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Optimal Advertising and Promotion Budgets in Dynamic

Markets with Brand Equity as a Mediating Variable
S. Sriram, Manohar U. Kalwani,

To cite this article:

S. Sriram, Manohar U. Kalwani, (2007) Optimal Advertising and Promotion Budgets in Dynamic Markets with Brand Equity as a
Mediating Variable. Management Science 53(1):46-60. http://dx.doi.org/10.1287/mnsc.1060.0604

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Vol. 53, No. 1, January 2007, pp. 46–60 doi 10.1287/mnsc.1060.0604

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Optimal Advertising and Promotion Budgets in

Dynamic Markets with Brand Equity as
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a Mediating Variable
S. Sriram
School of Business, University of Connecticut, 2100 Hillside Road, Storrs, Connecticut 06269,
ssriram@business.uconn.edu
Manohar U. Kalwani
Krannert Graduate School of Management, Purdue University, 403 W. State Street,
West Lafayette, Indiana 47907-2056, kalwani@purdue.edu

W e study the optimal levels of advertising and promotion budgets in dynamic markets with brand equity as
a mediating variable. To this end, we develop and estimate a state-space model based on the Kalman filter
that captures the dynamics of brand equity as influenced by its drivers, such as the brand’s advertising and sales
promotion expenditures. By integrating the Kalman filter with the random coefficients logit demand model, our
estimation allows us to capture the dynamics of brand equity as well as to model consumer heterogeneity using
store-level data. Using these demand model estimates, we determine the Markov perfect equilibrium advertising
and promotion strategies. Our empirical analysis is based on store-level scanner data in the orange juice category,
which comprises two major brands—Tropicana and Minute Maid. As expected, we find that sales promotions
have a significant positive effect on consumers’ utility and induce consumers to switch to the promoted brand.
However, there is also a negative effect of promotions on brand equity that carries over from period to period.
Overall, we find that while sales promotions have a net positive impact both in the short term and in the
long term, the implied total profit elasticity including the long-term effect is smaller than the short-term profit
elasticity. Correspondingly, we expect myopic decision makers to allocate higher than optimal expenditures to
sales promotions. Our results from the supply-side analysis reveal that the actual promotion levels for both
brands are indeed higher than the optimal budgets for the forward-looking (long-term orientation) as well as
the two-year planning horizon scenarios. Hence, it may be profitable for both brands to reduce their promotion
levels. Further, we find that although the forward-looking promotional spending levels are higher for the smaller
brand, Minute Maid, it is market leader Tropicana that spends more on sales promotions. Turning to optimal
advertising budgets, we find that the equilibrium forward-looking advertising levels are higher for Tropicana,
the brand that has higher brand equity and a higher responsiveness to advertising. Further, as expected, the
optimal forward-looking advertising levels are higher than the myopic levels and the two-year planning horizon
levels for both brands. However, the forward-looking advertising levels are lower than the actual advertising
expenditures for both brands. This implies that even when we consider the long-term effects of advertising, the
brands are overspending on advertising.
Key words: long-term profitability; Kalman filter; brand equity; optimal advertising/promotion budgets;
Markov perfect equilibrium
History: Accepted by Jagmohan S. Raju, marketing; received October 11, 2004. This paper was with the
authors 10 months for 2 revisions.

1. Introduction pricing strategy (Reitman 1992) while increasing its

Brand managers in packaged-goods firms often in- advertising expenditures (Ailawadi et al. 2001). The
crease sales promotion spending to meet short-term example illustrates the types of trade-offs that man-
sales and market share objectives. However, with doc- agers have to make between the short-term benefits of
umented evidence of the possible detrimental effects marketing actions versus their potential adverse long-
of sales promotions over the long term (Mela et al. term consequences. The issue of the optimal alloca-
1997, Jedidi et al. 1999), managers in many con- tion of the advertising and sales promotion budgets is
sumer packaged-goods firms are trying to increase especially critical for brand managers who are faced
their expenditures on brand-building activities such with flat or declining marketing budgets (Low and
as advertising, while cutting down their sales and Mohr 2000).
trade promotion budgets. Starting in the early 1990s, A key purpose of our study is to investigate the
Procter & Gamble, for example, reduced its trade optimum levels of advertising and promotion bud-
promotion spending and adopted an everyday low gets when both these marketing instruments have
46
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
Management Science 53(1), pp. 46–60, © 2007 INFORMS 47

long-term effects. Specifically, we consider the trade- the positive effect of sales promotions caused by an
offs that managers make between the short-term ben- increase in consumer utility. Hence, while the net
efits of marketing actions such as sales promotions short-term effect of sales promotions is positive, their
and their possible detrimental long-term effects. Our long-term impact on a brand’s market share and prof-
goal is to understand how the optimal marketing bud- itability can be negative due to their adverse impact
gets under short-term orientation differ from those on brand equity. As expected, we find that advertising
that consider the long-term consequences of market- spending has a positive effect on brand equity. On the
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ing actions. To this end, we formulate and estimate a supply side, our results reveal that the actual promo-
demand model wherein the long-term effects of these tion levels for both brands are higher than the optimal
variables are modeled with brand equity as a mediat- budgets for the forward looking as well as the two-
ing variable. This is in contrast to most of the extant year planning horizon scenarios. Hence, it may be
literature (with the exception of Jedidi et al. 1999), profitable for both brands to reduce their promotion
which examines the long-term implications of these levels. Further, we find that although the forward-
marketing actions with sales or market share as a looking promotional spending levels are higher for
mediating variable (see, for example, Dekimpe and the smaller brand, Minute Maid, it is market leader
Hanssens 1999, Naik et al. 2005). The use of brand Tropicana that spends more on sales promotions.
equity as a mediating variable allows us to examine With regard to advertising, we find that the equi-
whether there are adverse long-term consequences of, librium forward-looking advertising levels are higher
e.g., sales promotions, even when their impact in the for Tropicana, the brand that has higher brand equity
short term on the brand’s sales and profitability is and a higher responsiveness to advertising. Further,
positive. We use the demand model parameter esti- as expected, the optimal forward-looking advertis-
mates to compare the optimal Markov perfect equi- ing levels are higher than the myopic levels and the
librium (MPE) advertising and promotion budgets two-year planning horizon levels for both brands.
under the scenarios when the decision makers con- However, the forward-looking advertising levels are
sider only the short-term consequences of marketing lower than the actual advertising expenditures for
programs versus when they are long-term oriented. both brands. This implies that even when we consider
We perform our analysis in two stages. In the first the long-term effects of advertising, the brands are
stage, we estimate the demand-side parameters using overspending on advertising.
store-level sales data. To this end, we develop and The rest of this paper is organized as follows: We
estimate a state-space model based on the Kalman first review the related literature. Next, we present
filter that captures the dynamics of brand equity as the state-space model for estimating the demand-side
influenced by marketing actions such as a brand’s parameters and the details of the supply-side model
advertising and sales promotion expenditures. In the for estimating the MPE advertising and promotion
second stage, we use these demand-side estimates strategy profiles. We then discuss the estimation of
to compute the MPE advertising and sales promo- the demand-side and the supply-side models. Next,
tion expenditures. First, we investigate the equilib- we describe the data and the operationalization of the
rium advertising and sales promotion levels when the model variables. Subsequently, we present our empir-
decision makers are myopic and consider only the ical results based on the orange juice category and
current-period profits. We then compare these lev- discuss the equilibrium advertising and sales promo-
els with the case when the decision makers are for- tion strategy profiles under various scenarios. Finally,
ward looking and maximize the expected discounted we provide some concluding comments.
value of future profits. A comparison of the current-
strategy profiles with these two scenarios provides 2. Related Literature
useful insights into how the optimal advertising and As discussed in the previous section, we develop a
promotion budgets depend on the correct formulation framework for obtaining equilibrium advertising and
of the objective function. sales promotion strategies when both these variables
We carry out our empirical analysis in the orange have long-term effects on a brand’s performance. In
juice category using store-level sales data from a retail this regard, this paper is closely related to two recent
chain in the Chicago market. Our demand-side esti- papers in the marketing literature, Naik et al. (2005)
mation reveals that in the short term, sales promo- and Dube et al. (2005).
tions have a positive effect on consumers’ utility, Similar to this study, Naik et al. (2005) investigate
and they may induce consumers to switch to the the optimal allocation of resources to advertising
promoted brand. However, there is also an adverse and promotion programs when they have long-term
impact of sales promotions on brand equity that car- effects on a brand’s profitability. To this end, they
ries over from period to period. In the short term, extend the Lanchester model by incorporating interac-
the magnitude of this negative effect is smaller than tion effects between advertising and sales promotions
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
48 Management Science 53(1), pp. 46–60, © 2007 INFORMS

