PAPER FOR MSI COMPETITION AND SPECIAL ISSUE OF JMR ON PRACTITIONER-

ACADEMIC COLLABORATIVE RESEARCH

OPTIMAL PRICING STRATEGIES FOR AN AUTOMOTIVE AFTERMARKET RETAILER

Murali K. Mantrala**

P.B. (Seethu) Seetharaman

Rajeeve Kaul

Srinath Gopalakrishna

Antonie Stam

December 1, 2004 Revised: May 19, 2006

* Please do not cite without permission from authors. Comments are welcome. ** Murali K. Mantrala (e-mail: mantralam@missouri.edu,) is Sam M. Walton Distinguished Professor of Marketing, College of Business, University of Missouri, Columbia, Columbia, MO 65211; P.B. Seetharaman (e-mail: seethu@rice.edu) is Associate Professor of Management, Jesse H. Jones Graduate School of Management, Rice University, Houston, TX 77252-2932; Rajeeve Kaul (e-mail: rajeeve.kaul@autozone.com ) is Director of Pricing Optimization at Autozone, Inc., Memphis, TN; Srinath Gopalakrishna (e-mail: srinath@missour.edu) is Associate Professor of Marketing, College of Business, University of Missouri, Columbia, Columbia, MO 65211. Antonie Stam (e-mail: stama@missouri.edu) is Leggett & Platt Distinguished Professor of Management Information Systems, College of Business, University of Missouri , Columbia, MO 65211

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OPTIMAL PRICING STRATEGIES FOR AN AUTOMOTIVE AFTERMARKET RETAILER

Abstract

The extant retail category pricing optimization literature concentrates on grocery retailing. In contrast, this paper focuses on the problem of determining profit-improving store-level prices of failure-related ‘hard part’ product categories at a US specialty auto-part retailer with 3400 stores. Key institutional differences between automotive hard part and grocery retailing include: no syndicated data are available for hard parts; each sub-class of a hard part category contains variants that are ordered by quality (typically “Good,” “Better,” “Best,”); there is intra- but no inter-subclass competition; market shares of variants and their prices are not positively correlated within a sub-class; a consumer enters the market only infrequently; and at a purchase occasion, a consumer buys one and only one variant within a subclass, and one and only one unit of that variant. Utilizing two years of weekly sales histories from 800 stores, the authors develop store-level demand models for 23 subclasses of a hard part and employ these with available product cost data to set prices of variants of each subclass at each store that better satisfy demand and increase profit. The model-recommended prices for 10 subclasses are tested in a field experiment involving 500 stores, leading to a projection of an annual increase of over $610,000 in the retailer’s profit from these 10 subclasses if the new prices were applied at all stores. The empirical analysis also yields new insights with respect to asymmetric price competition across quality variants and deviations of actual from optimal prices that run counter to previous grocery retailing-based findings. Keywords: Automotive aftermarket retailing, Price elasticity estimation, Pricing optimization, Multinomial logit, Latent class, Empirical Bayes.

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1. INTRODUCTION Optimal retail category pricing (i.e., pricing of brands or variants in different product

categories) lies at the heart of many retailers’ category management efforts and,

accordingly, has received considerable research attention in recent years (e.g., Zenor

1994, Kim, Blattberg and Rossi 1995, Montgomery and Bradlow 1999, Basuroy,

Mantrala and Walters 2001, Anderson and Vilcassim 2001, Chintagunta 2002). A

convergence of significant advances in both the science (e.g., statistical modeling and

estimation of consumer price response functions) and technology (computing power, data

availability) of marketing management has made smarter pricing a critical success factor

in today’s retailing environment (e.g., Montgomery 2004, Shankar and Bolton 2004).

Fueled by the widespread availability of consumer transaction data collected via optical

bar code scanners, the grocery retail sector in particular has witnessed many

developments in the domain of pricing decision support systems. Two important trends

in this context are micromarketing and “demand-based management” which emphasize

tailoring supermarket retail chain prices to each individual store’s clientele, environment

and performance conditions (e.g., Hoch, Kim, Montgomery and Rossi 1995, Shankar and

Krishnamurthi 1996, Montgomery 1997, Chintagunta, Dube and Singh 2003).1

Micromarketing represents a manager’s interest to combine the advantages of large

operations with the flexibility of independent, yet “customized,” neighborhood stores.

However, few retail micromarketing model applications have been reported in the

literature. Also, extant research has concentrated on grocery retailers, largely ignoring

other major retailing sectors with different demand environments striving for better

pricing management. One example is automotive aftermarket retailing which caters to

DIY (‘do-it-yourselfers’) consumers, i.e., to consumers who maintain and repair their

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vehicles themselves. The DIY category witnessed a 5.0 % compounded annual growth

from nearly $22 billion in 1991 to $35 billion in 2001(AAIA Aftermarket Factbook,

2002).

In this research, we develop and apply an optimal category pricing solution for

quality-tiered product lines at a specialty automotive aftermarket retailer (AAR), with

3400 stores in 42 states of the US, customizing prices across these stores. Our research,

therefore, extends extant retail pricing optimization research to a new and important

retailing sector, develops and evaluates an implementable store-level pricing decision

model in a field setting, expands current knowledge regarding cross-price effects among

quality variants in a product line and adds to emerging studies of price customization in

retailing. In Section 2, we describe the institutional features of automotive aftermarket

retailing and some key differences between the aftermarket and grocery retail pricing

research contexts. Section 3 elaborates on our research goals with regard to the specific

pricing problem faced by our research sponsor AAR.

2. AUTOMOTIVE AFTERMARKET INDUSTRY BACKGROUND

The automotive aftermarket industry supplies replacement parts (excluding tires),

accessories, maintenance items, batteries and automotive fluids for cars and light trucks.

Replacement parts include, e.g., radiators, brake pads, fan belts, alternators, batteries,

spark plugs, clutches, engines and transmissions.

2.1 Aftermarket Segments

The automotive aftermarket is comprised of two consumer groups: DIY and DIFM

(‘do-it–for-me’). Our research focuses on retailers serving DIYers. AAIA (2005) reports

that 70 percent of U.S. households have someone who has personally performed vehicle

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maintenance or repair in the last year and 62 percent of DIYers are doing the same or a

greater amount of work than five years ago. The primary motivator for DIYers is to save

money and the growing demand from this segment in recent times is attributable to (1) an

economic downturn, leading to longer vehicle retention and a greater number of cars no

longer covered by warranty that need more repairs; (2) the threat of terrorism and other

factors, increasing the number of miles driven annually; (3) a higher cost of replacement

parts as a result of technological changes in recent models of vehicles; and (4) an

increasing number of light trucks and sport utility vehicles that require more expensive

parts, resulting in higher average sales per customer (AAIA 2002).

2.2 Automotive Market Structure

Traditionally, retailing in the DIY category has been highly fragmented, with

competition between multiple retailing formats including national and regional

automotive parts specialty retailers, wholesalers or jobber stores, independent operators,

automobile dealers that supply parts, and discount stores and mass merchandisers that

carry automotive products. However, as replacement parts have proliferated, discount

stores and mass merchandisers have found it increasingly difficult (because of their broad

scope) to maintain a wide and deep selection of high quality brand name automotive parts

and accessories that DIY customers demand, e.g., branded products such as Monroe,

Bendix, Purolator and AC Delco. This has given a strong competitive advantage to

specialty retailers such as AAR who do have the distribution capacity, sophisticated

information systems, and knowledgeable sales staff, to offer broad selection and value.

These retailers typically carry between 10,000 and 70,000 in-store stock-keeping units

(SKUs) with larger firms like AAR featuring nearly 1000 categories with about 200 items

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in each category per store. The AAIA (2005) reports that during the past year, 68 percent

of DIYers have purchased parts and supplies from a specialty store, with ‘quality’ as the

most important criterion driving store selection. High-margin failure-related replacement

or hard parts (e.g., brakes, mufflers, alternators) bought by DIYers account for the

majority of AAR’s net annual sales of several billion dollars and are the focus of this

research.

2.3 Specialty Auto Parts Retailer Strategies

Based on interviews with AAR managers, specialty automotive aftermarket retailer

strategies are focused on enhancing operating margins by improving supply chain,

distribution and inventory management; leveraging overall scale to reduce operating

expenses as a percentage of sales; implementing category management processes to

customize store-level assortments, in-stock availability, merchandising and marketing

initiatives; offering superior customer service and cross-selling by way of expert sales

associates, aided by fully-integrated point-of-sale store-level systems called “look-up”

systems; and designing optimal pricing strategies.

2.4 Institutional differences between Specialty Auto Part and Grocery Retailing

Impacting Demand Assessment

In automotive aftermarket retailing, application-specific hard part categories are

comprised of several subcategories or subclasses defined by a particular make, model,

and year of vehicle. For example, the hard part category that is the focus of our research,

hereafter labeled HPX for confidentiality reasons, includes a subclass of variants that are

only compatible with all Ford Taurus cars made between 1995 and 2001; another

subclass fits only Ford Truck S150 made between 1990 and 1999. Further, there is only

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one subclass of variants of HPX which fits a particular make, model and year of vehicle.

Effectively, therefore, each HPX subclass represents a different ‘automobile market’

comprised of consumers with quite distinct demographic profiles.

More generally, nine institutional differences between specialty auto hard part and the

more well-known grocery retailing that impact hard part demand assessment are

identified below:

(1) No syndicated point-of-sale (POS) data are yet available from major auto parts

retailers. Current mass merchandiser data are insufficient to guide auto part retailer

pricing decisions because they do not carry application products like brakes and engine

parts which represent the bulk of revenues. Over the past few years, AAIA's Category

Management Committee has worked with the NPD Group, (a global sales and marketing

information provider) and other companies to establish product category definitions for

exchanging point of sale (POS) data from industry retailers and traditional operators.

These collaborative efforts in the domain of POS data collection and exchange are still

developing and do not yet cover all aftermarket merchandise categories.

(2) Each sub-class contains variants (typically three) that are ordered by quality, e.g.,

each of about 30 subclasses of HPX stocked by AAR are comprised of a ‘Good’ or entry

grade brand, ‘Better’ or mid-level grade brand, and ‘Best’ or premium grade brand.

(3) A variant or brand is not a composite of underlying stock-keeping units (SKUs),

i.e., brand and SKU are interchangeable within a sub-class.

(4) As already mentioned, subclasses are not substitutable for each other.

