An Empirical Study of the Dynamic Brand Building

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An Empirical Study of the

Dynamics of Brand Building

Ron N. Borkovsky Avi Goldfarb Avery Haviv Sridhar Moorthy1

Rotman School of Management, University of Toronto

January 13, 2013

PRELIMINARY.

Abstract

Brand equity offers long-term benefits that are built over time. Therefore, brand equity is an inherently

dynamic process. In this paper, we explore this dynamic process through a model of brand building and

harvesting, in which firms invest in advertising in order to build and sustain brand equity. The model

allows us to address several fundamental questions on the nature of brand-building and competition:

How strong are the leading firm’s incentives to perpetuate its brand equity advantage? How strong are

the follower’s incentives to overcome the gap it faces? When should firms harvest brands? How efficient

is the conversion of advertising into brand equity and how quickly does brand equity depreciate? The

model also enables a dynamic measure of the value of a brand to a firm that accounts for the effect of

the brand on both current and future profits. We estimate this model using data from the stacked chips

category in the consumer packaged goods (CPG) industry. The stacked potato chip market is ideally

suited for this study because it is a duopoly that focuses a great deal on brand equity, displays interesting

brand equity dynamics over time, and is characterized by very high levels of spending on advertising.

1. [email protected], [email protected], [email protected],[email protected]

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1 Introduction

Brand equity is perhaps the single most important asset that marketing contributes to a firm. Strong brand

equity can generate awareness among consumers, induce repeat purchasing, and serve as a promise of high

quality. It is widely recognized that brand equity is a dynamic concept because firms must invest in both

building and sustaining it (Keller 1997, Ataman, Mela & van Heerde 2008, Erdem, Keane & Sun 2008).

Furthermore, brand equity delivers long-term benefits because it is not instantly depleted. However, thus

far little work has been done to explore brand strategy in a dynamic context. The purpose of this research

is to better understand brand building and harvesting and, accordingly, the evolution of brand equity in

oligopolistic industries. To this end, we build on the static structural approach to measuring the value of a

brand2 proposed in Goldfarb, Lu & Moorthy (2009) and apply the Pakes & McGuire (1994) quality ladder

model to the concept of brand equity. We estimate the model using data from the stacked potato chips

market.

Specifically, we build and estimate a dynamic model of brand building in which firms invest in advertising

and other promotional activities in order to build and sustain brand equity. The dynamic model is necessary

to address several fundamental questions on the nature of brand value, brand-building, and competition:

How strong are the leading firm’s incentives to perpetuate its brand equity advantage? How strong are the

follower’s incentives to overcome the gap it faces? When should firms harvest brands? How efficient is the

conversion of advertising into brand equity and how quickly does brand equity depreciate? In addition to

helping to answer these questions, the model and estimation process also provide a new tool that can beused to measure brand value in a dynamic equilibrium context, providing a more complete measure of the

value of a brand as an intangible asset.

We estimate this model using data from the stacked potato chip market in the consumer packaged goods

(CPG) industry. The stacked potato chip market is ideally suited for this study because it is a duopoly

that focuses a great deal on brand equity, displays interesting brand equity dynamics over time, has readily

available data on prices, advertising, and market shares, and is characterized by high levels of spending on

advertising.

We feel that the results of our estimation help us to better understand brand value and brand building in

a dynamic context. We find that in the stacked chips category, brand equity has the potential to increase the

value of a product by up to $1.29 billion. We find that STAX entry caused the value of the Pringles brand to

decrease. Moreover, we find that the competition that STAX entry induced in the category caused the value

2. Consistent with the prior literature, we define brand value as the value of a brand to a firm, whereas brand equity is the

value of a brand to consumers.

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of both the Pringles and STAX brands to decrease. In particular, from the third quarter of 2003–the quarter

before STAX entered–to the second quarter of 2006, the Pringles brand decreased in value by $118.04 million.

From the fourth quarter of 2003–the quarter in which STAX entered–to the second quarter of 2006, the STAX

brand decreased in value by $96.99 million. We are also able to learn several interesting things about the ways

in which firms build brands in the stacked chips category. First, a firm invests most heavily in advertising

when it has intermediate brand equity and its rival’s brand equity is low. Second, a firm’s advertising

spending is increasing in its own brand equity (up to a threshold) and decreasing in its rival’s brand equity.

Finally, we find that despite Pringles’ early brand equity advantage, STAX is likely to ultimately catch up

to it and, therefore, the likely long-run market structure in the stacked chips category is symmetric.

This paper also contributes to the methodological literature by estimating, rather than calibrating, the

Pakes & McGuire (1994) quality ladder model in a computationally feasible way. Our specification allows

for greater variability in the outcomes of firms in the market by introducing firm-specific shocks to marginal

cost and advertising effectiveness.

The paper proceeds as follows. In section 2, we discuss the relevant literature and our contribution to

it. In section 3, we discuss the data that we use to estimate the model. In section 4, we present the static

model of price competition and discuss our approach to estimating the model. We also discuss the results

that the estimation yields–in particular, quarterly estimates of the brand equities for Pringles and STAX

respectively and an estimate of the period profit function, which are treated as primitives in the dynamic

model. In section 5, we present the dynamic model of brand building and discuss our estimation strategy. In

section 6, we discuss the estimated equilibrium of the dynamic model and present results. Section 7 presents

counterfactuals that explore the effect of changes in industry fundamentals on brand building incentives, the

evolution of brand equity, and accordingly brand value.

2 Literature Review

This paper contributes to the literatures on (i) measuring brand value, (ii) brand equity dynamics, (iii)

dynamic models of advertising, and (iv) estimation and calibration of dynamic oligopoly models. Below, we

discuss these literatures and this paper’s contributions to them.

2.1 Measuring Brand Value

The long literature on brand value measurement has its origins in Rosen (1974) and Holbrook (1992). These

earlier approaches involved static reduced-form methods such as hedonic regression to estimate brand equity

Literature Review 3



as a price premium after controlling for various non-brand factors. Ailawadi, Lehmann & Neslin’s (2003)

revenue premium method calculates brand value as the difference between brand revenues and private

label revenues. Building on Ailawadi, Lehmann & Neslin (2003), Goldfarb, Lu & Moorthy (2009) make

two contributions. First, they measure brand value in terms of profit contribution as opposed to revenue

contribution or price premium. They do so by comparing the equilibrium profit earned by a brand and

the profit earned in a counterfactual equilibrium where the brand has "lost" its brand equity but retained

its search attributes. Second, their structural approach accounts for the effect of brand equity on both

the demand side - i.e., on consumers’ brand choices - and on the supply side - i.e., on manufacturer and

retailer pricing decisions. Ferjani, Jedidi, and Jagpal (2009) estimate brand value by combining conjoint-

based demand estimation with Goldfarb, Lu, and Moorthy’s (2009) equilibrium framework. The addition

of conjoint analysis enables a richer understanding of the role of specific search and experience attributes

in driving brand value. Our dynamic model complements these approaches by incorporating the long term

effects of brand equity into an estimator of brand value.

2.2 Brand Equity Dynamics

Brand equity dynamics have not yet been studied extensively. Simon & Sullivan (1993) do so implicitly by

conducting event studies that explore the effects of various marketing decisions on the brand equities of Coke

and Pepsi. They find that a Coke brand extension enhanced its brand equity and reduced Pepsi’s brand

equity; that both firms enhanced their brand equities through simultaneous reformulations; and that a failedreformulation attempt by Coke reduced its own brand equity and enhanced Pepsi’s brand equity. Sriram,

Balachander & Kalwani (2007) estimate static brand equity measures and then examine how changes in

advertising, sales promotion, and product innovation correlate with changes in brand equity. In the categories

they study (toothpaste and dish detergent) they find that advertising and product innovation enhance brand

equity. In comprehensive surveys of the academic branding literature, Ailawadi, Lehmann & Neslin (2003)

and Keller & Lehmann (2006) raise several important questions on the dynamics of brand equity. How does

brand equity evolve over time? How does brand equity evolve in the face of competition? Furthermore, as

much of the benefit of a brand to a firm comes from its future potential, how can one quantify the long-term

financial value of a brand? Finally, as a brand’s equity arises as the outcome of the equilibrium marketing

decisions made by a parent firm and its rivals, how can one estimate these relationships so as to understand

the very process by which firms firms develop high equity brands? Our model is specifically designed to

address many of these questions. As we show below, equilibrium dynamics in oligopolistic industries can

lead to surprising results on equilibrium returns to brand equity investments.

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2.3 Dynamic Models of Advertising

There is a long history of academic research on dynamic models of advertising. In a seminal paper, Nerlove

& Arrow (1962) characterize the optimal advertising policy of a single forward-looking firm that invests

in advertising in order to build a stock of goodwill. Horsky (1977) extends this model by incorporatingmarket rivals. However, as the model is solved as an optimal control problem, it does not capture strategic

interaction b etween firms. Several later papers incorporate strategic interaction by studying duopolistic

advertising competition in the context of a differential game (e.g. Rao 1984, Chintagunta & Vilcassim

1992); see Jorgensen (1982) and Rao (1990) for literature reviews. While differential games contributed

greatly to the advancement of this literature, they do have some limitations. First, they are quite stylized -

e.g., they do not include a model of sales, but rather simply an exogenous differential equation that reflects

how market structure responds to advertising. Second, it is difficult to incorporate more than two firms.

