Description
The fundamental theorem of demand states that the rate of consumption falls as the price of the good rises; this is called the substitution effect. Clearly, if one does not have enough money to pay the price, then they cannot buy any of that item. As prices rise, consumers will substitute away from higher priced goods and services, choosing less costly alternatives.
ABSTRACT
Title of Dissertation: Information, Consumer Choice, and Firm
Strategy in an Experience Good Market
Yan Chen, Doctor of Philosophy, 2008
Directed By: Professor Ginger Jin, Department of Economics
This paper models how consumers make brand choice when they have limited
information. In an experience good market with frequent product entry and exit,
consumers face two types of information problems: first, they have limited information
about product existence; second, even if they know a product exists, they do not have full
information about its quality until they purchase and consume the product. In this paper, I
incorporate purchase experience and brand advertising as two sources of information, and
examine how consumers utilize them in a dynamic process.
Specifically, to address the awareness problem, I model the consumer choice set as
a function of experience and advertising, which varies across consumers and evolves over
time. In terms of quality, I allow a first-time consumer to infer product quality from
advertising. Once she buys the product, she learns the quality perfectly. To better capture
the dynamics, I incorporate habit formation conditional on each consumer’s purchase
history.
The model is estimated using the AC Nielsen homescan data in Los Angeles,
which records grocery shopping histories for 1,402 households over six years. Taking
ready-to-eat cereal as an example, I find that consumers learn about new products quickly
and form strong habits. More specifically, advertising has a significant effect informing
consumers of product existence and signaling product quality. However, advertising's
prestige effect is not significant. I also find that incorporating limited information about
product existence leads to larger estimates of the price elasticity. Then I use instrument
variables based on differentiated-products firm competition models to address the
endogeneity problem of price and advertising with unobserved brand characteristics.
Based on the IV estimates, I summarize the substitution pattern and simulate consumer
choices under counterfactual experiments to evaluate a number of brand marketing
strategies and a policy on banning children-oriented cereal advertising.
Information, Consumer Choice, and Firm Strategy in an Experience
Good Market
By
Yan Chen
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park, in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2008
Advisory Committee:
Professor Ginger Jin, Chair
Professor John Rust
Professor Roger Betancourt
Professor Erkut Ozbay
Professor P.K.Kannan
© Copyright by
Yan Chen
2008
Dedication
To my parents.
ii
Acknowledgements
My first and greatest debt is to my advisor, Professor Ginger Jin. Ginger not only gives
me guidance in choosing the topic, obtaining the data, and conducting the research, but
also treats me like a sister in life.
I am grateful to Professor John Rust, Professor Roger Betancourt, Professor Erkut
Ozbay, Professor Dan Vincent, and Professor P.K.Kannan for their comments and
suggestions during the process this dissertation was written.
I have been blessed to meet many good friends at the University of Maryland and back
at the University of British Columbia. Thanks for making the past few years of my life
peaceful and offering many happy distractions from study and research.
As always, I have counted on the support and encouragement of my parents and my
brother. Thanks for having confidence in me and showering me with love all these years.
Although we are in different corners of the world, our hearts have always been together
and will always be. ??????????
iii
Table of Contents
Dedication ii
Acknowledgements iii
Table of Contents iv
List of Tables v
List of Figures vi
Chapter 1: Introduction, Background and Data Description 1
Section 1.1: Introduction 1
Section 1.2: Related Literature 5
Section 1.3: Industry Background and Data Description 7
1.3.1. Features of RTE Cereal Market 7
1.3.2. Data Description 8
Chapter 2: Demand Estimation without IV 11
Section 2.1: Demand 11
2.1.1.Demand Specification 11
2.1.2.Discussion 15
2.1.3.Identification 17
2.1.4.Estimation Issues 21
(1) Endogeneity 21
(2) Unobserved Consumer Heterogeneity 22
(3) Choice Set Simulation 22
(4) Properties of Estimator 23
Section 2.2: Results of Demand Estimation without IV 24
2.2.1.Estimation with Full Information 26
2.2.2.Estimation with Limited Information about Brand Quality 27
2.2.3.Estimation with Limited Information about Both Quality and Existence 27
2.2.4.Comparison of Goodness of Fit 30
Chapter 3: Instrumental Variable Estimation 34
Section 1: IV Estimation Algorithm 34
Section 2: IV Estimation Results 37
Chapter 4: Policy Experiments 39
Section 1: Pricing Strategy for Brand 28 39
Section 2: Advertising Strategy for Brand 28 41
Section 3: Effects of Banning Children-Oriented Cereal Advertising 43
Section 4:Concluding Remarks 45
Appendices 47
Bibliography 73
iv
List of Tables
Table 1. Brand Entry and Exit
Table 2. Brand Summary Statistics
Table 3. Summary Statistics of Homescan Data
Table 4. Summary of Variables in Estimation Sample
Table 5. Preliminary Regression Results
Table 6. Estimation Results
Table 7. Predicted Market Shares
Table 8. Own Price Elasticity for Top 10 Brands
Table 9. Estimated Price Elasticities for Top 25 Brands Based on IV Estimation
Table 10. Changes in Sales under Alternative Pricing Strategies
Table 11. Changes in Expenditure by Demographic Group under 5% Price Cut
Table 12. Changes in Expenditure by Demographic Group under Pulsing Strategy
Table 13. Food Ads Seen by Children of Different Ages
Table 14. Sugar and Fiber Contents of Brands by Segment
Table 15. Change in Segment Share After the Ban
Table 16. Effects of the Ban across Consumer Groups
v
List of Figures
Figure 1. Frequency Histogram of Household Brand Purchases
Figure 2. Repurchase Probability after First Experience with a Brand
Figure 3. Marginal Effect of Advertising on Choice Probability
Figure 4. Probability of a Brand Being Included in the Choice Set
Figure 5. Average Monthly Advertising, Price, and Sales for Brand 28
Figure 6. Average Daily Transaction Price for Brand 28
Figure 7. Observed v.s. Counterfactual Advertising Strategies for Brand 28
vi
Chapter 1: Introduction, Literature, and Data Summary
Section 1.1. Introduction
In an experience good market with frequent product entry and exit, consumers face at
least two informational problems when they make product choices: on the one hand, they
have limited information about product existence; on the other hand, even if consumers
know a product exists, they are uncertain about its quality before consumption. Consumer
choice in such an environment involves a dynamic process of information acquisition,
about which a large body of literature has developed. However, empirical research
typically deals with only one of the informational problems. To my knowledge, this paper
is the first attempt to incorporate both kinds of informational problems in a structural
framework and evaluate their relative importance using a rich panel of household
purchase data. In this sense, the paper brings the literature closer to the reality and sheds
new lights on both consumer demand and firm marketing strategies.
In this paper I focus on two mechanisms that alleviate the informational problems:
consumption experience and brand advertising. First, consumers learn about product
quality through experience. In particular, I assume that product quality can be fully
learned after the first try. This type of one-period learning is a limiting case of Bayesian
learning (the prior belief is updated to the true value after one experience) and is suitable
for goods whose characteristics can be ascertained quickly after use. Second, advertising
has two types of informative effects: signaling product quality (Nelson (1970, 1974),
Kihlstrom & Riordan (1984), Milgrom & Roberts (1986), etc), and affecting the
probability that a consumer is aware of the product (Butters (1977), Grossman & Shapiro
1
(1984)). In my empirical model, the former is captured in the utility function with
advertising interacted with a new brand
1
Advertising and experience can also directly affect a consumer's level of utility. On
the one hand, advertising can directly provide utility and have a prestige effect on all
consumers (Stigler & Becker (1977), Becker & Murphy (1993)). For example, a
consumer may obtain a higher level of satisfaction from wearing a pair of Nike sneakers
than from wearing an unknown brand of similar quality because of the image established
by Nike commercials. On the other hand, experience may also directly change utility
through habit formation if previous purchases of a product increase its current utility (and
choice probability). Allowing for habit formation in the choice process has important
implications for firm marketing strategy. For example, if consumers are habituated to a
product, then the introductory price of a new product may need to be set lower than when
there is only learning to warrant a product switch.
dummy, while the latter is captured by
advertising entering the choice set formulation.
Specifically, to address the awareness problem, I model the choice set as a function
of brand advertising and purchase experience. As a result, choice sets vary across
consumers and evolve over time. Previous research usually assumes a fixed choice set for
all consumers, which is reasonable if the market is in steady state equilibrium with a few
products. However, in many markets for experience goods, due to the large number of
products available and the high rate of new product introduction, one is unlikely to be
aware of all products for sale and has to restrict attention to a subset of products. This
subset forms the consumer's choice set, which evolves over time as information
accumulates through advertising and experience.
1
New brand in this paper means new to a specific consumer, not newly introduced into the market.
2
The consumer choice model is estimated on a panel of AC Nielsen homescan data in
the ready-to-eat (henceforth RTE) cereal market. A survey of 1,402 demographically
balanced U.S. households in the Los Angeles market, the homescan data keeps track of
on-going household purchasing of grocery products from December 1997 to December
2003. It records both the transaction information such as brand, price and quantity and the
household demographic information. In the estimation, the homescan data is
supplemented by two data sets on the supply side: manufacturer advertising data obtained
from TNS Media Intelligence Company, and brand nutritional data collected from
internet.
Empirical specifications with different information assumptions are estimated in the
paper. In the benchmark specification, consumers are assumed to have full information
about brand quality and existence. Then I introduce limited information about brand
quality. Consumers are aware of all brands available in the market but are uncertain about
the quality of unused brands. They form expectation about brand characteristics and infer
quality from advertising. Lastly, consumers are assumed to have limited information
about both brand quality and existence. Their choice sets are heterogeneous depending on
consumption history and brand advertising.
In addition to tests of how different specifications fit the data, estimation results
from different specifications are compared in terms of market share predictions. It is
shown that the model specification with both limited information on brand existence and
brand quality best captures consumer behavior. This model incorporates three sources of
consumer heterogeneity: choice sets, tastes, and experiences. The results suggest that
limited information about brand existence has a large impact on consumer behavior: price
3
sensitivity is much higher among the set of brands that consumers are aware of, implying
that demand is more elastic. I also distinguish different effects of advertising in the
estimation and find that advertising has a significant effect in providing information
about brand existence and signaling brand quality. However, the prestige effect of
advertising is not significant. The results imply that advertising works for new consumers
only. After the first experience with a brand, advertising will not change consumers’
utility level and what matters to the consumers is the purchase history.
Instrumental variables selected on basis of differentiated-products competition models
are applied to the limited information model to obtain consistent coefficient estimates.
The IV estimation does not change the qualitative results of the model. A Hausman test
of the IV coefficients and OLS coefficients also suggests that they are not systematically
different. Finally, some policy experiments are conducted to evaluate a number of firm
marketing strategies in pricing and advertising and to simulate the effect of banning
children-oriented cereal advertising. The consumer-level limited information model
offers new insights for pricing strategies and provides a micro foundation to evaluate the
pulsing strategy in advertising in the RTE cereal market, which supplements the study of
Dubé, Hitsch, and Manchanda (2005). The model can also be used to evaluate nutritional
policy changes. For example, in recent years child obesity has become a serious problem
in America and there have been renewed debates on whether food advertising targeted
toward children should be ban. Using the model I can estimate the effects of such a ban
on the nutritional intakes and expenditures of various demographic groups, which may
provide some empirical evidence in the policy debate.
4
The rest of this paper is organized as follows. The remaining sections of chapter 1
review the literature and discuss the industry background and data sets used for this
study. Chapter 2 specifies and estimates the demand system under different informational
assumptions. Instrumental variables are selected in Chapter 3 and the the IV estimation
algorithm is discussed and the results presented. Policy experiments are conducted in
Chapter 4 on a number of brand marketing strategies.
Section 1.2. Related Literature
The paper is related to several lines of literature. The consumer learning literature
addresses the problem of limited information about product quality. In their pioneer
work, Erdem and Keane (1996) estimate how consumers learn about the cleaning power
of laundry detergents. Both experience and advertising give consumers noisy signals
about the detergent's quality and consumers update their beliefs about quality in a
Bayesian way. Following this study, there have been many studies that model consumer
learning in a Bayesian framework in various markets (Ackerberg (2003), Crawford and
Shum (2005), Chintagunta, Jiang, and Jin (2007), to name a few). However, the
consumer learning literature usually takes the consumer choice set as homogenous. It
does not account for the fact that different consumers may be exposed to different sets of
products due to limited awareness, which is the central research question in the literature
on heterogeneous choice set (also called consideration set in the marketing literature).
There have been very few economic studies that consider heterogeneity in the choice
set. Goeree (2008) presents a model in which advertising influences the set of products
from which consumers choose to purchase. Specifically, the probability that a consumer
5
is informed of a product is a function of the effectiveness of the product's advertising and
the observed consumer characteristics. In the marketing literature, there are relatively
more papers allowing for heterogeneity in consideration set. Brand choice is usually
modeled as a two-stage process: at the first stage consumers identify a subset of brands
which constitute their consideration set. They then choose the brand with the highest
utility at the second stage. Roberts and Lattin (1997) review the theoretical and empirical
marketing studies that develop an individual level model of consideration set and analyze
how marketing mix affects consideration set and consumer choice including Andrews
and Srinivasan (1995) and Allenby and Ginter (1995). They also point out some
directions for future research including dynamics in consideration set, which is captured
in this paper. Swait (2001) assumes that the probability a specific consideration set is
formed is a function of the expected maximum utility from the alternatives in that set.
Mehta, Rajiv, and Srinivasan (2003) formulate the process of consideration set formation
as a trade-off between the expected benefit from including an additional brand and the
additional search cost incurred. Eliaz and Spiegler (2007) study a market model in which
firms use irrelevant alternatives to influence consumers’ consideration set. All these
studies, however, only model one-time purchase in a static setting and do not account for
variation in choices and choice sets over time.
In terms of how to model advertising, this paper learns from both theoretical (as
discussed above) and empirical literature on advertising (Ackerberg (2001, 2003), Anand
and Sharchar (2005), etc). This paper also benefits from the insights of the literature on
RTE cereal market that involves demand estimation (Hausman (1996), Nevo (2001),
Shum (2004), Hitsch (2006), etc). Due to the richness of my data, compared to the
6
previous studies, I am able to include more dynamics in consumer choice, identify
consumer learning from habit formation based on the difference in choice dependence
structure of new and old consumers as in Osbourne (2006), and distinguish different
effects of advertising.
Last but not least, this paper is an extension of the literature on analyzing demand
systems in differentiated product markets (Berry (1994), Berry, Levinsohn and Pakes
(1995, 2004), etc). With household level data, the parameters that vary with individual
households can be identified without any constraints on the distribution of unobserved
brand characteristics. The parameters that do not vary with individuals such as the mean
price coefficient need to be estimated with the market share data and instrumental
variables. This paper applies the estimation method to a limited information environment.
Section 1.3. Industry Background and Data Description
1.3.1. Features of RTE Cereal Market
Readers can refer to Section 2 of Nevo (2001) for a more complete picture of the RTE
cereal industry. For the purpose of this paper, there are several features of the RTE cereal
market that make it a good case study for the empirical work. First, cereal is an
experience good, the attributes of which are not completely known before consumption.
Second, brand entry and exit happen frequently in the RTE cereal market and none of the
national brands has a truly dominant hold on the market, which imposes a considerable
informational burden on consumers.
7
As an example, Table 1 shows the entries and exits of RTE cereal brands
2
from
December 1997 to December 2003 in the Los Angeles market. In the 6-year period, a
total of 62 (46) brands enter (exit)
3
the market, which accounts for about 47.3% (35.1%)
of the total number of brands existing at the end of 1997. Column 2 of Table 2 displays
sales-based market shares of major brands from December 1997 to December 2003. Due
to the existence of a large number of brands, in the table I select the top 50 brands
(together they account for about 79% of the market) and combine the remaining ones into
a composite brand, brand 51. The biggest brand (Brand 1
4
Third, the RTE cereal market is heavily advertised. Advertising over sales ratio for
RTE cereal was 13% in 2001. For well-established brands, the ratio was 18%
) has a market share of 6%
while most brands take up less than 1% of the market.
5
. In
comparison, the average ad over sales ratio across 200 industries was 3.2%
6
On the consumer side, I utilize AC Nielsen Homescan data on RTE cereal products from
December 1997 to December 2003. Tracking 1,402 demographically balanced
households in Los Angeles, the homescan data ties consumer purchase behavior with key
demographic measures. Homescan panelists scan items at home from each shopping trip,
. Heavy
advertising shows that firms believe advertising is effective in promoting sales, thus it is
important to analyze its effects in this market.
1.3. 2. Data Description
2
Brand definition follows the classification on each manufacturer’s website. Different box sizes are treated as the same
brand, while extensions of a brand name are distinct brands. For example, Cheerios, Honey Nut Cheerios, and Berry
Burst Cheerios are three different brands.
3
Brand entry and exit are defined using the AC Nielsen homescan data. A brand entry is observed if the first transaction
of the brand occurs after June 1998. A brand exit is observed if the last transaction of the brand occurs before June 2003.
4
Brand names are not revealed due to a confidential agreement with the data provider.
5
See Nevo (2001), page 311.
6
See Advertising Age, March 1, 2006
8
recording price and quantity purchased as well as the age, income, and other
demographic information of the shopper. The data set keeps track of on-going purchasing
from the same household over time, hence offers insights into households' consumption
habits and dynamics. On average a household stays in the homescan panel for 48 months.
Once a household leaves the panel, a new one that is similar in all demographic measures
is selected to take its place. Table 3 contains definitions and summary statistics of the key
variables in the homescan data.
Using the homescan data I can then summarize the consumption pattern in the RTE
cereal market. On average, a household makes 14 shopping trips with RTE cereal per
year. The households usually have a couple of brands that they purchase repeatedly over
time. Most brands are purchased once and never again (Figure 1 displays a histogram of
the number of times a household purchases a brand). After a brand was first purchased by
a household, the probability of the household repurchasing the brand is 14.1% on the next
shopping trip, 12.9% on the second shopping trip, and about 11% on the following trips
(Figure 2 shows the probability of repurchasing a brand on the shopping trips following
the first try). Both Figure 1 and Figure 2 suggest that learning in the cereal market is
mainly done after one shopping trip. Figure 2 also suggests that conditional on repurchase
after the first experience with a new brand, a household exhibits loyalty to that brand.
On the product side, I obtain advertising data from TNS Media Intelligence, which
tracks advertising expenditures of cereal manufacturers from January 1999 to December
2003. The advertising data covers 278 cereal brands across 11 different media types
7
7
The 11 media types include network TV, cable TV, sport TV, magazines, syndication, national sport radio, network
radio, Sunday magazines, local newspaper, outdoor billboard, and national newspaper. In this paper advertising
particularly refers to cereal manufacturers’ advertising expenditures in these media types. Although retailer advertising
such as retailer deal and store featuring is common in the RTE cereal market, it is not included in the estimation due to
lack of data on retailers.
.
9
The brand advertising expenditures include both national advertising and local
advertising. On average, national advertising accounts for 98.1% of the total advertising
expenditure and is mainly on network TV and cable TV, while local advertising accounts
for 1.9% of the total advertising and is mainly on local newspapers and outdoor
billboards. Average monthly advertising expenditures of the top 50 cereal brands in Los
Angeles are shown in Column 3 of Table 2.
Nutritional data on cereal brands is collected from www.nutritiondata.com
8
, with
nutrient information of 111 brands including calories, sugar, dietary fiber, protein, etc.
The fiber and sugar contents per serving (30 gram) for the 50 top brands are displayed in
Column 4 and Column 5 of Table 2. These two nutrients are selected because there is
little variation in other nutrients across brands.
In all data sets, the characteristics of brand 51, the composite brand, are calculated
as the average of all non top-50 brands.
8
The nutritional information was collected on Sep 10, 2006, from the website. There is no variation of nutrients over
time for the same brand.
10
Chapter 2: Demand Estimation without IV
Section 2.1. Demand
2.1.1. Demand Specification
Abstracting from quantity, the empirical model focuses on consumer brand choice
conditional on purchasing RTE cereal. Multiple brand purchases on one shopping trip are
treated as independent events
9
There are a number of consumers (index by i) choosing from a set of brands (indexed
by j) on different shopping trips (indexed by t). The brand choice is a two-stage process.
. For example, if on a shopping trip a consumer purchased
brands A, B, and C, it is estimated as if she had made three separate transactions with A,
B, and C within the same day. Suppose on the previous shopping trip the consumer
purchased brand A. Then in the transaction with brand A, the past choice dummy would
be set to 1. In the other two transactions, the past choice dummy would be set to 0. On the
next shopping trip, if the consumer purchased any one of brands A, B, and C, her last-
time choice dummy would be set to 1. Apart from not estimating the quantity choice, the
model also does not consider the store choice or the brand choice conditional on visiting
a store as store-level data are not available.
9
The model does not include non-purchase of RTE cereal as the outside good. There are two reasons for doing so: (i)
consumers may choose not to purchase because they have cereal inventory at home, not because the utility of non-
purchase is higher than all cereal brands. Treating non-purchase as the outside good, therefore, will bias the parameter
estimates downward in the utility function. (ii) Consumers choose not to purchase RTE cereals on about 2/3 of all
shopping trips. Including those shopping trips will further add to the already large computation burden. The model also
restricts to brand choice but not quantity choice. Taking quantity into consideration requires tracking consumer’s
stockpiling and inventory, which will greatly complicate the model. About 52% of the purchases are associated with
only one brand. Multiple-brand transactions are treated as independent transactions following Shum (2004). Shum
(2004) fails to find across–brand synergies in demand patterns of RTE cereals that would require modeling the
multiple-brand purchase decision. Readers interested in this can refer to Hendel (1999), Dubé(2004) for examples of
multiple-discrete choice model which allows multiple-unit and multiple-brand purchases on one shopping trip, and
Nevo and Hendel (2006) for an example of consumer inventory model.
11
At the first stage, based on previous purchase experience and brand advertising, the
consumer is informed of a subset of brands that constitute her choice set on that shopping
trip. At the second stage, the consumer chooses a brand from her choice set that
maximizes her expected utility. On a specific shopping trip, the consumer’s information
set includes the quality and characteristics of brands she has purchased before, and prices
and advertising intensities of all brands in her current choice set. Note that brands are
differentiated both horizontally and vertically. The horizontal differentiation is on brand
characteristics such as fiber and sugar contents. The vertical differentiation is on the
brand quality. The quality of a cereal brand is determined by the quality of ingredients
such as grain and rice, and the processing techniques.
Two assumptions are made about the choice set formulation. First, a brand purchased
before would stay in the choice set. In other words, once a consumer tries a brand she
never forgets about it, even though she may dislike it and choose not to purchase it again.
Second, the probability of consumers being informed of a previously unused brand is a
function of the brand's advertising stock. Formally, at time t, the probability that
consumer i has choice set C
it
is:
) 1 ( ) (
? ?
? ?
? =
it it
C k
ikt
C j
ijt it
q q C P (1)
where
ijt
q is the probability of consumer i being informed of brand j at time t, and
2
0 1 2 3 4
2
0 1 2 3 4
exp( )
1 exp( )
jt jt i jt i jt
ijt
jt jt i jt i jt
adv adv inc adv nokid adv
q
adv adv inc adv nokid adv
? ? ? ? ?
? ? ? ? ?
+ + + +
=
+ + + + +
? ?
? ?
,
it
j ? ??
=1,
it
j ? ?? (2)
where
it
E is consumer i’s experience set as of time t, i.e., the set of brands previously
purchased by consumer i up to time t. In the estimation, transactions in the first year of a
12
consumer’s purchase history are used to initialize her experience set. The variable adv
jt
is
a depreciated stock of advertising expenditures for brand j at time t. Specifically,
0
T
jt jt
adv a
?
?
?
?
?
=
=
?
(3)
where
jt
a denotes brand j’s advertising expenditure at time t,
10
2
jt
adv
and ? is the discount
factor. Using stock instead of current flow of advertising allows advertising to have a
lagged effect on consumer choice in the form of good will stock. Specifically, if a brand
entered a consumer’s choice set on the last shopping trip but was not purchased, the
probability of it re-entering the consumer’s current choice set may still be high even if the
brand is not advertised in the current period due to the lagged effects of previous
advertising. The term is included to account for the potential increasing or
decreasing returns to scale of advertising. In equation (2), adv
jt
is also interacted with
household income and whether there is any kid in the household to reflect the
heterogeneity in exposure to advertising for different types of households.
At the second stage, consumer i chooses brand j to maximize expected utility
conditional on her choice set. As is now standard in the discrete choice literature, the
expected utility consumer i obtains from brand j is a function of brand j’s characteristics.
( )
ijt j i i ijt i jt ijt i ijt jt
ijt jt ijt
U E X price adv unused unused adv
pastchoice
? ? ? ? ?
? ? ?
= + + + ? + ? ?
+ • + +
(4)
where X
j
=[fiber sugar]
j
, ?
i
=[?
1i
?
2i
]´, price
ijt
is the price of brand j when consumer i it at
time t. In the AC Nielsen Homescan data, the price of a brand is recorded as the weekly
10
Advertising data is monthly while purchase data is daily. Therefore advertising expenditure at time t means
advertising expenditure in the month that day t belongs to. In the empirical results reported in section 5, ?=0.95 and
T=6. I also estimate the model with ? varying from 0.8 to 0.99 and T from 3 to 12. The robustness checks do not yield
significant qualitative differences.
13
average price of that brand in the store where the brand was sold. In the estimation, I
subtract the manufacturer coupon value and the retailer deal value from the price if a
coupon or a deal is used
11
1 1
2 2
i
i
i i i
i
i
D v
? ?
? ?
? ?
? ?
? ?
( (
( (
( (
( (
= + ?• + ?•
( (
( (
( (
¸ ¸ ¸ ¸
.
Note that ?
i
, ?
i
,
?
i
, and ?
i
are individual coefficients. Specifically,
(5)
where
i
D is a vector of observed household characteristics including household income,
age of female household head, and presence of kids, and v
i
represents a vector of
unobserved household characteristics with standard normal distribution. The variable
unused
ijt
is a dummy which equals 1 if brand j was never purchased by consumer i before
time t. It interacts with adv
jt
, implying that advertising may provide information about the
quality of unused brands. For example, the fact that the cereal manufacturer is able to
spend a huge amount on promoting a brand may signal to consumers that the
manufacturer is in a good financial condition and can therefore product cereals with
better ingredients and better technology. The vector
ijt
pastchoice = [chosen
ijt-1
chosen
ijt-
2,
…, chosen
ijt-?