(5) No product other than the 3 variants within a subclass competes with the variants

within the subclass.

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(6) Market shares and prices are not positively correlated within a sub-class, as shown

later in our data.

(7) A DIY consumer enters the market for a sub-class only when there is a product

failure (i.e., very infrequently).

(8) The DIY consumer buys one and only one variant within a sub-class at a purchase

occasion.

(9) The DIY consumer buys one and only one unit of a variant within a sub-class at a

purchase occasion.

Employing historical store-level data on sales and prices of each of the variants in

the various subclasses of HPX stocked by AAR, we develop and analyze demand models

at the level of a subclass. Such single-category analysis is justified and, in fact, more

compelling in our case than in the supermarket context where consumers typically buy a

basket of goods (which warrants the application of multi-category demand models, see,

e.g., Seetharaman et al. 2005). By contrast, as noted above, DIY consumers seeking a

replacement for an automobile hard part that has failed, typically visit an autopart store

for that specific purpose, and if they choose to buy one of the quality variants in their

compatible hard part subclass, buy one unit of that particular hard part.

2.5 AAR’s Pricing Challenge

AAR has completed a merchandise category management study, called Enhanced

Line Review in the automotive industry (AAIA 2003), identifying categories and their

roles for different products (e.g., engine parts are core products) and defining category

hierarchies and major segments. AAR’s management now seeks to design and

implement models for optimal pricing of hard part subclasses, accounting for demand

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heterogeneity across stores. Currently, stores are grouped into five zones and prices are

varied by zone. Prices are reviewed once a year, but the process allows for occasional

adjustments during the year in response to local conditions e.g., the price of an item in a

store may be adjusted to within 10% of the same or similar item observed at a Wal-Mart

outlet in the same area. AAR’s relevant competitors vary across geographic markets.

3. RESEARCH OBJECTIVES and CONTRIBUTIONS

Our collaborative research goal is to develop and validate an implementable

model-based approach to set prices of variants of hard part product classes at the store

level in a way that increases profit for AAR. We focus on everyday or regular price

changes (not price promotions) as these are of great importance to the company. As

pointed out by Montgomery (1997), most retailer profits are earned by products sold at

their everyday prices, which are amenable to store-level customization.

More specifically, we seek to develop HPX subclass-specific models of store-

level demand, derived from the choice between “Good”, “Better,” “Best” and “No

Purchase” options in the subclass of interest to a DIY replacement part shopper. We use

historical data from 800 randomly-selected stores distributed across the nation to

parameterize the subclass-specific store-level demand models, with the remaining 2600

stores retained for validation of the parameterized models. We then aim to use the

validated demand models to derive store-subclass profit-maximizing prices for the

variants in each subclass at every store. Finally, to test the efficacy of our model-

recommended prices relative to current prices, we employ a field experiment involving

500 AAR stores. The field test is an important contribution of this research and is

described later in more detail. It produced positive results sufficient to motivate AAR

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management to apply the proposed approach to a second multi-million dollar hard part

category.

Our research benefits from access to a national, store-level database and product cost

data, which are rare in extant research. The empirical analysis contributes new findings

from a new retailing sector to the literature on cross-price effects in quality-tiered product

lines and also yields several intuitive generalizations with regard to the impact of

observable store characteristics, such as store type, number of years since opening and

latitude on estimated price response parameters of demand. These findings augment past

studies of the determinants of store-level price elasticities which have been limited to

regional or metropolitan retailers’ data (e.g., Hoch et al 1995). The availability of

product cost enables us to determine profit-maximizing, store-level prices in line with the

firm’s micromarketing goals and consistent with both first-degree and third-degree price

discrimination theories. The price optimization analysis also adds to emerging studies of

price customization in retailing (e.g., Iyer and Seetharaman 2003).

The rest of the paper is organized as follows. In Section 4, we develop our proposed

demand model that governs not only the market shares of different variants within a

product subclass, but also the demand for the subclass as a whole. In Section 5, we

formulate the price optimization problem for the retailer. Section 6 describes the data and

the nature of our empirical analysis. Section 7 presents our demand model estimation and

cross-validation results; new insights gained with respect to cross-price effects among the

quality variants within subclasses; findings with respect to the effects of store

characteristics on subclass demand parameters; and the store-specific prices of variants

of subclasses and profits yielded by the profit optimization model. We describe and

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report the results of the field test of the value of model-recommended store-specific

prices in Section 8. This test involved 500 AAR stores and 10 subclasses. Concluding

remarks, along with directions for future research, are made in Section 9.

4. MODEL DEVELOPMENT

We develop our subclass-level model of demand at each store in four steps: first, we

present the Multinomial Logit (MNL) model that captures consumer demand for SKUs,

namely, the quality variants within each HPX subclass; second, we accommodate the

effects of heterogeneity across AAR stores in the parameters of the MNL model using a

latent-class specification, where the heterogeneity is driven by both observed store

characteristics, and unobserved factors; third, we discuss how to estimate the parameters

of the proposed heterogeneous MNL model; fourth, we show how to employ an empirical

Bayes procedure, that uses the estimated heterogeneous MNL model as a “prior” for a

store, and the store’s data as the likelihood, to estimate a separate demand function for

each AAR store.

4.1 The Multinomial Logit (MNL) Model of SKU Demand within a Subclass

The MNL model was first applied to supermarket scanner panel data by Guadagni

and Little (1983) and has since been used to model consumer demand for packaged goods

in numerous applications. We believe that the MNL model is a more appropriate demand

model in our autopart retailing setting as compared to, say, the widely used log-log

demand model (e.g., Reibstein and Gatignon 1984) for two reasons: The log-log demand

model would involve nine price parameters as opposed to just one in the case of the MNL

model. Moreover, it would not yield a globally concave category profit function for the

retailer, making the calculation of optimal prices difficult (see Anderson and Vilcassim

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2001). In contrast, the MNL is a well-behaved model in terms of yielding sensible own-

and cross-price elasticities of demand as well as optimal prices in a category profit

maximization problem (Chintagunta, Dube and Singh 2003). In fact, the MNL is more

appropriate for our setting as compared to the packaged goods context where consumers

often buy multiple SKUs within the same product category, e.g., multiple flavors of

yogurt or ice cream, or multiple units of a given brand, e.g., two 2-liter bottles of Coke.

Both of these behaviors violate the basic underlying assumption of discrete choice, i.e.,

the consumer buys one object out of several, that is embedded in the MNL model. By

contrast, in the automotive aftermarket setting, a consumer shopping for a hard part buys

not only just one SKU within a product category, but also just one unit of the SKU.

The MNL model develops a consumer’s probability Prist of choosing alternative i

within a subclass at store s at a particular time t, from a collection of alternatives N =

{Good, Better, Best, None}, where Good, Better, Best refer to the 3 quality variants

within the subclass, and None refers to the no-purchase option. Accordingly, Prist is

given by:

Pr ,ist

jst

V

ist V

j N

ee

∈

=∑

i∈N; s=1,…,S; (1)

where S is the total number of stores and the attractiveness of alternative i, with i = 0

denoting the no-purchase option, at store s to the shopper at time t, Vist , is given by

0

P { , , }0,

ist i ist

st

V i Good Better BestV

,α β= + ∀ ∈=

s=1,…,S. (2)

In (2), αi denotes the consumer’s intrinsic preference for SKU i, β represents the

consumer’s price sensitivity, and Pist is the price of SKU i in store s at time t.

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Assuming a sufficiently large number of shoppers for the hard part at store s in each

time period t, the aggregate market share for alternative i in store s at time t is given by:2

,ist

jst

V

ist V

j N

eSe

∈

=∑

i∈N; s=1,…,S; t=1,…,T. (3)

The parsimonious MNL specification of market shares in (3) involves only 4 (unknown)

parameters, i.e., α1, α2, α3, β, to fully characterize the market shares of the 3 SKUs of the

product subclass as well as the no-purchase option. By explicitly allowing for the no-

purchase option as an alternative in the consumer’s choice process, the model in (3)

allows the three SKUs’ prices to affect not only their relative market shares (say, SGood,s,t /

SBetter,s,t), but also their share relative to the no-purchase option (say, SGood,s,t / S0,s,t). From

a normative standpoint, the no-purchase option in the MNL is important because ignoring

the option results in infinite optimal prices for all SKUs for any assumed values of model

parameters (we will expand on this in Section 5).

The market share model in (3) restricts its parameters {α1, α2, α3, β} to be identical

across stores, which may not be realistic. For example, it is possible that market shares of

different SKUs are more responsive to price changes within stores in the North than

within stores in the South. More generally, some stores may be characterized by

systematically higher values of price sensitivity than others because of variation in

readily observable (such as in the census) as well as unobservable characteristics of their

environments. Below, we extend the proposed MNL model to allow for such

heterogeneity in the model parameters arising from observed and/or unobserved

characteristics of stores.

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4.2 Incorporating Heterogeneity in MNL parameters across AAR stores

Using the latent class formulation of Kamakura and Russell (1989), we assume that the

MNL parameter vector δ = (α1, α2, α3, β)’ follows a multivariate discrete distribution

across stores, which is semi-parametric in the sense that it has K supports, whose

locations are given by δ1, δ2, …, δK and masses are given by π1, π2, …, πK (that sum to 1).

The locations and masses of this distribution are not specified according to any known

parametric discrete distribution and are allowed to be unrestricted. Usually, based on

managerial judgment and/or statistical tests, the value of K is chosen to be much smaller

than S. For example, as shown below, we use S = 800 AAR stores in the estimation, but

allow each store to probabilistically belong to one of K = 3 supports. That is, we allow

for heterogeneity in MNL parameters across stores which may be due to stores being in

different locations with different characteristics (e.g., store size) drawing differing mixes

of customers of the subclass. Thus, we specify the a priori masses of the heterogeneity

distribution as follows (Gupta and Chintagunta 1994):

1

,s k

s l

W

sk KW

l

e

e

γ

γπ

=

=

∑ s=1,…,S; k=1,…,K, (4)

where πsk represents the (prior) probability of store s belonging to support k of the

heterogeneity distribution, Ws = (1, ws1, …, wsL) is a row-vector of L variables

characterizing store s, and γk the corresponding Lx1 column-vector of parameters

capturing the effects of store characteristics on the probability of the store belonging to

support k. For identification purposes, γk is restricted to be a zero-vector for one of the K

supports (say, support 3 in the case K=3) and, therefore, the estimated γk’s for the

remaining supports should be interpreted as the effects of store characteristics on the

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relative probability of the store belonging to support k rather than support 3 (see below

for managerial interpretation of ‘supports’.)

