THE "84/14/2" RULE REVISITED:WHAT DRIVES CHOICE, INCIDENCE

AND QUANTITY ELASTICITIES?

by

D. IL BELL*

J. CHIANG**and

V. PADMANABHANt

97/16/MKT

* Anderson School of Management, UCLA, USA

** John M. Olin School of Business, Washington University, USA and The Hong Kong University ofScience and Technology, Hong Kong.

t Visiting Associate Professor of Marketing at INSEAD, Boulevard de Constance, Fontainebleau 77305Cedex, France.

A working paper in the INSEAD Working Paper Series is intended as a means whereby a faculty researcher'sthoughts and findings may be communicated to interested readers. The paper should be consideredpreliminary in nature and may require revision.

Printed at INSEAD, Fontainebleau, France.

The "84 / 14 / 2" Rule Revisited: What DrivesChoice, Incidence and Quantity Elasticities?

DAvID R. BELL

Anderson School of Management, UCLA

JEONGWEN CHIANG

John M. Olin School of Business, Washington Universityand

The Hong Kong University of Science and Technology

V. PADMANABHAN

Visiting Associate Professor of MarketingINSEAD

February 6th, 1997

Abstract

A brand's total price elasticity, conditional on a purchase occasion, can be decomposed into threecomponents: the brand choice, purchase incidence and purchase quantity elasticity. Gupta (1988) hasanalyzed this relationship within the context of a single product category. That study reported that themain impact of a price promotion falls on brand choice (84%), but to a lesser extent, purchase timingacceleration (14%) and stockpiling (2%), are also impacted.

This research makes three new substantive contributions. First, while we confirm that the majorityof the promotion effect is derived from choice, the relative emphasis on incidence and quantity variessystematically across categories. Storable products have relatively higher weight on quantity,perishable products have a higher weight on incidence. Second, we utilize a generalized least squaresmeta analysis procedure (Montgomery and Srinivasan, 1996) to show how factors such as marketingeffort, category structure, brand franchise and consumer demographic variables influence elasticities.One key finding is that unpredictability of marketing effort has more influence on elasticity responsethan does relative levels of marketing effort. Third, we show that in several instances where importantdecision variables do not affect total elasticities, this is due to offsetting effects within two or more ofthe three behavioral components of elasticity.

To calibrate our models, we use a multicategory scanner panel dataset to generate choice, incidenceand quantity promotion elasticity estimates for 173 brands within 13 categories. Managerialimplications for developing effective promotion strategies are discussed.

1 Introduction

Spending large sums of money on promotions is a fact of life for firms in almost all

industries today. Billions of dollars each year, representing two-thirds of marketing

expenditure, are spent on promotions for a simple reason – promotions work. By now,

it is a well-established fact that consumers respond to deals. In a realm of increasing

competitiveness, however, it is no longer enough for managers to merely recognize that

promotions enhance sales; it has become vital that promotions and promotional response

be addressed with greater sophistication. This is most relevant to firms who own multiple

product lines and/or brands, as is corroborated by recent organizational movements

toward category management. Such firms need to know where to expect the primary

effects of promotions to emerge, and, precisely how much sales will increase once the

money is spent. For example, do promotions induce switching (influence brand choice),

cause acceleration (drive purchase incidence), or encourage stockpiling (influence the

quantity decision), or some combination of these three events? More critically, these firms

need to know how and why these effects differ across the groups of brands and product

categories they manage. With such information, it becomes possible to draw better

guidelines for promotion policies, set priorities for promotional dollars, align promotional

campaigns, and even anticipate the moves and counter-moves of rivals.

Over the years academicians and practitioners alike have made significant strides in

answering these questions, but important tasks remain. As pointed out by Blattberg,

Briesch and Fox (1995, p.130), the field is in short supply of the general empirical reg-

ularities which frame a more integrated perspective. Following the lead of few notable

studies, this paper intends to take another step in that direction. In particular, we pur-

sue an empirical generalization of Gupta's (1988) finding regarding the decomposition of

price promotion effects on coffee purchases. That study indicates that brand-switching

accounts for the majority of the impact (84%), and that purchase time acceleration and

stockpiling have lesser significance (14% and 2%, respectively). A similar result was

obtained with a different approach by Chiang (1991). No one, however, has checked

1

the generalizability of this breakdown beyond coffee category. More important, only a

few papers (e.g., Bolton 1989, Raju 1992, Narasimhan, Neslin and Sen 1996) attempt

to generalize the drivers of promotional response, and no study has examined elasticity

drivers for each of the three behavioral decisions (brand choice, purchase incidence and

purchase quantity).

In this paper, we first estimate the price promotion effect on brand choice, purchase

incidence, and purchase quantity decisions jointly using data from 250 panelists. In

all, 519 price elasticities are generated for 173 brands in 13 different product categories

After examining the relative proportions of these elasticities across categories, we re-

port our observations with respect to the breakdown issue. We then conduct a meta

analysis to investigate what drives the variation within each elasticity component. In

particular, we aim to determine the extent to which variance in choice, incidence and

quantity elasticities can be attributed to four sets of variables: Marketing Effort (e.g.,

price variability, deal frequency, featuring, etc.) Category Structure (e.g., concentration,

penetration, etc.), Brand Franchise (e.g., brand penetration, brand purchase rates), and

Brand Demographics (e.g., the type of customers who purchase the brand).

Our paper contributes three new and important substantive findings to the extant

literature on promotional response. First, though we confirm that the majority of sales

volume from a price promotion is due to brand switching, we find the decomposition of

promotional effect reported in Gupta (1988) is only one of the exceptions (the break-

down varies widely depending on the product type). 1 However, based on our analysis, we

believe 80/10/10 split is a reasonable generalization for the proportions of promotional

effect on brand choice, incidence and stockpiling decisions. Second, there is consider-

able variability in the way our exogenous factors influence elasticity. Specifically, the

variables that describe the Category Structure (e.g., market concentration, etc.) have

the most impact on variation in elasticities across all three behaviors. Marketing Effort

variables are the next most important. Interestingly, we find that the uncertainty or

1 For example, storable products have a higher quantity elasticity; perishable products have a higherincidence elasticity.

2

unpredictability of promotions is significantly more relevant than the average level of

promotions in driving elasticities. Brand Franchise variables have a strong influence on

incidence elasticities, but less effect on choice and quantity. Brand Demographics (in

particular, age and education) influence the incidence elasticity but not that for choice

or quantity. Third, we find that the decomposition of elasticity response is especially

important: in several instances where the total elasticity appears not to be influenced

by a particular variable (e.g., variance in display activity), this is because of offsetting

effects within two or more of the three behaviors. This underscores the importance of

our approach.

The remainder of the paper is organized as follows. The next section reviews the rel-

evant literature and compares and contrasts our contribution with that of existing work.

Section 3 decribes the econometric model, meta analysis procedure and the dataset; sec-

tion 4 presents the substantive results. In section 5, we summarize the findings and the

managerial and research contributions of our work. Section 6 concludes the paper.

2 Relevant Literature

Findings from Previous Work. The earliest work in assessing the generalizability of find-

ings relating to price elasticity is Bolton (1989). She explored the relationship between

price elasticity and a set of covariates consisting of brand and category-specific charac-

teristics. Her data tracked sales of three brands in each of 4 categories across a set of 12

stores. She finds that the more elastic brands had smaller market shares, lower levels of

category and brand display activity, and higher levels of category and brand couponing.

Fader and Lodish (1990) present the results of an exploratory analysis about the

relationship between category structure (such as purchase cycle, penetration) and pro-

motional movement (such as volume sold on price cuts, display and feature). They use

IRI Marketing Factbook data for 331 product categories (their study is the first truly

cross-category analysis of promotional response). They observe systematic relationships

between category characteristics and promotional policies. For instance, high penetra-

3

tion, high frequency products are the most heavily promoted products (with the excep-

tion of manufacturer couponing). They highlight the role of household penetration in

influencing category movement. A limitation of their study highlighted by Narasimhan,

Neslin and Sen (1996) is that the dependent variable, percentage of volume sold on a

deal, is a mixture of promotional response as well as promotional frequency.