in addition to modeling their main effects. This allows marketing budget between advertising and sales pro-
for a marketing instrument to either amplify or attenu- motions when both these instruments have long-term
ate the effectiveness of another marketing instrument. effects. However, we use an approach similar to Dube
In their empirical application, they find that while the et al. (2005). Nevertheless, in addition to the equi-
main effects of advertising and sales promotions are librium advertising strategies that they investigate,
positive, there is a negative interaction between them we also compute the equilibrium promotion levels
implying that promotions decrease the effectiveness of when such promotions may have a long-term impact.
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advertising campaigns. The marketing-mix algorithm Hence, we build on Dube et al. (2005) by consider-
they develop thus incorporates this trade-off in addi- ing the trade-off between advertising and sales pro-
tion to modeling strategic foresight amongst compet- motions when temporary price cuts and promotional
ing firms. deals may have long-term consequences.
In deriving the equilibrium advertising strategies,
Dube et al. (2005) use a logit demand model that
3. Model
accounts for the dynamic effects of advertising. One
of the advantages of this demand system is the ability 3.1. Demand Model
to explain the optimality of pulsing advertising strate- We consider a market with utility-maximizing house-
gies, which was one of the objectives of their study. holds that while shopping at store s s = 1 2     S
However, the flexibility of the logit model implies that in period t may choose to purchase a brand j j = 1
one cannot obtain analytical solutions, especially for 2     J  within a category or may purchase an out-
closed-loop equilibria.1 Correspondingly, they use the side good (equivalent to not purchasing in the cate-
MPE solution concept, wherein the optimal advertis- gory, denoted by j = 0). The presence of the outside
ing strategies are computed numerically. alternative in our model allows for the potential mar-
Similar to Dube et al. (2005), we use a logit demand ket expansion and contraction. We represent the util-
model rather than the Lanchester model to investi- ity that household h derives from buying brand j, j =
gate the long-term effects of advertising and sales 1 2     J , in store s, s = 1 2     S, in period t, as
promotions on a brand’s profitability. There are a
number of advantages to using the logit demand Uhjst = 0hjst + h Pjst +
Xjst + h Prjst +jst + hjst 
model. First, the logit model is derived from the j = 0 1 2     J  s = 1 2     S (1)
behavioral assumption that consumers maximize util-
ity while choosing an alternative. Hence, it is better where 0hjst is the utility that household h derives
suited for modeling the impact of marketing actions from brand name j in store s at time t; Xjst is a vec-
on consumers’ utility, which in turn affects aggregate tor of factors that influence the household’s utility,
demand. For example, consider the long-term effect of including demand drivers such as seasonal factors;2
promotions on demand. Extant research reveals that Pjst and Prjst are the regular price and promotion,
promotions may have a detrimental effect on brand respectively, of brand j in store s in period t; jst is the
equity (see, for example, Jedidi et al. 1999), even if mean utility to consumers from brand j in store s in
they have a positive short-term effect on sales. We period t due to unobserved variables; and hjst repre-
cannot discern such differential short-term and long- sents the idiosyncratic preference of household h for
term effects using a Lanchester model. Using the logit brand j in store s in period t. In Equation (1), we
model, we can decompose the effect of promotions assume that consumers in each period will choose to
into two components—a short-term positive effect purchase one of the J brands or settle for the out-
and a long-term negative effect through its effect on side good depending on the utility that they expect
the dynamic brand equity. Such decomposition can to derive from each choice alternative. Their purchase
help in explaining why myopic decision makers are choice is thus based on a consideration of the char-
likely to choose higher-than-optimal promotion levels acteristics of alternative brands, the regular prices
and lower-than-optimal advertising levels—a practice of alternative brands, promotional deals, seasonality,
for which managers are routinely criticized. Second, and, of course, individual brand names.
a logit demand model is flexible enough to account In Equation (1), the term jst captures the effects
for consumer heterogeneity. Finally, the logit formu- of variables unobservable to the econometrician, but
lation is routinely used in the marketing literature to observed by the firm and the consumers. Such vari-
model demand. ables may include unobserved product characteristics
Substantively, as in Naik et al. (2005), our prob- such as a brand’s shelf location and other demand
lem deals with the issue of optimally allocating the drivers at the store that vary over time (Chintagunta

1 2
Chintagunta et al. (2006) obtain an analytic expression for open- Although seasonal factors are not expected to vary by store, we
loop advertising strategies using a logit demand model. have retained the store subscript for the sake of generality.
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
Management Science 53(1), pp. 46–60, © 2007 INFORMS 49

2002). Because firms observe jst , they may incorpo- equity such as revenue premium (Ailawadi et al.
rate this information in setting the price for period t, 2003), and those based on shareholder value (Simon
thus posing endogeneity issues that we will address and Sullivan 1993). While consumer-based measures
later in this paper. The coefficient vector
contains of brand equity can provide valuable insights and
consumer taste parameters for demand shifters such diagnostics for the marketing or brand manager
as seasonality, while h and h represent the respon- concerned about a brand’s value to consumers, firm-
siveness of household h to regular price and promo- based measures provide a single objective number
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tions, respectively. The parameters h , h , and
0hst = that is credible to senior management. Thus, firm- and
 0h1st      0hJst  are random coefficients such that consumer-based measures provide different but com-
= + plementary perspectives on brand equity and are both
h h h =  + h 
useful in managing brand equity.

0hst =
0st + 
0h  (2) Note that we allow for the brand equities to vary
where , , and
0st are the mean response param- over time, and thus capture the dynamics of brand
eters; and  h , h , and 
0h are the correspond- equity over time (see Equation (1)). We model the
ing household-specific deviations from these mean dynamics in a brand’s equity by allowing it to be a
parameters. We assume that the heterogeneity param- sum of three components as follows:
eters, 
0h   h  h  are drawn from a multivariate
normal distribution with covariance . For the sake 0jst = 0s + ¯ j + jst  j = 1 2     J  (6a)
of parsimony, we allow for correlations between the
equities of alternative brands, but restrict the remain- where 0s 4 is a store-specific intercept that allows each
ing parameters to be uncorrelated. For the purpose of store to have different mean equity for each brand,
identification, we set the mean utility of the outside ¯ j is the time- (and store)-invariant component of the
good to be equal to zero. Hence, Uh0st = h0st . mean equity of brand j, and jst is the dynamic com-
Following Berry et al. (1995), we can rewrite Uhjst in ponent of the brand equity of brand j. Note that the
Equation (1) as follows: store-specific intercepts, 0s , do not vary by brand and
capture any store-specific differences in category con-
Uhjst = jst + hjt + hjst  (3)
sumption that may affect all the brands. Consistent
where the mean utility level, jst , for brand j and with the notion that advertising and sales promotion
the household-specific random coefficient component have an impact on brand equity over time (see, for
hjst are defined as follows: example, Jedidi et al. 1999), we model the dynamic
component of the mean brand equities as a function
jst = +
Xjst + Pjst +  Prjst +jst  (4)
0jst of these variables. Similar to Dube et al. (2005), we
hjst =  0h + h Pjst + h Prjst  (5) assume the following time ordering of events. The
levels of advertising and sales promotion chosen by
Our definition of the utility of the outside good, Uh0st , the firm at the beginning of the period affect equity
implies that both 0st and h0st are normalized to be
of the brand and create the augmented brand equity,
zero. Further, we assume that jst ∼ N 0 2sj . a
0jst . Specifically,
The mean brand equity, 0jst , in Equation (4) cap-
tures the incremental utility that the average con- a
0jst = 0s + ¯ j + jst
a

