
Size 9 4.524 0:146 0:229
Size 12 4.895 0:299 0:210
Assortment Size -0.266 -0.142 0:034
Entropy Package Size 0.634 0.438 -0.124
102
Table 15: Parameter Estimates of SKU Choice Model:
Towel
Intercept Family Size Income
Price -2.547 0:191 0.175
Feature 1.344 0:045 0:014
Display 1.265 0:055 0:051
Brand Brawny -1.797 0:219 0:129
Brand Delta -2.637 0:086 0:134
Brand Gala -1.494 0:161 0:019
Brand Generic -3.127 0:343 -0.236
Brand Green Forest -2.720 0.570 0:027
Brand Hi Dri -2.946 0.540 0:099
Brand Job Squad -3.673 0:384 0:168
Brand Mardi Gras -2.953 0:066 0:002
Brand Private Label -2.875 0:220 0:113
Brand Scott -1.082 0:246 0:060
Brand So Dri -1.796 0:287 0:185
Brand Sparkle -2.086 0.391 0:123
Brand Versatile Viva -1.341 0:063 0:000
Size 2 -3.366 -0.764 0:105
Size 3 1.684 0:348 0:139
Func Asorw -0.686 0:276 0:079
Func Asst 0:414 0:495 0:035
Func Astcl 0:031 0:044 -0.119
Func Bddsn 0.480 0:004 0:072
Func Dcrtr 1.074 0:089 0:157
Func Fnprt -1.210 0:167 0:070
Func Mdlys -1.169 0:024 -0.187
Func Pastl 0:630 0:159 -0.275
Func Plnpr 0.750 0:088 0:061
Func Print 0.407 0:045 -0.098
Func Wht 0.424 0:169 0:004
Func Whtpr 0.619 0:041 0:041
Func Worpt 0:071 0:093 0:001
Assortment Size 0:084 0:052 0:027
Entropy Package Size 0:005 0:100 0:088
103
Table 15: (continued)
Intercept Family Size Income
Entropy Function 0:145 0:121 0:034
104
A.2 Parameter Estimates of Purchase Incidence Model
Table 16: Parameter Estimates of PI Model: Bacon
Intercept Family Size Income
Category Assortment Size -0.128 0:026 0:002
Category Entropy Brand 0:438 0:267 0:124
Category Entropy Package Size -2.406 0.517 0:063
Category Entropy Flavor 0:878 0:104 0:037
Last Purchased Quantity 0:083 0:079 0:017
Category Inclusive Value 0.205 0:004 0:014
Table 17: Parameter Estimates of PI Model: Coee
Intercept Family Size Income
Category Assortment Size 0:031 0:019 0:001
Category Entropy Brand -1.742 0:500 0:267
Category Entropy Package Size -4.577 -1.493 0:279
Category Entropy Flavor 1.216 -1.197 -0.411
Category Entropy Prod Desc 0:878 0.698 0:146
Last Purchased Quantity -0.251 0:001 0:021
Category Inclusive Value 0.206 0:004 0:003
105
Table 18: Parameter Estimates of PI Model: Tissue
Intercept Family Size Income
Category Assortment Size 0.043 0:005 0:005
Category Entropy Brand -3.420 0:140 0:127
Category Entropy Package Size -1.063 0:261 -0.201
Last Purchased Quantity -0.092 0:015 0:004
Category Inclusive Value 0.487 0:047 0:014
Table 19: Parameter Estimates of PI Model: Towel
Intercept Family Size Income
Category Assortment Size -0.030 0:006 0:006
Category Entropy Brand -1.518 0.606 0:014
Category Entropy Package Size 1.520 0:447 0.342
Category Entropy Function 0:278 0:059 0:078
Last Purchased Quantity -0.139 0:017 0:005
Category Inclusive Value 0.360 0:035 0:002
106
B Automobile: Deriving Estimation Equations
for Supply Side Behavior
B.1 Price Derivative of MNL
In the following result, I utilized the characteristics of MNL demand model. With
MNL model, the own- and cross-price elasticity can be derived as follows.