Under this latent class specification of heterogeneity, the aggregate market share Siskt

for alternative i in store s, given that store s belongs to support k, at time t can be written

as follows,

,iskt

jskt

V

iskt V

j N

eSe

∈

=∑

i∈N; s=1,…,S; k=1,…,K; t=1,…,T, (5)

where

0

P { , , },0,

iskt ik k ist

skt

V i Good Better BestV

α β= + ∀ ∈=

s=1,…,S; k=1,…,K; t=1,…,T. (6)

We use the latent class -- as opposed to hierarchical Bayes -- methodology to

incorporate heterogeneity across stores for the following reasons: (1) the methodology

has been widely used in choice modeling applications since Kamakura and Russell

(1989), and has been shown to do just as well as the hierarchical Bayes approach in

explaining most of the variance that arises on account of heterogeneity (Andrews, Ainslie

and Currim 2002, Andrews, Ansari and Currim 2002); (2) the hierarchical Bayes

procedure is computationally more demanding, while the latent class approach is easier to

automate for implementation purposes.

4.3 Estimation of the Parameters of the Heterogeneous MNL Model

The parameters of the heterogeneous MNL introduced in the previous two sub-

sections can be estimated by maximizing the likelihood function L,

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(7) ][0111

istNiskt

J

i

T

tsk

K

k

S

sSL ΠΠΠΠ

====

= π

where J is the total number of alternatives (including the no purchase option), Siskt is

given by equation (6), and Nist is the number of units of SKU i sold in store s during week

t. For the no purchase alternative, N0st is computed as Max t (∑j Njst) - ∑j Njst. In other

words, we treat the maximum weekly sales of the product (over all weeks) observed in

store s during the study period as the weekly market potential at the store (i.e., the total

number of consumers who walk in to store s during any given week, looking to buy in the

product sub-class). Therefore, this weekly market potential minus the observed product

sales during a given week is taken to be the number of no purchases during that week.

Managerial interpretation of ‘supports’ In equation (7), one can interpret k as

representing a consumer type. For example, K = 3 implies that there are three customer

types in the overall market for a subclass, and a store is represented as a mix of the three

consumer types, which makes the likelihood function a weighted average of three

conditional likelihood functions. To the extent that each store could face a different mix

of the same three consumer types, we make the assumption that store s ‘belongs to’

support or customer type 1 with probability πs1, support 2 with probability πs2, and so on,

and then compute the weighted average of the conditional likelihood functions implied by

each support, where the weights are the support membership probabilities πsk, given by

equation (4). Importantly, these weights are allowed to depend on observed store

characteristics, such as latitude and longitude, which would be expected to influence the

relative mixes of the three consumer types in the store’s local market.

The Schwartz Bayesian Criterion (SBC) is used to determine the optimal value of K.

Specifically, starting with K=1, we estimate heterogeneous MNL models for increasing

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values of K until the SBC fit criterion stops improving from adding more supports.

Sometimes, one would stop adding additional supports when the size of a newly

uncovered support (customer type) is not big enough to attract any managerial interest.

Thus, managerial judgment plays a role in determining the optimal value of K.

4.4 Estimation of Store-Specific Demand Parameters

The estimated parameters of the heterogeneous MNL, 1 2 3,{ , , , , } 1K

k k k k k kK α α α β π = , are

used in an empirical Bayes procedure to estimate store-specific demand parameters for

store s, as shown below (e.g., Kamakura and Russell 1989, Rossi and Allenby 1993).

Step 1: Compute the store’s conditional likelihood function Ls (δk) given that the store

belongs to support k:

, s=1,…,S; k=1,…,K. (8) 1 0

( ) istT J

Ns k iskt

t iL Sδ

= =

=ΠΠRepeat this calculation for each segment, to get Ls (δ1), …, Ls (δK).

Step 2: Use Bayes rule to get the store’s posterior support membership probability for

support k:

* ( ),postsk sk s kLπ π δ∝ s=1,…,S; k=1,…,K. (9)

Again, the priors are equal to the probability masses, πsk, estimated in the maximum

likelihood routine (see sub-section 4.3). Repeat this calculation for each support, to get

1 ,...,post posts sKπ π (appropriately re-normalizing them to add up to 1). The store-specific

demand parameters are now 1 2 3{ , , , , }post Kk k k k sk kα α α β π 1= . The store-specific demand

function is given by:

1

,iskt

jskt

VKpost post

ist ks Vk

j N

eSe

π=

∈

⎡ ⎤⎢

= ⎢⎢ ⎥⎣ ⎦

∑ ∑⎥⎥ s=1,…,S; k=1,…,K; t=1,…,T. (10)

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where Viskt is given by (6).

The above two-step procedure is repeated for all AAR stores in the sample to achieve

our ultimate goal of obtaining store-specific demand functions for all subclasses of HPX.

5. DETERMINING STORE-SPECIFIC PROFIT MAXIMIZING PRICES

Assuming that the store-specific demand function is constant over time, we drop the

subscript t in (10). Then, the retailer’s unconstrained profit optimization problem (see,

for example, Chintagunta 2002), is given by:

(11) ( )js 1{P }

1

Max (Profit ) ,Jj

Jpost

s js j jsj

P C S M=

=

= −∑

where Cj stands for the marginal cost (known to the retailer and available for this

research) associated with SKU j, M is the market size, and Sjspost is given by (10). The

solution to (11) is a triplet of prices, {PGood,s, PBetter,s, PBest,s}, that maximizes the retailer’s

profits from the subclass at store s.

The three SKUs’ market shares, , ,, , ,Post Post PostGood s Better s Best sS S S , do not add up to one. Instead,

they add up to 0,1 PostsS− . This yields a sensible interior solution for prices for the retailer’s

category profit maximization, with the no-purchase option having a crucial role from a

normative standpoint (as opposed to a descriptive standpoint, see Anderson and

Vilcassim 2001 for an insightful discussion about this point).

6. DATA AND EMPIRICAL ANALYSIS

6.1 Store-Level Sales Data

The data made available for this research represent historical sales figures over 2

years (i.e., T = 104 weeks), pulled from AAR’s transactions database, for 27 different

subclasses of HPX (numbered 1, 2, .., 30 by the company, with subclasses 3, 14, 24

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excluded from the outset). Specifically, the dataset comprises of weekly SKU-level sales

and prices (within each subclass) over a two-year period across a national sample of 800

stores (i.e., S = 800) randomly drawn from the population of 3400 stores. AAR also

provided data on several store demographic variables such as store size (square feet of

space), location (longitude, latitude), type of store (‘satellite’, ‘feeder’, ‘hub’) etc. and

product costs (wholesale prices) for price optimization purposes. Table 1 reports the

descriptive statistics, specifically, average sales and prices across the 800 stores and 104

weeks for all 27 subclasses.3 Note that the Good variant always has a lower price than the

Better (except in subclass 27), which, in turn, is always lower in price than the Best

variant. This indicates the existence of price/quality tiers in each subclass.

------------------------ Table 1 about here

------------------------ In terms of average weekly sales per store, the Better variant in subclass 1 and the Good

variant in subclass 13 appear to be the highest selling SKUs, with sales of 0.53 units and

0.51 units respectively. (A vast majority of the SKUs across all subclasses sell during less

than 10% of the weeks). The Best variant sells the most among the three options only in

subclasses 18 and 22 while it is the least selling variant in 21 subclasses. In terms of

average prices, the Good variant ranges from $26.28 to $129.72 while the Best variant

has a price range of $64.80 to $224.59 across all subclasses. Also, in comparing the

average prices for the Good with the Best variant, we see that the price gap varies from

$30.47 to $128.60. These descriptions suggest that our data capture a broad range of

prices across subclasses and stores.

19

6.2 Nature of Empirical Analysis

The proposed heterogeneous MNL model is estimated separately for each HPX

subclass using the Maximum Likelihood technique, as explained in Section 4.3. The

estimated MNL demand model for a given subclass is then used to derive a store-specific

demand model, as explained in Section 4.4. The estimated store-specific demand model,

as explained in Section 5, serves as the input to a store-level price optimization problem,

which is solved store-by-store to obtain optimal SKU prices for the given subclass for

each of the 800 stores in the sample. The same procedure is repeated to obtain store-

specific optimal SKU prices for all subclasses in our dataset. Subsequently, we examine

optimized profits and their sensitivity to price changes.

7. EMPIRICAL RESULTS

For a majority of the 27 HPX subclasses, a 3-support solution for unobserved

heterogeneity across stores (i.e., K = 3) was found to be appropriate, based on model fit

(i.e., SBC) and managerial judgment. For ease of exposition and to maintain consistency,

we use the 3-support solution for all subclasses, both in the reported estimation results in

this section and in the price optimization exercise at the store-level.4

7.1 Estimation Results for the Heterogeneous MNL

Tables 2 and 3 report the estimation results for the 3-support heterogeneous MNL for

each of the 27 subclasses. (The reader should keep in mind that each subclass represents

a distinct automobile market and, therefore, the 3 supports in each case are qualitatively

different.) Specifically, Table 2 presents the 3 sets of estimated brand preferences (i.e.,

{αGood,1, αBetter,1, αBest,1}, {αGood,2, αBetter,2, αBest,2}, {αGood,3, αBetter,3, αBest,3}), while Table

3 provides the corresponding estimated price sensitivities (β1, β2, β3), along with the

20

estimated baseline probability masses (i.e., ignoring store characteristics) of the three

supports (π1, π2, π3) in each subclass.

------------------------ Table 2 about here

-------------------------

From Table 2, we see that the estimated brand preferences are, for the most part,

negative. This is because the no-purchase option is, by far, the most dominant in almost

all subclasses. Since the brand preferences can be viewed as capturing baseline shares of

the SKUs in the subclass, estimates of these preferences must be interpreted as being

relative to the preference for no-purchase, set at 0 for identification purposes. As

expected, these estimates turn out smaller than the estimated preference for no-purchase.