Raju (1992) has a focus similar to that of Fader and Lodish (1990) in that he explores

the relationship between category characteristics (such as expensiveness, bulkiness and

promotional activity) and category sales. His dependent variable is the standard devia-

tion in category sales over time. Tracking data over 63 product categories, he finds that

higher variability in category sales is associated with deeper (albeit infrequent) dealing

in the category, cheaper products and the ability to stockpile. His dependent variable

has the same shortcoming as Fader and Lodish (1990).

Narasimhan, Neslin and Sen (1996) study the relationship between product category

characteristics and promotional elasticity using data across 108 product categories. They

consider three types of promotions (price cuts, feature and display) and seven category

characteristics (penetration, interpurchase time, price, private label share, number of

brands, impulse buying and the ability to stockpile). Their measure of promotional

response was generated from the IRI InfoScan Topical Marketing Report and their mea-

sures of category characteristics were generated from IRI's scanner panel data. They find

that promotions get the highest response for brands in easily stockpiled, high penetration

categories with short purchase cycles. Their results on the impact of price sheds light on

the complex reactions between price and other marketing variables and highlights the

importance of carefully analyzing different types of promotions.

Our Contribution. Our work is closest in spirit to both Bolton (1989) and Narasimhan,

Neslin and Sen (1996). We build on their respective contributions while being different

from their approaches in several ways. First and foremost, in addition to obtaining total

elasticities we decompose the total elasticity into three components: choice, incidence

and quantity. This allows us to identify cases where the promotion effect is significant

4

for one of the three behaviors, yet the total elasticity appears not to be affected (in the

statistical sense). This is often a result of offsetting forces within each of the three behav-

ioral components. Second, we obtain elasticity estimates across brands and categories

from the same set of household data. Thus, all purchase decisions are subject to the

same budget constraints and consumers are exposed to the common store environment.

Therefore, any potential cross-category substitution effects are implicitly absorbed in the

elasticity calculation. Third, store-level sales data like those used in Bolton's study are

generated weekly by different batches of consumers who happen to shop that week. In

this situation, it is impossible to know how this traffic issue affects elasticity estimates.

In contrast, we use observations from the same panelists and thus avoid this potentially

confounding factor. Fourth, as in Narasimhan, Neslin and Sen (1996) we incorporate

consumer factors such as product penetration into our meta-analysis. Again, to en-

hance consistency we calculate these variables based on our panel data instead of using

national averages. 2 Finally, we use an iterated GLS method (Montgomery and Srini-

vasan, 1996) for our meta-analysis which accounts for them potential heteroscedasticity

from two sources: measurement errors in the left-hand-side (elasticity estimates), and

cross-category modeling errors. This approach leads to model R 2 's that are substantially

higher than those found in previous work.

3 Methodology and Data

3.1 Assumptions, Model, and Price Elasticity

We assume consumers (households) have a linear additive utility function in which each

component represents the utility derived from a product category. For each product

category there is a set of brands available and consumers perceive them to be substitutes.

Following Gupta (1988) and Chiang (1991), we assume consumer i at each purchase

occasion t has to decide whether to purchase, respectively, each of the product categories,

and if so, which brand to choose and what amount to buy. To save space, we simply

2 For example, variables such as "Category Penetration" are defined with respect to our set of panelists.See §3 for details.

5

describe the essence of the model here and leave the detail in Appendix. For purchase

quantity, we have a system of log-log demand equations in which each demand equation

corresponds to a selected brand. For brand choice, we suggest that, conditional on the

purchase incidence, a brand is selected if and only if it yields the highest indirect utility

in that category. For purchase incidence we argue that consumers can forego purchasing

in the category if the purchase utility threshold is not crossed.

Our first goal is to estimate a band-specific price elasticity with respect to the in-

cidence, brand choice, and quantity decisions. Given the structure just described, we

can derive the exact expression for each elasticity component and show that the total

elasticity is simply the sum of three (see Appendix). Once the coefficients of the model

are estimated, the elasticites are calculated at the mean levels of all covariates using

these coefficients. However, since our main interest is in examining the elasticity differ-

ences across brands and categories, we have to first ensure these elasticities are indeed

comparable. For this to happen, two facts must be recognized: (1) categories are sold

in different units (e.g., 64 fl. oz for liquid detergents and 13 oz. for coffee), and (2) a

promotional price cut is, in general, for certain package size and consumers do not have

the option to buy other sizes to save money. In other words, if a consumer responds to

deals, the response has to be in the unit of the promotion size. To be consistent, we

first normalize all sizes within a category by the most commonly purchased size in that

category. Prices are, of course, adjusted accordingly. In this way, we ensure that all

categories are measured in their respective purchase units and eliminate any potential

`magnitude' problem in the following meta analysis which we now describe.

3.2 Meta Analysis Model

First, let ebic denote the elasticity estimate for consumer behavior b for brand j in

category c. Our three behaviors are brand choice, purchase incidence and purchase

quantity. The following equations detail our application of the Montgomery Srinivasan

(hereafter MS) Generalized Least Squares approach to meta analysis. Their approach

is predicated on the notion that errors across observations in the meta analysis will

6

not be i.i.d. We briefly present the rationale for why this makes sense, but refer the

interested reader to MS (1996) for details. First, note that our elasticity estimates are

generated from choice model parameter estimates that have been estimated with error

(we subsequently apply the Delta Method to derive the standard errors for the elasticity

estimates). Therefore, the relationship between the true and estimated elasticities is

given by:

ebjc = ebjc Ebjcl Ebjc N(0, a)

(1)

Furthermore, the true model that relates the elasticity to various exogenous factors that

determine that elasticity is:

ebjc = a-FE/3 X- fbjc %c, %c Civ)

(2)f =1

where cr 2 is the unique variance in the true elasticity measure, f indexes the classes ofVbjc

exogenous, Of is the parameter vector factor group f , and X fbic is the matrix of right

hand side variables for factor group f . Following MS, we assume that the estimation

errors (equation 1) and unique errors (equation 2) are uncorrelated so that the total

error is partitioned into the sum of these two components: and ObicIhrbjc = Ebjc Vbjc n

N (0 , o + (7,).

A natural question arises as to what classes of factors one would expect to influence

the elasticities. We select four sets of variables based on prior research (e.g., Bolton

1989; Narasimhan, Neslin and Sen 1996) and our own intuition about what should drive

variance in elasticities. The four sets of variables are: (1) Marketing Effort, (2) Category

Structure, (3) Brand Franchise and (4) Brand Demographics. We elaborate on the

specific righthand side variables in each class shortly. Our final meta equation is:

ebjc = a A- 131 X1jc 132X2c 133 X3jc 134X4jc Objc

(3)

where the subscripts 1, ... 4 denote the four categories of exogenous variables and ihkic

the total error in the elasticity estimate. MS show that this partitioning of the meta

7

regression error is especially important when estimates of the left hand side variable are

drawn from many studies conducted under different conditions.3

Estimates of the coefficient vectors, A, i E {1, ... 4} and the variance partitioning

are obtained iteratively, with standard errors of the elasticities serving as GLS weights

in the initial estimation. Subsequent weights are obtained iteratively, and we find that

in all cases convergence occurs rapidly in 5-6 iterations.4

3.3 Data

Source and Description. The data were generated from a "market basket" database

provided by IRI . Purchase records for a random sample of 250 panelists, shopping in

three supermarkets over a period of 78 weeks were used in the analysis. The first 26 weeks

of data were used to initialize within household market share variables; the remaining 52

weeks were used for calibration of the choice models given in the Appendix. One unique

feature of our database is that purchase records in each category are for the same set of

panelists and the same time period. As noted in the Introduction, this confers several

advantages to our research relative to existing studies that seek to explain variance in

elasticities. First, we are able to estimate elasticities directly from panel data (previous

studies often utilize aggregate elasticities that have been generated by a third party

supplier). Second, we estimate not only the total elasticities, but also elasticities for

each of the three behavioral components and the underlying standard errors. Finally,

our category-specific measures (e.g., penetration) are defined with respect to the set of

households that have been used in the model estimation.

The selection of product categories for analysis was quite deliberate. We sought to

include a range of categories that were heterogenous on several dimensions (e.g., purchase

frequency, number of competitors, "necessity" products, etc.). 5 Table 1 presents some

3 For example, meta analyses often combine work from several different authors, conducted over manydifferent time periods and datasets.

4The interested reader is referred to Montgomery and Srinivasan (1996) for complete details on thiseasy-to-implement iterative scheme.