sumer derives from brand name j in store s at
time t with respect to the outside alternative, and a
jst = jst + jAd ln1 + Adjt  + jPr Prjst  (6b)
this has been used previously in the marketing liter-
ature as a measure of brand equity (see, for exam- where jst is the dynamic component of brand equity
ple, Kamakura and Russell 1993, Jedidi et al. 1999). at the beginning of the period t before the advertis-
This measure is consistent with the operationalization ing and promotion levels are chosen, and jst a
is the
of brand equity in Srinivasan (1979) and Kamakura corresponding augmented value. It is this augmented
and Russell (1993) as the component of a consumer’s brand equity that affects product demand. Over time,
utility not explained by the objectively measured the augmented brand equity, a0jst , and its dynamic
attributes and the marketing-mix variables, and may component, jsta
, depreciate stochastically as follows:
be viewed as a consumer-based measure of brand
equity3 as distinct from firm-based measures of brand a
jst+1 = Rjst + ejst+1  = ¯ j + jst+1  (6c)
ojst+1

3
The intercept-based measure is just one of the ways of measuring
4
consumer-based brand equity. Alternatively, one way we can mea- While we use store-specific intercepts to capture differential sales
sure brand equity is by using consumer brand knowledge (Keller levels across stores, we do not explicitly model the store-choice
1993) or the price premium that consumers are willing to pay for decision made by the consumer. We would like to thank an anony-
the brand (Park and Srinivasan 1994). mous reviewer for pointing this out.
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
50 Management Science 53(1), pp. 46–60, © 2007 INFORMS

Correspondingly, 0jst+1 is the brand equity at the useful in obtaining time-varying estimates of unob-
beginning of period t + 1. In the above equations, Adjt served quantities such as brand equity. We present a
is the level of advertising for brand j in time period t, detailed description of the estimation procedure in the
and Prjst is the level of promotion for that brand j online appendices (provided in the e-companion).6
in store s at time t.5 The parameters jAd and jPr Assuming that the error terms hjst are distributed
capture the contemporaneous effects of advertising i.i.d. with a Type I extreme value density function, the
and sales promotions on brand j’s equity, respectively. probability of household h buying brand j in store s
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The parameter R captures the extent to which brand at time t is given by

equity carries over from period to period and can
expjst + hjst 
be interpreted as a measure of persistence in brand probhjst =
J  (7)
equity. The error term, ejst , captures the variation in 1 + j  =1 expj  st + hj  st 
customer preference for brand j at time t that is not
explained by either the carry-over of brand equity However, because we use aggregate data, we do not
from the previous period or the advertising and sales observe purchase probabilities at the individual level.
promotion variables. We assume that ejst ∼ N 0 e2js . We aggregate the probabilities from Equation (7)
The logarithmic transformation of advertising cap- across all households to obtain the market share for
tures the diminishing effect of advertising on brand brand j in store s for period t, sjst , as
equity. 
A comment or two about our representation of sjst = probhjst f h  dh  (8)
the dynamic component of brand equity in Equation
(6b) is in order. First, because brand equity carries In the above equation, f · is the joint distribution of
over from period to period, the impact of advertis- the heterogeneity parameters. Given random draws
ing and sales promotion on brand equity will also from the distribution of h , the integral in Equation (8)
carry over from period to period. This is consistent can be computed numerically.
with the finding that advertising and sales promo-
3.2. Modeling Firm Decisions: Supply Side
tion have long-term effects on brand equity (Jedidi
The trade-off between advertising and sales promo-
et al. 1999). Second, because the long-term effects of
tions traditionally derives from the fact that while
advertising and sales promotion are realized because
advertising may have a small short-term effect, it has
of the carry-over in brand equity, an implication of
a lasting effect on a brand’s performance because of
our model is that brand equity acts as a mediating
the carry-over in brand equity. On the other hand,
variable in determining the long-term consequences
although sales promotions may have a positive short-
of marketing actions. As mentioned, this is in contrast
term effect, they may have a negative effect on brand
to most of the extant literature, with the exception
equity that carries over from period to period. In this
of Jedidi et al. (1999), which models the long-term
section, we characterize the advertising and sales pro-
implications of marketing actions with sales or mar-
motion decisions that firms need to make, given these
ket share as the mediating variable (see, for exam-
trade-offs. While the demand-side model is calibrated
ple, Dekimpe and Hanssens 1999). We suggest that
at the store level, we model the supply side (firm deci-
using brand equity as a mediating variable can help
sions) at the aggregate market level. Correspondingly,
us better understand if there are any adverse long-
we do not include the effect of the store-level inter-
term consequences of some marketing actions such cepts, 0s , and drop the store subscript in the supply-
as sales promotions even if they may have a bene- side model.
ficial effect in the short term. Note that in Equation We assume that the exact timing of the advertis-
(6b), we do not observe the values of brand equity ing and sales promotion decisions is as follows. At
in each time period t, but need to estimate them. To the beginning of each time period, each firm observes
obtain estimates of this unobserved brand equity for the brand equity levels of all the firms, 0jt , j = 1
each period, we use the Kalman filter algorithm (Xie 2     J .7 In addition, the firms know the quarter
et al. 1997, Naik et al. 1998, Akcura et al. 2004). The of the year they are in and the associated demand
recursive nature of the algorithm enables updating of
the estimates of the unobserved state variables (which 6
The e-companion to this paper, which is part of the online version,
happens to be brand equity in our case) and is thus
is available at http://mansci.pubs.informs.org/.
7
The only time-varying component of brand equity is the dynamic
5
Although we include advertising at the geographical region where component, jt . Hence, computing the strategy profiles based on
the store is located, due to constraints in obtaining such data, we changes in the brand equity is tantamount to computing them
use a common advertising variable for all the stores. However, if based on changes in the dynamic component. Thus, the actual com-
one had access to such micro-level data, they could be used in the putation of the strategy profiles is based on the dynamic compo-
estimation. nent, jt .
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
Management Science 53(1), pp. 46–60, © 2007 INFORMS 51

changes that they can expect during the quarter due The strategy profile for all the firms is St  =
to seasonality. The brand equities of the various firms 1 St      J St , where j St  = Adjt  Prjt  lists the
in the market, along with seasonality (as character- decision rules of all the firms. Given the state vector St
ized by the quarterly dummies), constitute the state and the corresponding strategy profile, the expected
of the market. Formally, we define the state vector at present discounted value of profits for firm j is
time t, St =  01t  02t      0Jt  Qt , where Qt indicates  
the quarter of the year to which t belongs. The firms  *−t
Vj St
 = E  "j S*  j S* 
St  (11)
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make their marketing decisions (advertising and sales *=t