Two relatively recent papers have studied advertising dynamics using more flexible models of oligopolistic

competition devised in the Ericson & Pakes (1995) framework: Dubé, Hitsch & Manchanda (2005) explore

whether pulsing should arise in equilibrium. Doraszelski & Markovich (2007) contrast models of goodwill

and awareness advertising and assesses whether advertising can lead to a sustainable competitive advantage.

Many of the papers cited above estimate how sales and market shares respond to advertising (Horksy

1977, Chintagunta & Vilcassim 1992, Dubé & Manchanda 2005, Dubé, Hitsch & Manchanda 2005). Other

work has examined the relationship between advertising and goodwill (Doganoglu and Klapper 2006) and

advertising and brand perceptions (Clark, Doraszelski & Draganska 2009). Our model builds on thesefindings. We develop share-based estimates of brand equity and examine how they correlate with advertising

decisions. We structurally estimate a dynamic oligopoly model of advertising competition in the Ericson &

Pakes (1995) framework. This will allow us to avoid some of the limitations that have characterized many of

the previous approaches, as our model will (i) include advertising as an endogenous forward-looking decision

by firms; (ii) allow brands that interact strategically; and (iii) contain demand estimation that is rooted in

a model of consumer behavior.

2.4 Estimation and Calibration of Dynamic Oligopoly Models

The recent empirical literature on dynamic models of oligopolistic competition largely builds on Ericson &

Pakes (1995). This seminal paper provides a framework for estimation of models of dynamic competition

in an oligopolistic industry that includes investment, entry, and exit. (See Doraszelski & Pakes (2007)

for an extensive discussion of the framework and the related literature.) More recently, several papers

Literature Review 5



have introduced methods for structural estimation of models in the Ericson & Pakes (1995) framework

(Aguirregabiria & Mira 2007, Bajari, Benkard & Levin 2007, Pakes, Ostrovsky & Berry 2007, Pesendorfer

& Schmidt-Dengler 2008, and Su & Judd 2008). This has led to a number of applications. For example,

the framework has been used to study the dynamic R&D investment and pricing strategies of durable good

oligopolists in the PC microprocessor industry (Goettler & Gordon 2009), and bidding behaviour in auctions

for sponsored search advertising (Yao & Mela 2010). An alternative approach to structural estimation of

the dynamic game involves calibration in the spirit of Benkard (2004). Dubé, Hitsch & Rossi (2009) devise a

dynamic model of price competition that allows them to assess the effect of switching costs on the intensity

of price competition and calibrate the model using data from CPG categories. Dubé, Hitsch & Chintagunta

(2010) devise a model of platform competition that incorporates indirect network effects and propose a

method for measuring the increase in market concentration that is attributable to the presence of indirect

network effects; they calibrate the model using data on the video game console industry. As explained above,

we contribute to this literature by devising and structurally estimating a dynamic oligopoly model of brand

building.

3 Category Description and Data

In this section, we describe the stacked chip category and the data that we use to estimate our model.

3.1 Category Description

The stacked chip category originated with Pringles at Procter & Gamble (P&G) during the late 1960s, after

over a decade of product development. P&G’s plan was to distribute Pringles over its existing distribution

network, which was optimized for non-perishable items. To ensure the chips didn’t spoil while in transit, they

were to be packed in nitrogen, which necessitated a cheap airtight seal. This in turn lead to the now well-

known clindrical containers and the uniformly-shaped, stackable chips that would fit them. By the mid-1990s

more than $1 billion in annual sales. In 2012, P&G agreed to sell Pringles to Kellogg’s for nearly $2.7 billion. 3

Frito-Lay, a division of PepsiCo, launched Lays STAX in 2003. Like Pringles, STAX chips are packaged

in cylindrical containers and are are uniformly-shaped and stacked for improved packing efficiency. Our

data shows that STAX was able to capture a market share of 6 percent in the chips category and 20 percent

in the stacked chips category after only 3 years on the market.

3. “Kellogg’s buys Procter & Gamble’s Pringles chips for $2.7 billion”. Retrieved April 11, 2012.

http://articles.latimes.com/2012/feb/15/business/la-fi-mo-kellogg-pringles-sale-20120215

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3.2 Data

We estimate the model using data on the salty snacks category from the IRI Marketing Data Set (Bronnen-

berg, Kruger & Mela 2008). The sales data describe each purchase of a product in numerous catergories,

including potato chips, that was made in participating stores in each of 47 U.S. markets between January 1,

2001 and December 31, 2006. This data set is well-suited for this project for multiple reasons. First, it is very

detailed; for each sale, the price, volume, region, product characteristics, and week of purchase are reported.

All of these data items are necessary for estimating brand equity using a method like the one proposed

in Goldfarb, Lu & Moorthy (2009). Second, within the time period covered by the data set, we observe

interesting dynamics due to the entry of STAX, and the resulting competition. The variance in market

share and advertising allow us to identify the dynamic parameters in our model. Third, the IRI Marketing

Data Set contains advertising spending for the catergory that was provided by TNS Custom Research,

which spans from January 1, 2001 until June 30, 2006. These comprehensive data sets make it possible toapply our model to this industry, while the interesting dynamics and duopolistic industry structure make it

interesting to do so. We provisionally focus on the time period where both STAX and Pringles are active

in the market, which spans from the fourth quarter of 2003 to the second quarter of 2006. We deflate all

dollar amounts to year 2000 dollars using the Consumer Price Index.

3.3 Descriptives

Descriptive statistics for each brand are provided in tables 1 and 2 below. Plots of advertising spending, sales,

market share, and price are presented in figures A, B, C, and D, respectively. Figure A shows substantial

variability in ad spending by quarter for both brands. Figures B and C show that sales and market share

are more stable than advertising, though there is still substantial variation over time. Figure D shows that

STAX prices are slightly below Pringles, though the gap varies from almost zero in the second quarter of

2004 to close to 20 percent in the first quarter of 2006.

Pringles Descriptives Mean Standard Deviation Min MaxAdvertising (Millions of Dollars) 9.66 4.33 2.17 17.62

Price (Dollars) 1.18 0.05 1.10 1.26Market Share 0.21 0.01 0.19 0.23

Sales (Millions of Dollars) 4.89 0.38 4.49 5.42

Table 1.

STAX Descriptives Mean Standard Deviation Min MaxAdvertising (Millions) 4.01 4.73 0.00 12.56

Price (Dollars) 1.07 0.09 0.96 1.23Market Share 0.05 0.01 0.04 0.06

Sales (Millions) 1.12 0.12 0.93 1.28

Table 2.

Category Description and Data 7



4 Static Price Competition

In this section, we present the static model of price competition and discuss our approach to estimating the

model. We also present the results of the estimation, which yields quarterly estimates of brand equity for

Pringles and STAX respectively and an estimate of the period profit function. These are treated as primitives

in the dynamic model that is presented in section 5.

4.1 The Static Model of Price Competition

We assume that firms engage in price competition in each period given the brand equities that prevail in

that period. Because the static model of price competition is parameterized by the industry state of the

dynamic model–which comprises firms’ respective brand equities–we will first describe the state space of the

dynamic model.

Firms and states. Firm n ∈{1, 2} is described by its state ωn∈{0, 1, , M }. States 1, , M describe the

brand equity of a firm that is active in the product market, i.e., an incumbent firm, while state 0 identifies a

firm as being inactive, i.e., a potential entrant. The vector of firms’ states is ω = (ω1, ω2)∈{0, , M }2 and

we use ω [2] to denote the vector (ω2, ω1) obtained by interchanging firms’ states.

Product market competition. The product market is characterized by price competition between firms

with products that are vertically differentiated acording to their respective brand equities. In order to

estimate the model, we incorporate week-specific stochastic shocks to accomodate the inevitable variability in

price and sales within states and across weeks. Accordingly, we incorporate week-specific shocks to market

size and to each firm’s marginal cost. There is a continuum of consumers. Each consumer purchases at

most one unit of one product in each week. The utility that consumer i derives from purchasing from firm n

is u in (ωn) = g(ωn)−αpn + ζ n + ς + (1−σ)εin , where g: (0, 1, , M )→R is an increasing function that maps

brand equity state ωn into the consumer’s valuation of it (which is its brand equity4), pn is the price, ζ n is

a mean zero firm-specific shock, ς is a week-specific industry-wide shock, and εin represents the consumers’s

idiosyncratic preference for product n. We set g(0) = −∞; this ensure that potential entrants have zero

demand and thus do not compete in the product market. There is an outside alternative, product 0, which

has utility ς ′+ (1−σ)ε0. Assuming that the idiosyncratic preferences ε0, ε1, and ε2 have independent and

4. Formally, ωn is the brand equity state and g(ωn) is the brand equity. For ease of exposition, we sometimes refer to ωn

as “brand equity” as well.