In Table 3, we see that the estimated price sensitivities are, for the most part, negative as

expected. The estimated price sensitivities have the wrong sign, i.e., positive, for 4 out of

the 27 subclasses, i.e., 1, 4, 5 and 22.5 Therefore, these 4 subclasses were excluded from

the subsequent model validation and price optimization analyses (since positive price

coefficients imply infinite optimal prices which are unrealistic in practice).6 The

estimated baseline (i.e., ignoring store characteristics) probability masses of supports in

the remaining subclasses vary from 16% (support 1 in subclass 25) to 57% (support 2 in

subclass 27).

------------------------ Table 3 about here

------------------------

Model Validation

To increase confidence in the estimation results derived from the 800 calibration

sample stores, we proceeded to validate the 23 subclass demand models with

21

appropriately signed coefficients on the holdout sample consisting of the remaining 2600

stores. Subsequently, one of these 23 subclasses, specifically, subclass 21, had to be

dropped from this validation exercise due to insufficient data in the validation sample.

For each of the remaining 22 subclasses, Table 4 reports the validation log-likelihoods

(LL), i.e., summed log probabilities of the observed outcomes (SKU sales) for each

store/week combination in the holdout sample, applying the proposed 3-support model as

well as two benchmark models: (1) a homogeneous logit, and (2) a naïve market share

model, that predicts choice shares for each store/week combination in the holdout data to

be equal to the observed average market shares of alternatives in the calibration data.

More specifically, the proposed model-based probabilities of observed outcomes in the

holdout sample’s store (s)/week (t) combinations are computed as follows: First, we plug

in store s’s characteristics (Ws) in equation (4) to get store s’s predicted prior support

membership probabilities (πsk) for each of the 3 supports. Second, we compute the

predicted support-specific shares for the three alternatives (Siskt), as well as the no

purchase option (Sis0t), using equations (5) and (6), after plugging in the observed prices

of the three alternatives (Pist). We then use equation (7) to compute the validation

likelihood for the holdout sample. The logarithm of this quantity represents the validation

log-likelihood.

As shown in Table 4, the proposed heterogeneous model outperforms the two

benchmark models in all 22 subclasses, which lends further credibility to its good

empirical performance in the calibration sample stores.

------------------------ Table 4 about here

------------------------

22

7.2 Assessment of Estimated Elasticities

Using the estimated parameters in Tables 2 and 3 for the 22 validated demand

models, we derive the own- and cross-price elasticities of the three SKUs within each

subclass (i.e., a total of 9 price elasticities, comprising 3 own- and 6 cross-elasticities per

subclass).7 The computed own- and cross-price elasticities are reported in Table 5. For

all 22 subclasses, the elasticities have the correct sign, i.e., all own elasticities are

negative, while all cross-elasticities are positive.

------------------------ Table 5 about here

------------------------

Own-Price Effects

We note that the highest estimated own-price elasticities across the three quality variants

are in subclass 19. In fact, subclass 19 appears to be the most price-responsive among all

subclasses. The average own-price elasticities of Good, Better and Best variants, across

all 27 subclasses, are found to be -1.26, -1.80 and -3.60 respectively. Note that the mean

of these own-price elasticities across the quality variants is about -2.22 which is similar to

the mean estimate of about -2.5 found in the grocery retailing sector (Hanssens, Parsons

and Schultz 2001, pp 333-337).

Cross-Price Effects

The demand for the Good variant is least responsive to price, and also least vulnerable on

price, in subclass 25.8 This indicates that there is room to increase the price of the lowest

quality variant in subclass 25. The Good variant has its highest clout in subclass 19. The

Better variant is least responsive to price, and also least vulnerable in subclass 26, with

23

the highest clout in subclass 9.9 The Best variant is least responsive to price in subclass

22, least vulnerable in subclass 17, and has the most clout in subclass 18.

Asymmetric and Neighborhood Cross-price Effects

The model estimation results in Table 5 also shed light on an important general

question raised by our collaborator: What is the pattern of cross-price effects among the

Good (G), Better (b) and Best (B) variants in the various subclasses of HPX? In general,

this issue is of interest to other suppliers of quality-tiered product lines as well, e.g.,

gasoline retailers offering regular unleaded, super unleaded, premium grades of gasoline

and airlines offering first class, business class and economy class services etc., and has

received much attention in the previous retail pricing and promotions literature.

Within the context of grocery retailing, the seminal study by Blattberg and

Wisniewski (1989) observed that cross-price effects are asymmetric, i.e., price reductions

on a high price, high quality brand impact a lower-priced (lower quality) brand more so

than the reverse, a phenomenon later validated by Mulhern and Leone (1991), Allenby

and Rossi (1991b) among others. More recently, however, the validity and/or

generalizability of this finding has been questioned by several studies e.g., Bronnenberg

and Wathieu (1996), Heath et al. (1996). Sethuraman, Srinivasan and Kim (SSK) (1999).

Specifically, SSK argue that asymmetries in cross-price elasticities tend to favor

the higher-priced brand simply because of scaling effects due to considering percentage

changes shares and prices in the cross-price elasticity measure. Based on a meta-analysis

of 1080 previously reported cross-price effects between 280 brands from 19 different

grocery product categories SSK found: (a) the cross elasticity-based asymmetric price

effect “tends to disappear;” (b) support for the existence of “neighborhood price effects”,

24

i.e., brands priced closer to each other have greater cross-price effects than brands priced

farther apart; (c) a brand is most affected by discounts of a competing brand that is

immediately higher in price, followed by discounts of a brand that is immediately lower

in price. SSK argue that it these neighborhood pricing effects that are truly generalizable

findings. In another study, based on a model where the asymmetric price effect depends

on the relative price-quality positioning between the two brands, Bronnenberg and

Wathieu (1996) find evidence that the cross-price effects between two brands can be

opposite to the conventional asymmetric effects. In particular, if the lower-priced brand

has more favorable price-quality positioning, then the conventional asymmetry would be

reversed; in fact, the lower-priced, lower-quality brand may hurt the higher-priced brand

more through discounting than vice versa.

Interestingly, an analysis of our estimated cross-price elasticities in Table 5 leads

to results that are in part consistent with, and in part opposed to the findings of both

Blattberg and Wisniewski and SSK.10 To begin with, we note that the cross-price

elasticity measure’s scaling effects problem highlighted by SSK arises only when there is

a positive correlation between share and price as is common in grocery retailing, e.g.,

national brands have higher prices and higher market shares than store brands. This is

obviously not the case in auto parts retailing as indicated in Table 1 where we see that the

higher–priced Best variants sell the least in the majority of subclasses. Since price and

market share do not go hand-in-hand in our dataset, there need not be an a priori scaling

effect that would necessarily go one way. (That is, whether the price effect or the market

share effect dominates is an empirical question that is answered by our model-based

25

analysis.)11 A comparison of the average cross-price elasticities over the 22 subclasses

leads to the following results:

Result 1: Average Eb→G = 1.24 > Average EG→b = 1.13 Result 2: Average Eb→B = 1.24 > Average EB→b = 0.49 Result 3: Average EG→B = 1.13 > Average EB→G = 0.49 Result 4: Average Eb→B = 1.24 > Average EG→B = 1.13 Result 5: Average Eb→G = 1.24 > Average EB→G = 0.49

Result 6: Average EG→b = 1.13 > Average EB→b = 0.49 Thus, we see that only Result 1 is consistent with the asymmetric cross-price

effect observed by Blattberg and Wisniewski while Results 2 and 3 represent reversals of

this effect. Following Bronnenberg and Wathieu, this suggests the relative price-quality

positions of Better vs Best, and Good vs Best, favor the lower-quality brand in these

pairs. In contrast, Result 1 suggests that in the case of the Better-Good pair, the ratio of

the quality gap between these brands to the gap between their prices is relatively large,

favoring the Better variant’s price reductions. Recalling that the average Good-Better

price gap of $28.32 is significantly smaller that the average Better-Best price gap of

$38.95 (see Table 1), all three Results 1-3 are explainable if the Better variants in HPX

subclasses are closer in quality to the Best than to the Good variants, giving the Better

variant a positioning advantage relative to both the Good and Best variants. However,

considering its high price, the Best variant’s quality appears not to be sufficiently superior

to that of the Good variant, giving the latter a positioning advantage relative to the Best.

Discussions of specific products with management confirmed these conjectures about

relative price-quality positions of Good, Better and Best in the various subclasses.

26

Next, consistent with SSK’s observations, Results 4 & 5 indicate there are

neighborhood price effects in HPX subclasses. That is, the variants that are closer to each

other in price (and quality) have larger cross-price effects than those that are priced

farther apart. Interestingly, however, the last Result 6 represents a reversal of SSK’s

finding that “A brand is affected the most by discounts of its immediately higher-priced

brand, followed closely by discounts of its immediately lower-priced brand.” In the case

of the HPX category, we find that the impact of a change in Good’s price on Better is

stronger than the impact of Best’s price on Better.

Overall, we find that the pattern of cross-price effects in the HPX category of auto

parts is different from the empirical generalizations that have emanated from the

supermarket retailing context, underscoring the importance of extending retail pricing

research to non-grocery sector markets.

7. 3 Effects of Store Characteristics on Demand Model Parameters

To shed light on the estimated effects of eight store characteristics on store-support

membership probabilities for supports 1 and 2, relative to support 3, we report the

number of times each estimated effect is significant across the original 27 subclasses

below.12

1. Store size: 21 out of 54 estimates are significant,

2. Full years since opening (Full_Fys_Opened): 27 out of 54 estimates are significant,

3. Longitude: 19 out of 54 estimates are significant,

4. Latitude: 9 out of 54 estimates are significant,

5. Small (Satellite) Store: 20 out of 54 estimates are significant,

6. Medium (Feeder) Store: 0 out of 54 estimates are significant,

27

7. Large (Hub) Store: 11 out of 54 estimates are significant

8. Commercial B2B sales (Comm_Sales) : 25 out of 54 estimates are significant.

Overall, 132 out of the 432 estimates (i.e., 30%) are significant, which indicates these

store characteristics have good explanatory power. In other words, store characteristics

are at least partly responsible (with unobserved store characteristics being primarily

responsible) for the observed variation in both estimated brand preferences for different

quality variants as well as the estimated price sensitivities across AAR stores in our

sample. Further, a few intuitive generalizations about the effects of store characteristics

across product subclasses emerged upon examining the signs of the coefficients

associated with store characteristics (γk in equation 4 on page) in the support membership

probabilities These are summarized below.