promotions) based on the observed values of these
state variables. where  is the discount factor. Firms make the ad-
As discussed in §3.1 (Equations (6b) and (6c)), our vertising and sales promotion decisions that would
model implies that the effect of sales promotions maximize their expected present discounted profits.
stems from two sources: (a) a direct effect on the util- The computation of the expectation in Equation (11)
ity, which only has a contemporaneous effect, and requires knowledge regarding the evolution of the
(b) an indirect effect through its impact on the brand’s state variables. From Equation (6b), it is clear that the
equity, which carries over from period to period. On equity of brand j at time t, 0jt , follows a Markov
the other hand, the effect of advertising stems only process with transition density p·
0jt−1  Adjt  Prjt .
from its effect on brand equity. It is the carry-over of Given the definition of the time period as a quarter,
brand equity that induces the dynamics in our model, the Markov transition density for the other state vari-
which, in turn, implies that the advertising and sales able, Qt , is obvious. However, unlike the case of brand
promotion decisions have long-term consequences on equity, the transition probability for this state variable
consumer demand. Further, Equation (8) provides the will be nonstochastic and independent of the firm’s
link between market share and the state, as well as advertising and sales promotion decisions. Given our
the control variables. Given this market share and a assumption that the error terms in the system equa-
definition of the market size, we can compute the per- tion (Equation (6b)), ejt , are i.i.d., we can write the
period profit for brand j as transition density of the state vector as
  J
Prjt 
jt = Wjt − cj −
" Mt sjt St  Adjt  Prjt  jt  pSt+1
St  Adt  Prt  = pSjt+1
Sjt  Adjt  Prjt  (12)
% j=1
− Adjt  (9)
We assume that the firms make their advertising and
where Wjt is the wholesale price of brand j at time t, sales promotion decisions based only on the informa-
cj is the marginal cost of brand j, Mt is the mar- tion contained in the current state vector. Hence, the
ket size at time t, and % is the retail pass-through strategies are not time dependent. The value function
for the promotions. In our application, we restrict the in Equation (11) satisfies the Bellman equation
decision variables to advertising and sales promotion
spending levels and do not include price. Hence, the Vj S
 = max "j Sj S−j S
Adjt  Prjt >0
values of the retail and wholesale prices, retail pass-
through, market size, and the marginal cost are fixed 
while determining the optimal advertising and pro- + Vj S 
pS 
Sj S−j S dS   (13)
motion levels. We discuss the values at which these
variables are set in §5.2. As in Dube et al. (2005), In the above equation, j S = Adjt  Prjt  corresponds
we assume that the advertising and promotion deci- to the strategy profile of brand j given the state S, and
sions are made prior to the realization of the demand −j S is the strategy profile of all the other brands.
shocks, jt .8 Hence, these decisions are made based on Hence, given its strategy profile, j S, brand j makes
the expected profits, which is defined as an assumption about the competitive strategy pro-
file, −j S. These help in determining the transition
  Prjt

"jt = Wjt − cj − Mt sjt St  Adjt  Prjt  jt  probabilities, pSt+1
St  Adt  Prt . Hence, the strategy
% profile for brand j given the state vector S, j S, is
· pjt  djt − Adjt  (10) obtained by maximizing the value function defined by
Equation (13). However, the right-hand side of Equa-
tion (15) is defined conditional on a specific guess
8
Alternatively, one can argue that the advertising and promotion about the competitive strategy profile, −j S. Hence,
decisions are made based on the expected demand shocks. Under
such a scenario, as in Nair (2005), we need to include the demand
the strategy profile j S that maximizes the right-
shocks, jt , as state variables, which would significantly complicate hand side of Equation (13) is the best response by
the estimation. brand j given the assumption about the competitive
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
52 Management Science 53(1), pp. 46–60, © 2007 INFORMS

strategy profile, −j S. In equilibrium, these assump- files of its competitors by maximizing the right-
tions about the competitive strategy profile will coin- hand side of Equation (13) should coincide with the
cide with the optimal strategy profile of each of the strategy profiles of each of the competitors obtained
competitors. We discuss the computation of the equi- similarly. We obtain the MPE strategies numerically
librium strategies in the next section. given the demand-side estimates. In computing the
MPE strategies, we use brand equity and seasonal-
ity (quarter) as the state variables. We compute the
4. Estimation
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equilibrium using the following steps:

4.1. Demand Estimation Step 1. Start with some initial guesses of the strat-
The objective of our estimation is to recover three sets egy profiles of all the brands.
of parameters: (i) parameters ,1 = - 0s  ¯ j  
 . Step 2. Given the strategy profiles, compute the
that affect the mean utility of brand j at time t in value function for each value of the state vector that
the observation equation (Equation (4)), (ii) param- satisfies the right-hand side of Equation (13). Because
eters ,2 = -R jA  jP . that capture the dynamics of brand equity is a continuous variable, as in Nair
brand equity in the system equation (Equations (6b) (2005), we compute the value function at a few grid
and (6c)), and (iii) parameters ,3 that capture con- points and approximate the value function as a ten-
sumer heterogeneity. We proceed with the estimation sor product of a Chebyshev polynomial basis in each
as follows: continuous state dimension (Judd 1999).10
Step 1. For a given set of heterogeneity parameters, Step 3. Given these value functions and the com-
,3 , we evaluate the integral in Equation (8) numeri- petitive strategy profiles, determine the optimal strat-
cally. Using the numerically computed market shares, egy profile for each firm that would maximize the
we obtain the mean utility of brand j at time t right-hand side of Equation (13).
using the contraction-mapping algorithm proposed We iterate Steps 2 and 3 until the differences in
by Berry et al. (1995).9 the strategy profiles from two successive iterations are
Step 2. Next, we express the mean utilities thus lower than a preset level of tolerance for all the firms.
recovered as a linear function of the observed vari- At this point, we can infer that the competitive strat-
ables and the set of parameters ,1 in Equation (4). egy profile based on how a firm’s optimal strategy
This corresponds to the observation equation in the profile was obtained coincides with the best strategy
state-space framework. The equation that captures the profile for each of its competitors. Note that this is an
dynamics of brand equity (Equations (6b) and (6c)) equilibrium in pure strategies only. However, there is
corresponds to the system equation in the state-space no guarantee of the existence or uniqueness of this
framework. We then estimate the two-equation sys- equilibrium. The convergence of the above algorithm
tem comprised of the observation equation (Equa- is sufficient to prove the existence of an equilibrium
tion (4)) and the system equation (Equations (6b) and for a specific parameterization of the model (Benkard
(6c)) using a Kalman filter algorithm that is iterated 2004). However, it is not necessary that the equilib-
until convergence is reached to obtain efficient esti- rium be unique. We checked for the presence of mul-
mates of the equity of brand j at time t, 0jst , as well tiple equilibria by starting with different values of
as the error term in the observation equation, jst . We initial strategy profiles. Each time, we converged at
the same set of equilibrium strategy profiles. Hence,
use generalized method of moments (GMM) to esti-
the presence of multiple equilibria does not appear to
mate the parameters -,1  ,2  ,3 .. Sriram et al. (2006)
be a problem in our case.
use a similar estimation procedure based on GMM
and demonstrate its ability to recover the true param-
eters in Monte Carlo simulations. Appendix A in the
5. Data Description and
e-companion provides details regarding the estima- Operationalization of Variables
tion algorithm. 5.1. Data Description
Given that our main objective is to capture the dy-
4.2. Supply Side: Computing the Equilibrium namics of brand equities, we need a database that
Strategies spans an extended time period. This is because
As stated earlier, in equilibrium, for each value of the brand equity is an enduring construct and is unlikely
state vector, the strategy profile for brand j obtained to fluctuate on a weekly basis. An extended data
based on its assumption regarding the strategy pro-
10
Alternatively, instead of estimating the value function at a finite
9
Berry et al. (1995) prove that for each value of the observed mar- number of grid points, one can use the algorithm in Naik et al.
ket shares, given the identifying restriction that the mean utility (2005), which is based on finite element methods. Such an approach
of the outside alternative is equal to zero, the contraction-mapping can significantly reduce the computational burden as the number
algorithm will yield unique values of the mean utilities. of state dimensions increases.
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
Management Science 53(1), pp. 46–60, © 2007 INFORMS 53

Table 1 Descriptive Statistics

Average regular
Average quarterly Average regular wholesale price Average quarterly Average quarterly
Brand market share (%) price (cents/oz.) (cents/oz.) advertising (’000 $) promotion (cents/oz.)