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identically distributed type 1 extreme value distributions, and that ς and ς ′ have distributions depending on

σ such that ς + (1 − σ)εin and ς ′ + (1− σ)εi0 have extreme value distributions, the demand for incumbent

firm n’s product is

Dn( p;ω, m, ζ ) = mexp (

g(ωn)−αpn+ ζ n

1−σ )

C + C σ (1)

where p= ( p1, p2) the vector of prices, α is the price coefficient, m > 0 is the size of the market (the measure

of consumers), ζ = (ζ 1, ζ 2) is the vector of week-specific shocks to consumer utility for each brand, and

C = Σj=12 exp(g(ωj)−αpj + ζ j). The market size m is assumed to have an independent normal distribution

with mean µm and standard deviation σm. ζ n is assumed to have a mean zero normal distribution with

standard deviation σζ .

Incumbent firm n chooses the price pn of its product to maximize profits. Hence, its profits in state ω are

πn(ω, cn, m, ζ ) = max pn Dn(( pn, p−n);ω, m, ζ )( pn− cn), (2)

where p−n is the price charged by the rival and cn ≥ 0 is the marginal cost of production for firm n. We

assume that the marginal cost is drawn from a normal distribution with mean µc and standard deviation

σc and is independently and identically distributed across weeks. Given an industry state ω, a vector of

marginal costs c, and a vector of weekly shocks ζ , there exists a unique Nash equilibrium of the product

market game (Caplin & Nalebuff 1991). It is found easily by numerically solving the system of first-order

conditions corresponding to incumbent firms’ profit-maximization problems. Let πn∗(ω, c, m, ζ ) denote firm

n’s equilibrium profit. Integrating over the market size, marginal costs, and the weekly shocks to brandequity, we compute the expected equilibrium profit in industry state ω,

πn(ω) =

c,m,ζ

πn∗(ω, c, m, ζ )f c(c)f m(m)f ζ (ζ )dcdm dζ , (3)

where f c(c), f m(m), and f ζ(ζ ) are pdf functions of c, m, and ζ , respectively. Because product market

competition does not directly affect state-to-state transitions, πn(ω) can be computed before the Markov

perfect equilibria of the dynamic stochastic game are computed. This allows us to treat πn(ω) as a primitive

in what follows.

4.2 Estimating the Static Model of Price Competition

We conduct two stages of estimation–first estimating the static model of price competition and only then

estimating the dynamic model of brand building, which is presented in section 5–for the following reasons.

First, in estimating a model in the Ericson & Pakes (1995) framework, one typically observes the states in

Static Price Competition 9



the data. For example, in the Goettler & Gordon (2011) study on R&D competition between Intel and AMD,

the authors observe processor speed, which they regard as a proxy for product quality. In this study, we are

unable to observe brand equities, which serve as states in our model, and therefore must estimate them prior

to estimating the dynamic model. Our approach to estimating the static model of price competition yields

quarterly estimates of Pringles and STAX brand equities respectively. Second, the period profit function

in models in the Ericson & Pakes (1995) framework can be treated as a primitive because it does not affect

state-to-state transitions in the dynamic game. It follows that in estimating a model in the Ericson & Pakes

(1995) framework, one can estimate the period profit function before estimating the dynamic model. In the

first stage of estimation, we estimate the period profit function that results from the static model of price

competition. Having estimated brand equities and the period profit function, we are then able to proceed

to estimation of the dynamic game in the second stage.

We assume that firms engage in static price competition in each week given the brand equities that prevail

in that week. Moreover, we assume that brand equities are fixed within each quarter. We use the subscript t

to reference the value of a variable in week t andthesubscript q to reference the value of a variable in quarter q .

Estimation of the Demand Function. In this stage, we estimate the parameters that appear in the

demand function. Specifically, we estimate the brand equities g (ωqn), the price sensitivity parameter α, the

standard deviation of the shocks to brand utility σζ , and the mean µm and standard deviation σm of the

distribution from which market size is drawn. We estimate these parameters using a variant of the method

proposed by Goldfarb, Lu & Moorthy (2009). In particular, we estimate a nested logit demand model that

describes product market competition using instrumental varibles to account for the endogeneity of price.

The two stacked potato chips brands, Pringles and STAX, are in the same nest, while the outside good is

in a seperate nest. This captures the notion that brands of stacked potato chips will compete more fiercely

with each other than with other types of salty snacks. The brand equity of each firm in each quarter is

defined as the additional utility a consumer receives from consuming a branded product, as opposed to an

unbranded alternative. Operationally this is represented as a brand-quarter fixed effect in the consumer’s

utility function. The methodology allows us to map market shares and prices into brand equities. Recall

that the demand for good n is

Dn( pt;ω, mt, ζ t) = mt

exp (g(ωn)−αpnt+ ζ nt

1−σ )

C t + C tσ

And demand for the outside good, which exists in a seperate nest, is

D0( pt;ω, mt, ζ t) = mtC t

σ

C t + C tσ .

10 Section 4



In the case of stacked potato chips, the outside good is defined as all non-stacked chips, pretzels, popcorn,

and cheese snacks. The market size in each week, mt, is the total number of units of chips, cheese snacks,

pretzels, and popcorn sold in that week. We do not observe mt directly, as we only observe the stores

covered by the IRI database, so we approximate it as follows. From the data, for each week, we compute the

average household spending on all chips, pretzels, popcorn, and cheese snacks. We multiply this by the total

number of households in the U.S. to get an approximation of total U.S. spending on the aforementioned salty

snack categories. Because market size is defined in units, not dollars, we then multiply this by the average

number of units per dollar spent on these salty snacks. We use the first and second sample moments of these

approximations to estimate µt and σt. We are implicitly assuming that the stores represented in the IRI

database are a representitive sample of all U.S. stores.

Taking the difference between the log market share of a firm and the outside good, we have:

log

Dn(pt;ωq, mt, ζt)

mt

− log

D0(pt;ωq,mt, ζt)

mt

= g(ωqn)−αptn + σlog

Dn(pt;ωq, mt, ζt)

mt−D0(pt;ωq, mt, ζt)

+ ζ tn.

Because estimation of the above expression through standard ordinary least squares would be biased due

to the endogeneity of price (it is possible that firms observe ζ t before setting prices) and the inside share,

we use the price in the previous period and the average price of the outside good as instruments. Through

reduced form analysis we have found that there is a strong correlation between current prices and previous

period prices, and in our model the relationship between the current period and the previous period is

captured through brand equity, making this a valid instrument. Similarly, we find that the average price of

the outside good to be correlated with the market share of stacked chips, but in our model it is independent

of the brand-week specific shock to uility ζ t. We estimate demand on a weekly basis, with brand equities

which change each quarter. The results are presented in table 4. Figure E plots the estimated values of brand

equity for Pringles and STAX by quarter.

Estimation of the Marginal Cost Parameters. We use the first-order condition that characterizes

equilibrium price in the static period game to compute cnt the marginal cost each firm faced each week, given

the estimates of the parameters in the demand function.

Given the estimates of g(ωqn) and α, we can compute marginal costs in each period as

cnt = pnt− 1−σ

α

1− stn

1 + σC t

(σ−1) (4)

Figure F shows the estimated marginal cost values for Pringles and STAX over time. Given the estimates of

the marginal costs in each period, we can estimate µc and σc using the first and second sample moments of ctn.

Static Price Competition 11



Correlation between Brand Equity and Advertising. The table below shows the relationship between

estimated brand equity and advertising. In particular, the table shows the results of regressions of changes

in brand equity on advertising expenditures and a number of controls. In each specification, advertising and

brand equity are positively correlated. In columns 3 and 4, we do not find a significant brand-advertising

interaction. This allows us to use the same parameters to describe the returns to advertising for each firm.

Finally, regression 4 in table 3 shows that lagged brand equity has an important effect on the change in brand

equity. Firms with higher brand equities are more likely decline. This justifies our modeling assumption

that the probability of sucessful advertising is a decreasing function of the current brand equity state.

Model 1 Model 2 Model 3 Model 4(S.E.) (S.E.) (S.E.) (S.E.)

(Intercept) -0.105*** -0.164*** -0.189*** 0.175( 0.043) ( 0.06) ( 0.069) ( 0.159)

Advertising (Millions) 0.01* 0.014** 0.017** 0.013*(0.005) (0.006) (0.007) (0.007)

STAX . 0.086 0.133 -0.143( 0.061) ( 0.088) ( 0.137)

STAX × Advertising . . -0.01 -0.004(Millions) ( 0.013) ( 0.012)

Lagged Brand Equity . . . -0.238***(0.096)

Standard errors in parentheses. ∗ p < .10, ∗∗ p < .05, ∗∗∗ p < .01

Table 3.

Brand Equity Discretization. Because the Ericson & Pakes (1995) framework that we use to devise the

dynamic model has a discrete state space, we use a discrete approximation of the estimated brand equities.

The mapping from a firm’s brand equity state ωn∈{0, 1, , M } to its discretized brand equity is

g(ωn) =

−∞ if ωn = 0lωn + b if ωn > 0

for constants l > b≥ 0, and each estimated brand equity is assigned to the discrete brand equity to which it

is closest. Within this class of discretizations, we searched for b and l that would minimize l, the distance

between states, while ensuring that from period to period, a firm’s discretized brand equity would increase

by at most one unit and decrease by at most two units. We allow for decreases of two units in order to

accommodate several big decreases in brand equity, which can be seen in figure E. In section 5, we explain

how we allow for this in the dynamic model. Our search found that b = 0.07488 and l = 0.144 provide the

12 Section 4



best approximation, an we used the resulting discretization for the estimation of the dynamic model. We

observe a span of 14 states in the data, but use a span of 19 for each firm in our model to ensure that our

results are not being driven by the edge of the state space. This discretization is displayed in Figure E.