5These products cover 3 out of 4 PROMCLUS and PURCLUS groups, respectively, as defined inFader and Lodish (1990).

8

basic descriptive information on the product categories:

[ Table 1 about here ]

4 Results

We begin with some summary descriptive statistics from the models. This helps us mo-

tivate the importance of accounting for variance across behaviors and categories. We

then present the framework (independent variables) and results from the meta analysis.

In particular, we focus on which classes of variables (e.g., Marketing Effort, Category

Structure, etc.) have the greatest influence on the elasticities. In doing so, we com-

pare and contrast our research to existing work, and show how we are able to generate

important new insights into promotional response.

4.1 Overview of Estimation Results

We first present the range of elasticities over all 13 categories and the three behavioral

components. This descriptive analysis gives us some insight into the behavior of elastici-

ties across behaviors and categories and motivates our subsequent meta analyses. These

results are shown in Table 2.

[ Table 2 about here ]

Dispersion in Elasticities. These results illustrate two important points. First, there

is considerable across category variation in elasticity. Second, there is variation across

behaviors, within a category, but the pattern is consistent: choice elasticities are much

larger than incidence elasticities, which are somewhat larger than quantity elasticities

(8 out of 13 cases). The overall dispersion for each component (choice, incidence and

9

quantity) and for the total elasticity are presented in Figures 1-a to 1-d, respectively.

These patterns of dipersion suggest that there is potential to learn about what factors

drive a given elasticity, once one controls for marketing effort, category structure, brand

franchise and brand demographic factors.

[ Figures 1-a to 1-d about here ]

The "84/14/2" Rule. However, before engaging in such an investigation we first re-

visit the issue of relative promotion effects suggested in Gupta (1988). Table 3 speaks

to the "84/14/2 rule" and gives the breakdown in elasticity across behaviors within a

category. To our surprise, we find the breakdown is quite different from that reported in

Gupta (1988) or Chiang (1991). We observe the choice elasticity varies from a minimum

of 74% of total elasticity for coffee to a maximum of 95% for soft drinks; the incidence

elasticity ranges from a minimum of 2% of total elasticity for potato chips to a maxi-

mum of 23% for butter; the quantity elasticity ranges from a minimum of 0.3% of total

elasticity for margarine to a maximum of 24% for ground coffee.

[ Table 3 about here ]

Role of Storability. On average, choice accounts for about 86%, incidence about 6%,

and quantity about another 8% of the total elasticity for a brand. This represents a lesser

(greater) weight for the incidence (quantity) effect than that indicated in Gupta's study.

When these proportions are further sorted and compared, some interesting patterns

emerge: (1) all refrigerated products (Margarine, Ice-cream, Yogurt, Bacon, and Butter)

have much higher proportions for the incidence effect than for the quantity effect, and

(2) all storable products except Softdrinks (i.e., Liquid Detergent, Bathroom Tissue,

Paper Towels, and Ground Coffee) have just the opposite pattern. They have larger

10

stockpiling effects and smaller incidence effects. Both observations have intuitive appeal.

For example, in their field experiment, Litvack, Calantone and Warshaw (1985) find that

price elasticites are higher for storable items because consumers can stock up and take

the advantage of deals. When comparing these two types of products, we find the ratio

of average quantity elasticities for storable products to that for non-storbles is about

15:1.

A "New" Generalization. Some exceptions deserve further comments. Sugar and

Potato Chips are not refrigerated products but are both considered non-storable due

to freshness considerations. Their numbers suggest that consumers somehow would

purchase more potato chips but not more sugar when these products are on sale. We

speculate that consumers buy more potato chips because they want to consume mores

and it is unlikely for them to do this with sugar. Softdrinks have a surprisingly small

stockpiling effect despite being a storable item. When we further examine the history

of softdrink promotions, we find softdrinks are one of the most frequently promoted

products (particularly Coca-Cola and Pepsi). Together they promote over 50% of the

time in an alternating pattern; that is, literally, every other week Coke or Pepsi is on

sale (see Lal 1990). Clearly, with this kind of promotion frequency, consumers do not

need to stock up every time to take the advantage of deals (see Krishna, Currim, and

Shoemaker (1991)). Lastly, Dryer Softeners have roughly equal but small weights for

both incidence and quantity.

In sum, we confirm the notion that the majority of promotional volume comes from

switchers (i.e., choice). However, we find the decomposition of promotional effects is

product-specific and with a wide-range of dispersion. If the product is storable and

essential, the decomposition is about "80/5/15" (i.e., a lower incidence effect and a

higher quantity effect). The weight on the stockpiling effect is reduced when the product

is frequently promoted. In contrast, if the product is non-storable (e.g., a refrigerated

product), the distribution for the promotion effects is about "85/10/5" with heavier

6See Assuncao and Meyer (1993) and Bell, Ho and Tang (1996) for an analysis of of price-dependentconsumption by rational consumers.

11

weight on incidence rather and less weight on quantity. Note, however, that if consumers

increase consumption in response to price promotions (Assuncao and Meyer, 1993), then

the weight would shift more toward stockpiling effect.

Taken together, the findings in Tables 2 and 3 suggest that both brand and category-

specific factors drive the overall elasticities and the breakdown across behaviors. Clearly,

these patterns warrant further investigation. This leads us to pursue a more rigorous

investigation through the use of meta analysis.

4.2 Meta Analysis Variables and Results

4.2.1 Independent Variables

Our meta analysis model (equation 3) is estimated using 19 separate independent vari-

ables, each of which falls into one of four categories. The Marketing Effort variables

summarize managerial decisions (e.g., price variance, feature, etc.) that have the poten-

tial to influence the behavior of elasticities. The Category Structure variables describe

the brand's "operating environment" (e.g., competition, penetration, etc.) The Brand

Franchise variables describe the customer base in terms of buying behavior (e.g., brand

penetration and repeat rates) and the Brand Demographics relate brand elasticities to

observable characteristics of the brand's customers. The full list of variables is given in

Table 4.7

[ Table 4 about here ]

Table 4 is self explanatory for the most part. The key things to note are: (1)

our inclusion of variables that capute consumer uncertainty about marketing activity

(STDPRICE, STDFEAT, STDDISP), (2) emphasis on category descriptors (NECESS,

7We do not include average price as one of the right-hand-side variables because the magnitude ofprice varies greatly across categories (see Table 1). However, we are able to normalize the prices for eachbrand by subtracting the category mean and dividing by the category price standard deviation. Notethat the rest of variables are also either unit-free or have common measurement units.

12

STORAB) as well as market conditions (HERFIN, CATPEN), (3) summary measures

of the brand's reach and "loyalty" (BRANDPEN, BRDRATE), and (4) the inclusion of

demographic variables. In the case of the demographic variables, we use the modal value,

rather than the mean. For example, the variable MINC for a given brand reflects the

modal income of consumers who buy the brand. We use the mode in order to capture

the characteristics of the majority of consumers who buy that brand.8

4.2.2 Overview of Meta Analysis Results

Table 5 contains the meta analysis parameters for each of the three behaviors, and

Table 6 reports the corresponding results for the total elasticity. In each instance, the

t-statistics test the null hypothesis that the parameter estimate is zero.

[ Tables 5 and 6 about here ]

As shown in the tables the R 2 's are 0.60 for choice, 0.62 for incidence, 0.39 for quan-

tity, and 0.59 for the total elasticity. Each of the F-statistics are significant at the 0.01

level. Overall, the regression fits appear to be quite good considering the cross-sectional

nature of analysis. Specifically, these model fits are much higher than those obtained

in previous studies9 We attribute this to the fact that our dataset contains informa-

tion on the same panelists for each category, and our use of the MS GLS approach

to meta analysis. As shown in Tables 5 and 6, the Category Structure variables have

the greatest influence on the elasticities. Marketing Effort variables have some influ-

ence, however, variables that capture uncertainty (STDPRICE, STDDISP, STDFEAT)

have greater influence than those that capture promotional levels (NORMP, AVGFEAT,

AVGDISP). Brand Franchise variables influence all three behaviors, while Brand Demo-

8We experimented with mean values, however in this case all the demographic variables were insignif-icant. R2 's are marginally lower, and other parameter estimates are unchanged. Details are availablefrom the authors upon request.