With regard to the estimated preferences for brands at the store we find: (1) As

Full_Fys_Opened increases, the preferences for all three quality variants – Good, Better,

Best – with respect to the no-purchase option increase 65% of the time. That is, all

variants in a sub-class sell higher in AAR stores that have been open for a longer period

of time, which made intuitive sense to AAR management. (2) For a Satellite store, the

preferences for all three quality variants with respect to the no-purchase option is lower

than for a non-satellite store, and this is found to be true 63% of the time. This suggests

that smaller AAR stores in markets with a larger concentration of AAR stores are

associated with lower sales of all variants in the sub-class, probably due to greater inter-

store cannibalization than in other markets. (3) As Comm_Sales increases, the preference

for the Good quality variant increases, while market preferences for the Better and Best

quality variants decrease 60% of the time. This finding suggests that AAR stores that

28

have greater B2B sales are associated with a higher preference for the Good quality

variant, and lower preferences for the Better and Best quality variants. AAR

management’s interpretation of this finding is that business re-sellers (such as auto repair

shops etc.) typically buy the least expensive variant within a product sub-class from AAR

and sell it at a high margin to end-consumers.

For the remaining 5 store characteristics, no generalization emerges across sub-

classes with regard to market preferences for brands.

Next, with regard to the estimated price sensitivity at the store, we find: (1) As

Latitude increases, the price sensitivity at the store increases 61% of the time. This

suggests that AAR stores in the North are associated with more price-sensitive consumers

than AAR stores in the South. AAR management pays attention to store latitudes because

they believe that climate correlates with latitude and is an important driver of failure rates

and consumer behavior in these product sub-classes. (2) For a Satellite store, the price

sensitivity is lower than for a non-satellite store, and this is found to be true 61% of the

time. This finding suggests that the smaller AAR stores that exist in markets with larger

concentrations of AAR stores are associated with less price-sensitive consumers. AAR

managers found this observation consistent with the fact that satellite markets are those

where AAR faces less competition from other retailers (since AAR has already

“crowded” the market by placing a number of its own stores there), and to the extent that

prices at all AAR stores within a given market are similar, consumers have no real

alternatives to switch to when AAR increases price at a given store, which makes the

market less sensitive to price. For the remaining 6 store characteristics, no generalization

emerges across sub-classes with regard to price sensitivity.

29

The lack of directionally consistent effects of the majority of store characteristics

across subclasses, however, is not surprising as each sub-class is meant for a different

sub-category of automobiles, which in turn appeals to a segment of consumers whose

profile can be quite different from owners of another automobile type, e.g., Ford Taurus

versus Ford Truck owners. Thus, to the extent that a given store characteristic, e.g.,

longitude, is correlated differently with, say the geographic dispersions of high income

consumers versus low income consumers across stores, it may increase preference for the

Best variant in sub-class A, but decrease preference for the Best variant in sub-class B.

With grocery products, on the other hand, the same consumer buys multiple products

such as peanut butter, ketchup, margarine etc. Therefore, one is more likely to find effects

of consumer demographics or store characteristics that generalize across grocery product

categories.

We turn to the price optimization results in the next two sections. To shed light

on the derived magnitudes and patterns of optimal prices across variants within

subclasses in a compact fashion, Section 7.4 presents the store support – level price

optimization results by subclass. Ultimately, however, the goal of our study is to

determine the optimal store-specific prices. As indicated in Equation (11), these are based

on the store-specific posterior demand function, which is a weighted average of three

estimated prior logit functions, where the weights are store-specific and determined by

store characteristics as well as unobserved store-specific factors (as represented in the

store’s sales data). Section 7.5 summarizes the pattern of these optimal prices derived for

800 stores.

30

7.4 Store Support-Specific Optimal Prices

Using the price optimization procedure outlined in Section 5, we develop optimal

prices for the three quality variants (reported in Table 6) at the level of the three

estimated store supports within each subclass (excluding subclasses 1, 4, 5 , 21 and 22).

This is done by assuming store characteristics (Ws) to take the average observed value

across all stores in the sample, and further assuming that the resulting prior support

membership probabilities (πsk) for each of the 3 supports is equal to the posterior support

membership probabilities for the store.

------------------------ Table 6 about here

------------------------

Comparing these prices to the average observed prices in Table 1, we find that, on

average, the optimal prices are roughly equal to the observed prices (the average value of

optimal prices minus observed prices is about $1.14). However, the standard deviation of

optimal prices minus the observed prices is about $52, which indicates a fair amount of

variability in the difference between the observed and optimal prices. As a percentage of

observed average prices, the average deviation is 7.7%, while its standard deviation is

about 58%. This shows that the modeling procedure adopted in this study does indeed

prescribe substantively different prices from what AAR currently applies at its stores.

Table 6 also shows that the three-support estimation was effective in terms of designing

optimal pricing strategies which yield different prices across supports within a given

subclass. For instance, the optimal price for the Good variant in Subclass 13 varies from

$88.18 in Support 1 to $168.34 in Support 2 and $115.16 in Support 3. Similar

31

differentiation is found for other subclasses and variants. Thus the model recommends a

range of prices, depending on the store and subclass characteristics.

In the next section, we focus on the results of primary interest in our research –

the store-specific optimal prices of the variants for each subclass.

7. 5 Store-Specific Optimal Prices

The empirical Bayes procedure outlined in Section 4.4 yields 800 estimated sets

of the store-specific parameter vector, i.e., 1 2 3{ , , , , }post Kk k k k sk kα α α β π 1= (K = 3), within each

of 22 subclasses (i.e., the original 27 subclasses minus the excluded subclasses of 1, 4, 5,

21 and 22).13 We then utilize these estimates in the price optimization procedure outlined

in Section 5 to determine the optimal SKU prices at the store-level.

We are now in a position to examine two additional issues of interest to AAR

management at this stage: (1) Were the company’s stores currently underpricing or

overpricing HPX SKUs relative to the optimal prices in various subclasses? (2) Were the

current store-level price gaps or differences between prices of the Good and Best variants

in each subclass too large or too small? Since the store-specific current and model-

recommended prices of SKUs are too numerous to enumerate here, we examine these

questions with respect to a sample of 3 subclasses involving 317 cases (subclass-store

combinations) selected out of the 800 stores by management. The observed deviations

between the current (actual) and optimal store-specific prices of SKUs of these 3

subclasses at these selected stores are summarized in Table 7.

------------------------ Table 7 about here

------------------------

Optimal vs. current store-specific prices

32

As indicated in Table 7, we find that the optimal prices recommended by our

model fall into three ‘price gap’ scenarios:

Scenario 1: In this scenario, the gaps between the optimal prices of the Best and the

Good variants are smaller than the gaps between the observed prices of these variants.

That is, PG* > PG and PB

* < PB where PG and PB are the actual (observed) prices, and

PG*and PB

*are the optimal prices for the Good and Best variants respectively. Table 7

indicates that this occurred in about 12.3% of the 317 cases included in this analysis.

Scenario 2: Here, the optimal prices are slightly higher than the actual prices in the store

(PG < PG* < PB < PB

*). This is the case of underpricing - we note that in nearly 37.5% of

the sample cases, the optimal prices that the model recommends fall into this category.

Scenario 3: In this situation, the optimal prices are slightly lower than the actual prices in

the store (PG* < PG < PB

* < PB). This is the overpricing scenario, which happens in nearly

50% of the cases.

Therefore, this analysis of 3 subclasses suggests that the retailer would benefit

from a slight reduction of prices of all three variants in each subclass in a majority of the

stores. In a smaller fraction of stores, the retailer benefits from raising the prices.

It is also interesting to compare the differences between optimal and current

prices of the Best and the Good variants – the price ‘bandwidths’. As shown in Table 7,

across the three scenarios noted above, the average bandwidth of currently applied prices

is much greater, 50 to 70% greater, than the optimum bandwidth. That is, it appears that

AAR can benefit not only by adjusting its prices above or below current levels at specific

stores, but also by narrowing the price gap between the Good and Best variants at these

stores.

33

Overall, it is noteworthy that unlike grocery products where optimal prices are

typically higher than actual prices (see Hoch, Dreze and Purk 1994, Montgomery 2004),

we find in the case of AAR that optimal prices are higher than actual prices for some

product sub-classes, but lower for others.

The next section provides some insight into the sensitivity of profits to deviations

from model-recommended prices. Again for the sake of compact exposition, we revert to

the store support-level optimal pricing results in this analysis.

7. 6 Store Support-level Profit Optimization Analysis

Table 8 compares the total profit (summed across the three variants) yielded by

the support-level optimal prices (see Table 6) with estimated demand model-based

predicted profits at the current actual average weekly prices (see Table 1).

------------------------ Table 8 about here

------------------------

We see that for most subclasses (15 out of 22) the model-based total profits at

current prices are within 20% of the optimal total profit. For the other subclasses,

however, the actual profits are 23.5% to 63.2% lower than the optimized profits.

Subclasses 17, 19, 20 and 23 show the largest differences, suggesting that these have

substantial potential for improvement if the optimal pricing strategy would be

implemented. Summing across all subclasses, the model-based predicted profits at

current prices are 28.4% lower than the predicted profits at the optimal prices.

Subsequently, we explored the sensitivity of predicted profits to uniform

deviations (of -10%, -20%, -30%, +10%, +20% and +30%) from the variants’ optimal

price levels in each subclass and support. In general, the impact of a 10% deviation

34

(increase or decrease) from the optimal prices of variants in each subclass/store support

leads to reductions in optimized profit of 1 to 4 percent while a ±30% deviation from

optimal prices results in, for most subclasses, at least 20% reduction from optimum

profits. Further, consistent with the findings described in the previous paragraph, the

predicted profit levels for subclasses 19 and 23 are most sensitive to these deviations

from the optimal prices, while the profits achieved in subclasses 13, 17, 20 and 30 appear

to be the least sensitive (the profit reduction not exceeding 10% even with deviations

from optimal prices of ±30% ). Importantly, our sensitivity analyses reveal that the

profit reduction effects of deviations from optimal price levels are asymmetric.

Specifically, profits are typically much more sensitive to underpricing than overpricing.

This suggests that enhanced sales at lower prices do not adequately compensate for

reduced margins, implying the store managers should proceed with much more care when

considering a price reduction rather than increase. Overall, this sensitivity analysis

shows that the optimization model behaves reasonably and that such model-based

explorations of pricing strategies can be of great value to management.