Estimation of Expected Profits. We cannot dervive the expected profit in equation (3) analytically

because there is no closed-form solution for πn∗(ω , ct, mt, ζ t). This is because equilibrium prices must be

computed using numerical methods. We therefore approximate the expected profit in each state through

monte carlo simulation. As explained above, estimating the static model of price competition allowed us to

estimate the parameters of the distributions from which c, m, and ζ are drawn. From these distributions,

we drew 10,000 pairs of monte carlo samples, which we denote ci, mi, and ζ i5. Let p(ω |c, m , ζ ) be the

vector of equilibrium prices in industry state ω given c, m, and ζ . The monte carlo estimate of the expected

profit for firm n in industry state ω is

πn(ω)≈i=1

10,000 Dn( pn(ω |ci, mi, ζ i);ω, mi, ζ i)( pn(ω |ci, mi, ζ i)− ci)nsamples

.

We approximate the expected profit for each industry state ω ∈{1, , 19}×{0, 1, , 19}.

The plots of expected price, expected quantity demand, expected market share, and expected profit are

presented in Figure G. Both a firm’s market share and its profit increase relatively rapidly as its brand

equity increases. However, the gains to increases in brand equity are larger when competiting against a low

brand equity competitor.

5 The Dynamic Model of Brand Building

In this section, we present the dynamic model of brand building and discuss our estimation strategy. The

dynamic model is informed by the results of the estimation of the static model of price competition and

the descriptive empirical analysis of the relationship between our brand equity estimates and advertising

expenditures. In particular, because of the insights derived from these exercises, we make the following

assumptions in the dynamic model. First, we assume that from quarter to quarter, a firm’s brand equity

can increase by one unit and decrease by up to two units. This assumption is made to accommodate the

fact that while we see only relatively small increases in brand equity from period to period. we see a few

relatively big decrease in brand equity, as is seen in figure E. As explained above, this assumption allows

us to use a much finer discretization of the brand equity continuum than would be possible if we restricted

transitions to immediately adjacent brand equity states. Second, we assume that advertising stochastically

5. In the implementation, we analytically integrate over mt.

The Dynamic Model of Brand Building 13

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enhances brand equity, which is in line with the positive correlation between advertising expenditures and

changes in brand equity that is discussed in section 4.2. Third, we assume that the expected effectiveness

of a firm’s advertising is decreasing in its brand equity. This is motivated by the finding that the higher a

firm’s brand equity, the more likely it is to decline, discussed in section 4.2. Fourth, because we do not find

a significant brand-advertising interaction in the descriptive empirical analysis discussed in section 4.2, we

assume that firms are symmetric and therefore differences between firms are fully captured by the differences

between their respective brand equities, which arise endogenously. Fifth, we assume that brand equity is

subject to industry-wide depreciation (which is reflective of an increase in the equity of the outside good)—

as opposed to firm-specific depreciation—because we find that when controlling for advertising spending,

changes in brand equity are correlated across firms in each period (cor = .74, p=.014).

5.1 The Dynamic Model

We study advertising and brand equity within the context of a dynamic stochastic game in the Ericson &

Pakes (1995) framework. Our model is a richer version of the quality ladder model explored in Pakes &

McGuire (1994) and Borkovsky, Doraszelski, & Kryukov (2011). To allow for entry and exit in a way that

guarantees the existence of an equilibrium, we follow Doraszelski & Satterthwaite (2010) and assume that

setup costs and scrap values are privately observed random variables.

Timing. Each period is divided into two subperiods. In subperiod 1 the sequence of events is as follows.

1. Each incumbent firm draws a private, random effectiveness of advertising and decides how much to

invest in advertising.

2. The advertising investment decision of incumbent firms are carried out and their uncertain outcomes

are realized. A common industry industry-wide depreciation shock affecting all incumbents is realized.

As a result, the industry state transitions from ω to ω ′ ≡ (ωn′ , ω−n

′ ) and all firms observe the new

industry state.

3. Incumbent firms compete in the product market.

In subperiod 2, entry and exit decisions are made as follows.

1. Each incumbent firm draws a private, random scrap value and decides on exit. Each potential entrant

draws a private, random setup cost and decides on entry.

2. Entry and exit decisions are implemented. As a result, the industry state transitions from ω ′ to

ω ′′≡ (ωn′′, ω−n

′′ ) and all firms observe the new industry state.

14 Section 5



In the dynamic model, periods correspond to quarters. However, firms engage in static product market

competition in each week. While brand equity is held constant across quarters, market size, marginal costs,

and consumers’ idiosyncratic preferences for the two brands and the outside good–all of which are introduced

below–are redrawn each week.6 For the sake of conciseness, we omit time subscripts.

We first describe the static model of product market competition and then turn to advertising, entry,

and exit dynamics.

Incumbent firms. Suppose first that firm n is an incumbent firm, i.e., ωn 0. The state of the incumbent

firm n at the end of subperiod 1 is determined by the stochastic outcomes of its advertising decision and an

industry-wide depreciation shock. In particular, its state evolves according to the law of motion

ωn′ = ωn + τ n− η, (5)

where τ n ∈ {0, 1} is a random variable governed by the incumbent firm n’s advertising xn ≥ 0 and η ∈ {0,

1, 2} is an industry wide depreciation shock. If τ n = 1, advertising was successful and the brand equity of

incumbent firm n increases by one level. The probability of success is γ nxn

1+ γ nxn, where γ n > 0 is a measure of

the effectiveness of advertisement. The effectiveness of advertising is independent across all periods and firms.

We assume that γ n= eαn−k, where αn is a private drawn from a gamma distribution Γ(h, θ(ωn)) with shape

parameter h and scale parameter θ(ωn), and k > 0. We make this assumption about γ n—instead of simply

assuming that γ n itself is drawn from a gamma distribution—because it allows the model to accommodate

a larger variance in the advertising expenditure decisions that arise in equilibrium. Because αn is bounded

below by zero, we include the k term in γ n = eαn−k so as to ensure that the model admits “small” γ n values.

The probability density function of the gamma distribution is denoted by g(.|h, θ(ωn)). We assume that

θ(ωn) = exp (a ωn3 + bωn

2 + cωn + d), (6)

where c < b2

3a and a < 0; it follows that θ(.) is a stricly decreasing function and, accordingly, a firm’s expected

advertising effectiveness is strictly decreasing in its brand equity.

If η 0, the industry is hit by a depreciation shock that reduces each firms’ brand equity by either one

or two units. The depreciation shock is modeled as two independent and identically distributed draws from

a Bernoulli distribution with success probability δ . It follows that the distribution of the industry-wide

depreciation shock is

∆(η) =

(1− δ )2 if η = 0,

2δ (1− δ ) if η = 1,

δ 2 if η = 2.

6. We assume that firms engage in product market competition in each week because estimating the static model of

product market competition at the weekly level allows us to separately identify the brand equities and the price coefficient in

the consumer’s utility function.


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In subperiod 2, an incumbent firm decides whether to remain active or to exit. We model exit as a

transition from state ωn 0 to ωn′ = 0. We assume that at the beginning of subperiod 2, each incumbent

firm draws a random scrap value from a log normal distribution with scale parameter µ and shape parameter

σ. Scrap values are independently and identically distributed across firms and periods. Incumbent firm n

learns its scrap value φn prior to making its exit decision, but the scrap value or setup cost of its rival remains

unknown to it. If the scrap value is above a threshold φn, then incumbent firm n exits the industry and

perishes; otherwise it remains in the industry. This decision rule can be represented either with the cutoff

scrap value φn itself or with the probability ξ n∈ [0, 1] that incumbent firm n remains in the industry in state ω

because ξ n=

1(φn≤ φn)dF(φn) = F (φn) where 1(·) is the indicator function, is equivalent to φn= F −1(ξ n).

Potential entrants. Suppose next that firm n is a potential entrant, i.e., ωn= 0. In subperiod 2, a potential

entrant decides whether to enter the industry. We model entry as a transtion from state ωn = 0 to state

ωn

′

0. We assume that at the beginning of subperiod 2 each potential entrant draws a random setup costfrom a log normal distribution with scale parameter µe and shape parameter σe. Like scrap values, setup

costs are observed privately and are independently and identically distributed across firms and periods. If

the setup cost is below a threshold φn

e, then potential entrant n enters the industry; otherwise it persists

as a potential entrant. This decision rule can be represented with the probability ξ n∈ [0, 1] that potential

entrant n enters in the industry. Upon entry, potential entrant n becomes incumbent firm n and its state is

the exogenously given initial brand equity ωe.

Value and policy functions. Define V n(ω, αn) to be the expected net present value of firm n’s cash flows

if the industry is currently in state ω and it has drawn effectiveness of investment αn. Incumbent firm n’s

value function is V n : {1, , M } ×{0, , M } × [0,∞)→R, and its policy functions ξn : {1, , M } × {0, ,

M }→ [0, 1] and xn : {1, , M }×{0, , M }→ [0,∞) specify the probability that it remains in the industry

in state ω and its advertising in state ω given that it draws an effectiveness of advertising αn, respectively.