Minute Maid 21.73 3.568 2.642 125.24 0.348

Tropicana 41.50 3.935 2.901 191.81 0.399
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observation time period is also required to obtain sales promotion, as well as advertising during a given
stable parameter estimates using the Kalman fil- quarter. We operationalize the regular price variable
ter methodology. The Dominicks Finer Foods (DFF) as the weighted (by unit sales) average nonpromoted
database made available by the University of Chicago price per ounce of the UPCs of the brand. We define
meets these requirements. The data span almost eight the nonpromoted price of each UPC as the average
years from 1989 to 1997 and consist of weekly obser- price of the UPC when it was not on sale during that
vations of sales, shelf prices, and the possible presence quarter. Correspondingly, we compute the retail price
of sales promotions (coupons, bulk buy, or a special as the weighted average price per ounce of the UPCs
sale) by individual item (UPC) and daily store traffic offered by the brand in that quarter. The promotion
for the stores operated by DFF in the Chicago area.11 variable is operationalized as the difference between
We selected a random sample of 32 stores for our esti- the regular price and the retail price. In addition to
mation. We aggregated the sales data at the quarterly these two variables, we include three seasonal dum-
level for each store. We selected a quarter as the time mies for the first three quarters (with the last quarter
period for the level of aggregation for a number of of the year set to zero) as demand shifters. We con-
reasons. Given that brand equities are expected to be vert the national advertising to regional advertising
relatively stable over time, we do not expect signif- by assuming that the firms allocate their advertising
icant perceptible changes on a weekly basis. On the expenditures across different regions based on their
other hand, we need a sufficient number of observa- population. Because the Chicago metropolitan area
tions over time to be able to estimate the dynamics accounts for approximately 3.26% of the national pop-
in brand equities. Moreover, our advertising data are ulation, we assume that the same percentage of the
at the quarterly level. This aggregation at the quar- national advertising was spent in the Chicago region.
terly level yielded 30 periods of data, which is suffi-
Note that this advertising includes the advertising for
cient to estimate the dynamics of brand equities. We
all the products manufactured by the brands, includ-
supplement the store data with data on the quarterly
ing frozen and refrigerated nonorange juice drinks.
national advertising expenditures of brands, obtained
(b) Outside Alternative. Our estimation requires the
from Leading National Advertisers’ Ad Dollar summary.
definition of an outside good, or no-purchase alterna-
We perform our empirical analysis using store-level
tive. We assume that each household has the poten-
scanner data in the orange juice category. Tropicana
and Minute Maid, the two major brands in this cate- tial to consume 64 oz. of orange juice every week,
gory, together account for about 63% of the total mar- and then we multiply the store traffic in a quarter by
ket share. Our analysis is based on the two popular the quarterly consumption rate to define the market
sizes, viz., 64 oz. and 96 oz., of these two brands. size. We then subtract the sales of the brands under
Together, these two sizes account for about 95% of consideration to compute the “sales” of the outside
the total orange juice sales of these brands. Descrip- alternative. The respective shares are then computed
tive statistics for the brands included in our analy- from the sales of the brands, and the market size as
sis are displayed in Table 1. The leading brand in defined above. This approach is similar to that used
terms of market share is Tropicana, with an aver- by Chintagunta (2002).
age market share of over 41%. It also commands a (c) Instrumental Variables. We allow for endogene-
price premium over Minute Maid in terms of the price ity of price through the use of instrumental variables.
charged per ounce. The level of sales promotions, as The instrumental variables chosen should be such that
well as the average advertising expenditure, is higher they are strongly correlated with price, but uncorre-
for Tropicana versus Minute Maid. lated with the error term jst . A reasonable choice
is the wholesale prices because they are likely to be
5.2. Operationalization of Variables
correlated with the retail prices, but are unlikely to
5.2.1. Variables Used in the Demand Side. be chosen on a weekly basis by the manufacturers,
(a) Marketing-Mix Variables. The marketing-mix var- who typically make quarterly sales plans in these cat-
iables include a brand’s regular price and the level of egories. Wholesale prices have been used as instru-
ments in several previous studies in marketing (e.g.,
11
UPC stands for Universal Product Code. Chintagunta et al. 2003). We treat sales promotions as
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
54 Management Science 53(1), pp. 46–60, © 2007 INFORMS

exogenous because such decisions are generally made Table 2 Estimates of the Demand Model Using the Kalman Filter
on a quarterly basis and often require a lead time of
Parameter Estimate T-value
several weeks for effective implementation. Indeed,
based on conversations with local-chain managers, Observation equation Price −10
078 −4
925
Chintagunta et al. (2003) report that while the sales Promotion 0
965 3
904
Quarter 1 0
102 2
049
promotion calendar is determined in advance, pric- Quarter 2 −0
277 −3
559
ing decisions are made subsequently, conditional on Quarter 3 −0
266 −3
787
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the promotional calendar. Hence, they argue that Constant (MM) −3
817 −7
302
sales promotions can be treated as exogenous, unlike Constant (TROP) −3
446 −5
251
prices. Several other studies also treat sales promo- System equation Carryover 0
773 9
534
tions as exogenous (see, for example, Chintagunta Promotion (MM) −0
072 −0
792
2002, Pauwels et al. 2002). Promotion (TROP) −0
109 −1
661
Advertising (MM) 0
047 1
919
5.2.2. Variables in the Supply Side. As mentioned Advertising (TROP) 0
063 1
881
earlier, we restrict our investigation to the determina- Heterogeneity parameters∗ Sigma_1 0
434 0
581
tion of the optimal advertising and promotion levels. Sigma_2 0
226 0
415
Correspondingly, we compute the equilibrium poli- Sigma_price 4
422 4
616
Sigma_prom 0
463 0
901
cies in the supply side by fixing the regular prices Sigma_12 −0
666 −0
907
(both retail and wholesale), market size, marginal
∗
cost, and retail pass-through. We perform the supply- The heterogeneity parameters are to be interpreted as follows: Minute
Maid brand equity heterogeneity variance = (Sigma_1)2 , Tropicana brand
side analysis with the Chicago metropolitan area as
equity heterogeneity variance = (Sigma_2)2 + (Sigma_12)2 , Minute Maid
the basis. Following the assumption we made in the Tropicana brand equity heterogeneity covariance = (Sigma_1) ∗ (Sigma_12),
demand-side estimation, we assume that each house- Price heterogeneity variance = (Sigma_Price)2 , and Promotion heterogene-
hold has the potential of consuming 64 oz. of orange ity variance = (Sigma_Prom)2 . Because of space considerations, we have
juice every week. We then multiply this by the num- not presented the store-specific dummies.
ber of households in the Chicago area (3.16 million)
to obtain the total market size.12 Inherent in this is the (ii) the parameters in the system equation (Equations
assumption that the responsiveness of the brands to (6b) and (6c)), and (iii) the heterogeneity parame-
the changes in their marketing mix, as well as to the ters in Equation (5).13 We observe in Table 2 that
seasonal factors, is the same across all the chains in all the parameters in the observation equation are
the Chicago area. We fixed the retail and wholesale statistically significant at least at the 10% level in
prices at the average values reported in Table 1. As in a two-tailed test. As expected, the price coefficient
Jedidi et al. (1999), we assume that the marginal cost is negative p < 001 and the sales promotion coef-
is 30% of the wholesale price. As regards retail pass- ficient is positive p < 001. We discuss the price
through, several studies (see, for example, Besanko and promotion elasticities implied by these estimates
et al. 2005) have documented that the retailers may subsequently. The average brand equity across all
not pass on all the price reduction given by a man- the quarters and stores was −340 for Minute Maid
ufacturer. Following empirical findings in that paper, and −291 for Tropicana. Thus, Tropicana has higher
we assume a retail pass-through of 82%. We tested the brand equity than Minute Maid, which is not sur-
sensitivity of the results to the assumption regarding prising because Tropicana has a higher market share
retail pass-through by computing the optimal adver- and also commands a significant price premium in
tising and promotion levels for higher and lower val- the orange juice market. The average brand equity
ues of retail pass-through. The substantive results is negative because the mean utility of the outside
remained unaltered. alternative is fixed at zero, and the share of the out-
side alternative is significantly higher than that of
the inside goods. The intrinsic component of brand
6. Results equity that is invariant to marketing actions is −382
6.1. Demand Side for Minute Maid and −345 for Tropicana.14
We estimated the model for the two leading brands
in the orange juice category—Tropicana and Minute 13
In addition, we estimate the standard deviations of the obser-
Maid. Table 2 displays the parameter estimates from vation and the system equation errors. The observation equation
the demand-side estimation. For ease of exposition, error standard deviation was 1.653 and the system equation error
we divide the parameters into three groups: (i) the standard deviation was 234 × 10−3 .
14
parameters in the observation equation (Equation (4)), In consideration of space constraints, we do not report the esti-
mates corresponding to the store-specific intercepts in Table 2.
The store-specific intercepts (the term 0s in Equation (6a)) range
12
We obtained this information from Market Scope (1999). from a low of −0136 to 0.477. The higher store-specific intercepts
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
Management Science 53(1), pp. 46–60, © 2007 INFORMS 55