], where chosen
ijt-?
equals 1 if brand j was chosen ? shopping trips before
t
12
jt
? . The term represents brand j’s characteristics that are observed to the consumer but
not to the researcher at time t. In the case of RTE cereals,
jt
? encapsulates packaging,
11
I am not able to control for coupons and deals systematically as in Nevo and Hendel (2006) as I do not have store
level data and do not observe the availability of coupons and deals to consumers.
12
In the empirical results I use T=6. Compared to previous studies where T is often equal to 1, my results show a more
complete picture of time dependence of consumer choices. I also estimate the model with T=12 and the results are
similar.
14
shelf space, etc. Lastly,
ijt
? is a mean 0 stochastic term independent across time, brands
and consumers.
If brand j has not been purchased before, the consumer holds expectations of its
fiber and sugar contents according to the following rule: E(fiber
j
)=mean(fiber
k
), and
E(sugar
j
)=mean(sugar
k
) ? brand k tried by consumer i before and belonging to the same
segment as brand j (Following Hausman (1996) and Shum (2004), I divide the brands
into family, adult, and kid segments. The segment categorization is shown in column 7 of
Table 2). If the brand has been purchased before, then the consumer knows its
characteristics.
The utility maximization stage generates P(j|C
it
), the conditional probability that
brand j is chosen by consumer i at time t. By the law of conditional probability,
multiplying P(j|C
it
) and P(C
it
) yields P
ijt
, the unconditional probability of consumer i
choosing brand j at time t.
) | ( ) 1 (
it
S C C k
ikt
C j
ijt ijt
C j P q q P
it it it
? ? ?
? ? ?
? = , (6)
where S is the set of all choice sets that include brand j. Matching the choice probabilities
predicted by the model with the observed choices using maximum likelihood will then
give us the parameter estimates.
2.1.2. Discussion
Key features of the demand model merits additional discussion. First, the choice set
formation process addresses the informational problem about product existence. Even
though the choice set is aggregated to contain the 50 biggest national brands and a
15
composite brand, it is still unlikely that consumers would know and compare the utility of
all 51 brands on each purchase occasion. Allowing the choice set to depend on
consumption experience and brand advertising thus brings the model closer to real
consumer behavior. Since the choice set is not observable in the data, I need to simulate
them in the estimation. The details of simulation will be discussed in Section 4. Second,
consumers learn about brand quality after their first experience with the brand, which
captures learning in the RTE cereal market reasonably well as shown in Figure 2. Unlike
some complicated products, consumers usually can attain precise knowledge about a
cereal after consuming one box of it. Third, compared to most previous choice models
where only the past choice is included, choices on the previous 6 shopping trips are
included in the utility function. The coefficients on the set of past choice variables
provide a better description of the temporal dependence of brand choices than when there
is only the last time choice. For example, if a consumer’s brand choice history consists of
A, B, A, B, …, A, B, and only the last time choice dummy is included, then we would
wrongly infer that the consumer only seeks variety and is not subject to habituation. If we
extend the model to have additional past choices, then it is possible to better capture the
potential for habit formation. The distinction is important because if variety-seeking is
dominant, then temporary promotions’ impact on demand would be short-lived. On the
other hand, if consumers are susceptible to habit formation, temporary promotions may
affect sales well into the future. Thus adding more past choice variables not only better
describes time dependence, but also helps managers optimize decisions on marketing
strategies. Fourth, advertising has three roles in the model: (I) affecting consumer choice
set, which represents advertising’s informative effect on brand existence and is captured
16
by the ? parameters; (II) signaling quality of an unused brand, which represents
advertising’s informative effect on brand quality and is captured by the parameter ?; (III)
directly providing utility, which represents advertising’s prestige effect and is captured by
the parameter ?. Identification of the different effects will be discussed below.
In the demand setup, I assume that the consumer is myopic and maximizes her current
period utility. When state dependence (habit formation) is present, a forward-looking
consumer would consider the future effects of her current choice. Forward-looking is
important in many cases, especially in situations where the experimentation cost is high,
examples including choice of durable goods such as computer and digital camera and
decision about whether to accept a job offer or to continue job search. It is less critical in
this situation where consumers choose a frequently purchased product and the cost of
trying a new product is low as consumers can easily switch back to the brands they have
been using. Moreover, previous marketing research shows that consumers spend an
average of 13 seconds in selecting a brand out of the shelf
13
2.1. 3. Identification
. This is a very short time for
a consumer to plan her future choices. Therefore, I tend to believe that the myopic
assumption is reasonable in this application and in the choice process of many other
nondurable goods, for example, beverages and cosmetics.
Intuitive identification strategies are discussed in this subsection. The parameters to be
estimated ? include ?
0
,
?
1
, ?
2
,
?
3
, ?
4
. ?, ?, ?, ?, ?, ???,and ?. Variation of brand
choices corresponding to observed brand characteristics, price, and advertising for all
13
See Cesar Costantino, Ph.D. Dissertation, Chapter 4, “Gone in Thirteen Seconds: Advertising and Search in the
Supermarket”, 2004.
17
consumers is used to identify ?, ?, and ?. A RTE cereal may also have attributes that are
favored by a subgroup of consumers. For example, older consumers may prefer higher
fiber content while kids may prefer higher sugar content. Substitution pattern of
consumers with different demographics when brand characteristics vary helps identify ?.
And heterogeneity in substitution pattern of consumers with the same demographics
helps identify ?. Comparing the average probability of choosing a used brand with the
average probability of choosing an unused brand on each purchase occasion identifies ?.
Comparing the repurchase probability after purchase of a new brand with the repurchase
probability of a previously purchased brand identifies learning from habit formation, and
variation in brand choices over time pins down ?.
In terms of advertising’s different effects, the main identification assumption of the
prestige effect and informative effects is that the prestige effect does not vary by
consumption experiences. As in Ackerberg (2001, 2003), the prestige effect impacts both
experienced and inexperienced consumers in the same way, while the informative effects
only works on consumers who have never tried the brand before. Therefore, variation in
the ratio of choice probability between experienced and inexperienced consumers as
advertising intensity changes can be used to identify the informative effect from the
prestige effect. The two types of informative effect (coefficients ?
versus coefficient ?)
both affect the choice probability of inexperienced consumers. An inexperienced
consumer may choose to try a brand because advertising alerts her attention to the
existence of the brand or because advertising raises the expected quality of this brand.
Ignoring advertising’s prestige effect for the moment, if advertising’s only provides
information about brand existence, consumers will include the brand in their choice set
18
with a higher probability if the brand’s advertising increases. In this case, advertising
does not enter the consumer utility function and hence the marginal effect of advertising
on brand choice probability is independent of the observed brand characteristics. If two
brands with different characteristics increase advertising by the same percentage, their
choice probability will go up by the same percentage. If, furthermore, advertising
provides a signal about brand quality, then consumers have two information channels to
evaluate a brand --- the advertising signal and the other brand characteristics. They would
trade off the information inferred from advertising with the information observed from
the brand characteristics. If the quality perception of the brand is already high based on
the brand characteristics, the marginal effect of advertising on brand choice probability
would be small as there are fewer consumers on the margin who would switch to the
brand due to more exposure to advertising. If, on the other hand, the quality perception of
the brand is relatively low from the brand characteristics, then the marginal effect of a
surge in advertising would be big as more consumers would be convinced to switch.
Therefore, the two types of informative effect can be distinguished by whether the
marginal effect of advertising on brand choice probability depends on the brand
characteristics, as advertising only enters the utility function and interacts with the brand
characteristics if the informative effect about brand quality exists.
To see this mathematically, let us consider a simple example: there are two brands in
the market, one (brand 1) has been established for a long time and the other (brand 2) was
newly introduced. Consumers all know about brand 1, and brand 2 launches an
advertising campaign. Ignoring in this example the returns to scale of advertising in
choice set formation and heterogeneity in coefficients across households, if advertising’s
19
only effect is informing consumers of the existence of brand 2, then the probability that
consumers choose brand 2 is:
0 1 2 2 2
0 1 2 2 2
exp( ) exp( ( ) * )
*
1 exp( ) 1 exp( ( ) * )
adv E X price
P
adv E X price
? ? ? ?
? ? ? ?
+ + + ?
=
+ + + + + ?
(7)
where ? denotes the sum of variables in utility function other than price and observed
brand characteristics. The marginal effect of advertising on the change in choice
probability is:
1
2 0 1 2
ln( )
( ) 1 exp( )
P
adv adv
?
? ?
?
=
? + +
(8)
Note that equation (8) is independent of brand 2’s characteristics.
If advertising also provides information about quality, the choice probability of brand 2
is:
0 1 2 2 2 2
0 1 2 2 2 2
exp( ) exp( ( ) * * )
*
1 exp( ) 1 exp( ( ) * * )
adv E X price adv
P
adv E X price adv
? ? ? ? ?
? ? ? ? ?
+ + + + ?
=
+ + + + + + ?
(9)
The marginal effect of advertising on the change in choice probability is:
1
2 0 1 2 2 2 2
ln( )
( ) 1 exp( ) 1 exp( ( ) * * )
P
adv adv E X price adv
? ?
? ? ? ? ?
?
= +
? + + + + + + ?
(10)
The higher the utility consumers infer from the brand characteristics, the less the need to
rely on the information in advertising. Comparing equation (8) and equation (10), we can
see that whether marginal effect of advertising on choice probability is dependent on the
brand characteristics identifies the informative effect about brand quality from the
informative effect about brand existence. To illustrate this point, figure 3 depicts the
marginal effect of advertising on choice probability. The non-stochastic part of the utility
function other than advertising is denoted by Q. When only the informative effect about
existence exists, the marginal change in choice probability is a declining function of
20
advertising expenditure and is independent of Q. When advertising also signals quality,
the marginal change in choice probability is not only a declining function of advertising,
but also is a function of Q. As Q increases, the marginal change in choice probability
decreases.
2.1.4. Estimation Issues
Before I present and discuss the empirical results of demand estimation, it is appropriate
to discuss the issues that are encountered in the estimation and how I attempt to deal with
them.
(1) Endogeneity
If the manufacturers set up prices and advertising levels according to the consumers’
willingness to pay, then the endogeneity problem may arise as price and advertising
levels could be correlated with unobserved brand characteristics in the utility function.
For example, if the brand manager coordinates media advertising and store promotion
activities, then the unobserved brand characteristics such as shelf space or store featuring
can be correlated to the price and advertising expenditures of the brand. As a result the
coefficients on price and advertising can be overestimated. The best way to deal with the
endogeneity problem is to use instrumental variables. However, the notion of valid
instruments involves supply side specifications and IV estimation in this non-linear
consumer choice model is rather complicated. The focus in this section is on how demand
estimation varies with informational assumptions, thus the IV estimation is deferred to a
later section. In this part, I only include brand fixed effects to control for unobserved
brand characteristics invariant over time. For example, if the government dietary policies
21
promote the health effects of whole grain foods, then the price and advertising levels of
the whole grain cereals may be increased. Whether a cereal is a whole grain is invariant
over time and is absorbed by brand dummies and therefore this type of endogeneity is
controlled for.
(2) Unobserved Consumer Heterogeneity
In a model with lagged dependent variables, state dependence (habit formation) is
observationally equivalent to consumer heterogeneity as individual specific effects can
lead to persistence in choices. State dependence can be exaggerated if unobserved
consumer preferences are mistakenly assumed to be homogeneous. For example, an
overweight consumer can have a high preference for a low sugar cereal and repeatedly
purchase it. If consumer specific preference is not controlled for, repeated purchases will
be captured by the past choice variables and regarded as strong habit. Therefore, it is
important to disentangle the true state dependence from consumer heterogeneity. In the
estimation I use consumer-brand random effects to control for unobserved consumer
heterogeneity. The details of the implementation are provided in Appendix 1.
(3) Choice Set Simulation
To address the informational problem about brand existence I allow for heterogeneity in
consumer choice sets. The underlying choice sets over which consumers make utility
comparison are unobservable to researchers. Moreover, the number of potential choice
sets can be very large — with 51 brands in the market, the number of possible choice sets
is 2
51
. Hence instead of attempting to exhaust all possibilities, I simulate the choice sets.
In the simulation, the probability of a brand being included in a consumer’s choice set is
22
a function of brand advertising and purchase experience according to equation (2). The
details of the choice set simulation process are provided in Appendix 2.
(4) Properties of Estimator
After simulating the choice sets, I can calculate
ijt
P
ˆ
, the simulated choice probability of
each brand for each household on every purchase occasion, and conduct a maximum
simulated likelihood (MSL) estimation. The joint simulated likelihood function is:
Yijt
i t
ijt
p SL ) ( ˆ ) ( ? ?
??
= (11)
where Y
ijt
=1 if consumer i purchases brand j at time t, and Y
ijt
=0 otherwise. The joint
simulated log likelihood is:
)) ( ˆ log( ) ( ? ?
ijt
i t
ijt
p Y SLL
??
= (12)
The MSL estimator
?
? is a vector of parameters that maximize equation (12). Train
(2003) shows that if the number of simulation draws rises faster than square root of
sample size, then the MSL estimator is not only consistent but also efficient
asymptotically equivalent to the maximum likelihood estimator
14
) / , ( ~
ˆ
1 *
N H N
a
?
? ? ?
. Specifically, the MSL
estimator is distributed
(13)
where
*
? is the true parameter value, N is sample size, and
2 *
( )
( )
'
LL
H E
?
? ?
?
? = ?
? ?
is the
information matrix. In practice, I use
'
2
)
ˆ
(
ˆ
? ?
?
? ?
?
=
SLL
H to approximate the value of H and
calculate the estimated variance.
14
Monte-Carlo studies done by Keane (1994) and Geweke et al. (1994) also suggest that MSL has excellent small
sample properties if reasonably good simulators are used.
23
Section 2.2: Results of Demand Estimation without IV
The demand estimation is validated on the panel data in the Los Angeles RTE cereal
market
15
. There are 1,402 households with 69,134 cereal purchases in the LA market
from December 1997 to December 2003. The first 12 months of each household’s
purchase history are used to construct its experience set. As a result, households staying
in the homescan panel for less than 12 months are dropped out of the estimation. The unit
of observation in the estimation is a transaction, i.e., a household-purchase date-brand
combination. Observations with missing values on key estimation variables are dropped
out
16
To guide the choice of variables, I first run a preliminary regression --- multinomial
logit regression with full information. Consumers are assumed to know all brands for sale
and also their quality. The coefficient estimates are shown in Table 5. The interaction
terms of household demographics and brand characteristics that are not significant are
excluded in later regressions. Since the multinomial logit model is subject to
independence of irrelevant alternatives and does not capture the realistic substation
. The regressions start from July 1999 since the earliest advertising data is available
in January 1999 and to calculate the advertising stock we need advertising data six
months ago. The estimation sample consists of 844 households and 37,858 transactions,
which remains unchanged in all specifications. Values of the key variables in the
estimation sample are summarized in Table 4. In all specifications 50 brand dummies are
used.
15
The modeling technique and estimation method in this paper are not specific to a particular geographical market or a
particular experience good. I can apply the model to environments where consumers face the two types of
informational problems, for example, consumer choice of cosmetics, credit cards, health care plans, etc.
16
The missing values do no happen systematically so I am not concerned with a selection bias.
24
patterns, the random coefficient logit model is used instead where a random component is
added in the coefficients of price, advertising, fiber content, and sugar content,
respectively. After the variable selection guided by the multinomial logit, I run three
random coefficient logit models with different informational assumptions. First, I assume
that consumers have full information about both brand quality and brand existence. The
choice set is the same over time and across consumers. The second specification is a
regression with learning about quality information, where consumers are assumed to
know all brands for sale in the market but not the quality of unused brands. In the third
specification, consumers are assumed to have limited information about both the quality
of unused brands and the brand existence. A random coefficient logit with quality
learning and heterogeneous choice sets is estimated. Note that the three specifications are
non-nested. To compare them, ideally I would like to construct a test statistic with a
limiting distribution, so that I can select one specification over the other with some
confidence level. However, our panel data do not satisfy the distributional assumptions of
tests for non-nested models, for example, Vuong (1989) and Chen & Kuan (2002).
Therefore, to assess the goodness of fit I use two methods. First I compare the different
specifications using the Akaike Information Criterion (AIC) and using a measure of
predictive performance developed by Betancourt and Clague (1981). Then I construct a
variable which measures market share prediction errors of the three specifications to see
how well they predict consumer choices.
25
2.2.1. Estimation with Full Information
The benchmark specification is a random coefficient logit regression where consumer
choice sets include all 51 brands and characteristics of all brands are known. The
benchmark model allows me to examine in a simple way how price and advertising affect
demand and have a sense of the temporal dependence of consumer choices. The results
also serve as a baseline for later comparisons.
The parameter estimates of the benchmark specification are reported in column I of
Table 6. Price is negative and significant. The price sensitivity decreases as household
income increases and if the household has no kids. On average, advertising’s prestige
effect is negative and marginally significant. But the prestige effect increases as income
grows and when there is no kid in the household. unused is negative and significant. If we
calculate the odds ratio, we can see that the fact that a brand was never purchased before
decreases the brand choice probability by 75%. However, unused*adv is positive and
significant, suggesting that more advertising signals better quality to inexperienced
consumers. The signaling effect diminishes with income and when the household has no
kid. All six past choice variables are positive and significant. The coefficient of chosen_2
is slightly higher than that of chosen_1, consistent with the fact that consumers usually
switch away from the brand last purchased if the brand was a new try. Both fiber and
sugar are negative and significant. Older consumers without kids prefer more fiber and
less sugar.
26
2.2.2. Estimation with Limited Information about Brand Quality
In the second specification, I run a random coefficient logit regression where all
consumers face the same choice set of 51 brands but they do not know the quality of
brands not bought before. Consumers form expectation of brand characteristics based on
their previous experience with brands in the same segment. They also infer brand quality
from advertising and brand quality can be ascertained after one purchase. The signs of
many coefficients (column II of Table 5) are the same as those of the benchmark
regression, and for most coefficients the magnitudes are comparable. The coefficient on
adv is still negative but no longer significant. The only coefficient that changes sign is the
fiber coefficient, but it is not significant.
The similarity of the coefficients (and the log likelihood) to the benchmark suggests
that limited information about brand quality does not significantly affect consumer
behavior. This is probably due to the nature of the RTE cereal market — the cost of
experimenting with an unused brand is low, thus uncertainty about brand quality may not
be an important factor when consumers decide which brand to buy.
2.2.3. Estimation with Limited Information about Both Brand Quality and Brand
Existence
In the third specification consumers have limited information on both brand quality and
brand existence. They still infer quality of unused brands from experience and
advertising, but their choice sets are now heterogeneous and vary over time. The
probability of having a particular choice set for each consumer on each purchase occasion
follows equations (1) and (2), and the choice set is simulated as described in Appendix 2.
27
The price coefficients (column III of Table 5) suggest that allowing for heterogeneous
choice sets increases price sensitivity. The coefficient on price is significantly bigger than
in the first two scenarios. To get a sense of how the price coefficient translates into price
elasticity, I increase each brand’s price by 1% separately and simulate the consumer
choices based on the parameter estimates. Consumer choices are then aggregated to
calculate the % change in brand market shares resulting from the 1% price change. The
values of own price elasticity for the top 10 brands are reported in Table 7. Compared to
the previous two specifications, the price elasticity in the current one is much larger. The
estimated price elasticities in the third specification are more plausible since their
absolute values are all bigger than 1, which is consistent with the fact that profit-
maximizing firms should be operating at the elastic part of the demand curve.
When consumers have limited information about brand existence, they are not
aware of brands outside their choice set and therefore cannot respond to the price changes
of those brands. If we estimate the model as if consumers had full information about
brand existence, we are in essence imposing that consumers know the price changes of all
brands but choose not to respond to some of them. As a result, the price elasticity is lower
in the “full information” case. The price estimate in the third specification suggests that
consumers are actually much more sensitive to price changes of the brands that they are
aware of. Should the consumers have lower information search costs and know more
brands for sale, they would switch more frequently when price cuts are available.
Therefore, if the information problem about product existence is alleviated, the market
should be more competitive as consumers would be more responsive to price variations.
28
In the utility function, the coefficient on adv is negative but not significant,
implying that advertising’s prestige effect is not important. The coefficient on
unused*adv is positive and insignificant, suggesting that advertising’s informative effect
on brand quality is not significant. In the choice set formation, ?
1
(coefficients on adv in
equation (2)) is positive and significant while ?
4
(coefficients on adv
2
in equation (2)) is
negative and significant. Advertising raises the probability that consumers are informed
of the brand, but this effect exhibits decreasing returns to scale. The coefficient on
adv*inc, ?
2
, is negative and significant, suggesting that the informative effect of
advertising on brand existence decreases with household income. In contrast, the
coefficient on unused*adv*inc in the utility function is positive and significant,
suggesting the informative effect of advertising on brand quality increases with
household income. This makes sense if richer consumers have higher opportunity cost of
time and watch less TV commercials, but once they are alerted to the availability of an
unused brand, they rely more on advertising to obtain the quality information than other
methods of searching. The coefficient on adv*nokid in choic set formation, ?
3
, is positive
but not significant, implying that the effect of advertising does not vary with the presence
of kids. Figure 4 plots the probability of a brand entering a consumer's choice set against
the brand's advertising expenditure evaluated at the mean level of household income and
presence of kids. At the mean of advertising stock ($3.22 million), the probability of a
brand being included in the choice set is 88%. Increasing advertising stock by $1 million
from the mean will result in a probability of 99% that the brand is included in the choice
set. What is consistent over the three specifications is that advertising plays a significant
29
role in providing information to consumers but it does not have a significant prestige
effect.
The past choice variables are still positive and significant, suggesting that
consumers form persistent habit in cereal purchases. Compared to the results obtained
without heterogeneous choice sets, the dependence on the past choice variables falls. The
smaller coefficients on past choices are consistent with the larger (in absolute value)
coefficient on price: consumers are more likely to switch brands in response to price
changes when they rely less on previous experience.
2.2.4. Comparison of Goodness of Fit
To compare the goodness of fit of the three specifications, two measures are computed.
The first measure is the Akaike Information Criterion (AIC), which equals 2*k-2lnL,
where k is the number of parameters and lnL is the log likelihood. The AIC imposes a
penalization on more parameters and the smaller the value of AIC, the better the model
fit. The AIC for the first specification is 212930, for the second one is 201386, and for
the third one is 164516. Hence according to the AIC the third specification fit the data
best.
Second, I compute a measure of predictive performance for discrete choice models
developed by Betancourt and Clague (1981). The measure is based on the idea of
information entropy. It rewards correct predictions when predicted choices are the same
as observed choices and penalizes wrong predictions when predicted choices are different
from observed choices. Moreover, the summary measure scores each choice prediction
by giving it points not only in accordance with whether the prediction is correct but also
30
in a way that reflects the degree of certainty of the prediction
17
51
1
( log )
it ijt ijt
j
E P P
=
= ?
?
. To obtain the measure,
we first need to calculate the entropy for an observation in terms of predicted
probabilities, . Then the amount of information contained in the
predicted probabilities P
ijt
is defined as
max
1 /
it it
I E E = ? , where
max
1 1
log( )
51 51
E = ?
18
1 2
( ) / I I I N = ?
and
represents the maximum amount of uncertainty associated with the data distribution.
Defining a correct prediction as P
ijt
>1/51 when brand j is chosen at time t and P
ijt
< 1/51
when it is not chosen, we can calculate the amount of information contained in the
sample set of predictions as , where I
1
is the sum of information for all
correct predictions, I
2
is the sum of misinformation for all incorrect predictions, and N is
the number of observations. The specification with the highest value of I predicts the
data best
19
I . Applying the formula to our data, I obtain that the for the first specification
is -11.5, for the second one is -13.2, and for the third one is 0.8
20
Next I construct a variable to check how well the three specifications predict
aggregate consumer behavior. Using the parameter estimates, I first predict consumer
brand choice on each shopping occasion, which is the brand that generates the highest
.
Again the third
specification represents the best fit.
17
For a more detailed discussion of the measure, please refer to Section 4.6 of “Capital Utilization: A Theoretical and
Empirical Analysis”, Betancourt R. and C. Clague, Cambridge University Press, 1981. The original measure is defined
for cross-section data but can be easily extended to panel data. When choice sets are simulated, the probabilities used in
the calculation are the mean of simulated probabilities.
18
The formula is
max
1 1
log( ), E
J J
= ?
where J is the number of alternatives. In our case J=51.
19
Betancourt and Clague (1981) continue to develop several measures that capture the amount of information provided
by the introduction of the theoretical model relative to the information contained in the sample. Since my goal is only
to compare the three specifications, I do not calculate the other measures. Interesting readers should refer to their book
for more information.
20
A negative value of I
suggests that the misinformation contained in wrong predictions exceed the information
contained in correct predictions. It can arise for two reasons: (1) there more wrong predictions than correct predictions,
(2) the wrong predictions generate probabilities farther away from 1/51 relative to the correct predictions.
31
utility for the consumer on that shopping trip. Assuming that the consumer would
purchase the same quantity of cereal as in the data, I can then calculate the consumer
expenditure on that shopping trip. Summing up the consumer expenditures for each brand
in the sample period, I get the predicted brand sales and brand market shares. Then I
square the difference of predicted market share and observed market share for each
brand, sum up the squared differences for all brands, and take the squared root of it to
obtain the measure of market share prediction error. As shown in Table 8, the third
specification generates the smallest market share prediction error compared to the first
two.
In summary, introducing limited information about brand existence into the model
improves the data fit and better captures consumer behavior. Therefore, I will base the
following estimation on the limited information specification where consumer choice sets
are heterogeneous.
The estimated parameters have important implications for brand pricing and
advertising strategies. A brand’s pricing decision depends on the price elasticity of
demand. Advertising provides product information and impacts the composition of
consumer choice sets, which can also affect consumer substitution. Therefore, a brand’s
advertising level also depends on the consumers’ sensitivity to changes in advertising.
Given the parameter estimates in Column III of Table 6, I calculate the own and cross
price elasticities for the top 25 brands
21
21
The remaining 25 brands have market shares less than 1% and relatively few observations, therefore the simulation
errors might be big.
, which are reported in Table 9. The formula for
computing the price elasticities are included in Appendix 4. The price elasticities are
evaluated at the median of each brand’s price and the sample market shares.
32
As is previously mentioned, the researchers do not observe some brand characteristics
but market participants do. This leads to inconsistency in price and advertising
coefficients because firm pricing and advertising decisions are most likely related to the
unobserved brand characteristics. A solution to this endogeneity problem involves
instrument variables. BLP show that variables that shift markups are valid instruments for
price in a market of differentiated products. A similar argument also applies to
advertising. Therefore, in Chapter 3, I choose instruments for price and advertising and
re-estimate the demand function.