Potential entrant n’s value function is V n : {0} × {0, , M }→R, and its policy function ξn : {0} ×{0, ,

M }→ [0, 1] specifies the probability that it enters the industry in state ω .

Bellman equation and optimality conditions. Suppose first that firm n is an incumbent firm, i.e.,

ωn 0. We first present the problem that incumbent firm n faces in subperiod 1. The value functionV n :{1, ,

M }×{0, , M }× [0,∞)→R is implicitly defined by the Bellman equation

V n(ω, αn) = maxxn0

−xn + E [πn(ω ′)|ω, xn, x−n(ω, α−n), αn] + β ·E [W n(ω ′)|ω, xn, x−n(ω , α−n), αn], (7)

where β ∈ (0, 1) is the discount factor and

E [πn(ω ′)|ω, xn, x−n(ω, α−n), αn] = eαn−kxn

1 + eαn−kxn

Y n1(ω) +

eαn−kxn

1 + eαn−kxn

Y n0(ω) (8)

16 Section 5



is the expected profit that incumbent firm n earns in subperiod 1 through product market competition.

Y nτ n(ω) is incumbent firm n’s expected profit conditional on an investment success (τ n = 1) or failure (τ n= 0),

respectively, as given by

Y nτ n(ω) =

α−n

η∈{0,1,2}τ −n∈{0,1}

∆(η) eα−n−k ·x−n(ω, α−n)

1 + eα−n−k

·x−n(ω, α−n)τ −n

1

1 + eα−n−k

·x−n(ω, α−n)1−τ −n

×πn(max{min{ωn + τ n− η, M }, 1}, max {min{ω−n + τ −n− η, M }, 1})

×g(α−n|h, θ(ω))dα−n.

The min and max operators merely enforce the bounds of the state space. The continuation value in the

Bellman equation (7) is

E [W n(ω ′)|ω, xn, x−n(ω, α−n), αn] = eαn−kxn

1 + eαn−kxn

Z n1(ω) +

eαn−kxn

1 + eαn−kxn

Z n0(ω). (9)

W n(ω ′), which is defined formally below, denotes the expected net present value of all future cash flows to

incumbent firm n when it is in industry state ω

′

at the beginning of subperiod 2. Z nτ n

(ω) is the expected netpresent value of all future cash flows to incumbent firm n when it is in industry state ω at the beginning of

subperiod 1 conditional on an investment success (τ n = 1) or failure (τ n = 0), respectively, as given by

Z nτ n(ω) =

α−n

η∈{0,1,2}τ −n∈{0,1}

∆(η)

eα−n−k ·x−n(ω, α−n)

1 + eα−n−k ·x−n(ω , α−n)

τ −n

1

1 + eα−n−k ·x−n(ω , α−n)

1−τ −n

×W n(max{min{ωn + τ n− η, M }, 1}, max{min{ω−n + τ −n− η, M }, 1})

×g(α−n|h, θ(ωn))dα−n.

Solving the maximization problem that incumbent firm n faces in subperiod 1, which is on the right-

hand side of the Bellman equation (7), we obtain the complementary slackness condition for xn(ω, αn):

−1 + eαn−k

(1 + eαn−kxn(ω, αn))2T n(ω) 0,

xn(ω, αn)

−1 +

eαn−k

(1 + eαn−kxn(ω, αn))2T n(ω)

= 0, (10)

xn(ω, αn) 0,

where T n(ω)≡Y n1(ω)−Y n

0(ω) + β (Z n1(ω)−Z n

0(ω)). Solving the complementary slackeness condition (10) for

incumbent firm n’s optimal advertising spending, we find that

xn(ω, αn) = max0,−1 + eαn−kT n(ω)

eαn−k (11)

if T n(ω) 0 and xn(ω, αn) = 0 otherwise.

We now turn to the problem that incumbent firm n faces in subperiod 2. At the beginning of subperiod

2, the industry state is ω ′. The expected net present value of all future cash flows to incumbent firm n in

industry state ω ′ is

W n(ω ′) = maxξn∈[0,1]

(1− ξ n)E [φn|φnF −1(ξ n)] + ξ nβU nωn′

(ω ′). (12)




U nωn (ω ′) is the expected net present value of all future cash flows to incumbent firm n when it is in industry

state ω ′ at the beginning of subperiod 2 and it transitions to state ωn during subperiod 2, as given by

U nωn (ω ′) = ( 1− ξ −n(ω ′))V n(ωn, 0) + ξ −n(ω ′){l(ω−n

′ = 0)V n(ωn, ωe) + l(ω−n′ > 0)V n(ωn, ω−n

′ )},

where

V n(ω) =

αn

[−xn(ω, αn) + E [πn(ω ′)|ω, xn(ω , αn), x−n(ω, α−n), αn]

+β ·E [W n(ω ′)|ω, xn(ω, αn), x−n(ω, α−n), αn]]g(αn|h, θ(ωn)) dαn.

(13)

Instead of the unconditional expectation E (φn), an optimizing incumbent cares about the expectation of the

scrap value conditional on collecting it:

E {φn|φn≥F −1(ξ n)} = eµ−σ2Φ

µ+σ2− ln (F −1(ξn))

σ

Φ µ− ln (F −1(ξn))

σ

.

Solving the maximization problem on the right-hand side of equation (12) and using the fact that (1 −

ξ n)E [φn|φn≥F −1(ξ n)] =

φn≥F −1(ξn) φndF (φn), we obtain the first-order condition for ξ n(ω):

−F −1(ξ n(ω ′)) + βU nωn′

(ω ′) = 0. (14)

The complementary slackness condition (10) and the first-order condition (14) are both necessary and

sufficient.

Suppose next that firm n is a potential entrant, i.e., ωn = 0. The value function V n :{0}×{0, , M }→R

is implicitly defined by

V n(ω ′) = maxξn∈[0,1]

ξ n{−E {φne |φn

eF e

−1

(ξ n)}+ βU nωe(ω ′)}+ (1− ξ n)βU n

0(ω ′)}.

Instead of the unconditional expectation E (φne ), an optimizing potential entrant cares about the expectation

of the setup cost conditional on entering:

E {φne |φn

e ≥F e−1(ξ n)} = eµe−σe2

Φ

µe+σe2− ln (F −1(ξn))

σe

Φ µe− ln (F −1(ξn))

σE .

Using the fact that −ξ n{φne |φn

e ≤F e−1(ξ n)}=−

φne≤F e−1(ξn)

φnedFe(φn

e), we obtain the first-order condition

for ξ n(ω),

−F −1(ξ n(ω ′)) + β {U nωe(ω ′)−U n

0

(ω ′)}=0, (15)

which is both necessary and sufficient.

18 Section 5



Equilibrium. We restrict attention to symmetric Markov perfect equilibria in pure strategies. Existence is

guarenteed by an extension of the proof in Doraszelski & Satterthwaite (2010). 7 In a symmetric equilibrium,

the advertising decision taken by firm 2 in state ω when it has drawn an effectiveness of advertising of

α2 is identical to the advertising decision taken by firm 1 in state ω[2] when it has drawn an effectiveness

of advertising of α1, i.e., x2(ω, α2) = x1(ω[2], α2), and similarly for the value functions. Analogously, the

probability firm 2 is active in the next period in state ω is identical to the probability that firm 1 is active

in the next period given state ω[2] i.e. ξ 2(ω) = ξ 1(ω[2]). It therefore suffices to determine the value and

policy functions of only one firm, to which we will refer as firm n. Solving for an equilibrium for a particular

parameterization of the model amounts to finding a value function V n(·) and policy functions ξn(·) and xn(·)

that satisfy the Bellman equations and the optimality conditions for firm n.

This system comprises the incumbent firm’s Bellman equation

V n(ω, αn) = −xn(ω, αn) + E [πn(ω ′)|ω, xn(ω, αn), x−n(ω , α−n), αn] + β · E [W n(ω ′)|ω, xn(ω, αn), x−n(ω,α−n), αn] ,

and optimal advertising equation (11) for ω ∈{1, , M }×{0, , M } and αn∈ (0,∞); the incumbent firm’s

first-order condition (14) for ω ∈{1, , M }×{0, , M }; and the potential entrant’s Bellman equation

V n(ω) = ξ n(ω){−E {φne |φn

eF e

−1

(ξ n(ω))}+ βU nωe(ω)}+ (1− ξ n(ω))βU n

0(ω)} (16)

and first-order condition (15) for ω ∈{0}×{0, , M }.8

Becasue of the dependence of this system on αn, it would be both challenging and computationally

burdensome to solve for solutions of this system. We therefore integrate out over αn and instead solve for

an incumbent firm’s expected value and expected advertising spending. To this end, we define incumbent

firm n’s expected advertising spending in industry state ω ,

xn(ω) =

αn

xn(ω, αn)g(αn|h, θ(ωn))dαn,

and firm n’s expected probability of successful advertising in industry state ω ,

ρn(ω) =

αn

eαn−kxn(ω, αn)

1 + eαn−kxn(ω, αn)g(αn|h, θ(ωn))dαn.