In the system equation, the time-varying component Turning now to the heterogeneity parameters, the
of the brand equity (the term jst in Equation (6a)) estimates imply significant consumer heterogeneity
for Minute Maid ranges from −083 to 1.39 across only in the price coefficient. Although not signif-
32 stores. Across all 32 stores and over the 30 quar- icant, the covariance between the heterogeneity of
ters, Minute Maid’s brand equity ranges from −465 Tropicana and Minute Maid is negative. This implies
to −243. Similarly, the time-varying component of that consumers who have a higher preference for
Tropicana’s brand equity ranges from −118 to 1.95. Tropicana tend to have a lower preference for Minute
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Tropicana’s brand equity ranges from −463 to −150 Maid, and vice versa.
across all 32 stores over 30 quarters. The estimate of Based on these demand estimates, we computed the
the parameter that captures the carry-over of brand market share elasticities with respect to price, promo-
equity from period to period (LAG BE) is 0.773. This tion, and advertising. Because promotions and adver-
is consistent with our expectation that there should be tising affect the dynamic component of a brand’s
a positive and significant carryover of brand equity. equity (Equation (6b)), in addition to having a con-
We also observe in Table 2 that sales promotions
temporaneous effect, an increase in these variables
of both Minute Maid and Tropicana have a nega-
will also have a long-term effect on a brand’s equity.
tive effect on own-brand equity; the adverse impact
We present the implied market share elasticity esti-
is, however, larger and statistically significant p <
mates in Table 3. The estimate of market share elas-
01 in the case of Tropicana. This negative effect of
sales promotions on the two brands’ equity is consis- ticity with respect to price for Tropicana is −163 and
tent with the attribution theory, wherein consumers that for Minute Maid is −157. These values lie within
attribute their purchases to the offer of a promo- the range of price elasticity estimates reported by
tional deal rather than their underlying preference Tellis (1988). The slightly higher price elasticity for
for the brand (see, for example, Dodson et al. 1978). Tropicana may be due to fact that Tropicana has a
Moreover, prior research has documented that the fre- higher retail price than Minute Maid.
quent use of sales promotions can lower the reference The short-term market share elasticity with respect
price and thus adversely affect the price premium to sales promotions is positive for both brands and
that the brand can charge (see, for example, Kalwani is larger for Tropicana (0.41) than for Minute Maid
et al. 1990, Kalwani and Yim 1992, and Blattberg (0.28). This can be attributed to the higher promotion
et al. 1995). Hence, we expect that the premium- levels for Tropicana (see Table 1). This is despite the
priced Tropicana will be more prone to such an adverse effect of sales promotions on brand equity
adverse effect. Consistent with the prior research, our being higher for Tropicana. Because the effect of sales
demand-side results reveal that the magnitude of the promotions on brand equity that carries over from
detrimental effect of sales promotions is higher for period to period is negative, the long-term promo-
Tropicana than for Minute Maid. These results high- tional elasticity is negative for both Tropicana and
light a key advantage of estimating the dynamics of Minute Maid. It is larger in magnitude for Tropicana,
brand equity using the Kalman filter methodology— the brand for which the adverse effect of sales pro-
namely, a capability of isolating the effect of promo- motions on brand equity is larger and statistically sig-
tions on the utility versus that on brand equity. Note nificant. Interestingly, the total promotion elasticities
that, despite their adverse impact on brand equity, are still positive for both brands, albeit smaller than
the net short-term effect of sales promotions on mean the corresponding short-term promotional elasticities
utility and hence, market share, is positive for both (see Table 3). Consequently, we would expect myopic
brands.15 Finally, as expected, we observe in Table 2 versus forward-looking decision makers to allocate a
that advertising has a significant positive effect on
higher than optimal budget for sales promotions.
the equity of both brands. The effect is higher for
The short-term market share elasticities with re-
Tropicana than for Minute Maid. This is consistent
spect to advertising for Tropicana and Minute Maid
with Keller’s (1998) argument that the advertising of
brands with greater equity is more effective. We con-
sider the long-term effects of sales promotions and
advertising later in this section. Table 3 Implied Market Share Elasticity Estimates

Brand Short term Long term Total

correspond to stores that exhibit higher consumption of Minute
Maid and Tropicana refrigerated orange juice brands. Correspond- Price Minute Maid −1
572 −1
572
ingly, in stores that have lower store-specific intercepts, the con- Tropicana −1
625 −1
625
sumption of the outside alternative (including the store brand) is
Sales promotion Minute Maid 0
275 −0
075 0
2
higher.
Tropicana 0
409 −0
249 0
16
15
The total contemporaneous effect of sales promotions is obtained
Advertising Minute Maid 0
046 0
207 0
253
as the sum of the direct effect in the observation equation and the
Tropicana 0
06 0
316 0
366
brand-specific effect in the system equation.
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
56 Management Science 53(1), pp. 46–60, © 2007 INFORMS