9 Bolton and Narasimhan et al obtain R2 's in the low 0.20 range.

13

graphics (MMAGE and MMEDUC) affect only the incidence decision. In the following

sections we discuss the specific variables individually. In so doing, we seek to rational-

ize the nature of their impact through reference to economic and consumer behavior

theories.

4.2.3 Drivers of Choice, Incidence and Quantity Elasticities

(1) Marketing Effort

NORMP (Normalized Price). Promotions on brands with higher relative prices reduce

the incidence elasticity, but do not affect choice or quantity elasticities. Price cuts on

relatively premium brands do not cause acceleration??

STDPRICE (Variation in Price). A brand with higher variance in price is less elastic

with regard to choice and incidence and more elastic with regard to purchase quantity.

All of the coefficients are statistically significant. The results are encouraging in that

previous analyses (e.g., Bolton (1989) Fader and Lodish (1990)) report that price demon-

strates weak associations with promotional response. Price perception theory provides a

rationale for the result. The story here is that promotional price reductions are relatively

less discernible for brands with high variance in prices. Note that variance in prices can

be due to a larger spread between the extreme end of the prices for the brand. The We-

ber's law argument (e.g., Monroe 1973) would then suggest that a given price reduction

is less discernible for brands with higher price variance and hence the choice and inci-

dence results. The quantity results refine this intuition by suggesting that the segment

that does notice inflates their purchase quantity appropriately. An implication of this

rationalization is that the non-triers of a brand are less likely to discern price reductions

for that brand, whereas buyers of a brand pay attention to prices of their brand and act

on price reductions by amplifying their quantity decisions. The self-perception theory

of attributions supports this rationalization as well. This argues that a price reduction

for a brand with minimal variance in prices leads consumers away from attributing their

choice of the brand to the promotion.

14

The data reveal that consumers do not pay attention to prices in making their deci-

sions of when to buy and what brand to buy in environments where there is considerable

variations in a brand's price over time. The only effect of a price reduction in that

environment is forward buying on the part of a consumer. This is consistent with the

reference price view of price promotions. Higher variance in prices lead from the Thaler

(1985) perspective to greater erosion in the reference. This erosion in reference prices

lowers response to price promotions which is what is observed in the results on incidence

and choice. It should be noted that the discussion here is confined to the variance in

prices for a brand and not with the average prices for a brand. In that sense, these

results complement the earlier observations regarding price levels in Bolton (1989) and

Narasimhan, Neslin and Sen (1996).

AVGFEAT (Average Feature Activity). Higher levels of feature activity reduce elasticity

each for the three consumer behaviors. However, only the effect of feature activity on

quantity is statistically significant. The interpretation is that higher levels of feature

activity deflect consumer attention from price and thereby reduce the elasticity of these

behaviors to price changes. The result is consistent with the classical conditioning view

of promotions (e.g., Blair and Landon 1981), and ring true especially for low-involvement

contexts. Interestingly, a reference price based rationalization predicts the same outcome

but for a very different reason. Thaler (1985) and Winer (1986) argue that higher levels

of feature activity reduce consumer reference prices and thereby the impact of price

reductions on sales (implying lower elasticity). Their view of the impact of feature require

consumers to pay explicit attention to the price information in feature advertising. To

the extent that feature advertisements refer to regular as well as promoted prices, the

reference price argument seems a better reconciliation of the empirical results.

It should also be noted that the result we report is the opposite of Bolton (1989). She

finds that brand sales for frequently featured products are more elastic. She suggests

two possible rationalization for her results - one, existing buyers become more price

sensitive, or, new price sensitive buyers enter the market in response to feature activity.

15

Our approach of decomposing promotional response to incidence, choice and purchase

quantity would allow us to verify which if her two conjectures are more empirically

grounded. Unfortunately, the fact is that feature activity has the exact opposite effect.

STDFEAT (Variation in Featuring Activity). Greater uncertainty in feature activity for

a brand increases the incidence elasticity. The results suggest that feature activity is in-

formative only in highly uncertain environments. That its impact on choice and quantity

is insignificant (i.e., no appreciable switching or stockpiling effect) is perhaps indicative

of the fact primary role of feature activity in a very uncertain feature environment is that

of being a reminder to the loyal consumers. Consider a brand that is never featured or

almost always featured (i.e., minimal uncertainty about feature activity for the brand).

The estimates suggest that a price drop for this brand does not generate additional vol-

ume from incidence in the category. Consumers are so accustomed to the feature activity

for a brand that their behaviors remain largely unchanged. This is consistent with the

reference price viewpoint presented earlier.

A VGDISP (Average Display Activity for a Brand). None of the coefficients are statis-

tically significant. However, the results are directionally consistent with the finding of

Bolton (1989) that higher levels of display activity reduce the elasticity of the brand.

Her results related to total elasticity whereas our analysis suggests that it is true only

for the case of choice elasticity.

STDDISP (Variation in Display Activity). Greater uncertainty in display activity for

a brand reduces the incidence elasticity and increases choice and quantity elasticities.

Only the choice and incidence parameters are significantly different from zero. When a

brand has a larger value for STDDISP, it means (because of their sporadic nature) that

its displays catch the attention of who have decided to buy in the category. Therefore,

brands of this sort generate additional switching when they lower prices. Conversely, the

sporadic display attracts attention to the category, and causes shoppers who may not

have had the product in mind (prior to the store visit), to purchase in the category.

MDEAL (Frequency of Dealing). Other things being equal, more frequent dealing in-

16

creases the incidence elasticity and reduces the choice and quantity elasticity. Only

the quantity effect is statistically significant. The results suggest that frequent dealing

makes consumer less sensitive to price in their quantity/stockpiling decisions. The obvi-

ous interpretation being that more frequent dealing leads to consumers matching their

purchase decisions with the timing of deals. The result being that the deal produces little

by way of incidence or switching, and to make matters worse, does not get consumers to

alter their quantity decisions on the basis of the specific deal being offered. An extreme

interpretation would be that consumers do not pay any attention to the terms of the

deal and the only cue that is being leveraged by the consumers is the presence of a price

reduction. This is consistent with the literature on price expectations that finds that

more frequent dealing mutes consumer response to price (e.g., Krishna 1992).

MDEPTH (Depth of Discount). Other things being equal, deeper discounts reduces

incidence and choice elasticities and increases quantity elasticity. None of the effects

are statistically significant. Our results do not fit with Golabi (1985) and Helsen and

Schmittlein (1989). They find that deeper discounts lead to an increase in variability in

sales. This could be due to either cherry picking on the part of the non-loyal segment

or switching of loyal consumers who find the deeper deal irresistible despite their loyalty

to their most preferred brands. It should be noted that the correlation patterns in the

data do not involve MDEPTH in any significant manner. Therefore, it is not likely that

multi-collinearity drives the statistical insignificance of depth of discount on consumer

behaviors.

(2) Category Structure

HERFIN (The Herfindahl Coefficient of Industry Concentration). Other things being

equal, higher market concentration increases incidence and quantity elasticity and re-

duces choice elasticity. All three effects are statistically significant. Recall that the

herfindahl coefficient is the sum of market shares of the products in the category. A

higher herfindahl coefficient translates to lower competitive intensity. Since the herfind-

ahl index is a category level variable, the results do not speak to a particular brand as

17

such within a category. The estimates suggest that a price reduction in a category with

a strong brand (i.e., high herfindahl index) generates incremental incidence. Conditional

on incidence, the brand choice decision is more inelastic in a concentrated category im-

plying a decrease in the probability of switching brands. Therefore, other things being

equal, a promotion in a concentrated category accelerates the purchase of the preferred

brand. This result is consistent with Bawa, Landwehr and Krishna (1989) and contrary

to Narasimhan, Neslin and Sen (1996). The Bawa et al. (1989) argument is that an

increase in the number of brands should result in an increase in brand switching due

to a weakening of brand loyalty effects. An increase in the number of brands in a cat-

egory translates to a lower herfindahl index and the estimates show that this results

in increased switching through an increase in the choice elasticity. The Narasimhan,

Neslin and Sen (1996) result is more likely to be observed in markets where the brands

cater to niche segments so that there is little overlap between market segments. 10 Raju

(1989) reports that categories in which competitive intensity is high exhibit significantly

lower variability in category sales. Our results are consistent with his findings. A lower

herfindahl index implies a more competitive category and we find that category incidence

is less elastic in that case. Therefore, price promotions in highly competitive categories

do not affect category incidence significantly.