7. For any αn∈ (0,∞), the transition function for subperiod 1 that is defined above is unique investment choice admissible

(Doraszelski & Satterhtwaite 2010). It follows that for any industry stateω, the mapping from firm n’s advertising effectiveness

draw αn to its optimal advertising spending, xn(ω, ·), is a function. Moreover, this function is a unique best-reply to any

strategy played by firm n’s rival. In subperiod 2, firms play cutoff entry/exit strategies, as in (Doraszelski & Satterhtwaite

2010). It follows that there exists a symmetric Markov perfect equilibrium in pure strategies.

8. We restate both the incumbent firm’s and the potential entrant’s Bellman equations because within the context of the

full system of equilibrium conditions, one removes the max function from each and replaces the choice variables xn and ξn with

the corresponding equilibrium policy functions, xn(ω, αn) and ξn(ω).


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Incumbent firm n’s expected value in industry state ω , V n(ω), has already been defined above in equation

(13). Because αn is drawn from a gamma distribution, we can derive these analytically. In this case,

xn(ω) = T n(ω)

ek

2

2

2 + θ(ωn)

h

1−G

log

1

T n(ω)

+ k , h ,

2θ(ωn)2 + θ(ωn)

(17)

− ek

(1 + θ(ωn))1−G log 1

T n(ω)+ k , h ,

θ(ωn)

1 + θ(ωn)

if T n(ω) 0 and xn(ω) = 0 otherwise, and

ρn(ω) = 1−G

log

1

T n(ω)

+ k , h , θ(ωn)

− (18)

1−G

log

1

T n(ω)

+ k , h ,

2θ(ωn)

2+ θ(ωn)

T n(ω)

ek

2

2

2 + θ(ωn)

h

.

We can now rewrite the system of equilibrium conditions, integrating out over αn. Because we restrict

attention to symmetric equilibria, V 1(ω) = V 2(ω[2]), x1(ω) = x2(ω[2]), ρ1(ω) = ρ2(ω[2]), and ξ 1(ω) = ξ 2(ω[2]);

therefore, we can restrict attention to firm 1’s problem. It follows that the vector of unknowns in equilibrium

is

Φ =[V 1(0, 0), V 1(1, 0), , V 1(M , 0), V 1(0, 1), , V 1(M , M ),

ξ 1(0, 0), , ξ 1(M , M ), x1(1, 0), , x1(M , M ), ρ1(1, 0), , ρ1(M , M )].

The system comprises

V 1(ω) = −xn1(ω) + E

π1(ω ′)|ω, ρ1(ω), ρ1(ω[2])

+ β ·E

W 1(ω ′)|ω, ρ1(ω), ρ1(ω[2])

, (19)

and equations (17), (18) and (14) for ω ∈{1, , M }×{0, , M } and n = 1, and equations (16) and (15) for

ω ∈ {0} × {0, , M } and n = 1. Therefore, equilibria are characterized by a system of 2(M + 1)(2M + 1)

equations in 2(M + 1)(2M + 1) unknowns. In this system, because we have integrated out over αn, equations

(8) and (9) become

E [πn(ω ′)|ω, ρn(ω), ρ−n(ω)] = ρn(ω)Y n1(ω) + ( 1− ρn(ω))Y n

0(ω),

and

E [W n(ω ′)|ω, ρn(ω), ρ−n(ω)] = ρn(ω)Z n1(ω) + ( 1− ρn(ω))Z n

0(ω),

respectively.

5.2 Estimating the Dynamic Model

We estimate the dynamic model using maximum likelihood estimation. We maximize the likelihood of the

observed advertising spending decisions, entry/exit decisions, and state-to-state transitions. While we do

account for the entry/exit decisions in the likelihood function, we are not able to estimate the parameters of

the distributions from which setup costs and scrap values are drawn because we observe only one instance

of entry and no instances of exit. We therefore fix these parameters at values that seem reasonable. In

20 Section 5



particular, because we observe no instances of exit, we set the parameters of the log normal distribution from

which scrap values are drawn to values that will ensure that firms do not exit: µ =−20 and σ = 1. Because

there has been only one instance of entry since the stacked chips category was established 45 years ago, we

set ther parameters of the log normal distribution from which setup costs are drawn to values that yield

equilibrium entry probabilites of approximately 2% on an annual basis: µe= 16 and σe= 3. Finally, because

we cannot identify the discount factor β , we set β = 0.99, which corresponds to an annual interest rate of 4.1%.

We first explain how we derive the values of αn that rationalize the observed advertising spending decions

and then explain how we construct the likelihood function and estimate the model using mathematical

programming with equilibrium constraints (MPEC) (Su & Judd 2012).

Rationalizing Advertising Expenditures. In the case that advertising spending is positive, we invert

equation (11) in order to derive the values of αn that rationalize the observed advertising spending. Because

this inversion entails solving a quadratic equation, there are two values of αn that rationalize every positiveadvertising spending decision. Let αn

∗(ωq, xqn)≡ (αn1∗ (ωq, xqn), αn2

∗ (ωq, xqn)) be the vector of αn draws that

rationalizes observed advertising spending xqn by firm n in industry state ωq. It follows that

αn∗(ωq, xqn) =

2log

T n(ωq) + T n(ωq)− 4xqn

2xqn

+ k,

2log

T n(ωq)− T n(ωq)− 4xqn

2xqn

+ k

if T n(ωq)−4xqn≥0. To understand why two different αn draws rationalize an observed advertising spending

decision, consider a firm that spends a relatively low amount on advertising. There is a relatively low draw

of αn—which implies a relatively low advertising effectiveness—that would justify this. In this case, becaue

the returns to advertising are low, it is not worthwhile for the firm to invest very much in advertising.

Alternatively, a relatively high draw of αn—which implies a relatively high advertising effectiveness—would

justify this too. When advertising is highly effective, even a small amount of spending nearly guarantees

success and, therefore, it is not worthwhile for the firm to spend more.

If T n(ωq)− 4xqn < 0, then there is no draw of αn that rationalizes observed advertising spending xqn by

firm n in industry state ωq. This is because given any equilibrium, there is an endogenous upper bound to

advertising spending for each firm in each industry state: xn(ω)≤T n(ω)

4 . Intuitively, a firm never spends more

on advertising than the increase in the expected net present value of its future cash flows that would result if

its advertising were successful. Given an equilibrium, any advertising spending above this upper bound has

a likelihood of zero. Finally, it follows from equation (11) that given an equilibrium, if αn < k + log

1

T n(ω)

,

then xn(ω) = 0. Therefore, the probability of observing zero advertising spending by firm n in industry state

ω is G

k + log

1

T n(ω)

, h , θ(ωn)

.




MPEC. To estimate model, we use the MPEC approach proposed in Su and Judd (2012). In this approach,

we maximize the likelihood through a constrained optimization over both the parameters and the vector of

unknowns in equilibrium Φ, using the the equilibrium conditions as the set of constraints.

We use this approach for two reasons. First, we have found that thers is a significant increase in

computation speed relative to to tradtional nested fixed point estimation (Rust 1987). Second, in our

particular problem, there are large areas of the parameter space where the log likelihood is undefined. This

occurs when observed advertising spending exceeds the endogenous upper bound on advertising spending

implied by an equilibrium. The MPEC approach allows us to add additional constraints to ensure that the

algorithm avoids these areas of the parameter space.

Let αqn∗ = (αqn1

∗ , αqn2∗ ) be the vector of possible advertising effectiveness as calculated by equation (19).

To estimate the model, we solve for the joint log likelihood of firms’ entry/exit decisions, firms’ advertising

spending decisions, and state-to-state transitions:

max{a,b,c,d,h,δ,Φ}

q

log

n

[f n(xqn|ωq)l(xqn > 0)

+G

k + log

1

T n(ωq)

, h , θ(ωqn)

l(xqn =0)]

+log (P (ωq′|ωq, xq1, xq2))

+log

n

ξ n(ωq

′

)1−l(ωq+1,n′′

=0)(1− ξ n(ωq′))l(ωq+1,n=0)

where l(·) is the indicator function, f n(xqn|ωq) is the probability density function of firm n’s advertising

spending in state ωq for xqn > 0 , which is given by

f n(xqn|ωq) = g

2log T n(ωq) − T n(ωq)− 4x

qn 2xqn

+ k , h , θ(ωqn)

×2T n(ωq)− 4xqn

+

2xqn

T n(ωq)− 4xqn − T n(ωq)

T n(ωq)

− T n(ωq)− 4xqn

xqn

+g

2log

T n(ωq)

+ T n(ωq)− 4xqn

2xqn

+ k , h , θ(ωqn)

×2T n(ωq)− 4xqn

+

2xqn

T n(ωq)− 4xqn + T n(ωq)

T n(ωq)

+ T n(ωq)− 4xqn

xqn

,

and P (ωq′|ωq, xq1, xq2) is the probability of the transition observed in the first subperiod of quarter q , from

state ωq at the beginning of the subperiod to state ωq′

at the end of the subperiod:

P (ωq′|ωq, xq1, xq2) =

ν 1∈α1

∗(ωq,xq1)

ν 2∈α2

∗(ωq,xq2)

τ 1∈{0,1}

τ 2∈{0,1}

η∈{0,1,2}

l(ωq′ = (ωq + (τ 1, τ 2)− η × (1, 1))