@s
j
@p
j
= (1s
j
)s
j
(50)
@s
j
@p
k
=s
k
s
j
(51)
B.2 Calculation of SW
t
Suppressing t subscript, SW can be calculated as SW =SPPW where
SW [j;k] =
@s
j
@w
k
(52)
SP [j;k] =
@s
j
@p
k
(53)
PW [j;k] =
@p
j
@w
k
(54)
Assuming MNL demand, SP can be calculated analytically using equation 50
and equation 51. Therefore, PW is required to get SW .
107
B.3 Calculation of PW
The PW can be calculated by
PW =C
1
D (55)
where
C = (S
v
) + ( (M
h
SP ))I (56)
D = (S
v
I): (57)
Here denotes elementwise multiplication and means matrix multiplication.
All components are square matrices and they are dened as follows.
[j;k] =
jk
(58)
S
v
is a square matrix of which each row is equal to the vector of market share
s = (s
1
;s
2
;:::;s
J
). M
h
is a square matrix of which each column is equal to the
vector of retailer margin m = ((p
1
w
1
); (p
2
w
2
);:::; (p
J
w
J
)). I denotes an
identity matrix of dimension of JJ.
108
B.4 Derivation of PW
B.4.1 Using FOC of retailer j
The optimal retailer price p
j
will satisfy the following rst order condition.
1
+ (p
j
w
j
)(1s
j
)
X
k6=j
jk
(p
k
w
k
)s
k
= 0 (59)
By rearranging the terms, I get
1
+
jj
(p
j
w
j
) =
X
k6=j
jk
(p
k
w
k
)s
k
+
jj
(p
j
w
j
)s
j
(60)
since
jj
= 1. By taking the derivative with respect to w
j
, I get
jj
(
@p
j
@w
j
1) =
X
i6=j
ji
@p
i
@w
j
s
i
+ (p
i
w
i
)
@s
i
@w
j
+
jj
(
@p
j
@w
j
1)s
j
+ (p
j
w
j
)
@s
j
@w
j
(61)
jj
(
@p
j
@w
j
1) =
X
i
ji
@p
i
@w
j
s
i
+ (p
i
w
i
)
@s
i
@w
j
jj
s
j
(62)
jj
(
@p
j
@w
j
1 +s
j
) =
X
i
ji
@p
i
@w
j
s
i
+ (p
i
w
i
)
@s
i
@w
j
(63)
109
@p
j
@w
j
+ (s
j
1) =
X
i
ji
s
i
@p
i
@w
j
+
X
i
ji
(p
i
w
i
)
@s
i
@w
j
(64)
=
X
i
ji
s
i
@p
i
@w
j
+
X
i
ji
(
(p
i
w
i
)
X
l
@s
i
@p
l
@p
l
@w
j
)
(65)
=
X
i
ji
s
i
@p
i
@w
j
+
X
i
X
l
ji
(p
i
w
i
)
@s
i
@p
l
@p
l
@w
j
(66)
=
X
l
jl
s
l
@p
l
@w
j
+
X
i
X
l
ji
(p
i
w
i
)
@s
i
@p
l
@p
l
@w
j
(67)
=
X
l
"
jl
s
l
+
X
i
ji
(p
i
w
i
)
@s
i
@p
l
#
@p
l
@w
j
(68)
=
X
l6=j
"
jl
s
l
+
X
i
ji
(p
i
w
i
)
@s
i
@p
l
#
@p
l
@w
j
+
"
jj
s
j
+
X
i
ji
(p
i
w
i
)
@s
i
@p
j
#
@p
j
@w
j
(69)
By arranging terms with respect to
@p
l
@w
j
, (s
j
1) can be written as:
X
l6=j
"
jl
s
l
+
X
i
ji
(p
i
w
i
)
@s
i
@p
l
#
@p
l
@w
j
+
"
jj
(s
j
1) +
X
i
ji
(p
i
w
i
)
@s
i
@p
j
#
@p
j
@w
j
(70)
B.4.2 Using FOC of retailer k
The rst order condition for retailer k is simplied as
1
+
kk
(p
k
w
k
)(1s
k
) +
X
l6=k
kl
(p
l
w
l
)(s
l
) = 0 (71)
110
1
+
kk
(p
k
w
k
) =
X
i
ki
(p
i
w
i
)s
i
(72)
=
X
i6=j
ki
(p
i
w
i
)s
i
+
kj
(p
j
w
j
)s
j
(73)
By taking this FOC with respect to w
j
, I get
kk
@p
k
@w
j
=
X
i6=j
ki
@p
i
@w
j
s
i
+ (p
i
w
i
)
@s
i
@w
j
+
kj
(
@p
j
@w
j
1)s
j
+ (p
j
w
j
)
@s
j
@w
j
(74)
kk
@p
k
@w
j
+
kj
s
j
=
X
i
ki
@p
i
@w
j
s
i
+ (p
i
w
i
)
@s
i
@w
j
(75)
kk
@p
k
@w
j
+
kj
s
j
=
X
i
ki
@p
i
@w
j
s
i
+ (p
i
w
i
)
@s
i
@w
j
(76)
=
X
i
ki
@p
i
@w
j
s
i
+
X
i
ki
(p
i
w
i
)
X
l
@s
i
@p
l
@p
l
@w
j
(77)
=
X
i
ki
@p
i
@w
j
s