CATPEN (Category Penetration). Other things being

Price promotions in a category with higher penetration reduces the incidence elastic-

ity and increases choice and quantity elasticity. The incidence and quantity results are

statistically significant. In other words, high penetration categories are price inelastic

with respect to incidence. However, conditional on incidence, promotions in this cat-

egory do result in substantial stockpiling by consumers. The incidence result is quite

intuitive. Higher category penetration implies that are fewer potential consumers who

have not purchased in the category. A promotion therefore cannot be expected to have

'°Their hypothesis can be rationalized by the branded variants theory of Bergen, Dutta and Shugan(1996).

18

much of an impact in drawing additional consumers into the category. The stockpiling

result seems to suggest that promotion on a brand are being acted upon by the loyal

consumers (Krishnamurthi and Raj 1989) although we have no loyalty metrics to bear

this out.

The results suggest a refinement of the Narasimhan, Neslin and Sen (1996) hypothesis

that promotional response is positively related to category penetration. We find that a

brand's promotional response as a function of category penetration is not uniform when

it is decomposed into component consumer behaviors of incidence, choice and quantity.

The results suggest that the Narasimhan et al hypothesis generalizes to the quantity

decision but not to the incidence decision. The incidence result is intriguing because

high penetration categories feature higher levels of promotional activity (e.g., Fader and

Lodish (1990). 11 The rationale for heavy promotions is that these categories are almost

like commodities and are often used as loss leaders (Walters and Mackenzie 1988). We

find that these categories do not seem to be generating the response that loss leader

promotions try to get which is incidence. However, it should be noted that we do not

have measure of store switching which speaks to the elicited response most closely.

NECESS (The Product Category is a Necessity).

We created a dummy variable to assess the impact of category buy on promotional

response. The work on market baskets indicates that certain categories are more relevant

for all shopping baskets and certain others are less relevant. As can be seen from the

results, the impact of promotions do depend on the category classification. Category

incidence and brand choice decisions are more price elastic and the quantity decision is

price inelastic. All effects are statistically significant. In other words, a price reduction

makes it even more likely that the category will be included in the market basket, and

that consumers will switch. However, consumers are less likely to stockpile necessities.

(3) Brand Franchise

"This is true for our data set as well. Category penetration and average levels of display and featureare positively correlated and the correlation is statistically significant.

19

BRANDPEN (Brand Penetration). Higher brand penetration increases the incidence

and quantity elasticity and reduces choice elasticity. Only the incidence effect is signif-

icant. The results indicate that a price reduction on an brand with a large penetration

in the category generates increased incidence in the category. However, conditional on

incidence there is no significant effect on either the brand switching or purchase quan-

tity decision. Taken together, the results suggest that promotions on a brand with high

penetration tend to draw the marginal category user into the category. It is important

to note that the results point out that any impact on sales of the brand is not due con-

sumers switching from another brand. The brand penetration results are very different

from the category penetration results. High category penetration reduces incidence elas-

ticity whereas high brand penetration increases incidence elasticity. This suggests that

promotions on market leaders within a category generate significantly larger responses to

price reductions. The marginal promotional effect decreases as the category penetration

increases.

BRDRATE (Average Number of Purchases per Consumer).

Other things being equal, higher brand rate increases the incidence and quantity elas-

ticity and reduces the choice elasticity. The incidence and choice effect are statistically

significant. The direction of effects are identical to that of brand penetration. A higher

brand rate translates to shorter interpurchase cycles for consumers who buy the brand.

The results suggest that promotions on a brand with shorter interpurchase cycles cre-

ate higher levels of incidence and lower brand switching. Consumers who buy the brand

more frequently are loyal and therefore more likely to accelerate purchase of the brand in

response to promotion. However, that the consumer sticks to the preferred brand is clear

from the impact of brand rate on choice elasticity (i.e., brand with a higher consumption

rate responds less to price in the choice decision). The choice result is contrary to the

Bawa and Shoemaker (1987) and Narasimhan, Neslin and Sen (1996) findings. They

hypothesize that a shorter inter-purchase cycle (higher brand rate) implies a lower cost

of a switch in brand choice. The idea being that the consumer need only wait for a short

20

period before being in the market again for that category. In short, shorter purchase

cycles (higher brand rate) result in higher level of switching (i.e., more price elastic in

choice). We find that the exact opposite is true. A brand with a short purchase cycle for

its key customers (i.e., a brand with a core of loyal customers) can raise prices without

having these customers switch away. Conversely, the more "loyal" the core customers

are (higher brand rate), the more likely the product appeals to a particular niche; other

consumers are less likely to switch to this brand when it promotes. The core customers

respond to promotions on their preferred brand by accelerating their purchase. Taken

together, the results on brand penetration and brand rate suggest that a brand with

higher market share 12 is price inelastic in the choice decision and price elastic in the

incidence and quantity decision.

It is interesting to look at the results here and compare them with the results relating

to category penetration. It is the case that necessity goods in general have higher levels

of category penetration than non-necessity/impulse goods. 13 However, necessity and

category penetration have exactly opposite effects on incidence. A price reduction on a

high penetration category does little to generate incremental volume, however promotions

on necessity goods switch consumers into the "buy" decision.

(4) Brand Demographics

Until recently, the marketing literature has been somewhat ambivalent about the

influence of demographics on purchase behavior. Hoch et al (1996) show that price

elasticities in stores are related to the demographics of immediate constituents. A new

working paper by Ainslie and Rossi (1996) suggest that consumer characteristics have

a systematic effect on price response, and that "price sensitivity" is a consumer trait.

The findings from this study motivated us to develop Brand Demographic variables that

profile the brand's consumers. If "price sensitivity" is a trait, then perhaps it can be

12Market share is penetration times brand rate."It should be noted however that these variables speak to very different effects and there is variation

in their associations across categories. For instance, an impulse good such as salted snacks does havehigh penetration.

21

related to observable demographics. As shown in Tables 5 and 6, the influence of the

demographic variables appears minimal. Recall that our variables reflect the modal

characteristics of the brand's customer base. The marketing intuition is that the modal

demographic is the most prevalent customer.

Our results suggest that demographics only influence the incidence decision of the

consumers. Older consumers are less elastic in incidence, while more educated consumers

do accelerate purchase in response to price promotions. This is interesting news for

marketers as it is relatively easy to obtain information on the demographic makeup of

a brand's consumers. It is of particular interest to retailers to know that incidence

decisions can be influenced by the demographic characteristics of a brand's constituency.

4.2.4 Drivers of the Total Elasticity

We presented the results for the total elasticity (Table 6) for two reasons. First, it allows

us to make a more direct comparison with the findings of Bolton (1989) and Narasimhan,

Neslin and Sen (1996). (Recall that these studies did not decompose elasticity into

the underlying behavioral components). Second, we are able to determine instances in

which non-significant effects for the total elasticity result from offsetting effects for two

or more of the three behaviors. Thus, Table 6 demonstrates the benefits of analyzing

the decomposition. In Table 7 we present a direct comparison of parameter estimates

for the three behaviors, and those for the total elasticity. We present the standardized

coefficients so that the magnitudes of the coefficients are directly comparable. In order

to keep the table simple, we present only the significant coefficients for choice, incidence

and quantity. In the fourth column we report the standardized coefficient for the total

elasticity if it is significant; we report the sign of that coefficient if it is not significant.

[ Table 7 about here ]

Several interesting insights emerge from Table 7. First, the Marketing Effort vari-

22

ables generate a number of "false positives." In many cases (NORMPRICE, STDFEAT,

STDDISP, MDEAL), the total elasticity analysis yields insignificant parameter esti-

mates. However, this results from offsetting forces at the level of the three underlying

behaviors. The same holds true for the Brand Franchise variables. What appear to

be insignificant effects at the total elasticity level result from "cancelling out" of effects

for individual behaviors. Second, while all the Category Structure parameters are sig-

nificant in the total elasticity model, this is somewhat misleading. For example, while

CATPEN has an overall positive effect on total elasticity, this results from a relatively

large, positive and significant quantity effect dominating a smaller, negative and signifi-

cant incidence effect. Finally, none of the Brand Demographics emerge as significant in

the total elasticity, yet some of these effects are significant for purchase acceleration.