33
Chapter 3: Instrumental Variable Estimation
Section 3.1: IV Estimation Algorithm
A variety of differentiated-products pricing models predict that price is a function of
marginal cost and a mark-up term. If advertising is also included as a decision variable,
then the models also predict that advertising is a function of marginal cost and
characteristics of other brands.
The firm side competition suggests that the optimal price and advertising levels
depend on the characteristics, prices, and advertising levels of all brands offered. Brands
facing more competition (due to existence of close substitutes in the characteristic space)
will tend to have lower markups relative to brands facing less competition. If brand
characteristics are exogeneous, then the characteristics of other brands are valid
instruments for price and advertising. In the RTE cereal market, characteristics of a brand
will not change once the brand is introduced into the market. Therefore the exogeneity of
brand characteristics is a reasonable assumption. However, the price and advertising
levels of other brands are not valid instruments, since they are correlated with unobserved
brand characteristics through consumer utility maximization. On the other hand, variables
that shift production costs, for example, ingredient prices, wages of manufacturer
workers, are candidates for instruments too. The following section will present the results
of demand estimation using these instruments. Note that the estimation results do not
depend on any assumption on firm competition except that the firms are competing in a
differentiated product market by choosing both price and advertising.
34
In the nonlinear discrete choice model, IV estimation cannot be directly implemented
on the consumer level data. One way to make use of instrument variables involves
aggregating consumer choices and matching predicted brand market shares with observed
brand market shares, then inversing the market shares to get the component of utility
function that does not vary with individuals. This component is a linear function of price,
advertising, and other brand characteristics, and one can estimate this function with IV
for price and advertising.
Formally, let ?
jt
= [fiber
jt
sugar
jt
price
jt
adv
jt
]
22
1
2
i
i
i i
i
i
D v
?
?
?
?
?
(
(
(
= + ?• + ?•
(
(
(
¸ ¸
,
?
i
= , where
1
2
?
?
?
?
?
(
(
(
=
(
(
(
¸ ¸
, D
i
=
[income
i
age
i
nokid
i
]’, and v
i
=
[v
1i
v
2i
v
3i
v
4i
]’.
Then we can write the utility function as
(20)
ijt jt i ijt i ijt jt ijt jt ijt
U unused unused adv pastchoice ? ? ? ? ? ? ? = + ? + ? ? + • + +
Let
jt jt jt
x ? ? ? = + (21)
Note that although ?
,
?
,
? , ?, and ? can be estimated with micro data, we cannot
estimate ? without a further assumption to separate out the effect of ? from the effect of
? on ?. To provide consistent estimates of ? we will use IV for price and advertising.
All parameters are estimated simultaneously. The estimation involves three sets of
moment conditions:
22
Although the true fiber and sugar contents of brands do not vary over time, the expected fiber and sugar contents do.
35
(1)The consumer brand choices, which match the model’s predicted brand choice
probabilities to observed brand choices,
(2)Brand market shares, which match the model’s prediction for brand j’s market share in
year t to its observed market share in year t,
(3)Firms pricing and advertising decisions, which express an orthogonality between the
unobserved characteristics and the instruments.
To be more specific, the estimation algorithm consists of four steps. (i) Given an
initial guess of ?
,
?
,
? , ?, and ? , I first find the values of ?
jt
that equates the predicted
market shares (?
jt
(?, ? , ?
,
? , ?, ? ))
and the observed market shares (S
j
) using the
iteration
1
ln( ) ln( ( ))
h h h
jt jt jt jt
S ? ? ? ?
+
= + ? . The details of calculating ( , , , , , )
jt
? ? ? ? ? ? ?
and the
proof that the above iteration is a contraction mapping are provided in Appendix
3. (ii) Given ?
jt
, I provide random draws for unobserved consumer heterogeneity and for
choice set formation, then use maximum simulated likelihood to obtain estimates of ?,
?
,
? , ?, and ? by matching the observed choices with the predicted choice probabilities.
Note that these estimates do not depend on any distributional assumptions of ?. The
probability of a household with observed characteristics D
i
choosing brand j given
?, ?, ?
,
? , ?, and ? b is given by
51
1
exp( )
Pr( | , , , , , , ) ( ) ( )
exp( )
jt jt i jt ijt i ijt jt ijt
i
v
kt kt i kt ijt i ijt j ijt
k
D v unused unused adv pastchoice
j D f v d v
D v unused unused adv pastchoice
? ? ? ? ? ?
? ? ? ?
? ? ? ? ? ?
=
+ ? + ? + ? + ? ? + •
? ? =
+ ? + ? ? + ? ? + •
?
?
? ? ? ?
? ? ? ?
(22)
The integrals are computed by simulation. (iii) Given the new values of ?
,
?
,
? , ?, and
? , repeat the first two steps until ???
,
?
,
? , ?, and ? converge. (iv) Using the ?
jt
36
obtained in step (iii), construct the moment condition ( | ) 0
jt
E z ? = , where
jt jt jt
? ? ? ? = ? and z represents instrument variables, and estimate ? by minimizing the
sample moments ( )
j j
j
G z ? ? =
?
?
23
?
.
Section 3.2: IV Estimation Results
I implement the estimation algorithm with two sets of instruments. The first set of
instruments includes the fiber and sugar contents of all other brands. The second set of
instruments are the cost shifters, including wage of food workers, wage of advertising
managers, corn price, wheat price, gasoline price, and electricity price. From the website
of Bureau of Labor Statistics, I collect the hourly wage data for food workers (under the
category Food and Tobacco Roasting, Baking, and Drying Machine Operators and
Tenders) and for advertising mangers (under the category Advertising , and Public
Relations Managers) in the Los Angeles – Long Beach MSA from year 1999 to year
2003. Corn price and wheat price are obtained from the Farmdoc project of University of
Illinois. Gasoline and electricity prices are collected from the website of Energy
Information Administration of Department of Energy. These cost measures are interacted
with brand dummies to serve as instruments in the estimation. The estimates
combining both sets of instruments are reported in Column IV of Table 6.
To test the endogeneity of price and advertising, I run an OLS regression of equation
(21) after I obtain ?
jt
in step (iii) and compare the coefficients with the IV estimates. The
Hausman test of the two sets of estimates yields a P value of 0.55, therefore the OLS
23
Berry, Linton and Pakes (2004) show that in this type of BLP model with two sources of errors, the sampling error
and the simulation error, both the number of observations and the number of random draws for simulation need to grow
at rate J
2
for the parameter vector to have an asymptotically normal distribution.
37
estimates are not significantly different from with IV estimates. Hence the endogeneity of
price and advertising does not affect the coefficient estimates much in this application.
Since the price and advertising coefficient estimates without IV are much more precise
than the IV estimates (in the IV estimation only 255 observations (? by brand and by
year) can be used while in the estimations without IV 37,858 transactions are used), I will
conduct policy experiments using the estimates without IV in the following sections.
38
Chapter 4. Policy Experiments
In this chapter I conduct some counterfactual experiments to evaluate some of the brand
marketing strategies and a hypothetical food policy change. In the first two experiments, I
choose brand 28 as an example because it was newly introduced into the market in
January 2003 (Figure 5 summarizes brand 28’ average monthly prices, sales, and
advertising in the estimation sample). Marketing managers are usually concerned with
what price to charge and how to schedule advertising expenditures when a new product is
launched. Therefore looking into the data of brand 28 offers us an opportunity to evaluate
the marketing strategies of a product at the beginning of its life cycle. In the third
experiment, I try to explore the effect of a hypothetical policy change — banning cereal
advertising targeted to children — on consumer choices. A caveat should be born in
mind when we interpret the results of the experiments: I keep the strategies of other firms
unchanged when I simulate the results, thus the optimal responses of rival firms are not
taken into account
24
.
Section 4.1: Pricing Strategy for Brand 28
I first vary brand 28’s price from its observed price by +1%, +5%, -1%, and -5%,
separately. Each time under the new pricing scheme, I calculate every household’s
simulated choices and aggregate them to get brand market shares and sales. The resulting
24
To derive the optimal responses, we need to solve a competitive equilibrium. However, the static Bertrand
equilibrium is not realistic and the dynamic equilibrium is very hard to solve.
39
changes in market share and sales of brand 28 are reported in Table 10. We can see that if
the price is cut down by 5%, the sales improve by 2.3% compared to the sales figure
before the price cut. The market share expands by 6.5%, which more than compensates
for the reduction in price. Therefore, brand 28’s price was too high in general.
To see how the price cut affects different types of consumers, I calculate the changes
in expenditures for different demographic groups after the price drops by 5%. I divide
consumers by household income (high if household income>=$55,000, low otherwise),
by age of female household head (old if age>=32, young otherwise), and by the presence
of kid in the household. The results by demographic groups are shown in Table 11.
Consumers with lower income and having kids respond more to the price cut than their
counterparts, while the response does not vary with age groups.
Next I look at the average (weighted by volume) daily transaction prices of brand 28
at its introductory stage (the first 3 months of year 2003) and see if its sales can be
increased by altering the depth and frequency of the price discounts. The observed daily
transaction price series for brand 28 from Jan 2003 to March 2003 is shown in Figure 6.
The initial price was very high, followed by a period of medium price level. Deep price
discounts happened twice when the price was about 60% of the average level. I consider
an alternative pricing strategy, whereby price is set to be 70% of the average price in this
period for the first week of each of the 3 months and 100% of the average price in the
remaining weeks. The observed prices and the counterfactual prices in this period are
plotted in Figure 4. With the new pricing strategy, I find that brand 28’s market share
goes up by 1.5% and sales go up by 1.2%. High introductory price is not desirable in this
case because consumers are loyal to brands they are already using. To warrant a switch,
40
the utility associated with the new brand needs to be sufficiently high, which could be
achieved by lower introductory price. Consumers who are lured into purchase by the low
introductory prices will then form brand loyalty, thus the brand manager can profit by
setting price low initially and increasing it later.
There may be two reasons why the brand manager would set a high initial price as
observed in the data. On the one hand, higher prices may be used by the brand manager
as a signal for better quality in a market with limited information and hence attracts
consumers with higher willingness to pay. However, in the cereal market, many private
label products have been introduced at low prices and many consumers have come to
realize that lower price does not necessarily affect the quality or taste
25
. Therefore, a high
initial price would limit the consumer demand. On the other hand, the brand manager
may have underestimated the price elasticity. As shown in section 5, if demand is
estimated ignoring that consumers have limited information about product brand
existence, price elasticities would be understated, which could lead the manager to set a
higher than optimal price.
Section 4.2: Advertising Strategy for Brand 28
A major consideration of a brand manager is to determine the best schedule of advertising
expenditures for a certain budget. Conceptually, the manager could choose to do
continuous advertising (i.e., schedule ad expenditure smoothly over all times) or follow a
strategy of pulsing (i.e., advertise in some weeks of the year and not at other times). We
observe in Figure 5 that brand 28’s advertising was relatively smooth over time. In
25
See the article “Eating Well”, New York Times, September 22, 1993.
41
contrast, many advertisers of consumer packaged goods use pulsing strategies. For
example, Dubé, Hitsch, and Manchanda (2005) find that pulsing is the optimal
advertising strategy in the frozen entrée market. Naik , Mantrala , and Sawyer (1998)
develops a model of dynamic advertising that shows that pulsing strategies can generate
greater total awareness than the continuous advertising when the effectiveness of
advertisement varies over time. Specifically, ad effectiveness declines because of
advertising wears out during periods of continuous advertising and it restores during
periods of no advertising. Such dynamics make it worthwhile for advertisers to stop
advertising when ad effectiveness becomes very low and wait for ad quality to restore
before starting the next "burst" again. They also show that the form of the best
advertising spending strategy is pulsing for a major cereal brand.
To mimic the pulsing strategy, I reschedule brand 28’s advertising by equally
dividing the 2003 total ad expenditure into the six odd months, while in the six even
months advertising is set to zero (Figure 7 plots the observed advertising v.s. the
counterfactual pulsing advertising). Then I recalculate consumer choices under the new
advertising strategy. The results show that brand 28’s market share and sales both
increase by 1.9%. The pulsing strategy works better because it can increase the
probability of brand 28 entering the consumer choice set in the first two months after its
introduction. In the observed data, the advertising expenditure for brand 28 in January is
0 while in the pulsing strategy it is 3.3 million. The increase in the advertising
expenditure in January raises the probability of an average consumer (with mean income,
mean age, and mean presence of kid) being aware of brand 28 from almost 0 to 89.7%. In
February the pulsing strategy increases the advertising expenditure of brand 28 from 2.99
42
to 3.14 million and the probability of an average consumer being aware of brand 28 from
78.3% to 84.5%. In the following months an average consumer will be aware of the brand
with probability close to 1 in both strategies. Therefore, under the pulsing strategy, more
consumers are aware of the brand since the beginning and have a higher probability of
choosing it. Some of these consumers become habituated to the brand and hence the
pulsing strategy can increase the overall market share of this brand. I also examine how
different consumer groups respond to the pulsing strategy. Results in Table 12 suggest
that consumers with higher income and kids are more sensitive to the change in
advertising strategy, while age does not matter.
In the advertising data, 98.9% of advertising expenditure is spent on national media such
as network TV, national sport radio, and national newspaper. Therefore, the pulsing
strategy could also increase sales in other local markets without changing the advertising
budget, and could potentially be very profitable.
Section 4.3: Effects of Banning Children-Oriented Cereal Advertising
There have been many public debates on food marketing aimed at children. As early as in
1978, the FTC issued a staff report that concluded that “television advertising for any
product directed to children who are too young to appreciate the selling purpose of, or
otherwise comprehend or evaluate, the advertising is inherently unfair and deceptive”,
and that “it is hard to envision any remedy short of a ban adequate to cure this inherent
unfairness and deceptiveness.” Naturally FTC faced strong opposition from broadcasters,
ad agencies, and food and toy companies. And in 1980 Congress passed the Federal
Trade Commission Improvements Act of 1980 that barred the FTC from issuing industry-
43
wide regulations to stop unfair advertising practices
26
. However, as the childhood obesity
problem becomes more and more of a concern in recent years
27
A study by The Kaiser Family Foundation indicates that children of all age groups are
exposed to a large amount of food ads every day (Table 13). Of all genres on TV, shows
specifically designed for children under 12 have the highest proportion of food
advertising (50% of all ad time). And of all food ads that target children or teens, 28%
are for sugary cereal
, policymakers in
Congress, FTC, and some consumer advocates are calling for restrictions on advertising
to children about candy, sugary cereal, and other junk food.
28
In our data, I do not directly observe how much ad dollars are for marketing toward
children. In order to measure the effects of the policy change, I approximate the ban of
children oriented cereal advertising by eliminating the advertising expenditures for kid
cereal brands while holding other factors unchanged. In the experiment, I replace the ad
stock of these brands with 0, and calculate how the brand market shares change. The total
changes for each brand segment (Family, Adult, Kid) are summarized in Table 15. After
the hypothetical policy change, the total market share of kid brands goes down by about
6%, of which 2% goes to the adult brands and 4% goes to the family brands.
. Table 14 summarizes the sugar and fiber contents of different
types of cereal brands. Not surprisingly the kid brands are highest in sugar and lowest in
fiber. It is, therefore, interesting to see if the cereal TV advertising toward children were
to be banned, what would happen to consumer expenditures and nutritional intakes.
26
See the article “Limiting Food Marketing to Children” on www.cspinet.org/nutritionpolicy.
27
On Wikipedia.com, it is stated that the rate of overweight and obese children in the United Staes is 32% in 2008.
28
See “Food for Thought: Television Food Advertising to Children in the United States”, released by The Kaiser
Family Foundation, March 28, 2007.
44
Then I look at how the policy change affects the nutrition intakes and expenditures of
different consumer groups. The results are summarized in Table 16. Overall after the ban
of children oriented cereal advertising, consumers will consume more fiber and less sugar,
which is better for their health. Consumers who are younger, with lower income and with
kids reduce their sugar intake and increase their fiber intake more than their counterparts.
Therefore, the policy change seems to have more effect on the “right” group of
consumers. In the meantime, after the ban consumers of all demographic groups will
have to increase their expenditures after the policy change as they consume more adult
and family cereals, which are more expensive than kid cereals.
Section 4.4: Concluding Remarks
This paper considers limited information on both product existence and product quality in
a dynamic model of consumer choice in an experience good market. On each purchase
occasion, a consumer first forms a choice set depending on her purchase experience and
brand advertising. Conditional on the choice set, she then chooses the brand that
maximizes her expected utility. The empirical model is estimated on a rich panel of
household purchase data in the RTE cereal market. The results suggest that limited
information about product existence leads to larger estimates on price elasticity.
Advertising has a significant effect informing consumers of brand existence and signaling
product quality, while its prestige effect is not significant. I also find that conditional on
repurchase after the first experience with a brand, consumers form strong habits. The
counterfactual experiments show that the observed brand marketing strategies are not
always optimal: managers can increase sales by resetting price, rescheduling price
45
discounts, or altering their advertising strategies. An evaluation of a hypothetical policy
change – ban on cereal advertising toward children – suggests that the policy could direct
consumers to healthier diet.
The results of the experiments should be taken with caution though. In all of the
experiments I do not consider the competitive responses of other firms to the change in
brand strategies. Neither do I account for the fact that firms may change the way they
promote kid brands once the government regulation comes into play. To control for these
responses, I will need to solve the firm profit maximization problem. In a model with
brand loyalty on the consumer side, the firm side problem should involve dynamic
optimization: firms not only consider the effect of pricing and advertising on current
consumer choices, but also the effect on future demand and future profits. However, the
dynamic optimization problem with multiple firms each with multiple brands is
extremely hard to solve and thus left for future research. In addition, many brand
marketing strategies are decided by manufacturers and retailers together. This paper only
focuses on the role of manufacturers. A vertical competition model will be needed to
analyze the role of retailers.
46
Appendices
Appendix 1. Controlling for Unobserved Consumer Heterogeneity
I use introduce consumer-brand random effects to capture the unobserved consumer
heterogeneity in brand preferences. Specifically, the utility function can be written as:
ijt ijt ij ijt
U Z ? ? = •?+ +
where Z
ijt
represents the vector of explanatory variables, ? represents the vector of
coefficients corresponding to Z
ijt
, and
ij
? represents consumer i's unobserved preference
for brand j, which is independent from
ijt
Z and
ijt
? .
Let
ij ij j
? µ ? = + .
2
(0, )
ij ij
N µ ? ? , and ( )
j ij
E ? ? = is a constant. Assuming
ijt
? has a
Generalized extreme value distribution, then we can write the probability of consumer i
choosing j conditional on
1 i
µ ,
2 i
µ , …,
51 i
µ , and choice set
it
C as:
51 51
1 2 51 51
51 51
1
exp(( ) )
( | , ,..., , )
exp(( ) )
ijt i t ij j
i i i it
ilt i t il l
l
Z Z
P j C
Z Z
µ ? ?
µ µ µ
µ ? ?
=
? •?+ + ?
=
? •?+ + ?
?
51
1
exp( )
exp( )
ijt ij j
ilt il l
l
z
z
µ ?
µ ?
=
•?+ +
=
•?+ +
?
where for the second equal sign we use
51 ijt ijt i t
z Z Z = ? and
51 j j
? ? ? = ? .
( | )
it
p j C is equal to
1 2 51
( | , ,..., , )
i i i it
P j C µ µ µ integrated over the marginal
distribution of the
ij
µ ’s. Specifically, it is equal to
1 2 51 1 2 51 51
1
exp( )
... ( ) ( )... ( ) ...
exp( )
ijt ij j
i i i i i i
ilt il l
l
z
f f f d d d
z
µ ?
µ µ µ µ µ µ
µ ?
? ? ?
?? ?? ??
=
•?+ +
•?+ +
? ? ?
?
47
It is hard to compute ( | )
it
p j C analytically and I simulate it by taking S draws
from the distribution of
ij
µ , for all j. The simulator for ( | )
it
p j C is:
?
?
=
=
+ + ? •
+ + ? •
=
S
s
l
l
s
il ilt
j
s
ij ijt
it
z
z
S
C j p
1
51
1
) exp(
) exp(
1
) | ( ˆ
? µ
? µ
To reduce the number of parameters to be estimated, I allow
j
? to vary across
brand segment, and
2
ij
? to vary across both brand segment and whether the household has
kids or not. There are a total of eight parameters to estimate for unobserved consumer-
brand preferences, among which six are scale parameters:
2 2 2 2 2 2
, , , , ,
FK FN AK AN KK KN
? ? ? ? ? ? ,
where the first subscript denotes whether the brand belongs to family, adult or kid
segment, and the second subscript denotes whether there is any kid in the household; two
are location parameters:
A
? and
K
? , where the subscript denotes whether the brand
belongs to adult or kid segment.
F
? is normalized to zero.
Appendix 2. Choice Set Simulation Details
In the simulation, I assume that choice set is a function of brand advertising and purchase
experience as shown in equation (1) and equation (2). The specific choice set simulation
process is outlined as follows.
Step 1. Calculate
ijt
q (?) for each consumer, each brand, and each time, where ?=(?
0,
?
1,
?
2
).
Step 2. For each consumer-time-brand combination, draw a random number
r
ijt
u from the
uniform distribution between 0 and 1.
48
Step 3. If
r
ijt
u <
ijt
q , then brand j is included in consumer i's choice set at time t. Otherwise
it is not. This defines the choice set in the rth simulation
r
it
C .
After simulating the choice set, I can calculate simulated brand choice probabilities for
each consumer.
Step 4. Calculate ( | )
r
it
P j C , consumer i's probability of choosing brand j conditional on
r
it
C
.
(The formula for calculating ( | )
r
it
P j C
depends on the distributional assumption on the
error term in the utility function).
Step 5. Calculate (1 ) ( | )
r r
it it
r r
ijt ijt ikt it
j C k C
p q q P j C
? ?
= ? ×
? ?
, consumer i’s unconditional
probability of choosing brand j at time t in the rth simulation.
Step 6. Draw the random numbers
r
ijt
u repeatedly for R times, each time repeat steps 2-5.
Step 7. Calculate the simulated choice probability
?
=
=
R
r
r
ijt ijt
p
R
p
1
1
ˆ .
Appendix 3. Contraction Mapping Details
In the instrumental variable estimation, we need to find the ? that make predicted market
shares based on the model equal to the observed market shares. Given an initial guess of
?, ?, and ? , the predicted market share for brand j, ( , , , , , )
h
j
? ? ? ? ? ? ? , is calculates as
follows.
First, based on advertising data and household characteristics, simulate choice sets for
each consumer on each shopping occasion.
49
Second, given ?, ?, ? , ?, ?, and ?, a consumer compares the utility levels of all brands in
her choice set on the shopping occasion and chooses the one that yields the highest
utility.
Third, sum up consumer brand choices in a year to get predicted brand market shares.
To obtain the values of ? that solves ( , , , , , )
h
j
? ? ? ? ? ? ? =S
j
, we use the iteration
1
ln( ) ln( ( , , , , , ))
h h h
j j j j
S ? ? ? ? ? ? ?
+
= + ? ? ? . The proof that the iteration is a contraction
mapping follows Goeree (2007).
Define ( ) ln( ) ln( ( , , , , , ))
h
j j j j
f S ? ? ? ? ? ? ? = + ? ? ? . To show that f is a contraction
mapping, we need to show that ?j and m, ( ) / 0
j m
f ? ? ? ? ? , and
1
( ) / 1
J
j m
m
f ? ?
=
? ? <
?
.
We can write (1 ) ( | ) ( )
i j i i
j ilt ikt i
C l C k C
q q P j C f v dv ?
?? ? ?
= ?
? ? ?
?
,
where , and ?
j
denotes the set of choice sets that include j.
1
( ) / (1 ) ( | ) ( )
i j i i
m
j m ilt ikt i j
C l C k C j
f q q P j C Q f v dv ? ?
?
?? ? ?
? ? = ?
? ? ?
?
,
where
51
1
exp( )
( | ) ( ) ( )
exp( )
j j i j ij i ij j ij
i
v
k k i k ij i ij j ij
k
D v unused unused adv pastchoice
p j C f v d v
D v unused unused adv pastchoice
? ? ? ? ? ?
? ? ? ? ? ?
=
+ ? + ? + ? + ? ? + •
=
+ ? + ? ? + ? ? + •
?
?
? ? ? ?
? ? ? ?
exp( )
,
exp( )
0,
i
m m m i m im i im m im
j j
l l i l il i il l il
l C
j
D v unused unused adv pastchoice
Q if m
D v unused unused adv pastchoice
if m
? ? ? ? ? ?
? ? ? ? ? ?
?
+ ? + ? + ? + ? ? + •
= ??
+ ? + ? + ? + ? ? + •
= ??
?
? ? ? ?
? ? ? ?
Note that for m=j, ( | )
m
j i
Q P j C =
Since all elements in the integral are non-negative, we have ( ) / 0
j m
f ? ? ? ? ? .
Moreover,
, 51
1
j
m
j
m m
Q
?? ?
<
?
, therefore
, 51
( ) / 1
j
j m
m m
f ? ?
?? ?
? ? <
?
is satisfied.
50
Appendix 4. Price Elasticity Calculation
Suppressing the time subscript, we can write the consumer utility function as
ij i j j i ij
U p ? ? ?
?
= + ? + ?
where
3 33 3 i i
D v ? ? = + ? + ? ? ? , ?
j
represents the vector of variables other than price, and
?
?i
the vector of coefficients for ?
j
.
The formula for price elasticity is given by
1
1
1
ˆ ˆ (1 ) ( ) ,
1
ˆ ˆ ( ) ,
N
j
i ij ij
i
j
j
k
jk
N
k j k
i ij ik
i
j
p
p p f v dv j k
s N
s
p
p s p
p p f v dv j k
s N
?
?
?
=
=
¦
? =
¦
?
¦
= ? =
´
?
¦
? ?
¦
¹
?
?
?
?
where p
ij
represents the probability of consumer i choosing brand j.
In the estimation, I take NR random draws of v from f(v) to get ?
i
and compute ?
jk
using
the formula
1 1
1 1
1
ˆ ˆ (1 ),
*
ˆ
1
ˆ ˆ ,
*
i
i
N NR
j nr
ij ij
i nr
j
jk
N NR
nr k
ij ik
i nr
j
p
p p j k
s N NR
p
p p j k
s N NR
?
?
?
= =
= =
¦
? =
¦
¦
=
´
¦
? ?
¦
¹
??
??
51
Figure 1.
0
5
.
0
e
+
0
4
1
.
0
e
+
0
5
1
.
5
e
+
0
5
2
.