Given the promising nature of these support-level sensitivity analysis results, we

proceeded to conduct a field test of the value of the model-recommended store-specific

prices.

8. FIELD TEST OF MODEL RESULTS

Objective: The goal of this study was to test the value (incremental profit) from applying

store-specific model-recommended prices in the field. The basic design of this quasi-

experiment was a longitudinal “Before-After with control group” design. More

specifically, the duration of the quasi-experiment was 16 weeks (between June 15 and

35

August 15, 2005). The previous 8 weeks (April 15 to June 15, 2005) constitutes the

“Pre-test” period during which prices of variants of all subclasses of HPX at all stores

were in line with the company’s existing policy. Model-recommended prices were then

applied to a selected number (13) of subclasses of HPX in a set of 200 “Experimental”

stores for the next 8 weeks (test period), while the current pricing policy continued for

these subclasses in a comparable set of 300 “Control” stores. Subsequently, the

aggregate percentage changes in cumulative (8-week) gross profit of these selected

subclasses between the Pre- and Test Periods were recorded and compared to the

corresponding percentage changes in the Control stores. It should be noted that the

proposed field test design and execution were largely coordinated and monitored by the

company’s pricing management and not by the academic research team. The benefit of

this approach was that there was greater and faster acceptance and cooperation from store

management in executing a study that would affect actual business results. The

drawback, however, was that a perfectly controlled and executed study from an academic

viewpoint was difficult to achieve as managers tend to make ad hoc adjustments in the

“heat of ongoing operations”. Below, we describe some instances where actual execution

deviated from design, and report the results of the field test taking these into account.

Selection of stores and subclasses for the field test: First, management wished to subject

the model-recommended prices to a more “stringent” field test and therefore decided to

test the efficacy of the model-recommended prices at the 2600 holdout stores (not the

original 800 stores in our calibration sample). Considering in turn each of the 22

subclasses with validated models, the holdout stores’ recommended prices were derived

as follows: Step1: Each holdout store’s “prior” support membership probabilities are

36

computed by plugging in its store characteristics in the estimated probability mass

function from the calibration sample (see Equation 4). Step 2: Bayes rule (using the

holdout store’s observed sales data as the likelihood) was applied to compute the holdout

store’s “posterior” support membership probabilities. Step 3: The posterior probabilities

are used as weights to compute a weighted average of the 3 MNL logit functions

(characterizing the 3 estimated locations of the heterogeneity distributions in the

calibration sample) as the holdout store’s predicted demand function. Step 4: The price

optimization model (Equation 11) was applied to determine store-specific optimal prices.

AAR management found about 30% of these (unconstrained) model-

recommended prices to be either too high (or too low) relative to current prices.

Therefore, they retained only the remaining 70% of the optimal prices for the field test.

More specifically, when a variant within a subclass had optimal prices that were either

too high or too low, the entire subclass was excluded from the field test. Also, only “full”

subclasses, i.e., subclasses with all 3 variants present were retained. Thus, after this

screening, the total number of subclasses identified for the field test was reduced from 22

to 13, with the number of full subclasses in any given store ranging from 1 to 11.

Further, out of the original 2600 stores, only 1317 stores that had 5 to 11 full subclasses

each were used as a sampling frame from which 200 test stores and 300 control stores

were randomly selected. All of these 500 stores followed essentially the same pricing

strategy in the pre-test period which was a “5-10% lower price” than their leading

competitor in their respective pricing “zones”. (Recall that currently AAR stores across

the nation are grouped into five zones with varying prices.)

37

Prices in the experimental stores were changed from pre-test levels to model-

recommended levels for the 8-week test period. We assumed that prices would be

maintained at or very close to pre-test levels in the control stores. However, for internal

reasons, company management unexpectedly intervened to change the prices of 3

subclasses in the control group stores rather significantly (more than 10% from their pre-

test levels, during the test period). Due to this change in the control group condition, it

was then agreed that these three subclasses would be dropped from the field test.

Therefore, the field test evaluations of the model are based on 10 subclasses.

Performance metric: The focal performance measure of interest in the field test is

improvement in Gross Profit (GP) where GP = (Retail price per unit – wholesale cost per

unit) times Quantity sold. Basically, for each subclass we compute the percentage

change in gross profit between the test and pre-test periods realized in the experimental

group and compare this to the corresponding change in gross profit of the control group,

as shown in Table 9.

------------------------ Table 9 about here

------------------------

We see that in 7 out of the 10 subclasses, the model-recommended prices led to a greater

increment in gross profit in the experimental stores relative to that observed in the control

stores. Overall, the HPX gross profit performance of the test stores that used model-

recommended prices was noticeably superior to that of the control stores. Projecting the

overall net gain from these ten subclasses of HPX to a population of 3000 stores over 52

weeks, we arrive at an estimated annual increase of over $613,000 in gross profit from

the (10 subclasses of) HPX category for AAR by employing the model-based prices.

38

While the precise numbers may vary at additional stores, AAR management was

sufficiently impressed by these results to commission a similar model-building effort for

a second hard part category.

9. SUMMARY, CONCLUSIONS AND DIRECTIONS FOR FUTURE RESEARCH

This paper extends extant retail category pricing optimization research to a new and

important retailing sector – specialty auto part retailing – institutionally different from the

more well-studied grocery retailing sector in several respects impacting price-demand

assessment. Considering these novel features of specialty auto part demand, our research

develops a store-level pricing optimization model for a specialty auto part retailer, applies

and validates the model-recommended prices in a field setting, offers new insights into

cross-price effects among quality variants in a product line and adds to emerging studies

of price customization in retailing.

Using data on weekly sales and prices of 23 subclasses of a hard parts category, HPX,

from 800 of the retailer’s 3400 stores across the country, we estimate and validate

subclass-specific demand functions representing the responsiveness of sales of different

quality variants within each subclass to the chosen prices of the variants. We

accommodate the effects of both observed (i.e., due to store characteristics such as store

size and location) and unobserved heterogeneity across stores in the parameters of these

subclass specific demand functions. Using an empirical Bayes procedure, we transform

the estimated aggregate demand function for each subclass to 800 different store-specific

demand functions. Using these store-specific demand functions as inputs to a category

profit maximization problem, we generate store-specific optimal prices for the three

variants within each subclass. The proposed model recommended prices were

39

implemented in 200 stores for 10 subclasses in a field experiment with positive results,

leading to a projection of a profit increase of over $610, 000 from this one category for

the retailer if model recommendations were followed. Subsequently, the retailer has

decided to roll out the proposed modeling approach to a second hard part category in the

first quarter of 2006.

Our study integrates both descriptive and normative aspects of demand modeling in

marketing research. While the statistical methodologies used in our study have received

great attention in the academic literature, they have not been embraced with any degree

of familiarity in marketing practice, far less in automotive aftermarket retailing. We hope

our work will encourage retailers of various hues to employ modeling-based store-

customized pricing policies for their brands or products.

One caveat is in order. We ignore the effects of prices at competing retailers on

demand at the focal retailer. This is because prices at competing retailers were not

available to the authors. Supplementing our demand data with prices at competing

retailers, obtained using mystery shoppers, and re-calibrating the price elasticities both

across quality grades and across retailers, would be a useful avenue for future research.

40

Table 1

Descriptive Statistics – Average Weekly Sales per Store and Prices for 27 Subclasses

Average Weekly Sales (Units sold) Average Weekly Prices Good Better Best Good Better Best

Subclass 1 0.37 0.53 0.03 $26.28 $38.23 $64.80 2 0.10 0.21 0.02 $65.93 $81.12 $126.35 4 0.02 0.05 0.00 $114.09 $151.06 $188.50 5 0.07 0.10 0.00 $125.93 $162.51 $197.94 6 0.16 0.18 0.02 $92.59 $128.06 $166.21 7 0.02 0.03 0.00 $129.72 $154.10 $199.99 8 0.02 0.04 0.00 $112.60 $155.59 $199.99 9 0.00 0.05 0.01 $86.99 $133.01 $161.47 10 0.04 0.04 0.01 $92.46 $115.93 $148.75 11 0.05 0.09 0.00 $95.99 $134.09 $224.59 12 0.46 0.13 0.12 $66.32 $83.74 $133.29 13 0.51 0.06 0.06 $64.99 $93.92 $134.11 15 0.22 0.06 0.05 $64.38 $89.17 $132.19 16 0.31 0.06 0.04 $64.09 $84.11 $134.15 17 0.17 0.04 0.09 $66.39 $89.90 $134.82 18 0.25 0.07 0.25 $73.36 $100.04 $134.05 19 0.13 0.14 0.05 $100.37 $119.04 $140.69 20 0.23 0.05 0.02 $66.32 $95.29 $133.41 21 0.27 0.09 0.07 $76.34 $88.76 $134.19 22 0.07 0.02 0.10 $100.91 $129.82 $141.54 23 0.08 0.08 0.04 $95.90 $114.06 $140.72 25 0.37 0.00 0.01 $63.84 $100.94 $134.21 26 0.00 0.21 0.00 $87.99 $95.07 $118.46 27 0.06 0.01 0.03 $86.36 $81.46 $131.93 28 0.08 0.02 0.01 $90.52 $115.17 $143.08 29 0.02 0.05 0.02 $76.81 $92.36 $134.10 30 0.12 0.12 0.04 $69.56 $87.15 $131.86

** Average sales and prices are across 800 stores and 104 weeks

41

Table 2

3-Support Brand Preferences Estimation Results for 27 Subclasses

(Subclasses subsequently excluded from the price optimization are shown in bold)

Support 1 Support 2 Support 3 αGood,1 αBetter,1 αBest,1 αGood,2 αBetter,2 αBest,2 αGood,3 αBetter,3 αBest,3