Thus, our results allow managers and researchers a more complete picture of the

way in which price promotions really work. In some instances it may be sufficient for a

manager to know that frequency of dealing (MDEAL) has no effect on overall elasticities.

However, in other situations, both manufacturers and retailers might be interested to

know that more frequent dealing makes consumers less elastic with respect to stockpiling.

In the same way, even though we know that storability (STORAB) has a postive effect on

overall elasticities, it is important to know that this is driven by switching and stockpiling.

Lastly, we also investigate the relative explanatory power of our four classes of in-

dependent variables using the total elasticity results. It turns out that the adjusted R2

for models with only a single category of variables are: (a) Marketing Effort (0.298), (b)

Category Structure (0.462), (c) Brand Franchise (0.006) and (d) Brand Demographics

(0.008). 14 Given our discussions in previous sections and these statistics, we believe that

Category Structure is the most important set of predictor variables. Marketing Effort is

also very important, while Brand Franchise and Brand Demographics appear relatively

unimportant. This is a very interesting finding. How the brand is managed (i.e., what

marketing actions are taken), and its operating environment have a very strong influence

"It is incorrect to compare these R2 directly because the variables are not uncorrelated. However,these results provide a reasonable base for directional arguments.

23

on consumer response. However, the way customers by the brand (e.g., many customers,

low repeat; few customers, high repeat) and their demographic characteristics have very

little impact. This suggest to manufacturers and retailers that consumer response can

be "nutured" by marketing actions and favorable market conditions.

5 Summary and Managerial Implications

Our research has uncovered a number of interesting findings. We summarize these major

themes and their implications as follows:

• An Emerging Generalization: We confirm that, with no exceptions, the majority

of sales volume from a price promotion are due to brand switching. This fits

with the observations of Padmanabhan and Lal (1995) and Chiang (1996) that

promotional wars are essentially zero-sum games. From a managerial perspective,

this implies that the profitability of a promotion be viewed only with regard to

its ability to generate switching within a category. However, we find that the

early breakdown of 84/14/2 rule appears to be an exception. Within the spectrum

of these decompostions, we find that an 85/10/5 split is about the average for

nonstorable products (especially for refrigerated products). For storable products,

we find the weight is shifted toward quantity effect so the decomposition becomes

80/5/15. 15 We also observe the stockpiling effect for the storable goods reduces

significantly if the product is frequently promoted (as in the case of Softdrinks).

Hence, if given no product information, we believe 80/10/10 is an 'educated guess'

for the decomposition of the promotional effect on brand choice, incidence and

stockpiling decisions.

• The Category Reality: According to our analysis, promotional responses are mostly

influenced by the market structure that a brand operates in. There are two major

aspects of this category environment which are not controllable by a brand (at

least, in the short run): the degree of market concentration (how fragmented is the

15This has been speculated by Gupta (1988, p. 352).

24

market?) and category penetration (how big is the market?). For example, with

regard to these two points, we find promotions are much more effective in inducing

purchase incidence in a more concentrated market than in a less concentrated

market. In contrast, promotions are less effective in accelerating purchase in a

highly penetrated category. Since the structure of a market environment varies

across products, it is crucial for firms to recognize the limitation of promotions

each given category conditions and adjust their strategies accordingly.

• The Marketing Mystique: Marketing Effort is the second most important factor

(next to Category Structure) in explaining the variation of elasticities. However,

we find the uncertainty or unpredictability of promotions are more relevant than

the average level of promotions in determining promotional response. In particular,

we find the marginal impact is substantially larger if promotions are not expected

by consumers. In light of this finding, managers need to strike a balance between

the long- and short-term views of promotional activities. What this suggests is

that it may not pay to always react to competitors' promotions and, hence, as a

consequence become predictable. This true even though we confirm that brand-

switching phenomenon is the most important part of promotional response.

• Brand Power Surprisingly, market share does not play as important role as ex-

pected in explaining the variation of elasticities. Base on our analysis, we find

promotions from large brands, i.e., with high brand penetration and/or brand pur-

chase rate, are in fact relatively more effective in reminding consumers to buy the

category than in persuading them to buy these brands. The implication from this

is that there is a 'silver lining' for the rest of competitors when a market leader

promotes – it generates more 'traffic' to the category even though the most of ad-

ditional customers go to the market leader. It is also important news for retailers –

these are the brands that retailers would like to see promoted (in order to stimulate

volume).

25

• The Consumer Factor: Finally, we find there are few connections between consumer

types (as described by demographics) and variation in how consumers respond to

promotions. This does not imply that managers do not need to be concerned

about customer demographics when planning their promotional campaigns. One

of plausible reasons for this 'no-effect' result is that consumers have, overtime,

sorted themselves out (demographically speaking) in terms of what brands they

like and how they would react to promotions. In other words, the self-selection

process has made it difficult to detect any influences from demographics.

6 Concluding Remarks

An increasing concern with the burgeoning marketing literature on choice (e.g., Fader

and Lodish 1990) is that perhaps too much effort is currently invested in developing

sophisticated methodology, and perhaps too little effort in understanding the import

and generalizability of the major contributions in the literature. The words of Bass

(1995) on the state of marketing knowledge are relevant to the status of the choice

literature, "..the field has matured to the point where it seems desirable to take stock of

where we are, what we have learned, and fruitful directions for extending the knowledge

base" . We see this work as an important step in that direction.

We show in this paper that the category incidence, brand switching, and, purchase

quantity effects of marketing promotions are systematically related with brand's mar-

keting activities, category characteristics, brand franchise, and customer profiles. The

empirical findings have implications for academics and practitioners alike and we have

elaborated on some of these in earlier sections of the paper. A key contribution of our

work is that it allows both retailers and manufacturers to determine what conditions

and tools are more attractive from their respective point of views. For example, all else

equal retailers want to stimulate incidence; manufacturers want to influence choice; both

manufacturers and retailers want to increase purchase quantity.

There are few remaining issues that need to be addressed, some methodological, some

26

substantive:

• Can this "80/10/10" split of promotional effects be a result of using a GEV-type

probabilistic model? This is purely an empirical question, however, we believe it is

unlikely one would obtain very different results from other types of choice mode1.16

• We do not address the issue of coefficient heterogeneity in our estimation (Rossi

and Allenby (1993), Chintagunta, Jain, and Vilcassim (1991), Gonul and Srinivasan

(1993)). This is a very complicated problem here because there is room to capture

heterogeneity in all three decisions. To avoid complicating the estimation task

further, we do implement any statistical mechanism to capture such parameter

heterogeneity. In doing this, we are not saying that heterogeneity is not important.

Rather, in light of our focus in this study, we believe the qualitative nature of our

results are not compromised by the decision to exlude heterogeneity.

• We do no attempt to address store-switching issue. Clearly, the total elasticity can

be defined at a higher level of generality by including the consumer's store selection

decision. There have been some recent attempts to address this issue (e.g., Bell

and Lattin (1996)). An integrated approach to encompass all aspects of consumer

decisions is a desirable direction for future research.

• From our meta-analysis, we find that not all significant parameters have one and

only one interpretation and not all insignificant coefficients have explanations. We

hope by providing these main effects it paves the way for more in-depth consumer

behavior research that seeks to rationalize or challenge our findings.

References

Gupta, S. (1988), "Impact of Sales Promotions on When, What, and How Much toBuy," Journal of Marketing Research, 25(May), 342-55.

Chiang, J. (1991), "A Simultaneous Approach to the Whether, What, and How Muchto Buy Questions," Marketing Science, 10(4), 297-315

16 Bolton (1989) has demonstrated that the log-log form of demand equations works well in her study.

27

Chiang, J. (1995), "Competing Coupon Promotions and Category Sales," MarketingScience, 14(1), 105-122.

Krishna, A., I. C. Currim, and R. Shoemaker (1991), "Consumer Perceptions of Pro-motion Activity," Journal of Marketing, 55(April), 4-16.

Narasimhan, C., S. A. Neslin, and S. K. Sen (1996), "Promotional Elasticities andCategory Characteristics," Journal of Mrketing, 60(April), 17-30.

Bolton, R. N. (1989), "The Relationship Between Market Characerisitics and Promo-tional Price Elasticities," Marketing Science, 8(2), 153-169..