0
e
+
0
5
F
r
e
q
u
e
n
c
y
0 100 200 300
#of times a brand was purchased
#of Times a Brand was Purchased by a Household
Figure 2.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10 11 12
# of shopping trips since 1st purchase
Data Source: Neilsen Homescan Data 1997.12.to 2003.12.in L.A.
% of repurchasing after trying a new brand
52
Figure 3.
1 2 3 4 5 6 7 8 9 10
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
advertising expenditure
l
o
g
(
c
h
o
i
c
e
p
r
o
a
b
i
l
i
t
y
)
Effect of Advertising on Marginal Change in Choice Probability
information about existence
information about quality (Q=1)
information about quality (Q=2)
Figure 4.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Advertising Stock $M
P
r
o
b
a
b
i
l
i
t
y
Probability of a Brand Beiing Included in the Choice Set
53
Figure 5.
0
1
0
2
0
3
0
1 2 3 4 5 6 7 8 9 10 11 12
Month
advertising(m) avg monthly price(c/oz)
sales(50 dollars)
Source: TNS Media Intelligence and Neilsen Homescan,LA 2003.1-2003.12
Averge Monthly Advertising, Price, and Sales for Brand 28
Figure 6.
1
5
2
0
2
5
3
0
3
5
4
0
p
r
i
c
e
(
c
e
n
t
/
o
z
)
20 40 60 80 100
day
observed price counterfactual price
Source: Neilsen Homescan Data in L.A. 2003.1 to 2003.3
Average Daily Transaction Price for Brand 28
54
Figure 7.
0
1
2
3
4
a
d
v
e
r
t
i
s
i
n
g
(
m
)
0 5 10 15
Month
observed advertising counterfactual advertising
Monthly Advertisng for Brand 28
55
Table 1. Brand Entry and Exit
Enter Year 1998 1999 2000 2001 2002 Remaining Total
1998 & before 5 3 3 10 7 103 131
1999 0 1 4 1 2 10 18
2000 0 0 0 1 3 3 7
2001 0 0 0 1 3 8 12
2002 0 0 0 0 10 30 12
2003 0 0 0 0 0 13 13
Total 5 4 7 13 17 147 193
Data Source: Neilsen Homescan Data 1997.12. to 2003.12. in Los Angeles Market.
A brand entry is observed if the first transaction with the brand occurred after
1998.6. A brand exit is observed if the last transaction with the brand occurred
before 2003.7.
Exit Year
56
Table 2. Brand Summary Statistics
Brand
Number
Sample
Market
Share
1
(%)
Average
Transaction
Price
(cent/oz)
Average
Monthly
Advertising
($K)
Fiber
Content
(% Daily
Value per
30g)
Sugar
Content(%
Daily Value
per 30g)
Segment
2
1 5.73 17.22 1718.89 14.00 1.00 Family
2 4.51 18.44 1977.76 6.45 4.59 Family
6 4.45 12.26 2036.62 11.25 6.23 Adult
11 4.07 14.01 1045.85 5.90 6.39 Adult
8 3.99 11.95 1667.88 2.42 9.68 Family
7 3.69 11.96 1445.58 11.49 10.37 Family
3 3.56 15.85 1701.03 7.00 11.00 Family
12 2.88 14.98 406.50 4.12 12.39 Kid
4 2.71 17.74 785.01 5.00 10.00 Kid
16 2.50 13.71 319.99 3.56 6.71 Family
20 2.49 11.43 1623.61 10.34 4.40 Adult
9 2.38 18.22 878.28 0.03 7.91 Family
10 2.36 22.81 2143.30 9.15 5.21 Adult
15 2.35 18.66 437.65 6.00 13.00 Kid
13 2.09 13.80 1377.95 13.91 1.86 Adult
14 1.92 16.38 634.15 2.92 12.46 Kid
17 1.62 14.07 1293.78 7.50 7.03 Kid
23 1.62 9.60 5.65 14.75 8.64 Family
21 1.56 16.77 604.60 0.97 14.52 Family
18 1.55 15.61 698.44 8.30 8.61 Family
19 1.55 16.80 1243.06 1.59 13.39 Kid
38 1.48 17.48 435.98 4.00 13.00 Kid
5 1.39 20.91 1611.56 7.48 6.98 Adult
24 1.29 15.77 459.00 4.00 15.00 Kid
22 1.26 21.80 56.11 1.00 6.00 Adult
42 1.09 16.88 739.14 7.94 8.02 Adult
30 1.06 18.64 379.89 3.00 14.00 Kid
26 0.76 19.15 72.82 5.00 13.00 Family
25 0.72 19.11 423.71 4.00 11.00 Kid
47 0.72 15.08 746.76 3.10 11.38 Kid
46 0.71 17.01 87.48 8.69 5.88 Family
39 0.66 18.01 3.26 49.00 4.33 Adult
43 0.63 18.19 108.85 27.00 5.00 Adult
50 0.59 15.38 157.45 8.57 4.82 Adult
48 0.57 18.91 303.66 6.67 12.22 Kid
49 0.56 19.91 280.83 6.32 7.89 Family
27 0.54 19.55 0.00 7.09 7.64 Adult
40 0.52 15.64 102.95 1.94 10.65 Kid
45 0.46 21.43 177.74 4.36 6.00 Family
29 0.46 20.01 0.00 6.00 9.27 Family
31 0.44 23.30 208.99 2.00 13.00 Kid
37 0.43 21.49 381.66 0.00 12.00 Family
28 0.41 24.39 1653.81 12.00 10.00 Family
33 0.41 16.35 13.43 4.00 13.00 Family
44 0.35 16.95 229.33 8.13 6.10 Family
32 0.35 25.79 6.58 58.00 0.00 Adult
34 0.33 24.19 1.68 11.00 6.00 Family
57
Brand
Number
Sample
Market
Share
1
(%)
Average
Transaction
Price
(cent/oz)
Average
Monthly
Advertising
($K)
Fiber
Content
(% Daily
Value per
30g)
Sugar
Content(%
Daily Value
per 30g)
Segment
2
41 0.31 14.64 0.00 4.44 16.67 Kid
35 0.29 17.64 62.32 9.00 9.27 Adult
36 0.25 17.39 0.00 10.91 8.73 Adult
51 21.41 14.90 47.44 8.83 8.00 Family
Data Source: Columns II&III-AC Neilsen Homescan Data 1997.12 to 2003.12, Column IV-TNS Media Intelligen
Data Jan 1999 to Dec 2003, Columns V & VI - www.nutritiondata.com
1.Sample market is the Los Angeles Market from Dec 1997 to Dec 2003.
2.Brand segment categorization is based on each brand's description on manufacturer's website.
3. Characteristics of the 51th brand are computed as the average of the non top 50 brands.
58
Table 3: Summary Statistics of Homescan Data
Variable Definition NumObs Mean Std. Dev. Min Max
size household size 1402 3.25 1.53 1 9
inc household income ($K) 1402 57.11 29.58 2.5 125
age age of female household head 1402 48.86 12.99 20 70
nokid =1 if no kid in the household 1402 0.55 0.50 0 1
price transaction price (cent/oz) 69134 17.84 4.73 0 797.44
Data Source:Neilsen Homescan Data 1997.12. to 2003.12 in Los Angeles Market
59
Table 4. Summary of Variables in Estimation Sample
1
Variable Definition Mean Stdev Min Max
chosen 1{brand is chosen in current transaction} 0.02 0.14 0 1
price transaction price (cent/oz) 17.84 4.75 0 797.44
price*inc transcation price(cent/oz)*household income($K) 1031.84 629.38 0 13000
price*nokid transcation price(cent/oz)*1{household has nokid} 892.50 348.03 0 7400
adv stock of advertising expenditure ($M) 3.22 4.02 0 22.30
adv*inc advertising stock($M)*household income($K) 188.47 281.56 0 2787.46
adv*nokid advertising stock($M)*1{household has nokid} 1.95 3.51 0 22.30
unused 1{brand not purchased previously} 0.11 0.32 0 1
unused*adv 1{brand not purchased previously}*adv 1.82 3.29 0 22.30
unused*adv*inc 1{brand not purchased previously}*adv*household income($K) 106.57 223.03 0 2787.46
unused*adv*nokid 1{brand not purchased previously}*adv*1{household has nokid} 1.21 2.79 0 22.30
chosen_1 1{brand chosen on last shopping trip} 0.03 0.17 0 1
chosen_2 1{brand chosen 2 shopping trips ago} 0.03 0.17 0 1
chosen_3 1{brand chosen 3 shopping trips ago} 0.03 0.17 0 1
chosen_4 1{brand chosen 4 shopping trips ago} 0.03 0.17 0 1
chosen_5 1{brand chosen 5 shopping trips ago} 0.03 0.17 0 1
chosen_6 1{brand chosen 6 shopping trips ago} 0.03 0.17 0 1
sugar sugar content(% daily value per 30g) 8.81 3.73 0 16.67
sugar*age sugar content(% daily value per 30g)*age of female head 439.51 227.30 0 1166.67
sugar*nokid sugar content(% daily value per 30g)* 1{household has no kid} 5.22 5.19 0 16.67
fiber fiber content(% daily value per 30g) 8.58 10.28 0 58
fiber*age fiber content(% daily value per 30g)*age of female head 428.18 544.41 0 4060
fiber*nokid fiber content(% daily value per 30g)* 1{household has no kid} 5.08 8.96 0 58
adult*size 1{brand is adult brand}*household size 0.98 1.72 0 9
adult*inc 1{brand is adult brand}*household income($K) 17.25 30.98 0 125
adult*age 1{brand is adult brand}*age of female head 14.69 23.51 0 70
adult*nokid 1{brand is adult brand}*1{household has no kid} 0.16 0.37 0 1
kid*size 1{brand is kid brand}*household size 0.98 1.72 0 9
kid*inc 1{brand is kid brand}*household income($K) 17.22 30.95 0 125
kid*age 1{brand is kid brand}*age of female head 14.67 23.50 0 70
kid*nokid 1{brand is kid brand}*1{household has no kid} 0.16 0.37 0 1
1.Estimation sample consists of 890 households with 42396 transactions from 1999.1 to 2003.12 in LA market
60
Table 5. Preliminary Regression Results
Variable Coefficient
price 0.014**
(0.006)
price*inc 0.000***
(0.000)
price*age -0.000
(0.000)
price*nokid 0.012***
(0.003)
adv -0.004
(0.005)
adv*inc 0.000**
(0.000)
adv*age -0.000
(0.000)
adv*nokid -0.000
(0.003)
unused -1.802***
(0.018)
unused*adv 0.698***
(0.030)
unused*adv*inc -0.001**
(0.000)
unused*adv*age -0.001
(0.001)
unused*adv*nokid 0.037**
(0.015)
chosen_1 0.563***
(0.015)
chosen_2 0.589***
(0.015)
chosen_3 0.565***
(0.015)
chosen_4 0.503***
(0.015)
chosen_5 0.488***
(0.015)
chosen_6 0.491***
(0.015)
fiber -0.132***
(0.006)
fiber*age 0.000***
(0.000)
fiber*nokid 0.026***
(0.003)
61
sugar -0.136***
(0.013)
sugar*age -0.002***
(0.000)
sugar*nokid -0.033**
(0.006)
62
Table 6: Estimation Results
I II III IV
RCL RCL+Learning RCL+Learning+HCS
1
IV Estimation
price -0.164*** -0.187*** -0.233*** -0.368***
(0.003) (0.054) (0.009) (0.051)
price*inc 0.002*** 0.001** 0.001*** 0.001***
(0.000) (0.001) (0.000) (0.000)
price*nokid 0.127*** 0.129*** 0.118*** 0.014***
(0.003) (0.007) (0.007) (0.005)
adv -0.007* -0.018 -0.023 0.274
(0.004) (0.065) (0.050) (1.731)
adv*inc 0.001** 0.000 0.001*** 0.000***
(0.000) (0.001) (0.000) (0.000)
adv*nokid 0.073*** 0.009 0.073*** -0.003
(0.003) (0.006) (0.003) (0.003)
unused -1.874*** -2.071*** -1.800** -1.801***
(0.021) (0.017) (0.043) (0.091)
unused*adv 0.335*** 0.083*** 0.286*** 0.696***
(0.006) (0.010) (0.023) (0.041)
unused*adv*inc -0.004** -0.000 0.027*** 0.028***
(0.000) (0.001) (0.001) (0.001)
unused*adv*nokid -0.155*** -0.041 -0.019** -0.035
(0.005) (0.030) (0.009) (0.083)
chosen 1 0.614*** 0.649*** 0.578*** 0.563***
(0.017) (0.018) (0.018) (0.021)
chosen 2 0.638*** 0.629*** 0.603*** 0.590***
(0.017) (0.018) (0.018) (0.021)
chosen 3 0.612*** 0.574*** 0.577*** 0.565***
(0.017) (0.018) (0.019) (0.019)
chosen 4 0.548*** 0.504*** 0.514*** 0.503***
(0.017) (0.018) (0.019) (0.019)
chosen 5 0.531*** 0.466*** 0.497*** 0.488***
(0.017) (0.019) (0.019) (0.019)
chosen 6 0.534*** 0.468*** 0.501*** 0.491***
(0.017) (0.019) (0.019) (0.019)
fiber -0.112*** 0.014 -0.068*** 4.466***
(0.005) (0.046) (0.011) (0.853)
fiber*age 0.001*** 0.001 0.000 0.001***
(0.000) (0.001) (0.000) (0.000)
fiber*nokid 0.018*** 0.037*** 0.047*** 0.026***
(0.003) (0.011) (0.005) (0.004)
sugar -0.083*** -0.060 -0.099*** 1.996
(0.009) (0.059) (0.020) (2.293)
63
I II III IV
RCL RCL+Learning
RCL+Learning+HCS
1
IV Estimation
sugar*age 0.001 -0.001 0.000 -0.001***
(0.001) (0.003) (0.000) (0.000)
sugar*nokid -0.062** -0.007 -0.066*** -0.032***
(0.005) (0.006) (0.007) (0.005)
?
0
-7.350*** -7.350***
(0.005) (0.001)
?
1
2.996*** 2.996***
(0.001) (0.001)
?
2
-0.002*** -0.002***
(0.000) (0.000)
?
3
0.001 0.001***
(0.001) (0.000)
?
4
-0.001*** -0.001***
(0.000) (0.000)
?
11
0.187*** 0.081*** 0.512*** 0.512***
(0.001) (0.023) (0.007) (0.002)
?
22
0.000 0.000 0.005 0.005
(0.003) (0.094) (0.014) (0.004)
?
33
0.036*** 0.018 0.004 0.006**
(0.001) (0.033) (0.005) (0.003)
?
44
0.000 0.000 0.002 0.010***
(0.004) (0.090) (0.009) (0.003)
log likelihood -106389 -100617 -82177
Standard errors in parentheses, brand dummies not reported.
* significant at 10%; ** significant at 5%; ***significant at 1%
1. RCL denotes random coefficient logit. HCS denotes heterogeneous choice set. Number of draws for choice set simulation = 20
64
Table 7: Predicted Market Shares
Brand Number
Sample
Market
Share (%)
RCL
RCL+Quality
Learning
RCL+Quality
Learning+HCS
1 6.03 8.04 7.42 6.64
2 5.07 3.96 3.28 3.72
3 3.63 1.62 1.94 2.38
4 2.84 2.04 2.29 2.57
5 1.56 0.76 0.75 0.92
6 4.67 3.36 4.80 4.18
7 4.04 2.19 3.53 3.44
8 4.11 6.21 3.42 3.52
9 2.32 3.85 1.00 1.13
10 2.75 3.35 2.18 2.25
11 4.56 7.25 5.20 4.26
12 2.61 1.47 2.12 2.91
13 2.12 0.97 0.94 1.64
14 1.82 1.03 1.27 2.42
15 2.47 1.27 2.34 2.97
16 2.32 3.28 1.42 1.98
17 1.49 0.42 0.39 1.62
18 1.78 1.02 1.10 1.12
19 1.47 0.87 1.18 1.43
20 2.84 1.25 1.62 2.03
21 1.50 0.31 0.43 0.56
22 1.19 0.84 0.19 0.54
23 1.72 0.23 0.48 0.65
24 1.25 0.18 0.60 0.99
25 0.76 0.14 0.15 0.25
26 0.93 0.20 0.31 0.42
27 0.53 0.18 0.17 0.18
28 0.51 0.23 0.71 0.41
29 0.46 0.08 0.09 0.13
Brand Number
Sample
Market
Share (%)
RCL
RCL+Quality
Learning
RCL+Quality
Learning+HCS
30 0.97 0.14 0.20 0.83
31 0.44 0.04 0.03 0.14
32 0.36 0.00 0.27 0.29
33 0.37 0.00 0.02 0.00
34 0.28 0.01 0.11 0.01
35 0.26 0.00 0.00 0.02
36 0.23 0.00 0.01 0.00
37 0.44 0.08 0.06 0.05
38 1.44 0.31 0.45 0.98
39 0.83 0.00 0.59 0.62
40 0.38 0.02 0.02 0.04
41 0.30 0.01 0.07 0.08
42 1.09 0.21 0.35 0.88
43 0.62 0.07 0.27 0.34
44 0.26 0.01 0.01 0.01
45 0.50 0.23 0.09 0.24
65
46 0.75 0.18 0.23 0.36
47 0.61 0.10 0.08 0.19
48 0.53 0.04 0.14 0.17
49 0.49 0.12 0.10 0.24
50 0.66 0.04 0.03 0.05
Prediction Error 0 7.26 5.29 3.81
Data: estimation sample for all regressions
Prediction Error = Squareroot of sum of squared deviations of predicted market
share to sample markte share
66
Table 8. Own Price Elasticity for Top 10 Brands
Brand RCL
RCL &
Learning
RCL &
Learning &
HCS
1 -1.01 -1.27 -2.32
2 -1.27 -0.61 -2.63
6 -0.82 -0.68 -1.71
11 -1.27 -0.65 -1.39
8 -0.98 -0.74 -2.23
7 -0.68 -0.79 -1.66
3 -1.24 -1.04 -1.46
12 -0.98 -1.48 -2.82
4 -1.13 -1.63 -2.42
16 -1.42 -1.59 -2.57
67
Table 9. Estimated Price Elasticities for Top 25 Brands Based on IV Estimation
Brand # 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 -2.428 0.367 0.146 0.010 0.099 0.338 0.220 0.315 0.003 0.673 0.034 0.002 0.100 0.001
2 0.136 -2.768 0.265 0.018 0.178 0.612 0.398 0.569 0.005 1.217 0.062 0.003 0.180 0.003
3 0.120 0.594 -1.545 0.015 0.157 0.540 0.352 0.503 0.005 1.075 0.054 0.002 0.159 0.002
4 0.092 0.455 0.179 -3.703 0.120 0.414 0.269 0.385 0.004 0.823 0.042 0.002 0.122 0.002
5 0.070 0.349 0.137 0.009 -2.762 0.317 0.206 0.295 0.003 0.630 0.032 0.001 0.093 0.001
6 0.292 1.446 0.569 0.038 0.383 -1.994 0.856 1.223 0.012 0.815 0.133 0.006 0.387 0.005
7 0.212 1.051 0.414 0.027 0.278 0.955 -1.561 0.889 0.008 1.901 0.096 0.004 0.281 0.004
8 0.249 1.234 0.485 0.032 0.326 1.121 0.730 -2.209 0.010 1.331 0.113 0.005 0.330 0.005
9 0.047 0.232 0.091 0.006 0.061 0.211 0.137 0.196 -1.679 0.420 0.021 0.001 0.062 0.001
10 0.141 0.698 0.275 0.018 0.185 0.635 0.413 0.591 0.006 -4.991 0.064 0.003 0.187 0.003
11 0.045 0.222 0.087 0.006 0.059 0.202 0.131 0.188 0.002 0.401 -1.561 0.001 0.059 0.001
12 0.022 0.109 0.043 0.003 0.029 0.099 0.064 0.092 0.001 0.197 0.010 -2.798 0.029 0.000
13 0.153 0.756 0.298 0.020 0.200 0.688 0.448 0.640 0.006 1.368 0.069 0.003 -3.629 0.003
14 0.022 0.108 0.043 0.003 0.029 0.099 0.064 0.092 0.001 0.196 0.010 0.000 0.029 -1.094
15 0.033 0.165 0.065 0.004 0.044 0.150 0.098 0.140 0.001 0.299 0.015 0.001 0.044 0.001
16 0.044 0.217 0.085 0.006 0.057 0.197 0.128 0.183 0.002 0.392 0.020 0.001 0.058 0.001
17 0.116 0.573 0.225 0.015 0.152 0.520 0.339 0.484 0.005 1.035 0.052 0.002 0.153 0.002
18 0.034 0.168 0.066 0.004 0.045 0.153 0.100 0.142 0.001 0.305 0.015 0.001 0.045 0.001
19 0.078 0.385 0.152 0.010 0.102 0.350 0.228 0.326 0.003 0.697 0.035 0.002 0.103 0.001
20 0.168 0.831 0.327 0.022 0.220 0.755 0.492 0.703 0.007 1.503 0.076 0.003 0.222 0.003
21 0.027 0.136 0.053 0.004 0.036 0.123 0.080 0.115 0.001 0.245 0.012 0.001 0.036 0.001
22 0.014 0.070 0.028 0.002 0.019 0.064 0.042 0.059 0.001 0.127 0.006 0.000 0.019 0.000
23 0.116 0.573 0.225 0.015 0.152 0.521 0.339 0.485 0.005 1.036 0.053 0.002 0.153 0.002
24 0.025 0.126 0.049 0.003 0.033 0.114 0.074 0.106 0.001 0.227 0.012 0.001 0.034 0.000
25 0.031 0.155 0.061 0.004 0.041 0.141 0.092 0.131 0.001 0.280 0.014 0.001 0.041 0.001
Table 9. Estimated Price Elasticities for Top 25 Brands Based on IV Estimation
Brand # 15 16 17 18 19 20 21 22 23 24 25
1 0.001 0.065 0.261 0.027 0.115 0.469 0.004 0.004 0.011 0.003 0.001
2 0.001 0.077 0.306 0.032 0.135 0.551 0.005 0.004 0.013 0.003 0.003
3 0.001 0.014 0.058 0.006 0.025 0.104 0.001 0.001 0.002 0.001 0.004
4 0.001 0.043 0.173 0.018 0.076 0.312 0.003 0.002 0.008 0.002 0.004
5 0.001 0.014 0.055 0.006 0.024 0.099 0.001 0.001 0.002 0.001 0.001
6 0.003 0.007 0.027 0.003 0.012 0.049 0.000 0.000 0.001 0.000 0.002
68
Brand # 15 16 17 18 19 20 21 22 23 24 25
7 0.002 0.047 0.188 0.020 0.083 0.338 0.003 0.003 0.008 0.002 0.006
8 0.003 0.007 0.027 0.003 0.012 0.048 0.000 0.000 0.001 0.000 0.008
9 0.001 0.010 0.041 0.004 0.018 0.074 0.001 0.001 0.002 0.000 0.001
10 0.002 0.013 0.054 0.006 0.024 0.097 0.001 0.001 0.002 0.001 0.004
11 0.000 0.036 0.142 0.015 0.063 0.256 0.002 0.002 0.006 0.002 0.001
12 0.000 0.010 0.042 0.004 0.018 0.075 0.001 0.001 0.002 0.000 0.001
13 0.002 0.024 0.096 0.010 0.042 0.172 0.002 0.001 0.004 0.001 0.005
14 0.000 0.052 0.206 0.022 0.091 0.371 0.003 0.003 0.009 0.002 0.001
15 -1.351 0.008 0.034 0.004 0.015 0.061 0.001 0.000 0.001 0.000 0.001
16 0.000 -2.409 0.017 0.002 0.008 0.031 0.000 0.000 0.001 0.000 0.001
17 0.001 0.036 -3.788 0.015 0.063 0.256 0.002 0.002 0.006 0.002 0.003
18 0.000 0.008 0.031 -1.305 0.014 0.056 0.000 0.000 0.001 0.000 0.001
19 0.001 0.010 0.038 0.004 -2.384 0.069 0.001 0.001 0.002 0.000 0.002
20 0.002 0.092 0.010 0.041 0.166 -3.958 0.001 0.004 0.001 0.002 0.005
21 0.000 0.167 0.017 0.074 0.300 0.003 -1.434 0.007 0.002 0.004 0.001
22 0.000 0.148 0.015 0.065 0.265 0.002 0.002 -0.944 0.002 0.004 0.000
23 0.001 0.113 0.012 0.050 0.203 0.002 0.002 0.005 -3.178 0.003 0.003
24 0.000 0.087 0.009 0.038 0.156 0.001 0.001 0.004 0.001 -1.171 0.001
25 0.000 0.359 0.037 0.158 0.645 0.006 0.005 0.016 0.004 0.009 -1.409
69
Table 10. Change in Sales under Alternative Pricing Strategies
?price +1% +5% -1% -5%
brand 28
?market share(%) -1.23 -7.09 0.14 6.48
?sales (%) -0.78 -2.41 0.01 2.32
?market share = market share in the experiment - market share observed in data
?sales = sales in the experiment - sales obsered in data
Table 11. Change in Expenditure by Demographic Group under 5% Price Cut
? in expenditure
Highinc 1.21%
Lowinc 3.59%
Old 2.33%
Young 2.32%
Nokid 3.02%
WithKid 1.09%
70
Table 12. Change in Expenditure by Demographic Group under Pulsing Strate
? in expenditure
Highinc 2.64%
Lowinc 1.59%
Old 1.91%
Young 1.91%
Nokid 1.81%
WithKid 2.15%
Table 13. Food Ads Seen by Children of Different Ages
Age 2-7 Age 8-12 Age 13-17
Food ads seen per
12 21 17
Food ads seen per
year
4,400 6,000 7,600
Percentage of ads seen
where food was the main
product advertised
32% 25% 22%
in the United States”, The Kaiser Family Foundation, March 28, 2007
Source: "Food for Thought: Television Food Advertising to Children
71
Table 14. Sugar and Fiber Contents of Brands by Segment
Sugar (g per
serving)
Fiber (g
per
serving)
Kid Brands 10.98 5.41
Adult Brands 5.88 9.92
Family Brands 7.68 7.38
Table 15. Change in Segment Share After the Ban
? in
mktshare
kid -5.98%
adult 2.01%
family 3.96%
Table 16. Effects of the Ban across Consumer Groups
? in sugar ? in fiber
? in
expenditure
Highinc -3.41% 0.46% 6.43%
Lowinc -5.27% 2.67% 4.36%
Old -4.22% 0.95% 4.87%
Young -5.91% 4.24% 8.67%
Nokid -2.69% -1.24% 5.15%
Withkid -6.92% 7.10% 5.37%
72
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doc_829657064.pdf
The fundamental theorem of demand states that the rate of consumption falls as the price of the good rises; this is called the substitution effect. Clearly, if one does not have enough money to pay the price, then they cannot buy any of that item. As prices rise, consumers will substitute away from higher priced goods and services, choosing less costly alternatives.