Subclass 1 -2.8140 -2.3915 -5.0329 -2.7324 -2.7100 -6.2768 -2.2272 -3.8674 -6.9835 2 -1.3513 0.0241 -0.8285 -0.8493 0.1262 -1.0773 -1.9945 -0.6030 -1.2453 4 -3.3385 -2.1345 -7.9242 -2.2458 -1.1855 -6.3036 -3.9008 -2.2000 -7.1146 5 -4.1378 -4.0095 -10.028 -3.5746 -3.3397 -9.0859 -3.2553 -2.7651 -7.1596 6 -1.5074 -0.7991 -2.5447 -1.4926 -0.8487 -2.4501 -1.9731 -1.2231 -2.2525 7 0.0245 0.9671 -11.100 -1.6790 -0.5537 -10.000 -0.7436 -0.0806 -8.0011 8 -2.6334 -1.4391 -11.003 -3.4510 -1.7912 -12.001 -4.0912 -0.4407 -7.0248 9 -8.7265 1.5110 -1.0637 -8.1044 1.4374 -0.8424 -7.0376 1.6789 -0.3992 10 -0.9010 -0.2108 -2.1458 -0.9748 0.1485 -2.4088 -0.9422 -0.3522 -2.4837 11 -2.8256 -1.9025 -7.1195 -1.7818 -0.4571 -8.0278 -2.2169 -1.0318 -6.0339 12 -0.6843 -1.5951 -0.1787 -0.2779 -1.3641 -0.1510 -0.7779 -1.1289 -0.9412 13 -1.2678 -2.7364 -2.0285 -0.8715 -2.8926 -2.5094 -1.0406 -2.7154 -2.1147 15 -0.0955 -0.8186 0.4876 -0.7201 -1.3308 0.0068 -0.6494 -0.7887 -0.1885 16 0.5858 -0.4949 0.8252 0.3861 -0.2907 1.6195 0.4714 0.5850 0.1839 17 -1.8920 -3.5466 -2.6699 -2.2853 -3.3366 -1.7565 -2.1263 -2.6286 -1.4965 18 -1.5423 -2.7930 -0.7778 0.2208 0.8026 3.3282 1.0809 0.3222 3.6311 19 6.1147 7.8335 8.6564 5.5385 7.3170 8.1709 3.1336 4.4075 4.9707 20 -1.8083 -3.1982 -3.7781 -2.0728 -3.2541 -3.4749 -0.9276 -2.2639 -2.6071 21 0.2382 -0.6745 0.9513 -0.1031 -0.5825 0.9772 0.1334 -0.2644 0.5031 22 -1.8247 -2.1553 -0.4356 -3.2425 -4.3497 -2.6770 -2.3921 -3.2859 -1.8677 23 3.1843 4.5622 5.4749 3.3233 4.3742 5.1412 -0.0203 0.7601 0.9866 25 0.1107 -4.2366 -2.4549 -0.0720 -3.6325 -1.9084 0.4040 -3.2236 -1.6199 26 -3.6933 -0.4854 -6.4227 -6.9962 1.0846 -5.2173 -3.2980 -0.1150 -7.2705 27 -0.4715 -2.9918 -0.2155 -0.1367 -2.8559 0.5028 -0.6246 -2.8577 0.0578 28 -0.1676 -0.7453 -0.1078 0.1004 -0.4052 -0.2401 -0.0407 -1.3786 -1.5720 29 -3.7624 -3.1927 -4.0914 -3.2846 -1.9371 -2.9935 -2.5213 -2.1857 -2.3001 30 -1.7034 -2.2685 -1.9241 -1.8302 -2.8090 -1.5270 -0.9598 -2.1294 -1.1908

42

Table 3

Estimated 3-Support Price Sensitivities and Masses for 27 Subclasses

(Subclasses subsequently excluded from the price optimization are shown in bold)

Support 1 Support 2 Support 3 β1 π1 β2 π2 β3 π3

Subclass 1 0.0063 0.43 0.0255 0.36 -0.0046 0.21 2 -0.0293 0.41 -0.0249 0.35 -0.0283 0.24 4 -0.0093 0.62 -0.0111 0.26 0.0002 0.12 5 0.0045 0.39 0.0046 0.34 -0.0013 0.28 6 -0.0116 0.37 -0.0166 0.38 -0.0525 0.25 7 -0.0289 0.24 -0.0214 0.24 -0.0272 0.52 8 -0.0120 0.31 -0.0138 0.33 -0.0222 0.36 9 -0.0402 0.46 -0.0277 0.20 -0.0354 0.34 10 -0.0320 0.48 -0.0247 0.30 -0.0242 0.21 11 -0.0116 0.40 -0.0142 0.28 -0.0131 0.32 12 -0.0251 0.32 -0.0215 0.32 -0.0204 0.35 13 -0.0188 0.37 -0.0082 0.36 -0.0131 0.27 15 -0.0295 0.29 -0.0337 0.32 -0.0285 0.39 16 -0.0359 0.26 -0.0431 0.46 -0.0540 0.28 17 -0.0032 0.27 -0.0140 0.31 -0.0115 0.42 18 -0.0170 0.22 -0.0424 0.24 -0.0436 0.54 19 -0.0869 0.23 -0.0869 0.42 -0.0682 0.35 20 -0.0051 0.29 -0.0094 0.33 -0.0114 0.38 21 -0.0346 0.42 -0.0378 0.31 -0.0296 0.26 22 -0.0203 0.48 0.0008 0.33 -0.0084 0.18 23 -0.0673 0.38 -0.0617 0.16 -0.0402 0.46 25 -0.0248 0.16 -0.0342 0.54 -0.0353 0.30 26 -0.0251 0.26 -0.0346 0.29 -0.0159 0.45 27 -0.0241 0.19 -0.0350 0.57 -0.0361 0.24 28 -0.0388 0.22 -0.0352 0.51 -0.0250 0.26 29 -0.0067 0.24 -0.0114 0.52 -0.0107 0.24 30 -0.0152 0.55 -0.0201 0.16 -0.0182 0.29

43

Table 4

Model validation on 2600 holdout stores

Predictive Log-Likelihoods of Proposed and

Benchmark models

Subclass 3-support logit Homogeneous logit Naïve model

2 257948.92 261010.88 263713.71 6 301515.11 303968.77 306482.66 7 51200.54 51656.06 52070.57 8 46933.65 47410.49 47795.67 9 50573.81 51028.17 51825.98 10 81288.74 81851.78 82835.30 11 126603.78 127663.31 129129.87 12 443377.84 449046.03 451402.27 13 361662.18 369771.06 370200.64 15 254022.35 257596.83 260693.37 16 235930.79 239897.69 241731.01 17 195519.58 199070.59 199514.02 18 434062.09 439311.77 446327.98 19 253280.48 256667.28 261597.99 20 194562.26 197272.90 197475.56 23 166963.37 168930.84 170206.69 25 214983.61 218759.27 219800.55 26 153808.97 158379.33 157425.83 27 86285.37 91513.64 91946.80 28 76997.55 77965.25 78282.15 29 90467.76 91446.00 91568.66 30 148936.61 150731.84 151402.46

44

Table 5

Estimated Price Elasticities for 22 Subclasses

(G = Good, b = Better, B = Best) (Key: Eb→G refers to the elasticity of demand for Good with respect to the price of Better)

EG→G Eb→b EB→B Eb→G EB→G EG→b EB→b EG→B Eb→B

Subclass 2 -1.3033 -0.7965 -3.2159 1.4359 0.2612 0.5111 0.2612 0.5111 1.4359 6 -0.8645 -1.9375 -3.8198 1.1007 0.1235 1.3321 0.1235 1.3321 1.1007 7 -1.8512 -1.8408 -5.2427 2.1990 0.0002 1.5495 0.0002 1.5495 2.1990 8 -1.5024 -0.4554 -3.2522 2.0754 0.0008 0.3291 0.0008 0.3291 2.0754 9 -3.1362 -0.1629 -5.6285 4.6345 0.1953 0.0013 0.1953 0.0013 4.6345 10 -1.3884 -1.5644 -4.0448 1.6645 0.0981 1.1867 0.0981 1.1867 1.6645 11 -0.8052 -0.5941 -2.8739 1.1233 0.0026 0.4242 0.0026 0.4242 1.1233 12 -0.5419 -1.4736 -2.4436 0.3730 0.4956 0.9205 0.4956 0.9205 0.3730 13 -0.1758 -1.1360 -1.6211 0.1267 0.1819 0.6979 0.1819 0.6979 0.1267 15 -0.6759 -2.1818 -3.4291 0.5338 0.5965 1.2847 0.5965 1.2847 0.5338 16 -0.7531 -3.0173 -5.4914 0.7071 0.4487 2.0847 0.4487 2.0847 0.7071 17 -0.3391 -0.7550 -0.8845 0.1470 0.4683 0.3270 0.4683 0.3270 0.1470 18 -1.5392 -3.3658 -2.7202 0.3816 2.3013 1.2088 2.3013 1.2088 0.3816 19 -4.8441 -5.3638 -9.4809 4.2016 1.8242 3.2211 1.8242 3.2211 4.2016 20 -0.1405 -0.7145 -1.0951 0.1348 0.0939 0.4506 0.0939 0.4506 0.1348 23 -3.1316 -3.5284 -6.2319 2.6238 1.3581 2.0410 1.3582 2.0410 2.6238 25 -0.0425 -3.3095 -4.3751 0.0241 0.0572 2.0658 0.0572 2.0659 0.0241 26 -2.0320 -0.0611 -2.8067 2.1935 0.0024 0.0547 0.0024 0.0547 2.1935 27 -0.9333 -2.5349 -3.2269 0.1689 1.15218 1.9332 1.1522 1.9332 0.1689 28 -0.7345 -3.1706 -4.3398 0.6286 0.3801 2.2515 0.3801 2.2515 0.6285 29 -0.5745 -0.3995 -1.1267 0.5336 0.2282 0.2016 0.2282 0.2016 0.5336 30 -0.4559 -1.1725 -1.8065 0.2963 0.4159 0.7165 0.4159 0.7165 0.2963

45

Table 6

Optimal Support-Level Prices of Variants within Subclasses

Sup 1 Sup 2 Sup 3 PGood,1 PBetter,1 PBest,1 PGood,2 PBetter,2 PBest,2 PGood,3 PBetter,3 PBest,3