Fader, P. S. and L. M. Lodish (1990), "A Cross-Category Analysis of Category Structureand Promotional Activity for Grocery Products," Journal of Marketing, 54(Oct),52-65.

Raju, J. S. (1992), "The Effect of Price Promotions on Variability in Category Sales,"Marketing Science, 11(3), 207-220.

Krishnamurthi, L. and S. P. Raj (1988), "A Model of Brand Choice and PurchaseQuantity Price Sensitivities," Marketing Science, 7 (1), 1-20.

Litvack, D. S., R. J. Calantone, and P. R. Warshaw (1985) "An Examination of Short-Term Retail Grocery Price Effects," Journal of Retailing, 61(3),9 - 25.

Blattberg, R. C., R. Briesch, and E. J. Fox (1995), "How Promotions Work," MarketingScience, 14(3), 122-132.

7 Appendix

7.1 Model and the Likelihood Function

For each product category, let /it denotes a dichotomous indicator so that /it = 1 ifconsumer i purchases that category at occasion t and Iit = 0 otherwise. Furthermore,let B = {1, ..., J} denotes the set of brands so that Dijt = 1 indicates that brand j ischosen by the consumer and Dijt = 0 otherwise. Thus, E:i_ i Dijt = 1 conditional on apurchase.

Following the spirit of Hanemann (1984) and Chiang (1991), the choice decisions andthe interdependence between decisions are described as follows:

Qijt = Xijti3j + Eijt iff C/ijt +77ijt > Max{Uikt + nikt, Vk 0 j } &(lift + niit > Uiot + 7hot

0 iff Uiot + rhot > MaxWikt + Mkt, Vk1

28

where j E B, Qijt is the quantity demand for brand j, Xiit denotes the associatedcovariates, is the corresponding coefficients, (lift represents the perceived benefitsof brand j per dollar, [Act is the threshold of category purchase, and Eiit and Tlijt areunobservable error terms. To reflect the interdependency of decisions, Eiit and 'gift areassumed correlated. Moreover, Uijt may contain variables also in Xijt.

Note that to avoid unnecessary estimation complication, we assume decisions acrosscategories are independent except they all subject to the same budget constraint. 17 Byassuming ei and rij are correlated, the model in effect can be viewed as a hybrid ofKrishnamurthi and Raj (1988) and Chiang (1991).

We assume ei is normally distributed but 17 = \r/jot, -1 iijt) --MA) are jointlyGEV distributed. Specifically, let H(R) exp(-G(-e-10) denotes the joint cdf suchthat G(-e-71 ) = [EkEB exP(-71k I (1 - 6)] (1-6) + exp(-no) where 0 < b < 1. They areiid across all households and occasions. With these assumptions and the model, theincidence and the choice probabilities can be derived, respectively, as:

Pr(iit = 1)e (1 -6)-1n [E kEB

Akt/(1-6)]

e(1-6.)./.[EkEB eüikt/(1-6)]+ eUiot

Pr(Diit = 11.rit = 1) = e(1 -S) 1n[E kE B Akti (1-1 eUiOt

This specification is equivalent to a nested logit model (McFadden, 1987) in which the"inclusive value" has a special form of lnEkEB exp [Uikt/( 1 - 6)] and its correspondingcoefficient is (1 - 5). b is interpreted as the degree of similarity of brands.

Let J+ = {0, 1, 2, ..., B} denote the option set (including the non-purchase option),and let J+ = {0,1, j -1, j +1, ..., B} denote the set without the jth option. The jointcondition of Diit = 1 and = 1 can be re-written as follows: (i and t are suppressed)

Uj + > Max{ük +77k, k E J±i}

C/j > Max{ Clk + 77k ,k E -

Uj >

Given 7-1 - GEV as described in the model section, we can show that 77; Fi (•) suchthat

17This is not a serious flaw because we eventually adopt a Generalized Extreme Vaule distribution(GEV) for i error terms. Chiang and Lee (1992) show that the GEV distribution satisfies the necessaryand sufficient conditions which ensures the unbiasedness of the estimates when other categories areintentionally omitted .

e-6.'in[EkEs e t1 ikt / 0-61 +Ci/(1-5)

29

Fi (•) =77*/(1-5)

(el-a- + >kEJ,k#j e ) • e 3

(Jo (e ke 1-6 EkEJ,ks, 0-6 )1-6We assume (ck , k =1, ..., B has a pair-wise joint distribution denoted by B(Eic, nZ, Pk),

where pk represents the correlation. Though we do not know the shape of B( . ,.,.), weknow its both marginal distributions. Thus, the following trasformation identity can beestablished which maintains the same correlation coefficient: (Lee, 1983)

B ( Ek, 77Z, Pk) -7= BN (Clk, C2k, Pk)

where BN is a bivariate normal distribution, elk = 1.-1(<1.0r..)) = , and C2k =Crk Crk

(1)-1(F(71Z))•For any observation Qikt , k E J, the corresponding sample likelihood function is:

Likt = 4.-1(F(tf-i"))

hm(Qikt XiktOk

,C21c)de2k/-00where fbn (•, -) is the bivariate normal density. The evaluation of -1 (F(•)) can becarried out numerically during the MLE iterations.

The sample likelihood for I = 0 is simply 1 - Pr(/ = 1). Thus, the log likelihoodfunction is

LL = TT (Like /ttktInn Pr(Iit °)1-Itt • klIEJ

i 77,

7.2 Variables

Variables included in Xijt , and tIjot , respectively, are:

• Xijt = {constant, log - price, feature, display, inventory, familysize, andlog - expenditure}

• Uijt = {brandconstant, log - price, feature, display, lastpurchasebrand, lastpurchasesize, brandloyalty

• r/iot = {constant, log - expenditure, inventory}

7.3 Price Elasticity

It is easy to show that the total elasticity is the sum of the three elasticity components.Specifically, they can be expressed, respectively, s

ei OP • Pr(Di ll") • (1 - Pr(/))op

e(1 - 6)

(1 - Pr(Dj1/))

1 0(4)-1(Pr(Dj)) egilDj

EPA]) j, I) { 13139 + C7 3 Pr(Dj)

30

[4)-1(Pr(Di)) at. ' (Pr(Di)) + 91' (1 — 613r(Di l/) — (1 — .5)Pr(Di))]

app (1 — 6)

where OP is the price coefficient in Pr(Di l/). The variance of each elasticity estimate iscalculated via the delta method (Rao, 1974).

alty

P

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

3.25

3.5

3.75

4

4.25

4.5

4.75

5

0

-0CA

P o 9:., 9 Ivc.n t..) cs, i

O

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

3.25

3.5

3.75

4

4.25

4.5

4.75

5

P0 -...

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

3.25

3.5

3.75

4

4.25

4.5

4.75

5

0IV

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

3.25

3.5

3.75

4

4.25

4.5

4.75

5

Table 1Description of Product Categories

Category Alternatives1 Necessity Purchases Penetration2 Price Range3Bacon 6 No 844 0.72 (1.60, 2.69)Margarine 10 Yes 1504 0.85 (0.55, 1.44)Butter 4 Yes 388 0.48 (1.30, 1.85)Ice Cream 11 No 1168 0.80 (1.60, 4.01)Paper Towels 10 Yes 1442 0.83 (0.54, 1.08)Sugar 6 No 686 0.74 (1.61, 2.15)Liquid Detergents 25 Yes 886 0.68 (4.41, 9.80)Coffee 18 No 750 0.59 (4.65, 8.97)Softdrinks 15 No 967 0.68 (0.22, 6.99)Bath Tissue 20 Yes 2192 0.90 (0.92, 2.11)Potato Chips 20 No 1179 0.78 (1.09, 2.82)Dryer Softeners 18 No 288 0.43 (1.49, 2.76)Yogurt 10 No 318 0.61 (0.33, 2.35)

Totals 173 12,612

1 Unique Brand-Size Alternatives.2 Total Households = 250.3 In the model estimation, prices are normalized to a common unit.