ABSTRACT
Title of Dissertation: Information, Consumer Choice, and Firm
Strategy in an Experience Good Market
Yan Chen, Doctor of Philosophy, 2008
Directed By: Professor Ginger Jin, Department of Economics
This paper models how consumers make brand choice when they have limited
information. In an experience good market with frequent product entry and exit,
consumers face two types of information problems: first, they have limited information
about product existence; second, even if they know a product exists, they do not have full
information about its quality until they purchase and consume the product. In this paper, I
incorporate purchase experience and brand advertising as two sources of information, and
examine how consumers utilize them in a dynamic process.
Specifically, to address the awareness problem, I model the consumer choice set as
a function of experience and advertising, which varies across consumers and evolves over
time. In terms of quality, I allow a first-time consumer to infer product quality from
advertising. Once she buys the product, she learns the quality perfectly. To better capture
the dynamics, I incorporate habit formation conditional on each consumer’s purchase
history.
The model is estimated using the AC Nielsen homescan data in Los Angeles,
which records grocery shopping histories for 1,402 households over six years. Taking
ready-to-eat cereal as an example, I find that consumers learn about new products quickly
and form strong habits. More specifically, advertising has a significant effect informing
consumers of product existence and signaling product quality. However, advertising's
prestige effect is not significant. I also find that incorporating limited information about
product existence leads to larger estimates of the price elasticity. Then I use instrument
variables based on differentiated-products firm competition models to address the
endogeneity problem of price and advertising with unobserved brand characteristics.
Based on the IV estimates, I summarize the substitution pattern and simulate consumer
choices under counterfactual experiments to evaluate a number of brand marketing
strategies and a policy on banning children-oriented cereal advertising.
Information, Consumer Choice, and Firm Strategy in an Experience
Good Market
By
Yan Chen
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park, in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2008
Advisory Committee:
Professor Ginger Jin, Chair
Professor John Rust
Professor Roger Betancourt
Professor Erkut Ozbay
Professor P.K.Kannan
© Copyright by
Yan Chen
2008
Dedication
To my parents.
ii
Acknowledgements
My first and greatest debt is to my advisor, Professor Ginger Jin. Ginger not only gives
me guidance in choosing the topic, obtaining the data, and conducting the research, but
also treats me like a sister in life.
I am grateful to Professor John Rust, Professor Roger Betancourt, Professor Erkut
Ozbay, Professor Dan Vincent, and Professor P.K.Kannan for their comments and
suggestions during the process this dissertation was written.
I have been blessed to meet many good friends at the University of Maryland and back
at the University of British Columbia. Thanks for making the past few years of my life
peaceful and offering many happy distractions from study and research.
As always, I have counted on the support and encouragement of my parents and my
brother. Thanks for having confidence in me and showering me with love all these years.
Although we are in different corners of the world, our hearts have always been together
and will always be. ??????????
iii
Table of Contents
Dedication ii
Acknowledgements iii
Table of Contents iv
List of Tables v
List of Figures vi
Chapter 1: Introduction, Background and Data Description 1
Section 1.1: Introduction 1
Section 1.2: Related Literature 5
Section 1.3: Industry Background and Data Description 7
1.3.1. Features of RTE Cereal Market 7
1.3.2. Data Description 8
Chapter 2: Demand Estimation without IV 11
Section 2.1: Demand 11
2.1.1.Demand Specification 11
2.1.2.Discussion 15
2.1.3.Identification 17
2.1.4.Estimation Issues 21
(1) Endogeneity 21
(2) Unobserved Consumer Heterogeneity 22
(3) Choice Set Simulation 22
(4) Properties of Estimator 23
Section 2.2: Results of Demand Estimation without IV 24
2.2.1.Estimation with Full Information 26
2.2.2.Estimation with Limited Information about Brand Quality 27
2.2.3.Estimation with Limited Information about Both Quality and Existence 27
2.2.4.Comparison of Goodness of Fit 30
Chapter 3: Instrumental Variable Estimation 34
Section 1: IV Estimation Algorithm 34
Section 2: IV Estimation Results 37
Chapter 4: Policy Experiments 39
Section 1: Pricing Strategy for Brand 28 39
Section 2: Advertising Strategy for Brand 28 41
Section 3: Effects of Banning Children-Oriented Cereal Advertising 43
Section 4:Concluding Remarks 45
Appendices 47
Bibliography 73
iv
List of Tables
Table 1. Brand Entry and Exit
Table 2. Brand Summary Statistics
Table 3. Summary Statistics of Homescan Data
Table 4. Summary of Variables in Estimation Sample
Table 5. Preliminary Regression Results
Table 6. Estimation Results
Table 7. Predicted Market Shares
Table 8. Own Price Elasticity for Top 10 Brands
Table 9. Estimated Price Elasticities for Top 25 Brands Based on IV Estimation
Table 10. Changes in Sales under Alternative Pricing Strategies
Table 11. Changes in Expenditure by Demographic Group under 5% Price Cut
Table 12. Changes in Expenditure by Demographic Group under Pulsing Strategy
Table 13. Food Ads Seen by Children of Different Ages
Table 14. Sugar and Fiber Contents of Brands by Segment
Table 15. Change in Segment Share After the Ban
Table 16. Effects of the Ban across Consumer Groups
v
List of Figures
Figure 1. Frequency Histogram of Household Brand Purchases
Figure 2. Repurchase Probability after First Experience with a Brand
Figure 3. Marginal Effect of Advertising on Choice Probability
Figure 4. Probability of a Brand Being Included in the Choice Set
Figure 5. Average Monthly Advertising, Price, and Sales for Brand 28
Figure 6. Average Daily Transaction Price for Brand 28
Figure 7. Observed v.s. Counterfactual Advertising Strategies for Brand 28
vi
Chapter 1: Introduction, Literature, and Data Summary
Section 1.1. Introduction
In an experience good market with frequent product entry and exit, consumers face at
least two informational problems when they make product choices: on the one hand, they
have limited information about product existence; on the other hand, even if consumers
know a product exists, they are uncertain about its quality before consumption. Consumer
choice in such an environment involves a dynamic process of information acquisition,
about which a large body of literature has developed. However, empirical research
typically deals with only one of the informational problems. To my knowledge, this paper
is the first attempt to incorporate both kinds of informational problems in a structural
framework and evaluate their relative importance using a rich panel of household
purchase data. In this sense, the paper brings the literature closer to the reality and sheds
new lights on both consumer demand and firm marketing strategies.
In this paper I focus on two mechanisms that alleviate the informational problems:
consumption experience and brand advertising. First, consumers learn about product
quality through experience. In particular, I assume that product quality can be fully
learned after the first try. This type of one-period learning is a limiting case of Bayesian
learning (the prior belief is updated to the true value after one experience) and is suitable
for goods whose characteristics can be ascertained quickly after use. Second, advertising
has two types of informative effects: signaling product quality (Nelson (1970, 1974),
Kihlstrom & Riordan (1984), Milgrom & Roberts (1986), etc), and affecting the
probability that a consumer is aware of the product (Butters (1977), Grossman & Shapiro
1
(1984)). In my empirical model, the former is captured in the utility function with
advertising interacted with a new brand
1
Advertising and experience can also directly affect a consumer's level of utility. On
the one hand, advertising can directly provide utility and have a prestige effect on all
consumers (Stigler & Becker (1977), Becker & Murphy (1993)). For example, a
consumer may obtain a higher level of satisfaction from wearing a pair of Nike sneakers
than from wearing an unknown brand of similar quality because of the image established
by Nike commercials. On the other hand, experience may also directly change utility
through habit formation if previous purchases of a product increase its current utility (and
choice probability). Allowing for habit formation in the choice process has important
implications for firm marketing strategy. For example, if consumers are habituated to a
product, then the introductory price of a new product may need to be set lower than when
there is only learning to warrant a product switch.
dummy, while the latter is captured by
advertising entering the choice set formulation.
Specifically, to address the awareness problem, I model the choice set as a function
of brand advertising and purchase experience. As a result, choice sets vary across
consumers and evolve over time. Previous research usually assumes a fixed choice set for
all consumers, which is reasonable if the market is in steady state equilibrium with a few
products. However, in many markets for experience goods, due to the large number of
products available and the high rate of new product introduction, one is unlikely to be
aware of all products for sale and has to restrict attention to a subset of products. This
subset forms the consumer's choice set, which evolves over time as information
accumulates through advertising and experience.
1
New brand in this paper means new to a specific consumer, not newly introduced into the market.
2
The consumer choice model is estimated on a panel of AC Nielsen homescan data in
the ready-to-eat (henceforth RTE) cereal market. A survey of 1,402 demographically
balanced U.S. households in the Los Angeles market, the homescan data keeps track of
on-going household purchasing of grocery products from December 1997 to December
2003. It records both the transaction information such as brand, price and quantity and the
household demographic information. In the estimation, the homescan data is
supplemented by two data sets on the supply side: manufacturer advertising data obtained
from TNS Media Intelligence Company, and brand nutritional data collected from
internet.
Empirical specifications with different information assumptions are estimated in the
paper. In the benchmark specification, consumers are assumed to have full information
about brand quality and existence. Then I introduce limited information about brand
quality. Consumers are aware of all brands available in the market but are uncertain about
the quality of unused brands. They form expectation about brand characteristics and infer
quality from advertising. Lastly, consumers are assumed to have limited information
about both brand quality and existence. Their choice sets are heterogeneous depending on
consumption history and brand advertising.
In addition to tests of how different specifications fit the data, estimation results
from different specifications are compared in terms of market share predictions. It is
shown that the model specification with both limited information on brand existence and
brand quality best captures consumer behavior. This model incorporates three sources of
consumer heterogeneity: choice sets, tastes, and experiences. The results suggest that
limited information about brand existence has a large impact on consumer behavior: price
3
sensitivity is much higher among the set of brands that consumers are aware of, implying
that demand is more elastic. I also distinguish different effects of advertising in the
estimation and find that advertising has a significant effect in providing information
about brand existence and signaling brand quality. However, the prestige effect of
advertising is not significant. The results imply that advertising works for new consumers
only. After the first experience with a brand, advertising will not change consumers’
utility level and what matters to the consumers is the purchase history.
Instrumental variables selected on basis of differentiated-products competition models
are applied to the limited information model to obtain consistent coefficient estimates.
The IV estimation does not change the qualitative results of the model. A Hausman test
of the IV coefficients and OLS coefficients also suggests that they are not systematically
different. Finally, some policy experiments are conducted to evaluate a number of firm
marketing strategies in pricing and advertising and to simulate the effect of banning
children-oriented cereal advertising. The consumer-level limited information model
offers new insights for pricing strategies and provides a micro foundation to evaluate the
pulsing strategy in advertising in the RTE cereal market, which supplements the study of
Dubé, Hitsch, and Manchanda (2005). The model can also be used to evaluate nutritional
policy changes. For example, in recent years child obesity has become a serious problem
in America and there have been renewed debates on whether food advertising targeted
toward children should be ban. Using the model I can estimate the effects of such a ban
on the nutritional intakes and expenditures of various demographic groups, which may
provide some empirical evidence in the policy debate.
4
The rest of this paper is organized as follows. The remaining sections of chapter 1
review the literature and discuss the industry background and data sets used for this
study. Chapter 2 specifies and estimates the demand system under different informational
assumptions. Instrumental variables are selected in Chapter 3 and the the IV estimation
algorithm is discussed and the results presented. Policy experiments are conducted in
Chapter 4 on a number of brand marketing strategies.
Section 1.2. Related Literature
The paper is related to several lines of literature. The consumer learning literature
addresses the problem of limited information about product quality. In their pioneer
work, Erdem and Keane (1996) estimate how consumers learn about the cleaning power
of laundry detergents. Both experience and advertising give consumers noisy signals
about the detergent's quality and consumers update their beliefs about quality in a
Bayesian way. Following this study, there have been many studies that model consumer
learning in a Bayesian framework in various markets (Ackerberg (2003), Crawford and
Shum (2005), Chintagunta, Jiang, and Jin (2007), to name a few). However, the
consumer learning literature usually takes the consumer choice set as homogenous. It
does not account for the fact that different consumers may be exposed to different sets of
products due to limited awareness, which is the central research question in the literature
on heterogeneous choice set (also called consideration set in the marketing literature).
There have been very few economic studies that consider heterogeneity in the choice
set. Goeree (2008) presents a model in which advertising influences the set of products
from which consumers choose to purchase. Specifically, the probability that a consumer
5
is informed of a product is a function of the effectiveness of the product's advertising and
the observed consumer characteristics. In the marketing literature, there are relatively
more papers allowing for heterogeneity in consideration set. Brand choice is usually
modeled as a two-stage process: at the first stage consumers identify a subset of brands
which constitute their consideration set. They then choose the brand with the highest
utility at the second stage. Roberts and Lattin (1997) review the theoretical and empirical
marketing studies that develop an individual level model of consideration set and analyze
how marketing mix affects consideration set and consumer choice including Andrews
and Srinivasan (1995) and Allenby and Ginter (1995). They also point out some
directions for future research including dynamics in consideration set, which is captured
in this paper. Swait (2001) assumes that the probability a specific consideration set is
formed is a function of the expected maximum utility from the alternatives in that set.
Mehta, Rajiv, and Srinivasan (2003) formulate the process of consideration set formation
as a trade-off between the expected benefit from including an additional brand and the
additional search cost incurred. Eliaz and Spiegler (2007) study a market model in which
firms use irrelevant alternatives to influence consumers’ consideration set. All these
studies, however, only model one-time purchase in a static setting and do not account for
variation in choices and choice sets over time.
In terms of how to model advertising, this paper learns from both theoretical (as
discussed above) and empirical literature on advertising (Ackerberg (2001, 2003), Anand
and Sharchar (2005), etc). This paper also benefits from the insights of the literature on
RTE cereal market that involves demand estimation (Hausman (1996), Nevo (2001),
Shum (2004), Hitsch (2006), etc). Due to the richness of my data, compared to the
6
previous studies, I am able to include more dynamics in consumer choice, identify
consumer learning from habit formation based on the difference in choice dependence
structure of new and old consumers as in Osbourne (2006), and distinguish different
effects of advertising.
Last but not least, this paper is an extension of the literature on analyzing demand
systems in differentiated product markets (Berry (1994), Berry, Levinsohn and Pakes
(1995, 2004), etc). With household level data, the parameters that vary with individual
households can be identified without any constraints on the distribution of unobserved
brand characteristics. The parameters that do not vary with individuals such as the mean
price coefficient need to be estimated with the market share data and instrumental
variables. This paper applies the estimation method to a limited information environment.
Section 1.3. Industry Background and Data Description
1.3.1. Features of RTE Cereal Market
Readers can refer to Section 2 of Nevo (2001) for a more complete picture of the RTE
cereal industry. For the purpose of this paper, there are several features of the RTE cereal
market that make it a good case study for the empirical work. First, cereal is an
experience good, the attributes of which are not completely known before consumption.
Second, brand entry and exit happen frequently in the RTE cereal market and none of the
national brands has a truly dominant hold on the market, which imposes a considerable
informational burden on consumers.
7
As an example, Table 1 shows the entries and exits of RTE cereal brands
2
from
December 1997 to December 2003 in the Los Angeles market. In the 6-year period, a
total of 62 (46) brands enter (exit)
3
the market, which accounts for about 47.3% (35.1%)
of the total number of brands existing at the end of 1997. Column 2 of Table 2 displays
sales-based market shares of major brands from December 1997 to December 2003. Due
to the existence of a large number of brands, in the table I select the top 50 brands
(together they account for about 79% of the market) and combine the remaining ones into
a composite brand, brand 51. The biggest brand (Brand 1
4
Third, the RTE cereal market is heavily advertised. Advertising over sales ratio for
RTE cereal was 13% in 2001. For well-established brands, the ratio was 18%
) has a market share of 6%
while most brands take up less than 1% of the market.
5
. In
comparison, the average ad over sales ratio across 200 industries was 3.2%
6
On the consumer side, I utilize AC Nielsen Homescan data on RTE cereal products from
December 1997 to December 2003. Tracking 1,402 demographically balanced
households in Los Angeles, the homescan data ties consumer purchase behavior with key
demographic measures. Homescan panelists scan items at home from each shopping trip,
. Heavy
advertising shows that firms believe advertising is effective in promoting sales, thus it is
important to analyze its effects in this market.
1.3. 2. Data Description
2
Brand definition follows the classification on each manufacturer’s website. Different box sizes are treated as the same
brand, while extensions of a brand name are distinct brands. For example, Cheerios, Honey Nut Cheerios, and Berry
Burst Cheerios are three different brands.
3
Brand entry and exit are defined using the AC Nielsen homescan data. A brand entry is observed if the first transaction
of the brand occurs after June 1998. A brand exit is observed if the last transaction of the brand occurs before June 2003.
4
Brand names are not revealed due to a confidential agreement with the data provider.
5
See Nevo (2001), page 311.
6
See Advertising Age, March 1, 2006
8
recording price and quantity purchased as well as the age, income, and other
demographic information of the shopper. The data set keeps track of on-going purchasing
from the same household over time, hence offers insights into households' consumption
habits and dynamics. On average a household stays in the homescan panel for 48 months.
Once a household leaves the panel, a new one that is similar in all demographic measures
is selected to take its place. Table 3 contains definitions and summary statistics of the key
variables in the homescan data.
Using the homescan data I can then summarize the consumption pattern in the RTE
cereal market. On average, a household makes 14 shopping trips with RTE cereal per
year. The households usually have a couple of brands that they purchase repeatedly over
time. Most brands are purchased once and never again (Figure 1 displays a histogram of
the number of times a household purchases a brand). After a brand was first purchased by
a household, the probability of the household repurchasing the brand is 14.1% on the next
shopping trip, 12.9% on the second shopping trip, and about 11% on the following trips
(Figure 2 shows the probability of repurchasing a brand on the shopping trips following
the first try). Both Figure 1 and Figure 2 suggest that learning in the cereal market is
mainly done after one shopping trip. Figure 2 also suggests that conditional on repurchase
after the first experience with a new brand, a household exhibits loyalty to that brand.
On the product side, I obtain advertising data from TNS Media Intelligence, which
tracks advertising expenditures of cereal manufacturers from January 1999 to December
2003. The advertising data covers 278 cereal brands across 11 different media types
7
7
The 11 media types include network TV, cable TV, sport TV, magazines, syndication, national sport radio, network
radio, Sunday magazines, local newspaper, outdoor billboard, and national newspaper. In this paper advertising
particularly refers to cereal manufacturers’ advertising expenditures in these media types. Although retailer advertising
such as retailer deal and store featuring is common in the RTE cereal market, it is not included in the estimation due to
lack of data on retailers.
.
9
The brand advertising expenditures include both national advertising and local
advertising. On average, national advertising accounts for 98.1% of the total advertising
expenditure and is mainly on network TV and cable TV, while local advertising accounts
for 1.9% of the total advertising and is mainly on local newspapers and outdoor
billboards. Average monthly advertising expenditures of the top 50 cereal brands in Los
Angeles are shown in Column 3 of Table 2.
Nutritional data on cereal brands is collected from www.nutritiondata.com
8
, with
nutrient information of 111 brands including calories, sugar, dietary fiber, protein, etc.
The fiber and sugar contents per serving (30 gram) for the 50 top brands are displayed in
Column 4 and Column 5 of Table 2. These two nutrients are selected because there is
little variation in other nutrients across brands.
In all data sets, the characteristics of brand 51, the composite brand, are calculated
as the average of all non top-50 brands.
8
The nutritional information was collected on Sep 10, 2006, from the website. There is no variation of nutrients over
time for the same brand.
10
Chapter 2: Demand Estimation without IV
Section 2.1. Demand
2.1.1. Demand Specification
Abstracting from quantity, the empirical model focuses on consumer brand choice
conditional on purchasing RTE cereal. Multiple brand purchases on one shopping trip are
treated as independent events
9
There are a number of consumers (index by i) choosing from a set of brands (indexed
by j) on different shopping trips (indexed by t). The brand choice is a two-stage process.
. For example, if on a shopping trip a consumer purchased
brands A, B, and C, it is estimated as if she had made three separate transactions with A,
B, and C within the same day. Suppose on the previous shopping trip the consumer
purchased brand A. Then in the transaction with brand A, the past choice dummy would
be set to 1. In the other two transactions, the past choice dummy would be set to 0. On the
next shopping trip, if the consumer purchased any one of brands A, B, and C, her last-
time choice dummy would be set to 1. Apart from not estimating the quantity choice, the
model also does not consider the store choice or the brand choice conditional on visiting
a store as store-level data are not available.
9
The model does not include non-purchase of RTE cereal as the outside good. There are two reasons for doing so: (i)
consumers may choose not to purchase because they have cereal inventory at home, not because the utility of non-
purchase is higher than all cereal brands. Treating non-purchase as the outside good, therefore, will bias the parameter
estimates downward in the utility function. (ii) Consumers choose not to purchase RTE cereals on about 2/3 of all
shopping trips. Including those shopping trips will further add to the already large computation burden. The model also
restricts to brand choice but not quantity choice. Taking quantity into consideration requires tracking consumer’s
stockpiling and inventory, which will greatly complicate the model. About 52% of the purchases are associated with
only one brand. Multiple-brand transactions are treated as independent transactions following Shum (2004). Shum
(2004) fails to find across–brand synergies in demand patterns of RTE cereals that would require modeling the
multiple-brand purchase decision. Readers interested in this can refer to Hendel (1999), Dubé(2004) for examples of
multiple-discrete choice model which allows multiple-unit and multiple-brand purchases on one shopping trip, and
Nevo and Hendel (2006) for an example of consumer inventory model.
11
At the first stage, based on previous purchase experience and brand advertising, the
consumer is informed of a subset of brands that constitute her choice set on that shopping
trip. At the second stage, the consumer chooses a brand from her choice set that
maximizes her expected utility. On a specific shopping trip, the consumer’s information
set includes the quality and characteristics of brands she has purchased before, and prices
and advertising intensities of all brands in her current choice set. Note that brands are
differentiated both horizontally and vertically. The horizontal differentiation is on brand
characteristics such as fiber and sugar contents. The vertical differentiation is on the
brand quality. The quality of a cereal brand is determined by the quality of ingredients
such as grain and rice, and the processing techniques.
Two assumptions are made about the choice set formulation. First, a brand purchased
before would stay in the choice set. In other words, once a consumer tries a brand she
never forgets about it, even though she may dislike it and choose not to purchase it again.
Second, the probability of consumers being informed of a previously unused brand is a
function of the brand's advertising stock. Formally, at time t, the probability that
consumer i has choice set C
it
is:
) 1 ( ) (
? ?
? ?
? =
it it
C k
ikt
C j
ijt it
q q C P (1)
where
ijt
q is the probability of consumer i being informed of brand j at time t, and
2
0 1 2 3 4
2
0 1 2 3 4
exp( )
1 exp( )
jt jt i jt i jt
ijt
jt jt i jt i jt
adv adv inc adv nokid adv
q
adv adv inc adv nokid adv
? ? ? ? ?
? ? ? ? ?
+ + + +
=
+ + + + +
? ?
? ?
,
it
j ? ??
=1,
it
j ? ?? (2)
where
it
E is consumer i’s experience set as of time t, i.e., the set of brands previously
purchased by consumer i up to time t. In the estimation, transactions in the first year of a
12
consumer’s purchase history are used to initialize her experience set. The variable adv
jt
is
a depreciated stock of advertising expenditures for brand j at time t. Specifically,
0
T
jt jt
adv a
?
?
?
?
?
=
=
?
(3)
where
jt
a denotes brand j’s advertising expenditure at time t,
10
2
jt
adv
and ? is the discount
factor. Using stock instead of current flow of advertising allows advertising to have a
lagged effect on consumer choice in the form of good will stock. Specifically, if a brand
entered a consumer’s choice set on the last shopping trip but was not purchased, the
probability of it re-entering the consumer’s current choice set may still be high even if the
brand is not advertised in the current period due to the lagged effects of previous
advertising. The term is included to account for the potential increasing or
decreasing returns to scale of advertising. In equation (2), adv
jt
is also interacted with
household income and whether there is any kid in the household to reflect the
heterogeneity in exposure to advertising for different types of households.
At the second stage, consumer i chooses brand j to maximize expected utility
conditional on her choice set. As is now standard in the discrete choice literature, the
expected utility consumer i obtains from brand j is a function of brand j’s characteristics.
( )
ijt j i i ijt i jt ijt i ijt jt
ijt jt ijt
U E X price adv unused unused adv
pastchoice
? ? ? ? ?
? ? ?
= + + + ? + ? ?
+ • + +
(4)
where X
j
=[fiber sugar]
j
, ?
i
=[?
1i
?
2i
]´, price
ijt
is the price of brand j when consumer i it at
time t. In the AC Nielsen Homescan data, the price of a brand is recorded as the weekly
10
Advertising data is monthly while purchase data is daily. Therefore advertising expenditure at time t means
advertising expenditure in the month that day t belongs to. In the empirical results reported in section 5, ?=0.95 and
T=6. I also estimate the model with ? varying from 0.8 to 0.99 and T from 3 to 12. The robustness checks do not yield
significant qualitative differences.
13
average price of that brand in the store where the brand was sold. In the estimation, I
subtract the manufacturer coupon value and the retailer deal value from the price if a
coupon or a deal is used
11
1 1
2 2
i
i
i i i
i
i
D v
? ?
? ?
? ?
? ?
? ?
( (
( (
( (
( (
= + ?• + ?•
( (
( (
( (
¸ ¸ ¸ ¸
.
Note that ?
i
, ?
i
,
?
i
, and ?
i
are individual coefficients. Specifically,
(5)
where
i
D is a vector of observed household characteristics including household income,
age of female household head, and presence of kids, and v
i
represents a vector of
unobserved household characteristics with standard normal distribution. The variable
unused
ijt
is a dummy which equals 1 if brand j was never purchased by consumer i before
time t. It interacts with adv
jt
, implying that advertising may provide information about the
quality of unused brands. For example, the fact that the cereal manufacturer is able to
spend a huge amount on promoting a brand may signal to consumers that the
manufacturer is in a good financial condition and can therefore product cereals with
better ingredients and better technology. The vector
ijt
pastchoice = [chosen
ijt-1
chosen
ijt-
2,
…, chosen
ijt-?