×r(αq1, xq1)τ 1(1− r(αq2, xq1))1−τ 1

×r(αq1, xq2)τ 2(1− r(αq2, xq2))1−τ 2

× g(ν 1|h, θ(ωq1))

ψ∈α1∗(ωq,xq1)

g(ψ |h, θ(ωq1))×

g(ν 2|h, θ(ωq2))ψ∈α2

∗(ωq,xq2) g(ψ |h, θ(ωq2))

∆(η)

22 Section 5

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http://-/?-



if ωq∈{1, , M }×{1, , M },


ν 1∈α1

∗(ωq,xq1)

τ 1∈{0,1}

η∈{0,1,2}

l(ωq1′ =ωq1 + τ 1− η)

×r(αq1, xq1)τ 1(1− r(αq2, xq1))1−τ 1

× g(ν 1|h, θ(ωq1))


g(ψ |h, θ(ωq1))∆(η)

if ωq∈{1, , M }×{0}


ν 2∈α2

∗(ωq,xq2)∗

τ 2∈{0,1}

η∈{0,1,2}

l(ωq2′ =ωq2 + τ 2− η)

×r(αq1, xq2)τ 2(1− r(αq2, xq2))1−τ 2

× g(ν 2|h, θ(ωq2))


g(ψ |h, θ(ωq2))∆(η)

if ωq∈{0}×{1, , M }, and

P (ωq′ |ωq , xq1, xq2) = 1

if ωq′ =ωq = (0, 0), where

r(α, x) = eα−kx

1 + eα−kx

is the probability that a firm’s advertising is successful when it receives a draw of α and spends x on

advertising.9

We maximize the log-likelihood function subject to the system of equilibrium conditions described at the

end of section 5.1. To these equilibrium conditions, we add the aforementioned endogenous upper bounds

on advertising spending,

xqnT n(ωq)

4

for each xqn observed in the data, for the industry state ωq in which it is observed. Because these upper

bounds are endogenous, adding them to the system of constraints does not change the equilibrium set.

However, it does prevent the algorithm that we employ from searching for a solution in an infeasible region.

We have found that the algorithm suffers from convergence problems if these constraints are not included.

We coded the maximum likelihood estimation in GAMS and run the optimization using the KNITRO solver.

9. Note that the realization of the depreciation shock and the outcome of advertising spending may not be uniquely

identified in each period. For example, if both firms experience a one unit decrease in brand equity, this coudl be caused by

(i) a depreciation shock of one unit and unsuccessful advertising for both firms, or (ii) a depreciation shock of two units and

successful advertising for both firms.


http://-/?-

http://-/?-



6 Results

Our estimation yields parameter estimates of δ = 0.3342, a =−4.73×10−5, b =−8.98× 10−4, c =−0.0473,

d = 1.5639, h = 4.049, and an equilibrium of the model that is presented in Figure H. The parameters that

are not estimable are held fixed at the following values: β = 0.99, k = 10, µ =−20 , σ = 1, µe = 16, and σe = 3.

6.1 Measuring the Brand Value of Pringles and STAX

We are now able to devise a measure of brand value that accounts for the effect of a brand’s brand equity on

both current and future profits. To assess the value of a firm’s brand in a given industry state, we compare

the value of the brand in that industry state to its value in a counterfactual scenario in which it is endowed

with the lowest possible brand equity, while holding its rival’s brand equity fixed. That is, the value of firm

n’s brand when it possesses brand equity ωn in industry state ω = (ωn, ω−n) is10

υn(ω)≡V n(ω)−V n(1, ω−n).

This measure takes into consideration that if brand n were stripped of its brand equity, this would affect

both firms’ advertising spending decisions in the present and the future. Accordingly, this would affect the

market structure that would arise in the short-run and, potentially, in the long-run. These brand values

can be computed directly from the equilibrium value function presented in Figure H. That is, as exploring

the counterfactual scenario of interest involves changing the industry state but not the parameterization

of the model, one need not compute another equilibrium in order to measure the value of a firm’s brand.

We find that in the stacked chips category, brand equity has the potential to increase a brand’s value by

$1.29 billion. We find that a brand is most valuable when it possesses the highest possible brand equity

and it is a monopolist, i.e., in industry state (19, 0). We find that the entry of STAX causes the value of

the Pringles brand to decrease by $118.04 million, from υ(11, 0) = $614.13 million in the third quarter of

2003 to υ(10, 4)=$496.09 million in the second quarter of 2006. The value of the STAX brand decreased by

$96.99 million, from υ(6, 10)=$196.33 million in the fourth quarter of 2003—in which STAX entered—to

υ(4, 10)=$99.34 billion in the second quarter of 2006. This suggests that competition from STAX reduced

the value of Pringle’s brand and, moreover, that the increased competitiveness of the category resulted in a

reduction in value of both firms’ brands.

10. Because firms are symmetric, the value of firm 1’s brand in state ω is equal to the value firm 2’s brand in state ω[2],

i.e., υ1(ω) =υ2

ω[2]

. Hereafter, we drop the firm subscript and report brand values from the perspective of firm 1.

24 Section 6

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http://-/?-



6.2 The Drivers of Brand Value

The equilibrium advertising spending policy function is presented in Figure H. A firm’s advertising behaviour

is characterized by two properties. First, a firm’s investment in advertising is increasing in its own brand

equity up to a brand equity level of 14 and declining thereafter. The figure in the bottom-right panel of

Figure H presents the mean of the distribution from which αn is drawn; it shows that the effectiveness

of a firm’s advertising decreases quite rapidly as its brand equity increases. For brand equity levels above

14, advertising is sufficiently ineffective to induce a decline in advertising spending, despite the fact that a

firm’s period profits increase quite rapidly in its brand equity. Second, a firm’s investment in advertising is

declining in its rival’s brand equity. We are also able to comment on the probability of successful advertising,

which is presented in the bottom-left panel of Figure H. For sufficiently low levels of brand equity, a

firm’s advertising is successful approximately 80% of the time. However, this probability that advertising

is successful declines rapidly as a firm brand equity increases—even in the face of increasing equilibriumadvertising spending—because its advertising becomes less effective.

To explore the implications of the equilibrium behavior for the dynamics of the industry, both in the

short-run and in the long-run, we compute the transient distribution over states in period t starting from the

state observed in the final period of our data set (the fourth quarter of 2006), ω = (10, 4). Figure J displays

the transient distributions in periods 8, 24, and 256. From the transient distributions in periods 8 and 24,

we see that while Pringles is likely to retain its brand equity advantage in the short-term, STAX is likely to

narrow it. By period 256, the transient distributions have converged and, therefore, the transient distribution

for this period can be regarded as being reflective of the long-run industry structure. It shows that the

industry evolves toward a symmetric industry structure with a modal state of ω = (9, 9). That is, if firms

play the equilibrium advertising strategies presented in Figure H, then STAX is likely to eventually catch up

to Pringles. This occurs for multiple reasons. First, STAX never gives up—i.e., it never stops advertising—

no matter how far it falls behind Pringles. Second, even though Pringles invests more in advertising than

STAX when it is in the lead, STAX benefits from a higher advertising effectiveness. Therefore, STAX is

more likely to advertising successfully despite its lower advertising spending.

7 Counterfactual Experiments

In this section, we explore several counterfactual scenarios of interest. For each, we examine how the

counterfactual scenario impacts brand building incentives, the evolution of brand equities, and accordingly

brand values. In subsection 7.1, we explore the effects of various changes in industry fundamentals. In section

7.2, we explore scenarios in which a brand with high brand equity can exploit opportunities to leverage its

Counterfactual Experiments 25



brand equity that are not available to low equity brands. In section 7.3, we explore the effects of reducing

the uncertainty that firms face about the effectiveness of advertising.

7.1 The Effect of Industry Fundamentals on Brand Value

We explore the effects of changes in industry fundamentals—in particular, the effectiveness of advertising,

the rate of depreciaiton of brand equity, and the market size—on brand building incentives, the evolution

of brand equity over time, and accordingly brand value. We use the industry state observed in the final

period of our data set (the fourth quarter of 2006), ω = (10, 4), as a benchmark. The first row of Table 4

reports the brand values of Pringles and STAX, respectively, in industry state (10,4). It also reports the

modal states of transient distributions—computed using industry state (10,4) as the starting point—for

periods t = 8, t = 24, and t = 256, which are reflective of the evolution of industry structure over time.11 The

additional rows of Table 4 present the changes in the the brand values—relative to those that correspond to

the estimated parameterization—and the modal states of the transient distributions for the counterfactual

scenarios. To explore the effects of changes in the depreciation rate, δ , and the market size, m, we increase

and decrease the estimated parameter values by 20%. To explore the effects of changes in the effectiveness

of investment, γ n = eαn−k, we increase and decrease the value of γ n—for any possible draw of αn—by 20%

by changing k from its benchmark value of k = 10 to k = 10− ln (1.2) and k = 10− ln (0.8), respectively.

parameter value Pringles STAX t=8 t= 24 t= 256

Estimated equilibrium 496.1 99.3 (10,5) (9,7) (9,9)

Ad effectiveness: +20% k = 9.818 +3.0% +4.4% (10,5) (10,8) (9,9)Ad effectiveness: -20% k = 10.223 -3.5% -5.3% (10,5) (9,7) (8,8)

Depreciation rate: +20% δ = 0.40104 -19.2% -39.0% (9,4) (1,1) (1,1)Depreciation rate: -20% δ = 0.26736 +10.0% +26.0% (11,7) (11,10) (11,11)

Market size: +20% M = 786, 377, 772 +23.6% +25.3% (10,5) (10,8) (9,9)Market size: -20% M = 524, 251, 848 -22.8% -24.2% (10,5) (9,7) (8,8)

Table 4. Brand values and modal states of transient distributions for the estimated equilibrium and counterfactual

scenarios.