Table 4 Implied Profit Elasticity Estimates both brands. This implies that the short-term incre-
mental revenues generated by increasing advertising
Brand Short term Long term Total
do not cover the incremental advertising costs. On
Sales promotion Minute Maid 0
0057 −0
083 −0
0773 the other hand, the long-term elasticities are posi-
Tropicana 0
0119 −0
262 −0
2501 tive because an increase in advertising in period t
Advertising Minute Maid −2
035 0
324 −1
711 leads to an increase in brand equity and to increases
Tropicana −2
143 0
584 −1
559
in market shares in subsequent periods even if there
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is no increase in advertising in those periods. How-

ever, we find that the total profit elasticity with
are 0.06 and 0.05, respectively. Thus, Tropicana’s mar- respect to advertising—short-term plus long-term
ket share is more responsive to advertising than profit elasticity—is negative for both brands. This im-
Minute Maid’s market share. Note that the short-term plies that it will not be profitable for either Tropicana
advertising elasticity is much smaller in magnitude or Minute Maid to increase its advertising spend-
than the corresponding short-term promotional elas- ing. This is consistent with the findings of Lodish
ticity for both brands. The stronger positive effect of and his coauthors (1995), who report that generally
sales promotions in generating short-term sales may advertising has a very small impact in mature cat-
explain the increasing budget allocated to sales pro- egories and that changes in advertising expenditure
motions at the expense of advertising in recent years have a much smaller impact than changes in adver-
(Jedidi et al. 1999). The long-term market share elas- tising copy and quality. Hence, considering that the
ticity with respect to advertising is slightly larger in category we are studying is a mature one, we do not
magnitude for each brand as compared to the corre- expect high returns to increased advertising expendi-
sponding short-term elasticity. This is because adver- tures. In their analysis of another consumer packaged-
tising spending has a positive impact on brand equity goods category, Jedidi et al. (1999) also find that some
that carries over from period to period. We find that brands do overspend on advertising and may ben-
the brand with higher equity, Tropicana (0.32), has a efit by cutting their advertising expenditures. Nev-
much higher long-term elasticity than does Minute ertheless, the negative advertising profit elasticities
Maid (0.21). should be interpreted with some caution given that
we do not have the actual regional advertising data,
Although the market share elasticities with respect
but have inferred them from the national advertising
to advertising and sales promotions are positive, it
levels. Moreover, as stated earlier, the advertising data
still may not be profitable to increase their corre-
include the advertising dollars spent on all the prod-
sponding budgets. To assess whether an increase in
ucts manufactured by these brands, including frozen
either the advertising or promotion budgets may be
and refrigerated nonorange juice drinks.
profitable either in the short term or in the long term,
we compute the short-term and the long-term profit 6.2. Optimal Advertising and Promotion Budget
elasticities with respect to these instruments. In com- Allocation: Supply Side
puting these elasticities, we assume that the marginal In this section, we investigate the implications of the
cost is 30% of the wholesale price, and the market is demand-side estimates for optimal advertising and
comprised of the entire Chicago area, with a popula- promotion levels. Specifically, we derive and compare
tion of 3.16 million households. the equilibrium myopic and forward-looking promo-
Table 4 displays the short-term and long-term profit tion and advertising policies for Minute Maid and
elasticities with respect to sales promotions and adver- Tropicana with the actual promotion and advertising
tising. We find that the short-term profit elasticity with policies of the two brands. We derive optimal poli-
respect to sales promotions is positive for both brands. cies of myopic decision makers who consider only
This implies that increasing sales promotions by 1% the current-period profits by setting the discount fac-
will be profitable for both Tropicana and Minute Maid tor,  in Equation (11), equal to zero. We determine
if one considers only the short-term effects of sales the equilibrium policies of forward-looking decision
promotions.16 However, if one considers the adverse makers by setting  = 095. In addition, we consider
long-term impact of promotions, the total effect of an intermediate scenario wherein the discount factor,
sales promotions on profitability is negative for both , is set equal to 0.5, which implies that in the current
brands. period, profits two years hence (after eight quarters)
We observe in Table 4 that the short-term profit are worth only 0.4% of their value. This is akin to
elasticities with respect to advertising are negative for making decisions based on a two-year time frame, a
planning horizon that may be closer to current indus-
16
Note that we have not considered the fixed cost of sales promo- try practice. The equilibrium policies are computed as
tions. follows. For each period, we determine the average
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
Management Science 53(1), pp. 46–60, © 2007 INFORMS 57

Figure 1 Comparison of Promotion Levels for Minute Maid

Actual promotions
1.0
0.9 Delta = 0.5
0.8 Myopic promotions
0.7 Forward-looking promotions
0.6
0.5
0.4
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0.3
0.2
0.1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Quarter

Figure 2 Comparison of Promotion Levels for Tropicana

1.0
0.9 Actual promotions
0.8 Delta = 0.5
0.7 Myopic promotions
0.6 Forward-looking promotions
0.5
0.4
0.3
0.2
0.1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Quarter

value of the dynamic component of brand equity, jt , ones.17 The optimal promotion levels for the case
across all 32 stores and the quarter of the year cor- when  = 05 lie in-between these two extremes for
responding to that period. For the values of jt that both brands. A comparison of the average values in
lie outside of the grid points where we computed Table 5 implies that while the optimal myopic promo-
the MPE advertising and promotion levels, we deter- tion levels are higher than the actual levels for both
mine the equilibrium advertising and promotion lev- brands, the forward-looking promotion levels are sig-
els using Chebyshev interpolation (Judd 1999). nificantly lower. Further, Table 5 reveals that while the
actual promotion levels are closer to the case when
6.2.1. Equilibrium Promotion Policies. Figures 1  = 05 for Minute Maid, they are closer to the myopic
and 2 display a comparison of the equilibrium levels for Tropicana. Note that for Tropicana, the opti-
myopic, two-year planning horizon  = 05, and for- mal forward-looking policy is zero promotion (see
ward-looking promotion policies for the two brands Table 5). The finding that the forward-looking promo-
with the actual promotion policies of the two brands, tion levels are lower compared to the actual values
Minute Maid and Tropicana. We also present a com- is consistent with our finding that the profit elastic-
parison of the average sales promotion levels for the ity with respect to promotions is positive in the short
two brands across the four scenarios in Table 5. For term but negative in the long term for both brands.
this comparison, we compute the average promotion 6.2.2. Equilibrium Advertising Policies. As in the
levels for the two brands across all 32 stores. case of sales promotions, we present a comparison of
The results reveal that in the cases of both Tropi- the actual, myopic, two-year planning horizon; and
cana and Minute Maid, the forward-looking promo- the forward-looking advertising levels for the two
tion levels are significantly lower than the myopic brands in Figures 3 and 4, as well as in Table 6. The
results reveal that while the forward-looking adver-
tising levels are higher than the myopic and the two-
Table 5 Comparison of the Average Sales Promotion Levels (Cents Per year planning horizon levels for both brands, these
Ounce) are lower than the actual advertising levels. This
Brand Actual Myopic Delta = 0
5 Forward looking
17
The forward-looking promotion levels for Minute Maid exhibit
Minute Maid 0.348 0.380 0.324 0.049
some fluctuations with seasonality because seasonality was one of
Tropicana 0.399 0.443 0.295 0.000
the state variables in the computation of the equilibrium strategies.
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
58 Management Science 53(1), pp. 46–60, © 2007 INFORMS

Figure 3 Comparison of Advertising Levels for Minute Maid

Actual advertising
300 Delta = 0.5
Myopic advertising
250
Forward-looking advertising
200
150
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100