], where chosen
ijt-?
equals 1 if brand j was chosen ? shopping trips before
t
12
jt
? . The term represents brand j’s characteristics that are observed to the consumer but
not to the researcher at time t. In the case of RTE cereals,
jt
? encapsulates packaging,
11
I am not able to control for coupons and deals systematically as in Nevo and Hendel (2006) as I do not have store
level data and do not observe the availability of coupons and deals to consumers.
12
In the empirical results I use T=6. Compared to previous studies where T is often equal to 1, my results show a more
complete picture of time dependence of consumer choices. I also estimate the model with T=12 and the results are
similar.
14
shelf space, etc. Lastly,
ijt
? is a mean 0 stochastic term independent across time, brands
and consumers.
If brand j has not been purchased before, the consumer holds expectations of its
fiber and sugar contents according to the following rule: E(fiber
j
)=mean(fiber
k
), and
E(sugar
j
)=mean(sugar
k
) ? brand k tried by consumer i before and belonging to the same
segment as brand j (Following Hausman (1996) and Shum (2004), I divide the brands
into family, adult, and kid segments. The segment categorization is shown in column 7 of
Table 2). If the brand has been purchased before, then the consumer knows its
characteristics.
The utility maximization stage generates P(j|C
it
), the conditional probability that
brand j is chosen by consumer i at time t. By the law of conditional probability,
multiplying P(j|C
it
) and P(C
it
) yields P
ijt
, the unconditional probability of consumer i
choosing brand j at time t.
) | ( ) 1 (
it
S C C k
ikt
C j
ijt ijt
C j P q q P
it it it
? ? ?
? ? ?
? = , (6)
where S is the set of all choice sets that include brand j. Matching the choice probabilities
predicted by the model with the observed choices using maximum likelihood will then
give us the parameter estimates.
2.1.2. Discussion
Key features of the demand model merits additional discussion. First, the choice set
formation process addresses the informational problem about product existence. Even
though the choice set is aggregated to contain the 50 biggest national brands and a
15
composite brand, it is still unlikely that consumers would know and compare the utility of
all 51 brands on each purchase occasion. Allowing the choice set to depend on
consumption experience and brand advertising thus brings the model closer to real
consumer behavior. Since the choice set is not observable in the data, I need to simulate
them in the estimation. The details of simulation will be discussed in Section 4. Second,
consumers learn about brand quality after their first experience with the brand, which
captures learning in the RTE cereal market reasonably well as shown in Figure 2. Unlike
some complicated products, consumers usually can attain precise knowledge about a
cereal after consuming one box of it. Third, compared to most previous choice models
where only the past choice is included, choices on the previous 6 shopping trips are
included in the utility function. The coefficients on the set of past choice variables
provide a better description of the temporal dependence of brand choices than when there
is only the last time choice. For example, if a consumer’s brand choice history consists of
A, B, A, B, …, A, B, and only the last time choice dummy is included, then we would
wrongly infer that the consumer only seeks variety and is not subject to habituation. If we
extend the model to have additional past choices, then it is possible to better capture the
potential for habit formation. The distinction is important because if variety-seeking is
dominant, then temporary promotions’ impact on demand would be short-lived. On the
other hand, if consumers are susceptible to habit formation, temporary promotions may
affect sales well into the future. Thus adding more past choice variables not only better
describes time dependence, but also helps managers optimize decisions on marketing
strategies. Fourth, advertising has three roles in the model: (I) affecting consumer choice
set, which represents advertising’s informative effect on brand existence and is captured
16
by the ? parameters; (II) signaling quality of an unused brand, which represents
advertising’s informative effect on brand quality and is captured by the parameter ?; (III)
directly providing utility, which represents advertising’s prestige effect and is captured by
the parameter ?. Identification of the different effects will be discussed below.
In the demand setup, I assume that the consumer is myopic and maximizes her current
period utility. When state dependence (habit formation) is present, a forward-looking
consumer would consider the future effects of her current choice. Forward-looking is
important in many cases, especially in situations where the experimentation cost is high,
examples including choice of durable goods such as computer and digital camera and
decision about whether to accept a job offer or to continue job search. It is less critical in
this situation where consumers choose a frequently purchased product and the cost of
trying a new product is low as consumers can easily switch back to the brands they have
been using. Moreover, previous marketing research shows that consumers spend an
average of 13 seconds in selecting a brand out of the shelf
13
2.1. 3. Identification
. This is a very short time for
a consumer to plan her future choices. Therefore, I tend to believe that the myopic
assumption is reasonable in this application and in the choice process of many other
nondurable goods, for example, beverages and cosmetics.
Intuitive identification strategies are discussed in this subsection. The parameters to be
estimated ? include ?
0
,
?
1
, ?
2
,
?
3
, ?
4
. ?, ?, ?, ?, ?, ???,and ?. Variation of brand
choices corresponding to observed brand characteristics, price, and advertising for all
13
See Cesar Costantino, Ph.D. Dissertation, Chapter 4, “Gone in Thirteen Seconds: Advertising and Search in the
Supermarket”, 2004.
17
consumers is used to identify ?, ?, and ?. A RTE cereal may also have attributes that are
favored by a subgroup of consumers. For example, older consumers may prefer higher
fiber content while kids may prefer higher sugar content. Substitution pattern of
consumers with different demographics when brand characteristics vary helps identify ?.
And heterogeneity in substitution pattern of consumers with the same demographics
helps identify ?. Comparing the average probability of choosing a used brand with the
average probability of choosing an unused brand on each purchase occasion identifies ?.
Comparing the repurchase probability after purchase of a new brand with the repurchase
probability of a previously purchased brand identifies learning from habit formation, and
variation in brand choices over time pins down ?.
In terms of advertising’s different effects, the main identification assumption of the
prestige effect and informative effects is that the prestige effect does not vary by
consumption experiences. As in Ackerberg (2001, 2003), the prestige effect impacts both
experienced and inexperienced consumers in the same way, while the informative effects
only works on consumers who have never tried the brand before. Therefore, variation in
the ratio of choice probability between experienced and inexperienced consumers as
advertising intensity changes can be used to identify the informative effect from the
prestige effect. The two types of informative effect (coefficients ?
versus coefficient ?)
both affect the choice probability of inexperienced consumers. An inexperienced
consumer may choose to try a brand because advertising alerts her attention to the
existence of the brand or because advertising raises the expected quality of this brand.
Ignoring advertising’s prestige effect for the moment, if advertising’s only provides
information about brand existence, consumers will include the brand in their choice set
18
with a higher probability if the brand’s advertising increases. In this case, advertising
does not enter the consumer utility function and hence the marginal effect of advertising
on brand choice probability is independent of the observed brand characteristics. If two
brands with different characteristics increase advertising by the same percentage, their
choice probability will go up by the same percentage. If, furthermore, advertising
provides a signal about brand quality, then consumers have two information channels to
evaluate a brand --- the advertising signal and the other brand characteristics. They would
trade off the information inferred from advertising with the information observed from
the brand characteristics. If the quality perception of the brand is already high based on
the brand characteristics, the marginal effect of advertising on brand choice probability
would be small as there are fewer consumers on the margin who would switch to the
brand due to more exposure to advertising. If, on the other hand, the quality perception of
the brand is relatively low from the brand characteristics, then the marginal effect of a
surge in advertising would be big as more consumers would be convinced to switch.
Therefore, the two types of informative effect can be distinguished by whether the
marginal effect of advertising on brand choice probability depends on the brand
characteristics, as advertising only enters the utility function and interacts with the brand
characteristics if the informative effect about brand quality exists.
To see this mathematically, let us consider a simple example: there are two brands in
the market, one (brand 1) has been established for a long time and the other (brand 2) was
newly introduced. Consumers all know about brand 1, and brand 2 launches an
advertising campaign. Ignoring in this example the returns to scale of advertising in
choice set formation and heterogeneity in coefficients across households, if advertising’s
19
only effect is informing consumers of the existence of brand 2, then the probability that
consumers choose brand 2 is:
0 1 2 2 2
0 1 2 2 2
exp( ) exp( ( ) * )
*
1 exp( ) 1 exp( ( ) * )
adv E X price
P
adv E X price
? ? ? ?
? ? ? ?
+ + + ?
=
+ + + + + ?
(7)
where ? denotes the sum of variables in utility function other than price and observed
brand characteristics. The marginal effect of advertising on the change in choice
probability is:
1
2 0 1 2
ln( )
( ) 1 exp( )
P
adv adv
?
? ?
?
=
? + +
(8)
Note that equation (8) is independent of brand 2’s characteristics.
If advertising also provides information about quality, the choice probability of brand 2
is:
0 1 2 2 2 2
0 1 2 2 2 2
exp( ) exp( ( ) * * )
*
1 exp( ) 1 exp( ( ) * * )
adv E X price adv
P
adv E X price adv
? ? ? ? ?
? ? ? ? ?
+ + + + ?
=
+ + + + + + ?
(9)
The marginal effect of advertising on the change in choice probability is:
1
2 0 1 2 2 2 2
ln( )
( ) 1 exp( ) 1 exp( ( ) * * )
P
adv adv E X price adv
? ?
? ? ? ? ?
?
= +
? + + + + + + ?
(10)
The higher the utility consumers infer from the brand characteristics, the less the need to
rely on the information in advertising. Comparing equation (8) and equation (10), we can
see that whether marginal effect of advertising on choice probability is dependent on the
brand characteristics identifies the informative effect about brand quality from the
informative effect about brand existence. To illustrate this point, figure 3 depicts the
marginal effect of advertising on choice probability. The non-stochastic part of the utility
function other than advertising is denoted by Q. When only the informative effect about
existence exists, the marginal change in choice probability is a declining function of
20
advertising expenditure and is independent of Q. When advertising also signals quality,
the marginal change in choice probability is not only a declining function of advertising,
but also is a function of Q. As Q increases, the marginal change in choice probability
decreases.
2.1.4. Estimation Issues
Before I present and discuss the empirical results of demand estimation, it is appropriate
to discuss the issues that are encountered in the estimation and how I attempt to deal with
them.
(1) Endogeneity
If the manufacturers set up prices and advertising levels according to the consumers’
willingness to pay, then the endogeneity problem may arise as price and advertising
levels could be correlated with unobserved brand characteristics in the utility function.
For example, if the brand manager coordinates media advertising and store promotion
activities, then the unobserved brand characteristics such as shelf space or store featuring
can be correlated to the price and advertising expenditures of the brand. As a result the
coefficients on price and advertising can be overestimated. The best way to deal with the
endogeneity problem is to use instrumental variables. However, the notion of valid
instruments involves supply side specifications and IV estimation in this non-linear
consumer choice model is rather complicated. The focus in this section is on how demand
estimation varies with informational assumptions, thus the IV estimation is deferred to a
later section. In this part, I only include brand fixed effects to control for unobserved
brand characteristics invariant over time. For example, if the government dietary policies
21
promote the health effects of whole grain foods, then the price and advertising levels of
the whole grain cereals may be increased. Whether a cereal is a whole grain is invariant
over time and is absorbed by brand dummies and therefore this type of endogeneity is
controlled for.
(2) Unobserved Consumer Heterogeneity
In a model with lagged dependent variables, state dependence (habit formation) is
observationally equivalent to consumer heterogeneity as individual specific effects can
lead to persistence in choices. State dependence can be exaggerated if unobserved
consumer preferences are mistakenly assumed to be homogeneous. For example, an
overweight consumer can have a high preference for a low sugar cereal and repeatedly
purchase it. If consumer specific preference is not controlled for, repeated purchases will
be captured by the past choice variables and regarded as strong habit. Therefore, it is
important to disentangle the true state dependence from consumer heterogeneity. In the
estimation I use consumer-brand random effects to control for unobserved consumer
heterogeneity. The details of the implementation are provided in Appendix 1.
(3) Choice Set Simulation
To address the informational problem about brand existence I allow for heterogeneity in
consumer choice sets. The underlying choice sets over which consumers make utility
comparison are unobservable to researchers. Moreover, the number of potential choice
sets can be very large — with 51 brands in the market, the number of possible choice sets
is 2
51
. Hence instead of attempting to exhaust all possibilities, I simulate the choice sets.
In the simulation, the probability of a brand being included in a consumer’s choice set is
22
a function of brand advertising and purchase experience according to equation (2). The
details of the choice set simulation process are provided in Appendix 2.
(4) Properties of Estimator
After simulating the choice sets, I can calculate
ijt
P
ˆ
, the simulated choice probability of
each brand for each household on every purchase occasion, and conduct a maximum
simulated likelihood (MSL) estimation. The joint simulated likelihood function is:
Yijt
i t
ijt
p SL ) ( ˆ ) ( ? ?
??
= (11)
where Y
ijt
=1 if consumer i purchases brand j at time t, and Y
ijt
=0 otherwise. The joint
simulated log likelihood is:
)) ( ˆ log( ) ( ? ?
ijt
i t
ijt
p Y SLL
??
= (12)
The MSL estimator
?
? is a vector of parameters that maximize equation (12). Train
(2003) shows that if the number of simulation draws rises faster than square root of
sample size, then the MSL estimator is not only consistent but also efficient
asymptotically equivalent to the maximum likelihood estimator
14
) / , ( ~
ˆ
1 *
N H N
a
?
? ? ?
. Specifically, the MSL
estimator is distributed
(13)
where
*
? is the true parameter value, N is sample size, and
2 *
( )
( )
'
LL
H E
?
? ?
?
? = ?
? ?
is the
information matrix. In practice, I use
'
2
)
ˆ
(
ˆ
? ?
?
? ?
?
=
SLL
H to approximate the value of H and
calculate the estimated variance.
14
Monte-Carlo studies done by Keane (1994) and Geweke et al. (1994) also suggest that MSL has excellent small
sample properties if reasonably good simulators are used.
23
Section 2.2: Results of Demand Estimation without IV
The demand estimation is validated on the panel data in the Los Angeles RTE cereal
market
15
. There are 1,402 households with 69,134 cereal purchases in the LA market
from December 1997 to December 2003. The first 12 months of each household’s
purchase history are used to construct its experience set. As a result, households staying
in the homescan panel for less than 12 months are dropped out of the estimation. The unit
of observation in the estimation is a transaction, i.e., a household-purchase date-brand
combination. Observations with missing values on key estimation variables are dropped
out
16
To guide the choice of variables, I first run a preliminary regression --- multinomial
logit regression with full information. Consumers are assumed to know all brands for sale
and also their quality. The coefficient estimates are shown in Table 5. The interaction
terms of household demographics and brand characteristics that are not significant are
excluded in later regressions. Since the multinomial logit model is subject to
independence of irrelevant alternatives and does not capture the realistic substation
. The regressions start from July 1999 since the earliest advertising data is available
in January 1999 and to calculate the advertising stock we need advertising data six
months ago. The estimation sample consists of 844 households and 37,858 transactions,
which remains unchanged in all specifications. Values of the key variables in the
estimation sample are summarized in Table 4. In all specifications 50 brand dummies are
used.
15
The modeling technique and estimation method in this paper are not specific to a particular geographical market or a
particular experience good. I can apply the model to environments where consumers face the two types of
informational problems, for example, consumer choice of cosmetics, credit cards, health care plans, etc.
16
The missing values do no happen systematically so I am not concerned with a selection bias.
24
patterns, the random coefficient logit model is used instead where a random component is
added in the coefficients of price, advertising, fiber content, and sugar content,
respectively. After the variable selection guided by the multinomial logit, I run three
random coefficient logit models with different informational assumptions. First, I assume
that consumers have full information about both brand quality and brand existence. The
choice set is the same over time and across consumers. The second specification is a
regression with learning about quality information, where consumers are assumed to
know all brands for sale in the market but not the quality of unused brands. In the third
specification, consumers are assumed to have limited information about both the quality
of unused brands and the brand existence. A random coefficient logit with quality
learning and heterogeneous choice sets is estimated. Note that the three specifications are
non-nested. To compare them, ideally I would like to construct a test statistic with a
limiting distribution, so that I can select one specification over the other with some
confidence level. However, our panel data do not satisfy the distributional assumptions of
tests for non-nested models, for example, Vuong (1989) and Chen & Kuan (2002).
Therefore, to assess the goodness of fit I use two methods. First I compare the different
specifications using the Akaike Information Criterion (AIC) and using a measure of
predictive performance developed by Betancourt and Clague (1981). Then I construct a
variable which measures market share prediction errors of the three specifications to see
how well they predict consumer choices.
25
2.2.1. Estimation with Full Information
The benchmark specification is a random coefficient logit regression where consumer
choice sets include all 51 brands and characteristics of all brands are known. The
benchmark model allows me to examine in a simple way how price and advertising affect
demand and have a sense of the temporal dependence of consumer choices. The results
also serve as a baseline for later comparisons.
The parameter estimates of the benchmark specification are reported in column I of
Table 6. Price is negative and significant. The price sensitivity decreases as household
income increases and if the household has no kids. On average, advertising’s prestige
effect is negative and marginally significant. But the prestige effect increases as income
grows and when there is no kid in the household. unused is negative and significant. If we
calculate the odds ratio, we can see that the fact that a brand was never purchased before
decreases the brand choice probability by 75%. However, unused*adv is positive and
significant, suggesting that more advertising signals better quality to inexperienced
consumers. The signaling effect diminishes with income and when the household has no
kid. All six past choice variables are positive and significant. The coefficient of chosen_2
is slightly higher than that of chosen_1, consistent with the fact that consumers usually
switch away from the brand last purchased if the brand was a new try. Both fiber and
sugar are negative and significant. Older consumers without kids prefer more fiber and
less sugar.
26
2.2.2. Estimation with Limited Information about Brand Quality
In the second specification, I run a random coefficient logit regression where all
consumers face the same choice set of 51 brands but they do not know the quality of
brands not bought before. Consumers form expectation of brand characteristics based on
their previous experience with brands in the same segment. They also infer brand quality
from advertising and brand quality can be ascertained after one purchase. The signs of
many coefficients (column II of Table 5) are the same as those of the benchmark
regression, and for most coefficients the magnitudes are comparable. The coefficient on
adv is still negative but no longer significant. The only coefficient that changes sign is the
fiber coefficient, but it is not significant.
The similarity of the coefficients (and the log likelihood) to the benchmark suggests
that limited information about brand quality does not significantly affect consumer
behavior. This is probably due to the nature of the RTE cereal market — the cost of
experimenting with an unused brand is low, thus uncertainty about brand quality may not
be an important factor when consumers decide which brand to buy.
2.2.3. Estimation with Limited Information about Both Brand Quality and Brand
Existence
In the third specification consumers have limited information on both brand quality and
brand existence. They still infer quality of unused brands from experience and
advertising, but their choice sets are now heterogeneous and vary over time. The
probability of having a particular choice set for each consumer on each purchase occasion
follows equations (1) and (2), and the choice set is simulated as described in Appendix 2.
27
The price coefficients (column III of Table 5) suggest that allowing for heterogeneous
choice sets increases price sensitivity. The coefficient on price is significantly bigger than
in the first two scenarios. To get a sense of how the price coefficient translates into price
elasticity, I increase each brand’s price by 1% separately and simulate the consumer
choices based on the parameter estimates. Consumer choices are then aggregated to
calculate the % change in brand market shares resulting from the 1% price change. The
values of own price elasticity for the top 10 brands are reported in Table 7. Compared to
the previous two specifications, the price elasticity in the current one is much larger. The
estimated price elasticities in the third specification are more plausible since their
absolute values are all bigger than 1, which is consistent with the fact that profit-
maximizing firms should be operating at the elastic part of the demand curve.
When consumers have limited information about brand existence, they are not
aware of brands outside their choice set and therefore cannot respond to the price changes
of those brands. If we estimate the model as if consumers had full information about
brand existence, we are in essence imposing that consumers know the price changes of all
brands but choose not to respond to some of them. As a result, the price elasticity is lower
in the “full information” case. The price estimate in the third specification suggests that
consumers are actually much more sensitive to price changes of the brands that they are
aware of. Should the consumers have lower information search costs and know more
brands for sale, they would switch more frequently when price cuts are available.
Therefore, if the information problem about product existence is alleviated, the market
should be more competitive as consumers would be more responsive to price variations.
28
In the utility function, the coefficient on adv is negative but not significant,
implying that advertising’s prestige effect is not important. The coefficient on
unused*adv is positive and insignificant, suggesting that advertising’s informative effect
on brand quality is not significant. In the choice set formation, ?
1
(coefficients on adv in
equation (2)) is positive and significant while ?
4
(coefficients on adv
2
in equation (2)) is
negative and significant. Advertising raises the probability that consumers are informed
of the brand, but this effect exhibits decreasing returns to scale. The coefficient on
adv*inc, ?
2
, is negative and significant, suggesting that the informative effect of
advertising on brand existence decreases with household income. In contrast, the
coefficient on unused*adv*inc in the utility function is positive and significant,
suggesting the informative effect of advertising on brand quality increases with
household income. This makes sense if richer consumers have higher opportunity cost of
time and watch less TV commercials, but once they are alerted to the availability of an
unused brand, they rely more on advertising to obtain the quality information than other
methods of searching. The coefficient on adv*nokid in choic set formation, ?
3
, is positive
but not significant, implying that the effect of advertising does not vary with the presence
of kids. Figure 4 plots the probability of a brand entering a consumer's choice set against
the brand's advertising expenditure evaluated at the mean level of household income and
presence of kids. At the mean of advertising stock ($3.22 million), the probability of a
brand being included in the choice set is 88%. Increasing advertising stock by $1 million
from the mean will result in a probability of 99% that the brand is included in the choice
set. What is consistent over the three specifications is that advertising plays a significant
29
role in providing information to consumers but it does not have a significant prestige
effect.
The past choice variables are still positive and significant, suggesting that
consumers form persistent habit in cereal purchases. Compared to the results obtained
without heterogeneous choice sets, the dependence on the past choice variables falls. The
smaller coefficients on past choices are consistent with the larger (in absolute value)
coefficient on price: consumers are more likely to switch brands in response to price
changes when they rely less on previous experience.
2.2.4. Comparison of Goodness of Fit
To compare the goodness of fit of the three specifications, two measures are computed.
The first measure is the Akaike Information Criterion (AIC), which equals 2*k-2lnL,
where k is the number of parameters and lnL is the log likelihood. The AIC imposes a
penalization on more parameters and the smaller the value of AIC, the better the model
fit. The AIC for the first specification is 212930, for the second one is 201386, and for
the third one is 164516. Hence according to the AIC the third specification fit the data
best.
Second, I compute a measure of predictive performance for discrete choice models
developed by Betancourt and Clague (1981). The measure is based on the idea of
information entropy. It rewards correct predictions when predicted choices are the same
as observed choices and penalizes wrong predictions when predicted choices are different
from observed choices. Moreover, the summary measure scores each choice prediction
by giving it points not only in accordance with whether the prediction is correct but also
30
in a way that reflects the degree of certainty of the prediction
17
51
1
( log )
it ijt ijt
j
E P P
=
= ?
?
. To obtain the measure,
we first need to calculate the entropy for an observation in terms of predicted
probabilities, . Then the amount of information contained in the
predicted probabilities P
ijt
is defined as
max
1 /
it it
I E E = ? , where
max
1 1
log( )
51 51
E = ?
18
1 2
( ) / I I I N = ?
and
represents the maximum amount of uncertainty associated with the data distribution.
Defining a correct prediction as P
ijt
>1/51 when brand j is chosen at time t and P
ijt
< 1/51
when it is not chosen, we can calculate the amount of information contained in the
sample set of predictions as , where I
1
is the sum of information for all
correct predictions, I
2
is the sum of misinformation for all incorrect predictions, and N is
the number of observations. The specification with the highest value of I predicts the
data best
19
I . Applying the formula to our data, I obtain that the for the first specification
is -11.5, for the second one is -13.2, and for the third one is 0.8
20
Next I construct a variable to check how well the three specifications predict
aggregate consumer behavior. Using the parameter estimates, I first predict consumer
brand choice on each shopping occasion, which is the brand that generates the highest
.
Again the third
specification represents the best fit.
17
For a more detailed discussion of the measure, please refer to Section 4.6 of “Capital Utilization: A Theoretical and
Empirical Analysis”, Betancourt R. and C. Clague, Cambridge University Press, 1981. The original measure is defined
for cross-section data but can be easily extended to panel data. When choice sets are simulated, the probabilities used in
the calculation are the mean of simulated probabilities.
18
The formula is
max
1 1
log( ), E
J J
= ?
where J is the number of alternatives. In our case J=51.
19
Betancourt and Clague (1981) continue to develop several measures that capture the amount of information provided
by the introduction of the theoretical model relative to the information contained in the sample. Since my goal is only
to compare the three specifications, I do not calculate the other measures. Interesting readers should refer to their book
for more information.
20
A negative value of I
suggests that the misinformation contained in wrong predictions exceed the information
contained in correct predictions. It can arise for two reasons: (1) there more wrong predictions than correct predictions,
(2) the wrong predictions generate probabilities farther away from 1/51 relative to the correct predictions.
31
utility for the consumer on that shopping trip. Assuming that the consumer would
purchase the same quantity of cereal as in the data, I can then calculate the consumer
expenditure on that shopping trip. Summing up the consumer expenditures for each brand
in the sample period, I get the predicted brand sales and brand market shares. Then I
square the difference of predicted market share and observed market share for each
brand, sum up the squared differences for all brands, and take the squared root of it to
obtain the measure of market share prediction error. As shown in Table 8, the third
specification generates the smallest market share prediction error compared to the first
two.
In summary, introducing limited information about brand existence into the model
improves the data fit and better captures consumer behavior. Therefore, I will base the
following estimation on the limited information specification where consumer choice sets
are heterogeneous.
The estimated parameters have important implications for brand pricing and
advertising strategies. A brand’s pricing decision depends on the price elasticity of
demand. Advertising provides product information and impacts the composition of
consumer choice sets, which can also affect consumer substitution. Therefore, a brand’s
advertising level also depends on the consumers’ sensitivity to changes in advertising.
Given the parameter estimates in Column III of Table 6, I calculate the own and cross
price elasticities for the top 25 brands
21
21
The remaining 25 brands have market shares less than 1% and relatively few observations, therefore the simulation
errors might be big.
, which are reported in Table 9. The formula for
computing the price elasticities are included in Appendix 4. The price elasticities are
evaluated at the median of each brand’s price and the sample market shares.
32
As is previously mentioned, the researchers do not observe some brand characteristics
but market participants do. This leads to inconsistency in price and advertising
coefficients because firm pricing and advertising decisions are most likely related to the
unobserved brand characteristics. A solution to this endogeneity problem involves
instrument variables. BLP show that variables that shift markups are valid instruments for
price in a market of differentiated products. A similar argument also applies to
advertising. Therefore, in Chapter 3, I choose instruments for price and advertising and
re-estimate the demand function.