Subclass 2 87.72 97.29 110.22 96.08 105.64 118.57 87.74 97.30 110.23 6 151.95 153.64 190.88 121.38 123.07 160.31 74.79 76.48 113.72 7 115.15 125.16 130.00 125.74 135.74 140.00 115.47 125.47 130.00 8 143.87 149.13 150.00 130.46 135.80 150.00 103.74 109.10 142.25 9 93.06 94.56 121.96 102.54 110.69 138.09 90.55 100.03 127.46 10 84.95 90.88 128.07 97.03 102.96 140.16 96.72 102.65 139.84 11 148.83 175.98 183.58 136.52 163.67 171.27 140.42 167.57 175.17 12 76.83 85.24 105.33 87.39 95.80 115.89 87.72 96.13 116.22 13 88.18 96.59 116.68 168.34 176.75 196.84 115.16 123.57 143.66 15 74.26 80.64 100.73 66.00 72.38 92.47 74.10 80.48 100.57 16 66.52 74.93 95.02 59.98 68.39 88.48 52.54 60.95 81.04 17 366.65 375.06 395.15 106.24 114.65 134.74 124.64 133.05 153.14 18 96.93 104.17 124.26 69.73 76.97 97.06 70.85 78.09 98.18 19 77.12 92.46 108.41 73.34 88.68 104.62 68.55 83.89 99.84 20 257.29 266.85 279.78 160.48 170.04 182.97 147.15 156.71 169.64 23 70.60 85.94 101.89 74.40 89.74 105.68 73.17 88.51 104.46 25 78.02 82.40 106.52 63.36 67.73 91.86 63.89 68.26 92.39 26 80.73 90.31 121.32 73.60 81.67 112.23 109.87 119.45 150.45 27 79.01 83.38 107.51 63.99 68.36 92.49 66.09 70.46 94.59 28 66.22 77.05 110.95 70.33 81.16 115.06 83.94 94.77 128.67 29 183.64 192.05 212.14 122.65 131.06 151.15 130.49 138.90 158.99 30 101.47 109.88 129.96 83.52 91.93 112.02 92.56 100.97 121.06

46

Table 7

Actual versus Optimal Store-Specific Prices of Variants of Subclasses

Extent of price deviation from optimal Subclass Total Cases Scenario Sub-cases

Good Better Best

2 22 -14.9% 1.4% -1.6% 6 35

3 13 0.5% 1.6% 2.9%

16 146 3 146 6.1% 17.1% 24.4%

1 39 -10.5% 1.6% 8.4% 30 136

2 97 -21.2% -13.5% -3.8%

Total 317

Notes:

1. Scenario 1 is the mixed case where the optimal prices are fully within the actual bandwidth, Scenario 2 is the case of under pricing (actual < optimal) and Scenario 3 is the case of overpricing (actual > optimal).

2. Proportion of cases in Scenario 1 is 39/317=12.3%, Scenario 2 is 119/317=37.5% and Scenario 3 is 159/317=50.2%.

3. The optimal price bandwidth for the Good variant was $28.47 compared to the actual price bandwidth of $48.97. The respective values for the Better variant were $30.36 and $46.87 and for the Best variant they were $28.40 and $43.18.

47

48

Table 8

Predicted Profits with Support-level Optimal Prices vs. with Actual Prices

Subclass Optimal

Profit Actual Profit

% Decrease

Support

1 Support

2 Support

3 Total Support

1 Support

2 Support

3 Total Actual vs Optimal

2 3.29 5.58 2.08 10.95 2.78 4.23 1.78 8.8 19.63

6 10.44 5.52 0.16 16.13 9.07 5.25 0.07 14.39 10.79

7 3.7 2.07 1.86 7.63 3.14 1.98 1.62 6.74 11.66

8 4.38 2.22 2.66 9.26 4.28 2.15 1.96 8.39 9.40

9 2.58 7.45 4.63 14.67 1.43 6.59 3.19 11.21 23.59

10 2.29 5.19 4.07 11.54 2.01 5.04 3.96 11.01 4.59

11 2.61 6.13 4.36 13.11 2.1 5.31 3.7 11.11 15.26

12 6.24 10.18 7.83 24.25 5.81 9.4 7.29 22.5 7.22

13 4.2 16.21 8.3 28.71 3.84 9.1 6.51 19.45 32.25

15 7.62 3.56 6.24 17.42 6.89 3.02 5.63 15.54 10.79

16 7.88 6.05 3.26 17.19 7.12 4.56 2.44 14.12 17.86

17 23.4 4.03 7.14 34.56 7.44 3.64 6.07 17.16 50.35

18 6.28 14.24 16.02 36.53 6.01 9.58 11.36 26.95 26.23

19 21.09 17.31 9.38 47.78 9.05 5.67 3.24 17.97 62.39

20 11.68 4.33 8.98 24.98 3 1.98 4.2 9.18 63.25

23 11.22 13.67 3.79 28.69 5.05 8.07 2.71 15.84 44.79

25 6.87 3.38 4.78 15.03 6.42 3.28 4.67 14.38 4.32

26 2.69 5.06 8.81 16.56 2.67 4.7 8.1 15.47 6.58

27 6.69 4.66 2.87 14.22 6.37 3.49 2.03 11.89 16.39

28 2.6 4.11 6.02 12.73 1.84 3.27 5.88 10.99 13.67

29 3.32 4.41 5.99 13.72 2.23 3.9 5.14 11.27 17.86

30 5.13 3.09 6.81 15.03 4.67 2.95 6.36 13.98 6.99

Total 430.69 308.34 28.41

49

Table 9 Field Test Results for 10 subclasses

Pre-test Period (8 weeks) Test Period (8 weeks) Subclass Condition

Unit Sales Sales ($) Gross Profit ($) Unit Sales Sales ($) Gross Profit

($)

Gross Profit Ratio

Incremental Gross profit1

Experimental 182 14608 4164 162 15367 6028 1.448 9952 Control 263 20651 5685 284 22463 6872 1.209 Experimental 236 28344 14920 245 29535 15305 1.026 75

6 Control 335 39895 20829 344 40640 21260 1.021 Experimental 145 18508 7234 118 16156 6599 0.912 -506

11 Control 171 22797 9458 167 22744 9290 0.982 Experimental 256 21707 12404 254 24197 14210 1.146 824

12 Control 400 33957 19427 465 37954 20966 1.079 Experimental 150 12746 7082 287 22278 11036 1.558 -466

15 Control 262 22353 12421 413 35714 20173 1.624 Experimental 131 9484 5180 167 11324 5438 1.050 -1488

16 Control 218 16185 8803 304 22239 11770 1.337 Experimental 117 10572 6266 188 16699 9693 1.547 749

17 Control 210 20726 13028 278 29201 18595 1.427 Experimental 125 13027 7521 436 35977 17413 2.315 4809

18 Control 158 15982 9217 269 27698 15446 1.676 Experimental 71 5797 3334 120 9134 4848 1.454 1267

27 Control 128 10950 6465 132 11425 6944 1.074 Experimental 32 3359 2019 38 3704 2111 1.046 29

28 Control 41 4397 2658 45 4584 2742 1.031Total Incremental Gross Profit (200 stores, 8 weeks) $6,288

Estimated Annual Incremental Gross Profit (3000 stores) $613,000

1 Equals Experimental Group Gross profit (test) - Experimental Group Gross profit (pre-test) X Control Ratio. For example, in sub-class 12, Incremental Gross Profit = 6028 – 4164*1.209 = 995.

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Marketing Research, 31, 2, 202-213. ENDNOTES 1 Iyer and Seetharaman (2003) provide empirical evidence for such micro-marketing strategies governing prices and service decisions in gasoline retailing. 2 Allenby and Rossi (1991a) show that even if consumers are heterogeneous in their choice probabilities, as long as all consumers are exposed to the same marketing variables on a given shopping trip (as in our case), the aggregate MNL model is a good approximation to the mixed logit that would capture the suitably summed brand choice probabilities across heterogeneous consumers. If the heterogeneity distribution across different consumers entering the product market in each week does not change from one week to another (an assumption supported by our collaborator) then, given marketing mix homogeneity, Equation (3) is an appropriate representation of the aggregate market shares even if consumers are heterogeneous. 3 The reported sales in Table 1 are in units, and not in shares. On most weeks, the observed sale of an SKU is 0 units. During weeks when the SKU indeed sells, it typically sells 1 unit. This is the reason for why the averages for number of units sold per week are smaller than 1. 4 For all sub-classes, we found the correlations between the estimated residuals of the demand functions and the prices of the three brands to be quite small (of absolute magnitude less than or equal to 0.1) which precludes concerns about correcting for possible price endogeneity in the estimation. 5 For sub-classes 4 and 22, the wrongly signed price sensitivity is recovered for 1 segment only (accounting for 12 % and 33 % of consumers in the respective markets). For sub-classes 1 and 5, however, we have wrongly signed estimates of price sensitivity for 2 segments (accounting for 79 % and 73 % of consumers in the respective markets).

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6 According to the managers involved, there were intermittent stock-outs in subclasses 1 and 5 that happened at stores during weeks of the calibration sample data time horizon when prices were low. This led to their wrongly signed price coefficients. In the case of subclasses 4 and 22, a phenomenon called parts consolidation was at work. These subclasses were consolidated with others (that are not represented in our data) at some point during the study period in the sense that the variants in these sub-classes became suitable for a number of additional, newer automobile models (for which other sub-classes, not represented in our data, had been formerly suitable). This increased the demand for all three variants in these subclasses. At the same time, the average prices were increased for all variants in these sub-classes. This led to wrongly signed price coefficients. AAR confirmed that neither stockouts nor parts consolidation occurred in any of our 23 included product sub-classes.

7 The cross-elasticity of brand i’s demand with respect to brand j’s price is computed as follows: For a 1% change in price of brand j (∆Pj), we compute the change in demand for brand i (∆Qi) as the weighted average (where the weights are the prior probabilities of support membership computed at average values of store characteristics) of the changes in demand for brand i within the three support points (computed using the respective logit demand functions). The cross-elasticity is then given by (∆Qi /∆Pj) / (Qi /Pj). 8 Vulnerability of a SKU is defined as the sum of the elasticities associated with the SKU’s sales with respect to its competitors’ prices (Kamakura and Russell 1989). 9 Clout of a SKU is defined as the sum of the elasticities associated with the other SKUs’ sales with respect to the focal SKU’s price (Kamakura and Russell 1989). 10 SSK did acknowledge that whether or not their grocery retailing-based empirical generalizations hold for durable goods or industrial products was yet to be determined. 11 Furthermore, as the cross-elasticities in Table 5 are weighted averages of support-level elasticities, this further relaxes any restriction that may characterize the homogeneous model’s elasticities (since market shares vary across supports). 12 Since there are 27 subclasses, and 2 estimates per subclass (i.e., one each for segments 1 and 2), we have 54 estimates for each store characteristic. Interested readers can obtain the actual estimates from the authors. 13 For obvious reasons, we do not report these 800*27 sets of 4-dimensional parameter estimates in the paper. These are available from the authors upon request.

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