50
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Quarter

Figure 4 Comparison of Advertising Levels for Tropicana

350 Actual advertising

300 Delta = 0.5
Myopic advertising
250
Forward-looking advertising
200
150
100
50
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Quarter

implies that even if one were to consider the long- account cross-media synergies, it may understate the
term effects of advertising, the brands are overspend- optimal advertising budget (Naik and Raman 2003).18
ing on advertising. In this connection, recall that profit Finally, we compute the demand, and hence the rev-
elasticities with respect to advertising are negative enues, for 64 oz. and 96 oz. refrigerated orange juice
for both brands even after considering the long-term manufactured by the brands. However, the advertis-
effects. ing levels are more likely to be set by considering
Why are the two brands overspending on advertis- the revenues from all the products manufactured by
ing? First, recall that in deriving equilibrium optimal these brands, such as frozen juices, as well as nonor-
advertising budgets, we consider only the long-term ange refrigerated juices such as lemonade and grape-
profits that Tropicana and Minute Maid derive from fruit juice. Our analysis of the Dominick’s data during
the refrigerated orange juice market. However, the this period revealed that 64 oz. and 96 oz. refriger-
two brands may view advertising as an investment in ated orange juice accounted for about 52.9% of the
building brand equity that may: (i) act as a barrier to total sales (including frozen and refrigerated nonor-
entry in the refrigerated orange juice market, (ii) facil- ange juice drinks) for Minute Maid and 73.1% in the
itate introduction of line extensions in the orange juice case of Tropicana.
market, and (iii) help in the market launch of new To understand the consequence of relaxing this
product entries into related categories. Accounting for last caveat, we tried two alternative modifications.
these effects may render higher levels of advertising First, under the assumption that the sales of 64 oz.
optimal. Second, in deciding on the total advertising and 96 oz. refrigerated orange juice as a proportion
budget aggregated across multiple media, brand man- of total brand sales (including frozen and refriger-
agers may take into account both the media effective- ated nonorange juice drinks) is equal to 52.9% for
ness and cross-media synergies. To the extent that our Minute Maid and 73.1% for Tropicana, we scale up
derivation of the equilibrium policy does not take into the demand so that it includes the sales from all the
products.19 We then compute the MPE advertising
Table 6 Comparison of the Average Advertising Levels (Thousands of and promotion strategies with this level of demand.
Dollars)

Brand Actual Myopic Delta = 0
5 Forward looking 18

We thank an anonymous reviewer for suggesting this explana-
tion.
Minute Maid 125.24 8
877 12
261 32.874 19
This is tantamount to either increasing the market share sjt or the
Tropicana 191.81 15
664 21
727 60.162
market size M in Equation (12).
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
Management Science 53(1), pp. 46–60, © 2007 INFORMS 59

Table 7 Comparison of Average Actual and Forward-Looking Therefore, we expect myopic versus forward-looking
Advertising Levels Under Alternative Specifications decision makers to have higher sales promotion bud-
(Thousands of Dollars)
gets. Our results reveal that the actual promotion lev-
Minute Maid Tropicana els for both brands are indeed higher than the optimal
Actual Forward-looking Actual Forward-looking budgets for the forward-looking (long-term orienta-
advertising advertising advertising advertising tion), as well as the two-year planning horizon sce-
With scaled up 125
24 95
03 191
81 98.17 narios. Hence, it may be profitable for both brands to
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demand reduce their promotion levels. Further, we find that

With scaled down 66
25 56
39 140
21 76.79 although the forward-looking promotional spending
advertising
levels are higher for the smaller brand, Minute Maid,
it is the market leader, Tropicana, that spends more
In the second modification, we assume that the adver- on sales promotions.
tising expenses are apportioned between the vari- Turning to optimal advertising budgets, we find
ous products in the same proportion of their sales. that the equilibrium forward-looking advertising lev-
Using these scaled-down advertising levels for 64 oz. els are higher for Tropicana, the brand that has higher
and 96 oz. refrigerated orange juice, we reestimate brand equity and a higher responsiveness to adver-
demand and also reestimate the MPE advertising and tising. Further, as expected, the optimal forward-
promotion levels. We present a summary of the aver- looking advertising levels are higher than the myopic
age advertising levels from these two modifications levels and the two-year planning horizon levels for
in Table 7. Clearly, the modifications have reduced both brands. However, the forward-looking advertis-
the gap between the actual and the forward-looking ing levels are lower than the actual advertising expen-
advertising levels. Nevertheless, despite the adjust- ditures for both brands. This implies that even when
ments, the brands appear to be spending more than is we consider the long-term effects of advertising, the
optimal on advertising. Hence, although we can infer brands are overspending on advertising.
that the brands are overadvertising, given the nature We conclude with a few comments about the lim-
of our advertising data, we cannot exactly infer the itations of our study and some directions for future
extent to which they are overadvertising. research. First, our computation of the equilibrium
In sum, the results from the supply side indi- advertising and promotion levels is based on assump-
cate the following: (i) Under the myopic case, it tions regarding the size of the regional market, the
will be optimal to increase the promotion budgets advertising spending, marginal costs, and the retail
for both brands; (ii) however, the optimal forward- pass-through. The availability of more precise infor-
looking promotion levels are significantly lower than mation on these variables would clearly be useful.
the actual levels for both brands; and (iii) the myopic Second, while the computation of the optimal promo-
as well as the forward-looking advertising levels for tion levels are for a fixed value of retail pass-through,
both brands are lower than the actual levels. Overall, in reality, the level of pass-through may be influenced
the forward-looking advertising and promotion lev- by the level of manufacturer advertising promotions
els imply that it is optimal for both brands to reduce as well as brand equity. An integrated model that
their advertising and promotion levels. derives the optimal strategy profiles while consider-
ing retailer reactions may be a worthwhile addition to
the extant literature. Finally, it will be useful to inves-
7. Conclusions tigate the optimal levels of advertising and promotion
We study the optimal levels of advertising and pro- budgets across several categories so that we can make
motion budgets in dynamic markets with brand generalizations across a wide variety of product cate-
equity as a mediating variable. To this end, we de- gories and brands.
velop and estimate a state-space model based on the In conclusion, we present a methodology for evalu-
Kalman filter that captures the dynamics of brand ating the optimal levels of advertising and sales pro-
equity as influenced by its key drivers—advertising motion expenditures when these instruments have a
and sales promotions. The model allows us to decom- long-term effect on brand equity. The modeling of
pose the short-term impact of sales promotions into brand equity as a mediating variable allows us to
two components—a positive effect that induces con- track the impact of changes in the firm’s marketing
sumers to switch to the promoted brand and a neg- programs, and thus monitor the long-term health of
ative effect on brand equity that carries over from the brand. We hope that this paper will lead to more
period to period. The negative long-term effect of pro- empirical work across a variety of product categories.
motions implies that the total effect of promotions, An e-companion to this paper is available as part of
including the long-term adverse effect, is smaller in the online version that can be found at http://mansci.
magnitude than the short-term effect of promotions. pubs.informs.org/.
 Sriram and Kalwani: Optimal Advertising and Promotion Budgets in Dynamic Markets
60 Management Science 53(1), pp. 46–60, © 2007 INFORMS

Acknowledgments price expectations model of consumer brand choice. J. Market-

The authors thank Tolga Akcura, S. Balachander, Pradeep ing Res. 27(3) 251–262.
Chintagunta, V. Kumar, Harikesh Nair, Joseph Pancras, Kamakura, Wagner, Gary Russell. 1993. Measuring brand value
Rajkumar Venkatesan, and the participants at the 2004 with scanner data. Internat. J. Res. Marketing 10(1) 9–22.
Haring symposium at Indiana University for their com- Keller, Kevin Lane. 1993. Conceptualizing, measuring, and manag-
ments and suggestions. This paper is based on one of the ing customer-based brand equity. J. Marketing 57(1) 1–22.
essays in the first author’s doctoral dissertation. Keller, Kevin Lane. 1998. Strategic Brand Management. Prentice Hall,
Englewood Cliffs, NJ.
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Lodish, Leonard M., Jeane Livelsberger, Beth Lubetkin, Bruce

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