33
Chapter 3: Instrumental Variable Estimation
Section 3.1: IV Estimation Algorithm
A variety of differentiated-products pricing models predict that price is a function of
marginal cost and a mark-up term. If advertising is also included as a decision variable,
then the models also predict that advertising is a function of marginal cost and
characteristics of other brands.
The firm side competition suggests that the optimal price and advertising levels
depend on the characteristics, prices, and advertising levels of all brands offered. Brands
facing more competition (due to existence of close substitutes in the characteristic space)
will tend to have lower markups relative to brands facing less competition. If brand
characteristics are exogeneous, then the characteristics of other brands are valid
instruments for price and advertising. In the RTE cereal market, characteristics of a brand
will not change once the brand is introduced into the market. Therefore the exogeneity of
brand characteristics is a reasonable assumption. However, the price and advertising
levels of other brands are not valid instruments, since they are correlated with unobserved
brand characteristics through consumer utility maximization. On the other hand, variables
that shift production costs, for example, ingredient prices, wages of manufacturer
workers, are candidates for instruments too. The following section will present the results
of demand estimation using these instruments. Note that the estimation results do not
depend on any assumption on firm competition except that the firms are competing in a
differentiated product market by choosing both price and advertising.
34
In the nonlinear discrete choice model, IV estimation cannot be directly implemented
on the consumer level data. One way to make use of instrument variables involves
aggregating consumer choices and matching predicted brand market shares with observed
brand market shares, then inversing the market shares to get the component of utility
function that does not vary with individuals. This component is a linear function of price,
advertising, and other brand characteristics, and one can estimate this function with IV
for price and advertising.
Formally, let ?
jt
= [fiber
jt
sugar
jt
price
jt
adv
jt
]
22
1
2
i
i
i i
i
i
D v
?
?
?
?
?
(
(
(
= + ?• + ?•
(
(
(
¸ ¸
,
?
i
= , where
1
2
?
?
?
?
?
(
(
(
=
(
(
(
¸ ¸
, D
i
=
[income
i
age
i
nokid
i
]’, and v
i
=
[v
1i
v
2i
v
3i
v
4i
]’.
Then we can write the utility function as
(20)
ijt jt i ijt i ijt jt ijt jt ijt
U unused unused adv pastchoice ? ? ? ? ? ? ? = + ? + ? ? + • + +
Let
jt jt jt
x ? ? ? = + (21)
Note that although ?
,
?
,
? , ?, and ? can be estimated with micro data, we cannot
estimate ? without a further assumption to separate out the effect of ? from the effect of
? on ?. To provide consistent estimates of ? we will use IV for price and advertising.
All parameters are estimated simultaneously. The estimation involves three sets of
moment conditions:
22
Although the true fiber and sugar contents of brands do not vary over time, the expected fiber and sugar contents do.
35
(1)The consumer brand choices, which match the model’s predicted brand choice
probabilities to observed brand choices,
(2)Brand market shares, which match the model’s prediction for brand j’s market share in
year t to its observed market share in year t,
(3)Firms pricing and advertising decisions, which express an orthogonality between the
unobserved characteristics and the instruments.
To be more specific, the estimation algorithm consists of four steps. (i) Given an
initial guess of ?
,
?
,
? , ?, and ? , I first find the values of ?
jt
that equates the predicted
market shares (?
jt
(?, ? , ?
,
? , ?, ? ))
and the observed market shares (S
j
) using the
iteration
1
ln( ) ln( ( ))
h h h
jt jt jt jt
S ? ? ? ?
+
= + ? . The details of calculating ( , , , , , )
jt
? ? ? ? ? ? ?
and the
proof that the above iteration is a contraction mapping are provided in Appendix
3. (ii) Given ?
jt
, I provide random draws for unobserved consumer heterogeneity and for
choice set formation, then use maximum simulated likelihood to obtain estimates of ?,
?
,
? , ?, and ? by matching the observed choices with the predicted choice probabilities.
Note that these estimates do not depend on any distributional assumptions of ?. The
probability of a household with observed characteristics D
i
choosing brand j given
?, ?, ?
,
? , ?, and ? b is given by
51
1
exp( )
Pr( | , , , , , , ) ( ) ( )
exp( )
jt jt i jt ijt i ijt jt ijt
i
v
kt kt i kt ijt i ijt j ijt
k
D v unused unused adv pastchoice
j D f v d v
D v unused unused adv pastchoice
? ? ? ? ? ?
? ? ? ?
? ? ? ? ? ?
=
+ ? + ? + ? + ? ? + •
? ? =
+ ? + ? ? + ? ? + •
?
?
? ? ? ?
? ? ? ?
(22)
The integrals are computed by simulation. (iii) Given the new values of ?
,
?
,
? , ?, and
? , repeat the first two steps until ???
,
?
,
? , ?, and ? converge. (iv) Using the ?
jt
36
obtained in step (iii), construct the moment condition ( | ) 0
jt
E z ? = , where
jt jt jt
? ? ? ? = ? and z represents instrument variables, and estimate ? by minimizing the
sample moments ( )
j j
j
G z ? ? =
?
?
23
?
.
Section 3.2: IV Estimation Results
I implement the estimation algorithm with two sets of instruments. The first set of
instruments includes the fiber and sugar contents of all other brands. The second set of
instruments are the cost shifters, including wage of food workers, wage of advertising
managers, corn price, wheat price, gasoline price, and electricity price. From the website
of Bureau of Labor Statistics, I collect the hourly wage data for food workers (under the
category Food and Tobacco Roasting, Baking, and Drying Machine Operators and
Tenders) and for advertising mangers (under the category Advertising , and Public
Relations Managers) in the Los Angeles – Long Beach MSA from year 1999 to year
2003. Corn price and wheat price are obtained from the Farmdoc project of University of
Illinois. Gasoline and electricity prices are collected from the website of Energy
Information Administration of Department of Energy. These cost measures are interacted
with brand dummies to serve as instruments in the estimation. The estimates
combining both sets of instruments are reported in Column IV of Table 6.
To test the endogeneity of price and advertising, I run an OLS regression of equation
(21) after I obtain ?
jt
in step (iii) and compare the coefficients with the IV estimates. The
Hausman test of the two sets of estimates yields a P value of 0.55, therefore the OLS
23
Berry, Linton and Pakes (2004) show that in this type of BLP model with two sources of errors, the sampling error
and the simulation error, both the number of observations and the number of random draws for simulation need to grow
at rate J
2
for the parameter vector to have an asymptotically normal distribution.
37
estimates are not significantly different from with IV estimates. Hence the endogeneity of
price and advertising does not affect the coefficient estimates much in this application.
Since the price and advertising coefficient estimates without IV are much more precise
than the IV estimates (in the IV estimation only 255 observations (? by brand and by
year) can be used while in the estimations without IV 37,858 transactions are used), I will
conduct policy experiments using the estimates without IV in the following sections.
38
Chapter 4. Policy Experiments
In this chapter I conduct some counterfactual experiments to evaluate some of the brand
marketing strategies and a hypothetical food policy change. In the first two experiments, I
choose brand 28 as an example because it was newly introduced into the market in
January 2003 (Figure 5 summarizes brand 28’ average monthly prices, sales, and
advertising in the estimation sample). Marketing managers are usually concerned with
what price to charge and how to schedule advertising expenditures when a new product is
launched. Therefore looking into the data of brand 28 offers us an opportunity to evaluate
the marketing strategies of a product at the beginning of its life cycle. In the third
experiment, I try to explore the effect of a hypothetical policy change — banning cereal
advertising targeted to children — on consumer choices. A caveat should be born in
mind when we interpret the results of the experiments: I keep the strategies of other firms
unchanged when I simulate the results, thus the optimal responses of rival firms are not
taken into account
24
.
Section 4.1: Pricing Strategy for Brand 28
I first vary brand 28’s price from its observed price by +1%, +5%, -1%, and -5%,
separately. Each time under the new pricing scheme, I calculate every household’s
simulated choices and aggregate them to get brand market shares and sales. The resulting
24
To derive the optimal responses, we need to solve a competitive equilibrium. However, the static Bertrand
equilibrium is not realistic and the dynamic equilibrium is very hard to solve.
39
changes in market share and sales of brand 28 are reported in Table 10. We can see that if
the price is cut down by 5%, the sales improve by 2.3% compared to the sales figure
before the price cut. The market share expands by 6.5%, which more than compensates
for the reduction in price. Therefore, brand 28’s price was too high in general.
To see how the price cut affects different types of consumers, I calculate the changes
in expenditures for different demographic groups after the price drops by 5%. I divide
consumers by household income (high if household income>=$55,000, low otherwise),
by age of female household head (old if age>=32, young otherwise), and by the presence
of kid in the household. The results by demographic groups are shown in Table 11.
Consumers with lower income and having kids respond more to the price cut than their
counterparts, while the response does not vary with age groups.
Next I look at the average (weighted by volume) daily transaction prices of brand 28
at its introductory stage (the first 3 months of year 2003) and see if its sales can be
increased by altering the depth and frequency of the price discounts. The observed daily
transaction price series for brand 28 from Jan 2003 to March 2003 is shown in Figure 6.
The initial price was very high, followed by a period of medium price level. Deep price
discounts happened twice when the price was about 60% of the average level. I consider
an alternative pricing strategy, whereby price is set to be 70% of the average price in this
period for the first week of each of the 3 months and 100% of the average price in the
remaining weeks. The observed prices and the counterfactual prices in this period are
plotted in Figure 4. With the new pricing strategy, I find that brand 28’s market share
goes up by 1.5% and sales go up by 1.2%. High introductory price is not desirable in this
case because consumers are loyal to brands they are already using. To warrant a switch,
40
the utility associated with the new brand needs to be sufficiently high, which could be
achieved by lower introductory price. Consumers who are lured into purchase by the low
introductory prices will then form brand loyalty, thus the brand manager can profit by
setting price low initially and increasing it later.
There may be two reasons why the brand manager would set a high initial price as
observed in the data. On the one hand, higher prices may be used by the brand manager
as a signal for better quality in a market with limited information and hence attracts
consumers with higher willingness to pay. However, in the cereal market, many private
label products have been introduced at low prices and many consumers have come to
realize that lower price does not necessarily affect the quality or taste
25
. Therefore, a high
initial price would limit the consumer demand. On the other hand, the brand manager
may have underestimated the price elasticity. As shown in section 5, if demand is
estimated ignoring that consumers have limited information about product brand
existence, price elasticities would be understated, which could lead the manager to set a
higher than optimal price.
Section 4.2: Advertising Strategy for Brand 28
A major consideration of a brand manager is to determine the best schedule of advertising
expenditures for a certain budget. Conceptually, the manager could choose to do
continuous advertising (i.e., schedule ad expenditure smoothly over all times) or follow a
strategy of pulsing (i.e., advertise in some weeks of the year and not at other times). We
observe in Figure 5 that brand 28’s advertising was relatively smooth over time. In
25
See the article “Eating Well”, New York Times, September 22, 1993.
41
contrast, many advertisers of consumer packaged goods use pulsing strategies. For
example, Dubé, Hitsch, and Manchanda (2005) find that pulsing is the optimal
advertising strategy in the frozen entrée market. Naik , Mantrala , and Sawyer (1998)
develops a model of dynamic advertising that shows that pulsing strategies can generate
greater total awareness than the continuous advertising when the effectiveness of
advertisement varies over time. Specifically, ad effectiveness declines because of
advertising wears out during periods of continuous advertising and it restores during
periods of no advertising. Such dynamics make it worthwhile for advertisers to stop
advertising when ad effectiveness becomes very low and wait for ad quality to restore
before starting the next "burst" again. They also show that the form of the best
advertising spending strategy is pulsing for a major cereal brand.
To mimic the pulsing strategy, I reschedule brand 28’s advertising by equally
dividing the 2003 total ad expenditure into the six odd months, while in the six even
months advertising is set to zero (Figure 7 plots the observed advertising v.s. the
counterfactual pulsing advertising). Then I recalculate consumer choices under the new
advertising strategy. The results show that brand 28’s market share and sales both
increase by 1.9%. The pulsing strategy works better because it can increase the
probability of brand 28 entering the consumer choice set in the first two months after its
introduction. In the observed data, the advertising expenditure for brand 28 in January is
0 while in the pulsing strategy it is 3.3 million. The increase in the advertising
expenditure in January raises the probability of an average consumer (with mean income,
mean age, and mean presence of kid) being aware of brand 28 from almost 0 to 89.7%. In
February the pulsing strategy increases the advertising expenditure of brand 28 from 2.99
42
to 3.14 million and the probability of an average consumer being aware of brand 28 from
78.3% to 84.5%. In the following months an average consumer will be aware of the brand
with probability close to 1 in both strategies. Therefore, under the pulsing strategy, more
consumers are aware of the brand since the beginning and have a higher probability of
choosing it. Some of these consumers become habituated to the brand and hence the
pulsing strategy can increase the overall market share of this brand. I also examine how
different consumer groups respond to the pulsing strategy. Results in Table 12 suggest
that consumers with higher income and kids are more sensitive to the change in
advertising strategy, while age does not matter.
In the advertising data, 98.9% of advertising expenditure is spent on national media such
as network TV, national sport radio, and national newspaper. Therefore, the pulsing
strategy could also increase sales in other local markets without changing the advertising
budget, and could potentially be very profitable.
Section 4.3: Effects of Banning Children-Oriented Cereal Advertising
There have been many public debates on food marketing aimed at children. As early as in
1978, the FTC issued a staff report that concluded that “television advertising for any
product directed to children who are too young to appreciate the selling purpose of, or
otherwise comprehend or evaluate, the advertising is inherently unfair and deceptive”,
and that “it is hard to envision any remedy short of a ban adequate to cure this inherent
unfairness and deceptiveness.” Naturally FTC faced strong opposition from broadcasters,
ad agencies, and food and toy companies. And in 1980 Congress passed the Federal
Trade Commission Improvements Act of 1980 that barred the FTC from issuing industry-
43
wide regulations to stop unfair advertising practices
26
. However, as the childhood obesity
problem becomes more and more of a concern in recent years
27
A study by The Kaiser Family Foundation indicates that children of all age groups are
exposed to a large amount of food ads every day (Table 13). Of all genres on TV, shows
specifically designed for children under 12 have the highest proportion of food
advertising (50% of all ad time). And of all food ads that target children or teens, 28%
are for sugary cereal
, policymakers in
Congress, FTC, and some consumer advocates are calling for restrictions on advertising
to children about candy, sugary cereal, and other junk food.
28
In our data, I do not directly observe how much ad dollars are for marketing toward
children. In order to measure the effects of the policy change, I approximate the ban of
children oriented cereal advertising by eliminating the advertising expenditures for kid
cereal brands while holding other factors unchanged. In the experiment, I replace the ad
stock of these brands with 0, and calculate how the brand market shares change. The total
changes for each brand segment (Family, Adult, Kid) are summarized in Table 15. After
the hypothetical policy change, the total market share of kid brands goes down by about
6%, of which 2% goes to the adult brands and 4% goes to the family brands.
. Table 14 summarizes the sugar and fiber contents of different
types of cereal brands. Not surprisingly the kid brands are highest in sugar and lowest in
fiber. It is, therefore, interesting to see if the cereal TV advertising toward children were
to be banned, what would happen to consumer expenditures and nutritional intakes.
26
See the article “Limiting Food Marketing to Children” on www.cspinet.org/nutritionpolicy.
27
On Wikipedia.com, it is stated that the rate of overweight and obese children in the United Staes is 32% in 2008.
28
See “Food for Thought: Television Food Advertising to Children in the United States”, released by The Kaiser
Family Foundation, March 28, 2007.
44
Then I look at how the policy change affects the nutrition intakes and expenditures of
different consumer groups. The results are summarized in Table 16. Overall after the ban
of children oriented cereal advertising, consumers will consume more fiber and less sugar,
which is better for their health. Consumers who are younger, with lower income and with
kids reduce their sugar intake and increase their fiber intake more than their counterparts.
Therefore, the policy change seems to have more effect on the “right” group of
consumers. In the meantime, after the ban consumers of all demographic groups will
have to increase their expenditures after the policy change as they consume more adult
and family cereals, which are more expensive than kid cereals.
Section 4.4: Concluding Remarks
This paper considers limited information on both product existence and product quality in
a dynamic model of consumer choice in an experience good market. On each purchase
occasion, a consumer first forms a choice set depending on her purchase experience and
brand advertising. Conditional on the choice set, she then chooses the brand that
maximizes her expected utility. The empirical model is estimated on a rich panel of
household purchase data in the RTE cereal market. The results suggest that limited
information about product existence leads to larger estimates on price elasticity.
Advertising has a significant effect informing consumers of brand existence and signaling
product quality, while its prestige effect is not significant. I also find that conditional on
repurchase after the first experience with a brand, consumers form strong habits. The
counterfactual experiments show that the observed brand marketing strategies are not
always optimal: managers can increase sales by resetting price, rescheduling price
45
discounts, or altering their advertising strategies. An evaluation of a hypothetical policy
change – ban on cereal advertising toward children – suggests that the policy could direct
consumers to healthier diet.
The results of the experiments should be taken with caution though. In all of the
experiments I do not consider the competitive responses of other firms to the change in
brand strategies. Neither do I account for the fact that firms may change the way they
promote kid brands once the government regulation comes into play. To control for these
responses, I will need to solve the firm profit maximization problem. In a model with
brand loyalty on the consumer side, the firm side problem should involve dynamic
optimization: firms not only consider the effect of pricing and advertising on current
consumer choices, but also the effect on future demand and future profits. However, the
dynamic optimization problem with multiple firms each with multiple brands is
extremely hard to solve and thus left for future research. In addition, many brand
marketing strategies are decided by manufacturers and retailers together. This paper only
focuses on the role of manufacturers. A vertical competition model will be needed to
analyze the role of retailers.
46
Appendices
Appendix 1. Controlling for Unobserved Consumer Heterogeneity
I use introduce consumer-brand random effects to capture the unobserved consumer
heterogeneity in brand preferences. Specifically, the utility function can be written as:
ijt ijt ij ijt
U Z ? ? = •?+ +
where Z
ijt
represents the vector of explanatory variables, ? represents the vector of
coefficients corresponding to Z
ijt
, and
ij
? represents consumer i's unobserved preference
for brand j, which is independent from
ijt
Z and
ijt
? .
Let
ij ij j
? µ ? = + .
2
(0, )
ij ij
N µ ? ? , and ( )
j ij
E ? ? = is a constant. Assuming
ijt
? has a
Generalized extreme value distribution, then we can write the probability of consumer i
choosing j conditional on
1 i
µ ,
2 i
µ , …,
51 i
µ , and choice set
it
C as:
51 51
1 2 51 51
51 51
1
exp(( ) )
( | , ,..., , )
exp(( ) )
ijt i t ij j
i i i it
ilt i t il l
l
Z Z
P j C
Z Z
µ ? ?
µ µ µ
µ ? ?
=
? •?+ + ?
=
? •?+ + ?
?
51
1
exp( )
exp( )
ijt ij j
ilt il l
l
z
z
µ ?
µ ?
=
•?+ +
=
•?+ +
?
where for the second equal sign we use
51 ijt ijt i t
z Z Z = ? and
51 j j
? ? ? = ? .
( | )
it
p j C is equal to
1 2 51
( | , ,..., , )
i i i it
P j C µ µ µ integrated over the marginal
distribution of the
ij
µ ’s. Specifically, it is equal to
1 2 51 1 2 51 51
1
exp( )
... ( ) ( )... ( ) ...
exp( )
ijt ij j
i i i i i i
ilt il l
l
z
f f f d d d
z
µ ?
µ µ µ µ µ µ
µ ?
? ? ?
?? ?? ??
=
•?+ +
•?+ +
? ? ?
?
47
It is hard to compute ( | )
it
p j C analytically and I simulate it by taking S draws
from the distribution of
ij
µ , for all j. The simulator for ( | )
it
p j C is:
?
?
=
=
+ + ? •
+ + ? •
=
S
s
l
l
s
il ilt
j
s
ij ijt
it
z
z
S
C j p
1
51
1
) exp(
) exp(
1
) | ( ˆ
? µ
? µ
To reduce the number of parameters to be estimated, I allow
j
? to vary across
brand segment, and
2
ij
? to vary across both brand segment and whether the household has
kids or not. There are a total of eight parameters to estimate for unobserved consumer-
brand preferences, among which six are scale parameters:
2 2 2 2 2 2
, , , , ,
FK FN AK AN KK KN
? ? ? ? ? ? ,
where the first subscript denotes whether the brand belongs to family, adult or kid
segment, and the second subscript denotes whether there is any kid in the household; two
are location parameters:
A
? and
K
? , where the subscript denotes whether the brand
belongs to adult or kid segment.
F
? is normalized to zero.
Appendix 2. Choice Set Simulation Details
In the simulation, I assume that choice set is a function of brand advertising and purchase
experience as shown in equation (1) and equation (2). The specific choice set simulation
process is outlined as follows.
Step 1. Calculate
ijt
q (?) for each consumer, each brand, and each time, where ?=(?
0,
?
1,
?
2
).
Step 2. For each consumer-time-brand combination, draw a random number
r
ijt
u from the
uniform distribution between 0 and 1.
48
Step 3. If
r
ijt
u <
ijt
q , then brand j is included in consumer i's choice set at time t. Otherwise
it is not. This defines the choice set in the rth simulation
r
it
C .
After simulating the choice set, I can calculate simulated brand choice probabilities for
each consumer.
Step 4. Calculate ( | )
r
it
P j C , consumer i's probability of choosing brand j conditional on
r
it
C
.
(The formula for calculating ( | )
r
it
P j C
depends on the distributional assumption on the
error term in the utility function).
Step 5. Calculate (1 ) ( | )
r r
it it
r r
ijt ijt ikt it
j C k C
p q q P j C
? ?
= ? ×
? ?
, consumer i’s unconditional
probability of choosing brand j at time t in the rth simulation.
Step 6. Draw the random numbers
r
ijt
u repeatedly for R times, each time repeat steps 2-5.
Step 7. Calculate the simulated choice probability
?
=
=
R
r
r
ijt ijt
p
R
p
1
1
ˆ .
Appendix 3. Contraction Mapping Details
In the instrumental variable estimation, we need to find the ? that make predicted market
shares based on the model equal to the observed market shares. Given an initial guess of
?, ?, and ? , the predicted market share for brand j, ( , , , , , )
h
j
? ? ? ? ? ? ? , is calculates as
follows.
First, based on advertising data and household characteristics, simulate choice sets for
each consumer on each shopping occasion.
49
Second, given ?, ?, ? , ?, ?, and ?, a consumer compares the utility levels of all brands in
her choice set on the shopping occasion and chooses the one that yields the highest
utility.
Third, sum up consumer brand choices in a year to get predicted brand market shares.
To obtain the values of ? that solves ( , , , , , )
h
j
? ? ? ? ? ? ? =S
j
, we use the iteration
1
ln( ) ln( ( , , , , , ))
h h h
j j j j
S ? ? ? ? ? ? ?
+
= + ? ? ? . The proof that the iteration is a contraction
mapping follows Goeree (2007).
Define ( ) ln( ) ln( ( , , , , , ))
h
j j j j
f S ? ? ? ? ? ? ? = + ? ? ? . To show that f is a contraction
mapping, we need to show that ?j and m, ( ) / 0
j m
f ? ? ? ? ? , and
1
( ) / 1
J
j m
m
f ? ?
=
? ? <
?
.
We can write (1 ) ( | ) ( )
i j i i
j ilt ikt i
C l C k C
q q P j C f v dv ?
?? ? ?
= ?
? ? ?
?
,
where , and ?
j
denotes the set of choice sets that include j.
1
( ) / (1 ) ( | ) ( )
i j i i
m
j m ilt ikt i j
C l C k C j
f q q P j C Q f v dv ? ?
?
?? ? ?
? ? = ?
? ? ?
?
,
where
51
1
exp( )
( | ) ( ) ( )
exp( )
j j i j ij i ij j ij
i
v
k k i k ij i ij j ij
k
D v unused unused adv pastchoice
p j C f v d v
D v unused unused adv pastchoice
? ? ? ? ? ?
? ? ? ? ? ?
=
+ ? + ? + ? + ? ? + •
=
+ ? + ? ? + ? ? + •
?
?
? ? ? ?
? ? ? ?
exp( )
,
exp( )
0,
i
m m m i m im i im m im
j j
l l i l il i il l il
l C
j
D v unused unused adv pastchoice
Q if m
D v unused unused adv pastchoice
if m
? ? ? ? ? ?
? ? ? ? ? ?
?
+ ? + ? + ? + ? ? + •
= ??
+ ? + ? + ? + ? ? + •
= ??
?
? ? ? ?
? ? ? ?
Note that for m=j, ( | )
m
j i
Q P j C =
Since all elements in the integral are non-negative, we have ( ) / 0
j m
f ? ? ? ? ? .
Moreover,
, 51
1
j
m
j
m m
Q
?? ?
<
?
, therefore
, 51
( ) / 1
j
j m
m m
f ? ?
?? ?
? ? <
?
is satisfied.
50
Appendix 4. Price Elasticity Calculation
Suppressing the time subscript, we can write the consumer utility function as
ij i j j i ij
U p ? ? ?
?
= + ? + ?
where
3 33 3 i i
D v ? ? = + ? + ? ? ? , ?
j
represents the vector of variables other than price, and
?
?i
the vector of coefficients for ?
j
.
The formula for price elasticity is given by
1
1
1
ˆ ˆ (1 ) ( ) ,
1
ˆ ˆ ( ) ,
N
j
i ij ij
i
j
j
k
jk
N
k j k
i ij ik
i
j
p
p p f v dv j k
s N
s
p
p s p
p p f v dv j k
s N
?
?
?
=
=
¦
? =
¦
?
¦
= ? =
´
?
¦
? ?
¦
¹
?
?
?
?
where p
ij
represents the probability of consumer i choosing brand j.
In the estimation, I take NR random draws of v from f(v) to get ?
i
and compute ?
jk
using
the formula
1 1
1 1
1
ˆ ˆ (1 ),
*
ˆ
1
ˆ ˆ ,
*
i
i
N NR
j nr
ij ij
i nr
j
jk
N NR
nr k
ij ik
i nr
j
p
p p j k
s N NR
p
p p j k
s N NR
?
?
?
= =
= =
¦
? =
¦
¦
=
´
¦
? ?
¦
¹
??
??
51
Figure 1.
0
5
.
0
e
+
0
4
1
.
0
e
+
0
5
1
.
5
e
+
0
5
2
.