Table 4 shows that an increase (decrease) in the effectiveness of advertising increases (decreases) the

brand values of both brands by somewhat similar magnitudes. An increase (decrease) in the effectiveness

of advertising induces both firms to increase (decrease) ad spending. Accordingly, the expected brand

equities of both brands are slightly higher (lower) in all periods, relative to the baseline scenario. 12 While

11. The industry structure for t=256 can be regarded as the long-run industry structure becaue by this period, the transient

distributions have converged.

26 Section 7

http://-/?-

http://-/?-

http://-/?-

http://-/?-



of greater magnitude, the results for the market size counterfactuals are qualitatively similar. However, we

find that changes in the rate of depreciation have a much larger effect on the brand values of STAX than

those of Pringles. When the rate of depreciation is decreased by 20%, the brand values of both brands

increase significantly because the brand equities that arise in the long-run are higher than those in the

baseline scenario. However, the brand value of STAX increases much more than that of Pringles because

the the industry structure becomes more symmetric in the short-run, as is demonstrated by the modal

states presented in Table 4. When the rate of depreciation is increased by 20%, Table 4 shows that in the

long run, neither firm will be able to sustain any brand equity. However, because Pringles has much more

brand equity in industry state (10,4) than STAX does, it takes longer for all of Pringles brand equity to be

depleted. Accordingly, Pringles’ earns much higher cash flows as the industry transitions from industry state

(10,4) to (1,1).

7.2 Leveraging High Brand Equity

[TO BE ADDED.]

7.3 Reducing the Uncertainty about the Effectiveness of Advertising

[TO BE ADDED.]

8 Conclusion

Building on the Pakes & McGuire (1994) quality ladder model, we have developed an estimable model

of brand building and harvesting. We have estimated this model using data from the U.S. stacked chips

category. Our estimation has allowed us to measure the value of the Pringles and STAX brands. Moreover,

it has allowed us to explore the ways in which these brands build brand equity through advertising and,

accordingly, how their respective brand equities evolve over time.

As with any empirical paper, our approach has a number of limitations that can be seen as suggestions for

future research. First, because we chose to examine a duopoly, the computational feasibility of our model to

settings with three or more firms still needs to be explored. Second, both P&G and PepsiCo are multiproduct

firms that may not be directly maximizing brand-specific profit in their advertising and pricing decisions in

the stacked chips category. Third, we treat the competition between the brands as occuring at a national

level, while there are likely to be location-specific differences in preferences and ad effectiveness. And finally,

12. Because the change in expected brand equity is small, this is discerbale in some but not all of the modal states presented

for the ad effectiveness counterfactuals in Table 4.

Conclusion 27



in order to estimate a computationally feasible and economically informative model, we made a number

of other simplifying assumptions on the timing of decisions, the nature of competition, the homogeneity

of consumer preferences, the availability of distribution channels etc. In different empirical contexts with

different data, these assumptions could be altered to create a richer model.

Notwithstanding these limitations, we believe our model and estimates help improve our understanding

of the process through which firms build and harvest their brands.

28 Section 8



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32



Table 4. Demand Model Results

Quarter Pringles Brand

Equity

STAX Brand

Equity

Quarter Pringles Brand

Equity

STAX Brand

Equity

Q1-2000 2.0025***

(0.40!"A

Q1-200# 1.#2$***

(0.#454!

0.5$

(0.44%1!

Q2-2000 1.$%4***

(0.#%0#!"A

Q2-200# 1.1$14***

(0.##21!

0.4%5

(0.42!

Q#-2000 1.$&4#***

(0.#21!"A

Q#-200# 1.##0***

(0.#2%1!

0.55#5

(0.44&1!

Q4-2000 1.1$1***

(0.#4!"A

Q4-200# 1.1%14***

(0.#2&5!

0.2&&

(0.405!

Q1-2001 1.522***

(0.#$!"A

Q1-2004 1.20&2***

(0.#2%#!

0.#404

(0.#&0%!

Q2-2001 1.202***

(0.#%#! "AQ2-2004 1.1#4***

(0.#04&!

0.410

(0.4122!

Q#-2001 1.%024***

(0.#$4%!"A

Q#-2004 1.1&%***

(0.#15!

0.#&

(0.402!

Q4-2001 1.#$4#***

(0.##1!"A

Q4-2004 1.0#&$**

(0.#14!

0.1$&

(0.41%2!

Q1-2002 1.25&%***

(0.##&&!"A

Q1-2005 1.1$5***

(0.#142!

0.24$%

(0.#&14!

Q2-2002 1.0%5**

(0.#5&!"A

Q2-2005 1.122&***

(0.#14$!

0.252$

(0.#%&$!

Q#-2002 1.25%5***

(0.#41$!

"AQ#-2005 1.14%%***

(0.#211!

0.2#$5

(0.#%44!Q4-2002 1.2004***

(0.###!

0.5&1$

(0.4$1!

Q4-2005 0.%1%1**

(0.2&55!

0.025&

(0.#&25!

Pri'e

)ei'ient

-2.2&$***

(0.25!

Sig+a 0.0$***

(0.1$4!

Standard err)rs in ,arenteses. * p .05/ ** p .01/ *** p .001

33



0

5

1 0

1 5

Advertising (Millions of Dollars) by Quarter

Figure A: Brand Advertising by QuarterQuarter

A d v e r t i s i n g ( M i l l i o n s o f D o l l a r s )

PRINGLESSTAX

2001−Q1 2002−Q1 2003−Q1 2004−Q1 2005−Q1 2006−Q1

0

1

2

3

4

5

6

Sales (Millions

Figure B: B

S a l e s ( M i l l i o n s

o f D o l l a r s )

2001−Q1 2002−Q1 2003−Q

0 . 0

0

0 . 0

5

0 . 1 0

0 . 1

5

0 . 2

0

Market Share Over Time

Figure C: Brand Market Share by QuarterQuarter

M a r k e t S h a r e

2001−Q1 2002−Q1 2003−Q1 2004−Q1 2005−Q1 2006−Q1

0 . 0

0 . 5

1 . 0

1 . 5

Price pe

Figure D: B

P r i c e p e r U n i t ( D o l l a r s )

2001−Q1 2002−Q1 2003−Q



0 . 0

0 . 5

1 . 0

1 . 5

2 . 0

2 . 5

Brand Equity by Quarter

Figure E: Brand Equity and Discretization by QuarterQuarter

B r a n d E q u i t y

2001−Q1 2001−Q4 2002−Q3 2003−Q2 2004−Q1 2004−Q4 2005−Q3 2006−Q2

PRINGLES

STAX

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2

Marginal Costs Over Time

Figure F: Brand Marginal Costs by Quarter

Quarter

M a r g i n a l C o s t ( D o l l a r s )

PRINGLESSTAX

2001−Q1 2001−Q4 2002−Q3 2003−Q2 2004−Q1 2004−Q4 2005−Q3 2006−Q2

35



05

10 15

0

510

15

0

0.5

1

1.5

ω1

ω2

E x p e c t e d P r i c e ( D o

l l a r s )

05

1015

0

5

10

15

0

0.1

0.2

0.3

ω1

ω2

E x p

e c t e d M a r k e t S h a r e

05

1015

0

5

10

15

0

20

40

60

80

100

ω1

ω2

E x p e c t e d P r o f i t ( M i l l i o n s )

05

10 15

0

510

15

0

50

100

150

ω1

ω2

E x p e c t e d Q u a n t i t y D e m a n d

e d ( M i l l i o n s )

Figure G: Period Game Nash Equilibrium

(Functions presented are for firm 1.) 36



0

5

1015

0

5

10

15

0

2

4

6

ω1

Expected Advertising Cost (Millions)

ω2

x 1

( ω )

0

5

1015

0

5

10

15

0

0.2

0.4

0.6

0.8

1

ω1

Entry/Non−exit prob.

ω2

ξ 1

( ω )

0

5

10

15

0

5

10

15

0

0.2

0.4

0.6

0.8

ω1

Ad Sucess Prob.

ω2

ρ 1

( ω )

5 10 15 20

4

6

8

10

12

14

16

18

20

ω1

h θ ( ω 1

)

Figure H: Equilibrium Plots

(Functions presented are for firm 1.)

37



0

5

1015

0

5

10

15

0

0.01

0.02

0.03

0.04

0.05

0.06

ω1

Transient Distribution over States in Period 8

ω2

P ( ω )

0

5

1015

0

5

10

15

0

0.01

0.02

0.03

0.04

ω1


ω2

P ( ω )

0

5

10

15

0

5

10

15

0

0.01

0.02

0.03

0.04

ω1


ω2

P ( ω )

Figure I: Transient Distributions over States given Initial State (10,4)

38

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An Empirical Study of the Dynamic Brand Building