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Table 2Range of Elasticity Estimates

Category Total Choice Incidence Quantity(XT, o'T) (X:c , dc) (XI, di) (XQ, clQ)

Bacon

Margarine

Butter

Ice Cream

Paper Towels

Sugar

Liquid Detergents

Coffee

Softdrinks

Bath Tissue

Potato Chips

Dryer Softeners

Yogurt

(1.440, 1.560) 11.51 0.049

(1.031, 1.447)1.28 0.172

(0.067, 0.369)0.18 0.125

(0.040, 0.046)0.04 0.002

(2.258, 2.400) (2.046, 2.325) (0.069, 0.204) (0.006, 0.008)2.34 0.042 2.21 0.083 0.11 0.040 0.00 0.000

(1.907, 1.960) (1.050, 1.789) (0.106, 0.799) (0.058, 0.065)1.93 0.021 1.42 0.302 0.44 0.283 0.06 0.003

(2.679, 2.854) (2.342, 2.780) (0.057, 0.320) (0.017, 0.017)2.78 0.051 2.61 0.127 0.15 0.076 0.01 0.000

(4.937, 5.935) (3.708, 4.274) (0.090, 0.385) (0.664, 1.743)5.37 0.346 4.00 0.178 0.23 0.093 1.13 0.351

(4.211, 5.223) (3.499, 5.066) (0.102, 0.666) (0.046, 0.056)4.82 0.378 4.45 0.585 0.32 0.210 0.05 0.003

(4.113, 4.413) (3.481, 4.084) (0.028, 0.361) (0.248, 0.306)4.34 0.058 3.96 0.115 0.09 0.063 0.28 0.015

(2.153, 2.351) (1.579, 1.709) (0.022, 0.101) (0.453, 0.627)2.23 0.055 1.64 0.040 0.05 0.024 0.53 0.044

(2.716, 2.828) (2.478, 2.754) (0.051, 0.220) (0.018, 0.023)2.78 0.033 2.64 0.082 0.11 0.050 0.01 0.001

(4.511, 5.385) (3.802, 4.263) (0.019, 0.251) (0.408, 1.200)4.77 0.226 4.08 0.160 0.10 0.081 0.57 0.226

(2.954, 3.530) (2.285, 2.562) (0.036, 0.186) (0.427, 0.939)3.31 0.147 2.49 0.068 0.07 0.037 0.74 0.126

(4.269, 4.515) (3.813, 4.247) (0.044, 0.290) (0.010, 0.285)4.31 0.051 4.08 0.119 0.13 0.067 0.09 0.061

(1.765, 1.828) (1.340, 1.699) (0.049, 0.380) (0.029, 0.096)1.78 0.017 1.57 0.119 0.16 0.109 0.04 0.019

1 (Minimum, Maximum).

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Table 3Elasticity Decomposition Across Categories

CategoryPercent of Total Elastiticy Due to:Choice Incidence Quantity

Softdrinks 95.1 4.2 0.7Margarine 94.6 5.1 0.3Dryer Softeners 94.6 3.2 2.2Icecream 93.7 5.7 0.6Sugar 92.0 7.0 1.0Detergents (liquid) 91.3 2.1 6.6Yogurt 88.5 9.1 2.4Bathroom Tissue 85.7 2.3 12.0Bacon 84.6 12.5 2.9Potato Chips 75.5 2.2 22.3Paper Towels 74.8 4.3 20.9Butter 73.7 23.2 3.2Ground Coffee 73.6 2.6 23.8

Averages 86.0 6.4 7.6

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Table 4Description of Independent Variables

(a) Marketing EffortSTDPRICE3c : standard deviation of shelf price brand j, category c.AVGFEATic: average value of featuring for brand j, category c.STDFEATic : standard deviation of featuring for brand j in category c.AVGDISPic: average value of display for brand j, category c.STDDISPjc: standard deviation of display for brand j, category c.MDEALjc: percent of time that brand j, category c is on deal.MDEPTHjc: average deal depth, given that brand is on deal.

(b) Category StructureHERFINc: the Herfindal Index (i.e., Ei mss where msi is the market share of brand j).CATPENc: Category penetration, percentage of panelists who buy in category at least once.NECESSc: A 0/1 indicator of category as a necessity good.(c) Brand FranchiseBRANDPENjc: percentage of panelists that buy brand j, category c at least once.BRDRATEic: average number purchases of brand j made by panelists who buy brand.

Brand Demographics)MINCic: mean income of panelists who buy brand j in category c.MCHILD3c: mean number of children for buyers of brand j, category c.MMOCCic: mean occupation for buyers of brand j, category c.MMAGEic: mean age for buyers of brand j, category c.MMEDUCic: mean education for buyers of brand j, category c.

1 See Appendix B for a description of scale

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Table 5GLS Parameter Estimates

VariableChoice

Parameter t-ratioIncidence Quantity

Parameter t-ratio Parameter t-ratio

INTERCEPT(a) Marketing Effort

3.176 4.601 0.155 1.996 -1.469 -4.731

NORMPRICE 0.065 1.141 -0.012 -2.050 0.019 0.772STDPRICE -0.847 -4.546 -0.042 -2.025 0.228 2.705AVGFEAT -3.063 -1.565 -0.252 -1.196 -2.829 -3.282STDFEAT 0.928 0.695 0.346 2.376 0.462 0.782AVGDISP -1.386 -1.187 0.182 1.469 -0.005 -0.011STDDISP 2.070 2.224 -0.351 -3.492 0.204 0.498MDEAL -0.047 -0.182 0.043 1.499 -0.367 -3.160MDEPTH

(b) Category Structure-0.236 -0.573 -0.015 -0.341 0.241 1.326

HERFIN -4.814 -4.305 0.510 4.167 1.629 3.285CATPEN 0.792 1.405 -0.304 -4.773 1.893 7.446NECESS 0.544 3.611 0.070 4.177 -0.155 -2.306STORAB

(c) Brand Franchise0.541 3.182 0.022 1.247 0.344 4.602

BRANDPEN -0.283 -0.654 0.407 8.650 0.314 1.647BRDRATE

(d) Brand Demographics'-0.108 -2.564 0.016 3.487 0.008 0.451

MINC -0.039 -1.275 -0.004 -1.360 0.003 0.250MCHILD 0.018 0.554 -0.000 -0.228 -0.002 -0.134MMOCC -0.016 -1.082 0.001 0.956 -0.000 -0.058MMAGE -0.049 -1.132 -0.013 -2.777 0.005 0.297MMEDUC 0.022 0.795 0.009 3.077 0.020 1.625

Adjusted R2 0.60 0.62 0.39

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Table 6GLS Parameter Estimates for Total Elasticity

VariableTotal

Parameter t-ratio

INTERCEPT(a) Marketing Effort

2.023 2.550

NORMPRICE 0.081 1.216STDPRICE -0.739 -3.462AVGFEAT -6.374 -2.787STDFEAT 1.841 1.185AVGDISP -1.252 -0.911STDDISP 2.068 1.899MDEAL -0.317 -1.046MDEPTH

(b) Category Structure-0.059 -0.124

HERFIN -2.780 -2.139C ATP EN 2.228 3.438NECESS 0.465 2.672STORAB

(c) Brand Franchise0.898 4.507

BRANDPEN 0.449 0.889BRDRATE

(d) Brand Demographics-0.086 -1.767

MINC -0.041 -1.158MCHILD 0.017 0.435MMOCC -0.012 -0.701MMAGE -0.062 -1.230MMEDUC 0.049 1.491

Adjusted R2 0.59

37

Table 7Summary of Standardized Parameter Estimates

(Statistically Significant Coefficients Only')

Choice Incidence Quantity TotalVariable Parameters

(a) Marketing EffortNORMPRICE -0.109 +ve, n.sSTDPRICE -0.251 -0.108 0.185 -0.195AVGFEAT -0.628 -0.437STDFEAT 0.372 +ve, n.sAVGDISP -ye, n.sSTDDISP 0.284 -0.434 +ve, n.sMDEAL -0.227 -ye, n.sMDEPTH -ye, n.s

(b) Category StructureHERFIN -0.307 0.292 0.291 -0.155CATPEN -0.329 0.651 0.247NECESS 0.265 0.306 -0.212 0.198STORAB 0.266 0.475 0.385

(c) Brand FranchiseBRANDPEN 0.577 +ve, n.s.BRDRATE -0.133 0.179 -ye, n.s.

(d) Brand DemographicsMINC1 -ye, n.s.MCHILD1 +ve, n.s.MMOCC1 -ye, n.s.MMAGE1 -0.185 -ye, n.s.MMEDUC1 0.169 -ye, n.s.

'p< 0.01

38