0
e
+
0
5
F
r
e
q
u
e
n
c
y
0 100 200 300
#of times a brand was purchased
#of Times a Brand was Purchased by a Household
Figure 2.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10 11 12
# of shopping trips since 1st purchase
Data Source: Neilsen Homescan Data 1997.12.to 2003.12.in L.A.
% of repurchasing after trying a new brand
52
Figure 3.
1 2 3 4 5 6 7 8 9 10
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
advertising expenditure
l
o
g
(
c
h
o
i
c
e
p
r
o
a
b
i
l
i
t
y
)
Effect of Advertising on Marginal Change in Choice Probability
information about existence
information about quality (Q=1)
information about quality (Q=2)
Figure 4.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Advertising Stock $M
P
r
o
b
a
b
i
l
i
t
y
Probability of a Brand Beiing Included in the Choice Set
53
Figure 5.
0
1
0
2
0
3
0
1 2 3 4 5 6 7 8 9 10 11 12
Month
advertising(m) avg monthly price(c/oz)
sales(50 dollars)
Source: TNS Media Intelligence and Neilsen Homescan,LA 2003.1-2003.12
Averge Monthly Advertising, Price, and Sales for Brand 28
Figure 6.
1
5
2
0
2
5
3
0
3
5
4
0
p
r
i
c
e
(
c
e
n
t
/
o
z
)
20 40 60 80 100
day
observed price counterfactual price
Source: Neilsen Homescan Data in L.A. 2003.1 to 2003.3
Average Daily Transaction Price for Brand 28
54
Figure 7.
0
1
2
3
4
a
d
v
e
r
t
i
s
i
n
g
(
m
)
0 5 10 15
Month
observed advertising counterfactual advertising
Monthly Advertisng for Brand 28
55
Table 1. Brand Entry and Exit
Enter Year 1998 1999 2000 2001 2002 Remaining Total
1998 & before 5 3 3 10 7 103 131
1999 0 1 4 1 2 10 18
2000 0 0 0 1 3 3 7
2001 0 0 0 1 3 8 12
2002 0 0 0 0 10 30 12
2003 0 0 0 0 0 13 13
Total 5 4 7 13 17 147 193
Data Source: Neilsen Homescan Data 1997.12. to 2003.12. in Los Angeles Market.
A brand entry is observed if the first transaction with the brand occurred after
1998.6. A brand exit is observed if the last transaction with the brand occurred
before 2003.7.
Exit Year
56
Table 2. Brand Summary Statistics
Brand
Number
Sample
Market
Share
1
(%)
Average
Transaction
Price
(cent/oz)
Average
Monthly
Advertising
($K)
Fiber
Content
(% Daily
Value per
30g)
Sugar
Content(%
Daily Value
per 30g)
Segment
2
1 5.73 17.22 1718.89 14.00 1.00 Family
2 4.51 18.44 1977.76 6.45 4.59 Family
6 4.45 12.26 2036.62 11.25 6.23 Adult
11 4.07 14.01 1045.85 5.90 6.39 Adult
8 3.99 11.95 1667.88 2.42 9.68 Family
7 3.69 11.96 1445.58 11.49 10.37 Family
3 3.56 15.85 1701.03 7.00 11.00 Family
12 2.88 14.98 406.50 4.12 12.39 Kid
4 2.71 17.74 785.01 5.00 10.00 Kid
16 2.50 13.71 319.99 3.56 6.71 Family
20 2.49 11.43 1623.61 10.34 4.40 Adult
9 2.38 18.22 878.28 0.03 7.91 Family
10 2.36 22.81 2143.30 9.15 5.21 Adult
15 2.35 18.66 437.65 6.00 13.00 Kid
13 2.09 13.80 1377.95 13.91 1.86 Adult
14 1.92 16.38 634.15 2.92 12.46 Kid
17 1.62 14.07 1293.78 7.50 7.03 Kid
23 1.62 9.60 5.65 14.75 8.64 Family
21 1.56 16.77 604.60 0.97 14.52 Family
18 1.55 15.61 698.44 8.30 8.61 Family
19 1.55 16.80 1243.06 1.59 13.39 Kid
38 1.48 17.48 435.98 4.00 13.00 Kid
5 1.39 20.91 1611.56 7.48 6.98 Adult
24 1.29 15.77 459.00 4.00 15.00 Kid
22 1.26 21.80 56.11 1.00 6.00 Adult
42 1.09 16.88 739.14 7.94 8.02 Adult
30 1.06 18.64 379.89 3.00 14.00 Kid
26 0.76 19.15 72.82 5.00 13.00 Family
25 0.72 19.11 423.71 4.00 11.00 Kid
47 0.72 15.08 746.76 3.10 11.38 Kid
46 0.71 17.01 87.48 8.69 5.88 Family
39 0.66 18.01 3.26 49.00 4.33 Adult
43 0.63 18.19 108.85 27.00 5.00 Adult
50 0.59 15.38 157.45 8.57 4.82 Adult
48 0.57 18.91 303.66 6.67 12.22 Kid
49 0.56 19.91 280.83 6.32 7.89 Family
27 0.54 19.55 0.00 7.09 7.64 Adult
40 0.52 15.64 102.95 1.94 10.65 Kid
45 0.46 21.43 177.74 4.36 6.00 Family
29 0.46 20.01 0.00 6.00 9.27 Family
31 0.44 23.30 208.99 2.00 13.00 Kid
37 0.43 21.49 381.66 0.00 12.00 Family
28 0.41 24.39 1653.81 12.00 10.00 Family
33 0.41 16.35 13.43 4.00 13.00 Family
44 0.35 16.95 229.33 8.13 6.10 Family
32 0.35 25.79 6.58 58.00 0.00 Adult
34 0.33 24.19 1.68 11.00 6.00 Family
57
Brand
Number
Sample
Market
Share
1
(%)
Average
Transaction
Price
(cent/oz)
Average
Monthly
Advertising
($K)
Fiber
Content
(% Daily
Value per
30g)
Sugar
Content(%
Daily Value
per 30g)
Segment
2
41 0.31 14.64 0.00 4.44 16.67 Kid
35 0.29 17.64 62.32 9.00 9.27 Adult
36 0.25 17.39 0.00 10.91 8.73 Adult
51 21.41 14.90 47.44 8.83 8.00 Family
Data Source: Columns II&III-AC Neilsen Homescan Data 1997.12 to 2003.12, Column IV-TNS Media Intelligen
Data Jan 1999 to Dec 2003, Columns V & VI - www.nutritiondata.com
1.Sample market is the Los Angeles Market from Dec 1997 to Dec 2003.
2.Brand segment categorization is based on each brand's description on manufacturer's website.
3. Characteristics of the 51th brand are computed as the average of the non top 50 brands.
58
Table 3: Summary Statistics of Homescan Data
Variable Definition NumObs Mean Std. Dev. Min Max
size household size 1402 3.25 1.53 1 9
inc household income ($K) 1402 57.11 29.58 2.5 125
age age of female household head 1402 48.86 12.99 20 70
nokid =1 if no kid in the household 1402 0.55 0.50 0 1
price transaction price (cent/oz) 69134 17.84 4.73 0 797.44
Data Source:Neilsen Homescan Data 1997.12. to 2003.12 in Los Angeles Market
59
Table 4. Summary of Variables in Estimation Sample
1
Variable Definition Mean Stdev Min Max
chosen 1{brand is chosen in current transaction} 0.02 0.14 0 1
price transaction price (cent/oz) 17.84 4.75 0 797.44
price*inc transcation price(cent/oz)*household income($K) 1031.84 629.38 0 13000
price*nokid transcation price(cent/oz)*1{household has nokid} 892.50 348.03 0 7400
adv stock of advertising expenditure ($M) 3.22 4.02 0 22.30
adv*inc advertising stock($M)*household income($K) 188.47 281.56 0 2787.46
adv*nokid advertising stock($M)*1{household has nokid} 1.95 3.51 0 22.30
unused 1{brand not purchased previously} 0.11 0.32 0 1
unused*adv 1{brand not purchased previously}*adv 1.82 3.29 0 22.30
unused*adv*inc 1{brand not purchased previously}*adv*household income($K) 106.57 223.03 0 2787.46
unused*adv*nokid 1{brand not purchased previously}*adv*1{household has nokid} 1.21 2.79 0 22.30
chosen_1 1{brand chosen on last shopping trip} 0.03 0.17 0 1
chosen_2 1{brand chosen 2 shopping trips ago} 0.03 0.17 0 1
chosen_3 1{brand chosen 3 shopping trips ago} 0.03 0.17 0 1
chosen_4 1{brand chosen 4 shopping trips ago} 0.03 0.17 0 1
chosen_5 1{brand chosen 5 shopping trips ago} 0.03 0.17 0 1
chosen_6 1{brand chosen 6 shopping trips ago} 0.03 0.17 0 1
sugar sugar content(% daily value per 30g) 8.81 3.73 0 16.67
sugar*age sugar content(% daily value per 30g)*age of female head 439.51 227.30 0 1166.67
sugar*nokid sugar content(% daily value per 30g)* 1{household has no kid} 5.22 5.19 0 16.67
fiber fiber content(% daily value per 30g) 8.58 10.28 0 58
fiber*age fiber content(% daily value per 30g)*age of female head 428.18 544.41 0 4060
fiber*nokid fiber content(% daily value per 30g)* 1{household has no kid} 5.08 8.96 0 58
adult*size 1{brand is adult brand}*household size 0.98 1.72 0 9
adult*inc 1{brand is adult brand}*household income($K) 17.25 30.98 0 125
adult*age 1{brand is adult brand}*age of female head 14.69 23.51 0 70
adult*nokid 1{brand is adult brand}*1{household has no kid} 0.16 0.37 0 1
kid*size 1{brand is kid brand}*household size 0.98 1.72 0 9
kid*inc 1{brand is kid brand}*household income($K) 17.22 30.95 0 125
kid*age 1{brand is kid brand}*age of female head 14.67 23.50 0 70
kid*nokid 1{brand is kid brand}*1{household has no kid} 0.16 0.37 0 1
1.Estimation sample consists of 890 households with 42396 transactions from 1999.1 to 2003.12 in LA market
60
Table 5. Preliminary Regression Results
Variable Coefficient
price 0.014**
(0.006)
price*inc 0.000***
(0.000)
price*age -0.000
(0.000)
price*nokid 0.012***
(0.003)
adv -0.004
(0.005)
adv*inc 0.000**
(0.000)
adv*age -0.000
(0.000)
adv*nokid -0.000
(0.003)
unused -1.802***
(0.018)
unused*adv 0.698***
(0.030)
unused*adv*inc -0.001**
(0.000)
unused*adv*age -0.001
(0.001)
unused*adv*nokid 0.037**
(0.015)
chosen_1 0.563***
(0.015)
chosen_2 0.589***
(0.015)
chosen_3 0.565***
(0.015)
chosen_4 0.503***
(0.015)
chosen_5 0.488***
(0.015)
chosen_6 0.491***
(0.015)
fiber -0.132***
(0.006)
fiber*age 0.000***
(0.000)
fiber*nokid 0.026***
(0.003)
61
sugar -0.136***
(0.013)
sugar*age -0.002***
(0.000)
sugar*nokid -0.033**
(0.006)
62
Table 6: Estimation Results
I II III IV
RCL RCL+Learning RCL+Learning+HCS
1
IV Estimation
price -0.164*** -0.187*** -0.233*** -0.368***
(0.003) (0.054) (0.009) (0.051)
price*inc 0.002*** 0.001** 0.001*** 0.001***
(0.000) (0.001) (0.000) (0.000)
price*nokid 0.127*** 0.129*** 0.118*** 0.014***
(0.003) (0.007) (0.007) (0.005)
adv -0.007* -0.018 -0.023 0.274
(0.004) (0.065) (0.050) (1.731)
adv*inc 0.001** 0.000 0.001*** 0.000***
(0.000) (0.001) (0.000) (0.000)
adv*nokid 0.073*** 0.009 0.073*** -0.003
(0.003) (0.006) (0.003) (0.003)
unused -1.874*** -2.071*** -1.800** -1.801***
(0.021) (0.017) (0.043) (0.091)
unused*adv 0.335*** 0.083*** 0.286*** 0.696***
(0.006) (0.010) (0.023) (0.041)
unused*adv*inc -0.004** -0.000 0.027*** 0.028***
(0.000) (0.001) (0.001) (0.001)
unused*adv*nokid -0.155*** -0.041 -0.019** -0.035
(0.005) (0.030) (0.009) (0.083)
chosen 1 0.614*** 0.649*** 0.578*** 0.563***
(0.017) (0.018) (0.018) (0.021)
chosen 2 0.638*** 0.629*** 0.603*** 0.590***
(0.017) (0.018) (0.018) (0.021)
chosen 3 0.612*** 0.574*** 0.577*** 0.565***
(0.017) (0.018) (0.019) (0.019)
chosen 4 0.548*** 0.504*** 0.514*** 0.503***
(0.017) (0.018) (0.019) (0.019)
chosen 5 0.531*** 0.466*** 0.497*** 0.488***
(0.017) (0.019) (0.019) (0.019)
chosen 6 0.534*** 0.468*** 0.501*** 0.491***
(0.017) (0.019) (0.019) (0.019)
fiber -0.112*** 0.014 -0.068*** 4.466***
(0.005) (0.046) (0.011) (0.853)
fiber*age 0.001*** 0.001 0.000 0.001***
(0.000) (0.001) (0.000) (0.000)
fiber*nokid 0.018*** 0.037*** 0.047*** 0.026***
(0.003) (0.011) (0.005) (0.004)
sugar -0.083*** -0.060 -0.099*** 1.996
(0.009) (0.059) (0.020) (2.293)
63
I II III IV
RCL RCL+Learning
RCL+Learning+HCS
1
IV Estimation
sugar*age 0.001 -0.001 0.000 -0.001***
(0.001) (0.003) (0.000) (0.000)
sugar*nokid -0.062** -0.007 -0.066*** -0.032***
(0.005) (0.006) (0.007) (0.005)
?
0
-7.350*** -7.350***
(0.005) (0.001)
?
1
2.996*** 2.996***
(0.001) (0.001)
?
2
-0.002*** -0.002***
(0.000) (0.000)
?
3
0.001 0.001***
(0.001) (0.000)
?
4
-0.001*** -0.001***
(0.000) (0.000)
?
11
0.187*** 0.081*** 0.512*** 0.512***
(0.001) (0.023) (0.007) (0.002)
?
22
0.000 0.000 0.005 0.005
(0.003) (0.094) (0.014) (0.004)
?
33
0.036*** 0.018 0.004 0.006**
(0.001) (0.033) (0.005) (0.003)
?
44
0.000 0.000 0.002 0.010***
(0.004) (0.090) (0.009) (0.003)
log likelihood -106389 -100617 -82177
Standard errors in parentheses, brand dummies not reported.
* significant at 10%; ** significant at 5%; ***significant at 1%
1. RCL denotes random coefficient logit. HCS denotes heterogeneous choice set. Number of draws for choice set simulation = 20
64
Table 7: Predicted Market Shares
Brand Number
Sample
Market
Share (%)
RCL
RCL+Quality
Learning
RCL+Quality
Learning+HCS
1 6.03 8.04 7.42 6.64
2 5.07 3.96 3.28 3.72
3 3.63 1.62 1.94 2.38
4 2.84 2.04 2.29 2.57
5 1.56 0.76 0.75 0.92
6 4.67 3.36 4.80 4.18
7 4.04 2.19 3.53 3.44
8 4.11 6.21 3.42 3.52
9 2.32 3.85 1.00 1.13
10 2.75 3.35 2.18 2.25
11 4.56 7.25 5.20 4.26
12 2.61 1.47 2.12 2.91
13 2.12 0.97 0.94 1.64
14 1.82 1.03 1.27 2.42
15 2.47 1.27 2.34 2.97
16 2.32 3.28 1.42 1.98
17 1.49 0.42 0.39 1.62
18 1.78 1.02 1.10 1.12
19 1.47 0.87 1.18 1.43
20 2.84 1.25 1.62 2.03
21 1.50 0.31 0.43 0.56
22 1.19 0.84 0.19 0.54
23 1.72 0.23 0.48 0.65
24 1.25 0.18 0.60 0.99
25 0.76 0.14 0.15 0.25
26 0.93 0.20 0.31 0.42
27 0.53 0.18 0.17 0.18
28 0.51 0.23 0.71 0.41
29 0.46 0.08 0.09 0.13
Brand Number
Sample
Market
Share (%)
RCL
RCL+Quality
Learning
RCL+Quality
Learning+HCS
30 0.97 0.14 0.20 0.83
31 0.44 0.04 0.03 0.14
32 0.36 0.00 0.27 0.29
33 0.37 0.00 0.02 0.00
34 0.28 0.01 0.11 0.01
35 0.26 0.00 0.00 0.02
36 0.23 0.00 0.01 0.00
37 0.44 0.08 0.06 0.05
38 1.44 0.31 0.45 0.98
39 0.83 0.00 0.59 0.62
40 0.38 0.02 0.02 0.04
41 0.30 0.01 0.07 0.08
42 1.09 0.21 0.35 0.88
43 0.62 0.07 0.27 0.34
44 0.26 0.01 0.01 0.01
45 0.50 0.23 0.09 0.24
65
46 0.75 0.18 0.23 0.36
47 0.61 0.10 0.08 0.19
48 0.53 0.04 0.14 0.17
49 0.49 0.12 0.10 0.24
50 0.66 0.04 0.03 0.05
Prediction Error 0 7.26 5.29 3.81
Data: estimation sample for all regressions
Prediction Error = Squareroot of sum of squared deviations of predicted market
share to sample markte share
66
Table 8. Own Price Elasticity for Top 10 Brands
Brand RCL
RCL &
Learning
RCL &
Learning &
HCS
1 -1.01 -1.27 -2.32
2 -1.27 -0.61 -2.63
6 -0.82 -0.68 -1.71
11 -1.27 -0.65 -1.39
8 -0.98 -0.74 -2.23
7 -0.68 -0.79 -1.66
3 -1.24 -1.04 -1.46
12 -0.98 -1.48 -2.82
4 -1.13 -1.63 -2.42
16 -1.42 -1.59 -2.57
67
Table 9. Estimated Price Elasticities for Top 25 Brands Based on IV Estimation
Brand # 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 -2.428 0.367 0.146 0.010 0.099 0.338 0.220 0.315 0.003 0.673 0.034 0.002 0.100 0.001
2 0.136 -2.768 0.265 0.018 0.178 0.612 0.398 0.569 0.005 1.217 0.062 0.003 0.180 0.003
3 0.120 0.594 -1.545 0.015 0.157 0.540 0.352 0.503 0.005 1.075 0.054 0.002 0.159 0.002
4 0.092 0.455 0.179 -3.703 0.120 0.414 0.269 0.385 0.004 0.823 0.042 0.002 0.122 0.002
5 0.070 0.349 0.137 0.009 -2.762 0.317 0.206 0.295 0.003 0.630 0.032 0.001 0.093 0.001
6 0.292 1.446 0.569 0.038 0.383 -1.994 0.856 1.223 0.012 0.815 0.133 0.006 0.387 0.005
7 0.212 1.051 0.414 0.027 0.278 0.955 -1.561 0.889 0.008 1.901 0.096 0.004 0.281 0.004
8 0.249 1.234 0.485 0.032 0.326 1.121 0.730 -2.209 0.010 1.331 0.113 0.005 0.330 0.005
9 0.047 0.232 0.091 0.006 0.061 0.211 0.137 0.196 -1.679 0.420 0.021 0.001 0.062 0.001
10 0.141 0.698 0.275 0.018 0.185 0.635 0.413 0.591 0.006 -4.991 0.064 0.003 0.187 0.003
11 0.045 0.222 0.087 0.006 0.059 0.202 0.131 0.188 0.002 0.401 -1.561 0.001 0.059 0.001
12 0.022 0.109 0.043 0.003 0.029 0.099 0.064 0.092 0.001 0.197 0.010 -2.798 0.029 0.000
13 0.153 0.756 0.298 0.020 0.200 0.688 0.448 0.640 0.006 1.368 0.069 0.003 -3.629 0.003
14 0.022 0.108 0.043 0.003 0.029 0.099 0.064 0.092 0.001 0.196 0.010 0.000 0.029 -1.094
15 0.033 0.165 0.065 0.004 0.044 0.150 0.098 0.140 0.001 0.299 0.015 0.001 0.044 0.001
16 0.044 0.217 0.085 0.006 0.057 0.197 0.128 0.183 0.002 0.392 0.020 0.001 0.058 0.001
17 0.116 0.573 0.225 0.015 0.152 0.520 0.339 0.484 0.005 1.035 0.052 0.002 0.153 0.002
18 0.034 0.168 0.066 0.004 0.045 0.153 0.100 0.142 0.001 0.305 0.015 0.001 0.045 0.001
19 0.078 0.385 0.152 0.010 0.102 0.350 0.228 0.326 0.003 0.697 0.035 0.002 0.103 0.001
20 0.168 0.831 0.327 0.022 0.220 0.755 0.492 0.703 0.007 1.503 0.076 0.003 0.222 0.003
21 0.027 0.136 0.053 0.004 0.036 0.123 0.080 0.115 0.001 0.245 0.012 0.001 0.036 0.001
22 0.014 0.070 0.028 0.002 0.019 0.064 0.042 0.059 0.001 0.127 0.006 0.000 0.019 0.000
23 0.116 0.573 0.225 0.015 0.152 0.521 0.339 0.485 0.005 1.036 0.053 0.002 0.153 0.002
24 0.025 0.126 0.049 0.003 0.033 0.114 0.074 0.106 0.001 0.227 0.012 0.001 0.034 0.000
25 0.031 0.155 0.061 0.004 0.041 0.141 0.092 0.131 0.001 0.280 0.014 0.001 0.041 0.001
Table 9. Estimated Price Elasticities for Top 25 Brands Based on IV Estimation
Brand # 15 16 17 18 19 20 21 22 23 24 25
1 0.001 0.065 0.261 0.027 0.115 0.469 0.004 0.004 0.011 0.003 0.001
2 0.001 0.077 0.306 0.032 0.135 0.551 0.005 0.004 0.013 0.003 0.003
3 0.001 0.014 0.058 0.006 0.025 0.104 0.001 0.001 0.002 0.001 0.004
4 0.001 0.043 0.173 0.018 0.076 0.312 0.003 0.002 0.008 0.002 0.004
5 0.001 0.014 0.055 0.006 0.024 0.099 0.001 0.001 0.002 0.001 0.001
6 0.003 0.007 0.027 0.003 0.012 0.049 0.000 0.000 0.001 0.000 0.002
68
Brand # 15 16 17 18 19 20 21 22 23 24 25
7 0.002 0.047 0.188 0.020 0.083 0.338 0.003 0.003 0.008 0.002 0.006
8 0.003 0.007 0.027 0.003 0.012 0.048 0.000 0.000 0.001 0.000 0.008
9 0.001 0.010 0.041 0.004 0.018 0.074 0.001 0.001 0.002 0.000 0.001
10 0.002 0.013 0.054 0.006 0.024 0.097 0.001 0.001 0.002 0.001 0.004
11 0.000 0.036 0.142 0.015 0.063 0.256 0.002 0.002 0.006 0.002 0.001
12 0.000 0.010 0.042 0.004 0.018 0.075 0.001 0.001 0.002 0.000 0.001
13 0.002 0.024 0.096 0.010 0.042 0.172 0.002 0.001 0.004 0.001 0.005
14 0.000 0.052 0.206 0.022 0.091 0.371 0.003 0.003 0.009 0.002 0.001
15 -1.351 0.008 0.034 0.004 0.015 0.061 0.001 0.000 0.001 0.000 0.001
16 0.000 -2.409 0.017 0.002 0.008 0.031 0.000 0.000 0.001 0.000 0.001
17 0.001 0.036 -3.788 0.015 0.063 0.256 0.002 0.002 0.006 0.002 0.003
18 0.000 0.008 0.031 -1.305 0.014 0.056 0.000 0.000 0.001 0.000 0.001
19 0.001 0.010 0.038 0.004 -2.384 0.069 0.001 0.001 0.002 0.000 0.002
20 0.002 0.092 0.010 0.041 0.166 -3.958 0.001 0.004 0.001 0.002 0.005
21 0.000 0.167 0.017 0.074 0.300 0.003 -1.434 0.007 0.002 0.004 0.001
22 0.000 0.148 0.015 0.065 0.265 0.002 0.002 -0.944 0.002 0.004 0.000
23 0.001 0.113 0.012 0.050 0.203 0.002 0.002 0.005 -3.178 0.003 0.003
24 0.000 0.087 0.009 0.038 0.156 0.001 0.001 0.004 0.001 -1.171 0.001
25 0.000 0.359 0.037 0.158 0.645 0.006 0.005 0.016 0.004 0.009 -1.409
69
Table 10. Change in Sales under Alternative Pricing Strategies
?price +1% +5% -1% -5%
brand 28
?market share(%) -1.23 -7.09 0.14 6.48
?sales (%) -0.78 -2.41 0.01 2.32
?market share = market share in the experiment - market share observed in data
?sales = sales in the experiment - sales obsered in data
Table 11. Change in Expenditure by Demographic Group under 5% Price Cut
? in expenditure
Highinc 1.21%
Lowinc 3.59%
Old 2.33%
Young 2.32%
Nokid 3.02%
WithKid 1.09%
70
Table 12. Change in Expenditure by Demographic Group under Pulsing Strate
? in expenditure
Highinc 2.64%
Lowinc 1.59%
Old 1.91%
Young 1.91%
Nokid 1.81%
WithKid 2.15%
Table 13. Food Ads Seen by Children of Different Ages
Age 2-7 Age 8-12 Age 13-17
Food ads seen per
12 21 17
Food ads seen per
year
4,400 6,000 7,600
Percentage of ads seen
where food was the main
product advertised
32% 25% 22%
in the United States”, The Kaiser Family Foundation, March 28, 2007
Source: "Food for Thought: Television Food Advertising to Children
71
Table 14. Sugar and Fiber Contents of Brands by Segment
Sugar (g per
serving)
Fiber (g
per
serving)
Kid Brands 10.98 5.41
Adult Brands 5.88 9.92
Family Brands 7.68 7.38
Table 15. Change in Segment Share After the Ban
? in
mktshare
kid -5.98%
adult 2.01%
family 3.96%
Table 16. Effects of the Ban across Consumer Groups
? in sugar ? in fiber
? in
expenditure
Highinc -3.41% 0.46% 6.43%
Lowinc -5.27% 2.67% 4.36%
Old -4.22% 0.95% 4.87%
Young -5.91% 4.24% 8.67%
Nokid -2.69% -1.24% 5.15%
Withkid -6.92% 7.10% 5.37%
72
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