i
+
X
i
X
l
ki
(p
i
w
i
)
@s
i
@p
l
@p
l
@w
j
(78)
=
X
l
kl
@p
l
@w
j
s
i
+
X
l
X
i
ki
(p
i
w
i
)
@s
i
@p
l
@p
l
@w
j
(79)
=
X
l
(
kl
@p
l
@w
j
s
i
+
X
i
ki
(p
i
w
i
)
@s
i
@p
l
)
@p
l
@w
j
(80)
=
"
kk
s
k
+
X
i
ki
m
i
@s
i
@p
k
#
@p
k
@w
j
+
X
l6=k
"
kl
s
l
+
X
i
ki
m
i
@s
i
@p
l
#
@p
l
@w
j
(81)
111
By arranging the terms with respect to
@p
l
@w
j
, I get
kj
s
j
=
"
kk
(s
k
1) +
X
i
ki
m
i
@s
i
@p
k
#
@p
k
@w
j
+
X
l6=k
"
kl
s
l
+
X
i
ki
m
i
@s
i
@p
l
#
@p
l
@w
j
(82)
B.4.3 Simultaneous Equation
By stacking equation 70 and equation 82 vertically, I get the following matrix
equations
C
@p
@w
j
=d
j
(83)
where
@p
@w
j
is a column vector of [
@p
1
@w
j
;
@p
2
@w
j
;:::;
@p
J
@w
j
] and d
j
is a column vector of
[
1j
s
j
;:::; (s
j
1);:::;
Jj
s
j
]. C is a square matrix of dimension JJ of which
elements are dened as
C[k;k] =
kk
(s
k
1) +
X
i
ki
m
i
@s
i
@p
k
(84)
=
kk
s
k
+
X
i
ki
m
i
@s
i
@p
k
kk
(85)
C[k;l] =
kl
s
l
+
X
i
ki
m
i
@s
i
@p
l
(86)
Since matrix C takes the same form regardless of
@p
@w
j
or d
j
, horizontally
binding vector
@p
@w
j
for all j and d
j
for all j yields equation 55.
112
Abstract (if available)
Abstract
I study issues related to retail management in packaged goods and durable goods markets. In the packaged goods context, I investigate how brand- and category-level assortments impact consumers' purchase incidence and SKU choice decisions. I also investigate retail competition in the U.S. automobile industry by developing structural models and estimation approaches to (a) infer the nature of competition between manufacturers in the presence of exclusive retailers and (b) to identify how intra- and inter-channel competition varies by brands and across different geographical markets.
Linked assets
University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Kim, Tae-kyun
(author)
Core Title
Essays in retail management
School
Marshall School of Business
Degree
Doctor of Philosophy
Degree Program
Business Administration
Publication Date
08/03/2012
Defense Date
05/04/2010
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
automobile industry,OAI-PMH Harvest,retailing,structural model
Place Name
USA
(countries)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Siddarth, Sivaramakrishnan (
committee chair
), Dukes, Anthony J. (
committee member
), Dutta, Shantanu (
committee member
), Hsiao, Cheng (
committee member
)
Creator Email
elegant.simplicity@gmail.com,taekyunk@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m3261
Unique identifier
UC1105086
Identifier
etd-Kim-3876 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-368909 (legacy record id),usctheses-m3261 (legacy record id)
Legacy Identifier
etd-Kim-3876.pdf
Dmrecord
368909
Document Type
Dissertation
Rights
Kim, Tae-kyun
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
automobile industry
retailing
structural model